Modeling microbial reaction rates in a submarine hydrothermal vent chimney wall

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Modeling microbial reaction rates in a submarine hydrothermal vent chimney wall Douglas E. LaRowe a,⇑, Andrew W. Dale b, David R. Aguilera c,d, Ivan L’Heureux e, Jan P. Amend a,f, Pierre Regnier c,g a Department of Earth Sciences, University of Southern California, Los Angeles, CA, USA GEOMAR Helmholtz Centre for Ocean Research Kiel, Wischhofstrasse 1–3, 24148 Kiel, Germany c Department of Earth Science – Geochemistry, Utrecht University, 3508 TA Utrecht, Netherlands d DELTARES, Princetonlaan 6, 3584 CB Utrecht, Netherlands e Department of Physics, University of Ottawa, Ottawa, ON, Canada f Department of Biological Sciences, University of Southern California, Los Angeles, CA, USA g Department of Earth & Environmental Science, Universite´ Libre de Bruxelles, 1050 Brussels, Belgium b

Received 7 January 2013; accepted in revised form 3 September 2013; available online 17 September 2013

Abstract The fluids emanating from active submarine hydrothermal vent chimneys provide a window into subseafloor processes and, through mixing with seawater, are responsible for steep thermal and compositional gradients that provide the energetic basis for diverse biological communities. Although several models have been developed to better understand the dynamic interplay of seawater, hydrothermal fluid, minerals and microorganisms inside chimney walls, none provide a fully integrated approach to quantifying the biogeochemistry of these hydrothermal systems. In an effort to remedy this, a fully coupled biogeochemical reaction-transport model of a hydrothermal vent chimney has been developed that explicitly quantifies the rates of microbial catalysis while taking into account geochemical processes such as fluid flow, solute transport and oxidation– reduction reactions associated with fluid mixing as a function of temperature. The metabolisms included in the reaction network are methanogenesis, aerobic oxidation of hydrogen, sulfide and methane and sulfate reduction by hydrogen and methane. Model results indicate that microbial catalysis is generally fastest in the hottest habitable portion of the vent chimney (77–102 °C), and methane and sulfide oxidation peak near the seawater-side of the chimney. The fastest metabolisms are aerobic oxidation of H2 and sulfide and reduction of sulfate by H2 with maximum rates of 140, 900 and 800 pmol cm3 d1, respectively. The maximum rate of hydrogenotrophic methanogenesis is just under 0.03 pmol cm3 d1, the slowest of the metabolisms considered. Due to thermodynamic inhibition, there is no anaerobic oxidation of methane by sulfate (AOM). These simulations are consistent with vent chimney metabolic activity inferred from phylogenetic data reported in the literature. The model developed here provides a quantitative approach to describing the rates of biogeochemical transformations in hydrothermal systems and can be used to constrain the role of microbial activity in the deep subsurface. Ó 2013 Elsevier Ltd. All rights reserved.

1. INTRODUCTION A volume of water equivalent to that of the world’s oceans circulates through submarine hydrothermal systems

⇑ Corresponding author. Tel.: +1 213 821 2268.

E-mail address: [email protected] (D.E. LaRowe). 0016-7037/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.gca.2013.09.005

every 200,000 to one million years (Elderfield and Schultz, 1996; Johnson and Pruis, 2003). Seawater entering these systems encounters oceanic rocks and sediments over a wide range of temperatures and pressures resulting in significant chemical alteration of both the fluid and solid phases (Mottl, 1983; Von Damm, 1990, 1995; Elderfield and Schultz, 1996; Foustoukos and Seyfried, 2007). Consequently, these hydrothermal fluids are responsible for

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large-scale mass transfer between the ocean and oceanic crust (Wolery and Sleep, 1976; Corliss et al., 1979; Edmond et al., 1979; Thompson, 1983; Von Damm et al., 1985; Palmer and Edmond, 1989). Numerous studies have quantified the magnitude and rate of this rapid redistribution of elements such as Fe, S and Mg (see reviews by Elderfield and Schultz, 1996; Kelley et al., 2002). In particular, models have been developed that determine the underlying processes responsible for element fluxes associated with hydrothermal systems (see Lowell et al., 2008). However, this redistribution of mass is not due solely to abiotic processes. Hydrothermal fluids rich in volatiles from water–rock interactions mix with seawater producing an array of redox disequilibria. This creates ecological niches for chemolithotrophic microorganisms (Shock, 1992) and associated macrofauna (Tunnicliffe, 1991), whose activities in turn impact local mineralogy and fluid chemistry (Schrenk et al., 2008). For instance, microorganisms can serve as nucleation sites for mineral precipitation and thus alter their habitat’s porosity and fluid flow paths (Hannington et al., 1995; Juniper et al., 1995). They can help mobilize metals (Kelley et al., 2002) by reducing solid-phase Fe-oxyhydroxides and Mn-oxides (Schrenk et al., 2008) and potentially influence the geologic record by affecting the isotopic composition of sulfide, sulfate and carbonate minerals found in the subseafloor (Huber et al., 1989; Jørgensen et al., 1992). However, a quantitative treatment of the impact of microorganisms on hydrothermal systems is lacking despite compelling evidence that microbial communities are widespread in subseafloor hydrothermal systems (Huber et al., 1990, 2002; Straube et al., 1990; Deming and Baross, 1993; Haymon et al., 1993; Embley et al., 1995; Juniper et al., 1995; Karl, 1995; Delaney et al., 1998; Holden et al., 1998; Summit and Baross, 1998, 2001; Bach and Edwards, 2003; Schippers et al., 2005; Jørgensen and Boetius, 2007; Nakagawa and Takai, 2008; Schrenk et al., 2010; Takai and Nakamura, 2010; Edwards et al., 2011). Several theoretical studies have quantified the maximum amount of energy available to chemolithotrophs living under submarine hydrothermal conditions (Shock et al., 1995; McCollom and Shock, 1997; McCollom, 2000, 2007; Amend and Shock, 2001; Shock and Holland, 2004; LaRowe et al., 2008; Amend et al., 2011; Boettger et al., 2013). In addition, the potential metabolic energy yields of a wide variety of reactions in shallow marine and terrestrial hydrothermal systems have been estimated (Amend et al., 2003; Inskeep et al., 2005; Inskeep and McDermott, 2005; Rogers and Amend, 2005, 2006; Spear et al., 2005; Rogers et al., 2007; Skoog et al., 2007; Windman et al., 2007; Costa et al., 2009; Shock et al., 2010; Vick et al., 2010; Akerman et al., 2011). Yet, the integration of these thermodynamic constraints into a kinetic framework is lacking. The purpose of the present communication is to present a biogeochemical reaction-transport model that quantifies for the first time potential rates of microbial catabolism in submarine hydrothermal systems. It builds on a new generation of models that explicitly account for kinetic and bioenergetic limitations of a diverse set of metabolic pathways to elucidate the dominant controls on

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substrate turnover in low-temperature environments such as marine sediments and aquifers (Regnier et al., 2005, 2011; Dale et al., 2006, 2008a,b,c, 2010; Thullner et al., 2007; Bohlen et al., 2011; Arndt et al., 2013). Key developments in the present study include a detailed mathematical treatment of activity coefficients, chemical potentials and diffusion coefficients for solutes subject to sharp gradients in temperature, a temperature limiting term for microbial growth and the incorporation of a novel bioenergetic cost function (LaRowe et al., 2012). The model is used to simulate the concentrations of key metabolites as well as reaction rates across a hydrothermal chimney wall as a function of radial distance from the center of the chimney. The results show which metabolic pathways are likely to occur and how they are distributed throughout the wall. They also allow identification of the dominant thermal, kinetic and thermodynamic controls on the geomicrobial dynamics in focused hydrothermal systems. 2. OVERVIEW OF VENT CHIMNEY MODELS Since the discovery of active submarine hydrothermal vent chimneys in the late 1970s, a number of modeling studies have described the evolution of chimney mineralogy using reaction path models based on mineral-fluid equilibria (Janecky and Seyfried, 1984; Bowers et al., 1985; Janecky and Shanks, 1988). Using internally consistent thermodynamic data compiled and estimated by Helgeson and colleagues, e.g., (Helgeson and Kirkham, 1976; Helgeson et al., 1978, 1981; Shock and Helgeson, 1988; Shock et al., 1989), these models reproduce the general mineral zonation in hydrothermal vent chimneys. Recognizing the need to account for the effect of the physical environment on mixing within vent chimneys, Tivey and McDuff (1990) and Tivey (1995a) developed a model that explicitly takes into account how the physical properties of the chimney affect the transfer of heat and mass across it, and thus the mineralogical zonation and profiles of chemical species. This model has been used to explore the sensitivity of thermal and chemical profiles to different physical configurations and fluid chemistries (Tivey, 1995b, 2004). Because the rates of catabolism that are the focus of the current study are heavily dependent on the concentrations of reactant and product molecules and their transport rates are fast compared to the kinetics of mineral precipitation and dissolution (Tivey, 1995b, 2004), the effects of mineral-fluid reactions were assumed to be negligible. As interest in biogeochemical interactions grew, fluid mixing models were developed to assess biological potential as a function of temperature (McCollom and Shock, 1997; Shock and Holland, 2004; Houghton and Seyfried, 2010). In these models, the amount of energy available for a variety of oxidation–reduction reactions is calculated as a function of the mixing ratio between hydrothermal fluids and seawater. These ratios were then assumed to be proxies for distance in vent chimney walls, e.g., high ratios of hydrothermal fluid to seawater indicated mixing closer to the hydrothermal conduit. In contrast to the earlier models, those by McCollom and Shock (1997) and Shock and Hol-

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land (2004) do not take mineral precipitation/dissolution reactions into account. Instead, they focus on determining how much energy is available for microbial catalysis as a function of temperature, which they relate to different parts of the chimney wall. The model described by Houghton and Seyfried (2010) goes a step further by combining fluid mixing and mineral-fluid interaction modeling with geochemical and phylogenetic data to estimate how much energy is available from the most likely catabolic reactions in two vent chimneys. In all of these biogeochemical models, the potential for microbial catalysis is given in terms of joules per kilogram of fluid for specific reactions. These are maximum values of energy availability calculated from redox disequilibria, similar to the earlier reaction path models that focused on mineral saturation states at equilibrium. The model described below goes beyond these previous ones by simultaneously incorporating the physics of fluid flow, diffusion, heat transfer, the chemistry of hydrothermal fluids and seawater, and the impact of thermodynamics and high temperatures on catabolic reaction rates.

1983). Similar to other hydrothermal vent chimney simulations (e.g., Tivey and McDuff, 1990; Tivey, 1995a, 2004), the wall is particularly thin. This maximizes the thermal and concentration gradients through the porous chimney. In contrast to previous studies that used Cartesian coordinates to define the model dimensions, the simulations presented below are performed using a cylindrical coordinate system. This choice becomes necessary when the curvature of the wall becomes significant, that is, when the thickness of the wall is on the same order as the internal diameter of the vent pipe. Furthermore, since the chimney wall is characterized by a steep thermal gradient, the temperature dependence of activity and diffusion coefficients, equilibrium constants and rate constants are represented explicitly. Additional novel aspects of this study include dynamic calculation of the chemical potential of the solutes and reaction rates as a function of distance across the chimney wall.

3. A NEW MODEL

In porous media, the steady-state concentration of the ith solute, Ci, is calculated from diffusive and advective fluxes (J) as well as biogeochemical reactions (e.g., Crank, 1975; Berner, 1980),   X @Ci ðr; tÞ 1 @AJ  1 @AJ  R¼0 u ¼  þ @t A @r advection A @r diffusion

3.1. Overview The model described here simulates the steady-state transport and reaction of solutes in a porous hydrothermal vent chimney wall. The model vent structure (Fig. 1) is a cylinder with a d = 3 cm-thick wall surrounding a 3 cmwide inner conduit, through which 300 °C hydrothermal fluid flows upward. The exterior of the chimney wall is surrounded by ambient seawater at 2 °C. The wall is assumed to be composed of anhydrite, an abundant mineral in earlygrowth stage chimneys (Goldfarb et al., 1983; Haymon,

r1

d

r

Seawater Tsw = 2 oC

Rising vent fluids Tvf = 300 oC Fig. 1. Model schematic of a hydrothermal vent chimney. Rising fluids at 300 °C are separated from the outside 2 °C seawater by a porous anhydrite wall through which solutes can diffuse in the radial direction, r. The total radius of the vent structure, rt, is equal to r1 + d, which represent the radius of the inner tube and the thickness of the wall, respectively. In this study, r1 = 1.5 cm and d = 3 cm. The model is constructed such that the positive direction is outwards, as indicated on the Figure.

3.2. Conservation equations

ð1Þ where t stands for time, r corresponds to the radial distance from the center of the chimney (see Fig. 1) and A denotes the surface area of the cylindrical structure ignoring the upper and lower surfaces, equal to 2prh, where h is the height. The symbol RR in Eq. (1) represents the change in Ci due to all of the biogeochemical reactions considered. Cylindrical symmetry has been assumed so that the solution depends only on the distance r and vertical diffusion can be ignored. Hydrothermal vent chimney mineralogy, and thus porosity and thermal structure, are known to vary in space and time (Goldfarb et al., 1983; Haymon, 1983; Zhu et al., 2007), but in a first approximation, the porosity of the chimney wall (u) was assumed to be constant at 0.3. This value is typical of young vent chimneys that are largely composed of porous anhydrite (Goldfarb et al., 1983; Tivey and McDuff, 1990). The change in concentration of the ith species due to advection is given by:   1 @AJ  1 @  ruCi ðrÞvf ð2Þ ¼ A @r advection r @r where vf represents the horizontal advection rate of porewater through the chimney wall as a result of the pressure gradient normal to the fluid flow direction. In the cylindrical coordinate system used here for constant porosity, r  mf ðrÞ is constant due to the conservation of the flux across the vent chimney along the radial direction. The initial boundary value for vf was taken to be 100 cm yr1 based on calculations of turbulent pipe flow summarized by Tivey and McDuff (1990).

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The change in concentration due to molecular diffusion is linearly proportional to the gradient in its chemical potential, li (Katz and Ben-Yaakov, 1980):    1 @AJ  1 @ @li ðrÞ ruC ð3Þ ¼  ðrÞU ðrÞ i i A @r diffusion r @r @r where Ui is defined as the mobility of the ith species at infinite dilution (mol cm2 J1 yr1) and li designates the chemical potential (J mol1) of the ith species, which is related to the Gibbs energy of the system, G, by:   @G li ¼ ð4Þ @ni P ;T ;nk where P, T and nk indicate that the partial derivative is taken at constant pressure, temperature and moles of substances other than i. Both Ui and li are spatially dependent variables through the effect of temperature (see below). The forces arising from gradients of the electrical potential and the electrophoretic and relaxation effects are minor (Katz and Ben-Yaakov, 1980; Tivey and McDuff, 1990) and thus ignored here. Values of li are calculated using: li ðrÞ ¼ loi ðrÞ þ RT ðrÞ ln ai ðrÞ loi

ð5Þ 1

where denotes the standard state chemical potential of the ith species at a given temperature and pressure, R refers to the gas constant, T stands for temperature in Kelvin and ai corresponds to the activity of the ith species. The latter is related to concentration by the individual ion activity coefficient of the ith species, ci: ai ðr; tÞ ¼ ci ðrÞCi ðrÞ:

ð6Þ

The spatial variability of ci for charged species, due to their functional dependence on temperature, is calculated according to the procedure detailed in Appendix A. Although activity coefficients of neutral species can be estimated by using the Setche´now equation (e.g., Oelkers and Helgeson, 1991; Shvarov and Bastrakov, 1999), the absence of experimental high temperature data do not justify its use. Hence, following the recommendation by Helgeson et al. (1981), the activity coefficients of neutral species were taken to be unity for all temperatures. The value of ai for H2O was also taken to be equal to 1. Because li and ci are both temperature-dependent and T is a function of distance, the spatial derivative of li (Eq. (3)) is given by:   @li @T ðrÞ @loi RT ðrÞ @ci ðrÞ ¼ þ Rlnðci ðrÞCi ðrÞÞ þ @r ci ðrÞ @T @r @T þ

RT ðrÞ @C i ðrÞ C i ðrÞ @r

ð7Þ

where @T@rðrÞ on the right hand side of Eq. (7) describes the temperature gradient across the chimney wall (see below).

1

The standard state adopted in this study for aqueous species other than H2O corresponds to unit activity of the species in a hypothetical one molal solution referenced to infinite dilution at any pressure and temperature, consistent with the hydrogen ion convention (see Helgeson et al., 1981).

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Following Katz and Ben-Yaakov (1980), if Doi ðrÞ (cm2 yr1) is the molecular diffusion coefficient of species i at infinite dilution, then: Doi ðrÞu ¼ U i ðrÞRT ðrÞ

ð8Þ

where the porosity term corrects for the effects of tortuosity on diffusion using Archie’s Law with a coefficient m = 2 (Boudreau, 1997). Substitution of Eq. (7) and (8) into Eq. (3) gives an expression for the change in concentration of a chemical species due to molecular diffusion through the chimney wall:    1 @AJ  1@ @T ðrÞ 2 o ¼  C ðrÞD ðrÞ ru i i A @R diffusion r @r @r   o 1 @li 1 1 @ci ðrÞ þ lnðci ðrÞC i ðrÞÞ þ  RT ðrÞ @T T ðrÞ ci ðrÞ @T  1 @Ci ðrÞ : ð9Þ þ C i ðrÞ @r Note that in the case of zero temperature gradient (oT(r)/or = 0), the diffusive flux reduces to Fick’s Law for diffusion in cylindrical coordinates. Thus, the term in square brackets in Eq. (9) multiplied by oT(r)/or describes the impact of temperature on the diffusion of species in the chimney wall pore space through its effect on standard chemical potentials and activity coefficients. While the influence of the temperature dependence of activity coefficients was taken into account in previous models (Tivey and McDuff, 1990; Tivey, 1995a, 2004) those authors neglected to also consider the influence of temperature on chemical potential, including standard state chemical potential. The impact of temperature on chemical potential has not been taken into proper account before in any study of hydrothermal vent chimneys. The procedures used for calculating values of Doi and loi as a function of temperature are detailed in Appendix A. The overall mass conservation equation is: u

@C i ðrÞ 1 ¼ @t r

    @ @T 1 @C i ðrÞ  ruC i ðrÞtf ½::: þ ru2 C i ðrÞDoi ðrÞ @r @x C i ðrÞ @r Xj ut þ i;j Ri;j j¼1



ð10Þ

where the summation on the right hand side of Eq. (10) denotes the total change in Ci due to all reactions involving t moles of the ith species in the jth reaction (ti,j) proceeding at rate, Ri,j (mM yr1). The bracketed ellipsis in Eq. (10) is equivalent to the term in square brackets in Eq. (9). Solute concentrations in Eq. (1) were calculated in molar units and then reported in molal units using an extension of the equation of state for seawater given by Safarov et al. (2009) as described in Appendix B. 3.3. Temperature distribution across the wall In the model, temperature is treated as a conservative variable whose distribution in the wall is defined by the end member temperatures of seawater (Tsw) and hydrother-

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mal vent fluid (Tvf). An analytical solution of temperature can be obtained from the steady-state form of the heat conduction equation in cylindrical coordinates:   @T ðrÞ 1 @ @T ðrÞ rjðrÞ ¼0 ð11Þ qC p ¼ @t r @r @r

The resulting temperature profile is shown in Fig. 2. Both the curvature effect, i.e., cylindrical coordinates, and the temperature-dependence of conductivity contribute in comparable terms to the deviation from a constant temperature gradient (thick solid line). The thick dashed line in Fig. 2 shows that if Cartesian coordinates were used to calculate the thermal gradient, temperature would be overestimated throughout the chimney wall. In particular, the temperature in the central portion of the wall would be tens of degrees warmer.

where r indicates the distance from the center of the vent, q and Cp designate the density and specific heat capacity of anhydrite, respectively, and j corresponds to thermal conductivity which is dependent on r through the gradient in T. Values of j (W m1 K1) are calculated using: jðrÞ ¼ a  bT ðrÞ

3.4. Biogeochemistry – species concentrations

ð12Þ

Equation (10) was used to calculate the concentrations of the following species across the chimney wall: dissolved oxygen (O2), sulfate (SO42), dissolved methane (CH4), aqueous hydrogen (H2), aqueous carbon dioxide (CO2), bicarbonate (HCO3), carbonate (CO32), dissolved hydrogen sulfide (H2S), bisulfide (HS), the hydroxyl anion (OH) and protons (H+). At each time step and grid space, the proton concentration, [H+], was calculated using total hydrogen sulfide (TH2S), total dissolved inorganic carbon (TCO2), total alkalinity (TA) and the following 5th order polynomial (Zeebe and Wolf-Gladrow, 2001):

where T is in K and the parameters a (5.5 W m1 K1) and b (0.00433 W m1 K2) are derived from a linear regression of temperature-dependent thermal conductivity data for a low-porosity (20%) anhydrite chimney wall as compiled by Tivey and McDuff (1990). The temperature-dependence of anhydrite heat capacity can be found in Robie et al. (1989). Taking q Cp as the porosity-weighted product of the density and heat capacity for water and anhydrite, an average thermal Pe´clet number, PeT = vf d q Cp/j, of 6  104 can be estimated for the anhydrite chimney wall. As the ratio of advection to diffusion, this negligible value of PeT indicates that the advective term for the fluid phase in the temperature equation is small enough to be ignored. The temperatures at the inner and outer wall are assumed to be constant in time. Thus, Dirichlet boundary conditions were used to solve Eq. (11): T ðr1 Þ ¼ T vf and T ðr1 þ dÞ ¼ T SW

TCO2

!

  KS ½TH2 S KW þ  þ ½H  ¼ TA  ½TH2 S þ ½Hþ  ½Hþ  ! K1 K1 K2 ð16Þ  1þ þ þ þ 2 ; ½H  ½H 

where the equilibrium constants K1, K2, KS and KW refer to the dissociation constants between dissolved inorganic carbon species (K1 and K2), sulfide (KS) and water (Kw) at the temperatures of interest (see Table 1 for the corresponding reactions). The terms [TH2S], [TCO2] and TA are defined as:

ð13Þ

where Tvf and TSW represent the temperature on the inside and outside of the chimney, respectively, at distances r1 and r1 + d from the center of the vent (Fig. 1). The steady-state solution of Eq. (11) as a function of distance from the vent center, r, is: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a a2 2aT vf 2w lnðr=r1 Þ T ðrÞ ¼   þ T 2vf  ð14Þ b b b lnððr1 þ dÞ=r1 Þ b2

½TH2 S ¼ ½H2 S þ ½HS  ½TCO2  ¼ ½CO2  þ

ð17Þ

½HCO 3

þ

½CO2 3 

ð18Þ

and 2   þ TA ¼ ½HCO 3  þ 2½CO3  þ ½HS  þ ½OH   ½H  :

where W ¼ aðT SW

K1 2K1 K2 þ ½Hþ  ½Hþ 2

ð19Þ

+

b  T vf Þ  ðT 2SW  T 2vf Þ: 2

Once [H ] is known, the concentrations of CO2, HCO3, CO32, H2S, HS and OH can be calculated from the equilibrium reactions listed in Table 1 (Zeebe

ð15Þ

300

60

1

FD 40

T (oC)

FD f(T)

0.5

FD (-)

T

20

100

0

0 0

1

2

FD f(T) (-)

200

0

3

Distance from inner wall (cm) Fig. 2. Temperature, temperature-limiting function, FD, and the product of FD and f(T) across the hydrothermal vent chimney wall. The thick black line represents the temperature profile used in the simulations assuming non-constant thermal conductivity and a radial coordinate system. The thick dashed line compares the same profile using Cartesian coordinates.

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Table 1 Reaction network used in the model.

3.5. Biogeochemistry – reaction rates

Reaction

The microbially-mediated reactions considered here are those believed to be the most likely major inorganic sources of energy for the communities that inhabit hydrothermal vent structures (Schrenk et al., 2008; Brazelton et al., 2010a). They include the aerobic oxidation of CH4, H2 and H2S (Kelley et al., 2005), the anaerobic oxidation of methane (AOM) using SO42 as the electron acceptor, and hydrogenotrophic methanogenesis and sulfate reduction (Table 1). The abiotic rates of these reactions are assumed to be significantly slower than those that are biologically catalyzed and are therefore not taken into account. This assumption is largely based on a lack of abiotic reaction rate data for the reactions listed in Table 1 (see McCollom, 2000), with the exception of the knallgas reaction (H2 + 1/2O2 ! H2O), as noted below (Foustoukos et al., 2011). The rates at which the catabolic reactions are catalyzed depend on the concentrations of the electron donors and acceptors, the magnitude of their thermodynamic drive and the temperature at which they occur. These factors are formally expressed using a modified bimolecular rate law in which the rate of the jth biogeochemical reaction, Rj, is calculated from:

Stoichiometry

Reactions assumed to be at equilibrium H2S(aq) M HS + H+ Dissociation of hydrogen sulfide, KS Dissociation of H2CO3(aq) M HCO3 + H+ carbonic acid, K1 Dissociation of HCO3 M CO32 + H+ bicarbonate, K2 Dissociation of H2O M H+ + OH water, KW Metabolic reactions considered Methanogenesis CO2 + 4H2 ! CH4 + 2H2O (MET) Knallgas (KNG) 0.5O2 + H2 ! H2O Anaerobic SO42 + CH4 + 2H+ ! CO2 + 2H2O + H2S oxidation of methane (AOM) Hydrogenotrophic SO42 + 4H2 + 2H+ ! 4H2O + H2S sulfate reduction (HSR) Sulfide oxidation 2O2 + H2S ! SO42 + 2H+ (SOX) Methane oxidation 2O2 + CH4 ! CO2 + 2H2O (MOX) All species are aqueous. The symbols following the reactions assumed to be at equilibrium refer to the equilibrium constants for these reaction used in Eq. (16).

and Wolf-Gladrow, 2001). The effect of transport on the concentration of these species in the chimney wall is then computed according to Eq. (10). The dynamic transport of TH2S, TCO2 and TA by diffusion and advection is therefore defined as the sum of the individual species listed in Eq. (17)–(19). Note that the definition of [TH2S] above ignores the negligible contribution from S2, and TA ignores the contribution of borate since their concentrations are generally low in vent fluids (German and Von Damm, 2004). Silica is present at much higher concentrations in vent fluids than in seawater (0.1 c.f. 10 mmol kg1). However, due to the relatively low pH (<8) and relatively high dissociation constant for Si(OH)4 at the temperatures encountered (at 25 MPa, pK1 = 9.3 at 300 °C, pK1 = 8.7 at 175 °C and pK = 9.7 at 2 °C) (Sverjensky et al., 1997), the contribution of SiO(OH)3 to TA is negligible. At circumneutral to acidic pH, bisulfate (HSO4) can also be ignored since it is only present in significant concentrations relative to SO42 above 250 °C. At these high temperatures, reducing conditions prevail and the total sulfate concentration is low (see Application). Metal complexes of carbonate and sulfate were not considered in this study. Those for carbonate species are irrelevant under the conditions of the scenario presented below. Although sodium- and potassiumsulfate species are relevant under the hydrothermal conditions discussed below, these species are left out of the current study. See Appendix C for more information on metal complexing.

Rj ðrÞ ¼ f ðT Þk j CEDi ðrÞCEAi F T ;j ðrÞF D ðrÞ

ð20Þ

where kj stands for the second-order apparent rate constant for the jth reaction, C EDi and C EAi represent the concentrations of the ith electron donor and electron acceptor in the jth reaction, respectively (e.g., Van Cappellen and Gaillard, 1996), FT,j and FD refer to thermodynamic and temperature rate-limiting functions and f(T) determines the temperature dependency of the rate constant (see below). Due to the scarcity of experimental rate data for the reactions in Table 1, other kinetic expressions such as saturation-type behavior (Regnier et al., 2005, 2011; Thullner et al., 2007) were not considered in the simulations discussed below. Although some variation of the rate constants between different reactions is to be expected, they are currently unknown in hydrothermal environments. Therefore, rate constants at the lowest temperature considered in this study, 2 °C, were all assumed to be 108 mol L1 yr1 based on the values typically used in low-temperature, diffusive systems such as marine sediments (Van Cappellen and Wang, 1996; Berg et al., 2003; Luff and Wallmann, 2003). The temperature dependence of rate constants, f(T), is calculated using a Q10 value of 1.7: T T  ref f ðT Þ ¼ Q10 10 : ð21Þ That is, rate constants for all of the metabolic reactions considered in this study were taken to increase by a factor of 1.7 for every 10 degree increase in temperature relative to the reference temperature, Tref, of ambient seawater (2 °C). This value was estimated by comparing the growth rates of 89 methanogens with their optimal growth temperature (see Appendix D) over a range of 80 °C. Methanogens have been used for this purpose because they are known to live under the broadest range of temperatures of any metabolic group, from 22 to 122 °C (Singh et al., 2005; Takai

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et al., 2008). Although the growth rate is not strictly a proxy for rates of catabolism, it is assumed for practical purposes that it serves as a benchmark for calculating substrate turnover if the growth yield of the 89 species are comparable. The underlying hypothesis supporting this function relies on the presumption that there are microorganisms adapted to a range of temperatures (i.e., psychrophiles, mesophiles, hyperthermophiles, etc.) capable of catalyzing all of the metabolic reactions considered in this study. A thermodynamic limiting term, FT,j, is included in Eq. (20) to accommodate the limitation that energy yields have on catabolic reactions rates (Jin and Bethke, 2002). The expression used to calculate FT.j in this study is taken from LaRowe et al., 2012: 8 9 1 for DGr;j 6 0 = < DGr;j ðrÞþF Dw þ1 RT ðrÞ F T ;j ðrÞ ¼ exp ; ð22Þ : ; 0 for DGr;j  0 where DGr;j (J (mol e)1) stands for the Gibbs energy of the jth catalyzed reaction per mole of electrons transferred, DW (V) represents the electric potential that microbes maintain across energy-transducing membranes and F corresponds to the Faraday constant (C mol1). Values of FT,j vary between 0 and 1. Values of DGr,j are calculated for each metabolic reaction using: ! K j ðrÞ DGr;j ðrÞ ¼ RT ðrÞln ; ð23Þ Qj ðrÞ where Kj and Qj refer to the equilibrium constant and reaction quotient of the jth reaction, respectively. Values of Kj were calculated using the revised HKF equations of state (Tanger and Helgeson, 1988; Shock et al., 1992), the SUPCRT92 software package (Johnson et al., 1992) and thermodynamic data from Shock and Helgeson, 1988, 1990; Shock et al., 1989; Sverjensky et al., 1997; Schulte et al., 2001. Values of Qj, were calculated using: Y Qj ¼ avi i ; ð24Þ i

where ai designates the activity of the ith species and vi corresponds to the stoichiometric coefficient of the ith species in the jth reaction. These calculations have been carried out from 2 to 300 °C at 250 bars. The parameter FD in Eq. (20) is a temperature-limiting term which takes into account the consensus view that microbes do not grow or catalyze reactions over an infinite temperature range. It is defined as:

 ðrÞ exp a1 T a2

 F D ðrÞ ¼ ð25Þ ðrÞ 1 þ exp a1 T a2 where T is in Kelvin and a1 and a2 are parameters describing the decrease in FD as the temperature increases. They are listed in Table 3. The values of FD vary between 0 and 1 as a function of temperature as shown in Fig. 2. The FD term reduces reaction rates rapidly when temperatures exceed ca. 80 °C, which is 30 °C lower than the highest observed temperature for sulfate reduction (Jørgensen

et al., 1992) and 40 °C lower than the highest temperature at which a microbial isolate has been observed to grow in a laboratory setting (Takai et al., 2008). It should be noted that although FD acts to dampen catalytic rates at high temperatures, the fact that the rates increase as a function of increasing temperature (through the function f(T)) somewhat counteracts this. The thin dashed line in Fig. 2, the product of FD and f(T), shows how the temperature-limiting term and temperature dependence of rate constants combine to influence reaction rates. 3.6. Boundary conditions and numerical approach The boundary conditions on both sides of the vent chimney (Fig. 1) were imposed as fixed (Dirichlet) concentrations and correspond to the composition of seawater at the outer wall and of a hydrothermal fluid at the inner wall (Table 2). TH2S, TCO2, TA and pH are defined at the boundaries, from which the individual acid–base species can be calculated using the relevant equilibrium constants. The concentration of species in the vent fluid are meant to reflect sulfide-hosted, high temperature vents, e.g., German and Von Damm, 2004; Amend et al., 2011, while that for seawater was taken to be the same as mid-Atlantic Ridge bottom waters (Tivey, 1995b). The spatial derivatives of the coupled partial differential equations for the solutes considered in this study were approximated using finite differences and then solved using the method-of-lines (Boudreau, 1997) and the ordinary differential equation solver (NDSolve) in MATHEMATICA v. 7.0. All models were run for a long time (105 yr) to ensure steady state using a grid size with a constant thickness of 0.03 cm. The parameter values used in the model are reported in Table 3. 4. APPLICATION The model described in this study differs from earlier hydrothermal models in that it focuses on determining catabolic rates as a function of location within a chimney wall, not just energetic potential, while accounting simultaneously for the effect of steep thermal gradients on metabolite transport and reaction rates. Longer term processes such as mineralogical changes in the chimney well are not relevant to this study, and are thus ignored. Because the methodologies used to calculate concentrations of chemical species in vent walls differ from this study and those that

Table 2 Boundary concentrations.

O2 SO42 CH4 H2 TH2S TCO2 TA pH

Seawater

Hydrothermal fluid

0.209 28.9 1  106 0 0 2.2 2.18 7.83

0 0 1.0 3 7 20 0.01 4.6

Except pH, all units are mmol kg1.

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79

Table 3 Physical and biogeochemical parameters used in the model. Parameter

Description

Value

Unit

d TSW Tvf u vf F DW I a1 a2 R Q10 kknlg kmeth kmethox kSox kSred kAOM

Thickness of chimney wall Temperature of seawater Temperature of pure hydrothermal fluid Porosity of chimney wall Fluid advection velocity at the chimney inner wall Faraday constant Cellular membrane potential Ionic strength Parameter for temperature limitation of metabolism Parameter for temperature limitation of metabolism Gas constant Temperature coefficient for reaction rates Rate constant for knallgas reaction at 273 K Rate constant for methanogenesis at 273 K Rate constant for aerobic methanotrophy at 273 K Rate constant for aerobic sulfide oxidation at 273 K Rate constant for sulfate reduction at 273 K Rate constant for anaerobic methanotrophy at 273 K

3 275 573 0.3 100 96485 0.12 0.7 355 3 8.314 1.7 1  108 1  108 1  108 1  108 1  108 1  108

cm K K – cm yr1 C mol1 V mol (kg H2O)1 K K J K1 mol1 – mol L1 yr1 mol L1 yr1 mol L1 yr1 mol L1 yr1 mol L1 yr1 mol L1 yr1

precede it, the results differ considerably. For example, the pH profiles shown in Fig. 3i are consistently higher than those reported by Tivey and McDuff, 1990; Tivey, 1995b, 2004; Houghton and Seyfried, 2010. The concentration profiles of metabolites are more difficult to compare since those generated here are a complex function of chemical potential, which is unique to this study. The concentrations of, for example, CH4, H2, O2 and H2S decrease sharply from the interior or exterior chimney walls towards the center, whereas in other studies, (e.g., Tivey, 2004), the concentration profiles of solutes do not decrease so sharply. This reflects the consideration of temperature-related differences in chemical potential, which significantly affect diffusion and have not previously been properly considered, as well as the use of a cylindrical coordinate system for the modeling approach. Furthermore, it is reiterated that the purpose of our model is to determine catabolic rates within the habitable portions of hydrothermal vent chimney walls. 4.1. Concentrations across the chimney wall The baseline simulated concentrations of the species considered in this study are depicted in Fig. 3 as a function of distance across the vent chimney wall (black lines). In general, these profiles show that the most abundant species in the hydrothermal fluid (H2, CH4, H2S and CO2) decrease rapidly and highly non-linearly towards the seawater side of the wall. Similarly, the concentrations of O2, SO2 and 4 HCO 3 ; which are all higher in seawater, decrease quasiexponentially towards the inner part of the chimney. The peaks in HS- and CO32 concentrations in the inner and outer halves of the vent chimney, respectively, are due to the influence of temperature and pH on the speciation of TCO2 and TH2S. Slightly alkaline, seawater-like values of pH are observed in the cooler, outer part of the chimney wall that then decrease linearly through the middle section and then exhibit a steeper gradient to lower pH near the

inner side of the chimney wall, to a minimum pH of 4.6 characteristic of sulfide-hosted, high temperature vents. Although the diffusion coefficients decrease from 105 2 cm yr1 at the inner wall where the temperature is highest to 102 cm2 yr1 near the outer wall (see Appendix A), diffusion dominates the transport of the species through most of the chimney wall. This interpretation is supported by the values of Pe´clet numbers, Pe, (Boudreau, 1997) and similar simulations by Tivey and McDuff (1990), Tivey (1995a) and Tivey (2004). The Pe´clet number is the ratio of rates of advection to diffusion of a solute. As an example, values of Pe are shown in Fig. 4 for CH4. It can be seen in this Fig. that Pe is smaller than 1 across the entire wall. The imposed advection rate of fluid through the wall, 100 cm yr1, thus plays a small but not negligible role in the transport of solutes. With these observations in mind, it is noteworthy that the concentration profiles are not simple linear mixing curves that would be expected for a diffusion-dominated system. This departure from linearity is due to a cascading set of factors that are not easily disentangled. To begin with, the assumed radial symmetry of the chimney structure (Fig. 1) results in a pronounced nonlinear temperature profile (Fig. 2). This in turn influences the values of diffusion coefficients, chemical potentials and activity coefficients. For instance, it can be seen in Fig. 5 that the calculated activity coefficients for the ionic species depart, sometimes considerably, from 1. However, running the model with ci = 1 and oci/oT = 0 for all species (blue lines in Fig. 3) does not result in notable differences from the concentration profiles calculated using the baseline scenario (black lines in Fig. 3). The largest deviation from the baseline run occurs with SO42 and CO32, which have the lowest activity coefficients and therefore exhibit the strongest deviation from ideality. Because the activity coefficients for the neutral species (CO2, H2S, O2, CH4, and H2) are taken to be unity at all temperatures, there is no feedback of c on the

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30

2.5

(a) TCO2 (mmol kg-1)

12

(b) TA (meq kg-1)

0

50

10 0

30 0 25 0 20 0 15 0

Temperature (oC) 0

50

30 0 25 0 20 0 15 0

Temperature (oC) 0

50

10 0

15 0

30 0 25 0 20 0

Temperature (oC)

10 0

80

(c) TH2S (mmol kg-1)

2 20

8

1.5 1

10

4

0.5 0

0

0

30

20

2.5

(d) [CO2] (mmol kg-1)

20

10

0 12

2

12

1.5

8

1

4

0.5

0

0

(g) [H2S] (mmol kg-1)

12

(h) [HS-] (μmol kg-1) 120

(i) pH

10

8

8

80

6

4

40

0 12

(f) [HCO3-] (mmol kg-1)

(e) [CO32-] (μmol kg-1)

16

4

0

2

2.5

(j) pOH

5

(k) [CH4] (mmol kg-1)

10

2

4

8

1.5

3

6

1

2

4

0.5

1

2

0

0 0

250

30

(l) [H2] (mmol kg-1)

1

2

3

Distance from inner wall (cm)

(n) [O2] (μmol kg-1)

(m) [SO42-] (mmol kg-1) 200

20

150 100

10

50 0

0 0

1

2

Distance from inner wall (cm)

3

0

1

2

3

Distance from inner wall (cm)

Fig. 3. Simulated steady-state concentrations, pH and pOH profiles across the chimney wall. Results are shown for the baseline scenario (black lines), and a simulation with all activity coefficients, c, equal to 1 throughout the chimney wall, oc/oT = 0 (blue lines). The red lines refer to a simulation for which oc/oT = 0 and oli/oT = 0, while the green lines indicate a simulation for which oc/oT = 0, oli/oT = 0 and all reaction rates, Rj, are zero. The temperature gradient is considered in all cases. Note that the black and blue lines are identical for the neutral species (CO2, H2S, O2, CH4, and H2).

concentrations profiles for these species; therefore, the blue and black lines in Fig. 3 are indistinguishable (see Eq. (6)). Note, however, that the effect of activity coefficients on reaction rates is much more pronounced (see following section).

A much larger difference in steady state concentration profiles of chemical species is observed between the baseline simulation and a scenario in which ci = 1, @ci =@T ¼ 0 and @li =@T ¼ 0 (red lines in Fig. 3). Here, it can be seen that the concentration gradients of all of the species considered

0.1

4.2. Microbially catalyzed reaction rates 3

The computed rates of microbially catalyzed reactions (Table 1) are shown as a function of distance in the hydrothermal vent chimney wall in Fig. 6. The solid lines refer to the baseline simulation and the dashed lines refer to results generated from setting all activity coefficients (c) = 1 and @ci =@T ¼ 0 (blue curves in Fig. 3). Note that the panels are scaled differently due to the fact that maximum rates for the different reactions span 5 orders of magnitude, which is characteristic of deep environments (Orcutt et al., 2013). Because of the temperature limiting term, FD, defined by Eq. (25), there is little to no microbial activity in the hot, inner part of the chimney, where the temperatures are above 110 °C. Closer to the seawater side of the chimney, lower temperatures prevail and provide habitats for organisms that catalyze the knallgas reaction (aerobic oxidation of H2), sulfate reduction by H2, sulfide and methane oxidation by oxygen and methanogenesis. Despite its reported occurrence in some high temperature settings (Kallmeyer and Boetius, 2004; Holler et al., 2011; Biddle et al., 2012), AOM is endergonic throughout the chimney

30 0 25 0 20 0 15 0

Temperature (oC) 0

0 15

0

30 0 25 0 20 0

Temperature (oC)

50

10 0

30 0 25 0 20 0 15 0

Temperature (oC)

0

deviate strongly from the baseline scenario when the gradient in chemical potential is ignored. Even the shapes of the curves that describe the concentrations of species change dramatically when @ci =@T ¼ 0. The case of the pH profile (Fig. 3i) is particularly illuminating. In Fig. 3i, the pH value represented by the blue lines are calculated using Eq. (9) and setting ci = 1 and @ci =@T ¼ 0 . The result is nearly identical to that of baseline scenario. However, when @li =@T ¼ 0 as well (red line), the pH profile changes dramatically from being mostly near 7 throughout the wall,

50

Fig. 4. Pe´clet number, Pe, across the chimney wall for aqueous CH4. Values of Pe were calculated using Pe = vfd(r1/r)/DCH4 where vf stands for the fluid advection velocity at the boundary (100 cm yr1), d denotes the thickness of the chimney wall and DCH4 represents the diffusion coefficient for CH4. The factor r1/r takes into account the dependence of the velocity in cylindrical coordinates.

10 0

2

50

1

Distance from inner wall (cm)

0

0

10

Pe (-)

1

0.01

81

to being about 4.5 throughout most of the structure, which is much more similar to the pH values calculated for similar systems (e.g., Tivey and McDuff, 1990; Tivey, 1995a, 2004; Houghton and Seyfried, 2010). That is, because the temperature dependence of chemical potentials are explicitly taken into account in this study, drastically different concentration profiles are predicted for hydrothermal vent wall structures than in all previous studies.

0

50

10 0

15 0

30 0 25 0 20 0

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1

HCO3-

γ (-)

0.8

CO32-

H+

0.6 0.4 0.2 0 2

50

3

0

1

10 0

0

15 0

50

3

30 0 25 0 20 0

2

0

1

10 0

0

30 0 25 0 20 0 15 0

50

3

0

2

10 0

1

30 0 25 0 20 0 15 0

0

1

OH-

HS-

SO42-

γ (-)

0.8 0.6 0.4 0.2 0 0

1

2

Distance from inner wall (cm)

3

0

1

2

Distance from inner wall (cm)

3

0

1

2

Distance from inner wall (cm)

Fig. 5. Individual activity coefficients of the charges species across the chimney wall.

3

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Rate (pmol cm-3 d-1)

CO2 + 4H2 => CH4 + 2H2O 0.03

0.02

0.01

0 1

2

(b) KNG

0

50

0 10

-1 1

2

3

0

Distance from inner wall (cm)

SO42- + 4H2 + 2H+ => H2S + 4H2O

1

2

3

Distance from inner wall (cm)

2O2 + H2S => SO42- + 2H+

2O2 + CH4 => CO2 + 2H2O

1000

1200

0

(c) AOM

0

0

3

15

30 0 25 0 20 0

0

SO42- + CH4 + 2H+ => CO2 + 2H2O + H2S 1

Distance from inner wall (cm)

Rate (pmol cm-3 d-1)

Temperature (oC)

0.5O2 + H2 => H2O 160 140 120 100 80 60 40 20 0

(a) MET

0

50

30 0 25 0 20 0 15 0

Temperature (oC) 0

50

10 0

15 0

30 0 25 0 20 0

Temperature (oC)

10 0

82

60

(d) HSR

(e) SOX

(f) MOX

800 800

40

600 400

400

20

200 0

0 0

1

2

Distance from inner wall (cm)

3

0 0

1

2

Distance from inner wall (cm)

3

0

1

2

3

Distance from inner wall (cm)

Fig. 6. Calculated reaction rates in units of pmol cm3 d1. The rates are given per mole of the reactant underlined in the stoichiometric reaction (see Table 1). The solid lines show the baseline scenario and the dashed lines correspond to the simulation with activity coefficients, c, equal to 1 throughout the chimney wall (oc/oT = 0). Note that the panels are scaled differently due to the considerable variation in rates.

wall (see below and Fig. 7), and hence its rate is zero (Fig. 6c). The highest reaction rates are simulated for aerobic sulfide oxidation (900 pmol SO42 cm3 d1) towards the seawater-side of the chimney wall (Fig. 6e). At a slightly lower peak rate of about 800 pmol SO42 cm3 d1, sulfate reduction by H2 (Fig. 6d) is calculated to occur in the central portion of the chimney where oxygen concentrations are below 10 lM and temperatures are 100 °C (Fig. 6d). Microorganisms are also predicted to catalyze the knallgas reaction mostly in the middle of the chimney, yet slightly closer to the seawater-side, with a maximum rate of 140 pmol H2 cm3 d1 (Fig. 6b). Although it was not taken into account here, at these temperatures, the abiotic rates of the knallgas reaction are fast enough that microorganisms attempting to extract energy from this reaction could be significantly impeded (Foustoukos et al., 2011). Methanogens are most active towards the hotter side of the middle portion of the wall, but with maximum rates of only 0.03 pmol cm3 d1 (Fig. 6a). It is calculated that sulfide and methane oxidizing organisms occupy the same niche in two distinct zones within the wall (Figs. 6e and f). Sulfide oxidizers are most active near the seawater boundary and less so, 250 pmol H2S cm3 d1, in the center of the chimney wall. Similarly, methane oxidation maximizes at the seawater side of the vent, 55 pmol CH4 cm3 d1, with a secondary peak 1.7 cm from the inner wall (Fig. 6f). The faster rates for aerobic sulfide and methane oxidation at the outer wall result

from the steep gradient in O2 concentration while sulfide or methane concentrations show shallower gradients. The effect of the thermodynamic rate-limiting function, Eq. (22), on the calculated reaction rates is shown in Fig. 7. This function quantifies how microbial catalysis rates are influenced by low energy yields. FT decreases reaction rates notably if the Gibbs energy of catalysis, per electron transferred, approaches the amount of energy that microbes require to maintain membrane potentials of 0.12 V (LaRowe et al., 2012). For the aerobic oxidation of H2, H2S, and CH4, where DGr  0 throughout the entire chimney wall, values of FT are equal to 1 (Figs. 7b, e and f). That is, the reaction rates are not affected by energy yields. On the other hand, the computed rates of methanogenesis and sulfate reduction with H2 are significantly reduced by the low energy yields in the inner part of the chimney wall (Figs. 7a and d), and become 0 towards the outer part of the chimney when the values of DGr are positive. Without the FT term in the overall rate equation, Eq. (20), the predicted rate of AOM would be positive, and, for methanogenesis and sulfate reduction coupled to H2, the active zones within the chimney wall would be larger. As shown above (blue lines in Fig. 3), the activity coefficient effects on diffusive transport are minor and barely influence the distribution of reactive species across the wall. However, the spatial gradients in activity coefficients have a significant effect on reaction rates, as can be seen by comparing the baseline results with those in which values of ci

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-75

FT

0

-4 1

2

-80

FT

-85 0.5

-90

ΔGr

-95 0

-100 0

3

SO42- + 4H2 + 2H+ => H2S + 4H2O

0 1

2

Distance from inner wall (cm)

3

ΔGr (kJ mol e-1)

FT

-16 0

20 FT 0

1

-80 0.5 ΔGr

-100

0 1

2

0 3

(f) MOX 1

FT

-80

0.5 -90

ΔGr

-100

3

0 0

1

2

3

Distance from inner wall (cm)

Distance from inner wall (cm)  1

Fig. 7. Values of the thermodynamic rate-limiting term, FT () and DGr (kJ mol e ) catabolic reactions reported in Table 1.

are set to 1 for all species at all temperatures (dashed lines in Fig. 6). For methanogenesis and the knallgas reaction, the rates are lower when ci = 1, yet for sulfate reduction and sulfide oxidation the rates are higher when ci = 1. In addition, the contribution of variable activity coefficients to the energy yields and reaction rates are also notable. For instance, if the activity coefficient for sulfate in seawater is taken to be 1, then the quantitative impact of sulfate activity on its chemical potential, RT ln aSO2 , would be RT 4 ln (0.0289)(1) = 8.8 kJ mol1 at 25 °C, using the seawater sulfate concentration reported in Table 2. By taking the activity coefficient of sulfate into account, 0.16 at 25 °C in a 0.7 mM ionic strength solution, the energetic consequence is dramatic, RT ln (0.0289)(0.16) = 13.3 kJ mol1. This difference may not seem tremendously large, but it is sufficient to determine whether a group of microorganisms metabolizing close to the bioenergetic energy minimum is able to use sulfate as a viable substrate. Thus, ignoring the effect of activity coefficients on the energetics of metabolic reactions may lead to erroneous conclusions. The impact of reaction rates, i.e., microbial activity, on the steady state concentration profiles of the chemical species in a hydrothermal vent chimney wall are shown in Fig. 3 (green lines). Here, the results are compared to a computational scenario in which ci = 0, @ci =@T ¼ 0 , @li =@T ¼ 0 and all reaction rates are taken to be zero. This scenario only differs from the one portrayed by the red lines in that reaction rates are taken to be zero. A shallower concentration gradient can be observed for all species at the inner wall where diffusion coefficients are highest (see Fig. A2 in the Appendix). By mass conservation, therefore, a much steeper gradient is observed at the cooler outer wall where diffusion coefficients are orders of magnitude lower. In several instances, e.g., CO2, pH, pOH and SO42, the reaction rates do not have much of an influence on concentration profiles (compare red and green lines in Fig. 3e, i, j and m). However, for the rest of the species considered here,

2

2O2 + CH4 => CO2 + 2H2O

FT

0

1

Distance from inner wall (cm)

-70

-90

0.5

FT (-)

-8

-12

ΔGr

30

3

(e) SOX

-70

1

40

10

FT (-)

0.5

-4

FT (-)

ΔGr (kJ mol e-1)

-60

ΔGr

0

2

(c) AOM

2O2 + H2S => SO42- + 2H+ 1

(d) HSR

4

1

SO42- + CH4 + 2H+ => CO2 + 2H2O + H2S

Distance from inner wall (cm)

Distance from inner wall (cm)

8

1

ΔGr (kJ mol e-1)

0

50

FT (-)

0.1

ΔGr 0

0.5O2 + H2 => H2O (b) KNG

FT (-)

4

ΔGr (kJ mol e-1)

0.2

ΔGr (kJ mol e-1)

CO2 + 4H2 => CH4 + 2H2O (a) MET

FT (-)

ΔGr (kJ mol e-1)

8

83

across the hydrothermal vent chimney wall for the

the concentration profiles are significantly affected by reaction rates. For example, without the microbial consumption of O2 (green line, Fig 3n) the concentration of O2 is higher than that of the baseline scenario (black/blue line). With the microbial consumption accounted for in the reaction rate term, Eq. (10), O2 is consumed within 1 mm of the chimney wall (red line, Fig. 3n). Similarly, H2 is completely consumed midway through the wall (red line, Fig. 3l) mainly by sulfate reduction (Fig. 6d), leading to a local peak in alkalinity where T = 100 °C (red line, Fig 3b). 4.3. Natural systems The model scenario described in this study is compared to the biogeochemically well-characterized vent chimney structure (Finn) that Schrenk et al. (2003) recovered from the Mothra Vent Field on the Juan de Fuca Ridge. Before being detached from its hydrothermal setting, Finn was venting 302 °C hydrothermal fluids and was surrounded by 2–10 °C seawater. Although this means that the temperature difference across the chimney wall is the same as the one considered in our simulations, the wall thickness was considerably larger (5–43 cm), resulting in a weaker thermal gradient. Furthermore, Finn has a more complex mineralogy than the simple anhydrite layer considered here, which was used by Schrenk and colleagues to subdivide Finn into four zones. The outermost Zone 1 (outer 2–3 cm) was dominated by microorganisms that are influenced by the macrofauna attached to the exterior of the structure, including some evidence for sulfate reducers inhabiting the warmer part of this section. In our model, the highest catabolic rates near the seawater edge of the vent wall are attributed to aerobic methane and sulfide oxidation (Figs. 6e and f). Finn’s zone 2 (2–10 cm from the exterior of the chimney wall) contained the highest biomass and microorganisms include anaerobic hyperthermophiles and methanogens. Similarly, the rate profiles shown in Figs. 6a and d reveal that

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methanogenesis and hydrogenotrophic sulfate reduction are both viable metabolic pathways. Zone 3 was characterized by the presence of Archaeal biofilms while Zone 4 (the innermost section) consists mostly of sulfide minerals that suggest persistent temperature in excess of 150 °C. In the simulations, the FD function takes this extreme condition into consideration by preventing catabolic activity at these temperatures. Other studies have reported that higher temperature niches in hydrothermal vent systems are occupied by anaerobic iron and sulfur reducers, fermenters, methanogens, heterotrophs, denitrifiers, and methane oxidizers (Brazelton et al., 2006; Kormas et al., 2006; Ver Eecke et al., 2009; Wang et al., 2009; Zhou et al., 2009). Although not all of these metabolisms are considered here, the model results shown in Fig. 6 do predict microbial methanogenesis at the hottest part of the chimney where life can be maintained. Additionally, phylogenetic studies have identified the presence of both anaerobes and aerobes, including CH4, H2 and sulfide oxidizers in the cooler parts of chimney walls (Reysenbach and Cady, 2001; Schrenk et al., 2003; Kormas et al., 2006; Ver Eecke et al., 2009; Wang et al., 2009; Zhou et al., 2009; Brazelton et al., 2010b), which is also predicted by the model. Furthermore, McCollom, 2000 concludes that there is metabolic energy available from the knallgas reaction, sulfate reduction, methanogenesis and methanotrophy in calculations that mix seawater with hydrothermal fluids. Overall, the results presented in this study capture many previous observations of microbial activity in hydrothermal vent chimneys. 4.4. Uncertainties To our knowledge, literature data on microbial turnover rates in hydrothermal chimney walls are unavailable. The model-predicted rates are thus our best quantitative estimate of substrate turnover in these vent structures. The computed rates of hydrogenotrophic sulfate reduction are up to 3 orders of magnitude less than those reported for surface sediments in the diffuse hydrothermal sediments of Guaymas Basin (Elsgaard et al., 1994). This is most likely due to the much higher sulfate and organic matter concentrations in Guaymas and the fact that organic matter was not considered as an electron donor in the present study. As with most continental margin sediments, sulfate reduction in Guaymas Basin is substrate-limited, and rates tail off rapidly with depth in the sediment even though temperatures increase sharply (Elsgaard et al., 1994). In fact, substrate limitation is probably the major rate-limiting factor in most diffuse hydrothermal systems, with temperature playing a secondary role. Similarly, (Fishbain et al., 2003) reported a wide range of sulfate reduction rates in Yellowstone hot spring sediments (38 to 91 °C) that was attributed to variations in the supply of endogenous electron donors rather than temperature. Analogously, equally high rates of sulfate reduction coupled to AOM have been reported for Guaymas Basin (4 lmol SO42 cm3 d1) and cold surface marine sediments (4 °C) above gas hydrates where the supply of substrate (methane) to anaerobic

methanotrophs is enhanced by upward advection of methane-rich fluids (Treude et al., 2003; Dale et al., 2010). Being relatively thin and characterized by a much steeper temperature gradient, the chimney wall environment imposes a different set of constrains on microbial reaction rates than in sediments. The transport of reduced compounds through porous vent walls is so rapid that substrate concentrations are barely affected by microbial activity when the gradient in chemical potential is considered, as discussed previously. The thermodynamic drive for a metabolic reaction and, thus, microbial activity will mainly be a function of the rate of solute transport only, rather than the in situ production and consumption of solutes by reactive processes (Tivey, 1995a, 2004). Moreover, molecular diffusion (both neutral and ionic species) is the dominant solute transport pathway and the uncertainties in defining solute advection velocities are probably unimportant. In theory, then, the spatial domain where life can exist in chimney walls can be predicted from physical principles of molecular diffusion and bioenergetics only. Within the temperature range for which microorganisms can remain active, and providing that the catabolic reaction is exergonic, levels of microbial activity mainly scale to the magnitude of the rate constant for a given reaction. These values are largely unknown under the conditions that describe hydrothermal systems. An additional source of uncertainty is how these rate constants vary as a function of temperature. This is accomplished in this study using Q10, a catch-all parameter that simplifies how a complex microbial community responds to temperature regardless of other environmental variables such as nutrient availability, microbial population dynamics and community structure. Not only are values of Q10 unknown for hydrothermal vents, but they can also vary substantially for well-studied systems. For instance, in the review by Segers, 1998, values of Q10 for hydrogenotrophic methanogens in pure culture range from 1.3–12, while in natural systems, values of Q10 for methane production range from 2–28. However, these and other values of Q10 (e.g., Robador et al., 2009) are typically determined by observing the response of isolates or communities, which are adapted to a particular temperature, to increased temperature. In contrast, the value of Q10 adopted in this study (1.7) was determined by examining the maximum growth rates of 89 methanogens over a temperature range of 80 °C, and not how a given community responds to temperature change. Effectively, we assumed that microorganisms that can catabolize the reaction considered exist throughout the range of temperatures in which microorganism are known to live. Based on these observations, it can be concluded that the model results allow for predictions of the spatial extent over which a specific microbial reaction within porous vent walls is thermodynamically favorable. The robustness of these predictions, in turn, depends on the accuracy of the diffusive transport parameters over the range of temperatures encountered. In addition, the basic, yet fundamental question concerning the upper temperature limit at which thermophiles can thrive, puts another important constraint to the predictions. Perhaps most importantly, reaction

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rates, especially at high temperatures, remain poorly constrained. That is, if the microbially-catalyzed kinetics of a redox reaction are slower than the abiotic rates for the same reactions, then it would be difficult for microbial communities to capture much of the released energy (Shock and Holland, 2007). 5. CONCLUDING REMARKS A biogeochemical reaction transport model that quantifies the rates of microbial catabolic activity in a hydrothermal vent chimney wall has been developed. To our knowledge, this is the first time that reaction kinetics and bioenergetic constraints are coupled to advective and diffusive transport of chemical species in a system subjected to very steep natural thermal gradients. Novel aspects of the model include the use of cylindrical coordinates, the dynamic computation of chemical potentials as a function of temperature to constrain diffusive transport, a temperature-limiting term for catabolic activity, and the incorporation of a bioenergetic cost function affecting reaction rates. In addition, the temperature dependence of the rate constants from 2 to 300 °C has been estimated by examining the doubling times of methanogen isolates. The model predicts spatially resolved reaction rates based entirely on the physics of solute transport, the chemistry of a hydrothermal fluid and seawater and a thermally and bioenergetically modified biomolecular rate law: sulfate reduction by H2 and the knallgas reaction are predicted to dominate in the hottest part of the habitable zone of the chimney, the aerobic oxidation of sulfide and methane are more rapid towards the outer, cooler portions of the vent structure and methanogenesis is predicted to be carried out at much lower rates than those for the other catabolic activities considered. AOM is thermodynamically inhibited throughout the entire wall. The model described in this study could be applied to other hydrothermal systems in which fluid compositions, temperatures and potential catabolic reactions differ from those used here, or expanded considerably to simulate different biogeochemical environments that are also difficult to observe. For instance, all or part of the model could be used to assess the rates of microbial activity in diffuse submarine hydrothermal systems or in terrestrial subsurface settings where there are relatively sharp thermal gradients, such as those at Yellowstone National Park in the United States. The approach taken here could be modified to evaluate the catabolic potential in the oceanic lithosphere, a vast potential reservoir of life that is only now being probed for life (Edwards et al., 2011, 2012; Orcutt et al., 2011). Whatever the scale, the model developed here expands the possibility of quantifying the rates of biogeochemical reactions in a variety of subsurface settings, including extreme environments. ACKNOWLEDGEMENTS The research reported above was enabled by financial support from NSF-RIDGE Grant 0937337 (D.E.L and J.P.A), the Center for Dark Energy Biosphere Investigations, C-DEBI, Postdoctoral

85

Scholarship Program (DEL), the Netherlands Organization for Scientific Research, NWO, (P.R. and D.E.L.), the government of the Brussels-Capital region via the Brains back to Brussels Award (P.R.) and the Natural Sciences and Engineering Council of Canada (I.L.). This manuscript benefited substantially from the comments given by three reviewers. In particular, special thanks are reserved for Margaret K. Tivey, whose thorough review has significantly improved many aspects of this study. This is C-DEBI contribution 178.

APPENDIX A. CALCULATION OF ACTIVITY COEFFICIENTS, CHEMICAL POTENTIALS AND DIFFUSION COEFFICIENTS Individual ion activity coefficients of the ith species, ci, were calculated as a function of temperature, pressure and ionic strength using a modified version of the model proposed in Helgeson et al. (1981), 

log ci

Ac Z 2i I 1=2 þ  þ Cc þ ðxabs i bNaCl þ bNa Cl K 

 0:19ðjZ i j  1ÞÞ I

ðA:1Þ

where Ac (kg1/2 mol1/2) and K(unitless) Kterms, Zi is the charge of the ith ion, I¯ (mol kg H2O1) refers to the ‘true’ ionic strength of the solution (Helgeson, 1969), xabs i (J mol1)stands for the absolute Born solvation parameter for the ith electrolyte, bNaCl (kg J1) accounts for the dependence of solvation on ionic strength and bNaþ Cl (kg mol1) describes short-range interactions among ions. The Cc term has been omitted because it is intended to account for very high ionic strength solutions which are not relevant to this study. Eq. (A1) can be used to estimate activity coefficients of charged species over a wide range of temperatures, pressures and ionic strengths in which NaCl is the background electrolyte (Helgeson et al., 1981). Because they are functions of temperature, values of Ac, K, bNaCl and bNaþ Cl are also spatially dependent. The electrostatic Debye-Hu¨ckel term, Ac is given by: Ac

ð2pN Þ1=2 e3 q1=2 2:302585ð1000Þ1=2 ðekT Þ3=2

:

ðA:2Þ

It is a function of Avogadro’s number, N (6.02252  1023 mol1), the absolute electronic charge, e (1.6022  1019 C), Boltzmann’s constant, k (1.38065  1023 J K1), temperature, T (K), solution density, q (kg m3), and the dielectric constant of water, e (dimensionless). The latter two are also functions of temperature and pressure. Values of Ac, q, and e as a function of temperature and pressure are taken from (Helgeson and Kirkham, 1974). The “true” ionic strength term, I¯, in Eq. (A1) is related to the stoichiometric ionic strength of a solution, I (mol kg1), by:  1X 2 I ¼ Z mi ¼ ð1  aNaCl ÞI ðA:3Þ 2 i i where mi refers to the molality of the ith species and aNaCl (unitless) stands for the degree of association of NaCl in

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solution due to ion pairing. I¯ was used by (Helgeson, 1969) to account for the observation that above 100 °C, ion pairs start forming in solution as water becomes a less polar solvent. Values of aNaCl are calculated assuming an NaCl molality = 0.57 mol/kg,

which is a fit to the values given in Helgeson (1969), for temperature in Kelvin. The K electrostatic term is given by: ðA:5Þ

xabs ¼ xi  Z i xabs i Hþ

1

where Bc (kg mol cm ) is an electrostatic DebyeHu¨ckel parameter defined as:

μo (kJ mol-1)

-580

-480

HCO3-

1

CO32-

0

50

0

0

30 0 25 0 20 0

Temperature (oC) 0

30 0 25 0 20 0 15 0

Temperature (oC) 0

50

10 0

15 0

30 0 25 0 20 0

Temperature (oC)

ðA:7Þ

where xi stands for the conventional Born solvation parameter for the ith species and xabs , denotes the absolute Born Hþ

50

1/2

1/2

ðA:6Þ

10



1=2

and its value values as a function of temperature and pressure are taken from Helgeson and Kirkham (1974). The distance of closest approach, a˚, is also a function of temperature and pressure, but at temperatures <350 °C, it ˚ in NaCl dominated solutions varies little beyond 3.72 A (Helgeson et al., 1981). The absolute Born solvation parameter for the ith electrolyte, xabs i , is given by:

ðA:4Þ

Bc I 1=2 K ¼ 1 þ a

8pNe2 q 1000  ekT

15

aNaCl ¼ 2:7183  105  e0:01620ðT Þ

Bc

10 0

86

H+

-490 -590

-500 0 -510

-600

-520 -610

-530 0

1

μo (kJ mol-1)

16

2

3

2

3

0 -700

OH-

1

2

3

1

2

3

1

2

3

SO42-

-144

12

-720

-148 8 -152 4

-740

-156 -160 0

0

μo (kJ mol-1)

1

-140

HS-

0 1

2

3

-760 0

40

H2S

-20

20

-40

0

-60

-20

1

2

3

0 -320

O2

CO2

-360

-400

-80

-40 0

1

2

3

-440 0

1

2

3

0

Distance from inner wall (cm)

-30

μo (kJ mol-1)

-1 0

30

CH4

-40

20

-50

10

-60

0

-70

-10

-80

H2

-20 0

1

2

Distance from inner wall (cm)

3

0

1

2

3

Distance from inner wall (cm)

Fig. A1. Chemical potentials of species across the chimney wall in units of kJ mol1.

D.E. LaRowe et al. / Geochimica et Cosmochimica Acta 124 (2014) 72–97

Log Do (cm2 yr-1)

5

Log Do (cm2 yr-1)

ðA:8Þ

where CDi corresponds to a constant characteristic of the ith species and go represents the viscosity of pure water. Values of go as a function of T were taken from (Robinson

5

5

CO32-

4

4

3

3

3

2

2

2

1

2

3

0

1

5

HS-

2

3

0

4

4

4

3

3

3

2

2

2

0 5

1

2

3

0 5

H2S

1

2

3 5

O2

4

4

3

3

3

2

2

2

0

1

2

3

0

4

4

3

3

2

2 0

1

2

Distance from inner wall (cm)

3

2

3

0

50

0

0

2

3

1

2

3

1

2

3

CO2

0

Distance from inner wall (cm)

5

CH4

1

1

SO42-

0

4

5

H+

5

OH-

10

30 0 25 0 20 0

Temperature (oC) 0

50

10 0

30 0 25 0 20 0 15 0

0

50

CDi T ðrÞ go ðrÞ

4

0

Log Do (cm2 yr-1)

Doi ðrÞ ¼

Temperature (oC)

HCO3-

5

Log Do (cm2 yr-1)

10 0

30 0 25 0 20 0 15 0

Temperature (oC)

calculated as a function of temperature and pressure using the revised HKF equations of state (Helgeson et al., 1981; Tanger and Helgeson, 1988) and the SUPCRT software package (Johnson et al., 1992). Values of loi , are shown in Fig. A1. Values of molecular diffusion coefficients of the ith species at infinite dilution, Doi ðxÞ, for aqueous CO2, H2, O2 and H2S were calculated as a function of temperature using (Tivey and McDuff, 1990):

15

solvation parameter for the hydrogen ion, equal to 0.5387  105 cal mol1. The effective electrostatic radii of ions, on which xabs and xabs depend, vary as a function i Hþ of temperature and pressure and are calculated using the g function introduced by (Shock et al., 1992). However, even at 350 °C PSAT (pressures corresponding to the liquid–vapor equilibrium line for H2O), the value of xabs calHþ culated without the g function are only 0.18% different than those calculated with it, which is far less than the uncertainty in the values of xi. As a result values of xabs and Hþ xabs are assumed to be constant in this study. i In the classical aqueous electrolyte standard state, values of the standard state chemical potential of the ith species, loi , are taken to be equal to the molal Gibbs energy of formation of the ith species, DGf ;i . Values of DGf ;i are

87

H2

0

1

2

3

Distance from inner wall (cm)

Fig. A2. Molecular diffusion coefficients of species across the chimney wall in units of log cm2 yr1.

88

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and Stokes, 1959; Yusufova et al., 1978). Values of Doi ðrÞ for CH4 as a function of temperature were taken from (Oelkers and Helgeson, 1991). Values of Doi ðrÞfor HS and HCO3 were taken to be equal to the average of values of Doi ðrÞ for other 1 charged species (F, Cl, Br, I and NO3) as a function of temperature given in (Oelkers and Helgeson, 1988). Values of Doi ðrÞ for CO32 and SO42 were estimated by assuming that the difference in values of Doi ðrÞ between +2 and +1 aqueous species is equal to that between 2 and 1 species as a function of temperature. Average values of Doi ðrÞ were then calculated for +1 species (9 species) and +2 species (14 species) taken from Oelkers and Helgeson (1988) and combined with the aforementioned average Doi ðrÞ for 1 species to calculate values of Doi ðrÞ for CO32 and SO42. Values of Doi ðrÞ for the several compounds considered in this study are shown in Fig. A2.

0

50

10 0

15 0

30 0 25 0 20 0

Temperature (oC)

ρsw (kg L-1)

1.1 1 0.9 0.8 0.7 0

1

2

3

Distance from inner wall (cm) Fig. B1. Density of seawater (qsw) across the hydrothermal vent chimney wall in kg L1.

.01 CO

2 (aq)

.001 1e–4

–

HCO

3

activity

1e–5

CaHCO

+ 3

CaCO3

1e–6 1e–7

SrHCO3+

1e–8

–

NaCO3 1e–9 1e–10 300 275

250

225

200

175

150

125

2–

CO3

100

75

50

25

Temperature (C) .1

–

.01

NaSO4

–

HSO4

24

SO

activity

.001 –

KSO4 1e–4

1e–5

1e–6 300

275

250

225

200

175

150

125

100

75

50

25

Temperature (C) Fig. C1. Carbonate and sulfate speciation in seawater at pH 8 from 300 to 2 °C carried out using Geochemist’s Workbench.

D.E. LaRowe et al. / Geochimica et Cosmochimica Acta 124 (2014) 72–97

89

It should also be noted that because not all charged species in seawater were incorporated in this model, that the electroneutrality of the fluid was not a consideration. If it had been, the transport of all charged species together would lead to multicomponent diffusion effects whereby the diffusive transport is nonlinear, depending on the gradients of all charged species in the system. This obviously makes the system more complex. Fortunately, for most ions in seawater, multicomponent effects can be neglected (Van Cappellen and Gaillard, 1996).

1984), is nearly constant, 26.3 g/ (L H2O), from 0.01 to 200 °C (see Fig. B1). As a first approximation, this value was simply added to the density of pure seawater from 200 to 300 °C at 25 MPa in order to estimate the solution density in this temperature range. Alternatively, one can use the approach presented by (Bischoff and Rosenbauer, 1985) to calculate densities of seawater above 200 °C for fluids containing 3.2% NaCl.

APPENDIX B. CONVERSION OF MOLAR TO MOLAL UNITS

In order to explore the possibility of metal complexes of the charged species considered in the current study to form, seawater was speciated from 300 to 2 °C at pH 8 using Geochemist’s Workbench, which applies a slightly different activity coefficient model than the one adopted in the current communication. Complexes of carbonate and sulfate are shown in Fig. C1. Here, it can be seen that CO2(aq) is by far the most dominant species from 300 to about 145 °C. At cooler temperatures, HCO3 becomes the most dominant. In both cases, these species are at least an order of magnitude more abundant than their metal-complexed counterparts, except at the lowest temperatures. At 25 °C, HCO3 is still more than twice the sum of CaCO3(aq) and NaCO3, although the ratio shrinks as the temperature approaches 2 °C, the lowest temperature considered in this study. The effect of incorporating metal-complexing with carbonate species in the model would thus only slightly

APPENDIX C. METAL COMPLEXING

The concentration of the ith species, Ci, was converted to molality, mi, using mi

Ci qsoln

ðB:1Þ

where qsoln refers to the density of seawater in the chimney wall. From a temperature between 2 and 200 °C, values of qsoln were calculated from the Safarov et al. (2009) equation of state for seawater for a salinity of 35 at 25 MPa. Because the Safarov et al. (2009) equation of state does not extend to beyond 200 °C, values of qsoln from 200 to 300 °C were estimated by noting that the difference in the density of seawater and pure water at 25 MPa, calculated using the equations of state from (Levelt Sengers et al., 1983; Haar et al.,

2.5

-1

1/doubling time (h )

2

1.5

1

0.5

0 280

300

320

340

T

opt

360

380

(K)

Fig. D1. Plot of inverse doubling time versus optimal growth temperature for 89 methanogen isolates.

90

D.E. LaRowe et al. / Geochimica et Cosmochimica Acta 124 (2014) 72–97

alter the concentrations of carbonate at temperatures lower than 25 °C. For the higher temperatures, where most of the microbial activity is predicted to occur, the difference is effectively zero. The impact of these differences on the computed results would not be noticeable. However, the speciation of sulfate, also shown in Fig. C1, illustrates the importance of metal complexes and the shortcomings of the assumptions that have been made in this study. Here, for temperatures <250 °C, NaSO4 is the most abundant sulfate species, with SO42 becoming the second most abundant <220 °C. At 100 °C, the activity of NaSO4 is about 3 times that of NaSO4. At lower temperatures, this difference decreases, with the ratio becoming less than two. The next most abundant sulfate species, KSO42, is more than an order of magnitude less abundant than SO42 for temperatures <125 °C. The difference between the total activity of sulfate and the activities of SO42 and NaSO4 is certainly noteworthy. The impact of these activity differences for this manuscript is in the rates and Gibbs energies of metabolisms containing sulfate (actually, since the energetics influence the rates, they cannot be separated). The rates of sulfate-based metabolisms would be slightly lower due to the bimolecular rate law used in this study. Additionally, the energetics of reactions, and by extension the thermodynamic rate limiting function, FT, would be altered as well. It should be emphasized that the speciation calculations shown in Fig. C1 are for a fluid of seawater composition at a constant pH 8, which is somewhat different than the fluids used in the simulations discussed above. APPENDIX D. METHANOGEN ISOLATE REFERENCES The doubling times and optimal growing temperature of the 89 methanogens used to calculate Q10, shown plotted in Fig. D1, were taken from the following studies: (Stetter et al., 1981; Huber et al., 1982; Ko¨nig and Stetter, 1982; Rivard and Smith, 1982; Whitman et al., 1982; Wildgruber et al., 1982; Corder et al., 1983; Morii et al., 1983; Rivard et al., 1983; Sowers and Ferry, 1983; Jones et al., 1983a,b; Ko¨nig, 1984; Sowers et al., 1984; Winter et al., 1984; Zabel et al., 1984; Blotevogel and Fischer, 1985; Laurerer et al., 1986; van Bruggen et al., 1986; Worakit et al., 1986; Jain et al., 1987; Zellner et al., 1987, 1989a,b, 1998, 1999; Mathrani et al., 1988; Zhao et al., 1989; Burggraf et al., 1990; Liu et al., 1990; Patel and Sprott, 1990; Patel et al., 1990; Kurr et al., 1991; Maestrojua´n and Boone, 1991; Franzmann et al., 1992, 1997; Boone et al., 1993; Kotelnikova et al., 1993a,b, 1998; Ferrari et al., 1994; Kadam et al., 1994; Kadam and Boone, 1995; Leadbetter and Breznak, 1996; Elberson and Sowers, 1997; Ollivier et al., 1997, 1998; Jeanthon et al., 1998, 1999; Leadbetter et al., 1998; Lomans et al., 1999; Lyimo et al., 2000; Mori et al., 2000; Sprenger et al., 2000; Cuzin et al., 2001; Dianou et al., 2001; Lai and Chen, 2001; Simankova et al., 2001; Chong et al., 2002; Lai et al., 2002, 2004; Savant et al., 2002; Takai et al., 2002, 2004, 2008; von Klein et al., 2002; L’Haridon et al., 2003; Mikucki et al., 2003; Jiang et al., 2005; Ma et al., 2005,

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