A New Rate Law Describing Microbial Respiration

The rate of microbial respiration can be described by a rate law that gives the respiration rate as the product of a rate constant, biomass concentration, and three terms: one describing the kinetics of the electron-donating reaction, one for the kinetics of the electron-accepting reaction, and a thermodynamic term accounting for the energy available in the microbe's environment. The rate law, derived on the basis of chemiosmotic theory and nonlinear thermodynamics, is unique in that it accounts for both forward and reverse fluxes through the electron transport chain. Our analysis demonstrates how a microbe's respiration rate depends on the thermodynamic driving force, i.e., the net difference between the energy available from the environment and energy conserved as ATP. The rate laws commonly applied in microbiology, such as the Monod equation, are specific simplifications of the general law presented. The new rate law is significant because it affords the possibility of extrapolating in a rigorous manner from laboratory experiment to a broad range of natural conditions, including microbial growth where only limited energy is available. The rate law also provides a new explanation of threshold phenomena, which may reflect a thermodynamic equilibrium where the energy released by electron transfer balances that conserved by ADP phosphorylation.     

A new rate law describing microbial respiration

The rate of microbial respiration can be described by a rate law that gives the respiration rate as the product of a rate constant, biomass concentration, and three terms: one describing the kinetics of the electron-donating reaction, one for the kinetics of the electron-accepting reaction, and a thermodynamic term accounting for the energy available in the microbe's environment. The rate law, derived on the basis of chemiosmotic theory and nonlinear thermodynamics, is unique in that it accounts for both forward and reverse fluxes through the electron transport chain. Our analysis demonstrates how a microbe's respiration rate depends on the thermodynamic driving force, i.e., the net difference between the energy available from the environment and energy conserved as ATP. The rate laws commonly applied in microbiology, such as the Monod equation, are specific simplifications of the general law presented. The new rate law is significant because it affords the possibility of extrapolating in a rigorous manner from laboratory experiment to a broad range of natural conditions, including microbial growth where only limited energy is available. The rate law also provides a new explanation of threshold phenomena, which may reflect a thermodynamic equilibrium where the energy released by electron transfer balances that conserved by ADP phosphorylation.     

Thermodynamic and kinetic characterisation of individual haems in multicentre cytochromes c3

The characterisation of individual centres in multihaem proteins is difficult due to the similarities in the redox and spectroscopic properties of the centres. NMR has been used successfully to distinguish redox centres and allow the determination of the microscopic thermodynamic parameters in several multihaem cytochromes c(3) isolated from different sulphate-reducing bacteria. In this article we show that it is also possible to discriminate the kinetic properties of individual centres in multihaem proteins, if the complete microscopic thermodynamic characterisation is available and the system displays fast intramolecular equilibration in the time scale of the kinetic experiment. The deconvolution of the kinetic traces using a model of thermodynamic control provides a reference rate constant for each haem that does not depend on driving force and can be related to structural factors. The thermodynamic characterisation of three tetrahaem cytochromes and their kinetics of reduction by sodium dithionite are reported in this paper. Thermodynamic and kinetic data were fitted simultaneously to a model to obtain microscopic reduction potentials, haem-haem and haem-proton interacting potentials, and reference rate constants for the haems. The kinetic information obtained for these cytochromes and recently published data for other multihaem cytochromes is discussed with respect to the structural factors that determine the reference rates. The accessibility for the reducing agent seems to play an important role in controlling the kinetic rates, although is clearly not the only factor.     

Thermodynamic and kinetic characterisation of individual haems in multicentre cytochromes c3

The characterisation of individual centres in multihaem proteins is difficult due to the similarities in the redox and spectroscopic properties of the centres. NMR has been used successfully to distinguish redox centres and allow the determination of the microscopic thermodynamic parameters in several multihaem cytochromes c₃ isolated from different sulphate-reducing bacteria. In this article we show that it is also possible to discriminate the kinetic properties of individual centres in multihaem proteins, if the complete microscopic thermodynamic characterisation is available and the system displays fast intramolecular equilibration in the time scale of the kinetic experiment. The deconvolution of the kinetic traces using a model of thermodynamic control provides a reference rate constant for each haem that does not depend on driving force and can be related to structural factors. The thermodynamic characterisation of three tetrahaem cytochromes and their kinetics of reduction by sodium dithionite are reported in this paper. Thermodynamic and kinetic data were fitted simultaneously to a model to obtain microscopic reduction potentials, haem-haem and haem-proton interacting potentials, and reference rate constants for the haems. The kinetic information obtained for these cytochromes and recently published data for other multihaem cytochromes is discussed with respect to the structural factors that determine the reference rates. The accessibility for the reducing agent seems to play an important role in controlling the kinetic rates, although is clearly not the only factor.     

A dual-substrate steady-state model for biological hydrogen production in an anaerobic hydrogen fermentation process

Biological hydrogen production from anaerobic waste fermentation possesses potential benefits in simultaneously reducing organic wastes and generating sustainable energy sources. Three kinetic-based steady-state models for anaerobic fermentation of multiple substrates, including glucose and peptone, were evaluated. Experimental results obtained from a continuous stirred tank reactor (CSTR) were primarily used for model evaluation. The dual-substrate steady-state model developed and the associated kinetic parameters estimated in this study successfully described the anaerobic growth of hydrogen-producing bacteria. The model was able to capture the general trends of consumption of substrates and accumulation of products, including formate, acetate, butyrate, and hydrogen, at dilution rates (D) between 0.06 and 0.69/h. According to the model, the adverse effects of endogeneous and peptone metabolism on net hydrogen production can be minimized by increasing D. For the operational conditions of D > 0.69/h, however, substantial washout of hydrogen-producing bacteria from the CSTR was observed, and it resulted in a rapid drop in hydrogen production rate as well.     

A modified metabolic model for mixed culture fermentation with energy conserving electron bifurcation reaction and metabolite transport energy

A modified metabolic model for mixed culture fermentation (MCF) is proposed with the consideration of an energy conserving electron bifurcation reaction and the transport energy of metabolites. The production of H₂ related to NADH/NAD⁺ and Fdred/Fdox is proposed to be divided in three processes in view of energy conserving electron bifurcation reaction. This assumption could fine‐tune the intracellular redox balance and regulate the distribution of metabolites. With respect to metabolite transport energy, the proton motive force is considered to be constant, while the transport rate coefficient is proposed to be proportional to the octanol–water partition coefficient. The modeling results for a glucose fermentation in a continuous stirred tank reactor show that the metabolite distribution is consistent with the literature: (1) acetate, butyrate, and ethanol are main products at acidic pH, while the production shifts to acetate and propionate at neutral and alkali pH; (2) the main products acetate, ethanol, and butyrate shift to ethanol at higher glucose concentration; (3) the changes for acetate and butyrate are following an increasing hydrogen partial pressure. The findings demonstrate that our modified model is more realistic than previous proposed model concepts. It also indicates that inclusion of an energy conserving electron bifurcation reaction and metabolite transport energy for MCF is sound in the viewpoint of biochemistry and physiology. Biotechnol. Bioeng. 2013; 110: 1884–1894. © 2013 Wiley Periodicals, Inc.     

A combined kinetic push and thermodynamic pull as driving forces for outer membrane protein sorting and folding in bacteria

In vitro folding studies of outer membrane beta-barrels have been invaluable in revealing the lipid effects on folding rates and efficiencies as well as folding free energies. Here, the biophysical results are summarized, and these kinetic and thermodynamic findings are considered in terms of the requirements for folding in the context of the cellular environment. Because the periplasm lacks an external energy source the only driving forces for sorting and folding available within this compartment are binding or folding free energies and their associated rates. These values define functions for periplasmic chaperones and suggest a biophysical mechanism for the BAM complex.     

Thermodynamics of microbial growth and metabolism: an analysis of the current situation

This paper attempts to review in how far thermodynamic analysis can be used to understand and predict the performance of microorganisms with respect to growth and bio-product synthesis. In the first part, a simple thermodynamic model of microbial growth is developed which explains the relationship between the driving force for growth in terms of Gibbs energy dissipation and biomass yield. From the currently available literature, it appears that the Gibbs energy dissipation per C-mol of biomass grown, which represents the driving force for chemotrophic growth, may have been adapted by evolutionary processes to strike a reasonable compromise between metabolic rate and growth efficiency. Based on empirical correlations of the C-molar Gibbs energy dissipation, the wide variety of biomass yields observed in nature can be explained and roughly predicted. This type of analysis may be highly useful in environmental applications, where such wide variations occur. It is however not able to predict biomass yields in very complex systems such as mammalian cells nor is it able to predict or to assess bio-product or recombinant protein yields. For this purpose, a much more sophisticated treatment that accounts for individual metabolic pathways separately is required. Based on glycolysis as a test example, it is shown in the last part that simple thermodynamic analysis leads to erroneous conclusions even in well-known, simple cases. Potential sources for errors have been analyzed and can be used to identify the most important needs for future research.     

Effects of hydrogen and formate on the degradation of propionate and butyrate in thermophilic granules from an upflow anaerobic sludge blanket reactor.

Degradation of propionate and butyrate in whole and disintegrated granules from a thermophilic (55 degrees C) upflow anaerobic sludge blanket reactor fed with acetate, propionate, and butyrate as substrates was examined. The propionate and butyrate degradation rates in whole granules were 1.16 and 4.0 mumol/min/g of volatile solids, respectively, and the rates decreased 35 and 25%, respectively, after disintegration of the granules. The effect of adding different hydrogen-oxidizing bacteria (both sulfate reducers and methanogens), some of which used formate in addition to hydrogen, to disintegrated granules was tested. Addition of either Methanobacterium thermoautotrophicum delta H, a hydrogen-utilizing methanogen that does not use formate, or Methanobacterium sp. strain CB12, a hydrogen- and formate-utilizing methanogen, to disintegrated granules increased the degradation rate of both propionate and butyrate. Furthermore, addition of a thermophilic sulfate-reducing bacterium (a Desulfotomaculum sp. isolated in our laboratory) to disintegrated granules improved the degradation of both substrates even more than the addition of methanogens. By monitoring the hydrogen partial pressure in the cultures, a correlation between the hydrogen partial pressure and the degradation rate of propionate and butyrate was observed, showing a decrease in the degradation rate with increased hydrogen partial pressure. No significant differences in the stimulation of the degradation rates were observed when the disintegrated granules were supplied with methanogens that utilized hydrogen only or hydrogen and formate. This indicated that interspecies formate transfer was not important for stimulation of propionate and butyrate degradation.     

Binding of an RNA aptamer and a partial peptide of a prion protein: crucial importance of water entropy in molecular recognition

It is a central issue to elucidate the new type of molecular recognition accompanied by a global structural change of a molecule upon binding to its targets. Here we investigate the driving force for the binding of R12 (a ribonucleic acid aptamer) and P16 (a partial peptide of a prion protein) during which P16 exhibits the global structural change. We calculate changes in thermodynamic quantities upon the R12–P16 binding using a statistical-mechanical approach combined with molecular models for water which is currently best suited to studies on hydration of biomolecules. The binding is driven by a water-entropy gain originating primarily from an increase in the total volume available to the translational displacement of water molecules in the system. The energy decrease due to the gain of R12–P16 attractive (van der Waals and electrostatic) interactions is almost canceled out by the energy increase related to the loss of R12–water and P16–water attractive interactions. We can explain the general experimental result that stacking of flat moieties, hydrogen bonding and molecular-shape and electrostatic complementarities are frequently observed in the complexes. It is argued that the water-entropy gain is largely influenced by the geometric characteristics (overall shapes, sizes and detailed polyatomic structures) of the biomolecules.     

Modeling product formation in anaerobic mixed culture fermentations

The anaerobic conversion of organic matter to fermentation products is an important biotechnological process. The prediction of the fermentation products is until now a complicated issue for mixed cultures. A modeling approach is presented here as an effort to develop a methodology for modeling fermentative mixed culture systems. To illustrate this methodology, a steady-state metabolic model was developed for prediction of product formation in mixed culture fermentations as a function of the environmental conditions. The model predicts product formation from glucose as a function of the hydrogen partial pressure (P(H2)), reactor pH, and substrate concentration. The model treats the mixed culture as a single virtual microorganism catalyzing the most common fermentative pathways, producing ethanol, acetate, propionate, butyrate, lactate, hydrogen, carbon dioxide, and biomass. The product spectrum is obtained by maximizing the biomass growth yield which is limited by catabolic energy production. The optimization is constrained by mass balances and thermodynamics of the bioreactions involved. Energetic implications of concentration gradients across the cytoplasmic membrane are considered and transport processes are associated with metabolic energy exchange to model the pH effect. Preliminary results confirmed qualitatively the anticipated behavior of the system at variable pH and P(H2) values. A shift from acetate to butyrate as main product when either P(H2) increases and/or pH decreases is predicted as well as ethanol formation at lower pH values. Future work aims at extension of the model and structural validation with experimental data.     

Changes in product formation and bacterial community by dilution rate on carbohydrate fermentation by methanogenic microflora in continuous flow stirred tank reactor

Changes in product formation during carbohydrate fermentation by anaerobic microflora in a continuous flow stirred tank reactor were investigated with respect to the dilution rate in the reactor. In the fermentation by methanogenic microflora, stable methane fermentation, producing methane and carbon dioxide, was observed at relatively low dilution rates (less than 0.33 d(-1) on glucose and 0.20 d(-1) on cellulose). Decomposition of cellulose in the medium was a rate-limiting step in the reaction, because glucose was easily consumed at all applied dilution rates (0.07-4.81 d(-1)). Intermediate metabolites of methane fermentation, such as lactate, ethanol, acetate, butyrate, formate, hydrogen, and carbon dioxide, were accumulated as dilution rate increased. Maximum yield of hydrogen was obtained at 4.81 d(-1) of dilution rate (0.1 mol/mol glucose on glucose or 0.7 mol/mol hexose on cellulose). Lactate was the major product on glucose (1.2 mol/mol glucose), whereas ethanol was predominant on cellulose (0.7 mol/mol hexose). An analysis by denaturing gradient gel electrophoresis (DGGE) of PCR-amplified bacterial 16S rDNA of the microflora indicated that changes in the microbial community took place at various dilution rates, and these changes appeared to correspond to the changes in product distributions. Sequence analyses of the DGGE fragments revealed the probable major population of the microflora. A band closely related to the microorganisms of thermophilic anaerobic bacteria was detected with strong intensity on both glucose and cellulose. Differences in the production yield of hydrogen could have been caused by different populations of microorganisms in each microflora. In the case of cellulose, increasing the dilution rate brought about an accumulation of microorganisms related to Clostridia species that have cellulolytic activity, this being in accordance with the notion of cellulose decomposition being the rate-limiting reaction.     

Kinetics of consumption of fermentation products by anode-respiring bacteria

We determined the kinetic response of a community of anode-respiring bacteria oxidizing a mixture of the most common fermentation products: acetate, butyrate, propionate, ethanol, and hydrogen. We acclimated the community by performing three consecutive batch experiments in a microbial electrolytic cell (MEC) containing a mixture of the fermentation products. During the consecutive-batch experiments, the coulombic efficiency and start-up period improved with each step. We used the acclimated biofilm to start continuous experiments in an MEC, in which we controlled the anode potential using a potentiostat. During the continuous experiments, we tested each individual substrate at a range of anode potentials and substrate concentrations. Our results show low current densities for butyrate and hydrogen, but high current densities for propionate, acetate, and ethanol (maximum values are 1.6, 9.0, and 8.2 A/m², respectively). Acetate showed a high coulombic efficiency (86%) compared to ethanol and propionate (49 and 41%, respectively). High methane concentrations inside the MEC during ethanol experiments suggest that methanogenesis is one reason why the coulombic efficiency was lower than that of acetate. Our results provide kinetic parameters, such as the anode overpotential, the maximum current density, and the Monod half-saturation constant, that are needed for model development when using a mixture of fermentation products. When we provided no electron donor, we measured current due to endogenous decay of biomass (~0.07 A/m²) and an open-cell potential (−0.54 V vs Ag/AgCl) associated with biomass components active in endogenous respiration. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Reducing intrinsic biochemical noise in cells and its thermodynamic limit

In living cells, the specificity of biomolecular recognition can be amplified and the noise from non-specific interactions can be reduced at the expense of cellular free energy. This is the seminal idea in the Hopfield-Ninio theory of kinetic proofreading: The specificity is increased via cyclic network kinetics without altering molecular structures and equilibrium affinites. We show a thermodynamic limit of the specificity amplification with a given amount of available free energy. For a normal cell under physiological condition with sustained phosphorylation potential, this gives a factor of 10(10) as the upper bound in specificity amplification. We also study an optimal kinetic network design that is capable of approaching the thermodynamic limit.     

Geomicrobial Kinetics: Extrapolating Laboratory Studies to Natural Environments

Predicting metabolic rates and population sizes of microorganisms in natural environments is a central problem in geomicrobiology. Such predictions can be made on the basis of a thermodynamically consistent rate law that accounts for both kinetic and thermodynamic controls on microbial metabolism. Application of the rate law requires kinetic and growth parameters, the values of which have been determined for pure and mixed cultures growing in laboratory reactors. However, not all parameter values derived from laboratory studies can be validly applied to the environment. This article illustrates a best-choice approach for extrapolating experimentally-derived parameter values to natural environments, using microbial sulfate reduction coupled to acetate oxidation as an example. We compiled kinetic and growth parameters determined by previous laboratory studies and evaluated their applicability to natural environments. Our results suggest that some parameters, such as rate constants and maximum growth yields, can be applied directly to the environment; others, such as half-saturation constants and specific maintenance rates, are best determined using samples recovered from the environment of interest. The best-choice parameter values were applied to simulation of acetotrophic sulfate reduction in the sediments of a freshwater lake. Our analysis shows that the best-choice approach reduces the tasks of parameter fitting and simplifies the modeling exercise. The proposed approach also ensures that parameters in use are consistent with the physiology of indigenous microorganisms, and relevant to the environment of interest.     

The Non-Equilibrium Thermodynamics and Kinetics of Focal Adhesion Dynamics

Background

We consider a focal adhesion to be made up of molecular complexes, each consisting of a ligand, an integrin molecule, and associated plaque proteins. Free energy changes drive the binding and unbinding of these complexes and thereby controls the focal adhesion''s dynamic modes of growth, treadmilling and resorption.

Principal Findings

We have identified a competition among four thermodynamic driving forces for focal adhesion dynamics: (i) the work done during the addition of a single molecular complex of a certain size, (ii) the chemical free energy change associated with the addition of a molecular complex, (iii) the elastic free energy change associated with deformation of focal adhesions and the cell membrane, and (iv) the work done on a molecular conformational change. We have developed a theoretical treatment of focal adhesion dynamics as a nonlinear rate process governed by a classical kinetic model. We also express the rates as being driven by out-of-equilibrium thermodynamic driving forces, and modulated by kinetics. The mechanisms governed by the above four effects allow focal adhesions to exhibit a rich variety of behavior without the need to introduce special constitutive assumptions for their response. For the reaction-limited case growth, treadmilling and resorption are all predicted by a very simple chemo-mechanical model. Treadmilling requires symmetry breaking between the ends of the focal adhesion, and is achieved by driving force (i) above. In contrast, depending on its numerical value (ii) causes symmetric growth, resorption or is neutral, (iii) causes symmetric resorption, and (iv) causes symmetric growth. These findings hold for a range of conditions: temporally-constant force or stress, and for spatially-uniform and non-uniform stress distribution over the FA. The symmetric growth mode dominates for temporally-constant stress, with a reduced treadmilling regime.

Significance

In addition to explaining focal adhesion dynamics, this treatment can be coupled with models of cytoskeleton dynamics and contribute to the understanding of cell motility.     

Transepithelial transport and intraepithelial metabolism of short-chain fatty acids (SCFA) in the porcine proximal colon are influenced by SCFA concentration and luminal pH

Short-chain fatty acids (SCFA) are end products of bacterial fermentation in the colon and cecum of monogastric animals. As SCFA serve as relevant energy suppliers for colonocytes and various tissues, it is important to reveal fundamental mechanistic characteristics of their transepithelial transport subjected to transient variations of fermentations rates. We performed Ussing chamber studies with porcine (Sus scrofa) colon epithelium under physiological conditions and examined individual mucosal disappearance, metabolized loss, tissue concentrations and serosal release of acetate, propionate and butyrate by gas chromatography. Reduction of initial SCFA concentrations from 80 to 40 mmol/L resulted in diminished absolute flux rates, but the relative proportions of mucosal disappearance and intracellular metabolization of individual SCFA were slightly enhanced. Simulation of high fermentation rates by lowering the mucosal pH induced an increase in mucosal disappearance and serosal release of all SCFA, while their tissue contents trended to lower levels. With respect to the metabolization at lowered pH we found increased acetate concentrations and a decrease of propionate and butyrate. Our data indicate that the colon epithelium possesses a high adaptive capacity to ensure its energetic maintenance under various intraluminal fermentation rates by utilizing the unique features of individual SCFA as energy sources.     

Alanine as an end product during fermentation of monosaccharides byClostridium strain P2

The thermophilicClostridium P2 was isolated from a semi-continuously fed reactor with high ammonium concentration. This bacterium formed substantial amounts of L-alanine as a major fermentation product from glucose, fructose and mannose. Low amounts of acetate, butyrate, carbon dioxide and hydrogen were also formed. A high partial pressure of hydrogen inhibited the degradation of the monosaccharides, whereas hydrogen removal, in the form of methanogenesis was found to be stimulatory. However, the amount of alanine produced per mole of hexose degraded did not change. Hexose degradation and alanine production were favoured by high ammonium concentrations. Nuclear magnetic resonance spectroscopy studies provided strong evidence that an active Embden-Meyerhof-Parnas pathway existed and that alanine was produced via an amination of pyruvate.