Application of cybernetic models to metabolic engineering: investigation of storage pathways

A cybernetic model is proposed to examine generic features of storage pathways. This model is capable of describing synthesis of carbon and non-carbon storage polymers. The effect of environmental conditions is evaluated using storage polymer level as a fraction of total biomass as a gauge of pathway performance. The base wild-type pathway is then analyzed to determine the effect of genetic alterations upon system performance. Proposed modifications are tested using the cybernetic model as a diagnostic tool to ascertain the ramifications of potential genetic alterations. A methodology is developed within the cybernetic framework to describe alterations of enzyme activity and over-expression of pathway enzymes. Copyright 1998 John Wiley & Sons, Inc.     

Phytoenzyme systems as models for an understanding of general metabolic pathways.

A comparison is made between certain aspects of lipid metabolism in plant and animal tissues. While the general biochemical reactions are identical, a number of important variations are described and related to the general metabolic activities of the tissues.     

Information transfer in metabolic pathways. Effects of irreversible steps in computer models.

Various metabolic models have been studied by computer simulation in an effort to understand why allowing for the reversibility of the reaction catalysed by pyruvate kinase, normally considered as irreversible for all practical purposes, significantly altered the behaviour of the model of glycolysis in Trypanosoma brucei [Eisenthal, R. & Cornish-Bowden, A. (1998) J. Biol. Chem. 273, 5500-5505]. Studies of several much simpler models indicate that the enzymes catalysing early steps in a pathway must receive information about the concentrations of the metabolites at the end of the pathway if a model is to be able to reach a steady state; treating all internal steps as reversible is just one way of ensuring this. Feedback inhibition provides a much better way, and as long as feedback loops are present in a model it makes almost no difference to the behaviour whether the intermediate steps with large equilibrium constants are treated as irreversible. In the absence of feedback loops, ordinary product inhibition of all the enzymes in the chain can also transfer information; this is efficient for regulating fluxes but very inefficient for regulating intermediate concentrations. More complicated patterns of regulation, such as activation of a competing branch or forcing flux through a parallel route, can also serve to some degree as ways of passing information around an irreversible step. However, they normally do so less efficiently than inhibition, because the extent to which an enzyme or a pathway can be activated always has an upper limit (which may be below what is required), whereas most enzymes are inhibited completely at saturating concentrations of inhibitor.     

Directed evolution of metabolic pathways

The modification of cellular metabolism is of biotechnological and commercial significance because naturally occurring metabolic pathways are the source of diverse compounds used in fields ranging from medicine to bioremediation. Directed evolution is the experimental improvement of biocatalysts or cellular properties through iterative genetic diversification and selection procedures. The creation of novel metabolic functions without disrupting the balanced intracellular pool of metabolites is the primary challenge of pathway manipulation. The introduction of coordinated changes across multiple genetic elements, in conjunction with functional selection, presents an integrated approach for the modification of metabolism with benign physiological consequences. Directed evolution formats take advantage of the dynamic structures of genomes and genomic sub-structures and their ability to evolve in multiple directions in response to external stimuli. The elucidation, design and application of genome-restructuring mechanisms are key elements in the directed evolution of cellular metabolic pathways.     

Chromokinetics of metabolic pathways.

Some methods to study and intuitively understand steady-state flows in complicated metabolic pathways are discussed. For this purpose, a suitable decomposition of complex metabolic schemes into smaller subsystems is used. These independent subsystems are then interpreted as basic colors of a chromatic coloring scheme. The mixture of these basic colors allows an intuitive picture of how a steady state in a metabolic pathway can be understood. Furthermore, actions of drugs can be more easily investigated on this basis. An anaerobic variant of pyruvate metabolism in rat liver mitochondria is presented as a simple example. This experiment allows measurement of the percentage that each basic color contributes to the steady states resulting from different experimental conditions. Possible implementations of existing algorithms and rational design of new drugs are discussed. A MATHEMATICA program, based on a new algorithm for finding all basic colors of stoichiometric networks, is included.     

Mathematical models in genetics

In this study, we present some of the basic ideas of population genetics. The founders of population genetics are R.A. Fisher, S. Wright, and J. B.S. Haldane. They, not only developed almost all the basic theory associated with genetics, but they also initiated multiple experiments in support of their theories. One of the first significant insights, which are a result of the Hardy–Weinberg law, is Mendelian inheritance preserves genetic variation on which the natural selection acts. We will limit to simple models formulated in terms of differential equations. Some of those differential equations are nonlinear and thus emphasize issues such as the stability of the fixed points and time scales on which those equations operate. First, we consider the classic case when selection acts on diploid locus at which wу can get arbitrary number of alleles. Then, we consider summaries that include recombination and selection at multiple loci. Also, we discuss the evolution of quantitative traits. In this case, the theory is formulated in respect of directly measurable quantities. Special cases of this theory have been successfully used for many decades in plants and animals breeding.     

Novel metabolic pathways in Archaea

The Archaea harbor many metabolic pathways that differ to previously recognized classical pathways. Glycolysis is carried out by modified versions of the Embden-Meyerhof and Entner-Doudoroff pathways. Thermophilic archaea have recently been found to harbor a bi-functional fructose-1,6-bisphosphate aldolase/phosphatase for gluconeogenesis. A number of novel pentose-degrading pathways have also been recently identified. In terms of anabolic metabolism, a pathway for acetate assimilation, the methylaspartate cycle, and two CO2-fixing pathways, the 3-hydroxypropionate/4-hydroxybutyrate cycle and the dicarboxylate/4-hydroxybutyrate cycle, have been elucidated. As for biosynthetic pathways, recent studies have clarified the enzymes responsible for several steps involved in the biosynthesis of inositol phospholipids, polyamine, coenzyme A, flavin adeninedinucleotide and heme. By examining the presence/absence of homologs of these enzymes on genome sequences, we have found that the majority of these enzymes and pathways are specific to the Archaea.     

Recovering metabolic pathways via optimization

A metabolic pathway is a coherent set of enzyme catalysed biochemical reactions by which a living organism transforms an initial (source) compound into a final (target) compound. Some of the different metabolic pathways adopted within organisms have been experimentally determined. In this paper, we show that a number of experimentally determined metabolic pathways can be recovered by a mathematical optimization model.     

Parameter estimation in models combining signal transduction and metabolic pathways: the dependent input approach

Biological complexity and limited quantitative measurements pose severe challenges to standard engineering methodologies for modelling and simulation of genes and gene products integrated in a functional network. In particular, parameter quantification is a bottleneck, and therefore parameter estimation, identifiability, and optimal experiment design are important research topics in systems biology. An approach is presented in which unmodelled dynamics are replaced by fictitious 'dependent inputs'. The dependent input approach is particularly useful in validation experiments, because it allows one to fit model parameters to experimental data generated by a reference cell type ('wild-type') and then test this model on data generated by a variation ('mutant'), so long as the mutations only affect the unmodelled dynamics that produce the dependent inputs. Another novel feature of the approach is in the inclusion of a priori information in a multi-objective identification criterion, making it possible to obtain estimates of parameter values and their variances from a relatively limited experimental data set. The pathways that control the nitrogen uptake fluxes in baker's yeast (Saccharomyces cerevisiae) have been studied. Well-defined perturbation experiments were performed on cells growing in steady-state. Time-series data of extracellular and intracellular metabolites were obtained, as well as mRNA levels. A nonlinear model was proposed and was shown to be structurally identifiable given data of its inputs and outputs. The identified model is a reliable representation of the metabolic system, as it could correctly describe the responses of mutant cells and different perturbations.     

Bayesian modeling of complex metabolic pathways

Many chronic diseases are the result of a complex sequence of biochemical reactions involving exposures to various environmental agents, metabolized by a number of different genes. Routine epidemiologic analyses of such associations have tended to rely on standard contingency table or logistic regression methods, typically focusing on one variable at a time or pairwise combinations. We consider two statistical alternatives to this approach, one based on Bayesian model averaging, one based on pharmacokinetic modeling of the biochemical pathways. These approaches are illustrated using data from a case-control study of colorectal polyps in relation to tobacco smoking and consumption of well done red meat, both viewed as sources of heterocyclic amines and polycyclic aromatic hydrocarbons. The new analyses are structured in a manner that attempts to take advantage of prior knowledge of the metabolism of these classes of compounds and the various genes that regulate these pathways.     

Mathematical models of endocrine systems

There is proposed a generalized mathematical model of endocrine systems, consisting of a set of differential equations which describe a chain of chemical reactions. The product of each reaction stimulates or inhibits some other reaction in the chain except possibly the last, which may or may not influence the system. At least one reaction must be independent and able to proceed without stimulation or inhibition by the products of other reactions. If only two reactions of the type assumed constitute a closed chain, sustained periodic variations in the concentrations of the reaction products cannot occur. If the chain consists of three or more reactions forming a closed loop, sustained oscillations, such as are observed in the menstrual cycle or in the mental disorder called periodic catatonia, can occur under suitable conditions. In this case, the concentrations of the system components exhibit relaxation oscillations characterized by periodic degeneration of the system when an independent reaction becomes completely inhibited by other reaction products. A set of conditions sufficient to produce periodicities in component concentrations is presented. Application of the model to the normally periodic system of the menstrual cycle and to the abnormal endocrine system which causes periodic catatonia is discussed.     

Mathematical models of antibody response

An antigen triggers the clonal expansion of B lymphocytes accompanied by antibody production. This paper presents and compares the basic ideas of three mathematical models of B cell differentiation and proliferation.     

Unique sugar metabolic pathways of bifidobacteria

Bifidobacteria have many beneficial effects for human health. The gastrointestinal tract, where natural colonization of bifidobacteria occurs, is an environment poor in nutrition and oxygen. Therefore, bifidobacteria have many unique glycosidases, transporters, and metabolic enzymes for sugar fermentation to utilize diverse carbohydrates that are not absorbed by host humans and animals. They have a unique, effective central fermentative pathway called bifid shunt. Recently, a novel metabolic pathway that utilizes both human milk oligosaccharides and host glycoconjugates was found. The galacto-N-biose/lacto-N-biose I metabolic pathway plays a key role in colonization in the infant gastrointestinal tract. These pathways involve many unique enzymes and proteins. This review focuses on their molecular mechanisms, as revealed by biochemical and crystallographic studies.     

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.     

Kinetic modelling of plant metabolic pathways

This paper provides a review of kinetic modelling of plant metabolic pathways as a tool for analysing their control and regulation. An overview of different modelling strategies is presented, starting with those approaches that only require a knowledge of the network stoichiometry; these are referred to as structural. Flux-balance analysis, metabolic flux analysis using isotope labelling, and elementary mode analysis are briefly mentioned as three representative examples. The main focus of this paper, however, is a discussion of kinetic modelling, which requires, in addition to the stoichiometry, a knowledge of the kinetic properties of the constituent pathway enzymes. The different types of kinetic modelling analysis, namely time-course simulation, steady-state analysis, and metabolic control analysis, are explained in some detail. An overview is presented of strategies for obtaining model parameters, as well as software tools available for simulation of such models. The kinetic modelling approach is exemplified with discussion of three models from the general plant physiology literature. With the aid of kinetic modelling it is possible to perform a control analysis of a plant metabolic system, to identify potential targets for biotechnological manipulation, as well as to ascertain the regulatory importance of different enzymes (including isoforms of the same enzyme) in a pathway. Finally, a framework is presented for extending metabolic models to the whole-plant scale by linking biochemical reactions with diffusion and advective flow through the phloem. Future challenges include explicit modelling of subcellular compartments, as well as the integration of kinetic models on the different levels of the cellular and organizational hierarchy.     

Ab initio reconstruction of metabolic pathways

We propose a new formulation for the problem of ab initio metabolic pathway reconstruction. Given a set of biochemical reactions together with their substrates and products, we consider the reactions as transfers of atoms between the chemical compounds and we look for successions of reactions transferring a maximal (or preset) number of atoms between a given source and sink compound. We state this problem as the one of finding a composition of partial injections that maximizes the image size. First, we study the theoretical complexity of this problem, state some related problems and then give a practical algorithm to solve them. Finally, we present two applications of this approach to the reconstruction of the tryptophan biosynthesis pathway and to the glycolysis.