Is maximization of molar yield in metabolic networks favoured by evolution?

Stoichiometric analysis of metabolic networks allows the calculation of possible metabolic flux distributions in the absence of kinetic data. In order to predict which of the possible fluxes are present under certain conditions, additional constraints and optimization principles can be applied. One approach of calculating unknown fluxes (frequently called flux balance analysis) is based on the optimality principle of maximizing the molar yield of biotransformations. Here, the relevance and applicability of that approach are examined, and it is compared with the principle of maximizing pathway flux. We discuss diverse experimental evidence showing that, often, those biochemical pathways are operative that allow fast but low-yield synthesis of important products, such as fermentation in Saccharomyces cerevisiae and several other yeast species. Together with arguments based on evolutionary game theory, this leads us to the conclusion that maximization of molar yield is by no means a universal principle.     

Can biochemical properties serve as selective pressure for gene selection during inter-species and endosymbiotic lateral gene transfer?

During the evolution of endosymbiosis, only one orthologous gene, either from the invader or the invaded genome, is preserved. Genetic and environmental factors are usually invoked to explain this gene preference. How biochemical parameters can play a role in the selection of genes that code for enzymes that constitute a metabolic pathway is explored. Simple Michaelis-Menten-like enzymes are considered whose kinetic parameters are randomly generated to construct two parallel homologous pathways to account for the contributions of the invaded and the invader. Steady-state fluxes as targets of natural selection are focused. Enzymes are eliminated one by one so that the total flux through the pathway is least disturbed. Analysis of the results, done by different criteria, indicate that the maximal velocities, both forward and backward, are more influential in selection than the respective Michaelis constants. This inclination disappears as metabolite concentrations are increased. It is shown that kinetic selection criteria can result in a mosaicism of enzymes in the same pathway in terms of their genetic origin. Analysis of the results using the control coefficient paradigm disclosed an expected robust correlation between flux control coefficients of enzymes and their selective elimination. Similar analyses, performed for the case of single gene transfer or for gene replication with subsequent mutation, yielded essentially similar results. The results conform with the phenomenon of genetic mosaicism found in phylogenetic analyses of single or double endosymbioses and lateral gene transfer.     

Substrate flux through methylenetetrahydrofolate dehydrogenase: predicted effects of the concentration of methylenetetrahydrofolate on its partitioning into pathways leading to nucleotide biosynthesis or methionine regeneration

Folic acid exists in mammalian cells with a poly-gamma-glutamate tail that may regulate the flux of folates through the various cellular pathways. The substrate polyglutamate specificity of methylenetetrahydrofolate dehydrogenase from pig liver has been examined by using a competitive method and measuring apparent tritium kinetic isotope effects on Vmax/Km for methylenetetrahydrofolate. This competitive method yields very accurate ratios of Km values for alternate substrates of an enzyme and may also be applied to reactions with no isotope effect. In combination with published data from our own and other laboratories, the kinetic parameters of methylenetetrahydrofolate dehydrogenase were used to calculate the initial velocities of pig liver methylenetetrahydrofolate dehydrogenase, thymidylate synthase, and methylenetetrahydrofolate reductase, at physiological concentrations of substrates and enzymes. These calculations suggest that the cellular concentration of methylenetetrahydrofolate may regulate the flux of this metabolite into the pathways leading to nucleotide biosynthesis and methionine regeneration. An increase in the cellular level of methylenetetrahydrofolate would permit more one-carbon units to be directed toward nucleotide biosynthesis.     

Metabolic capabilities of Escherichia coli: I. synthesis of biosynthetic precursors and cofactors

Metabolism of living cells converts substrates into metabolic energy, redox potential and metabolic end products that are essential to maintain cellular function. The flux distribution among the various biochemical pathways is determined by the kinetic properties of enzymes which are subject to strict regulatory control. Simulation of metabolic behavior therefore requires the complete knowledge of biochemical pathways, enzyme kinetics as well as their regulation. Unfortunately, complete kinetic and regulatory information is not available for microbial cells, thus preventing accurate dynamic simulation of their metabolic behavior. However, it is possible to define wider limits on metabolic behavior based solely on flux balances of biochemical pathways. We present here comprehensive information about the catabolic pathways of the bacterium Escherichia coli. Using this biochemical database, we formulate a stoichiometric model of the bacterial network of fueling reactions. After logical structural reduction, the network consists of 53 metabolic fluxes and 30 metabolites. The solution space of this under-determined system of equations presents the bounds of metabolic flux distribution that the bacterial cell can achieve. We use specific objective functions and linear optimization to investigate the capability of E. coli catabolism to maximally produce the 12 biosynthetic precursors and three key cofactors within this solution space. For the three cofactors, the maximum yields are calculated to be 18.67 ATP, 11.6 NADH and 11 NADPH per glucose molecule, respectively. The yields of NADH and NADPH are less than 12 owing to the energy costs of importing glucose. These constraints are made explicit by the interpretation of shadow prices. The optimal yields of the 12 biosynthetic precursors are computed. Four of the 12 precursors (3-phosphoglycerate, phosphoenolpyruvate, pyruvate and oxaloacetate) can be made by E. coli with complete carbon conversion. Conversely, none of the sugar monophosphates can be made with 100% carbon conversion and analysis of the shadow prices reveals that this conversion is constrained by the energy cost of importing glucose. Three of the 12 precursors (acetyl-coA, α-ketoglutarate, and succinyl-coA) cannot be made with full carbon conversion owing to stoichiometric constraints; there is no route to these compounds without carrying out a decarboxylation reaction. Metabolite flux balances and linear optimization have thus been used to determine the catabolic capabilities of E. coli .     

A mathematical model for regulating monomer composition of the microbially synthesized polyhydroxyalkanoate copolymers

A mathematical model is proposed for predicting the copolymer composition of the microbially synthesized polyhydroxyalkanoate (PHA) copolymers. Based on the biochemical reactions involved in the precursor formation and polymerization pathways, the model correlates the copolymer composition with the cultivation conditions, the enzyme levels and selectivity, and the metabolic pathways. It suggests the following points: (1) in the case of a sole carbon source, the copolymer composition depends mainly on the topology of the metabolic pathways and the selectivity of both the enzymes involved in the precursor formation and the polymerization route; (2) the copolymer composition can be varied in a wide range via alteration of the flux ratio of different types of monomers channeled from two or more independent and simultaneous pathways; (3) the enzymes which should be over-expressed or inhibited to obtain the desired copolymer composition can be predicted. For example, inhibition of the beta-oxidation pathway will increase the content of the monomer units with longer chain length. To test the model, various experiments were envisaged by varying cultivation time, concentration and chain length of the sole carbon source, and molar ratio of the cosubstrates. The predictions from the model agree well with the experimental results. Therefore, the proposed model will be useful in predicting the PHA copolymer composition under different biochemical reaction conditions. In other words, it can provide a guide for the synthesis of desired PHA copolymers.     

产生L-异亮氨酸的黄色短杆菌的代谢途径分析

目的:代谢工程要解决的主要问题是改变某些途径中的碳架物质流量或改变碳架物质流在不同途径中的流量分布,其目标就是修饰初级代谢,将碳架物质流导入目的产物的载流途径,以获得产物的最大转化率。方法:利用途径分析方法对黄色短杆菌生产L-异亮氨酸的途径进行了分析。结果:建立了9种基础模型,确定L-异亮氨酸理论最高摩尔产率是1;确定了黄色短杆菌生产L-异亮氨酸的最佳途径的通量分布,并以此为依据进行发酵溶氧控制优化,溶氧分阶段控制发酵生产L-异亮氨酸比溶氧恒定控制方式发酵的产率提高了8.2%。结论:根据途径分析结果,通过改变发酵过程有关参数,可使目的产物产率得到提高。     

Adenine and adenosine salvage pathways in erythrocytes and the role of S-adenosylhomocysteine hydrolase. A theoretical study using elementary flux modes

This article is devoted to the study of redundancy and yield of salvage pathways in human erythrocytes. These cells are not able to synthesize ATP de novo. However, the salvage (recycling) of certain nucleosides or bases to give nucleotide triphosphates is operative. As the salvage pathways use enzymes consuming ATP as well as enzymes producing ATP, it is not easy to see whether a net synthesis of ATP is possible. As for pathways using adenosine, a straightforward assumption is that these pathways start with adenosine kinase. However, a pathway bypassing this enzyme and using S-adenosylhomocysteine hydrolase instead was reported. So far, this route has not been analysed in detail. Using the concept of elementary flux modes, we investigate theoretically which salvage pathways exist in erythrocytes, which enzymes belong to each of these and what relative fluxes these enzymes carry. Here, we compute the net overall stoichiometry of ATP build-up from the recycled substrates and show that the network has considerable redundancy. For example, four different pathways of adenine salvage and 12 different pathways of adenosine salvage are obtained. They give different ATP/glucose yields, the highest being 3:10 for adenine salvage and 2:3 for adenosine salvage provided that adenosine is not used as an energy source. Implications for enzyme deficiencies are discussed.     

鸟苷产生菌的代谢途径分析

代谢工程要解决的主要问题就是改变某些途径中的碳架物质流量或改变碳架物质流在不同途径中的流量分布,其目标就是修饰初级代谢,将碳架物质流导入目的产物的载流途径以获得产物的最大转化率。利用途径分析方法对枯草芽孢杆菌生产鸟苷的途径进行了分析,建立了3种基础模型,鸟苷理论摩尔产率分别是0．625、0．75和0．667,确定了枯草芽孢杆菌生产鸟苷的最佳途径的通量分布。     

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.     

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.     

Relationship between Photosynthetic Electron Transport and Stromal Enzyme Activity in Pea Leaves : Toward an Understanding of the Nature of Photosynthetic Control

The responses of the quantum efficiencies of photosystem (PS) II and PSI measured in vivo simultaneously with estimations of the activities and activation states of NADP-malate dehydrogenase, chloroplast fructose-1,6-bisphosphatase, and ribulose-1,5-bisphosphate carboxylase were used to study the relationship between electron transport and carbon metabolism. The effects of varying irradiance and CO₂ partial pressure on the relationship between the quantum efficiencies of PSI and II, and the activity of these enzymes shows that the interrelationships vary according to the limitations placed on the system. The relationship between the quantum efficiencies of PSII and PSI was linear in most situations. In response to increasing irradiance, the activity of all three enzymes increased. In the case of NADP-malate dehydrogenase this increase was well correlated with the estimated flux of electrons through PSI and PSII. The other two enzymes showed a more complex relationship with the estimated flux of electrons through both photosystems. These relationships are consistent with the known interactions between these stromal enzymes and the thylakoids. The response to varying CO₂ partial pressure is more complex. The efficiencies of PSI and II declined with decreasing CO₂ partial pressure and the activity of each enzyme varied uniquely. However, there are clear correlations between the activities of the enzymes and the flux of electrons through the photosystems. In contrast to the data obtained under conditions of varying irradiance, there is clear evidence of photosynthetic control of electron transport when the CO₂ concentration is varied.     

Metabolite damage and repair in metabolic engineering design

The necessarily sharp focus of metabolic engineering and metabolic synthetic biology on pathways and their fluxes has tended to divert attention from the damaging enzymatic and chemical side-reactions that pathway metabolites can undergo. Although historically overlooked and underappreciated, such metabolite damage reactions are now known to occur throughout metabolism and to generate (formerly enigmatic) peaks detected in metabolomics datasets. It is also now known that metabolite damage is often countered by dedicated repair enzymes that undo or prevent it. Metabolite damage and repair are highly relevant to engineered pathway design: metabolite damage reactions can reduce flux rates and product yields, and repair enzymes can provide robust, host-independent solutions. Herein, after introducing the core principles of metabolite damage and repair, we use case histories to document how damage and repair processes affect efficient operation of engineered pathways – particularly those that are heterologous, non-natural, or cell-free. We then review how metabolite damage reactions can be predicted, how repair reactions can be prospected, and how metabolite damage and repair can be built into genome-scale metabolic models. Lastly, we propose a versatile ‘plug and play’ set of well-characterized metabolite repair enzymes to solve metabolite damage problems known or likely to occur in metabolic engineering and synthetic biology projects.     

Early Steps in Isoprenoid Biosynthesis: Multilevel Regulation of the Supply of Common Precursors in Plant Cells

Isoprenoids are produced in all organisms but are especially abundant and diverse in plants. Two separate pathways operate in plant cells to synthesize prenyl diphosphate precursors common to all isoprenoids. Cytosolic and mitochondrial precursors are produced by the mevalonic acid (MVA) pathway whereas the recently discovered methylerythritol phosphate (MEP) pathway is located in plastids. However, both pathways may participate in the synthesis of at least some isoprenoids under certain circumstances. Although genes encoding all the enzymes from both pathways have already been cloned, little is known about the regulatory mechanisms that control the supply of isoprenoid precursors. Genetic approaches are providing valuable information on the regulation of both pathways. Thus, recent data from overexpression experiments in transgenic plants show that several enzymes share control over the metabolic flux through the MEP pathway, whereas a single regulatory step has been proposed for the MVA pathway. Identification of Arabidopsis thaliana mutants that are resistant to the inhibition of the MVA and the MEP pathways is a promising approach to uncover mechanisms involved in the crosstalk between pathways. The characterization of some of these mutants impaired in light perception and signaling has recently provided genetic evidence for a role of light as a key factor to modulate the availability of isoprenoid precursors in Arabidopsis seedlings. The picture emerging from recent data supports that a complex regulatory network appears to be at work in plant cells to ensure the supply of isoprenoid precursors when needed.     

Reaction routes in biochemical reaction systems: algebraic properties,validated calculation procedure and example from nucleotide metabolism

 Elementary flux modes (direct reaction routes) are minimal sets of enzymes that can operate at steady state, with all irreversible reactions used in the appropriate direction. They can be interpreted as component pathways of a (bio)chemical reaction network. Here, two different definitions of elementary modes are given and their equivalence is proved. Several algebraic properties of elementary modes are then presented and proved. This concerns, amongst other features, the minimal number of enzymes of the network not used in an elementary mode and the situations where irreversible reactions are replaced by reversible ones. Based on these properties, a refined algorithm is presented, and it is formally proved that this algorithm will exclusively generate all the elementary flux modes of an arbitrary network containing reversible or irreversible reactions or both. The algorithm is illustrated by a biochemical example relevant in nucleotide metabolism. The computer implementation in two different programming languages is discussed. Received: 1 January 2001 / Revised version: 17 December 2001 / Published online: 17 July 2002     

Matrix method for determining steps most rate-limiting to metabolic fluxes in biotechnological processes

The metabolic control theory developed by Kacser, Burns, Heinrich, and Rapoport is briefly outlined, extended, and transformed so as optimally to address some biotechnological questions. The extensions include (i) a new theorem that relates the control of metabolite concentrations by enzyme activities to flux ratios at branches in metabolic pathways; (ii) a new theorem that does the same for the control of the distribution of the flux over two branches; (iii) a method that expresses these controls into properties (the so-called elasticity coefficients) of the enzymes in the pathway; and (iv) a theorem that relates the effects of changes in metabolite concentrations on reaction rates to the effects of changes in enzyme properties on the same rates. Matrix equations relating the flux control and concentration control coefficients to the elasticity coefficients of enzymes in simple linear and branched pathways incorporating feedback are given, together with their general solutions and a numerical example. These equations allow one to develop rigorous criteria by which to decide the optimal strategy for the improvement of a microbial process. We show how this could be used in deciding which property of which enzyme should be changed in order to obtain the maximal concentration of a metabolite or the maximal metabolic flux.     

Shifts in growth strategies reflect tradeoffs in cellular economics

The growth rate‐dependent regulation of cell size, ribosomal content, and metabolic efficiency follows a common pattern in unicellular organisms: with increasing growth rates, cell size and ribosomal content increase and a shift to energetically inefficient metabolism takes place. The latter two phenomena are also observed in fast growing tumour cells and cell lines. These patterns suggest a fundamental principle of design. In biology such designs can often be understood as the result of the optimization of fitness. Here we show that in basic models of self‐replicating systems these patterns are the consequence of maximizing the growth rate. Whereas most models of cellular growth consider a part of physiology, for instance only metabolism, the approach presented here integrates several subsystems to a complete self‐replicating system. Such models can yield fundamentally different optimal strategies. In particular, it is shown how the shift in metabolic efficiency originates from a tradeoff between investments in enzyme synthesis and metabolic yields for alternative catabolic pathways. The models elucidate how the optimization of growth by natural selection shapes growth strategies.     

Substrate and energy costs of the production of exocellular enzymes by Bacillus licheniformis

Substrate and energy costs of the production of exocellular enzymes from glucose and citrate by B. Iicheniformis S1684 as well as molar growth yields corrected for these costs of product formation were calculated using data from chemostat experiments. The calculations showed that 1.46-1.73 mol glucose and 2.31-2.77 mol citrate are needed for formation and excretion of 1 mol protein. Consequently, the values of the maximal product yield from substrate (Y(psm') g/mol) are 80 < Y(psm) < 95 when product is formed from glucose and 50 < Y(psm) < 60 when product is formed from citrate. The higher substrate costs for product formation from citrate are due to a higher level of CO(2) production during protein formation and a higher substrate requirement for the energy supply of product formation and excretion than when product is formed from glucose. The theoretical ATP requirement for protein synthesis could be determined reasonably well, but the energy costs of protein excretion could not be determined exactly. The energy costs of protein formation are higher than those of biomass formation or protein excretion. Molar growth yields corrected for the substrate costs of product formation were high, indicating a high efficiency of growth.Growth and production parameters were determined as well from experimental data of recycling fermentor experiments using a parameter optimization procedure based on a mathematical model describing biomass growth as a linear function of the substrate consumption rate and the rate of product formation as a linear function of biomass growth rate. The fitting procedure yielded two growth and production domains during glucose limitation. In the first domain the values for the maximal growth yield and maintenance coefficient were in agreement with those found in chemostat experiments at corresponding values of Y(spm). Domain 2 could be described best with linear growth and product formation. In domain 2 the rate of product formation decreased and more substrate became available for biomass formation. As a consequence the specific growth rate increased in the shift from domain 1 to 2. Domain 2 behavior most probably is caused by the rel-status of B. Iicheniformis S1684.     

Identification of flux control in metabolic networks using non-equilibrium thermodynamics

A method is presented to identify flux controlling reactions in metabolic networks using experimentally determined flux distributions. The method is based on the application of Ziegler's principle for the maximization of entropy production. According to this principle a metabolic network tends to maximize the entropy production rate while satisfying mass balances and maximal rate constraints. Experimental flux data corresponding to four different metabolic states of Saccharomyces cerevisiae were used to identify the corresponding flux controlling reactions. The bottleneck nature of several of the identified reactions was confirmed by earlier studies on over-expression of the identified target genes. The method also explains the failure of all the previous trials of increasing the glycolysis rate by direct over-expression of several glycolytic enzymes. These findings point to a wider use of the method for identification of novel targets for metabolic engineering of microorganisms used for sustainable production of fuels and chemicals.