Control analysis of time-dependent metabolic systems

Metabolic Control Analysis is extended to time dependent systems. It is assumed that the time derivative of the metabolite concentrations can be written as a linear combination of rate laws, each one of first order with respect to the corresponding enzyme concentration. The definitions of the control and elasticity coefficients are extended, and a new type of coefficient ("time coefficient", "T") is defined. First, we prove that simultaneous changes in all enzyme concentrations by the same arbitrary factor, is equivalent to a change in the time scale. When infinitesimal changes are considered, these arguments lead to the derivation of general summation theorems that link control and time coefficients. The comparison of two systems with identical rates, that only differ in one metabolite concentration, leads to a method for the construction of general connectivity theorems, that relate control and elasticity coefficients. A mathematical proof in matrix form, of the summation and connectivity relationships, for time dependent systems is given. Those relationships allow one to express the control coefficients in terms of the elasticity and time coefficients for the case of unbranched pathway.     

The mathematics of metabolic control analysis revisited

In this minireview, several different approaches to derivation of the theorems and relationships of Metabolic Control Analysis (MCA) are discussed and an alternative approach is presented. This new approach consists of solving the steady-state mass balances for the intracellular metabolites using linearized kinetics. The application of linearized kinetics reflects the fact that MCA is based on linearization of the system equations in a reference steady state. Our derivation is valid for metabolic networks of arbitrary complexity, including those containing conserved moieties and branches. The value of our approach is its simplicity: the derivation is straightforward and therefore easy to follow. It can serve as a compact introduction to the mathematical basis of MCA.     

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.     

Nested genes and increasing organizational complexity of metazoan genomes

The most common form of protein-coding gene overlap in eukaryotes is a simple nested structure, whereby one gene is embedded in an intron of another. Analysis of nested protein-coding genes in vertebrates, fruit flies and nematodes revealed substantially higher rates of evolutionary gains than losses. The accumulation of nested gene structures could not be attributed to any obvious functional relationships between the genes involved and represents an increase of the organizational complexity of animal genomes via a neutral process.     

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.     

Sensitivity analysis of stoichiometric networks: an extension of metabolic control analysis to non-steady state trajectories

A sensitivity analysis of general stoichiometric networks is considered. The results are presented as a generalization of Metabolic Control Analysis, which has been concerned primarily with system sensitivities at steady state. An expression for time-varying sensitivity coefficients is given and the Summation and Connectivity Theorems are generalized. The results are compared to previous treatments. The analysis is accompanied by a discussion of the computation of the sensitivity coefficients and an application to a model of phototransduction.     

An ontological dilemma: epistemology and methodology of historical biogeography

The task of historical biogeography is to reveal and explain the history of biotas and their historical connections. Historical «relationship>> between biotas is defined as the sharing of descendants of the same ancestor. Several generalized patterns of relationship, rather than a single universal one, should be expected for any set of biotas or areas. Such generalized patterns must be sought by comparison of individual patterns, based on individual monophyletic groups. Generalized patterns of biota relationships are formally statements about numerical universals, while a pattern derived from an individual group is a statement about a particular. Such statements are not subject to testing in the Popperian sense; they may be falsified as well as verified. As in other historical sciences, explanation in historical biogeography is genetic in form and probabilistic in nature. An explanation is falsified when an explanatory premise is, and corroborated when an explanatory premise is verified. Two major methodologies exist to derive «area cladograms>> from substituted (taxon) cladograms, Component Analysis and Parsimony Analysis. It is argued that Parsimony Analysis is the theoretically more satisfactory of these because it treats all sources of «error>> in the same way, making no process-related assumptions about the sources of conflicts. The rooting of area dendrograms is problematic. The rooting by an «allzero>> outarea is theoretically unsound and the dendrogram should be rooted a posteriori adjacent to the ancestral area(s), or not at all.     

Metabolic design: how to engineer a living cell to desired metabolite concentrations and fluxes

A biotechnological aim of genetic engineering is to increase the intracellular concentration or secretion of valuable compounds, while making the other concentrations and fluxes optimal for viability and productivity. Efforts to accomplish this based on over-expression of the enzyme, catalyzing the so-called "rate-limiting step," have not been successful. Here we develop a method to determine the enzyme concentrations that are required to achieve such an aim. This method is called Metabolic Design Analysis and is based on the perturbation method and the modular ("top-down") approach-formalisms that were first developed for the analysis of biochemical regulation such as, Metabolic Control Analysis. Contrary to earlier methods, the desired alterations of cellular metabolism need not be small or confined to a single metabolite or flux. The limits to the alterations of fluxes and metabolite concentrations are identified. To employ Metabolic Design Analysis, only limited kinetic information concerning the pathway enzymes is needed.     

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.     

Biometry of stomata in Blechnum species (Blechnaceae) with some taxonomic and ecological implications for the ferns

Morphological stomatal traits, such as size, form and frequency, have been subject of much literature, including their relationships with environmental factors. However, little effort have focused on ferns, and very few in the genus Blechnum. Stomatal length, width and frequency (as stomatal index) of a number of specimens of fourteen Neotropical species of Blechnum were measured in adult pinnae. The aim of the work was to find biometrical relationships between stomatal traits and between stomatal traits and habit, habitat and ecosystem of the plants. Statistical analyses of data were conducted using Exploratory Data Analysis and Multivariate Statistical Methods. Stomatal length and width showed a very high correlation, suggesting an endogenous, genetic control, thus giving these traits a considerable diagnostic utility. With respect to the relationships between stomatal traits and environment, we found significant statistical relationships between altitude and stomatal index. We also addressed the interpretation of the ecological-selective significance of various assemblages of stomatal traits in a diverse conjunction of habits, habitats and ecosystems.     

Structure and Sentiment in Serbian Cousinship

Analysis of survey and interview data from modern Belgrade shows an interplay between the structural alignments of traditional Serbian kinship and the more individual considerations of affective relationships between parents and their siblings. Cousin relationships are a perpetuation of parental sibling relationships but are markedly affected by structural factors. "Liking" appears to be a matter of loyalty, trust, and obligation and is strongest along agnatic lines; the greatest continuity of positive affect is between the close fraternal relationships in the parental generation and the close relationship between mutual father's brother's sons. The virifocality of the system is shown for other facets of kinship including possible warping of genealogical perception and recall.     

Engineering a living cell to desired metabolite concentrations and fluxes: pathways with multifunctional enzymes

With molecular genetics enabling modulation of the concentrations of cellular enzymes, metabolic engineering becomes limited by the question of which modulations of the enzyme concentrations are required to bring about a desired pattern of cellular metabolism. In an earlier paper (Kholodenko et al. (1998). Biotechnol. Bioeng. 59, 239-247) we derived a method to determine the required modulations. This method, however, cannot be immediately applied to cellular pathways with enzymes catalyzing more than one step in metabolism (multifunctional enzymes). In the present paper we show to which extent the presence of multifunctional enzymes limits biotechological ambitions, which one might otherwise pursue in vain. In particular, it is impossible to change the concentration of a single intermediate and leave the rest of metabolism unperturbed if that intermediate interacts directly with a multifunctional enzyme. The analytical machinery of Metabolic Control Analysis is used to relate the desired and ensuing changes in the metabolic pattern. An explicit solution to this problem of engineering metabolism is then given in the form of a single matrix equation.     

Structure of the pigeon lysozyme and its relationship with other type c lysozymes

1. The secondary structure of the pigeon egg-white lysozyme shows important differences when compared to other type c lysozymes. These differences are mainly located at the region comprising residues 77-84. This segment contains one alpha-helix in the lysozymes c studied by means of an X-ray analysis, while the residues at such positions in pigeon lysozyme would form two beta-bends. 2. Analysis of the tertiary structure of the pigeon lysozyme by means of hydropathy profiles reveals that the above segment seems to be more hydrophilic in the pigeon enzyme than in other type c lysozymes. 3. Though a certain similarity to the calcium-binding loop of alpha-lactalbumins is detected in pigeon lysozyme, the circular dichroism spectra of the protein at neutral pH do not change in the presence of Ca2+ ions. 4. The presented structural analysis is discussed in terms of function-structure and antigenicity relationships between the type c lysozymes.     

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.     

Studies on the fate of homologous DNA applied to seedlings of Matthiola incana.

Seedlings of Matthiola incana (crucifer) are able to take up exogenous homologous DNA by the roots. DNA homogenously labelled with [3H]adenine and 5-bromodeoxyuridine is incorporated into the plants in a macromolecular form. Intact donor DNA and a fraction with a buoyant density intermediate between that of the donor and the recipient DNA can be recovered. Analysis of this intermediate fraction by ultrasonication and alkali treatment allows the suggestion that homologous DNA is integrated as a double-stranded DNA which becomes covalently linked to the recipient DNA. Control experiments in which seedlings were incubated in a mixture simulating donor DNA degradation products in the presence and absence of unlabelled competitors suggest that these results are not due to the breakdown of donor DNA and reincorporation of the products during DNA synthesis in the recipient plants. When ultrasonicated or thermally denatured DNA is applied to the plants it may be degraded and reused for recipient DNA synthesis but it is not recovered in a macromolecular form. The possibility that the intermediate DNA fraction arises by bacterial contamination of the plants can be excluded by several arguments. Autoradiographic studies show that at least part of the radioactivity of the donor DNA taken up by the plants is associated with the cell nucleus.     

A generalization of metabolic control analysis to conditions of no proportionality between activity and concentration of enzymes

The assumption currently considered in the Metabolic Control Theory that velocity of every isolated step is proportional to enzyme concentration, is analysed by considering that in some metabolic systems that condition could not be accomplished. Analysis of the main core of this theory is carried out removing this hypothesis, expressed as "epsilon ei vi is not necessarily equal to one". The results obtained supply a more general formulation of the main theorems of the Control Theory, extending its possible application to more complex metabolic systems.     

Plant-environment relationships on the Montlake wildlife area,Seattle, Washington,USA

Grassland vegetation on the Montlake fill was analyzed using TWINSPAN. Eight herb communities were recognized. Moisture, proximity to gas vents, and disturbance are the main factors that control species and community distributions. Binary discriminant analysis (BDA) and detrended correspondence analysis (DCA) were used to study species-environment relationships. BDA revealed complex species response patterns and the resultant indicator values were used to interpret the ordination axes. Species distributions are controlled primarily by moisture, but also influenced by soil pH. Multiple regressions revealed little about plant-environment relationships not discovered by BDA. Before robust nonlinear methods are available, BDA, metric ordination with data stratification and nonmetric ordination are methods that can yield satisfactory results in exploratory plant-environment studies. BDA alone is an efficient, useful first approach where response patterns of species are initially unknown.Abbreviations BDA Binary Discriminant Analysis - DCA Detrended Correspondence Analysis     

Integration of temporal analysis and control analysis of metabolic systems.

A theory is developed that integrates approaches to the analysis of pathway transient response and metabolic control analysis. A Temporal Control Coefficient is defined that is a measure of the system's transient response to modulation of enzyme activity or concentration. The approach allows for the analysis of the establishment of a steady state from rest, of the system's 'agility' of response to minor perturbations of a pre-existing steady state and of the macroscopic transition between steady states. In the last-mentioned case it is shown that, like the transient time itself, the control of transient response retains the property of independence from the mechanism of the transition. In consequence, the Temporal Control Coefficient can be defined in terms of the control properties of the initial and final states alone without reference to the mechanism of transition. A summation property is shown to apply to the Temporal Control Coefficients in each case. Connectivity relationships between elasticities and Temporal Control Coefficients are also established.     

Controversy and Consensus in Asteroid Systematics: New Insights to Ordinal and Familial Relationships

Phylogenetic approaches have sparked controversy in asteroidsystematics since 1987. Despite recent attempts at resolvingthese differences and evidence of some consensus, our understandingof relationships among asteroid taxa remains unsatisfactory.This paper presents results of an investigation into asteroidevolutionary history using DNA sequence data from mitochondrialtransfer RNA and the cytochrome oxidase c subunit I genes analyzedwith and without previously published ribosomal gene sequences.Analysis of these genes provides an assessment of familial relationshipsbut does little to elucidate ordinal relationships. A basalposition for the Paxillosida is not supported. However, closerelationships of some velatid and valvatid taxa are upheld.The resulting phylogenies are not a definitive answer to controversiesin asteroid systematics. However, with new insights to someasteroid relationships, they highlight the need for a redirectionof future systematic studies so a consensus can be made.