Enzyme kinetics and the maximum entropy production principle

A general proof is derived that entropy production can be maximized with respect to rate constants in any enzymatic transition. This result is used to test the assumption that biological evolution of enzyme is accompanied with an increase of entropy production in its internal transitions and that such increase can serve to quantify the progress of enzyme evolution. The state of maximum entropy production would correspond to fully evolved enzyme. As an example the internal transition ES?EP in a generalized reversible Michaelis-Menten three state scheme is analyzed. A good agreement is found among experimentally determined values of the forward rate constant in internal transitions ES→EP for three types of β-Lactamase enzymes and their optimal values predicted by the maximum entropy production principle, which agrees with earlier observations that β-Lactamase enzymes are nearly fully evolved. The optimization of rate constants as the consequence of basic physical principle, which is the subject of this paper, is a completely different concept from a) net metabolic flux maximization or b) entropy production minimization (in the static head state), both also proposed to be tightly connected to biological evolution.     

THE EVOLUTION OF GENES IN BRANCHED METABOLIC PATHWAYS

Simulation models of the evolution of genes in a branched metabolic pathway subject to stabilizing selection on flux are described and analyzed. The models are based either on metabolic control theory (MCT), with the assumption that enzymes are far from saturation, or on Michaelis–Menten kinetics, which allows for saturation and near saturation. Several predictions emerge from the models: (1) flux control evolves to be concentrated at pathway branch points, including the first enzyme in the pathway. (2) When flux is far from its optimum, adaptive substitutions occur disproportionately often in branching enzymes. (3) When flux is near its optimum, adaptive substitutions occur disproportionately often in nonbranching enzymes. (4) Slightly deleterious substitutions occur disproportionately often in nonbranching enzymes. (5) In terms of both flux control and patterns of substitution, pathway branches are similar to those predicted for linear pathways. These predictions provide null hypotheses for empirical examination of the evolution of genes in metabolic pathways.     

Metabolic networks evolve towards states of maximum entropy production

A metabolic network can be described by a set of elementary modes or pathways representing discrete metabolic states that support cell function. We have recently shown that in the most likely metabolic state the usage probability of individual elementary modes is distributed according to the Boltzmann distribution law while complying with the principle of maximum entropy production. To demonstrate that a metabolic network evolves towards such state we have carried out adaptive evolution experiments with Thermoanaerobacterium saccharolyticum operating with a reduced metabolic functionality based on a reduced set of elementary modes. In such reduced metabolic network metabolic fluxes can be conveniently computed from the measured metabolite secretion pattern. Over a time span of 300 generations the specific growth rate of the strain continuously increased together with a continuous increase in the rate of entropy production. We show that the rate of entropy production asymptotically approaches the maximum entropy production rate predicted from the state when the usage probability of individual elementary modes is distributed according to the Boltzmann distribution. Therefore, the outcome of evolution of a complex biological system can be predicted in highly quantitative terms using basic statistical mechanical principles.     

Identification of genome-scale metabolic network models using experimentally measured flux profiles

Genome-scale metabolic network models can be reconstructed for well-characterized organisms using genomic annotation and literature information. However, there are many instances in which model predictions of metabolic fluxes are not entirely consistent with experimental data, indicating that the reactions in the model do not match the active reactions in the in vivo system. We introduce a method for determining the active reactions in a genome-scale metabolic network based on a limited number of experimentally measured fluxes. This method, called optimal metabolic network identification (OMNI), allows efficient identification of the set of reactions that results in the best agreement between in silico predicted and experimentally measured flux distributions. We applied the method to intracellular flux data for evolved Escherichia coli mutant strains with lower than predicted growth rates in order to identify reactions that act as flux bottlenecks in these strains. The expression of the genes corresponding to these bottleneck reactions was often found to be downregulated in the evolved strains relative to the wild-type strain. We also demonstrate the ability of the OMNI method to diagnose problems in E. coli strains engineered for metabolite overproduction that have not reached their predicted production potential. The OMNI method applied to flux data for evolved strains can be used to provide insights into mechanisms that limit the ability of microbial strains to evolve towards their predicted optimal growth phenotypes. When applied to industrial production strains, the OMNI method can also be used to suggest metabolic engineering strategies to improve byproduct secretion. In addition to these applications, the method should prove to be useful in general for reconstructing metabolic networks of ill-characterized microbial organisms based on limited amounts of experimental data.     

Effects of the changes in enzyme activities on metabolic flux redistribution around the 2-oxoglutarate branch in glutamate production by<Emphasis Type="Italic"> Corynebacterium glutamicum</Emphasis>

An experimental method for metabolic control analysis (MCA) was applied to the investigation of a metabolic network of glutamate production by Corynebacterium glutamicum. A metabolic reaction (MR) model was constructed and used for flux distribution analysis (MFA). The flux distribution at a key branch point, 2-oxoglutarate, was investigated in detail. Activities of isocitrate dehydrogenase (ICDH), glutamate dehydrogenase (GDH), and 2-oxoglutarate dehydrogenase complex (ODHC) around this the branch point were changed, using two genetically engineered strains (one with enhanced ICDH activity and the other with enhanced GDH activity) and by controlling environmental conditions (i.e. biotin-deficient conditions). The mole flux distribution was determined by an MR model, and the effects of the changes in the enzyme activities on the mole flux distribution were compared. Even though both GDH and ICDH activities were enhanced, the mole flux distribution was not significantly changed. When the ODHC activity was attenuated, the flux through ODHC decreased, and glutamate production was markedly increased. The flux control coefficients of the above three enzymes for glutamate production were determined based on changes in enzyme activities and the mole flux distributions. It was found that the factor with greatest impact on glutamate production in the metabolic network was obtained by attenuation of ODHC activity.     

In vivo interpretation of model predicted inhibition in acrylate pathway engineered Lactococcus lactis

To maximize the productivity of engineered metabolic pathway, in silico model is an established means to provide features of enzyme reaction dynamics. In our previous study, Escherichia coli engineered with acrylate pathway yielded low propionic acid titer. To understand the bottleneck behind this low productivity, a kinetic model was developed that incorporates the enzymatic reactions of the acrylate pathway. The resulting model was capable of simulating the fluxes reported under in vitro studies with good agreement, suggesting repression of propionyl-CoA transferase (Pct) by carboxylate metabolites as the main limiting factor for propionate production. Furthermore, the predicted flux control coefficients of the pathway enzymes under steady state conditions revealed that the control of flux is shared between Pct and lactoyl-CoA dehydratase. Increase in lactate concentration showed gradual decrease in flux control coefficients of Pct that in turn confirmed the control exerted by the carboxylate substrate. To interpret these in silico predictions under in vivo system, an organized study was conducted with a lactic acid bacteria strain engineered with acrylate pathway. Analysis reported a decreased product formation rate on attainment of inhibitory titer by suspected metabolites and supported the model.     

Filament formation by metabolic enzymes—A new twist on regulation

Compartmentalization of metabolic enzymes through protein–protein interactions is an emerging mechanism for localizing and regulating metabolic activity. Self-assembly into linear filaments is a common strategy for cellular compartmentalization of enzymes. Polymerization is often driven by changes in the metabolic state of the cell, suggesting that it is a strategy for shifting metabolic flux in response to cellular demand. Although polymerization of metabolic enzymes is widespread, observed from bacteria to humans, we are just beginning to appreciate their role in regulating cellular metabolism. In most cases, one functional role of metabolic enzyme filaments is allosteric control of enzyme activity. Here, we highlight recent findings, providing insight into the structural and functional significance of filamentation of metabolic enzymes in cells.     

Analysis of optimal phenotypic space using elementary modes as applied to Corynebacterium glutamicum

Background  

Quantification of the metabolic network of an organism offers insights into possible ways of developing mutant strain for better productivity of an extracellular metabolite. The first step in this quantification is the enumeration of stoichiometries of all reactions occurring in a metabolic network. The structural details of the network in combination with experimentally observed accumulation rates of external metabolites can yield flux distribution at steady state. One such methodology for quantification is the use of elementary modes, which are minimal set of enzymes connecting external metabolites. Here, we have used a linear objective function subject to elementary modes as constraint to determine the fluxes in the metabolic network of Corynebacterium glutamicum. The feasible phenotypic space was evaluated at various combinations of oxygen and ammonia uptake rates.     

Metabolic design based on a coupled gene expression-metabolic network model of tryptophan production in Escherichia coli

The presumably high potential of a holistic design approach for complex biochemical reaction networks is exemplified here for the network of tryptophan biosynthesis from glucose, a system whose components have been investigated thoroughly before. A dynamic model that combines the behavior of the trp operon gene expression with the metabolic network of central carbon metabolism and tryptophan biosynthesis is investigated. This model is analyzed in terms of metabolic fluxes, metabolic control, and nonlinear optimization. We compare two models for a wild-type strain and another model for a tryptophan producer. An integrated optimization of the whole network leads to a significant increase in tryptophan production rate for all systems under study. This enhancement is well above the increase that can be achieved by an optimization of subsystems. A constant ratio of control coefficients on tryptophan synthesis rate has been identified for the models regarding or disregarding trp operon expression. Although we found some examples where flux control coefficients even contradict the trends of enzyme activity changes in an optimized profile, flux control can be used as an indication for enzymes that have to be taken into account in optimization.     

Evolution of enzymes in metabolism: a network perspective

Several models have been proposed to explain the origin and evolution of enzymes in metabolic pathways. Initially, the retro-evolution model proposed that, as enzymes at the end of pathways depleted their substrates in the primordial soup, there was a pressure for earlier enzymes in pathways to be created, using the later ones as initial template, in order to replenish the pools of depleted metabolites. Later, the recruitment model proposed that initial templates from other pathways could be used as long as those enzymes were similar in chemistry or substrate specificity. These two models have dominated recent studies of enzyme evolution. These studies are constrained by either the small scale of the study or the artificial restrictions imposed by pathway definitions. Here, a network approach is used to study enzyme evolution in fully sequenced genomes, thus removing both constraints. We find that homologous pairs of enzymes are roughly twice as likely to have evolved from enzymes that are less than three steps away from each other in the reaction network than pairs of non-homologous enzymes. These results, together with the conservation of the type of chemical reaction catalyzed by evolutionarily related enzymes, suggest that functional blocks of similar chemistry have evolved within metabolic networks. One possible explanation for these observations is that this local evolution phenomenon is likely to cause less global physiological disruptions in metabolism than evolution of enzymes from other enzymes that are distant from them in the metabolic network.     

In vitro control analysis of an enzyme system: Experimental and analytical developments

In this paper we describe a flow-through system for reconstituting parts of metabolism from purified enzymes. This involves pumping continuously into a reaction chamber, fresh enzymes and reagents so that metabolic reactions occur in the chamber. The waste products leave the chamber via the outflow so that a steady state can be setup. The system we chose consisted of a single enzyme, lactate dehydrogenase. This enzyme was chosen because it consumes NADH in the chamber which could be monitored spectrophotometrically. The aim of the work was to investigate whether a steady state could be achieved in the flow system and whether a metabolic control analysis could be done. We measured two control coefficients, C_LDH and C_pump for the enzyme flux and NADH concentration and confirmed that the summation theorem applied to this system. The advantage of a flow-through system is that the titrations necessary to estimate the control coefficients can be easily and precisely controlled; this means that accurate estimates for the control coefficients can be obtained. In the paper, we discuss some statistical aspects of the data analysis and some possible applications of the technique, including a method to determine the presence of metabolic channelling between two different enzymes.     

Engineering and adaptive evolution of Escherichia coli for d-lactate fermentation reveals GatC as a xylose transporter

Despite the abundance of xylose in nature, the production of chemicals from C5 sugars remains challenging in metabolic engineering. By deleting xylFGH genes and using adaptive evolution, an efficient E. coli strain capable of producing d-lactate from xylose was engineered. Quantitative proteomics and genome sequencing were used to understand the new phenotype and the metabolic limitations of xylose conversion to d-lactate. Proteomics identified major changes in enzyme concentration in the glycolytic and tricarboxylic acid pathways. Whole genome sequencing of the evolved strain identified a point mutation in the gatC gene, which resulted in a change from serine to leucine at position 184 of the GatC protein. The knockout of gatC in a number of strains and the insertion of the mutation in the non-evolved strain confirmed its activity as a xylose transporter and demonstrated that the mutation is responsible for the high xylose consumption phenotype in the evolved strain. The newly found xylose transporter is a candidate for future strain engineering for converting C5-C6 syrups into valuable chemicals.     

Adaptive evolution of metabolic pathways in Drosophila

The adaptive significance of enzyme variation has been of central interest in population genetics. Yet, how natural selection operates on enzymes in the larger context of biochemical pathways has not been broadly explored. A basic expectation is that natural selection on metabolic phenotypes will target enzymes that control metabolic flux, but how adaptive variation is distributed among enzymes in metabolic networks is poorly understood. Here, we use population genetic methods to identify enzymes responding to adaptive selection in the pathways of central metabolism in Drosophila melanogaster and Drosophila simulans. We report polymorphism and divergence data for 17 genes that encode enzymes of 5 metabolic pathways that converge at glucose-6-phosphate (G6P). Deviations from neutral expectations were observed at five loci. Of the 10 genes that encode the enzymes of glycolysis, only aldolase (Ald) deviated from neutrality. The other 4 genes that were inconsistent with neutral evolution (glucose-6-phosphate dehydrogenase [G6pd]), phosphoglucomutase [Pgm], trehalose-6-phosphate synthetase [Tps1], and glucose-6phosphatase [G6pase] encode G6P branch point enzymes that catalyze reactions at the entry point to the pentose-phosphate, glycogenic, trehalose synthesis, and gluconeogenic pathways. We reconcile these results with population genetics theory and existing arguments on metabolic regulation and propose that the incidence of adaptive selection in this system is related to the distribution of flux control. The data suggest that adaptive evolution of G6P branch point enzymes may have special significance in metabolic adaptation.     

Toward a systems biology perspective on enzyme evolution

Large superfamilies of enzymes derived from a common progenitor have emerged by duplication and divergence of genes encoding metabolic enzymes. Division of the functions of early generalist enzymes enhanced catalytic power and control over metabolic fluxes. Later, novel enzymes evolved from inefficient secondary activities in specialized enzymes. Enzymes operate in the context of complex metabolic and regulatory networks. The potential for evolution of a new enzyme depends upon the collection of enzymes in a microbe, the topology of the metabolic network, the environmental conditions, and the net effect of trade-offs between the original and novel activities of the enzyme.     

Sensitivity of pathway rate to activities of substrate-cycle enzymes: application to gluconeogenesis and glycolysis

In a study of metabolic regulation, it is frequently useful to consider the degree to which an enzyme can influence the rate of its pathway. The most productive expression of rate-controlling influence is the fractional change in pathway rate per fractional change in enzyme activity (called control strength or sensitivity coefficient). We have developed a system for considering how a substrate-cycle enzyme's control strength depends on its flux and reaction order and on related features of other enzymes of its pathway. We have applied this system to the gluconeogenic pathway of rat liver and the glycolytic pathway of bovine sperm, where enough fluxes and reaction orders have been published to allow valid estimates of several control strengths. In normal fed animals where gluconeogenesis is slow and unidirectional substrate-to-product and product-to-substrate fluxes are comparable, all substrate-cycle limbs have very high and similar control strengths regardless of their flux rates and positions in the pathway. The activity of a step affects all substrate-cycle control strengths similarly as it affects unidirectional end-to-end fluxes relative to net rate. Control strengths of non-substrate-cycle enzymes are negligible compared to those of substrate cycles. In fasting animals, on the other hand, where unidirectional Pyr----Glc flux is much greater than Glc----Pyr flux, upstream enzymes (near Pyr) have a regulatory advantage over downstream enzymes (near Glc). In this circumstance, control strength of each substrate-cycle enzyme is inversely related to rate limitingness between its substrate and the pathway substrate. Because the Pyr/PEP cycle is significantly rate limiting, the control strength of the Pyr----PEP limb is much greater than that of pyruvate kinase and all downstream enzymes. In the glycolytic pathway of bovine sperm, strong product inhibition of hexokinase detracts greatly from its rate limitingness and control strength, which are very small despite its position at the beginning of the pathway and its large free energy. Because the glucose-transport-hexokinase segment is not rate limiting, phosphofructo 1-kinase has almost as much control strength as it would have as the first enzyme of the pathway, and because the F6P/FDP cycle is only moderately rate limiting, Fru-1,6-P2ase and enzymes further downstream have substantial control strengths. When glycolysis is accelerated by stimulation of phosphofructo 1-kinase, control strength shifts from phosphofructo-1-kinase and all downstream enzymes to the transporthesokinase segment.(ABSTRACT TRUNCATED AT 400 WORDS)