Control of hydrogen partial pressures on the rates of syntrophic microbial metabolisms: a kinetic model for butyrate fermentation

A new model describing the rate of syntrophic butyrate fermentation is constructed based on a thermodynamically consistent rate law and the metabolic pathway. This model takes into account the mechanism of reverse electron transfer and proposes that the net amount of energy saved by microorganisms as ATP depends on hydrogen partial pressures in the environment. Hydrogen partial pressures thus control not only the energy available in the environment but also the energy conserved by microorganisms. This new model predicts the rates of butyrate fermentation as a product of a kinetic factor and a thermodynamic potential factor: the kinetic factor describes how butyrate concentration controls the rates; the thermodynamic factor accounts for how the thermodynamic driving force controls the rates. Increases in hydrogen partial pressures decrease the energy available, lowering the driving force and fermentation rates. To maintain butyrate fermentation at significant rates, microorganisms decrease the amount of energy conserved, maximizing the driving force. Application of the new model demonstrates that the thermodynamic driving force is a dominant factor in controlling the rates of butyrate fermentation.     

Run-to-run fed-batch optimization for protein production using recombinant Escherichia coli

A two-phase design approach is introduced to determine the optimal feed rate, fed glucose concentration and fermentation time to maximize protein productivity using recombinant Escherichia coli BL21 (pBAW2) strain. The first phase is applied to determine a primary S-system kinetic model using batch time-series data. Two runs were carried out in the second phase to achieve the maximum protein productivity for the fed-batch fermentation process. The computational results using the S-system kinetic model obtained from the second run are in better agreement with the experiments than those using the kinetic model obtained from batch time-series data. For cross-validation, two extra fed-batch experiments with different feed strategies were carried out for comparison with the optimal fed-batch result. From the experimental results, this approach could improve productivity by at least 3%.     

Mass balance and thermodynamic description of solid state fermentation of lignocellulosics byPleurotus ostreatus for animal feed production

This study was focused primarily on the degradation of lignin in water hyacinth and barley straw for animal-feed production. The experiment was performed in a 1.5-L Applikon fermenter for 30 days, varying the air flow rate from 0.022 VVM/0.047 VMM to 0.048 VVM/0.102 VMM. A novel approach was introduced for prediction of a kinetic model by using instantaneous respiratory quotient (RQ) measurements and steady state elemental balances. Growth kinetics were determined for the fungus in a 30-day fermentation with a mixture of barley straw and water hyacinth as the substrate. The instantaneous heat-interaction profile was predicted from steady state balances. Fermentation data were checked for consistency using the entropy balance inequality, and thermodynamic efficiency was calculated to show that degradation of lignocellulosics byPleurotus ostreatus followed more than one metabolic pathway during the course of the fermentation. Growth ofP. ostreatus on lignocellulosics, such as water hyacinth and barley straw, was di-auxic or possibly tri-auxic during the 30 days of fermentation.     

From nonequilibrium thermodynamics to nonlinear dynamics

Differences between the thermodynamic and kinetic approaches were discussed by using a system with two or more different steady states as an example. It was shown that the behavior of such systems can be described adequately by the kinetic approach only.     

Non-equilibrium thermodynamics of temporally oscillating chemical reactions.

Two thermodynamic quantities are introduced: the entropy change due to a variation of chemical affinity from a steady, state. to some other state and the corresponding entropy production. The entropy change is always negative definite except at the steady state and is capable of being a Liapunov function. The phase-plane behaviour of the entropy production along the trajectory generated by kinetic equations is investigated in connection with the stability of steady state. The examples taken on that occasion are the Volterra-Lotka and Prigogine-Lefever models. The non-equilibrium thermodynamic properties common to the oscillating reactions in two-variable system are in general considered with an emphasis on the thermodynamic analysis for the direction of rotation of the trajectory generated by the two-variable kinetic equations.     

Horseradish peroxidase catalyzed hydroxylation of phenol: II. Kinetic model

A numeric kinetic model of the horseradish peroxidase catalyzed hydroxylation of phenol is proposed to complete the previous thermodynamic analysis. As previously stated, the basic role of HRP is to catalyze the production of DHF* radicals. These further form hydroxyl radicals that hydroxylate phenol via noncatalyzed reactions. The transient differential equations of the model are solved numerically. Several kinetic constants are adjusted to fit basic experimental data. This set of values is then kept constant to simulate additive experiments carried out under different conditions. Predictions of the model concerning the effects of HRP concentration, temperature variation, and presence of catalase and superoxide dismutase are consistent with the experimental results. The quantitative kinetic approach consequently fully confirmed the previous thermodynamic conclusions.     

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.     

Kinetic and thermodynamic aspects of lipid translocation in biological membranes

A theoretical analysis of the lipid translocation in cellular bilayer membranes is presented. We focus on an integrative model of active and passive transport processes determining the asymmetrical distribution of the major lipid components between the monolayers. The active translocation of the aminophospholipids phosphatidylserine and phosphatidylethanolamine is mathematically described by kinetic equations resulting from a realistic ATP-dependent transport mechanism. Concerning the passive transport of the aminophospholipids as well as of phosphatidylcholine, sphingomyelin, and cholesterol, two different approaches are used. The first treatment makes use of thermodynamic flux-force relationships. Relevant forces are transversal concentration differences of the lipids as well as differences in the mechanical states of the monolayers due to lateral compressions. Both forces, originating primarily from the operation of an aminophospholipid translocase, are expressed as functions of the lipid compositions of the two monolayers. In the case of mechanical forces, lipid-specific parameters such as different molecular surface areas and compression force constants are taken into account. Using invariance principles, it is shown how the phenomenological coefficients depend on the total lipid amounts. In a second approach, passive transport is analyzed in terms of kinetic mechanisms of carrier-mediated translocation, where mechanical effects are incorporated into the translocation rate constants. The thermodynamic as well as the kinetic approach are applied to simulate the time-dependent redistribution of the lipid components in human red blood cells. In the thermodynamic model the steady-state asymmetrical lipid distribution of erythrocyte membranes is simulated well under certain parameter restrictions: 1) the time scales of uncoupled passive transbilayer movement must be different among the lipid species; 2) positive cross-couplings of the passive lipid fluxes are needed, which, however, may be chosen lipid-unspecifically. A comparison of the thermodynamic and the kinetic approaches reveals that antiport mechanisms for passive lipid movements may be excluded. Simulations with kinetic symport mechanisms are in qualitative agreement with experimental data but show discrepancies in the asymmetrical distribution for sphingomyelin.     

A prediction of mRNA hybridization kinetics based on polypeptide abundances

An oscillating chemical reaction dealt with in this paper is the Brusselator, which is capable of generating a limit cycle oscillation beyond instability point. The rate equations of this reaction scheme are solved by two-time scale method. An evolution criterion is derived for the limit cycle to first order approximation. The time average of entropy change over the period of the limit cycle takes a definite negative value, which is dependent not on the initial conditions but on the external parameters bringing the kinetic behaviour of the system under control. It can be expressed as the product of two quantities. The first, which is kinetic in character, is the areal velocity of the limit cycle. The second, which is thermodynamic in character, is the rotation of anti-symmetric flow with respect to thermodynamic force. It is shown that the latter is equivalent to the irreversible circulation of fluctuation.     

General theoretical approach to the thermodynamic and kinetic properties of cooperative intramolecular transformations of linear biopolymers

A general method to calculate experimentally accessible thermodynamic and kinetic quantities for any type of cooperative transitions is developed. Special attention has been directed to transition curves and mean relaxation times. The procedure is applied to the most general case of nearest-neighbor cooperativity by using the linear Ising model and the matrix method of evaluation. The various potential types of end effects arid the resulting chain length dependences are discussed in detail. The significance of the theory with respect to the helix-coil transition of polypeptides as well as to the polyproline I-II transition is indicated.     

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.     

Dimer-monomer conformational equilibrium of gramicidin A in 1-alkanols as studied by h.p.l.c. and fluorescence spectroscopy

High performance size-exclusion chromatograph (HPSEC) has been successfully used to characterized the dimer-monomer conformational equilibrium of gramicidin A (GA) in a series of 1-alkanols, from methanol to 1-pentanol. The chromatographic methodology proposed has allowed a rapid and accurate determination of kinetic and thermodynamic constants in the different alcohols assayed. The validity of this chromatographic approach has been tested by comparing the values of the kinetic and thermodynamic constants obtained with those reported in the literature deduced from spectroscopic techniques. Taking advantage of the chromatographic results, the differential fluorescent features of the monomer relative to the dimer have been investigated in terms of the quantum yields ratio of the individual species, as a function of solvent polarity. Finally, the possibility of applying this HPSEC approach to the study of other auto-associating polypeptides and of GA incorporated in liposomes is also considered.     

Dynamic modeling and analyses of simultaneous saccharification and fermentation process to produce bio-ethanol from rice straw

The rice straw, an agricultural waste from Asians’ main provision, was collected as feedstock to convert cellulose into ethanol through the enzymatic hydrolysis and followed by the fermentation process. When the two process steps are performed sequentially, it is referred to as separate hydrolysis and fermentation (SHF). The steps can also be performed simultaneously, i.e., simultaneous saccharification and fermentation (SSF). In this research, the kinetic model parameters of the cellulose saccharification process step using the rice straw as feedstock is obtained from real experimental data of cellulase hydrolysis. Furthermore, this model can be combined with a fermentation model at high glucose and ethanol concentrations to form a SSF model. The fermentation model is based on cybernetic approach from a paper in the literature with an extension of including both the glucose and ethanol inhibition terms to approach more to the actual plants. Dynamic effects of the operating variables in the enzymatic hydrolysis and the fermentation models will be analyzed. The operation of the SSF process will be compared to the SHF process. It is shown that the SSF process is better in reducing the processing time when the product (ethanol) concentration is high. The means to improve the productivity of the overall SSF process, by properly using aeration during the batch operation will also be discussed.     

Sequence-based prediction of protein solubility

In order to investigate the relationship between the thermodynamics and kinetics of protein aggregation, we compared the solubility of proteins with their aggregation rates. We found a significant correlation between these two quantities by considering a database of protein solubility values measured using an in vitro reconstituted translation system containing about 70% of Escherichia coli proteins. The existence of such correlation suggests that the thermodynamic stability of the native states of proteins relative to the aggregate states is closely linked with the kinetic barriers that separate them. In order to create the possibility of conducting computational studies at the proteome level to investigate further this concept, we developed a method of predicting the solubility of proteins based on their physicochemical properties.     

Thermal stability of proteins in intermolecular complexes.

A general phenomenological model is proposed for the estimation of the influence of the formation of complexes with ligands on thermal stability of proteins. In this model the reversible processes of unfolding-refolding and of association-dissociation of protein-ligand complexes and of the irreversible chemical degradation of the unfolded protein were analyzed jointly. By using certain approximations, the analytical expressions for both the thermodynamic and kinetic stabilization are obtained. Two thermodynamic and four kinetic regimes of stabilization and destabilization can exist in such system. Each thermodynamic regime appears to be compatible with three different kinetic regimes. The effect of the formation of complexes on thermodynamic and kinetic stability of the protein is determined by the degrees of binding of the ligand to the folded and unfolded protein species and by the rates of irreversible degradation of free protein and protein in complex.     

A miniaturized technique for assessing protein thermodynamics and function using fast determination of quantitative cysteine reactivity

Protein thermodynamic stability is a fundamental physical characteristic that determines biological function. Furthermore, alteration of thermodynamic stability by macromolecular interactions or biochemical modifications is a powerful tool for assessing the relationship between protein structure, stability, and biological function. High-throughput approaches for quantifying protein stability are beginning to emerge that enable thermodynamic measurements on small amounts of material, in short periods of time, and using readily accessible instrumentation. Here we present such a method, fast quantitative cysteine reactivity, which exploits the linkage between protein stability, sidechain protection by protein structure, and structural dynamics to characterize the thermodynamic and kinetic properties of proteins. In this approach, the reaction of a protected cysteine and thiol-reactive fluorogenic indicator is monitored over a gradient of temperatures after a short incubation time. These labeling data can be used to determine the midpoint of thermal unfolding, measure the temperature dependence of protein stability, quantify ligand-binding affinity, and, under certain conditions, estimate folding rate constants. Here, we demonstrate the fQCR method by characterizing these thermodynamic and kinetic properties for variants of Staphylococcal nuclease and E. coli ribose-binding protein engineered to contain single, protected cysteines. These straightforward, information-rich experiments are likely to find applications in protein engineering and functional genomics.     

Thermodynamic and kinetic parameters of lipase-catalyzed ester hydrolysis in biphasic systems with varying organic solvents

Kinetics of lipase-catalyzed hydrolysis of esters were modeled using reactant activities for aqueous-organic, biphasic systems. By using thermodynamic activities of the substrates in ordinary rate equations, the kinetic parameters were corrected for the contribution of substrate-solvent interactions and a uniform quantification of the substrates for lipase attached to the interface can be achieved. The kinetic parameters, on the basis of their thermodynamic activities, should be constant in different systems, provided that the solvents do not interfere with the binding of the substrates to the enzyme nor affect the catalytic mechanism. Experimental and computational methods on how to obtain the thermodynamic activities of the substrates are presented. Initial rates were determined for Pseudomonas cepacia lipase (PcL)-catalyzed hydrolysis of decyl chloroacetate in dynamic emulsions with various solvents. The thermodynamic equilibrium and corrected kinetic constants for this reaction appeared to be similar in various systems. The kinetics of PcL in an isooctane-aqueous biphasic system could be adequately described with the rate equation for a ping-pong mechanism. The observed inhibitory effect of decanol appeared to be a consequence of this mechanism, allowing the backreaction of the decanol with the chloroacetyl-enzyme complex. The kinetic performance of PcL in systems with toluene, dibutyl ether, and methyl isobutyl ketone could be less well described. The possible causes for this and for the remaining differences in corrected kinetic parameters are discussed. (c) 1995 John Wiley & Sons, Inc.     

The temperature jump relaxation technique.

The temperature jump relaxation technique is a convenient and general means of studying rapid reversible reactions of biological macromolecules. Recent advances in automatic data acquisition and the introduction of different optical detection systems will soon allow us to exploit the full potential of kinetic measurements near equilibrium. On the other hand, the kinetic approach can be quite limited if not accompanied by detailed structural and thermodynamic studies. Finally, we must accept the fact that one can rarely demonstrate a reaction mechanism to the exclusion of all plausible alternative models.     

The thermodynamics of water-protein interactions

Information about the effects of water on protein structure and function can be obtained from studies on freeze dried protein powders of varying water content. Sorption isotherms of water on proteins can be used to obtain thermodynamic quantities for water-protein interactions. Since such isotherms show hysteresis, there is doubt in regard to their interpretation.General expressions for the thermodynamic quantities of sorption are derived. If isotherms represent data at equilibrium, it is possible to calculate these thermodynamic quantities.There are two types of hysteresis, non-equilibrium hysteresis and equilibrium hysteresis. Absorption and desorption isotherms can show equilibrium hysteresis if different protein conformations, which are only slowly interconvertible, can be present. In this case valid thermodynamic quantities can be obtained. Experimental tests for equilibrium hysteresis are presented. More experiments are needed before definite conclusions can be drawn in regard to isotherms in the literature.If the protein conformation in a protein powder is similar to the protein conformation in aqueous solution, equilibrium data obtained from sorption isotherms can be used to approximate thermodynamic quantities for the interaction of water with proteins in aqueous solution. Examination of what experimental evidence is available indicates that the protein in powders prepared by desorption of water should have a conformation similar to that in solution. Further study of such samples will help to clarify the thermodynamics of water-protein interactions in aqueous solution.