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.     

Evolutionary optimization of metabolic pathways. Theoretical reconstruction of the stoichiometry of ATP and NADH producing systems

The structural design of ATP and NADH producing systems, such as glycolysis and the citric acid cycle (TCA), is analysed using optimization principles. It is assumed that these pathways combined with oxidative phosphorylation have reached, during their evolution, a high efficiency with respect to ATP production rates. On the basis of kinetic and thermodynamic principles, conclusions are derived concerning the optimal stoichiometry of such pathways. Extending previous investigations, both the concentrations of adenine nucleotides as well as nicotinamide adenine dinucleotides are considered variable quantities. This implies the consideration of the interaction of an ATP and NADH producing system, an ATP consuming system, a system coupling NADH consumption with ATP production and a system consuming NADH decoupled from ATP production. It is examined in what respect real metabolic pathways can be considered optimal by studying a large number of alternative pathways. The kinetics of the individual reactions are described by linear or bilinear functions of reactant concentrations. In this manner, the steady-state ATP production rate can be calculated for any possible ATP and NADH producing pathway. It is shown that most of the possible pathways result in a very low ATP production rate and that the very efficient pathways share common structural properties. Optimization with respect to the ATP production rate is performed by an evolutionary algorithm. The following results of our analysis are in close correspondence to the real design of glycolysis and the TCA cycle. (1) In all efficient pathways the ATP consuming reactions are located near the beginning. (2) In all efficient pathways NADH producing reactions as well as ATP producing reactions are located near the end. (3) The number of NADH molecules produced by the consumption of one energy-rich molecule (glucose) amounts to four in all efficient pathways. A distance measure and a measure for the internal ordering of reactions are introduced to study differences and similarities in the stoichiometries of metabolic pathways.     

A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks

A set of linear pathways often does not capture the full range of behaviors of a metabolic network. The concept of 'elementary flux modes' provides a mathematical tool to define and comprehensively describe all metabolic routes that are both stoichiometrically and thermodynamically feasible for a group of enzymes. We have used this concept to analyze the interplay between the pentose phosphate pathway (PPP) and glycolysis. The set of elementary modes for this system involves conventional glycolysis, a futile cycle, all the modes of PPP function described in biochemistry textbooks, and additional modes that are a priori equally entitled to pathway status. Applications include maximizing product yield in amino acid and antibiotic synthesis, reconstruction and consistency checks of metabolism from genome data, analysis of enzyme deficiencies, and drug target identification in metabolic networks.     

Optimal stoichiometric designs of ATP-producing systems as determined by an evolutionary algorithm.

The design of metabolic pathways is thought to be the result of an optimization process such that the structure of contemporary metabolic routes maximizes a particular objective function. Recently, it has been shown that some essential stoichiometric properties of glycolysis can be explained on the basis of the requirement for a high ATP production rate. Because the number of stoichiometrically feasible designs increases strongly with the number of reactions involved, a systematic analysis of all the possibilities turns out to be inaccessible beyond a certain system size. We present, therefore, an alternative approach to compute in a more efficient way the optimal design of glycolysis interacting with an external ATP-consuming reaction. The algorithm is based on the laws of evolution by natural selection, and may be viewed as a particular version of evolutionary algorithms. The following conclusions are derived: (a) evolutionary algorithms are very useful search strategies in determining optimal stoichiometries of metabolic pathways. (b) Essential topological features of the glycolytic network may be explained on the basis of flux optimization. (c) There is a strong interrelation between the optimal stoichiometries and the thermodynamic and kinetic properties of the participating reactions. (d) Some subsequences of reactions in optimal pathways are strongly conserved at variation of system parameters, which may be understood by applying principles of metabolic control analysis.     

Integrating thermodynamic and enzymatic constraints into genome-scale metabolic models

Stoichiometric genome-scale metabolic network models (GEMs) have been widely used to predict metabolic phenotypes. In addition to stoichiometric ratios, other constraints such as enzyme availability and thermodynamic feasibility can also limit the phenotype solution space. Extended GEM models considering either enzymatic or thermodynamic constraints have been shown to improve prediction accuracy. In this paper, we propose a novel method that integrates both enzymatic and thermodynamic constraints in a single Pyomo modeling framework (ETGEMs). We applied this method to construct the EcoETM (E. coli metabolic model with enzymatic and thermodynamic constraints). Using this model, we calculated the optimal pathways for cellular growth and the production of 22 metabolites. When comparing the results with those of iML1515 and models with one of the two constraints, we observed that many thermodynamically unfavorable and/or high enzyme cost pathways were excluded from EcoETM. For example, the synthesis pathway of carbamoyl-phosphate (Cbp) from iML1515 is both thermodynamically unfavorable and enzymatically costly. After introducing the new constraints, the production pathways and yields of several Cbp-derived products (e.g. L-arginine, orotate) calculated using EcoETM were more realistic. The results of this study demonstrate the great application potential of metabolic models with multiple constraints for pathway analysis and phenotype prediction.     

The rationalization of high enzyme concentration in metabolic pathways such as glycolysis

The cellular concentration of enzymes of some major metabolic pathways, such as glycolysis, can approach millimolarity. This concentration of enzyme can catalyze in vitro rates which are 100-fold higher than maximum pathway flux. In an attempt to understand the need for such high enzyme concentration, an artificial metabolic pathway of five enzymes (apropos the central enzymes of glycolysis) has been modeled. Numerical methods were then used to determine the effect of enzyme concentration on: (1) the change in total free metabolite concentration as the pathway changes from low flux to high flux, (2) the time lag (transient time) in the rate of final product formation upon the transition from low flux to high flux. Both the changes in metabolite pool size and the transient time decreased with increased enzyme concentrations. When all enzymatic reactions were assigned Keq of unity, a concentration for each enzyme of 25 microM is sufficient to provide a transient time of 1 sec. When Keq different from unity are introduced, more enzyme is required to provide comparably short transient times. Under the latter condition, a pathway of sufficiently low transient time would require all the enzyme available in mammalian muscle. It is shown that there is little scope for further increases in either enzyme concentration or of catalytic efficiency of independent enzymes. Therefore, an alternative method of increasing efficiency is considered in which enzyme-bound metabolites can serve directly as substrates for subsequent enzymes in a metabolic pathway.     

Effect of evolution on the kinetic properties of enzymes

1. The likely effect of a selective pressure in the direction of higher reaction fluxes on rate parameters for enzyme reactions confirming to Michaelis-Menten kinetics has been analyzed on the basis of relationships which take into account the changes in metabolite concentrations that must be associated with mutational changes of the kinetic properties of enzymes participating in metabolic pathways. 2. Arguments are presented to show that such a pressure should tend to increase kcat, whereas Km may decrease or increase depending on what stage of evolutionary development the enzyme has reached. While the early evolution of enzymes must have been associated with decreasing Km values, an increase of both kcat and Km is mandatory for enhancement of the rate performance of extensively developed enzymes which exhibit kcat/Km ratios approaching the diffusion-control limit. The latter limit is dependent on the equilibrium constant for the catalysed reaction. 3. Enzymes which have reached the diffusion-control limit for their second-order rate performance cannot be considered as perfectly evolved catalysts, but may well undergo further development towards a higher catalytic efficiency in response to the improvement of other enzymes in the metabolic pathway with regard to the criterion of an enhanced reaction flux. Such evolution is associated with an increase of the metabolite levels in the pathway, and a simple model system is examined in order to illustrate the ultimate limits for the metabolite levels and reaction flux that may obtain. 4. The theoretical evidence presented lends no support to previous proposals that certain enzymes (e.g. triosephosphate isomerase), or enzymes showing certain kinetic characteristics (e.g. kcat/Km quotients approaching 10(9) s-1 M-1), have reached the end of their evolutionary development. A claim that any specific enzyme has reached catalytic perfection would provide the unreasonable inference that all enzymes participating in intermediary metabolism have reached catalytic perfection.     

Cysteine and iron accelerate the formation of ribose-5-phosphate,providing insights into the evolutionary origins of the metabolic network structure

The structure of the metabolic network is highly conserved, but we know little about its evolutionary origins. Key for explaining the early evolution of metabolism is solving a chicken–egg dilemma, which describes that enzymes are made from the very same molecules they produce. The recent discovery of several nonenzymatic reaction sequences that topologically resemble central metabolism has provided experimental support for a “metabolism first” theory, in which at least part of the extant metabolic network emerged on the basis of nonenzymatic reactions. But how could evolution kick-start on the basis of a metal catalyzed reaction sequence, and how could the structure of nonenzymatic reaction sequences be imprinted on the metabolic network to remain conserved for billions of years? We performed an in vitro screening where we add the simplest components of metabolic enzymes, proteinogenic amino acids, to a nonenzymatic, iron-driven reaction network that resembles glycolysis and the pentose phosphate pathway (PPP). We observe that the presence of the amino acids enhanced several of the nonenzymatic reactions. Particular attention was triggered by a reaction that resembles a rate-limiting step in the oxidative PPP. A prebiotically available, proteinogenic amino acid cysteine accelerated the formation of RNA nucleoside precursor ribose-5-phosphate from 6-phosphogluconate. We report that iron and cysteine interact and have additive effects on the reaction rate so that ribose-5-phosphate forms at high specificity under mild, metabolism typical temperature and environmental conditions. We speculate that accelerating effects of amino acids on rate-limiting nonenzymatic reactions could have facilitated a stepwise enzymatization of nonenzymatic reaction sequences, imprinting their structure on the evolving metabolic network.

The evolutionary origins of metabolism are largely unknown. This study shows that the prebiotically available proteinogenic amino acid cysteine can promote the metabolism-like rate-limiting formation of ribose-5-phosphate, suggesting that early metabolic pathways could have emerged thought the stepwise enzymatization of non-enzymatic reaction sequences.     

Rewiring and regulation of cross-compartmentalized metabolism in protists

Plastid acquisition, endosymbiotic associations, lateral gene transfer, organelle degeneracy or even organelle loss influence metabolic capabilities in many different protists. Thus, metabolic diversity is sculpted through the gain of new metabolic functions and moderation or loss of pathways that are often essential in the majority of eukaryotes. What is perhaps less apparent to the casual observer is that the sub-compartmentalization of ubiquitous pathways has been repeatedly remodelled during eukaryotic evolution, and the textbook pictures of intermediary metabolism established for animals, yeast and plants are not conserved in many protists. Moreover, metabolic remodelling can strongly influence the regulatory mechanisms that control carbon flux through the major metabolic pathways. Here, we provide an overview of how core metabolism has been reorganized in various unicellular eukaryotes, focusing in particular on one near universal catabolic pathway (glycolysis) and one ancient anabolic pathway (isoprenoid biosynthesis). For the example of isoprenoid biosynthesis, the compartmentalization of this process in protists often appears to have been influenced by plastid acquisition and loss, whereas for glycolysis several unexpected modes of compartmentalization have emerged. Significantly, the example of trypanosomatid glycolysis illustrates nicely how mathematical modelling and systems biology can be used to uncover or understand novel modes of pathway regulation.     

An algorithm for efficient identification of branched metabolic pathways

This article presents a new graph-based algorithm for identifying branched metabolic pathways in multi-genome scale metabolic data. The term branched is used to refer to metabolic pathways between compounds that consist of multiple pathways that interact biochemically. A branched pathway may produce a target compound through a combination of linear pathways that split compounds into smaller ones, work in parallel with many compounds, and join compounds into larger ones. While branched metabolic pathways predominate in metabolic networks, most previous work has focused on identifying linear metabolic pathways. The ability to automatically identify branched pathways is important in applications that require a deeper understanding of metabolism, such as metabolic engineering and drug target identification. The algorithm presented in this article utilizes explicit atom tracking to identify linear metabolic pathways and then merges them together into branched metabolic pathways. We provide results on several well-characterized metabolic pathways that demonstrate that the new merging approach can efficiently find biologically relevant branched metabolic pathways.     

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.     

Evolution of vitamin B6 (pyridoxine) metabolism by gain and loss of genes

Vitamin B(6) (VB6) functions as a cofactor of many diverse enzymes in amino acid metabolism. Three metabolic pathways for pyridoxal 5'-phosphate (PLP; the active form of VB6) are known: the de novo pathway, the salvage pathway, and the fungal type pathway. Most unicellular organisms and plants biosynthesize VB6 using one or two of these three biosynthetic pathways. However, animals such as insects and mammals do not possess any of the pathways and, thus, need to intake VB6 in their diet to survive. It is conceivable that breakdowns of these pathways occurred in the evolutionary lineages of insects and mammals, and one of the major reasons for this would be the loss of pertinent genes. We studied the evolution of VB6 biosynthesis from the view of the gain and loss of 10 pertinent genes in 122 species whose genome sequences were completely determined. The results revealed that each gene in the pathways was lost more than once in the entire evolutionary lineages of the 122 species. We also found the following three points regarding the evolution of PLP biosynthesis: (1) the breakdown of the PLP biosynthetic pathways occurred independently at least three times in animal lineages, (2) the de novo pathway was formed by the generation of pdxB in gamma-proteobacteria, and (3) the order of the gene loss in VB6 metabolism was conserved among different evolutionary lineages. These results suggest that the evolution of VB6 metabolism was subject to gains and frequent losses of related genes in the 122 species examined. This dynamic nature of the evolutionary changes must have been responsible for the breakdowns of the pathways, resulting in profound differentiation of heterotrophy among the species.     

Channeling in native microbial pathways: Implications and challenges for metabolic engineering

Intracellular enzymes can be organized into a variety of assemblies, shuttling intermediates from one active site to the next. Eukaryotic compartmentalization within mitochondria and peroxisomes and substrate tunneling within multi-enzyme complexes have been well recognized. Intriguingly, the central pathways in prokaryotes may also form extensive channels, including the heavily branched glycolysis pathway. In vivo channeling through cascade enzymes is difficult to directly measure, but can be inferred from in vitro tests, reaction thermodynamics, transport/reaction modeling, analysis of molecular diffusion and protein interactions, or steady state/dynamic isotopic labeling. Channeling presents challenges but also opportunities for metabolic engineering applications. It rigidifies fluxes in native pathways by trapping or excluding metabolites for bioconversions, causing substrate catabolite repressions or inferior efficiencies in engineered pathways. Channeling is an overlooked regulatory mechanism used to control flux responses under environmental/genetic perturbations. The heterogeneous distribution of intracellular enzymes also confounds kinetic modeling and multiple-omics analyses. Understanding the scope and mechanisms of channeling in central pathways may improve our interpretation of robust fluxomic topology throughout metabolic networks and lead to better design and engineering of heterologous pathways.     

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.     

Revisiting the Thermodynamic Theory of Optimal ATP Stoichiometries by Analysis of Various ATP-Producing Metabolic Pathways

The stoichiometry of ATP-producing metabolic pathways had been analysed theoretically by several authors by using evolutionary arguments and optimality principles. Waddell et al. (Biochem Educ 27:12–13, 1999) analysed (lactate-producing) glycolysis and used linear irreversible thermodynamics. The result was that half of the free-energy difference should be converted into free-energy of ATP and the remaining half should be used to drive the pathway. The calculated stoichiometry is in agreement with the observed yield of two moles of ATP per mole of glucose. Using the same approach, we here analyse eight other metabolic pathways. Although the deviation is not very large, the calculated values do not fit as nicely as for glycolysis as leading to lactate. For example, for O₂ respiration, the theoretical ATP yield equals 27.9. The real value varies among organisms between 26 and 38. For mixed-acid fermentation in Escherichia coli, the theoretical and experimental values are 2.24 and 2, respectively. For arginine degradation in M. pneumoniae, the calculated value is 2.43 mol of ATP, while in vivo only one mole is produced. During evolution, some pathways may not have reached their optimal ATP net production because energy yield is not their only function. Moreover, it should be acknowledged that the approach by linear irreversible thermodynamics is a rough approximation.     

Stress eating and tuning out: Cancer cells re-wire metabolism to counter stress

Abstract

Cancer cells reprogram metabolism to maintain rapid proliferation under often stressful conditions. Glycolysis and glutaminolysis are two central pathways that fuel cancer metabolism. Allosteric regulation and metabolite driven post-translational modifications of key metabolic enzymes allow cancer cells glycolysis and glutaminolysis to respond to changes in nutrient availability and the tumor microenvironment. While increased aerobic glycolysis (the Warburg effect) has been a noted part of cancer metabolism for over 80 years, recent work has shown that the elevated levels of glycolytic intermediates are critical to cancer growth and metabolism due to their ability to feed into the anabolic pathways branching off glycolysis such as the pentose phosphate pathway and serine biosynthesis pathway. The key glycolytic enzymes phosphofructokinase-1 (PFK1), pyruvate kinase (PKM2) and phosphoglycerate mutase 1 (PGAM1) are regulated by upstream and downstream metabolites to balance glycolytic flux with flux through anabolic pathways. Glutamine regulation is tightly controlled by metabolic intermediates that allosterically inhibit and activate glutamate dehydrogenase, which fuels the tricarboxylic acid cycle by converting glutamine derived glutamate to α-ketoglutarate. The elucidation of these key allosteric regulatory hubs in cancer metabolism will be essential for understanding and predicting how cancer cells will respond to drugs that target metabolism. Additionally, identification of the structures involved in allosteric regulation will inform the design of anti-metabolism drugs which bypass the off-target effects of substrate mimics. Hence, this review aims to provide an overview of allosteric control of glycolysis and glutaminolysis.     

Ordering events of biochemical evolution

Metabolic pathways exhibit structures resulting from an evolutionary process. Pathways have been inherited through time with modification, from the earliest periods of life. It is possible to compare the structure of pathways as done in comparative anatomy, i.e. for inferring ancestral pathways or parts of it (ancestral enzymatic functions), using standard phylogenetic reconstruction. Thus a phylogenetic tree of pathways provides a relative ordering of the rise of enzymatic functions. It even becomes possible to order the birth of each complete pathway in time. This particular "DNA-free" conceptual approach to evolutionary biochemistry is reviewed, gathering all the justifications given for it. Then, the method of assigning a given pathway to a time span of biochemical development is revisited. The previous method used an implicit "clock" of metabolic development that is difficult to justify. We develop a new clock-free approach, using functional biochemical arguments. Results of the two methods are not significantly different; our method is just more precise. This suggests that the clock assumed in the first method does not provoke any important artefact in describing the development of biochemical evolution. It is just unnecessary to postulate it. As a result, most of the amino acid metabolic pathways develop forwards, confirming former models of amino acid catabolism evolution, but not those for amino acid anabolism. The order of appearance of sectors of universal cellular metabolism is: (1) amino acid catabolism, (2) amino acid anabolism and closure of the urea cycle, (3) glycolysis and glycogenesis, (4) closure of the pentose-phosphate cycle, (5) closure of the Krebs cycle and fatty acids metabolism, (6) closure of the Calvin cycle.     

Expanding Metabolic Capabilities Using Novel Pathway Designs: Computational Tools and Case Studies

Design and selection of efficient metabolic pathways is critical for the success of metabolic engineering endeavors. Convenient pathways should not only produce the target metabolite in high yields but also are required to be thermodynamically feasible under production conditions, and to prefer efficient enzymes. To support the design and selection of such pathways, different computational approaches have been proposed for exploring the feasible pathway space under many of the above constraints. In this review, an overview of recent constraint‐based optimization frameworks for metabolic pathway prediction, as well as relevant pathway engineering case studies that highlight the importance of rational metabolic designs is presented. Despite the availability and suitability of in silico design tools for metabolic pathway engineering, scarce—although increasing—application of computational outcomes is found. Finally, challenges and limitations hindering the broad adoption and successful application of these tools in metabolic engineering projects are discussed.