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Ecological and soil hydraulic implications of microbial responses to stress – A modeling analysis
Accepted Manuscript
Ecological and soil hydraulic implications of microbial responses to stress - A modeling analysis Albert C. Brangar´ı, Daniel Fernandez-Garcia, Xavier Sanchez-Vila, ` Stefano Manzoni PII: DOI: Reference:
S0309-1708(17)30727-3 10.1016/j.advwatres.2017.11.005 ADWR 3010
To appear in:
Advances in Water Resources
Received date: Revised date: Accepted date:
19 July 2017 5 November 2017 6 November 2017
Please cite this article as: Albert C. Brangar´ı, Daniel Fernandez-Garcia, Xavier Sanchez-Vila, ` Stefano Manzoni, Ecological and soil hydraulic implications of microbial responses to stress - A modeling analysis, Advances in Water Resources (2017), doi: 10.1016/j.advwatres.2017.11.005
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Highlights • A new mechanistic model to predict the proliferation of biofilm in soils is proposed. • Ecological and soil hydraulic consequences of microbial accumulation are explored
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• Microbial dynamics respond to different environmental conditions and stresses.
• The biofilm compartment consists of active and dormant cells, EPS and enzymes.
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• The release/use of EPS and dormancy are key microbial processes.
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Ecological and soil hydraulic implications of microbial responses to stress - A modeling analysis
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Albert C. Brangar´ıa,b , Daniel Fern`andez-Garciaa,b , Xavier Sanchez-Vilaa,b , Stefano Manzonic,d a Department
of Civil and Environmental Engineering, Universitat Polit` ecnica de Catalunya (UPC), Jordi Girona 1-3, 08034 Barcelona, Spain. b Associated Unit: Hydrogeology Group (UPC-CSIC). c Department of Physical Geography, Stockholm University, Stockholm, Sweden. d Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden.
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Abstract
A better understanding of microbial dynamics in porous media may lead to improvements in the design and management of a number of technological applications, ranging from the degradation of contaminants to the optimization of agricultural systems. To this aim, there is a recognized need for predicting the proliferation of soil microbial biomass
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(often organized in biofilms) under different environments and stresses. We present a general multi-compartment model to account for physiological responses that have been extensively reported in the literature. The model is used as an explorative tool to elu-
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cidate the ecological and soil hydraulic consequences of microbial responses including the production of extracellular polymeric substances (EPS), the induction of cells into
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dormancy, and the allocation and reuse of resources between biofilm compartments. The mechanistic model is equipped with indicators allowing the microorganisms to monitor environmental and biological factors and react according to the current stress pressures.
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The feedbacks of biofilm accumulation on the soil water retention are also described. Model runs simulating different degrees of substrate and water shortage show that adap-
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tive responses to the intensity and type of stress provide a clear benefit to microbial colonies. Results also demonstrate that the model may effectively predict qualitative patterns in microbial dynamics supported by empirical evidence, thereby improving our understanding of the effects of pore-scale physiological mechanisms on the soil macroscale phenomena. Keywords: biofilm, porous media, extracellular polymeric substances, active 2
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microorganisms, dormant innactive cells, enzymes, substrate and water shortage.
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1. Introduction Almost all microorganisms on Earth are found in biofilms growing in soils and other
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surfaces of natural or manufactured origin (Vu et al., 2009). In most ecosystems, they
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grow under changing and often unfavorable conditions, which in soils are characterized
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by relatively long periods of drying and rapid rewetting, accompanied by sharp changes
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in carbon availability. The evolutionary success of biofilms lies in their versatility to
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adapt to a wide range of environments, and their capacity to buffer, counteract or even
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benefit from external stresses. In general, biofilms provide a number of advantages to the
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embedded microbial colonies, increasing the hydration status, improving the efficiency
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of their digestive system, and reducing their mortality (Flemming and Wingender, 2010;
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Flemming et al., 2016; Or et al., 2007a). However, the mechanisms by which the microbial
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habitat is regulated and the potential impact of biofilm growth on porous media remain
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mostly unknown (Flemming and Wingender, 2010; Or et al., 2007b). There is thus a
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need for understanding the response of biofilms to environmental conditions, with sig-
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nificant implications for the carbon cycle (Schimel and Schaeffer, 2012), the degradation
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of contaminants (Marmonier et al., 2012), the design and management of technological
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and agricultural applications (DeJong et al., 2013; Thullner, 2010), and even human life
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(Flemming et al., 2016; Selker et al., 1999).
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The release of a polymeric matrix (e.g., Roberson and Firestone, 1992; Tamaru et al.,
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2005) and the capacity of organisms to be induced into dormancy (e.g., Konopka, 1999;
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Lennon and Jones, 2011) are recognized as key microbial responses to stress. The biofilm
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matrix is a complex heterogeneous mixture of extracellular polymeric substances (EPS)
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of microbial origin resulting from deliberate secretions and lysis products. EPS consti-
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tute a variable proportion of the biofilm's total organic matter, ranging from 2 to 90%
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(Chenu, 1995; Donlan, 2002; Flemming and Wingender, 2010), consisting of polysaccha-
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rides, proteins, nucleic acids, lipids, DNA (Stoodley et al., 2002), and variable amounts
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of water (Or et al., 2007a). The EPS actual structure, quantity and composition are the
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result of the balance between needs versus opportunities in a framework of biological and
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Preprint submitted to Advances in Water Resources
November 6, 2017
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environmental factors (Kim et al., 2010; Wilking et al., 2011). The nature of the ma-
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trix depends on the producer community and maturation stage (Flemming et al., 2016;
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Roman´ı et al., 2008), but it is further determined by environmental conditions such as wa-
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ter flow rate, pH, temperature, soil water content, and availability of nutrients/electron
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acceptors (Hand et al., 2008; More et al., 2014). Moreover, microorganisms may mod-
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ulate the synthesis rates of EPS in response to such factors (Roberson and Firestone,
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1992; Sandhya and Ali, 2015), thereby counteracting the harmful effects of environmental
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stresses. EPS help maintaining cell functions and turgor, contribute to the uptake and
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assimilation of nutrients, and mediate cell adhesion to surfaces (Chenu and Roberson,
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1996; Flemming and Wingender, 2010; Or et al., 2007a,b). In addition to the release of
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EPS, responses to stress include the induction of a reversible state of dormancy (Blago-
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datskaya and Kuzyakov, 2013). When resources are limiting or environmental conditions
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are not appropriate, dormant cells can persist for extended periods of time in a state of
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low to zero activity in which the mortality rate is lower than that for active cells (Brown
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et al., 1988; Stoodley et al., 2002). When conditions improve, inactive cells can grad-
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ually recover their functionality (Stolpovsky et al., 2011). In general, those organisms
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that are efficient at switching between states present advantages, particularly in those
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environments that experience recurrent and prolonged periods of stress (Konopka, 1999;
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Lennon and Jones, 2011).
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Hence, microorganisms can use, at least, two well-identified mechanisms to improve
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their fitness. The resulting increase in the total biomass enlarges their capacity to repli-
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cate and survive in a competitive environment. Responses might combine an improve-
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ment of the environmental characteristics with a reduction of the requirements for micro-
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bial preservation. The decision making process of the microbial community is somehow
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similar to the quorum sensing mechanism of stimuli/response (Donlan, 2002; Parsek and
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Greenberg, 2005). Cells continuously interpret physicochemical signals (some of them
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released by themselves), which may regulate the deployment of these strategies. This
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way, microbial dynamics are modulated according to the nature and intensity of the
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stress (Chang and Halverson, 2003; Sandhya and Ali, 2015).
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Table 1: Nomenclature, parameter definition, and units of the model parameters.
a AC ADD
Description
Units
Experimental parameter for the water retention capacity of EPS
[L]
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Symbol
[M L−3 ]
Mass of AC per unit volume of soil
[M L−3 T −1 ]
Effective external supply of POM
b
Experimental parameter for the water retention capacity of EPS
[−]
c
Maximum volumetric density of EPS
[−]
Diffusion coefficient of DOC and EZ in water
DC
Mass of DC per unit volume of soil
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D0
[L2 T −1 ] [M L−3 ] [M L−3 ]
Concentration of DOC in water
DOCb
Concentration of DOC in the biofilm bodies
[M L−3 ]
DOCeq
Concentration of DOC at saturation
[M L−3 ]
DOCK
Half-saturation constant of DOC
[M L−3 ]
DOCpm
Concentration of DOC in the pore-matrix water
[M L−3 ] [M L−3 ]
Half-saturation constant of EPS
[M L−3 ]
Dry mass of EZ per unit volume of water
[M L−3 ]
EZK
Half-saturation constant of EZ
[M L−3 ]
AC KD
Decay rate coefficient for AC
[T −1 ]
Decay rate coefficient for DC
[T −1 ]
Decay rate coefficient for EPS
[T −1 ]
Decay rate coefficient for EZ
[T −1 ]
EP S EP SK EZ
DC KD EP S KD
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EZ KD
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Dry mass of EPS per unit volume of soil
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DOC
n
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P OM
P OMK
Van Genuchten's parameter for the SWRC of the biofilm-free soil
[−]
Dry mass of POM per unit volume of soil
[M L−3 ]
Half-saturation constant of POM
[M L−3 ]
t
Time variable
[T ]
tc
Characteristic time of the effects of the rain
[T ]
tR
Time of the last rainfall event
[T ]
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— Continued — Symbol
Description
Units [LT −1 ]
Averaged velocity of water
Y
Yield coefficient of respiration
[−]
z
Coordinate parallel to the water flow direction
[L]
α
Van Genuchten's parameter for the SWRC of the biofilm-free soil
βP
Shape factor controlling the curvature of ξψ,P
βθb
Shape factor controlling the curvature of ξψ,θb
∆tR
Return period of rainfall events
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vw
[L−1 ] [−] [−] [T ]
Shape parameter for the solute diffusion coefficient
Γ
Mass exchange function
θb
Volume of water in biofilm bodies
[−]
Volume of pore-matrix water
[−]
θpm
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γ
[−]
[M L−3 T −1 ]
Residual water content of the soil
[−]
θs
Saturated water content of the soil
[−]
λd
Decayed mass reallocation ratio
[−]
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θr
Effective coefficient of carbon allocation diverted towards EPS
[−]
λEP S
Maximum coefficient of carbon allocation diverted towards EPS
[−]
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λ∗EP S
Effective coefficient of carbon allocation diverted towards EZ
[−]
λEZ
Maximum coefficient of carbon allocation diverted towards EZ
[−]
Parameter denoting the channeled architecture of biofilms
[−]
N µC
Maximum specific consumption rate
[T −1 ]
Maximum specific decomposition rate of EPS
[T −1 ]
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µEP S
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λ∗EZ
[T −1 ]
Maximum specific decomposition rate of POM
ξDOC
Environmental coefficient based on the concentration of DOC in the biofilm phase
[−]
ξEP S
Environmental coefficient based on the concentration of EPS
[−]
Environmental coefficient based on the concentration of EZ
[−]
Environmental coefficient based on the concentration of POM
[−]
ξτ
Solute diffusion coefficient
[−]
ξχ
Environmental coefficient based on the concentration of the generic variable χ
[−]
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µP OM
ξEZ
ξP OM
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— Continued — Symbol
Description
Units
ξψ,P
Quorum sensing coefficient based on cell population
[−]
ξψ,θb
Quorum sensing coefficient based on θb
[−]
Density of the microbial cells
ρw
Density of water
τa
Maximum rate of cell reactivation
τi
Maximum rate of cell inactivation
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[M L−3 ]
ρc
[M L−3 ] [T −1 ] [T −1 ]
Effective porosity of the soil
φM
Maximum effective pore volume susceptible to be occupied by water
χ χK
[−]
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φef
[−]
Mass of the generic variable χ per unit volume of water or soil
[M L−3 ]
Half-saturation constant of the generic variable χ
[M L−3 ]
Matric suction
ψ0
Matric suction in the natural state of the soil
[L]
Ω
Shape parameter for the solute diffusion coefficient
[−]
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ψ
Despite the benefits described above, these survival strategies entail side effects. First,
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the production of EPS involves significant investments of carbon, decreasing the amount
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of resources allocated to growth. Furthermore, the viability of natural and mutant non-
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producer strains (e.g., Seminara et al., 2012; Vandevivere and Baveye, 1992a) indicate
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that EPS are not essential for life. One could argue that evolution would not preserve
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organisms that produce functionless substances misusing energy and nutrients (Chenu,
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1995). Therefore, EPS should provide a competitive (or cooperative) advantage for the
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embedded microorganisms. A similar reasoning can be held for dormancy: despite inac-
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tive cells remain in a state of alertness, they cannot respond immediately when conditions
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improve (Blagodatskaya and Kuzyakov, 2013). Cells must undergo a transition to recover
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their activity, potentially missing favorable periods. Therefore, dormancy could even be
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counterproductive in certain cases.
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Understanding the benefits and tradeoffs of such cooperative behaviors frames the
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scope of this contribution. Difficulties mostly arise from the complex dynamics of the 7
[L]
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interactions and feedbacks between environmental and biological factors.
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1.1. The Impact of Biofilms on Pore-scale Conditions The self-organization of microorganisms in biofilms results in a number of direct and
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indirect effects. First of all, the proliferation of biofilms in soils alters the hydraulic prop-
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erties of porous media (Engesgaard et al., 2006; Rockhold et al., 2002; Volk et al., 2016),
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changing their capacity to transport and retain water and solutes. This effect emerges
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from the hydraulic attributes of the biofilm-soil system and its interaction at the pore-
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scale (Brangar´ı et al., 2017). The most widely reported effect in bio-amended soils is
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bioclogging, i.e., a decrease in hydraulic conductivity due to EPS (e.g., Thullner et al.,
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2002; Yarwood et al., 2006) or cell accumulation (e.g., Vandevivere and Baveye, 1992b;
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Wu et al., 1997). The reduction of water flow helps reducing detachment rates, preserv-
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ing the hydration status and mitigating nutrient dilution and enzyme losses. However,
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under certain scenarios, the decrease in nutrient supply by impaired advection transport
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(Stewart, 2012; Thullner et al., 2002) may turn dense biofilms into apparently undesired
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structures.
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Bio-accumulation also enhances the retention of water (Rosenzweig et al., 2012;
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Rubol et al., 2014), thereby improving the conditions in the vicinities of cells (Or et al.,
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2007b). Under wet conditions, the coating matrix forms an open structure that holds
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up many times its weight in water. When dried, such a structure shrinks, becoming a
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dense and amorphous frame that remains moist over a wide range of water potential.
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This capacity depends on the morphology of the EPS matrix (Brangar´ı et al., 2017),
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but also on its composition. In this line, Chenu (1993) found significant differences
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in the water retained by EPS, with decreasing retention in the order: xanthan>EPS
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rhizobia>scleroglucan>dextran.
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In addition to the hydraulic implications, biofilm may contribute to the efficiency of
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the microorganisms digestive system by increasing nutrient uptake rates in a number of
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ways. First, despite the fluxes through biofilms are lower than those for free water (Stew-
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art, 2003), the increase in hydration modifies the advection-diffusion pathways (Chenu 8
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and Roberson, 1996), with significant implications for substrate availability. Second,
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contact times and duration of periods suitable for growth or acclimation are lengthened
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(Or et al., 2007a). Third, biofilms act as a reservoir that retains nutrients, enzymes, and
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catalysis products close to the cells (Flemming and Wingender, 2010). Fourth, the matrix
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behaves as a molecular sieve sequestering dissolved and particulate substrate from the
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environment (Flemming et al., 2003, 2016). Fifth, the carbon-rich EPS may be used as a
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source of carbon during periods of low resource availability. In contrast, when resources
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are abundant, microbes may allocate preferential resources to produce extra amounts
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of EPS (Kakumanu et al., 2013; Roberson and Firestone, 1992). Finally, despite being
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beyond the scope of this paper, EPS also alleviate the salt stress effect on cells (Sandhya
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and Ali, 2015) and facilitates the attachment of them to surfaces and to other cells (Vu
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et al., 2009).
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1.2. Survival Strategies: Experimental Evidence and Modeling
Due to the great importance of the aforementioned survival strategies on microbial
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proliferation, a large number of experimental and theoretical studies have been con-
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ducted.
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Several experimental studies have pointed out that the release of EPS is modulated as
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a direct response to environmental stresses and microbial needs. Roberson and Firestone
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(1992) and Chang and Halverson (2003) found that biofilms growing in dry conditions
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contain larger amounts of EPS. Sandhya and Ali (2015) reported a significant increase
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in their production also on bacteria exposed to high temperature or salinity. Tamaru
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et al. (2005) showed that EPS help maintaining cellular viability under deep desiccation.
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More et al. (2014), Redmile-Gordon et al. (2015) and Roberson and Firestone (1992)
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identified the EPS as a resource storage pool. Despite this compelling evidence, most
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modeling approaches (especially at the ecosystem level) do not include EPS and their
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responses to stressors. Most models do not even differentiate between cells (responsible
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of activity) and other types of attached biomass (inactive but having other properties)
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(e.g., Ezeuko et al., 2011; Pintelon et al., 2012; Rosenzweig et al., 2014; Soleimani et al., 9
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2009; Thullner and Baveye, 2008). Other models do describe various microbial compart-
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ments (e.g., Aquino and Stuckey, 2008; Laspidou and Rittmann, 2002a, 2004). Often,
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the mass balance of EPS (or of total biomass in simpler approaches) is defined as a
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more or less complex scheme of growth, decay and detachment (e.g., Ezeuko et al., 2011;
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Pintelon et al., 2012; Rosenzweig et al., 2014). An early study included the direct trans-
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formation of cells to EPS (Hsieh et al., 1994), disassociating production from substrate
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use, which is fundamental for modeling resource reallocation. Some models included a
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metabolic pathway in which the EPS could be decomposed and reused by cells as labile
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carbon (e.g., Aquino and Stuckey, 2008; Laspidou and Rittmann, 2004). Following an
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alternative approach, Maggi and Porporato (2007) included the competition of bacteria
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for water and space through limitations in their activity. However, none of these models
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account for the full feedbacks between the EPS and the environmental conditions. The
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most notable gaps in the representation of these processes encompass: (i) the EPS mod-
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ulation of stress; (ii) the link between cellular demands (increased during stress) and the
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EPS synthesis; (iii) the EPS reuse as a source of carbon; and (iv) the impact of EPS on
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hydration status and nutrient uptake rate.
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Regarding the effects of dormancy, Mart´ınez-Lavanchy (2009) measured significant al-
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terations of the microbial activity as a response to changes in carbon and oxygen supply.
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Stolpovsky et al. (2011) associated such phenomena to a massive inactivation under inap-
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propriate conditions. In Kaprelyants and Kell (1993), cells exposed to starvation could
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recover their functionality after a long period of dormancy. Other studies found that
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dormant cells tend to accumulate in the deepest regions of the biofilms (Kim et al., 2009;
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Williamson et al., 2012), pointing out that transport limitations inside biofilm structures
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may induce dormancy even under apparently favorable conditions. The studies model-
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ing the phenomenon of dormancy include approaches that control the switching between
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activity stages with different degrees of complexity (e.g., Konopka, 1999; Manzoni et al.,
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2014; Stolpovsky et al., 2011). These models, however, have not been tested in scenarios
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with complex interactions between the microbial pools and the environmental conditions.
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1.3. Model Rationale and Objectives Despite the empirical evidence, relating the production of EPS and dormancy to envi-
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ronmental stresses, drivers and consequences with process-based models is still difficult.
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This is mainly because biofilms (and more broadly soils) can be seen as an emerging
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property of a complex system that encompasses nonlinear and interconnected biogeo-
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chemical processes in a high-dimensional phase space. To the best of our knowledge,
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theoretical studies have tackled only some aspects of this complexity, and there are no
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empirical studies characterizing all the elements and mechanisms involved.
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The aim of this paper is then to shed some light on these complex microbial dynamics
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by means of a multi-compartment soil microbial mechanistic model named SMMARTS
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for Soil Microbial Model to Account for Responses To Stress. The model includes up
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to seven spatially-lumped and chemically-homogeneous compounds (compartments) that
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approximate the behavior of functionally-different carbon pools in soils. The dynamics
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of biomass synthesis, inactivation/reactivation, decay, and allocation and reuse of carbon
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among biofilm components are modulated according to biological needs and competition
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for space, water and substrate. To this aim, the model uses indicators that allow the
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microorganisms to monitor environmental variables and biofilm status and react accord-
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ingly. The feedbacks of biofilms on soil water retention and their consequences on the
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nutrient uptake capacity are described at the pore-scale.
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A model with such a complexity is necessary to: (i) quantify microbial growth by
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including the most relevant carbon fluxes at the biofilm level; (ii) include mechanisms
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to modulate microbial dynamics according to experimental observations, with emphasis
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on responses to stress; and (iii) estimate the feedbacks of biofilms on the soil hydraulic
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properties and the overall environmental conditions. The resulting general model is de-
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veloped in order to facilitate the study of the patterns of biofilm dynamics in porous
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media at the micro/meso-scale, reproducing the smart bioengineering that governs the
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proliferation of microbial communities. It can then be employed as an explorative tool
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to disentangle external (i.e., environmental) and internal (i.e., nonlinearities) drivers of
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biofilms and their responses to environmental conditions. After some simplifications, we 11
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use this still very complex approach to explore scenarios based on reasonable ranges of
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parameter values mapping microbial traits. In this way, the ecological benefits of these
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survival strategies are evaluated under substrate or water shortage.
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2. Materials and Methods
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2.1. SMMARTS Development
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2.1.1. Model Compartments
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The heterotrophic biofilm is differentiated into four lumped compartments: active
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cells (AC), dormant cells (DC), extracellular polymeric substances (EPS), and extra-
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cellular enzymes (EZ). The AC compartment consists of the functional microorganisms
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within the biofilm (considering mainly attached cells but it may also include plank-
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tonic organisms) that lead the behavior of the entire biofilm system. The DC represents
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the microorganisms that have undergone a reversible inactive state. The EPS pool is
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composed of soluble compounds, macromolecules and particulate materials that con-
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stitute the microbial matrix. Finally, the EZ compartment is formed by extracellular
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agents of microbial foraging (treated as a solute species) responsible for the decomposi-
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tion/solubilization of complex compounds.
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Biofilms require energy from organic matter to proliferate. Here, for simplicity, the
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dynamics of nutrients and of the electron acceptors are neglected, albeit they can be eas-
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ily incorporated. The non-microbial carbon compartments include: particulate organic
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matter (POM), dissolved organic matter in the pore-matrix water phase (DOCpm ), and
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dissolved organic matter inside the biofilm (DOCb ).
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In this model, each compartment is assumed to be homogeneous in a specific control
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volume. The dynamics of the compartments are expressed as a system of mass balance
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equations (illustrated in Figure 1). All model parameters are listed in Table 1.
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Figure 1: Sketch illustrating the biofilm, water, and air (of variable volume) inside a solid porous matrix and the biological processes described in the model. The solid arrows describe the fluxes between compartments, whereas the dotted arrows indicate C exchanges with the environment. The microbial
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compartments are differentiated into active cells (AC), dormant cells (DC), the polymeric matrix (EPS), and extracellular enzymes (EZ); and the substrate compartments into particulate organic matter (POM), dissolved organic matter in water (DOCpm ), and dissolved organic matter in biofilm phase (DOCb ). Each compartment is drawn on the phase(s) with which may be in contact (air, water or biofilm), as
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indicated by different shading. Dashed boxes represent compounds dissolved or in suspension. Granular material and air phase are considered passive with regard to the carbon cycle.
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To account for the feedbacks between biofilm accumulation, hydraulic properties and
environmental conditions, the distribution of pore-matrix water and biomass is defined at
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2.1.2. Biofilm Effects on Water Distribution
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the pore-scale level based on the framework presented in Brangar´ı et al. (2017). Despite
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using the simple capillary tube analogy, this approach effectively reproduced saturation
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changes in bio-amended soils. The model considers a biofilm that may retain variable
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amount of water depending on suction. Such a volume of water in biofilms (θb [−])
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may be defined from the water retention capacities of EPS and including some spatial 13
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restrictions ! EP S −b cEP S aψ , , φM , θb = min ρw ρw
(1)
where the overbar indicates the average concentration of a compartment (here the
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dry mass of EPS) over a unit volume of soil [M L−3 ], ρw [M L−3 ] is the water density,
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ψ [L] is the matric suction, a [L], b [−] and c [−] are experimental parameters for the
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water retention capacity of EPS, and φM [−] is the maximum volume available, which is
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susceptible to be occupied by any of the phases studied.
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The first term in (1) represents the shrinking/swelling capacity of the biofilm, which
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depends mainly on the composition of the EPS. Rosenzweig et al. (2012) reported that
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a = 105.76cm and b = 0.489 for pure xanthan (when suction is expressed in cm of wa-
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ter), whereas Chenu (1993) observed that dextran shows almost no retention capacity
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(a → 0). The impact of microbial cells on the soil water retention curve (SWRC) is here
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not included to better isolate the effects of EPS, neglecting the role of the cellular water
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in extracellular processes. The second term restricts the maximum volumetric density
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of EPS. In this line, Chenu (1993) observed that xanthan may retain up to 70 times its
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weight in water (c = 70). The third term constrains θb to spatial and water limitations.
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In fully-hydrated porous media, φM is equal to the effective porosity of the soil φef [−],
250
i.e., spatially restricted to the saturated minus the residual water content (φef = θs −θr ).
251
Nevertheless, when water availability is limited, the water-suction equilibrium assumed
252
in the first part of (1) might not be achieved and θb becomes limited by φM (the maxi-
253
mum amount of water available, defined from the soil suction in (16), Section 2.2).
255
M
ED
PT
CE
254
AN US
240
Biofilm bodies comprise complex structures that form pores, voids, and channels,
which induce significant structural changes in the pore-matrix. Their accumulation there-
257
fore alters the size and geometry of the pore space, leading to indirect changes in the
258
macroscopic retention properties. When pore-scale effects are integrated over the whole
259
control volume, the volume of pore-matrix water (θpm , [−]) retained in the open pore
260
space not occupied by biofilm may be written as
AC
256
14
ACCEPTED MANUSCRIPT
"
n
θpm = [φef − θb ] 1 + α ψ
n
φef − θb N φef
n2 # n1 −1
+ θr ,
(2)
where n [−] and α [L−1 ] are the experimental van Genuchten's parameters (van
262
Genuchten, 1980) obtained with biofilm-free soils, and N [−] is a theoretical parameter
263
that accounts for the channeled architecture of biofilm. The larger is N , the more intricate
264
is the morphology of the biofilm-soil system at the pore-scale, resulting in a potential
265
increase in water holding capacity. The reader is referred to Brangar´ı et al. (2017) for
266
derivation and details.
267
2.1.3. Non-Microbial Carbon
AN US
CR IP T
261
Carbon is used to synthetize new cells, enzymes and matrix compounds, and to pro-
269
duce energy for their maintenance. In our model scheme, non-microbial carbon is par-
270
titioned between particulate (POM) and dissolved forms (DOC) (as in e.g., Greskowiak
271
et al., 2005; Schimel and Weintraub, 2003); and the latter is further distinguished between
272
DOCpm (in the pore-matrix water) and DOCb (in the biofilm) (as in e.g., Orgogozo et al.,
273
2010). Such a differentiation is required to account for the relatively large differences in
274
concentration that may exist between them (Billings et al., 2015; Stewart, 2003, 2012).
275
This scheme is simple, but may effectively represent the wide range of forms in which
276
organic matter is found in ecosystems.
ED
M
268
277
POM here includes diverse materials that range from the coarser fraction of the
279
organic matter to molecules of complex composition. POM cannot be directly assimilated
280
into microbial biomass, but requires an enzyme-mediated extracellular de-polymerization
281
step to be reduced to simpler dissolved compounds (here DOC) (Roman´ı et al., 2004).
282
In porous materials, decomposition rates are constrained by the spatial limitations on
283
solute diffusion, which depend on soil tortuosity. Such a process is also rate-limited by
284
the solubility of POM (as in Greskowiak et al., 2005), in which DOCeq represents the
285
concentration of DOC at saturation. The mass balance for POM in time (t, [T ]) may
286
then be expressed as
AC
CE
PT
278
15
ACCEPTED MANUSCRIPT
∂P OM = ∂t
θb DOCeq − DOCb ADD − ξτ µP OM ξP OM EZ θb + θpm DOCeq | {z } {z } |
POM input
POM decomposition
(3)
CR IP T
θpm DOCeq − DOCpm − , ξτ µP OM ξP OM EZ θb + θpm DOCeq {z } | POM decomposition
where P OM [M L−3 ] is the dry mass of POM per unit volume of soil, EZ [M L−3 ]
288
is the dry mass of EZ per unit volume of water (pore-matrix + biofilm), DOCb [M L−3 ]
289
and DOCpm [M L−3 ] are the concentrations of DOC in the respective pools, ADD
290
[M L−3 T −1 ] is the external supply of POM, ξτ [−] is the coefficient modulating solute
291
transfer, µP OM [T −1 ] is the maximum specific decomposition rate, and ξP OM [−] is an
292
environmental coefficient limiting decomposition according to the amount of POM.
AN US
287
293
The decomposition fluxes in (3) are proportional to the enzyme concentration, and
295
driven by the disequilibrium of DOC in the individual pools. The solute diffusion coeffi-
296
cient ξτ for partially-saturated soils is based on Archie's second law for solute diffusivities
297
(see Hamamoto et al., 2010, for details)
M
294
ED
ξτ = θsΩ
θb + θpm θs
γ
,
(4)
where Ω [−] and γ [−] are two shape parameters. Thresholds in the original Archie's
299
law are assumed equal to 0 in (4). With this premise, decomposition rates are ensured
300
even at very low saturation (≈ θr ) since water (solvent) and POM are considered in
301
contact at the pore-scale and diffusion is likely to occur. Note also that ξτ is the inverse
302
of the tortuosity and depends on soil type by means of (2). Yet, the reduced diffusivity
303
through biofilm bodies (described in e.g., Or et al., 2007a) is neglected.
CE
AC
304
PT
298
305
The coefficient ξP OM limits the decomposition rate as P OM decreases and is de-
306
scribed by a generalized saturating function based on the Michaelis-Menten kinetic model
ξχ = 307
χ , χK + χ
(5)
where χK [M L−3 ] (here P OMK ) is the half-saturation constant of a generic variable 16
ACCEPTED MANUSCRIPT
308
χ (here POM).
309
Carbon decomposed in (3) is then diverted to the DOC compartments. DOCpm and
311
DOCb are affected by various processes of transport, formation and consumption defined
312
in (6) and (7) (Figure 1).
CR IP T
310
DOCeq − DOCpm ∂θpm DOCpm θpm − = ξτ µP OM ξP OM EZ ∂t θb + θpm DOCeq {z } | POM decomposition - DOC formation
θpm ∂DOCpm ∂ 2 DOCpm + ξτ D0 − ∂z } θb + θpm ∂z 2 | {z }
Advection
AN US
vw [θpm − θr ] | {z
Diffusion
∂θb DOCb θb DOCeq − DOCb = ξτ µP OM ξP OM EZ − ∂t θb + θpm DOCeq {z } |
Γ |{z}
(6)
Γ |{z}
(7)
Mass transfer
POM decomposition - DOC formation
Advection
Diffusion
Mass transfer
ED
Consumption
M
∂ 2 DOCb ∂DOCb θb ξτ D0 µC ξφ,P ξDOC AC − vw θb + + ∂z 2 {z } | {z∂z } |θb + θpm {z | }
µC [T −1 ] is the maximum specific consumption rate, ξDOC [−] is an environmental
314
coefficient limiting consumption rates, ξψ,P [−] is a quorum sensing coefficient, vw [LT −1 ]
315
is the velocity of water, z [L] is the coordinate parallel to the direction of flow, D0 [L2 T −1 ]
316
is the solute diffusion coefficient in water, and Γ [M L−3 T −1 ] is a mass exchange function.
PT
313
318
CE
317
Consumption rates are mathematically modulated by the coefficients ξDOC and ξψ,P .
They simulate the microorganisms' capacity to monitor and respond to environmental
320
and biological variables. The coefficient ξDOC consists in a nonlinear term defined in (5),
321
just replacing χ by DOCb . It can easily include growth limitation caused by electron
322
acceptor shortage (as in Laspidou and Rittmann, 2002b; Rodr´ıguez-Escales et al., 2014).
323
Note that only DOCb , which is in the immediate vicinity of microbial cells, is used for
324
metabolic processes. The coefficient ξψ,P reduces carbon uptake when the microbial
325
population is high,
AC
319
17
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ξφ,P
"
AC + DC = 1− ρc φef
#βP
,
(8)
where AC and DC are the dry masses of AC and DC per unit volume of soil [M L−3 ],
327
and ρc [M L−3 ] is the volumetric mass density of the microbial cells. βP [−] is a shape
328
factor that determines the strength of the population regulation. It ranges from 0 to
329
∞ for mechanistic rationale and defines the curvature of the inhibition expression. The
330
resulting ξψ,P tends to 1 (no inhibition) when the volume of cells is much smaller than
331
the free space and decreases with increasing total microbial population (AC + DC) as
332
space becomes limiting.
CR IP T
326
AN US
333
Advection and diffusion terms in the mass balance equations for DOC represent pow-
335
erful transport processes that may either provide or flush out dissolved carbon from the
336
system. For simplicity, water velocity is considered phase independent (averaged and
337
then assumed equal in open pores and in biofilms), and the effect of solute diffusion is
338
linearized. Note that, due to the similarity between process-regulators at the pore-scale,
339
the effective diffusion is determined by ξτ (recall (4)).
M
334
340
The mass transfer function Γ controls the flow of carbon between the two DOC
342
compartments. It is driven by the difference in DOC concentration, the size of the
343
intricate surface of contact, and the advective-dispersive flow. The sooner the exchange of
344
mass, the faster the equilibrium is reached. When the characteristic time of consumption
345
is much longer than that of the mass transfer (rates and contact areas are relatively large
346
at the pore-scale), equilibrium can be assumed (DOCb == DOCpm ).
347
2.1.4. Microbial Compartments
PT
CE
The main carbon fluxes in biofilms represent the synthesis of new biomass, the pro-
AC
348
ED
341
349
duction and reuse of EPS, the transition to and from the dormant state, the losses of
350
different nature, and the reallocation of decay products. Accordingly, the mass balance
351
equations describing the four microbial compartments are (Figure 1)
18
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∂AC = Y [1 − λ∗EP S − λ∗EZ ]µC ξφ,P ξDOC AC + Y µEP S ξEP S ξEZ [1 − ξDOC ]AC {z } ∂t | {z } | AC synthesis (EPS decomposition)
− τi [1 − ξDOC ]ξφ,P AC + τa ξDOC DC {z } {z } | | Reactivation
Inactivation
| {z } AC decay
∂EP S = Y λ∗EP S µC ξφ,P ξDOC AC − µEP S ξEP S ξEZ [1 − ξDOC ]AC {z } ∂t | {z } | EPS decomposition
EPS synthesis
(9)
AC − KD AC ,
CR IP T
AC synthesis (DOC consumption)
(10)
AC DC EP S + λD [KD AC + KD DC] − KD EP S , {z } | {z } | Decayed mass reallocation
EPS decay
Inactivation
AN US
∂DC DC = τi [1 − ξDOC ]ξφ,P AC − τa ξDOC DC − KD DC , {z } | {z } ∂t {z } | | Reactivation
∂[θb + θpm ]EZ EZ = Y λ∗EZ µC ξφ,P ξDOC AC − KD [θb + θpm ]EZ − ∂t | {z } | {z } EZ synthesis
EZ decay
M
∂EZ ∂ 2 EZ vw [θb + θpm − θr ] + ξτ D0 , 2 ∂z } | | {z {z∂z } Advection
(11)
DC decay
(12)
Diffusion
where Y [−] is the yield coefficient; ξEZ [−] and ξEP S [−] are limiting environmental
353
coefficients based on the requirements of EZ and EPS; λ∗EZ [−] and λ∗EP S [−] are effective
354
coefficients of carbon allocation; µEP S [T −1 ] is the maximum specific consumption rate
355
of EPS; τi [T −1 ] and τa [T −1 ] are the maximum rates of inactivation and reactivation of
356
cells, respectively; KD [T −1 ] are decay rate coefficients for the compartments indicated
357
in the superscripts; and λD [−] is the decayed mass reallocation ratio.
359
360
PT
CE
358
ED
352
The fraction Y of the carbon substrate taken up (not lost by respiration) is converted
to new biomass. It is equivalent to the microbial carbon-use efficiency (CUE) when DOC is the only source of carbon (AC synthesis via EPS reuse is not taking place; see
362
details below). The allocation coefficients λ∗EP S and λ∗EZ indicate the effective fraction of
363
carbon diverted to produce EPS and EZ, respectively (based on the formation coefficients
364
described in Laspidou and Rittmann, 2004). Different from previous approaches, the
365
synthesis of EPS and EZ is modulated to improve the well-being of microorganisms
AC 361
366
according to environmental and biological variables. An effective use of carbon permits 19
ACCEPTED MANUSCRIPT
367
investing additional amounts of resources to AC when EPS or EZ requirements are low.
368
Such adaptive modulations may be described by λ∗EP S = λEP S ξφ,θb ,
λ∗EZ = λEZ [1 − ξEZ ],
CR IP T
(13)
(14)
where λEP S [−] and λEZ [−] are the maximum coefficients of carbon allocation, and
370
ξEZ governs the release of EZ (again, obtained using (5)). ξψ,θb [−] is a quorum sensing
371
factor that regulates the production of EPS according to their concentration and water
372
requirements as
ξφ,θb
AN US
369
"
θb = 1− φef
#βθb
.
(15)
ξψ,θb tends to 1 (no inhibition) when the volume of water in the biofilm phase is much
374
smaller than φef , and therefore the resulting effective ratio of allocation is approximately
375
λEP S . ξψ,θb decreases with increasing θb , as a function of the shape factor βθb .
M
373
376
Biofilm dynamics are readjusted when DOC is scarce (ξDOC < 1). On one hand, mi-
378
croorganisms are able to decompose EPS, using them as a carbon source to produce AC
379
exclusively (in agreement with de Silva and Rittmann, 2000). The process is governed
380
by ξEZ , since EZ catalyze the reaction (Flemming and Wingender, 2010), and ξEP S .
381
The latter term hampers the decomposition rates of EPS when their concentration is
382
low compared to the value of EP SK (recall (5)). When EPS reuse occurs, the CUE
383
decreases because a lower percentage of carbon is assimilated (Y is first applied in (10)
384
to produce EPS and then in (9) to synthetize AC). On the other hand, some microorgan-
385
isms switch in and out from the dormancy state (in (11) and (12)) according to nutrient
386
availability. Such a physiological response occurs at a rate that is a function of τi , τa ,
387
and ξDOC ; always fulfilling the restrictions imposed by population density defined by (8).
AC
CE
PT
ED
377
388
389
Biomass losses are controlled by decay, including ageing effects (natural decay), de-
390
mands for maintenance and functioning (endogenous decay), and reallocation of carbon 20
ACCEPTED MANUSCRIPT
(induced decay). Decay rates are defined as proportional to the amount of biomass and
392
AC DC EP S EZ the decay coefficients KD , KD , KD and KD , in which the superscripts indicate
393
the corresponding compartment. DC and EPS are the compartments least affected by
394
AC DC AC EP S decay (KD /KD >> 1, KD /KD >> 1), conferring large durability regardless of
395
environmental conditions. The fraction λD of decayed cells is assumed biodegradable
396
and remains in the system becoming part of the EPS (as in Laspidou and Rittmann,
397
2002b, 2004) and not as POM (as in Riley et al., 2014). Such a simple mechanism allows
398
producing EPS as a form of carbon reallocation (e.g., in Kakumanu et al., 2013). Later
399
on, these EPS can be used as a carbon source. As a consequence, the total consumption
400
rate is defined by Y times the sum of DOC used and EPS decomposed.
401
2.2. Numerical Simulations Set-Up
AN US
CR IP T
391
The coupled system of equations presented in (1-15) was solved numerically using
403
an implicit Crank-Nicolson scheme. Concentrations of the studied compartments were
404
updated every time step. Such steps were dynamically chosen according to convergence
405
criteria and to avoid numerical instabilities. The resulting time steps were in the order
406
of seconds-minutes. Each simulation was performed until quasi-steady-state conditions
407
were achieved; i.e., when no relative changes in the biomass of all compartments were
408
observed (for constant environmental conditions), or temporal patterns reached a stable
409
cycle (for cyclic environmental conditions). A minimum time of simulation was set to
410
365d, which was assumed the behavior in the long-term.
PT
ED
M
402
411
All simulations were performed in a porous medium of 1cm3 volume, albeit the results
413
can be extrapolated to larger scales by combining multiple volumes. Different sets of sim-
414
ulations were carried out to conduct a sensitivity analysis in which either one parameter
415
or combinations of two parameters were allowed to vary. Most of these parameters were
CE
412
set based on the literature, while others (when no information was available) were con-
417
strained to a reasonable range or value (Table 2). Sensitivity analyses were not meant to
418
quantify the uncertainty propagation. Due to the high sensitivity and little knowledge
419
of the value of the parameters under each scenario, simulations were employed then as
420
an explorative rather than predictive tool to disentangle qualitative patterns and the
AC 416
421
driving forces governing microbial dynamics under different situations of stress. 21
ACCEPTED MANUSCRIPT
Table 2: Simulation parameters for microbial dynamics, specific values from the literature, and sources.
Parameter
Units
Significant
Comments
Value
References
a
cm
105.76, 1
CR IP T
values
To check the impact of different types of EPS. From Rosenzweig et al. (2012) for pure xan-
than (105.76), and small value simulating EPS of lower retention capacity (1) gcm−3
5.5x10−5
−
0.489
(t = 0) b
From Brangar´ı et al. (2017)
AN US
AC
From Rosenzweig et al. (2012) for pure xanthan
c DC
From Chenu (1993) for pure xanthan
−
70
gcm−3
0, 1x10−3
(t = 0)
conditions
gcm−3
PT gcm−3
AC
CE
DOCeq
2x10−5
ED
(t = 0)
M
DOC
Two different scenarios assumed at the initial
Relation 10xDOCK to ensure appropriate initial carbon conditions.
DOC = DOCb =
DOCpm assumed Kinzelbach et al. (1991),
2x10−3
Assumed large (1000xDOCK ) to avoid growth limitations at equilibrium
1.43x10−5 ,
Greskowiak
5.1x10−4 ,
et al. (2005),
1x10−3 xP OM Bengtson and Bengtsson (2007)
— Continues on the next page —
22
ACCEPTED MANUSCRIPT
— Continued — Parameter
Units
Significant
Comments
Value
References values
DOCK
gcm−3
2x10−6
CR IP T
[Soleimani
Experimental variable used in Ezeuko et al.
1x10−4 ]
(2011)
EP S
0
gcm−3
5.5x10−3
gcm−3
6x10−6
(t = 0) gcm−3
6x10−6
min−1
6.6x10−5
PT min−1
CE
DC KD
AC
EP S KD
EZ KD
and Van Geel (2007)]
Mean from Manzoni et al. (2014) (2x10−6 to
1x10−5 )
ED
AC KD
(2009)-Mostafa
Assumed from the relation θef /c in 1
min−1
Assumed equal to EZ(t = 0)
M
EZK
AN US
EZ
et al.
Assumed 0 at the initial conditions
gcm−3
(t = 0) EP SK
[7.99x10−7 -
6.6x10−6
Relation µC /100 in Ezeuko et al. (2011), despite also incorporated EPS decay
[8.33x10−6 2.78x10−4 ]
(2014)Laspidou and Rittmann (2004)] [Manzoni et al.
AC /10 inspired by Manzoni et al. Relation KD
(2014)
AC /10[KD
(2014)-
AC /4.2] KD
Konopka (1999)] Laspidou and
0, 6.6x10−6
Decay of EPS was neglected or assumed equal to
min−1
[Manzoni et al.
6.6x10−5
DC KD
for simplicity
AC Assumed equal to KD
— Continues on the next page —
23
1.18x10−4
Rittmann (2002b)
[6.94x10−6 -
Manzoni et al.
3.47x10−5 ]
(2014)
ACCEPTED MANUSCRIPT
— Continued — Parameter
Units
Significant
Comments
Value
References values
P OM
−
1.23
Value for sand, loam and sandy-clay (from Carsel and Parrish (1988))
gcm−3
1.5x10−2
Assumed equal to the 1% of soil's mass
gcm−3
1.5x10−5
Assumed small (P OM /1000) to avoid POM
(t = 0) P OMK
limitations min
5 days was assumed reasonable according to
7200
AN US
tc
CR IP T
2.68, 1.56, n
our personal experience
vw
Y
cmmin−1
Assumed
0
−
Experimental variable used in Ezeuko et al.
0.34
α
M
(2011)
0.145, 0.036,
cm−1
−
βθ b
− −
CE
γ
PT
βP
AC
Γ
θr
θs
ED
0.027
gcm−3 min−1 −
Carsel and Parrish (1988))
1
Assumed 1 to reduce the non-linearity
1
Assumed 1 to reduce the non-linearity Standard value for sands, and calibrated from
2, 2.9
loamy-clayey soil data. Both from Hamamoto et al. (2010) DOCb and DOCpm always under equilibrium
∞ 0.045, 0.078, 0.1
0.38
Value for sand, loam and sandy-clay (from Carsel and Parrish (1988))
0.43, 0.43, −
Value for sand, loam and sandy-clay (from
Value for sand, loam and sandy-clay (from Carsel and Parrish (1988))
— Continues on the next page —
24
[Mostafa and Van Geel [0.05-0.61] (2012)-Dupin et al. (2001)]
ACCEPTED MANUSCRIPT
— Continued — Parameter
Units
Value
Significant
Comments
References values Laspidou and
−
Assumed 0 to isolate the effects of the deliber-
0
ated release of EPS λEP S
−
0.23, [0 -0.4 ]
0.2
CR IP T
λd
Rittmann (2002b)
Sum of formation coefficients for EPS and
utilization-associated products in Laspidou and Rittmann (2004) −
0.01
N
−
1, 5
Assumed to fulfill that λEZ << λEP S
AN US
λEZ
Assumed 1 or 5 to simulate a biofilm with simple or more complex morphology at the-pore
1.6, 6.3,
Brangar´ı et al.
[1 -100 ]
(2017)
scale
µC
min−1
6.6x10−3
Experimental variable used in Ezeuko et al.
µEP S
M
(2011) for biomass
min−1
0, 1x10−3
To evaluate the effects of EPS as a source of C or not
min−1
1
Assumed
ρc
gcm−3
1
Assumed equal to ρw according with Phillips
PT
ρw
ED
µP OM
gcm−3
1
et al. (2013) Known
0, 9.23x10−5 ,
min−1
CE AC
τa
τi
Ω
min−1
−
[7x10−8 -
To check the effects of dormancy.
7x10−3 ]
τi /1.43 in Konopka (1999) (9.23x10−5 )
6.94x10−4
Manzoni et al. (2014)
0, 1.32x10−4 , [1x10−7 -
To check the effects of dormancy.
1x10−2 ]
DC in Konopka (1999) (1.32x10−4 ) 20xKD
1.5
Relation
Value for all soil types. From Hamamoto et al. (2010)
422
Relation
Numbers in italic mark those values not derived from experimental data.
25
6.94x10−4
Manzoni et al. (2014)
ACCEPTED MANUSCRIPT
Simulations were conducted in synthetic scenarios in order to explore the carbon dy-
424
namics in shallow soils. Supplies feeding the system were adapted to simulation needs,
425
differentiating between two main scenarios. The first scenario assumed that the microbial
426
community was fed by the decomposition of POM accumulated in the upper soil profile,
427
i.e., DOC was not directly supplied. To focus on the effects of DOC limitation, P OM was
428
assumed at steady-state and set to a constant value, much larger than P OMK , so that
429
ξP OM ≈ 1. The second scenario considered artificial sudden changes in the availability of
430
DOC. Therefore, the mass balance for POM (in (3)) becomes redundant for the scenar-
431
ios studied. Additionally, the mass transfer rate between the two DOC compartments
432
is assumed large enough to maintain equilibrium, and therefore DOCb and DOCpm are
433
equal to the concentration DOC in the now undistinguished dissolved carbon pool. The
434
inflow/outflow diffusion fluxes were considered balanced and could be neglected. Addi-
435
tional details are provided later in each case-study section.
AN US
CR IP T
423
436
To explore the wide range of saturations found in natural environments, simulations
438
were performed on soils under synthetic extreme scenarios consisting in: full saturation,
439
moderately dry conditions, or intermittent rainfall events. Such conditions were speci-
440
fied by the soil suction status, which determine the availability of water. The saturated
441
scheme assumed that ψ = 0 and therefore the volumetric water content was maximum
442
and equal to θs . The dry scenario assumed conditions of water limitation (with no addi-
443
tional water supplied during simulations), where the initial θb + θpm was determined by
444
(1) and (2) at a constant ψ of 50cm of water. When biofilm proliferated, the equilibrium
445
was lost and φM was set to the value of θb + θpm at t = 0, regardless of microbial dy-
446
namics. Finally, the scenarios of intermittent rainfall events started from a dry scenario
447
that included periodic sudden raises of the water content (ψ = 0, representing the rain-
448
fall event) with a return period ∆tR . Water inputs were assumed to contain no DOC
AC
CE
PT
ED
M
437
449
and EZ to represent the conditions of rainwater, and thus causing a potential dilution of
450
these dissolved components in the control volume. After the rain event, soils underwent
451
a transient period of pressure redistribution, gradually readapting their saturation to
452
the natural suction state (ψ0 = 50cm). Water drainage flushed out a fraction of the
453
dissolved components, preserving their concentrations. The effect of matric suction was 26
ACCEPTED MANUSCRIPT
454
not studied as an independent stress, but only as a driver of the water content (using (1)
455
and (2)). The changes in suction were modeled as
ψ(t) = ψ0 − ψ0 exp
tR − t , tc
(16)
where tR [T ] is the time of the last rainfall event and tc [T ] is the characteristic time
457
of the effects of the rain on ψ. The time of the first episode was set to ∆tR /2. The
458
impact of evapotranspiration rates on saturation was neglected.
459
3. Results and Discussion
CR IP T
456
We start by evaluating the effect of soil texture and biofilm characteristics, i.e., re-
461
tention properties and pore-scale morphology. We then continue by examining the de-
462
ployment of survival mechanisms responding to stresses characterized by the synthesis of
463
EPS, their reuse as a source of C, the inactivation/reactivation of cells, and the combined
464
effect of dormancy and EPS production.
465
3.1. The Effect of Soil Type and Biofilm Properties
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The soil pore-size distribution strongly determines the availability of elements essen-
467
tial for the proliferation of biofilms. First, the water saturation, which is a key factor in
468
microbial habitats, is itself a function of the size, the shape and the interconnection of
469
pores (Alaoui et al., 2011). This relationship determines the SWRC (see Supplementary
470
material Figure ??), which typically depicts lower saturations at a given matric suction
471
in coarse grain soils because large pores can be easily drained. Second, DOC availability
472
not only depends on water saturation but also on its diffusivity in the soil. Substrate
473
supply turns into a prominent limiting factor when water content is low since diffusive
474
and conductive transport become small (Manzoni et al., 2016). Although the larger wa-
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ter holding capacity of fine-textured soils, the increased tortuosity of the diffusion paths
476
in their thin pores (lower ξτ ) reduces the capacity of solutes to reach the microbial cells.
477
According to (4), such diffusion limitation is determined by the parameters Ω, γ, and θs ,
478
which are soil-type dependent. It is worth noting here that the model does not account
479
for reduced microbial growth caused by oxygen limitation that may occur in highly sat-
AC 475
480
urated environments (see Skopp et al., 1990), and for increased carbon losses that may 27
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481
occur in soils of low tortuosity (with potentially higher advection-diffusion fluxes).
482
These hydraulic properties are not static, but depend on the presence of biomass,
484
which leads to direct (θb ) and indirect (θpm ) increases in the overall retention of water
485
for a given suction. In Figure ??, the retention properties of biofilms are illustrated by
486
comparing the effect determined by an EPS of a very low water retention capacity (a
487
assumed equal to 1cm), with that of pure xanthan (with better retention properties,
488
a = 105.76cm). The first scenario requires many times the mass of xanthan to obtain
489
an analogous change in the SWRC. Therefore, as b and c are here assumed independent
490
of the type of EPS, the overall change in saturation is governed by the product axEP S
491
(recall (1)). Additionally, the more intricate is the architecture of the biofilm at the
492
pore-scale (denoted by N ), the stronger the transformation of the pore-matrix and the
493
higher is the total saturation increase. According to the previous statements, an increase
494
of water saturation implies a potential increase in the rates of carbon consumption by
495
microbial cells. The influence of EPS on microbial dynamics is discussed in more detail
496
in Section 3.2, but a simple analysis of the results shown in Figure ?? already suggests
497
that the greater the impact of biofilm on the SWRC is, the more benefits are potentially
498
achieved by the embedded microorganisms (supporting the speculation of Brangar´ı et al.
499
(2017) and Lawrence et al. (1991)).
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3.2. The Effect of EPS on Microbial Dynamics
502
3.2.1. Water Availability and Hydric Stress In this section, we analyze the impact of EPS accumulation under variable soil mois-
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504
ture on the proliferation of biofilms. To better identify the effects of hydric stress and
505
the role of EPS, we simulate the effect of having or not having colonies embedded in a polymeric matrix (0.015 or 0 g of EPS cm−3 ), indicated by dotted and solid curves
507
in Figure 2, respectively. The retention capacity of EPS was taken from that of pure
508
xanthan to emphasize its impact on soils. The production of additional EPS, their de-
509
cay, and the switch into dormancy were all deactivated in these simulations by setting
510
EP S λEP S = 0, KD = 0, λd = 0, and τi = 0. In this way, the EPS pool was treated as a
AC 506
511
static compartment, allowing us to isolate its effects. Results show the proliferation of 28
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512
biofilms in a soil under moderately dry and fully saturated conditions (in the top panel),
513
and under instantaneous rainfall events that are followed by drainage periods of 5 and
514
10 days of duration (bottom panel).
515
In moist conditions (absence of major stresses and of dilution effects), microorganisms
517
grew fast, efficiently, and reached large active biomass values (blue curves in Figure 2,
518
top). Large POM decomposition rates permitted high respiration rates and activity (re-
519
call that O2 is not considered a limiting factor). As shown by the overlapping solid and
520
dashed blue curves in Figure 2 (top), the presence of EPS did not have an apparent role
521
under such circumstances. In contrast, in rather dry soils, the growth of microorganisms
522
was limited by the availability of DOC (due to low ξτ ), which hampered the synthesis of
523
new biomass (green curves). The presence of EPS in such dry scenarios (dotted curves)
524
increased water saturation, contributing to the improvement of microbial fitness com-
525
pared to cases without EPS (solid curves).
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526
According to Dutta et al. (2015) and Fierer and Schimel (2002), the periodicity and
528
intensity of the stress episodes control the proliferation of microbial colonies. Along this
529
line, results in Figure 2 (bottom) show a significant increase in the respiration rates
530
during each rainfall event (known as Birch effect; Birch, 1958). The enhancement of the
531
decomposition rates by the sudden increase in the saturation was counterbalanced by the
532
dilution of EZ and DOC. In fact, soils transiently readapted their water content to ψ0 ,
533
triggering losses of dissolved components and EZ by leaching. Those colonies embedded in
534
EPS attained the largest cell populations because EPS mitigated both water and carbon
535
stresses by: (i) emulating the conditions of colonies growing at a smaller hydric stress that
536
remain saturated for a wider range of suctions (Or et al., 2007a); (ii) acting as a reservoir
537
that retains DOC and EZ, which mitigates the effects of dilution and drainage (Or et al.,
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538
2007b); and (iii) increasing DOC supply during dry periods (Chenu and Roberson, 1996).
539
Moreover, these positive effects are more pronounced under scenarios with higher rainfall
540
frequency (red dotted curves in Figure 2, bottom). These points may indicate feasible
541
mechanisms by which EPS allowed microorganisms to benefit from rainfall events that
542
otherwise would inhibit biofilm proliferation. This result provides also possible insights 29
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on the drivers of respiration pulses at rewetting (Birch, 1958; Lado-Monserrat et al., 2014;
544
Meisner et al., 2013). For a pulse to occur, DOC and EZ must be retained in the system,
545
which is more feasible with a well-developed EPS matrix. This link between respiration
546
pulses and EPS had not been previously explored, and emerges in the dynamics only
547
when the complexity of microbial-soil pore space is described.
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Figure 2: Impact of water availability on microbial dynamics. Simulations were performed for a soil under A) moderately dry conditions (green), fully saturated (blue), and B) under instantaneous rainfall events followed by drainage periods ∆tR of 5 days (red) and 10 days (black). The colony of microorganisms
AC
was assumed to be either embedded (EP S = 0.015g cm−3 , dotted lines) or not (EP S = 0, solid lines)
in a polymeric matrix. Multiple plots show the dynamics of the total water content θb + θpm , the active cell population AC, the respiration rate (indicated by Resp.), the dissolved organic carbon concentration DOC, the enzyme density EZ, and the cumulative amount of carbon consumed (C cons.).
30
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548
3.2.2. Production of EPS The simulations are now extended by introducing the dynamics of EPS. The hypoth-
550
esis being tested here was that the production of EPS should provide an advantage to the
551
organisms embedded, even though some resources are diverted from cell growth. This
552
effect was studied by increasing the potential allocation of carbon to the production of
553
EPS (λEP S = 0, λEP S = 0.23, λEP S = 0.4, as indicated by different colors in Figure
554
3). Unlike previous simulations, EPS production (determined by environmental stresses,
555
recall (13)) and decay (stress independent) were activated so that EPS dynamically in-
556
teracted with other compartments. The columns of Figures 3 and 4 illustrate these
557
dynamics under different soil moisture regimes (two different rainfall frequencies and full
558
saturation).
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Under saturated conditions (Figure 3, right), since the production of large amounts
561
of EPS was unfruitful, the resources diverted to EPS were downregulated. λ∗EP S tended
562
to zero and EP S reached a pseudo-steady state. This phenomenon might explain why
563
soils under small water stress tend to exhibit low EPS to biomass ratios (e.g., in Rubol
564
et al., 2014; Vandevivere and Baveye, 1992b). As a consequence of regulation, the dy-
565
namics obtained were not sensitive to λEP S . When such a mechanism was disabled (by
566
assuming ξψ,θb = 1, not shown), EPS were continuously synthetized at the expenses of
567
population growth.
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Dynamics under variable soil moisture are illustrated in Figure 3 by showing the
570
results under periodic rainfall events with a return period of 100 (left column) and 10
571
days (center column). Under such conditions, the large allocation of carbon to EPS re-
572
sulted in significant improvements in microbial fitness (i.e., biomass). Yet, results show
573
that microorganisms required moderately long periods to adapt the biofilm (and the soil
AC
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574
habitat) to their needs. With time, each microbial system tended to reach high active
575
biomass values as long as the production of EPS was larger than their decay. Note the re-
576
lation between microbial bloom and EP S in the black and red curves in the top panel of
577
Figure 3. The more frequent were the rain events, the faster the steady-state conditions
578
were achieved, thanks to the higher mean soil moisture. Figure 4 shows the averaged 31
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Figure 3: Simulation of biofilm proliferation under permanent wet conditions (plots in the right column), and environments affected by rainfall events with a return period of 100 (left column) and 10 days (center column). From top to bottom: active microbial biomass (AC), amount of EPS (EP S), effective
AC
coefficient of carbon allocation to synthetize new EPS (λ∗EP S ), total water content (θb + θpm ), and respiration rate (Resp.). The maximum coefficient of carbon allocation diverted towards EPS λEP S values are 0 (blue), 0.23 (red), and 0.4 (black).
579
biomass after 1 year of simulation. Results suggest that for EPS to be effective at the
580
annual scale, larger investments (λEP S ) are required under progressively more stressful
581
conditions. 32
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582
In all cases, EPS concentrations increased during biofilm establishment (first month
584
in Figure 3, but not appreciable in the current y-axis scale), as noted by Roman´ı et al.
585
(2004). For the studied set of parameters, the presence of a small amount of EPS did not
586
compensate for the resources currently diverted to their production and AC remained
587
low compared to the non-producer strain. However, when EP S reached higher values,
588
compensatory mechanisms started to work, leading to higher respiration and the syn-
589
thesis of new biomass (on average, but particularly during activity peaks, Figure 3).
590
In those scenarios with stronger water stress, larger amounts of EPS were accumulated
591
(in agreement with Chang and Halverson, 2003; Roberson and Firestone, 1992; Sandhya
592
and Ali, 2015). When dry periods are sufficiently intense (not enough water available
593
to maintain equilibrium in (1)), such a large accumulation of EPS did not improve the
594
hydration status and nutrient uptake, and therefore EPS investments were unfavorable
595
(results not shown). However, highly bio-amended soils under periodic rainfall events re-
596
mained almost fully saturated even at high matric suctions by counteracting the adverse
597
diluting effects and facilitating conditions recovery after rewetting (e.g., Dutta et al.,
598
2015). This fitness improvement resulted from the dynamic synthesis of EPS in response
599
to the intensity of the water stress. Production of EPS remained low during dry spells
600
(λ∗EP S < λEP S ), but decreased or even stopped (λ∗EP S → 0) during rainfall events. Ef-
601
fective downregulation of EPS synthesis occurred when EPS could not provide further
602
benefits in saturation (denoted by ξφ,θb ), allowing organisms to divert resources to AC.
603
If the downregulation mechanism had been disabled, the synthesis of unnecessary matrix
604
would have negatively affected microbial fitness. In that case, Figure 4 would have shown
605
a bell-shape relation between AC and λEP S .
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As an alternative to the time series representation shown in Figure 3, the relations
AC
607
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608
between microbial metabolism and environmental conditions can be represented in the
609
phase space, by showing respiration rate as a function of soil moisture (Supplementary
610
material Figure ??). The model simulations showed that respiration rates decreased
611
during soil drying, following a pattern that has often been observed (see Manzoni et al.,
612
2012, for a review). Upon rewetting, respiration rate increased with a short delay, partly 33
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Figure 4: Partitioning of the biofilm compartments in long-term simulations (dry-wet cycle-averaged
values after 1 year of simulation) assuming values of the maximum coefficient of carbon allocation diverted towards EPS (λEP S ) ranging from 0 to 0.4, and the maximum rate of cell inactivation τi = 0
(dormancy was not allowed). Simulations were performed under periodic rainfall events with ∆tR = 100
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days (left), 10 days (center), and permanently wet conditions (right).
due to DOC dilution effects, causing counterclockwise hysteretic loops (as reported else-
614
where, see Zhang et al., 2015). Therefore, the maximum respiration rate was achieved
615
only when soil moisture had already started to decrease.
616
3.2.3. Reuse of EPS
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The potential benefits of storing carbon in EPS for late use were tested by compar-
618
ing EPS-producer microorganisms (λEP S = 0.23) with different capacity to reuse the
619
carbon previously invested in EPS, assuming µEP S equal to 1x10−3 min−1 (reuse) or 0
620
(no reuse). Two different EPS water retention capacities were also studied comparing
621
a = 105.76 and a = 1cm. Simulations obtained for these four combinations of λEP S and
622
a are shown in Figure 5, for a soil affected by periodic rainfall events with ∆tR = 10 days.
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624
625
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For the studied set of parameters, it was found that when µEP S << 1x10−3 g cm−3 ,
the EPS production clearly dominated over the reuse rates, resulting in EPS accumulation for any water retention capacity (solid blue and dashed green curves in Figure 5). In
627
contrast, for larger reuse rates, EPS tended to be depleted by consumption, eventually
628
reaching a periodic asymptotic value. The benefits of such an EPS accumulation to the
629
microbial community emerged from the competition between antagonistic properties of
630
EPS: water retention versus carbon storage capacity. On one hand, as already shown be-
AC 626
631
fore, large EPS concentrations entailed a mitigation of the adverse effects of rain events. 34
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Figure 5: Dynamics of a microbial colony growing in a soil affected by rainfall events with ∆tR =
10 days, assuming contrasting EPS properties that alter their reuse as a source of carbon: different decomposition rate capabilities (denoted by the maximum specific decomposition rate µEP S = 0 and µEP S = 1x10−3 min−1 ) and EPS water retention capacity (a = 105.76 and 1cm). Plots starting from top left show the dynamics of the active cell population AC, the total water content θb + θpm , the EPS concentration EP S, the carbon-use efficiency (CUE = AC growth over equivalent DOC consumed), the
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EPS reuse ratio, and the effective coefficient of carbon allocation λ∗EP S .
On the other hand, the carbon stored in EPS was used as a temporary source of carbon.
633
When these EPS were consumed, the carbon feeding the colony increased, but at the
634
same time, EP S and therefore their capacity to mitigate stresses decreased. The sign
635
of the impact depended then on the combination of parameters: the own compositional
636
characteristics of the EPS (denoted by a), their capacity to be reused (µEP S ), and again
637
on the environmental circumstances (mainly water inputs).
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638
Results in Figure 5 show that only with low EPS retention capacities, the reuse
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639
of EPS slightly increased the active biomass (compare dashed green and dotted black
641
curves), because the carbon surplus in EPS helped compensating the dilution and the
AC
640
642
carbon lost after rainfall. However, when the modeled EPS had a large capacity to retain
643
water, the largest AC was obtained when reuse was disabled. The EPS with the lowest
644
retention properties allowed larger potential of carbon accumulation in EPS, because the
645
production rates (characterized by λ∗EP S , recall (15) and (1)) remained high, even though
646
relatively large EP S was reached. Even though the EPS reuse could improve microbial 35
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647
fitness under specific conditions, it was a rather inefficient mechanism in terms of carbon
648
use. The synthesis of biomass by the reuse of EPS required a double respiration cost: for
649
synthesizing EPS first (CUE = Y ) and for using them to produce new biomass (dotted
650
lines show efficiencies of DOC conversion to biomass lower than Y ).
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These results suggest that fitness can be improved by synthesizing EPS of specific
653
composition. We thus speculate that biofilm characteristics could be adapted to envi-
654
ronmental conditions to which they are more frequently exposed. For instance, the mi-
655
croorganisms benefitting from EPS reuse may promote large µEP S values by synthetizing
656
enzymes that are efficient at taking carbon from EPS. In a similar way, microbes could
657
adapt the composition of the released compounds to facilitate their later reuse. Lastly,
658
the combination of reuse and reallocation of decay products, which may be induced by
659
AC cells through the values of KD and λd , results in a cycle of full carbon reallocation.
660
This process would allow producing any microbial compartment (prioritizing those that
661
are most useful under the actual circumstances), with lower dependence on the external
662
availability of carbon sources.
663
3.3. The Effect of Dormancy on Microbial Dynamics
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The capacity to switch in and out of the dormancy state was evaluated by comparing
665
the dynamics non-EPS producer microorganisms unable to become dormant (τi = 0,
666
dashed curves in Figure 6) with those that can turn dormant and are characterized by
667
different switching rates between the two states (τi = 1.32x10−4 and 1.32x10−3 min−1 ,
668
depicted by dotted and solid curves, respectively). The reactivation rate τa was set
669
equal to 1.43/τi (based on Konopka, 1999). The switch to a dormant stage was trig-
670
gered by artificially changing the DOC in a fully saturated soil from 1x10−6 to 0g cm−3 ,
671
which modulated the effective transition rates via the coefficient ξDOC . This approach,
AC
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672
based on resource availability, is conceptually (but not mathematically) similar to previ-
673
ous models of activity (Stolpovsky et al., 2011) or physiological state (Blagodatsky and
674
Richter, 1998). Other models assume that dormancy is instead triggered by a change in
675
soil water content (B¨ar et al., 2002) or by water potential (Manzoni et al., 2014). The
676
latter approach assumes that transition to dormancy is not caused by carbon starvation 36
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per se, but rather by accumulation of osmolytes or loss of turgor pressure. These alter-
678
native approaches (dormancy driven by carbon starvation vs. hydric stress) give similar
679
results in dry soils, where carbon availability is reduced by transport limitations. How-
680
ever, predictions diverge in wet scenarios, where carbon may be limited by dilution and
681
inactivation is predicted only in models in which dormancy is triggered by low carbon
682
availability.
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683
At the early stage of biofilm colonization, with moderately high carbon availability
685
(ξDOC = 0.33) and no competition for space (ξψ,P ' 1), large growth rates were ob-
686
tained (all curves in Figure 6). Those microorganisms with lower inactivation capacity
687
(τi → 0) grew faster (dashed lines). When τi > 0, since ξDOC 6= 1, some of the newly
688
synthetized cells switched to a dormant state (dotted red and solid black curves). This
689
phenomenon led to a delay in the initial growth of the AC pool and in the total amount
690
of cells (AC + DC). As a consequence, the inactivation process seemed apparently coun-
691
terproductive. After this initial transient stage, the total biomass reached similar values
692
during periods of abundant carbon regardless of their dormancy capacity, even though
693
the colonies with larger τi depicted slightly smaller active populations. When the cell
694
number reached their maximum (characterized by low ξψ,P , in (7)), microbial activity
695
decreased and therefore the amount of carbon consumed increased more slowly. For this
696
set of conditions, the maximum consumption rate was observed at AC ≈ 0.2g cm−3 .
697
Above this point, the cellular metabolism was acclimated to meet maintenance require-
698
ments rather than growth.
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699
When DOC conditions deteriorated at ∆t days (DOC and therefore ξDOC decreased
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700
to 0), the beneficial effect of dormancy became apparent. Those organisms that switched
702
more rapidly to a dormant state experienced lower losses and maintained significantly
AC
701
703
larger total cell densities, despite a faster AC decrease is observed (compare the dy-
704
namics of dashed blue and solid blacks lines in Figure 6). Lower mortality rates in DC
705
moderated the total population decline, conferring larger survival chances.
706
707
When conditions of high DOC availability were restored again (at 2∆t, 4∆t), or37
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ganisms rapidly proliferated. In line with the discussion provided in Blagodatskaya and
709
Kuzyakov (2013), respiration increased exponentially after substrate input, reaching its
710
maximum in less than a day and then decreased sharply when the maximum amount of
711
cells was reached or when substrate was removed. Upon DOC removal, the AC pool was
712
fed by the reactivation of DC (if available), reducing the synthesis of new cells (and the
713
carbon consumed). As a consequence, dormancy can be considered an efficient strategy
714
to recycle energy and carbon, allowing lower carbon consumption to achieve the same
715
biomass (bottom panel in Figure 6).
716
3.4. The Combined Effect of Dormancy and EPS on Microbial Dynamics
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The combined effect of EPS and rate of transition to the dormant state was studied
718
by analyzing the long term concentration of biofilms with different allocation coefficients
719
λEP S = 0 and λEP S = 0.23. Three different scenarios are shown in Figure 7: wet-dry
720
events with ∆tR = 100 and ∆tR = 10 days, and permanent saturation.
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717
721
Results showed that those organisms with larger rates of transition to and from dor-
723
mancy achieved larger populations in all scenarios after 1 year of simulation, regardless
724
of the capacity to produce EPS (top and bottom panels of Figure 7). This indicated that
725
such a mechanism may improve survival chances under a wide range of environmental
726
conditions. Even though the amount of AC in permanently wet scenarios was only slightly
727
altered by the inactivation capacity of cells, the total amount of cells experienced a 26%
728
increase (all DC). Nevertheless, under alternating wet-dry conditions, those biofilms with
729
τi ≥ 1x10−5 min−1 increased their total population by 10 to 100 times compared with the
730
non-dormant ones. Moreover, these colonies had up to a 70-95% of inactive cells (hardly
731
observable in the top plots). The more intense was the water stress, the greater was
732
the benefit resulting from inactivation, being the percentage of DC strongly determined
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by the environmental constraints. The ratios between active and inactive populations
734
obtained are hardly comparable with the wide range of values reported in the literature
735
(e.g., in the review by Blagodatskaya and Kuzyakov, 2013). A sensitivity analysis (not
736
shown) indicated that other parameter choices could align simulations with alternative
737
empirical evidence.
AC 733
738
38
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Figure 6: Temporal evolution of biofilm growing in a fully saturated soil that experiences sudden changes in the concentration of DOC every 35 (left) and 7 days (right). The capacity of switching in and out of a dormant state was evaluated by studying microorganisms unable to become dormant (maximum rate of
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cell inactivation τi = 0) and others with different switching rates between the two states (τi = 1.32x10−4 and 1.32x10−3 min−1 ). τa was set equal to 1.43xτi . From top to bottom: environmental coefficient representing DOC availability (ξDOC ), total amount of cells (AC + DC), active cells (AC), quorum
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sensing coefficient based on the cell population (ξψ,P ), and cumulative amount of carbon consumed per cm3 of soil (C cons.).
Moreover, the combined effect of dormancy and EPS production under periodic rain-
740
fall events helped mitigating the carbon and water stress (low saturation and dilution).
741
The additional accumulation of EPS improved microbial fitness, while preserving the
742
positive impact of inactivation, producing a population rise between 2− to 100-fold. For
743
the studied set of conditions, the stress remission was so efficient that the cell population
AC 739
744
reached values comparable to those achieved without stress (see Figure 7, bottom center). 39
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Figure 7: Mass of the biofilm compartments as a function of the maximum rate of cell inactivation (τi ). Long-term simulations (of 1 year) considered values of τi ranging from 1x10−7 to 1x10−2 min−1 . The role of EPS was evaluated by comparing the results obtained by the environmental coefficient λEP S = 0 (top row) and λEP S = 0.23 (bottom row). Simulations shown were performed under periodic rainfall
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events with ∆tR = 100 days (left), 10 days (center), and wet conditions (right).
745
Figure 8 depicts contour plots of the long-term concentrations of the AC, AC+DC and
747
EPS compartments as a function of λEP S and τi . This figure summarizes how combining
748
the release of EPS (λEP S ) and the capacity of organisms to be induced into dormancy
749
(τi ) had significant effects on the carbon partition in the biofilm. The growth of biofilms
750
under fully-saturated conditions was not much affected by λEP S and τi because of the
751
downregulation effect and the suitability of the environmental conditions (bottom panel).
752
The inactivation of cells generated colonies with slightly larger amounts of cells, while the
753
population of active microbes remained almost stable. In contrast, biofilm proliferation
754
was limited in environments alternating wet and dry conditions (top panel), particularly
AC
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746
755
common in shallow natural soils, due to the nature and intensity of stressors. Under such
756
circumstances, results confirmed that the combination of the two mechanisms could effi-
757
ciently counteract the effects of stress, producing a clear improvement of biofilm fitness
758
and microbial survival (as evident from higher AC + DC with increasing λEP S and τi in
759
the top central plot). 40
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Figure 8: Contour plot depicting the averaged concentrations of biofilm compartments after a longterm simulation of 1 year. (left: active cells (AC), center: total cells (AC + DC), right: EPS (EP S). The maximum coefficient of carbon allocation towards EPS (λEP S ) was varied from 0 to 0.4 and the
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maximum rate of cell inactivation (τi ) from 1x10−7 to 1x10−2 min−1 , and under periodic rainfall events
761
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with ∆tR = 10 days (top), and wet conditions (bottom).
Based on these results, the significant differences in biofilm composition reported in
the literature (e.g., Chenu, 1995; Blagodatskaya and Kuzyakov, 2013) could be attributed
763
to the adaptation of microbes to the heterogeneous conditions in their habitats, in terms
AC
762
764
of substrate availability, mean saturation and temporal distribution of wetting events.
765
3.5. Model Limitations and Future Developments
766
The validation of the model cannot be accomplished easily due to the lack of experi-
767
mental data and of suitable and non-disruptive techniques to sample the pools considered, 41
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768
and because of the difficulties in empirically confirming the specific contribution of some
769
of the different parameters included.
770
Moreover, despite the considerable complexity of the model presented, some processes
772
occurring within the biofilm-soil system are not thoroughly addressed. On one hand, the
773
dynamics of nutrients such as nitrogen and phosphorus and of the electron acceptors
774
like oxygen are neglected. We thereby focus on conditions of carbon limitation that are
775
prevalent in shallow mineral soils (C:N and C:P ratios are generally lower than the criti-
776
cal ratios for inorganic nutrient immobilization and O2 is abundant). On the other hand,
777
the feedbacks between bioclogging and detachment rates are considered beyond of the
778
scope of this analysis, although they may dominate biofilm proliferation particularly in
779
areas of high flow velocity. Yet, their significance in most surface soils is minor compared
780
to the studied microbial responses to stress. For this reason, their incorporation in the
781
SMMARTS flexible framework is kept for future research.
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However, despite the assumptions made, the model can be used as a tool to better
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understanding or even predicting the dynamics of biofilm proliferating under a wide range
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of environmental conditions (and the stressors associated). With slight modifications, this
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framework could also be applied to non-porous environments such as surfaces in aquatic
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ecosystems.
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4. Conclusions
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A micro/meso-scale mechanistic model to predict patterns of microbial dynamics un-
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der a wide range of conditions (SMMARTS) is presented and analyzed. This general
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model differentiates the microbial biomass and byproducts into active and dormant cells,
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EPS, and extracellular enzymes; and the substrate between particulate and dissolved or-
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ganic matter. This approach allows disentangling the consequences of contrasting stress
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response strategies in microbial communities, including synthesis and reuse of EPS, tran-
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sition to a dormant state, and dynamic allocation of carbon among microbial compart-
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ments. These strategies are modulated according to biological needs and competition
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for space, water and carbon substrates in a porous environment. For this purpose, the
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model is equipped with: (i) indicators that allow the microorganisms to monitor envi-
799
ronmental and biological factors, and react accordingly to the current pressures; and (ii)
800
the pore-scale feedbacks existing between biofilm accumulation, carbon availability, and
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the water retention capacity in bio-amended soils.
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Although several assumptions have been made, the most relevant microbial processes
804
involved have been included and the results obtained from the simulations are qualita-
805
tively in agreement with a number of experimental observations reported in the literature.
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The model can thus be employed as a tool for theoretical exploration and for generat-
807
ing new hypotheses concerning the drivers of biofilm dynamics and their responses to
808
environmental conditions. Results show that microorganisms may utilize smart bioengi-
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neering designs to improve their fitness by adapting the physiological response to the
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intensity and type of stress. On one hand, the composition and amount of EPS can be
811
readjusted to mitigate preferentially water stress or carbon limitation. First, if EPS has
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a high water retention capacity, the investments in their production are rewarded by
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increasing both the overall water content and the carbon availability. Second, those EPS
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with lower water retention capacity may be used to store more competently the surplus
815
of carbon acquired when conditions are favorable, which can be used at later times if
816
conditions worsen. Third, the amount of EPS produced is modulated according to mi-
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crobial needs, which are adapted to environmental circumstances. On the other hand,
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microorganisms able to switch between active and dormant states are more efficient in
819
terms of carbon use and survival. The combination of these two strategies provides a
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clear benefit to colonies in environments affected by alternate wet-dry cycles, which are
821
predominant in surface soils in most ecosystems.
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Acknowledgments
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This research has received funding from projects ACWAPUR (MICINN. INICIA-
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TIVA INTERNACIONAL PCIN-2015-239), WE-NEED (1076 PCIN-2015-248), and IN-
826
DEMNE (MICINN CGL2015-69768-R). Additional support was provided by the Spanish
827
Ministry of Economy and Competitiveness (fellowship FPI BES-2013-063419). SM was 43
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partly funded by the Swedish Research Councils, Formas (2015-468) and VR (2016-
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04146). Data and details regarding the simulations can be requested by contacting the
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corresponding author.
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Ecological and soil hydraulic implications of microbial responses to stress - A modeling analysis Albert C. Brangar´ı, Daniel Fernandez-Garcia, Xavier Sanchez-Vila, ` Stefano Manzoni PII: DOI: Reference:
S0309-1708(17)30727-3 10.1016/j.advwatres.2017.11.005 ADWR 3010
To appear in:
Advances in Water Resources
Received date: Revised date: Accepted date:
19 July 2017 5 November 2017 6 November 2017
Please cite this article as: Albert C. Brangar´ı, Daniel Fernandez-Garcia, Xavier Sanchez-Vila, ` Stefano Manzoni, Ecological and soil hydraulic implications of microbial responses to stress - A modeling analysis, Advances in Water Resources (2017), doi: 10.1016/j.advwatres.2017.11.005
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Highlights • A new mechanistic model to predict the proliferation of biofilm in soils is proposed. • Ecological and soil hydraulic consequences of microbial accumulation are explored
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• Microbial dynamics respond to different environmental conditions and stresses.
• The biofilm compartment consists of active and dormant cells, EPS and enzymes.
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• The release/use of EPS and dormancy are key microbial processes.
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Ecological and soil hydraulic implications of microbial responses to stress - A modeling analysis
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Albert C. Brangar´ıa,b , Daniel Fern`andez-Garciaa,b , Xavier Sanchez-Vilaa,b , Stefano Manzonic,d a Department
of Civil and Environmental Engineering, Universitat Polit` ecnica de Catalunya (UPC), Jordi Girona 1-3, 08034 Barcelona, Spain. b Associated Unit: Hydrogeology Group (UPC-CSIC). c Department of Physical Geography, Stockholm University, Stockholm, Sweden. d Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden.
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Abstract
A better understanding of microbial dynamics in porous media may lead to improvements in the design and management of a number of technological applications, ranging from the degradation of contaminants to the optimization of agricultural systems. To this aim, there is a recognized need for predicting the proliferation of soil microbial biomass
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(often organized in biofilms) under different environments and stresses. We present a general multi-compartment model to account for physiological responses that have been extensively reported in the literature. The model is used as an explorative tool to elu-
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cidate the ecological and soil hydraulic consequences of microbial responses including the production of extracellular polymeric substances (EPS), the induction of cells into
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dormancy, and the allocation and reuse of resources between biofilm compartments. The mechanistic model is equipped with indicators allowing the microorganisms to monitor environmental and biological factors and react according to the current stress pressures.
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The feedbacks of biofilm accumulation on the soil water retention are also described. Model runs simulating different degrees of substrate and water shortage show that adap-
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tive responses to the intensity and type of stress provide a clear benefit to microbial colonies. Results also demonstrate that the model may effectively predict qualitative patterns in microbial dynamics supported by empirical evidence, thereby improving our understanding of the effects of pore-scale physiological mechanisms on the soil macroscale phenomena. Keywords: biofilm, porous media, extracellular polymeric substances, active 2
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microorganisms, dormant innactive cells, enzymes, substrate and water shortage.
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1. Introduction Almost all microorganisms on Earth are found in biofilms growing in soils and other
3
surfaces of natural or manufactured origin (Vu et al., 2009). In most ecosystems, they
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grow under changing and often unfavorable conditions, which in soils are characterized
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by relatively long periods of drying and rapid rewetting, accompanied by sharp changes
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in carbon availability. The evolutionary success of biofilms lies in their versatility to
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adapt to a wide range of environments, and their capacity to buffer, counteract or even
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benefit from external stresses. In general, biofilms provide a number of advantages to the
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embedded microbial colonies, increasing the hydration status, improving the efficiency
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of their digestive system, and reducing their mortality (Flemming and Wingender, 2010;
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Flemming et al., 2016; Or et al., 2007a). However, the mechanisms by which the microbial
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habitat is regulated and the potential impact of biofilm growth on porous media remain
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mostly unknown (Flemming and Wingender, 2010; Or et al., 2007b). There is thus a
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need for understanding the response of biofilms to environmental conditions, with sig-
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nificant implications for the carbon cycle (Schimel and Schaeffer, 2012), the degradation
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of contaminants (Marmonier et al., 2012), the design and management of technological
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and agricultural applications (DeJong et al., 2013; Thullner, 2010), and even human life
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(Flemming et al., 2016; Selker et al., 1999).
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The release of a polymeric matrix (e.g., Roberson and Firestone, 1992; Tamaru et al.,
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2005) and the capacity of organisms to be induced into dormancy (e.g., Konopka, 1999;
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Lennon and Jones, 2011) are recognized as key microbial responses to stress. The biofilm
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matrix is a complex heterogeneous mixture of extracellular polymeric substances (EPS)
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of microbial origin resulting from deliberate secretions and lysis products. EPS consti-
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tute a variable proportion of the biofilm's total organic matter, ranging from 2 to 90%
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(Chenu, 1995; Donlan, 2002; Flemming and Wingender, 2010), consisting of polysaccha-
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rides, proteins, nucleic acids, lipids, DNA (Stoodley et al., 2002), and variable amounts
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of water (Or et al., 2007a). The EPS actual structure, quantity and composition are the
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result of the balance between needs versus opportunities in a framework of biological and
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Preprint submitted to Advances in Water Resources
November 6, 2017
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environmental factors (Kim et al., 2010; Wilking et al., 2011). The nature of the ma-
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trix depends on the producer community and maturation stage (Flemming et al., 2016;
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Roman´ı et al., 2008), but it is further determined by environmental conditions such as wa-
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ter flow rate, pH, temperature, soil water content, and availability of nutrients/electron
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acceptors (Hand et al., 2008; More et al., 2014). Moreover, microorganisms may mod-
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ulate the synthesis rates of EPS in response to such factors (Roberson and Firestone,
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1992; Sandhya and Ali, 2015), thereby counteracting the harmful effects of environmental
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stresses. EPS help maintaining cell functions and turgor, contribute to the uptake and
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assimilation of nutrients, and mediate cell adhesion to surfaces (Chenu and Roberson,
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1996; Flemming and Wingender, 2010; Or et al., 2007a,b). In addition to the release of
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EPS, responses to stress include the induction of a reversible state of dormancy (Blago-
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datskaya and Kuzyakov, 2013). When resources are limiting or environmental conditions
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are not appropriate, dormant cells can persist for extended periods of time in a state of
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low to zero activity in which the mortality rate is lower than that for active cells (Brown
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et al., 1988; Stoodley et al., 2002). When conditions improve, inactive cells can grad-
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ually recover their functionality (Stolpovsky et al., 2011). In general, those organisms
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that are efficient at switching between states present advantages, particularly in those
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environments that experience recurrent and prolonged periods of stress (Konopka, 1999;
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Lennon and Jones, 2011).
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Hence, microorganisms can use, at least, two well-identified mechanisms to improve
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their fitness. The resulting increase in the total biomass enlarges their capacity to repli-
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cate and survive in a competitive environment. Responses might combine an improve-
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ment of the environmental characteristics with a reduction of the requirements for micro-
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bial preservation. The decision making process of the microbial community is somehow
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similar to the quorum sensing mechanism of stimuli/response (Donlan, 2002; Parsek and
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Greenberg, 2005). Cells continuously interpret physicochemical signals (some of them
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released by themselves), which may regulate the deployment of these strategies. This
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way, microbial dynamics are modulated according to the nature and intensity of the
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stress (Chang and Halverson, 2003; Sandhya and Ali, 2015).
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Table 1: Nomenclature, parameter definition, and units of the model parameters.
a AC ADD
Description
Units
Experimental parameter for the water retention capacity of EPS
[L]
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Symbol
[M L−3 ]
Mass of AC per unit volume of soil
[M L−3 T −1 ]
Effective external supply of POM
b
Experimental parameter for the water retention capacity of EPS
[−]
c
Maximum volumetric density of EPS
[−]
Diffusion coefficient of DOC and EZ in water
DC
Mass of DC per unit volume of soil
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D0
[L2 T −1 ] [M L−3 ] [M L−3 ]
Concentration of DOC in water
DOCb
Concentration of DOC in the biofilm bodies
[M L−3 ]
DOCeq
Concentration of DOC at saturation
[M L−3 ]
DOCK
Half-saturation constant of DOC
[M L−3 ]
DOCpm
Concentration of DOC in the pore-matrix water
[M L−3 ] [M L−3 ]
Half-saturation constant of EPS
[M L−3 ]
Dry mass of EZ per unit volume of water
[M L−3 ]
EZK
Half-saturation constant of EZ
[M L−3 ]
AC KD
Decay rate coefficient for AC
[T −1 ]
Decay rate coefficient for DC
[T −1 ]
Decay rate coefficient for EPS
[T −1 ]
Decay rate coefficient for EZ
[T −1 ]
EP S EP SK EZ
DC KD EP S KD
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EZ KD
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Dry mass of EPS per unit volume of soil
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DOC
n
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P OM
P OMK
Van Genuchten's parameter for the SWRC of the biofilm-free soil
[−]
Dry mass of POM per unit volume of soil
[M L−3 ]
Half-saturation constant of POM
[M L−3 ]
t
Time variable
[T ]
tc
Characteristic time of the effects of the rain
[T ]
tR
Time of the last rainfall event
[T ]
— Continues on the next page —
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— Continued — Symbol
Description
Units [LT −1 ]
Averaged velocity of water
Y
Yield coefficient of respiration
[−]
z
Coordinate parallel to the water flow direction
[L]
α
Van Genuchten's parameter for the SWRC of the biofilm-free soil
βP
Shape factor controlling the curvature of ξψ,P
βθb
Shape factor controlling the curvature of ξψ,θb
∆tR
Return period of rainfall events
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vw
[L−1 ] [−] [−] [T ]
Shape parameter for the solute diffusion coefficient
Γ
Mass exchange function
θb
Volume of water in biofilm bodies
[−]
Volume of pore-matrix water
[−]
θpm
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γ
[−]
[M L−3 T −1 ]
Residual water content of the soil
[−]
θs
Saturated water content of the soil
[−]
λd
Decayed mass reallocation ratio
[−]
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θr
Effective coefficient of carbon allocation diverted towards EPS
[−]
λEP S
Maximum coefficient of carbon allocation diverted towards EPS
[−]
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λ∗EP S
Effective coefficient of carbon allocation diverted towards EZ
[−]
λEZ
Maximum coefficient of carbon allocation diverted towards EZ
[−]
Parameter denoting the channeled architecture of biofilms
[−]
N µC
Maximum specific consumption rate
[T −1 ]
Maximum specific decomposition rate of EPS
[T −1 ]
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µEP S
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λ∗EZ
[T −1 ]
Maximum specific decomposition rate of POM
ξDOC
Environmental coefficient based on the concentration of DOC in the biofilm phase
[−]
ξEP S
Environmental coefficient based on the concentration of EPS
[−]
Environmental coefficient based on the concentration of EZ
[−]
Environmental coefficient based on the concentration of POM
[−]
ξτ
Solute diffusion coefficient
[−]
ξχ
Environmental coefficient based on the concentration of the generic variable χ
[−]
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µP OM
ξEZ
ξP OM
— Continues on the next page —
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— Continued — Symbol
Description
Units
ξψ,P
Quorum sensing coefficient based on cell population
[−]
ξψ,θb
Quorum sensing coefficient based on θb
[−]
Density of the microbial cells
ρw
Density of water
τa
Maximum rate of cell reactivation
τi
Maximum rate of cell inactivation
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[M L−3 ]
ρc
[M L−3 ] [T −1 ] [T −1 ]
Effective porosity of the soil
φM
Maximum effective pore volume susceptible to be occupied by water
χ χK
[−]
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φef
[−]
Mass of the generic variable χ per unit volume of water or soil
[M L−3 ]
Half-saturation constant of the generic variable χ
[M L−3 ]
Matric suction
ψ0
Matric suction in the natural state of the soil
[L]
Ω
Shape parameter for the solute diffusion coefficient
[−]
M
ψ
Despite the benefits described above, these survival strategies entail side effects. First,
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the production of EPS involves significant investments of carbon, decreasing the amount
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of resources allocated to growth. Furthermore, the viability of natural and mutant non-
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producer strains (e.g., Seminara et al., 2012; Vandevivere and Baveye, 1992a) indicate
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that EPS are not essential for life. One could argue that evolution would not preserve
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organisms that produce functionless substances misusing energy and nutrients (Chenu,
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1995). Therefore, EPS should provide a competitive (or cooperative) advantage for the
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embedded microorganisms. A similar reasoning can be held for dormancy: despite inac-
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tive cells remain in a state of alertness, they cannot respond immediately when conditions
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improve (Blagodatskaya and Kuzyakov, 2013). Cells must undergo a transition to recover
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their activity, potentially missing favorable periods. Therefore, dormancy could even be
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counterproductive in certain cases.
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Understanding the benefits and tradeoffs of such cooperative behaviors frames the
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scope of this contribution. Difficulties mostly arise from the complex dynamics of the 7
[L]
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interactions and feedbacks between environmental and biological factors.
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1.1. The Impact of Biofilms on Pore-scale Conditions The self-organization of microorganisms in biofilms results in a number of direct and
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indirect effects. First of all, the proliferation of biofilms in soils alters the hydraulic prop-
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erties of porous media (Engesgaard et al., 2006; Rockhold et al., 2002; Volk et al., 2016),
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changing their capacity to transport and retain water and solutes. This effect emerges
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from the hydraulic attributes of the biofilm-soil system and its interaction at the pore-
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scale (Brangar´ı et al., 2017). The most widely reported effect in bio-amended soils is
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bioclogging, i.e., a decrease in hydraulic conductivity due to EPS (e.g., Thullner et al.,
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2002; Yarwood et al., 2006) or cell accumulation (e.g., Vandevivere and Baveye, 1992b;
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Wu et al., 1997). The reduction of water flow helps reducing detachment rates, preserv-
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ing the hydration status and mitigating nutrient dilution and enzyme losses. However,
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under certain scenarios, the decrease in nutrient supply by impaired advection transport
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(Stewart, 2012; Thullner et al., 2002) may turn dense biofilms into apparently undesired
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structures.
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Bio-accumulation also enhances the retention of water (Rosenzweig et al., 2012;
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Rubol et al., 2014), thereby improving the conditions in the vicinities of cells (Or et al.,
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2007b). Under wet conditions, the coating matrix forms an open structure that holds
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up many times its weight in water. When dried, such a structure shrinks, becoming a
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dense and amorphous frame that remains moist over a wide range of water potential.
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This capacity depends on the morphology of the EPS matrix (Brangar´ı et al., 2017),
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but also on its composition. In this line, Chenu (1993) found significant differences
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in the water retained by EPS, with decreasing retention in the order: xanthan>EPS
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rhizobia>scleroglucan>dextran.
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In addition to the hydraulic implications, biofilm may contribute to the efficiency of
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the microorganisms digestive system by increasing nutrient uptake rates in a number of
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ways. First, despite the fluxes through biofilms are lower than those for free water (Stew-
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art, 2003), the increase in hydration modifies the advection-diffusion pathways (Chenu 8
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and Roberson, 1996), with significant implications for substrate availability. Second,
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contact times and duration of periods suitable for growth or acclimation are lengthened
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(Or et al., 2007a). Third, biofilms act as a reservoir that retains nutrients, enzymes, and
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catalysis products close to the cells (Flemming and Wingender, 2010). Fourth, the matrix
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behaves as a molecular sieve sequestering dissolved and particulate substrate from the
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environment (Flemming et al., 2003, 2016). Fifth, the carbon-rich EPS may be used as a
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source of carbon during periods of low resource availability. In contrast, when resources
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are abundant, microbes may allocate preferential resources to produce extra amounts
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of EPS (Kakumanu et al., 2013; Roberson and Firestone, 1992). Finally, despite being
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beyond the scope of this paper, EPS also alleviate the salt stress effect on cells (Sandhya
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and Ali, 2015) and facilitates the attachment of them to surfaces and to other cells (Vu
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et al., 2009).
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1.2. Survival Strategies: Experimental Evidence and Modeling
Due to the great importance of the aforementioned survival strategies on microbial
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proliferation, a large number of experimental and theoretical studies have been con-
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ducted.
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Several experimental studies have pointed out that the release of EPS is modulated as
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a direct response to environmental stresses and microbial needs. Roberson and Firestone
126
(1992) and Chang and Halverson (2003) found that biofilms growing in dry conditions
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contain larger amounts of EPS. Sandhya and Ali (2015) reported a significant increase
128
in their production also on bacteria exposed to high temperature or salinity. Tamaru
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et al. (2005) showed that EPS help maintaining cellular viability under deep desiccation.
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More et al. (2014), Redmile-Gordon et al. (2015) and Roberson and Firestone (1992)
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identified the EPS as a resource storage pool. Despite this compelling evidence, most
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modeling approaches (especially at the ecosystem level) do not include EPS and their
133
responses to stressors. Most models do not even differentiate between cells (responsible
134
of activity) and other types of attached biomass (inactive but having other properties)
135
(e.g., Ezeuko et al., 2011; Pintelon et al., 2012; Rosenzweig et al., 2014; Soleimani et al., 9
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2009; Thullner and Baveye, 2008). Other models do describe various microbial compart-
137
ments (e.g., Aquino and Stuckey, 2008; Laspidou and Rittmann, 2002a, 2004). Often,
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the mass balance of EPS (or of total biomass in simpler approaches) is defined as a
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more or less complex scheme of growth, decay and detachment (e.g., Ezeuko et al., 2011;
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Pintelon et al., 2012; Rosenzweig et al., 2014). An early study included the direct trans-
141
formation of cells to EPS (Hsieh et al., 1994), disassociating production from substrate
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use, which is fundamental for modeling resource reallocation. Some models included a
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metabolic pathway in which the EPS could be decomposed and reused by cells as labile
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carbon (e.g., Aquino and Stuckey, 2008; Laspidou and Rittmann, 2004). Following an
145
alternative approach, Maggi and Porporato (2007) included the competition of bacteria
146
for water and space through limitations in their activity. However, none of these models
147
account for the full feedbacks between the EPS and the environmental conditions. The
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most notable gaps in the representation of these processes encompass: (i) the EPS mod-
149
ulation of stress; (ii) the link between cellular demands (increased during stress) and the
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EPS synthesis; (iii) the EPS reuse as a source of carbon; and (iv) the impact of EPS on
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hydration status and nutrient uptake rate.
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Regarding the effects of dormancy, Mart´ınez-Lavanchy (2009) measured significant al-
154
terations of the microbial activity as a response to changes in carbon and oxygen supply.
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Stolpovsky et al. (2011) associated such phenomena to a massive inactivation under inap-
156
propriate conditions. In Kaprelyants and Kell (1993), cells exposed to starvation could
157
recover their functionality after a long period of dormancy. Other studies found that
158
dormant cells tend to accumulate in the deepest regions of the biofilms (Kim et al., 2009;
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Williamson et al., 2012), pointing out that transport limitations inside biofilm structures
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may induce dormancy even under apparently favorable conditions. The studies model-
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ing the phenomenon of dormancy include approaches that control the switching between
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activity stages with different degrees of complexity (e.g., Konopka, 1999; Manzoni et al.,
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2014; Stolpovsky et al., 2011). These models, however, have not been tested in scenarios
164
with complex interactions between the microbial pools and the environmental conditions.
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1.3. Model Rationale and Objectives Despite the empirical evidence, relating the production of EPS and dormancy to envi-
168
ronmental stresses, drivers and consequences with process-based models is still difficult.
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This is mainly because biofilms (and more broadly soils) can be seen as an emerging
170
property of a complex system that encompasses nonlinear and interconnected biogeo-
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chemical processes in a high-dimensional phase space. To the best of our knowledge,
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theoretical studies have tackled only some aspects of this complexity, and there are no
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empirical studies characterizing all the elements and mechanisms involved.
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The aim of this paper is then to shed some light on these complex microbial dynamics
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by means of a multi-compartment soil microbial mechanistic model named SMMARTS
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for Soil Microbial Model to Account for Responses To Stress. The model includes up
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to seven spatially-lumped and chemically-homogeneous compounds (compartments) that
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approximate the behavior of functionally-different carbon pools in soils. The dynamics
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of biomass synthesis, inactivation/reactivation, decay, and allocation and reuse of carbon
181
among biofilm components are modulated according to biological needs and competition
182
for space, water and substrate. To this aim, the model uses indicators that allow the
183
microorganisms to monitor environmental variables and biofilm status and react accord-
184
ingly. The feedbacks of biofilms on soil water retention and their consequences on the
185
nutrient uptake capacity are described at the pore-scale.
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A model with such a complexity is necessary to: (i) quantify microbial growth by
188
including the most relevant carbon fluxes at the biofilm level; (ii) include mechanisms
189
to modulate microbial dynamics according to experimental observations, with emphasis
190
on responses to stress; and (iii) estimate the feedbacks of biofilms on the soil hydraulic
191
properties and the overall environmental conditions. The resulting general model is de-
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veloped in order to facilitate the study of the patterns of biofilm dynamics in porous
193
media at the micro/meso-scale, reproducing the smart bioengineering that governs the
194
proliferation of microbial communities. It can then be employed as an explorative tool
195
to disentangle external (i.e., environmental) and internal (i.e., nonlinearities) drivers of
196
biofilms and their responses to environmental conditions. After some simplifications, we 11
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use this still very complex approach to explore scenarios based on reasonable ranges of
198
parameter values mapping microbial traits. In this way, the ecological benefits of these
199
survival strategies are evaluated under substrate or water shortage.
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2. Materials and Methods
202
2.1. SMMARTS Development
203
2.1.1. Model Compartments
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The heterotrophic biofilm is differentiated into four lumped compartments: active
205
cells (AC), dormant cells (DC), extracellular polymeric substances (EPS), and extra-
206
cellular enzymes (EZ). The AC compartment consists of the functional microorganisms
207
within the biofilm (considering mainly attached cells but it may also include plank-
208
tonic organisms) that lead the behavior of the entire biofilm system. The DC represents
209
the microorganisms that have undergone a reversible inactive state. The EPS pool is
210
composed of soluble compounds, macromolecules and particulate materials that con-
211
stitute the microbial matrix. Finally, the EZ compartment is formed by extracellular
212
agents of microbial foraging (treated as a solute species) responsible for the decomposi-
213
tion/solubilization of complex compounds.
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Biofilms require energy from organic matter to proliferate. Here, for simplicity, the
216
dynamics of nutrients and of the electron acceptors are neglected, albeit they can be eas-
217
ily incorporated. The non-microbial carbon compartments include: particulate organic
218
matter (POM), dissolved organic matter in the pore-matrix water phase (DOCpm ), and
219
dissolved organic matter inside the biofilm (DOCb ).
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In this model, each compartment is assumed to be homogeneous in a specific control
222
volume. The dynamics of the compartments are expressed as a system of mass balance
223
equations (illustrated in Figure 1). All model parameters are listed in Table 1.
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Figure 1: Sketch illustrating the biofilm, water, and air (of variable volume) inside a solid porous matrix and the biological processes described in the model. The solid arrows describe the fluxes between compartments, whereas the dotted arrows indicate C exchanges with the environment. The microbial
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compartments are differentiated into active cells (AC), dormant cells (DC), the polymeric matrix (EPS), and extracellular enzymes (EZ); and the substrate compartments into particulate organic matter (POM), dissolved organic matter in water (DOCpm ), and dissolved organic matter in biofilm phase (DOCb ). Each compartment is drawn on the phase(s) with which may be in contact (air, water or biofilm), as
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indicated by different shading. Dashed boxes represent compounds dissolved or in suspension. Granular material and air phase are considered passive with regard to the carbon cycle.
226
To account for the feedbacks between biofilm accumulation, hydraulic properties and
environmental conditions, the distribution of pore-matrix water and biomass is defined at
AC
227
2.1.2. Biofilm Effects on Water Distribution
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225
228
the pore-scale level based on the framework presented in Brangar´ı et al. (2017). Despite
229
using the simple capillary tube analogy, this approach effectively reproduced saturation
230
changes in bio-amended soils. The model considers a biofilm that may retain variable
231
amount of water depending on suction. Such a volume of water in biofilms (θb [−])
232
may be defined from the water retention capacities of EPS and including some spatial 13
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233
restrictions ! EP S −b cEP S aψ , , φM , θb = min ρw ρw
(1)
where the overbar indicates the average concentration of a compartment (here the
235
dry mass of EPS) over a unit volume of soil [M L−3 ], ρw [M L−3 ] is the water density,
236
ψ [L] is the matric suction, a [L], b [−] and c [−] are experimental parameters for the
237
water retention capacity of EPS, and φM [−] is the maximum volume available, which is
238
susceptible to be occupied by any of the phases studied.
239
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The first term in (1) represents the shrinking/swelling capacity of the biofilm, which
241
depends mainly on the composition of the EPS. Rosenzweig et al. (2012) reported that
242
a = 105.76cm and b = 0.489 for pure xanthan (when suction is expressed in cm of wa-
243
ter), whereas Chenu (1993) observed that dextran shows almost no retention capacity
244
(a → 0). The impact of microbial cells on the soil water retention curve (SWRC) is here
245
not included to better isolate the effects of EPS, neglecting the role of the cellular water
246
in extracellular processes. The second term restricts the maximum volumetric density
247
of EPS. In this line, Chenu (1993) observed that xanthan may retain up to 70 times its
248
weight in water (c = 70). The third term constrains θb to spatial and water limitations.
249
In fully-hydrated porous media, φM is equal to the effective porosity of the soil φef [−],
250
i.e., spatially restricted to the saturated minus the residual water content (φef = θs −θr ).
251
Nevertheless, when water availability is limited, the water-suction equilibrium assumed
252
in the first part of (1) might not be achieved and θb becomes limited by φM (the maxi-
253
mum amount of water available, defined from the soil suction in (16), Section 2.2).
255
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Biofilm bodies comprise complex structures that form pores, voids, and channels,
which induce significant structural changes in the pore-matrix. Their accumulation there-
257
fore alters the size and geometry of the pore space, leading to indirect changes in the
258
macroscopic retention properties. When pore-scale effects are integrated over the whole
259
control volume, the volume of pore-matrix water (θpm , [−]) retained in the open pore
260
space not occupied by biofilm may be written as
AC
256
14
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"
n
θpm = [φef − θb ] 1 + α ψ
n
φef − θb N φef
n2 # n1 −1
+ θr ,
(2)
where n [−] and α [L−1 ] are the experimental van Genuchten's parameters (van
262
Genuchten, 1980) obtained with biofilm-free soils, and N [−] is a theoretical parameter
263
that accounts for the channeled architecture of biofilm. The larger is N , the more intricate
264
is the morphology of the biofilm-soil system at the pore-scale, resulting in a potential
265
increase in water holding capacity. The reader is referred to Brangar´ı et al. (2017) for
266
derivation and details.
267
2.1.3. Non-Microbial Carbon
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Carbon is used to synthetize new cells, enzymes and matrix compounds, and to pro-
269
duce energy for their maintenance. In our model scheme, non-microbial carbon is par-
270
titioned between particulate (POM) and dissolved forms (DOC) (as in e.g., Greskowiak
271
et al., 2005; Schimel and Weintraub, 2003); and the latter is further distinguished between
272
DOCpm (in the pore-matrix water) and DOCb (in the biofilm) (as in e.g., Orgogozo et al.,
273
2010). Such a differentiation is required to account for the relatively large differences in
274
concentration that may exist between them (Billings et al., 2015; Stewart, 2003, 2012).
275
This scheme is simple, but may effectively represent the wide range of forms in which
276
organic matter is found in ecosystems.
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POM here includes diverse materials that range from the coarser fraction of the
279
organic matter to molecules of complex composition. POM cannot be directly assimilated
280
into microbial biomass, but requires an enzyme-mediated extracellular de-polymerization
281
step to be reduced to simpler dissolved compounds (here DOC) (Roman´ı et al., 2004).
282
In porous materials, decomposition rates are constrained by the spatial limitations on
283
solute diffusion, which depend on soil tortuosity. Such a process is also rate-limited by
284
the solubility of POM (as in Greskowiak et al., 2005), in which DOCeq represents the
285
concentration of DOC at saturation. The mass balance for POM in time (t, [T ]) may
286
then be expressed as
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15
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∂P OM = ∂t
θb DOCeq − DOCb ADD − ξτ µP OM ξP OM EZ θb + θpm DOCeq | {z } {z } |
POM input
POM decomposition
(3)
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θpm DOCeq − DOCpm − , ξτ µP OM ξP OM EZ θb + θpm DOCeq {z } | POM decomposition
where P OM [M L−3 ] is the dry mass of POM per unit volume of soil, EZ [M L−3 ]
288
is the dry mass of EZ per unit volume of water (pore-matrix + biofilm), DOCb [M L−3 ]
289
and DOCpm [M L−3 ] are the concentrations of DOC in the respective pools, ADD
290
[M L−3 T −1 ] is the external supply of POM, ξτ [−] is the coefficient modulating solute
291
transfer, µP OM [T −1 ] is the maximum specific decomposition rate, and ξP OM [−] is an
292
environmental coefficient limiting decomposition according to the amount of POM.
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293
The decomposition fluxes in (3) are proportional to the enzyme concentration, and
295
driven by the disequilibrium of DOC in the individual pools. The solute diffusion coeffi-
296
cient ξτ for partially-saturated soils is based on Archie's second law for solute diffusivities
297
(see Hamamoto et al., 2010, for details)
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294
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ξτ = θsΩ
θb + θpm θs
γ
,
(4)
where Ω [−] and γ [−] are two shape parameters. Thresholds in the original Archie's
299
law are assumed equal to 0 in (4). With this premise, decomposition rates are ensured
300
even at very low saturation (≈ θr ) since water (solvent) and POM are considered in
301
contact at the pore-scale and diffusion is likely to occur. Note also that ξτ is the inverse
302
of the tortuosity and depends on soil type by means of (2). Yet, the reduced diffusivity
303
through biofilm bodies (described in e.g., Or et al., 2007a) is neglected.
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AC
304
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298
305
The coefficient ξP OM limits the decomposition rate as P OM decreases and is de-
306
scribed by a generalized saturating function based on the Michaelis-Menten kinetic model
ξχ = 307
χ , χK + χ
(5)
where χK [M L−3 ] (here P OMK ) is the half-saturation constant of a generic variable 16
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308
χ (here POM).
309
Carbon decomposed in (3) is then diverted to the DOC compartments. DOCpm and
311
DOCb are affected by various processes of transport, formation and consumption defined
312
in (6) and (7) (Figure 1).
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310
DOCeq − DOCpm ∂θpm DOCpm θpm − = ξτ µP OM ξP OM EZ ∂t θb + θpm DOCeq {z } | POM decomposition - DOC formation
θpm ∂DOCpm ∂ 2 DOCpm + ξτ D0 − ∂z } θb + θpm ∂z 2 | {z }
Advection
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vw [θpm − θr ] | {z
Diffusion
∂θb DOCb θb DOCeq − DOCb = ξτ µP OM ξP OM EZ − ∂t θb + θpm DOCeq {z } |
Γ |{z}
(6)
Γ |{z}
(7)
Mass transfer
POM decomposition - DOC formation
Advection
Diffusion
Mass transfer
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Consumption
M
∂ 2 DOCb ∂DOCb θb ξτ D0 µC ξφ,P ξDOC AC − vw θb + + ∂z 2 {z } | {z∂z } |θb + θpm {z | }
µC [T −1 ] is the maximum specific consumption rate, ξDOC [−] is an environmental
314
coefficient limiting consumption rates, ξψ,P [−] is a quorum sensing coefficient, vw [LT −1 ]
315
is the velocity of water, z [L] is the coordinate parallel to the direction of flow, D0 [L2 T −1 ]
316
is the solute diffusion coefficient in water, and Γ [M L−3 T −1 ] is a mass exchange function.
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318
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317
Consumption rates are mathematically modulated by the coefficients ξDOC and ξψ,P .
They simulate the microorganisms' capacity to monitor and respond to environmental
320
and biological variables. The coefficient ξDOC consists in a nonlinear term defined in (5),
321
just replacing χ by DOCb . It can easily include growth limitation caused by electron
322
acceptor shortage (as in Laspidou and Rittmann, 2002b; Rodr´ıguez-Escales et al., 2014).
323
Note that only DOCb , which is in the immediate vicinity of microbial cells, is used for
324
metabolic processes. The coefficient ξψ,P reduces carbon uptake when the microbial
325
population is high,
AC
319
17
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ξφ,P
"
AC + DC = 1− ρc φef
#βP
,
(8)
where AC and DC are the dry masses of AC and DC per unit volume of soil [M L−3 ],
327
and ρc [M L−3 ] is the volumetric mass density of the microbial cells. βP [−] is a shape
328
factor that determines the strength of the population regulation. It ranges from 0 to
329
∞ for mechanistic rationale and defines the curvature of the inhibition expression. The
330
resulting ξψ,P tends to 1 (no inhibition) when the volume of cells is much smaller than
331
the free space and decreases with increasing total microbial population (AC + DC) as
332
space becomes limiting.
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Advection and diffusion terms in the mass balance equations for DOC represent pow-
335
erful transport processes that may either provide or flush out dissolved carbon from the
336
system. For simplicity, water velocity is considered phase independent (averaged and
337
then assumed equal in open pores and in biofilms), and the effect of solute diffusion is
338
linearized. Note that, due to the similarity between process-regulators at the pore-scale,
339
the effective diffusion is determined by ξτ (recall (4)).
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340
The mass transfer function Γ controls the flow of carbon between the two DOC
342
compartments. It is driven by the difference in DOC concentration, the size of the
343
intricate surface of contact, and the advective-dispersive flow. The sooner the exchange of
344
mass, the faster the equilibrium is reached. When the characteristic time of consumption
345
is much longer than that of the mass transfer (rates and contact areas are relatively large
346
at the pore-scale), equilibrium can be assumed (DOCb == DOCpm ).
347
2.1.4. Microbial Compartments
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The main carbon fluxes in biofilms represent the synthesis of new biomass, the pro-
AC
348
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341
349
duction and reuse of EPS, the transition to and from the dormant state, the losses of
350
different nature, and the reallocation of decay products. Accordingly, the mass balance
351
equations describing the four microbial compartments are (Figure 1)
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∂AC = Y [1 − λ∗EP S − λ∗EZ ]µC ξφ,P ξDOC AC + Y µEP S ξEP S ξEZ [1 − ξDOC ]AC {z } ∂t | {z } | AC synthesis (EPS decomposition)
− τi [1 − ξDOC ]ξφ,P AC + τa ξDOC DC {z } {z } | | Reactivation
Inactivation
| {z } AC decay
∂EP S = Y λ∗EP S µC ξφ,P ξDOC AC − µEP S ξEP S ξEZ [1 − ξDOC ]AC {z } ∂t | {z } | EPS decomposition
EPS synthesis
(9)
AC − KD AC ,
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AC synthesis (DOC consumption)
(10)
AC DC EP S + λD [KD AC + KD DC] − KD EP S , {z } | {z } | Decayed mass reallocation
EPS decay
Inactivation
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∂DC DC = τi [1 − ξDOC ]ξφ,P AC − τa ξDOC DC − KD DC , {z } | {z } ∂t {z } | | Reactivation
∂[θb + θpm ]EZ EZ = Y λ∗EZ µC ξφ,P ξDOC AC − KD [θb + θpm ]EZ − ∂t | {z } | {z } EZ synthesis
EZ decay
M
∂EZ ∂ 2 EZ vw [θb + θpm − θr ] + ξτ D0 , 2 ∂z } | | {z {z∂z } Advection
(11)
DC decay
(12)
Diffusion
where Y [−] is the yield coefficient; ξEZ [−] and ξEP S [−] are limiting environmental
353
coefficients based on the requirements of EZ and EPS; λ∗EZ [−] and λ∗EP S [−] are effective
354
coefficients of carbon allocation; µEP S [T −1 ] is the maximum specific consumption rate
355
of EPS; τi [T −1 ] and τa [T −1 ] are the maximum rates of inactivation and reactivation of
356
cells, respectively; KD [T −1 ] are decay rate coefficients for the compartments indicated
357
in the superscripts; and λD [−] is the decayed mass reallocation ratio.
359
360
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358
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352
The fraction Y of the carbon substrate taken up (not lost by respiration) is converted
to new biomass. It is equivalent to the microbial carbon-use efficiency (CUE) when DOC is the only source of carbon (AC synthesis via EPS reuse is not taking place; see
362
details below). The allocation coefficients λ∗EP S and λ∗EZ indicate the effective fraction of
363
carbon diverted to produce EPS and EZ, respectively (based on the formation coefficients
364
described in Laspidou and Rittmann, 2004). Different from previous approaches, the
365
synthesis of EPS and EZ is modulated to improve the well-being of microorganisms
AC 361
366
according to environmental and biological variables. An effective use of carbon permits 19
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367
investing additional amounts of resources to AC when EPS or EZ requirements are low.
368
Such adaptive modulations may be described by λ∗EP S = λEP S ξφ,θb ,
λ∗EZ = λEZ [1 − ξEZ ],
CR IP T
(13)
(14)
where λEP S [−] and λEZ [−] are the maximum coefficients of carbon allocation, and
370
ξEZ governs the release of EZ (again, obtained using (5)). ξψ,θb [−] is a quorum sensing
371
factor that regulates the production of EPS according to their concentration and water
372
requirements as
ξφ,θb
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369
"
θb = 1− φef
#βθb
.
(15)
ξψ,θb tends to 1 (no inhibition) when the volume of water in the biofilm phase is much
374
smaller than φef , and therefore the resulting effective ratio of allocation is approximately
375
λEP S . ξψ,θb decreases with increasing θb , as a function of the shape factor βθb .
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373
376
Biofilm dynamics are readjusted when DOC is scarce (ξDOC < 1). On one hand, mi-
378
croorganisms are able to decompose EPS, using them as a carbon source to produce AC
379
exclusively (in agreement with de Silva and Rittmann, 2000). The process is governed
380
by ξEZ , since EZ catalyze the reaction (Flemming and Wingender, 2010), and ξEP S .
381
The latter term hampers the decomposition rates of EPS when their concentration is
382
low compared to the value of EP SK (recall (5)). When EPS reuse occurs, the CUE
383
decreases because a lower percentage of carbon is assimilated (Y is first applied in (10)
384
to produce EPS and then in (9) to synthetize AC). On the other hand, some microorgan-
385
isms switch in and out from the dormancy state (in (11) and (12)) according to nutrient
386
availability. Such a physiological response occurs at a rate that is a function of τi , τa ,
387
and ξDOC ; always fulfilling the restrictions imposed by population density defined by (8).
AC
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377
388
389
Biomass losses are controlled by decay, including ageing effects (natural decay), de-
390
mands for maintenance and functioning (endogenous decay), and reallocation of carbon 20
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(induced decay). Decay rates are defined as proportional to the amount of biomass and
392
AC DC EP S EZ the decay coefficients KD , KD , KD and KD , in which the superscripts indicate
393
the corresponding compartment. DC and EPS are the compartments least affected by
394
AC DC AC EP S decay (KD /KD >> 1, KD /KD >> 1), conferring large durability regardless of
395
environmental conditions. The fraction λD of decayed cells is assumed biodegradable
396
and remains in the system becoming part of the EPS (as in Laspidou and Rittmann,
397
2002b, 2004) and not as POM (as in Riley et al., 2014). Such a simple mechanism allows
398
producing EPS as a form of carbon reallocation (e.g., in Kakumanu et al., 2013). Later
399
on, these EPS can be used as a carbon source. As a consequence, the total consumption
400
rate is defined by Y times the sum of DOC used and EPS decomposed.
401
2.2. Numerical Simulations Set-Up
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391
The coupled system of equations presented in (1-15) was solved numerically using
403
an implicit Crank-Nicolson scheme. Concentrations of the studied compartments were
404
updated every time step. Such steps were dynamically chosen according to convergence
405
criteria and to avoid numerical instabilities. The resulting time steps were in the order
406
of seconds-minutes. Each simulation was performed until quasi-steady-state conditions
407
were achieved; i.e., when no relative changes in the biomass of all compartments were
408
observed (for constant environmental conditions), or temporal patterns reached a stable
409
cycle (for cyclic environmental conditions). A minimum time of simulation was set to
410
365d, which was assumed the behavior in the long-term.
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402
411
All simulations were performed in a porous medium of 1cm3 volume, albeit the results
413
can be extrapolated to larger scales by combining multiple volumes. Different sets of sim-
414
ulations were carried out to conduct a sensitivity analysis in which either one parameter
415
or combinations of two parameters were allowed to vary. Most of these parameters were
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412
set based on the literature, while others (when no information was available) were con-
417
strained to a reasonable range or value (Table 2). Sensitivity analyses were not meant to
418
quantify the uncertainty propagation. Due to the high sensitivity and little knowledge
419
of the value of the parameters under each scenario, simulations were employed then as
420
an explorative rather than predictive tool to disentangle qualitative patterns and the
AC 416
421
driving forces governing microbial dynamics under different situations of stress. 21
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Table 2: Simulation parameters for microbial dynamics, specific values from the literature, and sources.
Parameter
Units
Significant
Comments
Value
References
a
cm
105.76, 1
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values
To check the impact of different types of EPS. From Rosenzweig et al. (2012) for pure xan-
than (105.76), and small value simulating EPS of lower retention capacity (1) gcm−3
5.5x10−5
−
0.489
(t = 0) b
From Brangar´ı et al. (2017)
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AC
From Rosenzweig et al. (2012) for pure xanthan
c DC
From Chenu (1993) for pure xanthan
−
70
gcm−3
0, 1x10−3
(t = 0)
conditions
gcm−3
PT gcm−3
AC
CE
DOCeq
2x10−5
ED
(t = 0)
M
DOC
Two different scenarios assumed at the initial
Relation 10xDOCK to ensure appropriate initial carbon conditions.
DOC = DOCb =
DOCpm assumed Kinzelbach et al. (1991),
2x10−3
Assumed large (1000xDOCK ) to avoid growth limitations at equilibrium
1.43x10−5 ,
Greskowiak
5.1x10−4 ,
et al. (2005),
1x10−3 xP OM Bengtson and Bengtsson (2007)
— Continues on the next page —
22
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— Continued — Parameter
Units
Significant
Comments
Value
References values
DOCK
gcm−3
2x10−6
CR IP T
[Soleimani
Experimental variable used in Ezeuko et al.
1x10−4 ]
(2011)
EP S
0
gcm−3
5.5x10−3
gcm−3
6x10−6
(t = 0) gcm−3
6x10−6
min−1
6.6x10−5
PT min−1
CE
DC KD
AC
EP S KD
EZ KD
and Van Geel (2007)]
Mean from Manzoni et al. (2014) (2x10−6 to
1x10−5 )
ED
AC KD
(2009)-Mostafa
Assumed from the relation θef /c in 1
min−1
Assumed equal to EZ(t = 0)
M
EZK
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EZ
et al.
Assumed 0 at the initial conditions
gcm−3
(t = 0) EP SK
[7.99x10−7 -
6.6x10−6
Relation µC /100 in Ezeuko et al. (2011), despite also incorporated EPS decay
[8.33x10−6 2.78x10−4 ]
(2014)Laspidou and Rittmann (2004)] [Manzoni et al.
AC /10 inspired by Manzoni et al. Relation KD
(2014)
AC /10[KD
(2014)-
AC /4.2] KD
Konopka (1999)] Laspidou and
0, 6.6x10−6
Decay of EPS was neglected or assumed equal to
min−1
[Manzoni et al.
6.6x10−5
DC KD
for simplicity
AC Assumed equal to KD
— Continues on the next page —
23
1.18x10−4
Rittmann (2002b)
[6.94x10−6 -
Manzoni et al.
3.47x10−5 ]
(2014)
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— Continued — Parameter
Units
Significant
Comments
Value
References values
P OM
−
1.23
Value for sand, loam and sandy-clay (from Carsel and Parrish (1988))
gcm−3
1.5x10−2
Assumed equal to the 1% of soil's mass
gcm−3
1.5x10−5
Assumed small (P OM /1000) to avoid POM
(t = 0) P OMK
limitations min
5 days was assumed reasonable according to
7200
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tc
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2.68, 1.56, n
our personal experience
vw
Y
cmmin−1
Assumed
0
−
Experimental variable used in Ezeuko et al.
0.34
α
M
(2011)
0.145, 0.036,
cm−1
−
βθ b
− −
CE
γ
PT
βP
AC
Γ
θr
θs
ED
0.027
gcm−3 min−1 −
Carsel and Parrish (1988))
1
Assumed 1 to reduce the non-linearity
1
Assumed 1 to reduce the non-linearity Standard value for sands, and calibrated from
2, 2.9
loamy-clayey soil data. Both from Hamamoto et al. (2010) DOCb and DOCpm always under equilibrium
∞ 0.045, 0.078, 0.1
0.38
Value for sand, loam and sandy-clay (from Carsel and Parrish (1988))
0.43, 0.43, −
Value for sand, loam and sandy-clay (from
Value for sand, loam and sandy-clay (from Carsel and Parrish (1988))
— Continues on the next page —
24
[Mostafa and Van Geel [0.05-0.61] (2012)-Dupin et al. (2001)]
ACCEPTED MANUSCRIPT
— Continued — Parameter
Units
Value
Significant
Comments
References values Laspidou and
−
Assumed 0 to isolate the effects of the deliber-
0
ated release of EPS λEP S
−
0.23, [0 -0.4 ]
0.2
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λd
Rittmann (2002b)
Sum of formation coefficients for EPS and
utilization-associated products in Laspidou and Rittmann (2004) −
0.01
N
−
1, 5
Assumed to fulfill that λEZ << λEP S
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λEZ
Assumed 1 or 5 to simulate a biofilm with simple or more complex morphology at the-pore
1.6, 6.3,
Brangar´ı et al.
[1 -100 ]
(2017)
scale
µC
min−1
6.6x10−3
Experimental variable used in Ezeuko et al.
µEP S
M
(2011) for biomass
min−1
0, 1x10−3
To evaluate the effects of EPS as a source of C or not
min−1
1
Assumed
ρc
gcm−3
1
Assumed equal to ρw according with Phillips
PT
ρw
ED
µP OM
gcm−3
1
et al. (2013) Known
0, 9.23x10−5 ,
min−1
CE AC
τa
τi
Ω
min−1
−
[7x10−8 -
To check the effects of dormancy.
7x10−3 ]
τi /1.43 in Konopka (1999) (9.23x10−5 )
6.94x10−4
Manzoni et al. (2014)
0, 1.32x10−4 , [1x10−7 -
To check the effects of dormancy.
1x10−2 ]
DC in Konopka (1999) (1.32x10−4 ) 20xKD
1.5
Relation
Value for all soil types. From Hamamoto et al. (2010)
422
Relation
Numbers in italic mark those values not derived from experimental data.
25
6.94x10−4
Manzoni et al. (2014)
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Simulations were conducted in synthetic scenarios in order to explore the carbon dy-
424
namics in shallow soils. Supplies feeding the system were adapted to simulation needs,
425
differentiating between two main scenarios. The first scenario assumed that the microbial
426
community was fed by the decomposition of POM accumulated in the upper soil profile,
427
i.e., DOC was not directly supplied. To focus on the effects of DOC limitation, P OM was
428
assumed at steady-state and set to a constant value, much larger than P OMK , so that
429
ξP OM ≈ 1. The second scenario considered artificial sudden changes in the availability of
430
DOC. Therefore, the mass balance for POM (in (3)) becomes redundant for the scenar-
431
ios studied. Additionally, the mass transfer rate between the two DOC compartments
432
is assumed large enough to maintain equilibrium, and therefore DOCb and DOCpm are
433
equal to the concentration DOC in the now undistinguished dissolved carbon pool. The
434
inflow/outflow diffusion fluxes were considered balanced and could be neglected. Addi-
435
tional details are provided later in each case-study section.
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423
436
To explore the wide range of saturations found in natural environments, simulations
438
were performed on soils under synthetic extreme scenarios consisting in: full saturation,
439
moderately dry conditions, or intermittent rainfall events. Such conditions were speci-
440
fied by the soil suction status, which determine the availability of water. The saturated
441
scheme assumed that ψ = 0 and therefore the volumetric water content was maximum
442
and equal to θs . The dry scenario assumed conditions of water limitation (with no addi-
443
tional water supplied during simulations), where the initial θb + θpm was determined by
444
(1) and (2) at a constant ψ of 50cm of water. When biofilm proliferated, the equilibrium
445
was lost and φM was set to the value of θb + θpm at t = 0, regardless of microbial dy-
446
namics. Finally, the scenarios of intermittent rainfall events started from a dry scenario
447
that included periodic sudden raises of the water content (ψ = 0, representing the rain-
448
fall event) with a return period ∆tR . Water inputs were assumed to contain no DOC
AC
CE
PT
ED
M
437
449
and EZ to represent the conditions of rainwater, and thus causing a potential dilution of
450
these dissolved components in the control volume. After the rain event, soils underwent
451
a transient period of pressure redistribution, gradually readapting their saturation to
452
the natural suction state (ψ0 = 50cm). Water drainage flushed out a fraction of the
453
dissolved components, preserving their concentrations. The effect of matric suction was 26
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454
not studied as an independent stress, but only as a driver of the water content (using (1)
455
and (2)). The changes in suction were modeled as
ψ(t) = ψ0 − ψ0 exp
tR − t , tc
(16)
where tR [T ] is the time of the last rainfall event and tc [T ] is the characteristic time
457
of the effects of the rain on ψ. The time of the first episode was set to ∆tR /2. The
458
impact of evapotranspiration rates on saturation was neglected.
459
3. Results and Discussion
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456
We start by evaluating the effect of soil texture and biofilm characteristics, i.e., re-
461
tention properties and pore-scale morphology. We then continue by examining the de-
462
ployment of survival mechanisms responding to stresses characterized by the synthesis of
463
EPS, their reuse as a source of C, the inactivation/reactivation of cells, and the combined
464
effect of dormancy and EPS production.
465
3.1. The Effect of Soil Type and Biofilm Properties
M
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460
The soil pore-size distribution strongly determines the availability of elements essen-
467
tial for the proliferation of biofilms. First, the water saturation, which is a key factor in
468
microbial habitats, is itself a function of the size, the shape and the interconnection of
469
pores (Alaoui et al., 2011). This relationship determines the SWRC (see Supplementary
470
material Figure ??), which typically depicts lower saturations at a given matric suction
471
in coarse grain soils because large pores can be easily drained. Second, DOC availability
472
not only depends on water saturation but also on its diffusivity in the soil. Substrate
473
supply turns into a prominent limiting factor when water content is low since diffusive
474
and conductive transport become small (Manzoni et al., 2016). Although the larger wa-
CE
PT
ED
466
ter holding capacity of fine-textured soils, the increased tortuosity of the diffusion paths
476
in their thin pores (lower ξτ ) reduces the capacity of solutes to reach the microbial cells.
477
According to (4), such diffusion limitation is determined by the parameters Ω, γ, and θs ,
478
which are soil-type dependent. It is worth noting here that the model does not account
479
for reduced microbial growth caused by oxygen limitation that may occur in highly sat-
AC 475
480
urated environments (see Skopp et al., 1990), and for increased carbon losses that may 27
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481
occur in soils of low tortuosity (with potentially higher advection-diffusion fluxes).
482
These hydraulic properties are not static, but depend on the presence of biomass,
484
which leads to direct (θb ) and indirect (θpm ) increases in the overall retention of water
485
for a given suction. In Figure ??, the retention properties of biofilms are illustrated by
486
comparing the effect determined by an EPS of a very low water retention capacity (a
487
assumed equal to 1cm), with that of pure xanthan (with better retention properties,
488
a = 105.76cm). The first scenario requires many times the mass of xanthan to obtain
489
an analogous change in the SWRC. Therefore, as b and c are here assumed independent
490
of the type of EPS, the overall change in saturation is governed by the product axEP S
491
(recall (1)). Additionally, the more intricate is the architecture of the biofilm at the
492
pore-scale (denoted by N ), the stronger the transformation of the pore-matrix and the
493
higher is the total saturation increase. According to the previous statements, an increase
494
of water saturation implies a potential increase in the rates of carbon consumption by
495
microbial cells. The influence of EPS on microbial dynamics is discussed in more detail
496
in Section 3.2, but a simple analysis of the results shown in Figure ?? already suggests
497
that the greater the impact of biofilm on the SWRC is, the more benefits are potentially
498
achieved by the embedded microorganisms (supporting the speculation of Brangar´ı et al.
499
(2017) and Lawrence et al. (1991)).
ED
M
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483
500
3.2. The Effect of EPS on Microbial Dynamics
502
3.2.1. Water Availability and Hydric Stress In this section, we analyze the impact of EPS accumulation under variable soil mois-
CE
503
PT
501
504
ture on the proliferation of biofilms. To better identify the effects of hydric stress and
505
the role of EPS, we simulate the effect of having or not having colonies embedded in a polymeric matrix (0.015 or 0 g of EPS cm−3 ), indicated by dotted and solid curves
507
in Figure 2, respectively. The retention capacity of EPS was taken from that of pure
508
xanthan to emphasize its impact on soils. The production of additional EPS, their de-
509
cay, and the switch into dormancy were all deactivated in these simulations by setting
510
EP S λEP S = 0, KD = 0, λd = 0, and τi = 0. In this way, the EPS pool was treated as a
AC 506
511
static compartment, allowing us to isolate its effects. Results show the proliferation of 28
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512
biofilms in a soil under moderately dry and fully saturated conditions (in the top panel),
513
and under instantaneous rainfall events that are followed by drainage periods of 5 and
514
10 days of duration (bottom panel).
515
In moist conditions (absence of major stresses and of dilution effects), microorganisms
517
grew fast, efficiently, and reached large active biomass values (blue curves in Figure 2,
518
top). Large POM decomposition rates permitted high respiration rates and activity (re-
519
call that O2 is not considered a limiting factor). As shown by the overlapping solid and
520
dashed blue curves in Figure 2 (top), the presence of EPS did not have an apparent role
521
under such circumstances. In contrast, in rather dry soils, the growth of microorganisms
522
was limited by the availability of DOC (due to low ξτ ), which hampered the synthesis of
523
new biomass (green curves). The presence of EPS in such dry scenarios (dotted curves)
524
increased water saturation, contributing to the improvement of microbial fitness com-
525
pared to cases without EPS (solid curves).
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516
526
According to Dutta et al. (2015) and Fierer and Schimel (2002), the periodicity and
528
intensity of the stress episodes control the proliferation of microbial colonies. Along this
529
line, results in Figure 2 (bottom) show a significant increase in the respiration rates
530
during each rainfall event (known as Birch effect; Birch, 1958). The enhancement of the
531
decomposition rates by the sudden increase in the saturation was counterbalanced by the
532
dilution of EZ and DOC. In fact, soils transiently readapted their water content to ψ0 ,
533
triggering losses of dissolved components and EZ by leaching. Those colonies embedded in
534
EPS attained the largest cell populations because EPS mitigated both water and carbon
535
stresses by: (i) emulating the conditions of colonies growing at a smaller hydric stress that
536
remain saturated for a wider range of suctions (Or et al., 2007a); (ii) acting as a reservoir
537
that retains DOC and EZ, which mitigates the effects of dilution and drainage (Or et al.,
AC
CE
PT
ED
M
527
538
2007b); and (iii) increasing DOC supply during dry periods (Chenu and Roberson, 1996).
539
Moreover, these positive effects are more pronounced under scenarios with higher rainfall
540
frequency (red dotted curves in Figure 2, bottom). These points may indicate feasible
541
mechanisms by which EPS allowed microorganisms to benefit from rainfall events that
542
otherwise would inhibit biofilm proliferation. This result provides also possible insights 29
ACCEPTED MANUSCRIPT
on the drivers of respiration pulses at rewetting (Birch, 1958; Lado-Monserrat et al., 2014;
544
Meisner et al., 2013). For a pulse to occur, DOC and EZ must be retained in the system,
545
which is more feasible with a well-developed EPS matrix. This link between respiration
546
pulses and EPS had not been previously explored, and emerges in the dynamics only
547
when the complexity of microbial-soil pore space is described.
CE
PT
ED
M
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CR IP T
543
Figure 2: Impact of water availability on microbial dynamics. Simulations were performed for a soil under A) moderately dry conditions (green), fully saturated (blue), and B) under instantaneous rainfall events followed by drainage periods ∆tR of 5 days (red) and 10 days (black). The colony of microorganisms
AC
was assumed to be either embedded (EP S = 0.015g cm−3 , dotted lines) or not (EP S = 0, solid lines)
in a polymeric matrix. Multiple plots show the dynamics of the total water content θb + θpm , the active cell population AC, the respiration rate (indicated by Resp.), the dissolved organic carbon concentration DOC, the enzyme density EZ, and the cumulative amount of carbon consumed (C cons.).
30
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548
3.2.2. Production of EPS The simulations are now extended by introducing the dynamics of EPS. The hypoth-
550
esis being tested here was that the production of EPS should provide an advantage to the
551
organisms embedded, even though some resources are diverted from cell growth. This
552
effect was studied by increasing the potential allocation of carbon to the production of
553
EPS (λEP S = 0, λEP S = 0.23, λEP S = 0.4, as indicated by different colors in Figure
554
3). Unlike previous simulations, EPS production (determined by environmental stresses,
555
recall (13)) and decay (stress independent) were activated so that EPS dynamically in-
556
teracted with other compartments. The columns of Figures 3 and 4 illustrate these
557
dynamics under different soil moisture regimes (two different rainfall frequencies and full
558
saturation).
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549
559
Under saturated conditions (Figure 3, right), since the production of large amounts
561
of EPS was unfruitful, the resources diverted to EPS were downregulated. λ∗EP S tended
562
to zero and EP S reached a pseudo-steady state. This phenomenon might explain why
563
soils under small water stress tend to exhibit low EPS to biomass ratios (e.g., in Rubol
564
et al., 2014; Vandevivere and Baveye, 1992b). As a consequence of regulation, the dy-
565
namics obtained were not sensitive to λEP S . When such a mechanism was disabled (by
566
assuming ξψ,θb = 1, not shown), EPS were continuously synthetized at the expenses of
567
population growth.
PT
568
ED
M
560
Dynamics under variable soil moisture are illustrated in Figure 3 by showing the
570
results under periodic rainfall events with a return period of 100 (left column) and 10
571
days (center column). Under such conditions, the large allocation of carbon to EPS re-
572
sulted in significant improvements in microbial fitness (i.e., biomass). Yet, results show
573
that microorganisms required moderately long periods to adapt the biofilm (and the soil
AC
CE
569
574
habitat) to their needs. With time, each microbial system tended to reach high active
575
biomass values as long as the production of EPS was larger than their decay. Note the re-
576
lation between microbial bloom and EP S in the black and red curves in the top panel of
577
Figure 3. The more frequent were the rain events, the faster the steady-state conditions
578
were achieved, thanks to the higher mean soil moisture. Figure 4 shows the averaged 31
PT
ED
M
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CE
Figure 3: Simulation of biofilm proliferation under permanent wet conditions (plots in the right column), and environments affected by rainfall events with a return period of 100 (left column) and 10 days (center column). From top to bottom: active microbial biomass (AC), amount of EPS (EP S), effective
AC
coefficient of carbon allocation to synthetize new EPS (λ∗EP S ), total water content (θb + θpm ), and respiration rate (Resp.). The maximum coefficient of carbon allocation diverted towards EPS λEP S values are 0 (blue), 0.23 (red), and 0.4 (black).
579
biomass after 1 year of simulation. Results suggest that for EPS to be effective at the
580
annual scale, larger investments (λEP S ) are required under progressively more stressful
581
conditions. 32
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582
In all cases, EPS concentrations increased during biofilm establishment (first month
584
in Figure 3, but not appreciable in the current y-axis scale), as noted by Roman´ı et al.
585
(2004). For the studied set of parameters, the presence of a small amount of EPS did not
586
compensate for the resources currently diverted to their production and AC remained
587
low compared to the non-producer strain. However, when EP S reached higher values,
588
compensatory mechanisms started to work, leading to higher respiration and the syn-
589
thesis of new biomass (on average, but particularly during activity peaks, Figure 3).
590
In those scenarios with stronger water stress, larger amounts of EPS were accumulated
591
(in agreement with Chang and Halverson, 2003; Roberson and Firestone, 1992; Sandhya
592
and Ali, 2015). When dry periods are sufficiently intense (not enough water available
593
to maintain equilibrium in (1)), such a large accumulation of EPS did not improve the
594
hydration status and nutrient uptake, and therefore EPS investments were unfavorable
595
(results not shown). However, highly bio-amended soils under periodic rainfall events re-
596
mained almost fully saturated even at high matric suctions by counteracting the adverse
597
diluting effects and facilitating conditions recovery after rewetting (e.g., Dutta et al.,
598
2015). This fitness improvement resulted from the dynamic synthesis of EPS in response
599
to the intensity of the water stress. Production of EPS remained low during dry spells
600
(λ∗EP S < λEP S ), but decreased or even stopped (λ∗EP S → 0) during rainfall events. Ef-
601
fective downregulation of EPS synthesis occurred when EPS could not provide further
602
benefits in saturation (denoted by ξφ,θb ), allowing organisms to divert resources to AC.
603
If the downregulation mechanism had been disabled, the synthesis of unnecessary matrix
604
would have negatively affected microbial fitness. In that case, Figure 4 would have shown
605
a bell-shape relation between AC and λEP S .
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M
ED
PT
As an alternative to the time series representation shown in Figure 3, the relations
AC
607
CE
606
CR IP T
583
608
between microbial metabolism and environmental conditions can be represented in the
609
phase space, by showing respiration rate as a function of soil moisture (Supplementary
610
material Figure ??). The model simulations showed that respiration rates decreased
611
during soil drying, following a pattern that has often been observed (see Manzoni et al.,
612
2012, for a review). Upon rewetting, respiration rate increased with a short delay, partly 33
CR IP T
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Figure 4: Partitioning of the biofilm compartments in long-term simulations (dry-wet cycle-averaged
values after 1 year of simulation) assuming values of the maximum coefficient of carbon allocation diverted towards EPS (λEP S ) ranging from 0 to 0.4, and the maximum rate of cell inactivation τi = 0
(dormancy was not allowed). Simulations were performed under periodic rainfall events with ∆tR = 100
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days (left), 10 days (center), and permanently wet conditions (right).
due to DOC dilution effects, causing counterclockwise hysteretic loops (as reported else-
614
where, see Zhang et al., 2015). Therefore, the maximum respiration rate was achieved
615
only when soil moisture had already started to decrease.
616
3.2.3. Reuse of EPS
M
613
The potential benefits of storing carbon in EPS for late use were tested by compar-
618
ing EPS-producer microorganisms (λEP S = 0.23) with different capacity to reuse the
619
carbon previously invested in EPS, assuming µEP S equal to 1x10−3 min−1 (reuse) or 0
620
(no reuse). Two different EPS water retention capacities were also studied comparing
621
a = 105.76 and a = 1cm. Simulations obtained for these four combinations of λEP S and
622
a are shown in Figure 5, for a soil affected by periodic rainfall events with ∆tR = 10 days.
PT
ED
617
624
625
CE
623
For the studied set of parameters, it was found that when µEP S << 1x10−3 g cm−3 ,
the EPS production clearly dominated over the reuse rates, resulting in EPS accumulation for any water retention capacity (solid blue and dashed green curves in Figure 5). In
627
contrast, for larger reuse rates, EPS tended to be depleted by consumption, eventually
628
reaching a periodic asymptotic value. The benefits of such an EPS accumulation to the
629
microbial community emerged from the competition between antagonistic properties of
630
EPS: water retention versus carbon storage capacity. On one hand, as already shown be-
AC 626
631
fore, large EPS concentrations entailed a mitigation of the adverse effects of rain events. 34
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Figure 5: Dynamics of a microbial colony growing in a soil affected by rainfall events with ∆tR =
10 days, assuming contrasting EPS properties that alter their reuse as a source of carbon: different decomposition rate capabilities (denoted by the maximum specific decomposition rate µEP S = 0 and µEP S = 1x10−3 min−1 ) and EPS water retention capacity (a = 105.76 and 1cm). Plots starting from top left show the dynamics of the active cell population AC, the total water content θb + θpm , the EPS concentration EP S, the carbon-use efficiency (CUE = AC growth over equivalent DOC consumed), the
M
EPS reuse ratio, and the effective coefficient of carbon allocation λ∗EP S .
On the other hand, the carbon stored in EPS was used as a temporary source of carbon.
633
When these EPS were consumed, the carbon feeding the colony increased, but at the
634
same time, EP S and therefore their capacity to mitigate stresses decreased. The sign
635
of the impact depended then on the combination of parameters: the own compositional
636
characteristics of the EPS (denoted by a), their capacity to be reused (µEP S ), and again
637
on the environmental circumstances (mainly water inputs).
PT
ED
632
638
Results in Figure 5 show that only with low EPS retention capacities, the reuse
CE
639
of EPS slightly increased the active biomass (compare dashed green and dotted black
641
curves), because the carbon surplus in EPS helped compensating the dilution and the
AC
640
642
carbon lost after rainfall. However, when the modeled EPS had a large capacity to retain
643
water, the largest AC was obtained when reuse was disabled. The EPS with the lowest
644
retention properties allowed larger potential of carbon accumulation in EPS, because the
645
production rates (characterized by λ∗EP S , recall (15) and (1)) remained high, even though
646
relatively large EP S was reached. Even though the EPS reuse could improve microbial 35
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647
fitness under specific conditions, it was a rather inefficient mechanism in terms of carbon
648
use. The synthesis of biomass by the reuse of EPS required a double respiration cost: for
649
synthesizing EPS first (CUE = Y ) and for using them to produce new biomass (dotted
650
lines show efficiencies of DOC conversion to biomass lower than Y ).
CR IP T
651
These results suggest that fitness can be improved by synthesizing EPS of specific
653
composition. We thus speculate that biofilm characteristics could be adapted to envi-
654
ronmental conditions to which they are more frequently exposed. For instance, the mi-
655
croorganisms benefitting from EPS reuse may promote large µEP S values by synthetizing
656
enzymes that are efficient at taking carbon from EPS. In a similar way, microbes could
657
adapt the composition of the released compounds to facilitate their later reuse. Lastly,
658
the combination of reuse and reallocation of decay products, which may be induced by
659
AC cells through the values of KD and λd , results in a cycle of full carbon reallocation.
660
This process would allow producing any microbial compartment (prioritizing those that
661
are most useful under the actual circumstances), with lower dependence on the external
662
availability of carbon sources.
663
3.3. The Effect of Dormancy on Microbial Dynamics
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652
The capacity to switch in and out of the dormancy state was evaluated by comparing
665
the dynamics non-EPS producer microorganisms unable to become dormant (τi = 0,
666
dashed curves in Figure 6) with those that can turn dormant and are characterized by
667
different switching rates between the two states (τi = 1.32x10−4 and 1.32x10−3 min−1 ,
668
depicted by dotted and solid curves, respectively). The reactivation rate τa was set
669
equal to 1.43/τi (based on Konopka, 1999). The switch to a dormant stage was trig-
670
gered by artificially changing the DOC in a fully saturated soil from 1x10−6 to 0g cm−3 ,
671
which modulated the effective transition rates via the coefficient ξDOC . This approach,
AC
CE
PT
ED
664
672
based on resource availability, is conceptually (but not mathematically) similar to previ-
673
ous models of activity (Stolpovsky et al., 2011) or physiological state (Blagodatsky and
674
Richter, 1998). Other models assume that dormancy is instead triggered by a change in
675
soil water content (B¨ar et al., 2002) or by water potential (Manzoni et al., 2014). The
676
latter approach assumes that transition to dormancy is not caused by carbon starvation 36
ACCEPTED MANUSCRIPT
per se, but rather by accumulation of osmolytes or loss of turgor pressure. These alter-
678
native approaches (dormancy driven by carbon starvation vs. hydric stress) give similar
679
results in dry soils, where carbon availability is reduced by transport limitations. How-
680
ever, predictions diverge in wet scenarios, where carbon may be limited by dilution and
681
inactivation is predicted only in models in which dormancy is triggered by low carbon
682
availability.
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677
683
At the early stage of biofilm colonization, with moderately high carbon availability
685
(ξDOC = 0.33) and no competition for space (ξψ,P ' 1), large growth rates were ob-
686
tained (all curves in Figure 6). Those microorganisms with lower inactivation capacity
687
(τi → 0) grew faster (dashed lines). When τi > 0, since ξDOC 6= 1, some of the newly
688
synthetized cells switched to a dormant state (dotted red and solid black curves). This
689
phenomenon led to a delay in the initial growth of the AC pool and in the total amount
690
of cells (AC + DC). As a consequence, the inactivation process seemed apparently coun-
691
terproductive. After this initial transient stage, the total biomass reached similar values
692
during periods of abundant carbon regardless of their dormancy capacity, even though
693
the colonies with larger τi depicted slightly smaller active populations. When the cell
694
number reached their maximum (characterized by low ξψ,P , in (7)), microbial activity
695
decreased and therefore the amount of carbon consumed increased more slowly. For this
696
set of conditions, the maximum consumption rate was observed at AC ≈ 0.2g cm−3 .
697
Above this point, the cellular metabolism was acclimated to meet maintenance require-
698
ments rather than growth.
PT
ED
M
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684
699
When DOC conditions deteriorated at ∆t days (DOC and therefore ξDOC decreased
CE
700
to 0), the beneficial effect of dormancy became apparent. Those organisms that switched
702
more rapidly to a dormant state experienced lower losses and maintained significantly
AC
701
703
larger total cell densities, despite a faster AC decrease is observed (compare the dy-
704
namics of dashed blue and solid blacks lines in Figure 6). Lower mortality rates in DC
705
moderated the total population decline, conferring larger survival chances.
706
707
When conditions of high DOC availability were restored again (at 2∆t, 4∆t), or37
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ganisms rapidly proliferated. In line with the discussion provided in Blagodatskaya and
709
Kuzyakov (2013), respiration increased exponentially after substrate input, reaching its
710
maximum in less than a day and then decreased sharply when the maximum amount of
711
cells was reached or when substrate was removed. Upon DOC removal, the AC pool was
712
fed by the reactivation of DC (if available), reducing the synthesis of new cells (and the
713
carbon consumed). As a consequence, dormancy can be considered an efficient strategy
714
to recycle energy and carbon, allowing lower carbon consumption to achieve the same
715
biomass (bottom panel in Figure 6).
716
3.4. The Combined Effect of Dormancy and EPS on Microbial Dynamics
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708
The combined effect of EPS and rate of transition to the dormant state was studied
718
by analyzing the long term concentration of biofilms with different allocation coefficients
719
λEP S = 0 and λEP S = 0.23. Three different scenarios are shown in Figure 7: wet-dry
720
events with ∆tR = 100 and ∆tR = 10 days, and permanent saturation.
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717
721
Results showed that those organisms with larger rates of transition to and from dor-
723
mancy achieved larger populations in all scenarios after 1 year of simulation, regardless
724
of the capacity to produce EPS (top and bottom panels of Figure 7). This indicated that
725
such a mechanism may improve survival chances under a wide range of environmental
726
conditions. Even though the amount of AC in permanently wet scenarios was only slightly
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altered by the inactivation capacity of cells, the total amount of cells experienced a 26%
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increase (all DC). Nevertheless, under alternating wet-dry conditions, those biofilms with
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τi ≥ 1x10−5 min−1 increased their total population by 10 to 100 times compared with the
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non-dormant ones. Moreover, these colonies had up to a 70-95% of inactive cells (hardly
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observable in the top plots). The more intense was the water stress, the greater was
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the benefit resulting from inactivation, being the percentage of DC strongly determined
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by the environmental constraints. The ratios between active and inactive populations
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obtained are hardly comparable with the wide range of values reported in the literature
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(e.g., in the review by Blagodatskaya and Kuzyakov, 2013). A sensitivity analysis (not
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shown) indicated that other parameter choices could align simulations with alternative
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empirical evidence.
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Figure 6: Temporal evolution of biofilm growing in a fully saturated soil that experiences sudden changes in the concentration of DOC every 35 (left) and 7 days (right). The capacity of switching in and out of a dormant state was evaluated by studying microorganisms unable to become dormant (maximum rate of
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cell inactivation τi = 0) and others with different switching rates between the two states (τi = 1.32x10−4 and 1.32x10−3 min−1 ). τa was set equal to 1.43xτi . From top to bottom: environmental coefficient representing DOC availability (ξDOC ), total amount of cells (AC + DC), active cells (AC), quorum
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sensing coefficient based on the cell population (ξψ,P ), and cumulative amount of carbon consumed per cm3 of soil (C cons.).
Moreover, the combined effect of dormancy and EPS production under periodic rain-
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fall events helped mitigating the carbon and water stress (low saturation and dilution).
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The additional accumulation of EPS improved microbial fitness, while preserving the
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positive impact of inactivation, producing a population rise between 2− to 100-fold. For
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the studied set of conditions, the stress remission was so efficient that the cell population
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reached values comparable to those achieved without stress (see Figure 7, bottom center). 39
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Figure 7: Mass of the biofilm compartments as a function of the maximum rate of cell inactivation (τi ). Long-term simulations (of 1 year) considered values of τi ranging from 1x10−7 to 1x10−2 min−1 . The role of EPS was evaluated by comparing the results obtained by the environmental coefficient λEP S = 0 (top row) and λEP S = 0.23 (bottom row). Simulations shown were performed under periodic rainfall
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events with ∆tR = 100 days (left), 10 days (center), and wet conditions (right).
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Figure 8 depicts contour plots of the long-term concentrations of the AC, AC+DC and
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EPS compartments as a function of λEP S and τi . This figure summarizes how combining
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the release of EPS (λEP S ) and the capacity of organisms to be induced into dormancy
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(τi ) had significant effects on the carbon partition in the biofilm. The growth of biofilms
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under fully-saturated conditions was not much affected by λEP S and τi because of the
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downregulation effect and the suitability of the environmental conditions (bottom panel).
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The inactivation of cells generated colonies with slightly larger amounts of cells, while the
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population of active microbes remained almost stable. In contrast, biofilm proliferation
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was limited in environments alternating wet and dry conditions (top panel), particularly
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common in shallow natural soils, due to the nature and intensity of stressors. Under such
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circumstances, results confirmed that the combination of the two mechanisms could effi-
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ciently counteract the effects of stress, producing a clear improvement of biofilm fitness
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and microbial survival (as evident from higher AC + DC with increasing λEP S and τi in
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the top central plot). 40
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Figure 8: Contour plot depicting the averaged concentrations of biofilm compartments after a longterm simulation of 1 year. (left: active cells (AC), center: total cells (AC + DC), right: EPS (EP S). The maximum coefficient of carbon allocation towards EPS (λEP S ) was varied from 0 to 0.4 and the
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maximum rate of cell inactivation (τi ) from 1x10−7 to 1x10−2 min−1 , and under periodic rainfall events
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with ∆tR = 10 days (top), and wet conditions (bottom).
Based on these results, the significant differences in biofilm composition reported in
the literature (e.g., Chenu, 1995; Blagodatskaya and Kuzyakov, 2013) could be attributed
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to the adaptation of microbes to the heterogeneous conditions in their habitats, in terms
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of substrate availability, mean saturation and temporal distribution of wetting events.
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3.5. Model Limitations and Future Developments
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The validation of the model cannot be accomplished easily due to the lack of experi-
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mental data and of suitable and non-disruptive techniques to sample the pools considered, 41
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and because of the difficulties in empirically confirming the specific contribution of some
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of the different parameters included.
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Moreover, despite the considerable complexity of the model presented, some processes
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occurring within the biofilm-soil system are not thoroughly addressed. On one hand, the
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dynamics of nutrients such as nitrogen and phosphorus and of the electron acceptors
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like oxygen are neglected. We thereby focus on conditions of carbon limitation that are
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prevalent in shallow mineral soils (C:N and C:P ratios are generally lower than the criti-
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cal ratios for inorganic nutrient immobilization and O2 is abundant). On the other hand,
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the feedbacks between bioclogging and detachment rates are considered beyond of the
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scope of this analysis, although they may dominate biofilm proliferation particularly in
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areas of high flow velocity. Yet, their significance in most surface soils is minor compared
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to the studied microbial responses to stress. For this reason, their incorporation in the
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SMMARTS flexible framework is kept for future research.
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However, despite the assumptions made, the model can be used as a tool to better
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understanding or even predicting the dynamics of biofilm proliferating under a wide range
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of environmental conditions (and the stressors associated). With slight modifications, this
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framework could also be applied to non-porous environments such as surfaces in aquatic
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ecosystems.
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4. Conclusions
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A micro/meso-scale mechanistic model to predict patterns of microbial dynamics un-
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der a wide range of conditions (SMMARTS) is presented and analyzed. This general
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model differentiates the microbial biomass and byproducts into active and dormant cells,
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EPS, and extracellular enzymes; and the substrate between particulate and dissolved or-
793
ganic matter. This approach allows disentangling the consequences of contrasting stress
794
response strategies in microbial communities, including synthesis and reuse of EPS, tran-
795
sition to a dormant state, and dynamic allocation of carbon among microbial compart-
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ments. These strategies are modulated according to biological needs and competition
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for space, water and carbon substrates in a porous environment. For this purpose, the
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42
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model is equipped with: (i) indicators that allow the microorganisms to monitor envi-
799
ronmental and biological factors, and react accordingly to the current pressures; and (ii)
800
the pore-scale feedbacks existing between biofilm accumulation, carbon availability, and
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the water retention capacity in bio-amended soils.
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Although several assumptions have been made, the most relevant microbial processes
804
involved have been included and the results obtained from the simulations are qualita-
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tively in agreement with a number of experimental observations reported in the literature.
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The model can thus be employed as a tool for theoretical exploration and for generat-
807
ing new hypotheses concerning the drivers of biofilm dynamics and their responses to
808
environmental conditions. Results show that microorganisms may utilize smart bioengi-
809
neering designs to improve their fitness by adapting the physiological response to the
810
intensity and type of stress. On one hand, the composition and amount of EPS can be
811
readjusted to mitigate preferentially water stress or carbon limitation. First, if EPS has
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a high water retention capacity, the investments in their production are rewarded by
813
increasing both the overall water content and the carbon availability. Second, those EPS
814
with lower water retention capacity may be used to store more competently the surplus
815
of carbon acquired when conditions are favorable, which can be used at later times if
816
conditions worsen. Third, the amount of EPS produced is modulated according to mi-
817
crobial needs, which are adapted to environmental circumstances. On the other hand,
818
microorganisms able to switch between active and dormant states are more efficient in
819
terms of carbon use and survival. The combination of these two strategies provides a
820
clear benefit to colonies in environments affected by alternate wet-dry cycles, which are
821
predominant in surface soils in most ecosystems.
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Acknowledgments
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This research has received funding from projects ACWAPUR (MICINN. INICIA-
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TIVA INTERNACIONAL PCIN-2015-239), WE-NEED (1076 PCIN-2015-248), and IN-
826
DEMNE (MICINN CGL2015-69768-R). Additional support was provided by the Spanish
827
Ministry of Economy and Competitiveness (fellowship FPI BES-2013-063419). SM was 43
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partly funded by the Swedish Research Councils, Formas (2015-468) and VR (2016-
829
04146). Data and details regarding the simulations can be requested by contacting the
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corresponding author.
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