Control, regulation and thermodynamics of free-energy transduction

The quantitative formalism called Metabolic Control Theory makes it possible to be precise in discussions of metabolic control. To illustrate this, I will mention 2 experimental systems where free energy is converted from one form to another, i.e., bacteriorhodopsin liposomes and mitochondrial oxidative phosphorylation. More specifically I shall discuss how the distribution of the control of fluxes, concentrations and potentials, among the various enzymes (catalysts) in these systems has been measured and how this distribution can be understood in terms of the enzyme properties. From the outset, Metabolic Control Theory was valid for branched metabolic pathways with non-linear kinetics. Yet, it seemed to be limited to metabolic pathways without enzyme-enzyme interactions and to steady states. It is now clear that these limitations were apparent only and recent extensions to Metabolic Control Theory deal explicitly with enzyme-enzyme interaction and with transient-time analysis. Other limitations are inherent. For instance, Metabolic Control Theory pays for its clarity and exactness by being limited to small modulations. Mosaic Non Equilibrium Thermodynamics and Biochemical System Analysis are formalisms that deal with larger changes, at the cost of accuracy and exactness.     

Distribution of the flux control in convergent metabolic pathways: theory and application to experimental and simulated systems

1. Metabolic systems involving branched convergent pathways are analyzed under Flux Control Theory, obtaining a relationship between the contribution of every convergent pathway to the total flux and its Flux Control Coefficient. 2. An experimental model system is carried out to demonstrate the physical application of some conclusions of theoretical treatment. 3. Two different types of branched pathways are simulated by computer. 4. In both cases results are in agreement with the theoretical conclusions, showing in addition some new aspects on metabolic control.     

Control theory of metabolic channelling

Various factors appear to control muscle energetics, often in conjunction. This calls for a quantitative approach of the type provided by Metabolic Control Analysis for intermediary metabolism and mitochondrial oxidative phosphorylation. To the extent that direct transfer of high energy phosphates and spatial organization plays a role in muscle energetics however, the standard Metabolic Control Theory does not apply, neither do its theorems regarding control.This chapter develops the Control Theory that does apply to the muscle system. It shows that direct transfer of high energy phosphates bestows a system with enhanced control: the sum of the control exerted by the participating enzymes on the flux of free energy form the mitochondrial matrix to the actinomyosin may well exceed the 100% mandatory for ideal metabolic pathways. It is also shown how sequestration of high energy phosphates may allow for negative control on pathway flux. The new control theory gives methods functionally to diagnose the extent to which channelling and metabolite sequestration occur.     

A formal investigation of Cultural Selection Theory: acoustic adaptation in bird song

The greatest challenge for Cultural Selection Theory lies is the paucity of evidence for structural mechanisms in cultural systems that are sufficient for adaptation by natural selection. In part, clarification is required with respect to the interaction between cultural systems and their purported selective environments. Edmonds et al. have argued that Cultural Selection Theory requires simple, conclusive, unambiguous case studies in order to meet this challenge. To that end, this paper examines the songs of the Rufous-collared Sparrow, which seem to exhibit cultural adaptations minimizing signal degradation relative to local environments. Specifically, the more forested the habitat, the more the tail end of the song resembles a whistle rather than a trill; yet, variation in song is uncorrelated with genetic variation. This paper explores the mechanisms responsible for these putative acoustic adaptations through a series of computer simulations. The main point of this research is not to test this model, but to demonstrate that models of this type have the resources to meet the in-principle objections that have been raised against Cultural Selection Theory. This research lends much-needed empirical support to Cultural Selection Theory by clarifying the nature of the interaction between culture and environment. It also contributes to evolutionary theory by clarifying the scope and limits of adaptation by natural selection.     

Control theory of metabolic channelling

Various factors appear to control muscle energetics, often in conjunction. This calls for a quantitative approach of the type provided by Metabolic Control Analysis for intermediary metabolism and mitochondrial oxidative phosphorylation. To the extent that direct transfer of high energy phosphates and spatial organization plays a role in muscle energetics however, the standard Metabolic Control Theory does not apply, neither do its theorems regarding control.This paper develops the Control Theory that does apply to the muscle system. It shows that direct transfer of high energy phosphates bestows a system with enhanced control: the sum of the control exerted by the participating enzymes on the flux of free energy from the mitochondrial matrix to the actinomyosin may well exceed the 100% mandatory for ideal metabolic pathways. It is also shown how sequestration of high energy phosphates may allow for negative control on pathway flux. The new control theory gives methods functionally to diagnose the extent to which channelling and metabolite sequestration occur.This article was published in Molecular and Cellular Biochemistry133/134: 313–331, 1994. Kluwer Academic Publishers regret the publication of the uncorrected version.     

Optimal Management of Two-Species Bioeconomics Systems

1IntroductionOptimalmanagementofsystemsofrenewableresourcesisanimportantbranchofMathemati-calEcology.Theoptimalmanagementofbiologicalspecies,asatypicalrepresentativeoftheopti-malmanagementofrenewableresourcesisbeingattachedmuchmoreinportancebyBioeconomistandbecameanindependentbranchinthe1980's.C.W.ClarkandR.W.Mcklvey,etc,didalotofresearchworkinthisfield.Themajorcharacteristicoftheoptimalmanagementofbioeconomicsystemistooptimizetheharvestrevenueonthebasisofecologicalbalance(e.g.,permanentex…     

Biochemical systems theory and metabolic control theory: 2. the role of summation and connectivity relationships

Perhaps the major obstacle to recognizing the relatedness of Biochemical Systems Theory (BST) and a subsequently developed approach some have called Metabolic Control Theory (MCT) is the summation and connectivity relationships. These are the most visible and central features of the MCT approach to the understanding of intact biochemical systems, whereas in the BST approach they appear to be invisible and peripheral. Generalized versions of these relationships are shown to be inherent to BST, and it is shown how their role differs from that within MCT. The significance of summation and connectivity relationships is shown to be historical and secondary in the sense that one can understand fully the integrated behavior of complex biochemical systems in steady state with BST and never explicitly invoke these relationships. It also is shown that the summation and connectivity relationships in MCT have inherent limitations that make them inadequate as the basis for a general theory of biochemical systems. The results in this paper, together with those in the previous paper, clearly demonstrate that MCT is a special case of BST.     

Effects of epistasis on phenotypic robustness in metabolic pathways

It is an open question whether phenomena such as phenotypic robustness to mutation evolve as adaptations or are simply an inherent property of genetic systems. As a case study, we examine this question with regard to dominance in metabolic physiology. Traditionally the conclusion that has been derived from Metabolic Control Analysis has been that dominance is an inevitable property of multi-enzyme systems and hence does not require an evolutionary explanation. This view is based on a mathematical result commonly referred to as the flux summation theorem. However it is shown here that for mutations involving finite changes (of any magnitude) in enzyme concentration, the flux summation theorem can only hold in a very restricted set of conditions. Using both analytical and simulation results we show that for finite changes, the summation theorem is only valid in cases where the relationship between genotype and phenotype is linear and devoid of non-linearities in the form of epistasis. Such an absence of epistasis is unlikely in metabolic systems. As an example, we show that epistasis can arise in scenarios where we assume generic non-linearities such as those caused by enzyme saturation. In such cases dominance levels can be modified by mutations that affect saturation levels. The implication is that dominance is not a necessary property of metabolic systems and that it can be subject to evolutionary modification.     

Biochemical systems theory: operational differences among variant representations and their significance

An appropriate language or formalism for the analysis of complex biochemical systems has been sought for several decades. The necessity for such a formalism results from the large number of interacting components in biochemical systems and the complex non-linear character of these interactions. The Power-Law Formalism, an example of such a language, underlies several recent attempts to develop an understanding of integrated biochemical systems. It is the simplest representation of integrated biochemical systems that has been shown to be consistent with well-known growth laws and allometric relationships--the most regular, quantitative features that have been observed among the systemic variables of complex biochemical systems. The Power-Law Formalism provides the basis for Biochemical Systems Theory, which includes several different strategies of representation. Among these, the synergistic-system (S-system) representation is the most useful, as judged by a variety of objective criteria. This paper first describes the predominant features of the S-system representation. It then presents detailed comparisons between the S-system representation and other variants within Biochemical Systems Theory. These comparisons are made on the basis of objective criteria that characterize the efficiency, power, clarity and scope of each representation. Two of the variants within Biochemical Systems Theory are intimately related to other approaches for analyzing biochemical systems, namely Metabolic Control Theory and Flux-Oriented Theory. It is hoped that the comparisons presented here will result in a deeper understanding of the relationships among these variants. Finally, some recent developments are described that demonstrate the potential for further growth of Biochemical Systems Theory and the underlying Power-Law Formalism on which it is based.     

Hierarchies and causal relationships in interpretative models of the neoplastic process

The aim of this paper is to present a critical analysis of the kind of biological systems identified in the main explanatory theories of cancer (i.e. Somatic Mutation Theory and Tissue Organization Field Theory) and how references to the hierarchical organization of these biological systems are used in their explanatory arguments. I will discuss these aspects in terms of the isolation of the "locus of control" (Bechtel and Richardson 2010); that is, the point at which decisions are made shaping the explanatory endeavour. In fact, the current view of the neoplastic process, not as a static circumstance but as an evolving molecular and cellular process, makes it evident that the choice of the right level of analysis is not self-evident. This focus clarifies some epistemological reasons for the divergence between reductionist and organicist accounts and seems to suggest that the basis for distinctions among causal relationships that scientists sometimes make can be found in the hierarchical character of complex biological systems. I will argue that these different causal relationships reflect different levels of epistemic concern.     

Kinetics of metabolic pathways. A system in vitro to study the control of flux.

A method for determining Control Coefficients is proposed for systems studied in vitro and applied to a model pathway. Rat liver extract, which converts glucose into glycerol 3-phosphate, was used with the addition to the incubation mixture of fructose-bisphosphate aldolase, triose-phosphate isomerase and glycerol-3-phosphate dehydrogenase as 'auxiliary' enzymes, which leaves all the control on the first three enzymes. The flux of the metabolic pathway was recorded by assaying NADH decay. Flux Control Coefficients (CJE) of hexokinase, glucose-6-phosphate isomerase and phosphofructokinase were calculated by titration of the system with increasing quantities of extraneous enzymes. It is shown that the summation property is fulfilled. The applicability of this procedure to study the control in any metabolic pathway is discussed. Possible relevance of the method to conditions in vivo and its limitations are considered.     

Metabolic flux analysis in plants: coping with complexity

Theory and experience in metabolic engineering both show that metabolism operates at the network level. In plants, this complexity is compounded by a high degree of compartmentation and the synthesis of a very wide array of secondary metabolic products. A further challenge to understanding and predicting plant metabolic function is posed by our ignorance about the structure of metabolic networks even in well-studied systems. Metabolic flux analysis (MFA) provides tools to measure and model the functioning of metabolism, and is making significant contributions to coping with their complexity.
This review gives an overview of different MFA approaches, the measurements required to implement them and the information they yield. The application of MFA methods to plant systems is then illustrated by several examples from the recent literature. Next, the challenges that plant metabolism poses for MFA are discussed together with ways that these can be addressed. Lastly, new developments in MFA are described that can be expected to improve the range and reliability of plant MFA in the coming years.     

Systems biology towards life in silico: mathematics of the control of living cells

Systems Biology is the science that aims to understand how biological function absent from macromolecules in isolation, arises when they are components of their system. Dedicated to the memory of Reinhart Heinrich, this paper discusses the origin and evolution of the new part of systems biology that relates to metabolic and signal-transduction pathways and extends mathematical biology so as to address postgenomic experimental reality. Various approaches to modeling the dynamics generated by metabolic and signal-transduction pathways are compared. The silicon cell approach aims to describe the intracellular network of interest precisely, by numerically integrating the precise rate equations that characterize the ways macromolecules’ interact with each other. The non-equilibrium thermodynamic or ‘lin–log’ approach approximates the enzyme rate equations in terms of linear functions of the logarithms of the concentrations. Biochemical Systems Analysis approximates in terms of power laws. Importantly all these approaches link system behavior to molecular interaction properties. The latter two do this less precisely but enable analytical solutions. By limiting the questions asked, to optimal flux patterns, or to control of fluxes and concentrations around the (patho)physiological state, Flux Balance Analysis and Metabolic/Hierarchical Control Analysis again enable analytical solutions. Both the silicon cell approach and Metabolic/Hierarchical Control Analysis are able to highlight where and how system function derives from molecular interactions. The latter approach has also discovered a set of fundamental principles underlying the control of biological systems. The new law that relates concentration control to control by time is illustrated for an important signal transduction pathway, i.e. nuclear hormone receptor signaling such as relevant to bone formation. It is envisaged that there is much more Mathematical Biology to be discovered in the area between molecules and Life.     

Subcellular metabolic organization in the context of dynamic energy budget and biochemical systems theories

The dynamic modelling of metabolic networks aims to describe the temporal evolution of metabolite concentrations in cells. This area has attracted increasing attention in recent years owing to the availability of high-throughput data and the general development of systems biology as a promising approach to study living organisms. Biochemical Systems Theory (BST) provides an accurate formalism to describe biological dynamic phenomena. However, knowledge about the molecular organization level, used in these models, is not enough to explain phenomena such as the driving forces of these metabolic networks. Dynamic Energy Budget (DEB) theory captures the quantitative aspects of the organization of metabolism at the organism level in a way that is non-species-specific. This imposes constraints on the sub-organismal organization that are not present in the bottom-up approach of systems biology. We use in vivo data of lactic acid bacteria under various conditions to compare some aspects of BST and DEB approaches. Due to the large number of parameters to be estimated in the BST model, we applied powerful parameter identification techniques. Both models fitted equally well, but the BST model employs more parameters. The DEB model uses similarities of processes under growth and no-growth conditions and under aerobic and anaerobic conditions, which reduce the number of parameters. This paper discusses some future directions for the integration of knowledge from these two rich and promising areas, working top-down and bottom-up simultaneously. This middle-out approach is expected to bring new ideas and insights to both areas in terms of describing how living organisms operate.     

ECA: control in ecosystems

Although metabolic control analysis (MCA) cannot be applied directly to microbial ecological systems because of mass conservation and stoichiometric constraints, we demonstrate here that Hierarchical Control Analysis (HCA) can be applied to such systems. We illustrate the approach for a particular ecosystem example of the biological synthesis of acetic acid from glucose, and uncover some surprising aspects to the control of this miniature ecosystem.     

Modular metabolic control analysis of large responses

Deciphering the laws that govern metabolic responses of complex systems is essential to understand physiological functioning, pathological conditions and the outcome of experimental manipulations of intact cells. To this aim, a theoretical and experimental sensitivity analysis, called modular metabolic control analysis (MMCA), was proposed. This field was previously developed under the assumptions of infinitesimal changes and/or proportionality between parameters and rates, which are usually not fulfilled in vivo. Here we develop a general MMCA for two modules, not relying on those assumptions. Control coefficients and elasticity coefficients for large changes are defined. These are subject to constraints: summation and response theorems, and relationships that allow calculating control from elasticity coefficients. We show how to determine the coefficients from top-down experiments, measuring the rates of the isolated modules as a function of the linking intermediate (there is no need to change parameters inside the modules). The novel formalism is applied to data of two experimental studies from the literature. In one of these, 40% increase in the activity of the supply module results in less than 4% increase in flux, while infinitesimal MMCA predicts more than 30% increase in flux. In addition, it is not possible to increase the flux by manipulating the activity of demand. The impossibility of increasing the flux by changing the activity of a single module is due to an abrupt decrease of the control of the modules when their corresponding activities are increased. In these cases, the infinitesimal approach can give highly erroneous predictions.     

CONVERSION EFFICIENCIES IN HETEROTROPHIC ORGANISMS

1. The maximum possible efficiency at which living systems are able to convert input nutrients to their own biomass is between 70 and 80 %. 2. Conversion efficiency in bacteria, protozoa and metazoan cells in culture approximates more closely to 60%. 3. Conversion efficiency during embryonic development begins below 60% and rises above this level in the later stages. 4. Very young, post-natal organisms have high net efficiencies; 50 to 70% in homeotherms and 50 to 80 % in poikilotherms. 5. In cellular systems, capable of proliferation, conversion efficiency is independent of food supply. This means that conversion is directly dependent on nutrient supply. 6. Control of growth at the tissue level may occur through the control of the supply of nutrients to the tissues and its entry into the cells. 7. Compensatory growth, after and during undernutrition, involves increased absorption efficiency and reduced metabolic costs.     

Colour of environmental noise affects the nonlinear dynamics of cycling, stage-structured populations

Populations fluctuate because of their internal dynamics, which can be nonlinear and stochastic, and in response to environmental variation. Theory predicts how the colour of environmental stochasticity affects population means, variances and correlations with the environment over time. The theory has not been tested for cycling populations, commonly observed in field systems. We applied noise of different colours to cycling laboratory beetle populations, holding other statistical properties of the noise fixed. Theory was largely validated, but failed to predict observations in sufficient detail. The main period of population cycling was shifted up to 33% by the colour of environmental stochasticity. Noise colour affected population means, variances and dominant periodicities differently for populations that cycled in different ways without noise. Our results show that changes in the colour of climatic variability, partly caused by humans, may affect the main periodicity of cycling populations, possibly impacting industry, pest management and conservation.