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A glyco-competitive assay to demonstrate the stochasticity of fate decisions in Escherichia coli
Accepted Manuscript Title: A glyco-competitive assay to demonstrate the stochasticity of fate decisions in Escherichia coli Author: Giuseppina Simone PII: DOI: Reference:
S1359-5113(16)30410-X http://dx.doi.org/doi:10.1016/j.procbio.2016.12.007 PRBI 10879
To appear in:
Process Biochemistry
Received date: Revised date: Accepted date:
13-9-2016 14-11-2016 8-12-2016
Please cite this article as: Simone Giuseppina.A glyco-competitive assay to demonstrate the stochasticity of fate decisions in Escherichia coli.Process Biochemistry http://dx.doi.org/10.1016/j.procbio.2016.12.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A glyco-competitive assay to demonstrate the stochasticity of fate decisions in Escherichia coli Giuseppina Simone1 1
Mechanical Engineering, Microsystem, Northwestern Polytechnical University
127 West Youyi Road, Xi’an Shaanxi, 710072, P.R. China Email: [email protected]; Phone : +86 029 88460353 620
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Abstract Interaction bacteria-gut, via glycan associations, contribute to the selection of microbial communities along the gastrointestinal tract, influencing cancer development. The mechanism causing microbiome alterations is unknown, while this understanding would be pivotal to identify medical therapies. The molecular associations between Escherichia coli bacteria and glucose, both in solution and immobilized at the surface, were studied showing the dependence of E. coli glucose binding on the sugar form. Classical kinetic models were used to derive the reaction equilibrium and adsorption constants, 8 mM−1 and 1 (cell/mL)-1 and to explain the uptake. E. coli preferred the free glucose, whereas in a deprived environment, the anchored glucose became the major source of carbon for the bacteria. A stochastic algorithm disclosed that after initial transient, E. coli privileged the anchored glucose rather than the free sugar, independently on the concentration. The biochemical approach alone failed to describe the effective behavior of the cells and that several parameters can affect the behavior of the bacteria. From this result, more sophisticated models of the destruction of the gut barrier can be derived, such as the mechanism whereby E. coli can switch the immune system on and off to cause cancer and its metastasis.
Keywords: Competitive assay; E. coli; glycomics; stochastics
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Highlights:
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E. coli - glucose binding in solution and immobilized at the surface were studied.
Glucose is the major source of carbon for the bacteria in deprived environment.
Reaction equilibrium and adsorption constants were 8 mM−1 and 1 (cell/mL)-1.
Stochastic approach shows failure of biochemistry alone to describe E. coli behavior.
E. coli privileged the anchored glucose after an initial transient.
Graphical abstract In vivo
In vitro
Inflammation of the stomach wall induced by E. coli
Binding mechanism decision by E. coli
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1. Introduction Gut microbes contribute to cancer cell death. The link between the microbiome and cancer seems to reside in the immune system [1], where microbes can either dial up inflammation or tamp it down and can modulate immune cell vigilance for invaders. It has been shown that inflammatory signals, which induce regulation, are dictated by the composition of the microbiome in the gut. The immune system appears to be at the root of how the microbiome interacts with cancer therapies and it also appears to mediate how bacteria, fungi, and viruses influence cancer development. E. coli are involved in this mechanism [2]. These gram-negative bacteria play an important role in the gut [3], such as underpinning the interaction between bacteria and mucin glycans. The interactions between the bacteria contribute to the selection of microbial communities along and across the gastrointestinal tract. It has been shown that altered glycosylation of the gut barrier can be symptomatic of inflammatory or malignant diseases associated with altered microbiota composition [4–6]. The interaction between the bacteria and glycans situated on the gut barrier (Fig. 1a) occurs via adhesins existing within the bacterial membrane (close up Fig. 1a). The regulation, controlled by a cell surface protein, directs bacteria to gut-associated lymphoid tissues, which suggests that these bacteria shuttle between the gut and spleen. Studies are beginning to explore the structural nature of sugars and adhesins to establish a relationship between different structures and functions and their biological roles [7]. At this point, understanding the mechanism of adhesion between bacteria and glycans becomes pivotal for engineering bacterial behavior. Current knowledge and competencies in micro- and nano-systems can aid research aimed at explaining cellular phenomena connected to bacterial behavior as well as identify potential therapies. Using stochastic models to analyze cell behavior provides a means to decipher the mechanisms according to which bacteria show preference in ambiguous processes. This approach offers a method to control and engineer the behavior and actions in E. coli. Stochasticity is synonymous with randomness [8, 9]. Intrinsic stochasticity is generated by the dynamics of the system from the random timing of individual reactions [10]. Extrinsic stochasticity is generated by the system interacting with other stochastic systems, for example, in the cell or micro-environment. In general, biochemical reactions, which describe the molecular recognition between the bacteria and binding molecules, induce stochasticity through intermolecular collisions. Stochastic models of reactions provide a detailed understanding of the
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biochemical reactions [11] and are necessary when the biological phenomena observed exhibit fluctuations, e.g., switching between two favorable states of the system. It is worth mentioning that in a deterministic model, the output is strongly dependent on the initial conditions, where changing those conditions will affect the final response of the system; stochastic models possess some inherent randomness, which will be such that the same set of parameter values and initial conditions will lead to different outputs. The living natural world is a typical example buffeted by stochasticity and randomness, which makes it more complicated to model. Competition, as an example of fluctuation, is described by stochastic models, and was introduced and investigated by Gillespie [12]. In biological systems, there are numerous sources of stochasticity, such as heterogeneity of cellular populations [13] and gene regulation [14]. To date, the entire world of small organisms and bio-reactions is best described using stochastic rather than deterministic models [15]. Working from that premise, this study develops through two different methodologies. The first is based on an experimental investigation to determine kinetic parameters and to observe the decisional behavior of the cells. The experimental platform aims to mimic the cellular environment, especially the gut. The scheme of the problem described here is shown in Fig. 1b. Sugar molecules are either available in solution or immobilized (anchored) at the substrate surface. The bacteria can freely decide where and how to uptake and bind to the sugars [16]. This is referred to as competitive inhibition and involves biochemical reactions at equilibrium and is usually carried out to describe the specificity of a biochemical assay. Fig. 1c displays Equations of the model [17]. The second section is based on the development of a mathematical model to describe the behavior of the bacteria. The stochastic model has been implemented analogously with the Gillespie algorithm: a fixed volume contains a spatially uniform mixture of N chemical species that can interact through specified chemical equilibrium reaction channels. The problem develops in the competition between the free and immobilized glycan epitopes. Indeed, the equilibriums of two chemical reactions can be established between the bacteria and the free and immobilized sugars. In perspective, understanding the decisional ability of E. coli and gaining the tools to control the adhesion on bio-substrates supports progress in the fields of biomedicine, cell culturing, and tissue engineering. It is thought that sugar uptake serves to prevent extinction even if the uptake mechanism is not clear. The exploration of this issue, thus, does not show a clear benefit for this specific form of decision; however, the survey of this investigation is extremely important because it reveals a mechanism of seeding that does not depend on the physiological state of
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the cell. It is possible that the advantage of this form of decision-making is only seen in fluctuating environments, which could be an interesting path for future research.
2. Materials and Methods 2.1.
Materials
Glass slides (25 mm × 50 mm × 1 mm) were kindly provided by Sigma-Aldrich (Germany); Plexiglas© sheets (1 mm thick) were provided by Evonik Rohm GmbH; polyacrylic double-tape (100 m thick) and amine functionalized polystyrene beads (5% v/v, 2.9 m diameter) from Spherotech; 3-aminopropyl trimethoxysilane (APTMS), N-hydroxysuccinimide (NHS), succinic anhydride,
diisopropylcarbodiimide
(DIC),
dimethylformamide
(DMF),
4,7,10-trioxa-1,13-
tridecanediamine diethylene glycol diglycidyl ether and hydrazine monohydrate NH 2NH2*H2O, PBS, NaHCO3, Na2HPO4, and NaH2PO4 were supplied by Sigma-Aldrich and the pGLO™ Bacterial Transformation Kit was provided by Bio-Rad.
2.2.
E. coli and binding
For the experiment, the E. coli bacteria HB101 K-12 strain were used. To express GFP, the strain was transformed with the plasmid pGLO that carries the GFP gene. The modification of the bacteria was done according to the information provided by the supplier (http://www.biorad.com/webroot/web/pdf/lse/literature/1660033.pdf) and developed at the University of Chester (UK). GFP-tagged bacteria applied with arabinose medium emit the fluorescent signal at 485 nm. To modify the E. coli, normal bacteria were treated with a solution of calcium chloride to make them competent. Ampicillin treatment enabled the selection of the fraction of bacteria able to survive. The addition of arabinose sugar to the broth caused RNA polymerase to start transcribing the GFP gene. Before the binding experiment, the E. coli were grown at 37°C for 24 h in plastic tubes (15 mL). Then, the bacteria were suspended in media at the concentrations according to the experimental requirements. The E. coli were spiked in PBS solution, dropped (100 L) on the slides, and incubated at 37°C. The binding of the bacteria on the slides was controlled at different times by analyzing the fluorescence emitted by the E. coli. To count the bacteria, a certain number of pictures using a setup including inverted Olympus microscope connected with CCD Hamamatsu Orca 3 (between 3 and 5 images were captured) of the functionalized slides were captured at fixed times [18, 19]. Imagej software (https://imagej.nih.gov/ij/) was used for the analysis of the pictures. An identical analytic approach was followed for the competitive
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experiments, where solutions with different concentrations of glucose were prepared and used. All incubations were carried out for 3 h.
2.3.
Fabrication of the glucose substrates
A membrane made in Polydimethylsiloxane, PDMS, bearing the microfluidic design and fabricated according to the protocol described in [20] was used to assemble the temporary microfluidic channel and to functionalize the surface in situ. After assembling, a solution of 30% v/v APTMS: methanol was perfused inside the channel and incubated for 4 h at room temperature to deposit primary amine groups onto the surface according to the protocols reported elsewhere [18]. To deposit N-hydroxysuccinimide groups on the surface of the aminecoated glass slides, a solution of succinic anhydride (3%) in DMF was perfused inside the channel and incubated for 3 h. The device was washed with DMF before a solution of DIC (3%) and NHS (3%) in DMF was introduced and allowed to incubate for 3 h. The channel was washed with DMF, and incubated with a solution of 4,7,10-trioxa-1,13-tridecanediamine (3%) with DMF for 3 h, then washed again with DMF. A solution of DIC (3%) and NHS (3%) in DMF was pumped into the channel and incubated for 3 h. After washing with DMF, the devices were dried by purging with argon gas. Hydrazide beads were prepared from primary aminefunctionalized microbeads (NH2, 15–20 meq/g solid). The amine-coated beads were reacted with diethylene glycol diglycidyl ether for 2 h at room temperature in the presence of NaHCO 3 (10 mM, pH 8.3) to form the oxirane beads. The latter were washed in PBS and reacted with 1 mmol NH 2NH2*H2O in 10 mL of 2 N NaOH at 50°C to yield the hydrazide moieties. Finally, the beads were washed five times with Milli-Q water. For the preparation of the biochemical microenvironment, the hydrazide beads in sodium carbonate buffer (NaHCO3, 10 mM, pH 8.3) were manually infused into the microfluidic device and incubated for 3 h at 25°C. During incubation, the hydrazide beads became chemically bound to the NHS groups on the glass surface. Beads that remained in free solution were removed by flushing the channel with PBS at a flow rate of 10 mL/min for 15 min. The hydrazide moieties on the immobilized beads were then used to chemically bind the carbohydrates from solution. Glucose was diluted in printing buffer (0.79 mL of 1 M Na2HPO4, 141.9 g/L, 9.21 mL of 1 M NaH2PO4, 119.8 g/L, and 40 mL glycerol, and then 40 mL of Milli-Q water added to the solution at pH to 5.0 with 10 M phosphoric acid) and incubated in the microfluidic devices for 12 h at 50°C. Following this, a washing buffer (PBS and 0.1% Tween20) was pumped through the channel. A blocking buffer was then incubated in the channel for 30 min before being washed
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out. Once the sample incubation time was elapsed, the membrane and the top layer of the microfluidic channel were removed, in order to facilitate the analysis at the microscope.
2.4.
The biochemical model
The bacterial cells C decide to link to the substrates (denoted as G with subscript S for substrate), or to bind the sugar in bulk (denoted as G for glucose with subscript B for bulk), thus generating the complexes CGS or CGB according to the following reactions (see also Fig. 1c): R1 R2
The reaction R1 is typically described as an adsorption reaction and happens between the bacteria and sugars decorating the substrates; the reaction R2 is an equilibrium established between the suspended bacteria and the glucose-free diluted in bulk. For the reaction R1, the kinetic constants of the direct and inverse reactions are k 1 and k2, respectively, whose ratio k1/k2 yields the adsorption constant KADS. For the reaction R2, the kinetic constants of the direct and inverse reactions are k3 and k4, whose the ratio k3/k4 yields the equilibrium constant KD. Here, the reactions were studied neglecting cell death and the presence of free species (C, G B, and GS) existing between the products of the reactions. Furthermore, the model was developed ignoring the dynamics of the cells once they bind the sugar, so that the characteristic time in consideration includes migration and uptake, but it ignores the growth time. This macroscopic model did not consider the mechanisms taking place at the interface bulk-surface that would need the involvement of other physical forces (i.e. surface tension)
According to these restriction, the kinetics of the reactions have the expressions of Equation (1):
Eq. (1a) Eq. (1b)
where ri is the rate of reaction, ki is association and dissociation rate constants; C and Gi indicate the concentrations. The mass balances of the single species are the following (Equation (2)) [21]:
Eq. (2a)
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Eq. (2b) Eq. (2c) Eq. (2d)
.
2.5.
Eq. (2e)
The stochastic model
In order to describe the model, the Stochastic System Algorithm was implemented according to the following steps: (1) generate random numbers uniformly distributed in (0, 1) range, (2) compute the transition probability from the state i to the state j, and compute the probability of the state space. Furthermore, given the dynamic of the evolution, it is crucial (3) to compute the time when the next transition takes place [12]. In particular, the random numbers are r1, r2, the propensity function is ai (t), while the probability is a dt = probability with reaction takes place, where
∑
( ). The time t+ describes when the next chemical * +. At this time, the j-th reaction takes place and the
algorithm updates the numbers of reactants and products. A loop to iterate n-times the stochastic algorithm was also included in the model, which used a custom code, implemented MATLAB environment (release MATLABR2015a). The model used the parameters detailed and referenced in Table S1. The dynamic state of the system was specified by the composition vector X(t) = (C(t) GS(t) GB(t) CGS(t) CGB(t)), where each component was the number of the species present in the reaction environment at time t. For the elementary reaction mechanisms described above, the propensity functions were computed as the production of stochastic rate constant and the number of distinct reactions available in the current state of the system. The propensity functions for the adsorption reaction were a1 = k1 GS C and a2 = k2 C GS; for the equilibrium reaction, the propensity functions were defined as a3 = k3 GB C and a4 = k4 C GB [22]. Using the vector of the concentrations, as defined above, the numerical strings associated with the direct and inverse reactions were (−1, −1, 1) and (1, 1, −1). The probability was given by the ratio of the propensity function of the single reaction to the total one (ai/atot) and the following events were recorded: (1) no changes over the time of the reaction could take place; (2) the first equilibrium only is established; (3) the second equilibrium only is established; and (4) both equilibriums are established. Combining those conditions, the time
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evolution of the system under consideration is described by the chemical master equation, which provides the probability of the system in the given state at the given time. The master equation for the problem is analysis is the following (Equation (3); see ESI 2): (
)
(
) ( ) (
) ) ) (
)
)(
) (
(
) ) (
(
)
) (
.
( )
( )( (
Eq. (3).
3. Results 3.1.
Competitive experiment
Glucose is a fundamental molecule for the E. coli’s vital functions. In vivo mechanisms linked with this molecule are described by equilibrium reactions and summarized by R1 and R2 (Fig. 1c) [23]. Here, to determine in a head-to-head fashion the equilibrium dissociation constant (KD) related to the reaction R2, a competitive growth environment in the presence of free and immobilized glucose was replicated. For this experiment, a final concentration of 2.5 × 105 cell/mL of E. coli were mixed with glucose rich buffer, at different concentrations ranging between 0.01 M and 0.1 M. A volume of 10 L of E. coli was dropped on the top of the glucose surface and incubated for 3 h inside the microfluidic chamber. After the incubation, the microfluidic chamber was gently washed, the waste collected and analyzed at the fluorescent microscope to count the E. coli free inside; then, the top layer of the chamber and the fluidic membrane were taken off according to the protocol in order to analyze the adherent bacteria. In this environment, during the bacterial mechanism of glucose uptake, the glucose diluted in solution competed with the immobilized glucose ligands, according to the scheme of reactions R1 and R2. During the experiments, to closely mimic the scenario where the microbiome encounters colon tumor development, the concentrations of the glucose immobilized at the surface (0.058 mg mm−2) [18] and of the bacteria in solution were kept constant (2.5 × 105 cell/mL). In opposition, the concentration of the glucose in the solution (GB) was gradually augmented from 0.01 M to 0.1 M. The glucose concentration in tumors, indeed, is often much lower than in normal tissues. The experimental goal was to observe the behavior of the bacteria exposed to the two different concentrations of glucose.
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The results of the investigation are summarized in Fig. 2 and they refer to the formation of E. coli with the free or anchored glucose. Indeed, during the interval of time in consideration, the bacteria cannot form complexes with the free glucose first and with the anchored in a subsequent time. In fact, the kinetic of the latter mechanism becomes too slow, due to the fact that the bacteria have saturated most of the anchor points [24].
The scatter plot in Fig. 2 referred to the inverse of the adherent bacteria versus the inverse of the initial glucose in solution, where the adherent bacteria concentration is associated to the signal of fluorescence expressed by The variation of the concentration of the species in analysis is reported in Fig. S1 ESI. As a result, when increasing the concentration of the glucose diluted in solution, a reduction of the number of the bacteria anchored at the surface was observed. Besides, the dynamics at 0.01 M glucose concentration in solution was more realistic than at 0.1 M. In fact, at 0.1 M, the bacteria behavior could be affected more by the quantity of sugar than by effective decisional fate; so that the 0.1 M of glucose in solution induced the E. coli to uptake preferentially that form of glucose. Conversely, at 0.01 M concentration of glucose in bulk, the bacteria discriminated against the two sugar forms, and according to the recorded results, they decided to bind the glucose at the surface and the number of bacteria binding the sugar at the substrate increased. In conclusion, in an environment deprived of glucose, which closely mimics the tumor environment, the bacteria deal with this situation by remaining anchored at the surface, which ideally could be the gut barrier. Tumor glucose concentrations are frequently 3- to 10-fold lower than in non-transformed tissues. In fact, it has been shown the difference of these values for colon and breast and it shows the differences between normal and tumor tissues [25]. Furthermore, in a wider interpretation of the results, this shift of behavior linked with the concentration of sugar in solution could be one of the causes that induce bacteria to bind and activate the dendritic cells, which, in turn, present antigens to cells that kill the cancer cell. This dynamics could be crucial in explaining the reason why mice treated with microbiome-altered antibiotics display lower and smaller colon tumors than animals with undisturbed microbiome [26]. To complete the analysis, the experimental data were fit with an isotherm Langmuir-like model, displaying the linear form of Equation (4) [27]:
,
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(Eq. 4)
where KD is the equilibrium constant of the reaction R2 and G and GMAX are, respectively, the actual and saturation concentrations of the glucose in solution. The solid line in Fig. 2 shows the linear fit of the experimental data. Using the fitting parameters, the equilibrium constant KD for the glucose–E. coli system is 8 mM−1.
3.2.
Adsorption of bacteria on sugar slides
The real reasons and mechanisms to explain why bacteria decide to uptake one sugar rather than another are unclear, even if this preferential mechanism was observed and described by Warburg [28]. Moreover, a crucial aspect of the decisional mechanism involves the form of the sugar to be assimilated. Above, it has been shown the behavior of the cell in competitive environment and it has been deducted that E. coli behavior depend on concentrations of free glucose in solution. The question is now to understand the mechanism of uptake when only glucose at the surface is available. The protocol used for the preparation of the slides has been widely characterized elsewhere [16]. In particular, a concentration of glucose of 0.058 mg mm−2 of beads was immobilized (a flat surface prepared using the same protocol binds 0.010 mg of glucose mm−2). To study the affinity between the bacteria and the anchored glucose, a volume of 10 L of the E. coli (concentration ranging between 1 and 8 × 105 cell/mL) were incubated inside the microfluidics as described above. After washing to remove the unbound bacteria and peel off of the top layer of the chamber, the bound E. coli were counted (analyzing the UV signal), with the aim to measure the cell surface coverage. The binding between the bacteria and the immobilized glucose is displayed in Figs. 3a and 3b (bright field filter and UV filter at 40×, respectively). First, according to this analysis, the bacteria discriminated between the surface coated with the sugar and preferred to bind the glucose rather than the free substrate (see points ① and ② highlighted in Fig. 3a). The normalized signal, as elaborated by pictures recorded at the UV wavelength, versus the concentration of bacteria is displayed in Fig. 3c. The normalized signal refers to the signal of the actual number of bacteria at the surface to the signal of the maximum number of bacteria (MAX). According to this analysis, in a range of concentrations between 0 and 1.0 × 105 cell/mL, the valueMAX grew slowly and, indeed, a value MAX close to zero was recorded. Starting from a concentration of 1.5 × 105 cell/mL on, the corresponding MAX increased faster and it was roughly 1 when the concentration reached 4.5 × 105 cell/mL. From this concentration on, the curve had a plateau, which was interpreted as the saturation value at the surface. It was interesting to observe that at a concentration of 2.5 × 105 cell/mL, the signal from the sample incubated in glucose environment was three times 13
higher than the signal recorded in lactose (Fig. S2a ESI). Albeit, in general, the curves suggested that the binding affinity of E. coli with the glucose was higher than that recorded for the other sugars, such as galactose and mannose (Fig. S2b ESI). To study the interaction strength between the immobilized carbohydrates and the E. coli via lectins and derive the adsorption constant (KADS), the experimental data were fitted using the Frumkin-like isotherm model. This kinetic model has the form of Equation (5) [29]:
*(
)
[ ]
+
(Eq. 5)
where [C] is the concentration of bacteria in solution, KADS is the adsorption coefficient, is the cell surface coverage as defined above, and a is the Frumkin-like interaction parameter, which displays whether the adsorbing molecules exhibit attractive or repulsive interactions [30, 31]. Being this is an equilibrium, it was characterized by the direct and inverse constant of association, referred as k1 and k2, and the ratio provided KADS. The parameters of the linear fit resulted in a value of the adsorption constant, KADS = (Cell/mL)
-1
(Fig. 3d), with the unit of
measure in agreement with the biological model based on cell adsorption [32].
3.3.
The stochastic model
Based on the observations of the experimental findings and considering that cellular metabolism comprises thousands of biochemical reactions, a significant conclusion was that the cell bacteria decision can be determined by the prevalent biochemical equilibrium. A deterministic approach, aimed to schematize the system, displayed that the number of the free bacteria C decreased during the time of the incubation (Fig. S3A, ESI), whereas the number of complexes formed between the E. coli and the glucose in solution or at the surface, CGB and CGS, respectively, increased. The complex CGB (Fig. S3B, ESI) increased faster than the complex CGS (Fig. S3C, ESI). Plotting the numbers of CGB versus CGS, the graph was located above the main diagonal (Fig. S3D, ESI), as consequence of the fact that the E. coli bacteria preferred to uptake the glucose in solution rather than the glucose at the surface, in accord with the experiments. Unfortunately, the deterministic model did not describe any dependence on glucose concentration, and this lack was interpreted as not full –descriptive model. Furthermore, in a system with a large number of interacting molecules and reactions, the overall macroscopic state of the system is highly unpredictable. As conclusion of those observation, a stochastic algorithm could describe the phenomenon of this system that otherwise would be impossible to predict as it was observed by experimental analysis.
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To determine the outcome of glucose uptake, a stochastic model of the adhesion, using the Gillespie algorithm, was settled. Cellular behavior was simulated over 40 min and the response of the bacteria was recorded every 0.01 s. The results of the numerical analysis are displayed in Fig. 4. Panels a, b, and c of the figure display the Chemical Master Equation of the species in the network: the concentration of the cell bacteria C, of the complexes CG S and CGB versus the time, were reported, respectively. By an analysis of the data, the number of bacteria decreased while the number of both the complexes increased, which is in accord with the experiments and the deterministic algorithm. However, the stochastic algorithm prospected a wider and more significant impact on the understanding of bacterial behavior. Analyzing the results of Fig. 4, the stochastic plot of the number of CGB as functions of time highlighted that after initial transient time, the composition fluctuated around the average value. Furthermore, the number of units of complexes formed with the anchored glucose (CGS) grew faster than that of the complexes formed with the free glucose (CGB). Indeed, after 20 min, the average number of CGS was 50 units against the number of CGB, which was 25 units. The analysis of the first instance of the simulation (see the square embedded in Fig. 4b) highlighted that the formation of the complex CGS at the surface had an evident delay in starting the formation, as if the model could account for a characteristic time required for bacteria to seed and perceive the sugar at the surface. As a consequence, a decisional threshold was identified (the solid line embedded in panels b and c of Fig. 4). The analysis of the threshold event suggested that once 10 CGB were formed (t = 5 min), the velocity of formation of CGB decreased (as provided by the slope of the curves), whereas the complex CGS remained roughly constant over the time of analysis. Changes to the complexes over a short time only denoted the relative order of solution versus substrate preference, but say nothing about the kinetics of these two processes, demonstrating that uptake is not firmly constrained to occur in a specific order. As conclusion of the master equation analysis, the plot of the numbers of CG B versus CGS (Fig. 4d) evidenced first a concave then convex curvature, confirming that in the first minutes of incubation, the E. coli preferred to uptake the free sugar in the medium rather than the glucose on the substrate. Afterwards, the uptake of glucose at the surface became the prevalent mechanism pursued by the bacteria. To the other end, the delay of the cells in binding the glucose, as recorded by the model, could be also interpreted as linked to the behavior emphasized by the experiments that is the GB –dependence. However, how the delay time of the experiments and the concentration of glucose diluted in bulk could be linked has not been
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investigated here; it is just hazarded that in presence of 0.1 M of glucose in solution, the E. coli do not see the surface, so that any possible mechanism can be hidden. According to the stochastic nature of the problem, the appropriate number of independent simulations generated a sample of time courses that were used for the stochastic properties of the system [33]. The results of the product number according to the time are displayed in Figs. 5a and 5b; for the complexes CGS and CGB, the cumulative distributions are shown in Fig. 5c. Other parameters influenced the behavior of the bacteria. For example, it was observed that an increase of the bacteria resized the extent of stochasticity of the problem as the model loses the fluctuations and becomes deterministic. Conversely, changing the concentration of the two forms of the glucose did not affect the system dynamics, but varied the equilibrium of the systems (Fig. S4, ESI).
4. Discussion The adhesion of bacteria to surfaces occurs during the formation of tissues and organs, infections, and biofilms. Advances in medical applications can be influenced by progress in this field as the elucidation of the mechanisms involved in cell adhesion could be crucial for understanding E. coli behavior. In particular, the decision to induce and uptake glucose is relevant for studying the colonization of surfaces by bacteria and for investigating the details of the initial adhesion process, a mechanism that can be crucial understanding the etiology of colon cancer. In this paper, a transient uptake mechanism of glucose and consequent bacteria cell fate were studied.
To tackle the highly specified systems and isolate the effects of detailed structural variations, this complexity was narrowed down to distinct saccharide moieties: the monosaccharides. The decision of the mechanism of glucose uptake concerned both the reactions, the adsorption, and equilibrium. Here, speculations based on the experimental results proved that the bacteria were able to recognize both the free and bound forms of the glucose, and both mechanisms were mediated by recognition receptors, with a discretely high discriminative ability (Figs. 2 and 3).
An analysis of both the experimental and numerical results highlights that during the decisional event, the bacteria do not randomly choose their fate. An energetic process indeed dominates the mechanism of decision; that is, the glucose in solution was at once available to the bacteria and any energetic jump was not demanded using such a form of the sugar. Conversely, in an environment deprived of glucose in solution, the bacteria decide to use the glucose at the
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surface. A deterministic analysis was not able to predict the sensitivity of the bacteria on the sugar concentration. Furthermore, it was not able to predict the time lag of the uptake mechanisms described by the experiments. Indeed, according to the deterministic model, the biochemistry of the system influenced the bacteria uptake. Together with the basic concepts, the lack in describing the real cell behavior motivated a common trend to describe the bacteria choices stochastically instead of deterministically [34]. As such, the importance to explore a stochastic model to describe the mechanism and dynamics of sugar uptake went beyond the accurate description of the experiments. On the other hand, this trend is acquiring specific understanding of bacteria cells fluctuating and dynamic environments [35].
The real reason that makes significant the use of a stochastic model is that it enables to answer the following question: if the biochemistry is not able alone to explain the delay existing between the two mechanisms of uptake, which is the threshold event from where one event is privileged rather than the other as well as the switching? Is it possible to predict and explain the experimental results? Indeed, from one side, the deterministic model does not provide an answer to these questions, to the other side, the experiments provide the real system behavior without explaining the motivations. The stochastic algorithm fills this gap. The result of the model described here shows an intrinsic delay time (Figs. 5a–5c), which was purely due to how cells simultaneously detect the two sugar forms and how they decide the threshold (Fig. 5). The relative deviation from the average, measured by the ratio of the standard deviation of the mean, supported this analysis (Fig. 6). Indeed, this ratio is typically referred to as the coefficient of variation, or noise. The intrinsic noises in the decision-making process did not depend on the parameters of the process and this was a crucial difference with the deterministic algorithm being the intrinsic noise of the system independent of the initial conditions and related with the fluctuations of the biological system. Observing the result reported in Figs. 6a and 6b, the mean (solid lines) and standard deviation (color bands) for the species in the network, respectively, it is evident that the instability of the system in solution is wider than the complex at the surface. The higher fluctuations of the system in solution drives the formed complex to find a more stable dynamic equilibrium and brings the cells to upload the sugar at the surface.
5. Conclusions and outlook
17
In conclusion, the stochastic model produces correctly the kinetics of the systems, displaying the same results of the experimental investigation and finding a reasonable explanation for dynamics of late cell cycle events while neglecting internal cellular pathways. However, the lack of this information has not limited this investigation and it will not limit the development of studies in the future. This model could be expanded to the study of E. coli decision-making and could have a broader impact in health and disease conditions where cell glycan complexes play a role. An important and innovative aspect of this investigation concerns the implementation of the model as the first approach explaining the decisional state of the bacteria when many sources are available. Furthermore, due to the combination of experimental results in the stochastic algorithm, the problem accounted for real-world application. To date, based on the stochastic behavior of the biochemical reactions, which have been shown to play a pivotal role in cell functions, the E. coli decision is crucial for designing new processes mimicking in vivo mechanisms.
Acknowledgments The author is grateful to the technicians of the Department of Chemical Engineering at the University of Chester for supporting in E. Coli culturing and GFP protocol.
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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21
a
c
b
(1). E. coli (2). Gut barrier (3). Mucin-adhesin binding in gut-bacteria interactions (4). Glucose in solution, GB (5). Glucose substrate, GS (6). E. coli-glucose solution, CGB (7). E. coli-glucose substrate, CGS
Fig. 1. A. In vivo mechanism of binding between E. coli and gut receptors. b. Illustration of the experiment. c. Equilibrium reactions characterizing the biochemical system. R1 and R2 refer to the reactions of the E. coli with the glucose anchored to the surface and free glucose, respectively.
22
Fig. 2. Reaction R2. Normalized fluorescent signal versus concentration of free glucose in bulk solution. 1/GB is the inverse of the initial glucose concentration in bulk solution. The Langmuirlike model applied to the competitive experiment based on glucose—the linear solid line— provided the equilibrium constant KD. The correlation values has been estimated to be R2 = 0.98.
23
a
c
b
d
Fig. 3. Reaction R1. a. Bright field of the cell attached to the surface after 3 h incubation. b. UVexcited E. coli with modified pGLO plasmid: ① bead surface; ② beadless surface. Scale Bar: 10 m. c. Normalized fluorescent signal according to the concentration of the cells. d. the Frumkinlike equation right term plotted versus with linear model (solid line). The intercept and slope of the curve provided the 2a and ln KADS parameters, respectively.
24
a
b
c
d
Fig. 4. Stochastic model. Chemical Master Equation solution of the species in the network: a. C; b. GS; c. GB; and d. GB versus GS. The square highlights the delay of the GS formation. The horizontal dotted line represents the threshold. The rectangular inset highlights the delay time at the beginning of the process.
25
a
b
c
Fig. 5. N-loop of the stochastic model. a. Profile of complex number cell-glucose in bulk (CGB). b. Profile of complex number cell-glucose on the substrate (CGS). c. Cumulative distributions of the number of the two complexes CGB and CGS according to the data number.
26
a
b
Fig. 6. Chemical Master Equation solution: mean (solid lines) and standard deviation (color bands) for the species in the network: a. GS; b. GB.
27
S1359-5113(16)30410-X http://dx.doi.org/doi:10.1016/j.procbio.2016.12.007 PRBI 10879
To appear in:
Process Biochemistry
Received date: Revised date: Accepted date:
13-9-2016 14-11-2016 8-12-2016
Please cite this article as: Simone Giuseppina.A glyco-competitive assay to demonstrate the stochasticity of fate decisions in Escherichia coli.Process Biochemistry http://dx.doi.org/10.1016/j.procbio.2016.12.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A glyco-competitive assay to demonstrate the stochasticity of fate decisions in Escherichia coli Giuseppina Simone1 1
Mechanical Engineering, Microsystem, Northwestern Polytechnical University
127 West Youyi Road, Xi’an Shaanxi, 710072, P.R. China Email: [email protected]; Phone : +86 029 88460353 620
1
Abstract Interaction bacteria-gut, via glycan associations, contribute to the selection of microbial communities along the gastrointestinal tract, influencing cancer development. The mechanism causing microbiome alterations is unknown, while this understanding would be pivotal to identify medical therapies. The molecular associations between Escherichia coli bacteria and glucose, both in solution and immobilized at the surface, were studied showing the dependence of E. coli glucose binding on the sugar form. Classical kinetic models were used to derive the reaction equilibrium and adsorption constants, 8 mM−1 and 1 (cell/mL)-1 and to explain the uptake. E. coli preferred the free glucose, whereas in a deprived environment, the anchored glucose became the major source of carbon for the bacteria. A stochastic algorithm disclosed that after initial transient, E. coli privileged the anchored glucose rather than the free sugar, independently on the concentration. The biochemical approach alone failed to describe the effective behavior of the cells and that several parameters can affect the behavior of the bacteria. From this result, more sophisticated models of the destruction of the gut barrier can be derived, such as the mechanism whereby E. coli can switch the immune system on and off to cause cancer and its metastasis.
Keywords: Competitive assay; E. coli; glycomics; stochastics
2
Highlights:
3
E. coli - glucose binding in solution and immobilized at the surface were studied.
Glucose is the major source of carbon for the bacteria in deprived environment.
Reaction equilibrium and adsorption constants were 8 mM−1 and 1 (cell/mL)-1.
Stochastic approach shows failure of biochemistry alone to describe E. coli behavior.
E. coli privileged the anchored glucose after an initial transient.
Graphical abstract In vivo
In vitro
Inflammation of the stomach wall induced by E. coli
Binding mechanism decision by E. coli
4
1. Introduction Gut microbes contribute to cancer cell death. The link between the microbiome and cancer seems to reside in the immune system [1], where microbes can either dial up inflammation or tamp it down and can modulate immune cell vigilance for invaders. It has been shown that inflammatory signals, which induce regulation, are dictated by the composition of the microbiome in the gut. The immune system appears to be at the root of how the microbiome interacts with cancer therapies and it also appears to mediate how bacteria, fungi, and viruses influence cancer development. E. coli are involved in this mechanism [2]. These gram-negative bacteria play an important role in the gut [3], such as underpinning the interaction between bacteria and mucin glycans. The interactions between the bacteria contribute to the selection of microbial communities along and across the gastrointestinal tract. It has been shown that altered glycosylation of the gut barrier can be symptomatic of inflammatory or malignant diseases associated with altered microbiota composition [4–6]. The interaction between the bacteria and glycans situated on the gut barrier (Fig. 1a) occurs via adhesins existing within the bacterial membrane (close up Fig. 1a). The regulation, controlled by a cell surface protein, directs bacteria to gut-associated lymphoid tissues, which suggests that these bacteria shuttle between the gut and spleen. Studies are beginning to explore the structural nature of sugars and adhesins to establish a relationship between different structures and functions and their biological roles [7]. At this point, understanding the mechanism of adhesion between bacteria and glycans becomes pivotal for engineering bacterial behavior. Current knowledge and competencies in micro- and nano-systems can aid research aimed at explaining cellular phenomena connected to bacterial behavior as well as identify potential therapies. Using stochastic models to analyze cell behavior provides a means to decipher the mechanisms according to which bacteria show preference in ambiguous processes. This approach offers a method to control and engineer the behavior and actions in E. coli. Stochasticity is synonymous with randomness [8, 9]. Intrinsic stochasticity is generated by the dynamics of the system from the random timing of individual reactions [10]. Extrinsic stochasticity is generated by the system interacting with other stochastic systems, for example, in the cell or micro-environment. In general, biochemical reactions, which describe the molecular recognition between the bacteria and binding molecules, induce stochasticity through intermolecular collisions. Stochastic models of reactions provide a detailed understanding of the
5
biochemical reactions [11] and are necessary when the biological phenomena observed exhibit fluctuations, e.g., switching between two favorable states of the system. It is worth mentioning that in a deterministic model, the output is strongly dependent on the initial conditions, where changing those conditions will affect the final response of the system; stochastic models possess some inherent randomness, which will be such that the same set of parameter values and initial conditions will lead to different outputs. The living natural world is a typical example buffeted by stochasticity and randomness, which makes it more complicated to model. Competition, as an example of fluctuation, is described by stochastic models, and was introduced and investigated by Gillespie [12]. In biological systems, there are numerous sources of stochasticity, such as heterogeneity of cellular populations [13] and gene regulation [14]. To date, the entire world of small organisms and bio-reactions is best described using stochastic rather than deterministic models [15]. Working from that premise, this study develops through two different methodologies. The first is based on an experimental investigation to determine kinetic parameters and to observe the decisional behavior of the cells. The experimental platform aims to mimic the cellular environment, especially the gut. The scheme of the problem described here is shown in Fig. 1b. Sugar molecules are either available in solution or immobilized (anchored) at the substrate surface. The bacteria can freely decide where and how to uptake and bind to the sugars [16]. This is referred to as competitive inhibition and involves biochemical reactions at equilibrium and is usually carried out to describe the specificity of a biochemical assay. Fig. 1c displays Equations of the model [17]. The second section is based on the development of a mathematical model to describe the behavior of the bacteria. The stochastic model has been implemented analogously with the Gillespie algorithm: a fixed volume contains a spatially uniform mixture of N chemical species that can interact through specified chemical equilibrium reaction channels. The problem develops in the competition between the free and immobilized glycan epitopes. Indeed, the equilibriums of two chemical reactions can be established between the bacteria and the free and immobilized sugars. In perspective, understanding the decisional ability of E. coli and gaining the tools to control the adhesion on bio-substrates supports progress in the fields of biomedicine, cell culturing, and tissue engineering. It is thought that sugar uptake serves to prevent extinction even if the uptake mechanism is not clear. The exploration of this issue, thus, does not show a clear benefit for this specific form of decision; however, the survey of this investigation is extremely important because it reveals a mechanism of seeding that does not depend on the physiological state of
6
the cell. It is possible that the advantage of this form of decision-making is only seen in fluctuating environments, which could be an interesting path for future research.
2. Materials and Methods 2.1.
Materials
Glass slides (25 mm × 50 mm × 1 mm) were kindly provided by Sigma-Aldrich (Germany); Plexiglas© sheets (1 mm thick) were provided by Evonik Rohm GmbH; polyacrylic double-tape (100 m thick) and amine functionalized polystyrene beads (5% v/v, 2.9 m diameter) from Spherotech; 3-aminopropyl trimethoxysilane (APTMS), N-hydroxysuccinimide (NHS), succinic anhydride,
diisopropylcarbodiimide
(DIC),
dimethylformamide
(DMF),
4,7,10-trioxa-1,13-
tridecanediamine diethylene glycol diglycidyl ether and hydrazine monohydrate NH 2NH2*H2O, PBS, NaHCO3, Na2HPO4, and NaH2PO4 were supplied by Sigma-Aldrich and the pGLO™ Bacterial Transformation Kit was provided by Bio-Rad.
2.2.
E. coli and binding
For the experiment, the E. coli bacteria HB101 K-12 strain were used. To express GFP, the strain was transformed with the plasmid pGLO that carries the GFP gene. The modification of the bacteria was done according to the information provided by the supplier (http://www.biorad.com/webroot/web/pdf/lse/literature/1660033.pdf) and developed at the University of Chester (UK). GFP-tagged bacteria applied with arabinose medium emit the fluorescent signal at 485 nm. To modify the E. coli, normal bacteria were treated with a solution of calcium chloride to make them competent. Ampicillin treatment enabled the selection of the fraction of bacteria able to survive. The addition of arabinose sugar to the broth caused RNA polymerase to start transcribing the GFP gene. Before the binding experiment, the E. coli were grown at 37°C for 24 h in plastic tubes (15 mL). Then, the bacteria were suspended in media at the concentrations according to the experimental requirements. The E. coli were spiked in PBS solution, dropped (100 L) on the slides, and incubated at 37°C. The binding of the bacteria on the slides was controlled at different times by analyzing the fluorescence emitted by the E. coli. To count the bacteria, a certain number of pictures using a setup including inverted Olympus microscope connected with CCD Hamamatsu Orca 3 (between 3 and 5 images were captured) of the functionalized slides were captured at fixed times [18, 19]. Imagej software (https://imagej.nih.gov/ij/) was used for the analysis of the pictures. An identical analytic approach was followed for the competitive
7
experiments, where solutions with different concentrations of glucose were prepared and used. All incubations were carried out for 3 h.
2.3.
Fabrication of the glucose substrates
A membrane made in Polydimethylsiloxane, PDMS, bearing the microfluidic design and fabricated according to the protocol described in [20] was used to assemble the temporary microfluidic channel and to functionalize the surface in situ. After assembling, a solution of 30% v/v APTMS: methanol was perfused inside the channel and incubated for 4 h at room temperature to deposit primary amine groups onto the surface according to the protocols reported elsewhere [18]. To deposit N-hydroxysuccinimide groups on the surface of the aminecoated glass slides, a solution of succinic anhydride (3%) in DMF was perfused inside the channel and incubated for 3 h. The device was washed with DMF before a solution of DIC (3%) and NHS (3%) in DMF was introduced and allowed to incubate for 3 h. The channel was washed with DMF, and incubated with a solution of 4,7,10-trioxa-1,13-tridecanediamine (3%) with DMF for 3 h, then washed again with DMF. A solution of DIC (3%) and NHS (3%) in DMF was pumped into the channel and incubated for 3 h. After washing with DMF, the devices were dried by purging with argon gas. Hydrazide beads were prepared from primary aminefunctionalized microbeads (NH2, 15–20 meq/g solid). The amine-coated beads were reacted with diethylene glycol diglycidyl ether for 2 h at room temperature in the presence of NaHCO 3 (10 mM, pH 8.3) to form the oxirane beads. The latter were washed in PBS and reacted with 1 mmol NH 2NH2*H2O in 10 mL of 2 N NaOH at 50°C to yield the hydrazide moieties. Finally, the beads were washed five times with Milli-Q water. For the preparation of the biochemical microenvironment, the hydrazide beads in sodium carbonate buffer (NaHCO3, 10 mM, pH 8.3) were manually infused into the microfluidic device and incubated for 3 h at 25°C. During incubation, the hydrazide beads became chemically bound to the NHS groups on the glass surface. Beads that remained in free solution were removed by flushing the channel with PBS at a flow rate of 10 mL/min for 15 min. The hydrazide moieties on the immobilized beads were then used to chemically bind the carbohydrates from solution. Glucose was diluted in printing buffer (0.79 mL of 1 M Na2HPO4, 141.9 g/L, 9.21 mL of 1 M NaH2PO4, 119.8 g/L, and 40 mL glycerol, and then 40 mL of Milli-Q water added to the solution at pH to 5.0 with 10 M phosphoric acid) and incubated in the microfluidic devices for 12 h at 50°C. Following this, a washing buffer (PBS and 0.1% Tween20) was pumped through the channel. A blocking buffer was then incubated in the channel for 30 min before being washed
8
out. Once the sample incubation time was elapsed, the membrane and the top layer of the microfluidic channel were removed, in order to facilitate the analysis at the microscope.
2.4.
The biochemical model
The bacterial cells C decide to link to the substrates (denoted as G with subscript S for substrate), or to bind the sugar in bulk (denoted as G for glucose with subscript B for bulk), thus generating the complexes CGS or CGB according to the following reactions (see also Fig. 1c): R1 R2
The reaction R1 is typically described as an adsorption reaction and happens between the bacteria and sugars decorating the substrates; the reaction R2 is an equilibrium established between the suspended bacteria and the glucose-free diluted in bulk. For the reaction R1, the kinetic constants of the direct and inverse reactions are k 1 and k2, respectively, whose ratio k1/k2 yields the adsorption constant KADS. For the reaction R2, the kinetic constants of the direct and inverse reactions are k3 and k4, whose the ratio k3/k4 yields the equilibrium constant KD. Here, the reactions were studied neglecting cell death and the presence of free species (C, G B, and GS) existing between the products of the reactions. Furthermore, the model was developed ignoring the dynamics of the cells once they bind the sugar, so that the characteristic time in consideration includes migration and uptake, but it ignores the growth time. This macroscopic model did not consider the mechanisms taking place at the interface bulk-surface that would need the involvement of other physical forces (i.e. surface tension)
According to these restriction, the kinetics of the reactions have the expressions of Equation (1):
Eq. (1a) Eq. (1b)
where ri is the rate of reaction, ki is association and dissociation rate constants; C and Gi indicate the concentrations. The mass balances of the single species are the following (Equation (2)) [21]:
Eq. (2a)
9
Eq. (2b) Eq. (2c) Eq. (2d)
.
2.5.
Eq. (2e)
The stochastic model
In order to describe the model, the Stochastic System Algorithm was implemented according to the following steps: (1) generate random numbers uniformly distributed in (0, 1) range, (2) compute the transition probability from the state i to the state j, and compute the probability of the state space. Furthermore, given the dynamic of the evolution, it is crucial (3) to compute the time when the next transition takes place [12]. In particular, the random numbers are r1, r2, the propensity function is ai (t), while the probability is a dt = probability with reaction takes place, where
∑
( ). The time t+ describes when the next chemical * +. At this time, the j-th reaction takes place and the
algorithm updates the numbers of reactants and products. A loop to iterate n-times the stochastic algorithm was also included in the model, which used a custom code, implemented MATLAB environment (release MATLABR2015a). The model used the parameters detailed and referenced in Table S1. The dynamic state of the system was specified by the composition vector X(t) = (C(t) GS(t) GB(t) CGS(t) CGB(t)), where each component was the number of the species present in the reaction environment at time t. For the elementary reaction mechanisms described above, the propensity functions were computed as the production of stochastic rate constant and the number of distinct reactions available in the current state of the system. The propensity functions for the adsorption reaction were a1 = k1 GS C and a2 = k2 C GS; for the equilibrium reaction, the propensity functions were defined as a3 = k3 GB C and a4 = k4 C GB [22]. Using the vector of the concentrations, as defined above, the numerical strings associated with the direct and inverse reactions were (−1, −1, 1) and (1, 1, −1). The probability was given by the ratio of the propensity function of the single reaction to the total one (ai/atot) and the following events were recorded: (1) no changes over the time of the reaction could take place; (2) the first equilibrium only is established; (3) the second equilibrium only is established; and (4) both equilibriums are established. Combining those conditions, the time
10
evolution of the system under consideration is described by the chemical master equation, which provides the probability of the system in the given state at the given time. The master equation for the problem is analysis is the following (Equation (3); see ESI 2): (
)
(
) ( ) (
) ) ) (
)
)(
) (
(
) ) (
(
)
) (
.
( )
( )( (
Eq. (3).
3. Results 3.1.
Competitive experiment
Glucose is a fundamental molecule for the E. coli’s vital functions. In vivo mechanisms linked with this molecule are described by equilibrium reactions and summarized by R1 and R2 (Fig. 1c) [23]. Here, to determine in a head-to-head fashion the equilibrium dissociation constant (KD) related to the reaction R2, a competitive growth environment in the presence of free and immobilized glucose was replicated. For this experiment, a final concentration of 2.5 × 105 cell/mL of E. coli were mixed with glucose rich buffer, at different concentrations ranging between 0.01 M and 0.1 M. A volume of 10 L of E. coli was dropped on the top of the glucose surface and incubated for 3 h inside the microfluidic chamber. After the incubation, the microfluidic chamber was gently washed, the waste collected and analyzed at the fluorescent microscope to count the E. coli free inside; then, the top layer of the chamber and the fluidic membrane were taken off according to the protocol in order to analyze the adherent bacteria. In this environment, during the bacterial mechanism of glucose uptake, the glucose diluted in solution competed with the immobilized glucose ligands, according to the scheme of reactions R1 and R2. During the experiments, to closely mimic the scenario where the microbiome encounters colon tumor development, the concentrations of the glucose immobilized at the surface (0.058 mg mm−2) [18] and of the bacteria in solution were kept constant (2.5 × 105 cell/mL). In opposition, the concentration of the glucose in the solution (GB) was gradually augmented from 0.01 M to 0.1 M. The glucose concentration in tumors, indeed, is often much lower than in normal tissues. The experimental goal was to observe the behavior of the bacteria exposed to the two different concentrations of glucose.
11
The results of the investigation are summarized in Fig. 2 and they refer to the formation of E. coli with the free or anchored glucose. Indeed, during the interval of time in consideration, the bacteria cannot form complexes with the free glucose first and with the anchored in a subsequent time. In fact, the kinetic of the latter mechanism becomes too slow, due to the fact that the bacteria have saturated most of the anchor points [24].
The scatter plot in Fig. 2 referred to the inverse of the adherent bacteria versus the inverse of the initial glucose in solution, where the adherent bacteria concentration is associated to the signal of fluorescence expressed by The variation of the concentration of the species in analysis is reported in Fig. S1 ESI. As a result, when increasing the concentration of the glucose diluted in solution, a reduction of the number of the bacteria anchored at the surface was observed. Besides, the dynamics at 0.01 M glucose concentration in solution was more realistic than at 0.1 M. In fact, at 0.1 M, the bacteria behavior could be affected more by the quantity of sugar than by effective decisional fate; so that the 0.1 M of glucose in solution induced the E. coli to uptake preferentially that form of glucose. Conversely, at 0.01 M concentration of glucose in bulk, the bacteria discriminated against the two sugar forms, and according to the recorded results, they decided to bind the glucose at the surface and the number of bacteria binding the sugar at the substrate increased. In conclusion, in an environment deprived of glucose, which closely mimics the tumor environment, the bacteria deal with this situation by remaining anchored at the surface, which ideally could be the gut barrier. Tumor glucose concentrations are frequently 3- to 10-fold lower than in non-transformed tissues. In fact, it has been shown the difference of these values for colon and breast and it shows the differences between normal and tumor tissues [25]. Furthermore, in a wider interpretation of the results, this shift of behavior linked with the concentration of sugar in solution could be one of the causes that induce bacteria to bind and activate the dendritic cells, which, in turn, present antigens to cells that kill the cancer cell. This dynamics could be crucial in explaining the reason why mice treated with microbiome-altered antibiotics display lower and smaller colon tumors than animals with undisturbed microbiome [26]. To complete the analysis, the experimental data were fit with an isotherm Langmuir-like model, displaying the linear form of Equation (4) [27]:
,
12
(Eq. 4)
where KD is the equilibrium constant of the reaction R2 and G and GMAX are, respectively, the actual and saturation concentrations of the glucose in solution. The solid line in Fig. 2 shows the linear fit of the experimental data. Using the fitting parameters, the equilibrium constant KD for the glucose–E. coli system is 8 mM−1.
3.2.
Adsorption of bacteria on sugar slides
The real reasons and mechanisms to explain why bacteria decide to uptake one sugar rather than another are unclear, even if this preferential mechanism was observed and described by Warburg [28]. Moreover, a crucial aspect of the decisional mechanism involves the form of the sugar to be assimilated. Above, it has been shown the behavior of the cell in competitive environment and it has been deducted that E. coli behavior depend on concentrations of free glucose in solution. The question is now to understand the mechanism of uptake when only glucose at the surface is available. The protocol used for the preparation of the slides has been widely characterized elsewhere [16]. In particular, a concentration of glucose of 0.058 mg mm−2 of beads was immobilized (a flat surface prepared using the same protocol binds 0.010 mg of glucose mm−2). To study the affinity between the bacteria and the anchored glucose, a volume of 10 L of the E. coli (concentration ranging between 1 and 8 × 105 cell/mL) were incubated inside the microfluidics as described above. After washing to remove the unbound bacteria and peel off of the top layer of the chamber, the bound E. coli were counted (analyzing the UV signal), with the aim to measure the cell surface coverage. The binding between the bacteria and the immobilized glucose is displayed in Figs. 3a and 3b (bright field filter and UV filter at 40×, respectively). First, according to this analysis, the bacteria discriminated between the surface coated with the sugar and preferred to bind the glucose rather than the free substrate (see points ① and ② highlighted in Fig. 3a). The normalized signal, as elaborated by pictures recorded at the UV wavelength, versus the concentration of bacteria is displayed in Fig. 3c. The normalized signal refers to the signal of the actual number of bacteria at the surface to the signal of the maximum number of bacteria (MAX). According to this analysis, in a range of concentrations between 0 and 1.0 × 105 cell/mL, the valueMAX grew slowly and, indeed, a value MAX close to zero was recorded. Starting from a concentration of 1.5 × 105 cell/mL on, the corresponding MAX increased faster and it was roughly 1 when the concentration reached 4.5 × 105 cell/mL. From this concentration on, the curve had a plateau, which was interpreted as the saturation value at the surface. It was interesting to observe that at a concentration of 2.5 × 105 cell/mL, the signal from the sample incubated in glucose environment was three times 13
higher than the signal recorded in lactose (Fig. S2a ESI). Albeit, in general, the curves suggested that the binding affinity of E. coli with the glucose was higher than that recorded for the other sugars, such as galactose and mannose (Fig. S2b ESI). To study the interaction strength between the immobilized carbohydrates and the E. coli via lectins and derive the adsorption constant (KADS), the experimental data were fitted using the Frumkin-like isotherm model. This kinetic model has the form of Equation (5) [29]:
*(
)
[ ]
+
(Eq. 5)
where [C] is the concentration of bacteria in solution, KADS is the adsorption coefficient, is the cell surface coverage as defined above, and a is the Frumkin-like interaction parameter, which displays whether the adsorbing molecules exhibit attractive or repulsive interactions [30, 31]. Being this is an equilibrium, it was characterized by the direct and inverse constant of association, referred as k1 and k2, and the ratio provided KADS. The parameters of the linear fit resulted in a value of the adsorption constant, KADS = (Cell/mL)
-1
(Fig. 3d), with the unit of
measure in agreement with the biological model based on cell adsorption [32].
3.3.
The stochastic model
Based on the observations of the experimental findings and considering that cellular metabolism comprises thousands of biochemical reactions, a significant conclusion was that the cell bacteria decision can be determined by the prevalent biochemical equilibrium. A deterministic approach, aimed to schematize the system, displayed that the number of the free bacteria C decreased during the time of the incubation (Fig. S3A, ESI), whereas the number of complexes formed between the E. coli and the glucose in solution or at the surface, CGB and CGS, respectively, increased. The complex CGB (Fig. S3B, ESI) increased faster than the complex CGS (Fig. S3C, ESI). Plotting the numbers of CGB versus CGS, the graph was located above the main diagonal (Fig. S3D, ESI), as consequence of the fact that the E. coli bacteria preferred to uptake the glucose in solution rather than the glucose at the surface, in accord with the experiments. Unfortunately, the deterministic model did not describe any dependence on glucose concentration, and this lack was interpreted as not full –descriptive model. Furthermore, in a system with a large number of interacting molecules and reactions, the overall macroscopic state of the system is highly unpredictable. As conclusion of those observation, a stochastic algorithm could describe the phenomenon of this system that otherwise would be impossible to predict as it was observed by experimental analysis.
14
To determine the outcome of glucose uptake, a stochastic model of the adhesion, using the Gillespie algorithm, was settled. Cellular behavior was simulated over 40 min and the response of the bacteria was recorded every 0.01 s. The results of the numerical analysis are displayed in Fig. 4. Panels a, b, and c of the figure display the Chemical Master Equation of the species in the network: the concentration of the cell bacteria C, of the complexes CG S and CGB versus the time, were reported, respectively. By an analysis of the data, the number of bacteria decreased while the number of both the complexes increased, which is in accord with the experiments and the deterministic algorithm. However, the stochastic algorithm prospected a wider and more significant impact on the understanding of bacterial behavior. Analyzing the results of Fig. 4, the stochastic plot of the number of CGB as functions of time highlighted that after initial transient time, the composition fluctuated around the average value. Furthermore, the number of units of complexes formed with the anchored glucose (CGS) grew faster than that of the complexes formed with the free glucose (CGB). Indeed, after 20 min, the average number of CGS was 50 units against the number of CGB, which was 25 units. The analysis of the first instance of the simulation (see the square embedded in Fig. 4b) highlighted that the formation of the complex CGS at the surface had an evident delay in starting the formation, as if the model could account for a characteristic time required for bacteria to seed and perceive the sugar at the surface. As a consequence, a decisional threshold was identified (the solid line embedded in panels b and c of Fig. 4). The analysis of the threshold event suggested that once 10 CGB were formed (t = 5 min), the velocity of formation of CGB decreased (as provided by the slope of the curves), whereas the complex CGS remained roughly constant over the time of analysis. Changes to the complexes over a short time only denoted the relative order of solution versus substrate preference, but say nothing about the kinetics of these two processes, demonstrating that uptake is not firmly constrained to occur in a specific order. As conclusion of the master equation analysis, the plot of the numbers of CG B versus CGS (Fig. 4d) evidenced first a concave then convex curvature, confirming that in the first minutes of incubation, the E. coli preferred to uptake the free sugar in the medium rather than the glucose on the substrate. Afterwards, the uptake of glucose at the surface became the prevalent mechanism pursued by the bacteria. To the other end, the delay of the cells in binding the glucose, as recorded by the model, could be also interpreted as linked to the behavior emphasized by the experiments that is the GB –dependence. However, how the delay time of the experiments and the concentration of glucose diluted in bulk could be linked has not been
15
investigated here; it is just hazarded that in presence of 0.1 M of glucose in solution, the E. coli do not see the surface, so that any possible mechanism can be hidden. According to the stochastic nature of the problem, the appropriate number of independent simulations generated a sample of time courses that were used for the stochastic properties of the system [33]. The results of the product number according to the time are displayed in Figs. 5a and 5b; for the complexes CGS and CGB, the cumulative distributions are shown in Fig. 5c. Other parameters influenced the behavior of the bacteria. For example, it was observed that an increase of the bacteria resized the extent of stochasticity of the problem as the model loses the fluctuations and becomes deterministic. Conversely, changing the concentration of the two forms of the glucose did not affect the system dynamics, but varied the equilibrium of the systems (Fig. S4, ESI).
4. Discussion The adhesion of bacteria to surfaces occurs during the formation of tissues and organs, infections, and biofilms. Advances in medical applications can be influenced by progress in this field as the elucidation of the mechanisms involved in cell adhesion could be crucial for understanding E. coli behavior. In particular, the decision to induce and uptake glucose is relevant for studying the colonization of surfaces by bacteria and for investigating the details of the initial adhesion process, a mechanism that can be crucial understanding the etiology of colon cancer. In this paper, a transient uptake mechanism of glucose and consequent bacteria cell fate were studied.
To tackle the highly specified systems and isolate the effects of detailed structural variations, this complexity was narrowed down to distinct saccharide moieties: the monosaccharides. The decision of the mechanism of glucose uptake concerned both the reactions, the adsorption, and equilibrium. Here, speculations based on the experimental results proved that the bacteria were able to recognize both the free and bound forms of the glucose, and both mechanisms were mediated by recognition receptors, with a discretely high discriminative ability (Figs. 2 and 3).
An analysis of both the experimental and numerical results highlights that during the decisional event, the bacteria do not randomly choose their fate. An energetic process indeed dominates the mechanism of decision; that is, the glucose in solution was at once available to the bacteria and any energetic jump was not demanded using such a form of the sugar. Conversely, in an environment deprived of glucose in solution, the bacteria decide to use the glucose at the
16
surface. A deterministic analysis was not able to predict the sensitivity of the bacteria on the sugar concentration. Furthermore, it was not able to predict the time lag of the uptake mechanisms described by the experiments. Indeed, according to the deterministic model, the biochemistry of the system influenced the bacteria uptake. Together with the basic concepts, the lack in describing the real cell behavior motivated a common trend to describe the bacteria choices stochastically instead of deterministically [34]. As such, the importance to explore a stochastic model to describe the mechanism and dynamics of sugar uptake went beyond the accurate description of the experiments. On the other hand, this trend is acquiring specific understanding of bacteria cells fluctuating and dynamic environments [35].
The real reason that makes significant the use of a stochastic model is that it enables to answer the following question: if the biochemistry is not able alone to explain the delay existing between the two mechanisms of uptake, which is the threshold event from where one event is privileged rather than the other as well as the switching? Is it possible to predict and explain the experimental results? Indeed, from one side, the deterministic model does not provide an answer to these questions, to the other side, the experiments provide the real system behavior without explaining the motivations. The stochastic algorithm fills this gap. The result of the model described here shows an intrinsic delay time (Figs. 5a–5c), which was purely due to how cells simultaneously detect the two sugar forms and how they decide the threshold (Fig. 5). The relative deviation from the average, measured by the ratio of the standard deviation of the mean, supported this analysis (Fig. 6). Indeed, this ratio is typically referred to as the coefficient of variation, or noise. The intrinsic noises in the decision-making process did not depend on the parameters of the process and this was a crucial difference with the deterministic algorithm being the intrinsic noise of the system independent of the initial conditions and related with the fluctuations of the biological system. Observing the result reported in Figs. 6a and 6b, the mean (solid lines) and standard deviation (color bands) for the species in the network, respectively, it is evident that the instability of the system in solution is wider than the complex at the surface. The higher fluctuations of the system in solution drives the formed complex to find a more stable dynamic equilibrium and brings the cells to upload the sugar at the surface.
5. Conclusions and outlook
17
In conclusion, the stochastic model produces correctly the kinetics of the systems, displaying the same results of the experimental investigation and finding a reasonable explanation for dynamics of late cell cycle events while neglecting internal cellular pathways. However, the lack of this information has not limited this investigation and it will not limit the development of studies in the future. This model could be expanded to the study of E. coli decision-making and could have a broader impact in health and disease conditions where cell glycan complexes play a role. An important and innovative aspect of this investigation concerns the implementation of the model as the first approach explaining the decisional state of the bacteria when many sources are available. Furthermore, due to the combination of experimental results in the stochastic algorithm, the problem accounted for real-world application. To date, based on the stochastic behavior of the biochemical reactions, which have been shown to play a pivotal role in cell functions, the E. coli decision is crucial for designing new processes mimicking in vivo mechanisms.
Acknowledgments The author is grateful to the technicians of the Department of Chemical Engineering at the University of Chester for supporting in E. Coli culturing and GFP protocol.
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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21
a
c
b
(1). E. coli (2). Gut barrier (3). Mucin-adhesin binding in gut-bacteria interactions (4). Glucose in solution, GB (5). Glucose substrate, GS (6). E. coli-glucose solution, CGB (7). E. coli-glucose substrate, CGS
Fig. 1. A. In vivo mechanism of binding between E. coli and gut receptors. b. Illustration of the experiment. c. Equilibrium reactions characterizing the biochemical system. R1 and R2 refer to the reactions of the E. coli with the glucose anchored to the surface and free glucose, respectively.
22
Fig. 2. Reaction R2. Normalized fluorescent signal versus concentration of free glucose in bulk solution. 1/GB is the inverse of the initial glucose concentration in bulk solution. The Langmuirlike model applied to the competitive experiment based on glucose—the linear solid line— provided the equilibrium constant KD. The correlation values has been estimated to be R2 = 0.98.
23
a
c
b
d
Fig. 3. Reaction R1. a. Bright field of the cell attached to the surface after 3 h incubation. b. UVexcited E. coli with modified pGLO plasmid: ① bead surface; ② beadless surface. Scale Bar: 10 m. c. Normalized fluorescent signal according to the concentration of the cells. d. the Frumkinlike equation right term plotted versus with linear model (solid line). The intercept and slope of the curve provided the 2a and ln KADS parameters, respectively.
24
a
b
c
d
Fig. 4. Stochastic model. Chemical Master Equation solution of the species in the network: a. C; b. GS; c. GB; and d. GB versus GS. The square highlights the delay of the GS formation. The horizontal dotted line represents the threshold. The rectangular inset highlights the delay time at the beginning of the process.
25
a
b
c
Fig. 5. N-loop of the stochastic model. a. Profile of complex number cell-glucose in bulk (CGB). b. Profile of complex number cell-glucose on the substrate (CGS). c. Cumulative distributions of the number of the two complexes CGB and CGS according to the data number.
26
a
b
Fig. 6. Chemical Master Equation solution: mean (solid lines) and standard deviation (color bands) for the species in the network: a. GS; b. GB.
27