Metabolic control therapy and biochemical systems theory: different objectives, different assumptions, different results

The metabolic control theory: Its development and its application to mitochondrial oxidative phosphorylation

Metabolic Control Theory (MCT) and Metabolic Control Analysis (MCA) are the two sides, theoretical and experimental, of the measurement of the sensitivity of metabolic networks in the vicinity of a steady state. We will describe the birth and the development of this theory from the first analyses of linear pathways up to a global mathematical theory applicable to any metabolic network. We will describe how the theory, given the global nature of mitochondrial oxidative phosphorylation, solved the problem of what controls mitochondrial ATP synthesis and then how it led to a better understanding of the differential tissue expression of human mitochondrial pathologies and of the heteroplasmy of mitochondrial DNA, leading to the concept of the threshold effect.

Evolution of Henrik Kacser's thought: Early publications on the organization of the whole system

Although the papers of Kacser and Burns (1973) and Heinrich and Rapoport (1974a,b) are commonly taken as the birth of metabolic control analysis, many of the ideas in them are foreshadowed in earlier papers, from 1956 onwards, when Kacser first argued for taking a systemic view of genetics and biochemistry.

Temporal decomposition: a strategy for building mathematical models of complex metabolic systems

In 'Discovering complexity' Bechtel and Richardson (1993) highlighted the connection between how biologists investigate the world and the type of explanations they give. This paper extends their account of how we investigate the world by examining the strategies used by researchers to build mathematical models of complex metabolic systems between the 1970s and 1990s. Bechtel and Richardson analysed how researchers decompose complex systems by reducing the number of variables included in the model, thus simplifying them and making them suitable objects for research and understanding. Bechtel and Abrahamsen (2005) later distinguished two types of decomposition: 1) Structural decomposition, starting with the identification of the relevant component parts and 2) functional decomposition, starting with the identification of the relevant component operations. I use my case studies to argue that temporal decomposition should be recognised as an additional strategy for investigating complex metabolic systems. Temporal decomposition involves the identification of the relevant dynamic variables. Existing accounts of decomposition are based on the assumption of a spatial hierarchy which classifies modules according to the frequency of interactions between components. Temporal decomposition is based on the assumption of a time hierarchy which classifies variables as dynamic or constant according to the relative speed with which properties of the system change.

The evolution of control and distribution of adaptive mutations in a metabolic pathway

In an attempt to understand whether it should be expected that some genes tend to be used disproportionately often by natural selection, we investigated two related phenomena: the evolution of flux control among enzymes in a metabolic pathway and properties of adaptive substitutions in pathway enzymes. These two phenomena are related by the principle that adaptive substitutions should occur more frequently in enzymes with greater flux control. Predicting which enzymes will be preferentially involved in adaptive evolution thus requires an evolutionary theory of flux control. We investigated the evolution of enzyme control in metabolic pathways with two models of enzyme kinetics: metabolic control theory (MCT) and Michaelis-Menten saturation kinetics (SK). Our models generate two main predictions for pathways in which reactions are moderately to highly irreversible: (1) flux control will evolve to be highly unequal among enzymes in a pathway and (2) upstream enzymes evolve a greater control coefficient then those downstream. This results in upstream enzymes fixing the majority of beneficial mutations during adaptive evolution. Once the population has reached high fitness, the trend is reversed, with the majority of neutral/slightly deleterious mutations occurring in downstream enzymes. These patterns are the result of three factors (the first of these is unique to the MCT simulations while the other two seem to be general properties of the metabolic pathways): (1) the majority of randomly selected, starting combinations of enzyme kinetic rates generate pathways that possess greater control for the upstream enzymes compared to downstream enzymes; (2) selection against large pools of intermediate substrates tends to prevent majority control by downstream enzymes; and (3) equivalent mutations in enzyme kinetic rates have the greatest effect on flux for enzymes with high levels of flux control, and these enzymes will accumulate adaptive substitutions, strengthening their control. Prediction 1 is well supported by available data on control coefficients. Data for evaluating prediction 2 are sparse but not inconsistent with this prediction.

Unresolved boundaries of evolutionary theory and the question of how inheritance systems evolve: 75 years of debate on the evolution of dominance

One of the key issues in the evolution of life is the evolution of inheritance systems. In population genetics, the earliest attempt at addressing the latter problem revolved around Fisher's theory on the evolution of dominance. Fisher's hypothesis was that inheritance systems could be modified during the evolutionary process in such a way that wild-type phenotypes could become dominant with respect to mutant phenotypes. This would result in the buffering of a population against the deleterious effects of mutations. The debate that ensued on this topic has been one of the most longstanding in evolutionary theory. At present, the prevalent view is that dominance cannot evolve as a direct result of selection. Furthermore, it has been argued that due to inherent constraints in biochemical systems, the manifestation of dominance is a default expectation and hence evolutionary explanations are not necessary. This has led to the position that the subject is generally resolved and no further debate is necessary. However, there are also several studies indicating that dominance levels can be modified as a result of changes in the genetic background. Furthermore, other studies have indicated that dominance selection is possible in certain circumstances. To a large degree, conclusions from both of the latter types of studies have been ignored. In this article, the history of several intellectual and methodological traditions that have contributed to this debate are traced, including experimental genetics, theoretical population genetics and theoretical biochemistry. In the light of both old and contemporary works on this topic, it is argued that contrary to the prevalent view, the evolution of dominance is not a resolved issue. A re-examination of this issue is essential, given that dominance evolution is likely to be an important stepping stone towards understanding the evolution of inheritance systems.

Metabonomics in Toxicology: A Review

Metabonomics and its many pseudonyms (metabolomics, metabolic profiling, etc.) have exploded onto the scientific scene in the past 2 to 3 years. Nowhere has the impact been more profound than within the toxicology community. Within this community there exists a great deal of uncertainty about whether metabonomics is something to count on or just the most recent technological flash in the pan. Much of the uncertainty is due to unfamiliarity with analytical and chemometric facets of the technology and the attendant fear of any "black-box." With those fears in mind, metabonomics technology is reviewed with particular emphasis on toxicologic applications in preclinical drug development. The jargon, logistics, and applications of the technology are covered in some detail with emphasis on recent work in the field.

Evolution of dominance in metabolic pathways

Dominance is a form of phenotypic robustness to mutations. Understanding how such robustness can evolve provides a window into how the relation between genotype and phenotype can evolve. As such, the issue of dominance evolution is a question about the evolution of inheritance systems. Attempts at explaining the evolution of dominance have run into two problems. One is that selection for dominance is sensitive to the frequency of heterozygotes. Accordingly, dominance cannot evolve unless special conditions lead to the presence of a high frequency of mutant alleles in the population. Second, on the basis of theoretical results in metabolic control analysis, it has been proposed that metabolic systems possess inherent constraints. These hypothetical constraints imply the default manifestation of dominance of the wild type with respect to the effects of mutations at most loci. Hence, some biologists have maintained that an evolutionary explanation is not relevant to dominance. In this article, we put into question the hypothetical assumption of default metabolic constraints. We show that this assumption is based on an exclusion of important nonlinear interactions that can occur between enzymes in a pathway. With an a priori exclusion of such interactions, the possibility of epistasis and hence dominance modification is eliminated. We present a theoretical model that integrates enzyme kinetics and population genetics to address dominance evolution in metabolic pathways. In the case of mutations that decrease enzyme concentrations, and given the mechanistic constraints of Michaelis-Menten-type catalysis, it is shown that dominance of the wild type can be extensively modified in a two-enzyme pathway. Moreover, we discuss analytical results indicating that the conclusions from the two-enzyme case can be generalized to any number of enzymes. Dominance modification is achieved chiefly through changes in enzyme concentrations or kinetic parameters such as k(cat), both of which can alter saturation levels. Low saturation translates into higher levels of dominance with respect to mutations that decrease enzyme concentrations. Furthermore, it is shown that in the two-enzyme example, dominance evolves as a by-product of selection in a manner that is insensitive to the frequency of heterozygotes. Using variation in k(cat) as an example of modifier mutations, it is shown that the latter can have direct fitness effects in addition to dominance modification effects. Dominance evolution can occur in a frequency-insensitive manner as a result of selection for such dual-effects alleles. This type of selection may prove to be a common pattern for the evolution of phenotypic robustness to mutations.

The modelling of a primitive 'sustainable' conservative cell

The simple sustainable or 'eternal' cell model, assuming preservation of all proteins, is designed as a building block, a primitive element upon which one can build more complete functional cell models of various types, representing various species. In the modelling we emphasize the electrophysiological aspects, in part because these are a well-developed component of cell models and because membrane potentials and their fluctuations have been generally omitted from metabolically oriented cell models in the past. Fluctuations in membrane potential deserve heightened consideration because probably all cells have negative intracellular potentials and most cells demonstrate electrical activity with vesicular extrusion, receptor occupancy, as well as with stimulated excitation resulting in regenerative depolarization. The emphasis is on the balances of mass, charge, and of chemical species while accounting for substrate uptake, metabolism and metabolite loss from the cell. By starting with a primitive representation we emphasize the conservation ideas. As more advanced models are generated they must adhere to the same basic principles as are required for the most primitive incomplete model.

Advantages and disadvantages of aggregating fluxes into synthetic and degradative fluxes when modelling metabolic pathways

It is now widely accepted that mathematical models are needed to predict the behaviour of complex metabolic networks in the cell, in order to have a rational basis for planning metabolic engineering with biotechnological or therapeutical purposes. The great complexity of metabolic networks makes it crucial to simplify them for analysis, but without violating key principles of stoichiometry or thermodynamics. We show here, however, that models for branched complex systems are sometimes obtained that violate the stoichiometry of fluxes at branch points and as a result give unrealistic metabolite concentrations at the steady state. This problem is especially important when models are constructed with the S-system form of biochemical systems theory. However, the same violation of stoichiometry can occur in metabolic control analysis if control coefficients are assumed to be constant when trying to predict the effects of large changes. We derive the appropriate matrix equations to analyse this type of problem systematically and to assess its extent in any given model.

Model of the pH-dependence of the concentrations of complexes involving metabolites, haemoglobin and magnesium ions in the human erythrocyte

The rate of glucose consumption and the concentrations of glycolytic intermediates in human erythrocytes have long been known to be pH sensitive. Despite the extensive literature on modelling erythrocyte metabolism, no model developed so far can adequately describe all of these pH-dependent changes. None of these models have included all the significant association reactions between metabolites, Hb and Mg2+ that will influence metabolism. As part of a larger enterprise to develop a detailed model of erythrocyte glycolysis, we present a sub-model which predicts, as a function of pH and oxygenation state, the concentrations of free and Mg(2+)-bound metabolites that are substrates, co-factors and effectors of glycolysis. This model shows that pH changes around physiological values can cause large changes in the distribution of metabolites between free, bound and Mg(2+)-complexed forms, based on binding interactions alone; in oxygenated cells, at pH 7.2-7.6, many glycolytic intermediates undergo changes in concentration of 50-100%. The model also predicts intracellular concentrations of free Mg2+ in erythrocytes to be 0.4 mM and 0.64 mM in oxygenated and deoxygenated cells, respectively, assuming a total magnesium concentration of 3 mM (approximately 88% of the total magnesium usually found in erythrocytes). This is in close agreement with the values found by Flatman [Flatman, P. W. (1980) J. Physiol. 300, 19-30] and the finding by Flatman and Lew [Flatman, P. & Lew, V. L. (1977) Nature 267, 360-362] that the main Mg2+ buffer systems bind approximately 90% of Mg2+ in the cell. Hexokinase has a high 'flux control coefficient' in human erythrocyte glycolysis, so the dependence of its rate on the pH and oxygenation state of haemoglobin is important. With a low oxygen tension and an intracellular pH of 7.34, the major inhibitor of its activity (2,3-bisphosphoglycerate) is 85% bound to either haemoglobin or Mg2+, and the maximum possible flux of substrate via it would be 2.05 mmol L erythrocytes-1 h-1. However, if the haemoglobin were saturated with oxygen, and the pH were 7.2, it was calculated that the maximum rate would be 1.48 mmol L erythrocytes-1 h-1; this is primarily due to a doubling of the free 2,3-bisphosphoglycerate concentration. However, the full extent of the inhibition is counteracted because the concentration of the Mg(2+)-2,3-bisphosphoglycerate would be approximately doubled. Many other similar comparisons are possible with this new model, which highlights the complex network of interactions between haemoglobin, Mg2+, H+ and the metabolites as substrates and effectors of the glycolytic reactions.

Qualitative analysis of biochemical reaction systems

The qualitative analysis of biochemical reaction systems is presented. A discrete event systems approach is used to represent and analyze bioreaction pathways. The approach is based on Petri nets, which are particularly suited to modeling stoichiometric transformations, i.e. the inter-conversion of metabolites in fixed proportions. The properties and methods for the analysis of Petri nets, along with their interpretation for biochemical systems, are presented. As an example, the combined glycolytic and pentose phosphate pathway of the erythrocyte cell is presented to illustrate the concepts of the methodology.

Metabolic control analysis: a survey of its theoretical and experimental development

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