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J H Hofmeyr

Publications and source records attributed to J H Hofmeyr.

16 recordsLinked to original sources
PubMed2001

Building the cellular puzzle: control in multi-level reaction networks.

Quantitative conceptual tools dealing with control and regulation of cellular processes have been mostly developed for and applied to the pathways of intermediary metabolism. Yet, cellular processes are organized in different levels, metabolism forming the lowest level in a cascade of processes. Well-known examples are the DNA-mRNA-enzyme-metabolism cascade and the signal transduction cascades consisting of covalent modification cycles. The reaction network that constitutes each level can be viewed as a "module" in which reactions are linked by mass transfer. Although in principle all of these cellular modules are ultimately linked by mass transfer, in practice they can often be regarded as "isolated" from each other in terms of mass transfer. Here modules can interact with each other only by means of regulatory or catalytic effects-a chemical species in one module may affect the rate of a reaction in another module by binding to an enzyme or transport system or by acting as a catalyst. This paper seeks to answer two questions about the control and regulation of such multi-level reaction networks: (i) How can the control properties of the system as a whole be expressed in terms of the control properties of individual modules and the effects between modules? (ii) How do the control properties of a module in its isolated state change when it is embedded in the whole system through its connections with the other modules? In order to answer these questions a quantitative theoretical framework is developed and applied to systems containing two, three or four fully interacting modules; it is shown how it can be extended in principle to n modules. This newly developed theory therefore makes it possible to quantitatively dissect intermodular, internal and external regulation in multi-level systems.

Animals↗
PubMed1997

The reversible Hill equation: how to incorporate cooperative enzymes into metabolic models.

MOTIVATION: Realistic simulation of the kinetic properties of metabolic pathways requires rate equations to be expressed in reversible form, because substrate and product elasticities are drastically different in reversible and irreversible reactions. This presents no special problem for reactions that follow reversible Michaelis-Menten kinetics, but for enzymes showing cooperative kinetics the full reversible rate equations are extremely complicated, and anyway in virtually all cases the full equations are unknown because sufficiently complete kinetic studies have not been carried out. There is a need, therefore, for approximate reversible equations that allow convenient simulation without violating thermodynamic constraints. RESULTS: We show how the irreversible Hill equation can be generalized to a reversible form, including effects of modifiers. The proposed equation leads to behaviour virtually indistinguishable from that predicted by a kinetic form of the Adair equation, despite the fact that the latter is a far more complicated equation. By contrast, a reversible form of the Monod-Wyman-Changeux equation that has sometimes been used leads to predictions for the effects of modifiers at high substrate concentration that differ qualitatively from those given by the Adair equation.

Binding Sites↗
PubMed1996

Co-response analysis: a new experimental strategy for metabolic control analysis.

The formulation of the standard summation and connectivity relationships as a statement that the matrix of all the elasticities in a system is the inverse of the matrix of all the control coefficients is completely general, provided that only control coefficients for independent fluxes and concentrations are considered, and that the elasticity matrix is written to take account of the stoichiometry of the pathway and the implied dependences between concentrations. This generally implies that co-response analysis is also general, i.e. that all of the elasticities and all of the control coefficients in any system, regardless of branching, feedback effects, moiety conservation or other complications, can be determined by comparing the effects of perturbations of the enzyme activities on the steady-state fluxes and concentrations of the pathway. The approach requires no quantitative information about the magnitudes of the effects on the individual enzyme activities, and consequently no enzymes need to be studied in isolation from the pathway.

Animals↗
PubMed1995

Metabolic regulation: a control analytic perspective.

A possible basis for a quantitative theory of metabolic regulation is outlined. Regulation is defined here as the alteration of reaction properties to augment or counteract the mass-action trend in a network reactions. In living systems the enzymes that catalyze these reactions are the "handles" through which such alteration is effected. It is shown how the elasticity coefficients of an enzyme-catalyzed reaction with respect to substrates and products are the sum of a mass-action term and a regulatory kinetic term; these coefficients therefore distinguish between mass-action effects and regulatory effects and are recognized as the key to quantifying regulation. As elasticity coefficients are also basic ingredients of metabolic control analysis, it is possible to relate regulation to such concepts as control, signalling, stability, and homeostasis. The need for care in the choice of relative or absolute changes when considering questions of metabolic regulation is stressed. Although the concepts are illustrated in terms of a simple coupled reaction system, they apply equally to more complex systems. When such systems are divided into reaction blocks, co-response coefficients can be used to measure the elasticities of these blocks.

Animals↗
PubMed1994

Determination of control coefficients in intact metabolic systems.

The control structure of a metabolic system can in principle be determined without the need for purification of the component enzymes and study of their kinetic properties, provided that their activities can be perturbed by amounts sufficient to produce measurable changes in the steady-state variables, i.e. the fluxes through the system and the concentrations of the intermediates. Each perturbation is characterized in terms of the co-response coefficients of all pairs of variables, i.e. the slopes of the lines produced when the logarithm of one variable is plotted against the logarithm of another, both varying in response to the same perturbation. If all the co-response coefficients are assembled into a matrix, the inverse of this matrix can be transformed into a matrix containing all the component elasticities, which can be inverted to provide the complete matrix of control coefficients. In a simple three-enzyme pathway studied, the analysis proves not to require unrealistically high accuracy in the original co-response measurements: even with errors with standard deviation +/- 5.77 degrees in the angles to the horizontal of the lines in the co-response plots (equivalent at best to errors of +/- 20% in the corresponding co-response coefficients), the final control coefficient matrix may be adequate for assessing the control structure of the system. Examination of literature data from studies of mitochondrial respiration and of gluconeogenesis indicates that considerably higher precision than this is achievable.

Enzymes↗
PubMed1994

Getting to the inside of cells using metabolic control analysis.

Metabolic control analysis can relate control properties of an intact system to kinetic properties (elasticity coefficients) of the enzymes within that system. The method formulating the former as matrix inverse of the latter is elaborated here for the general case and founded in standard metabolic control theory. Then a method is developed that accomplishes the reverse: it is shown that a matrix containing all elasticity coefficients and information concerning the pathway structure equals the inverse of a matrix containing flux and concentration control coefficients. As a consequence, by measuring the control properties of an intact system, one is able to deduce its in situ pathway structure and enzyme kinetic properties: This solves the ever-present question of whether the kinetic properties of enzymes in their isolated state differ from those under the conditions prevailing in the cell.

Cells↗
PubMed1993

Taking enzyme kinetics out of control; putting control into regulation.

The matrix formulation of metabolic control analysis, which states that multiplying the elasticity matrix for any system by the corresponding control matrix yields an identity matrix, can be transformed into a statement that multiplying a matrix expressing internal regulatory properties by a matrix expressing external regulatory properties also yields an identity matrix. This transformation supplies the formal basis for metabolic regulation analysis, and provides the key to determining the control structure of a system without the need to know the exact changes in enzyme activities that are made to measure control coefficients.

Enzymes↗
PubMed1993

Inhibition of cytochrome P-450(11)beta by some naturally occurring acetophenones and plant extracts from the shrub Salsola tuberculatiformis.

Ingestion of the Namibian shrub Salsola tuberculatiformis Botsch. by virgin female rats extends the dioestrus period of their oestrous cycles. Methanol extracts of the plant also inhibit adrenal steroidogenesis in the rat. With the aid of a bioassay, in which vaginal smears were used to follow the oestrous cycles of virgin rats, active fractions could be obtained which indicated that the plant contains a number of active compounds. The most active of these are highly unstable compounds which could not be isolated in pure form. However, two stable but less active compounds were identified as 4-hydroxyacetophenone and 4-hydroxy-3-methoxyacetophenone. This study investigated the influence of these acetophenones, their glucosides, and that of ethanol extracts of S. tuberculatiformis on adrenal steroidogenesis. Acetovanillon, a structurally related natural product also known as compound Z, was included in this study. Results show that the shrub contains active substances which interfere with adrenal 11 beta-hydroxylase, the terminal enzyme in glucocorticoid biosynthesis. This interaction with the cytochrome P-450(11)beta-dependent hydroxylase, as well as the inhibition of the conversion of deoxycorticosterone to corticosterone, was used to develop two sensitive and reliable assays for the rapid identification of small amounts of active compounds from S. tuberculatiformis.

Acetophenones↗
PubMed1991

Quantitative assessment of regulation in metabolic systems.

We show how metabolic regulation as commonly understood in biochemistry can be described in terms of metabolic control analysis. The steady-state values of the variables of metabolic systems (fluxes and concentrations) are determined by a set of parameters. Some of these parameters are concentrations that are set by the environment of the system; they can act as external regulators by communicating changes in the environment to the metabolic system. How effectively a system is regulated depends both on the degree to which the activity of the regulatory enzyme with which a regulator interacts directly can be altered by the regulator (its regulability) and on the ability of the regulatory enzyme to transmit the changes to the rest of the system (its regulatory capacity). The regulatory response of a system also depends on its internal organisation around key variable metabolites that act as internal regulators. The regulatory performance of the system can be judged in terms of how sensitivity the fluxes respond to the external stimulus and to what degree homeostasis in the concentrations of the internal regulators is maintained. We show how, on the level of both external and internal regulation, regulability can be quantified in terms of an elasticity coefficient and regulatory capacity in terms of a control coefficient. Metabolic regulation can therefore be described in terms of metabolic control analysis. The combined response relationship of control analysis relates regulability and regulatory capacity and allows quantification of the regulatory importance of the various interactions of regulators with enzymes in the system. On this basis we propose a quantitative terminology and analysis of metabolic regulation that shows what we should measure experimentally and how we should interpret the results. Analysis and numerical simulation of a simple model system serves to demonstrate our treatment.

Animals↗
PubMed1991

MetaModel: a program for modelling and control analysis of metabolic pathways on the IBM PC and compatibles.

MetaModel is a user-friendly program for calculating steady-state fluxes and metabolite concentrations of metabolic systems on the IBM PC and compatible computers. For any steady state that is obtained, one can then calculate a matrix of elasticity coefficients at that steady state, or a matrix of control and response coefficients. It thus offers a simple way to calculate the control structure of a pathway: it provides not only an educational tool that allows the student to verify empirically the classic summation relationships of metabolic control analysis but also a research tool for addressing 'what if?' questions about the behaviour of metabolic systems. Results can not only be printed or stored in a file, but can also be written to a special file that can be read by popular spreadsheet programs, thereby giving access to rapid, flexible and powerful methods for subsequent analysis and plotting of these results.

Algorithms↗
PubMed1989

Control-pattern analysis of metabolic pathways. Flux and concentration control in linear pathways.

Metabolic control analysis [Kacser and Burns (1973) Symp. Soc. Exp. Biol. 27, 65-104; Heinrich and Rapoport (1974) Eur. J. Biochem. 42, 89-95] leads to a description of the systemic properties of a metabolic system (expressed as control coefficients) in terms of the local kinetic properties of the individual enzyme-catalyzed reactions (expressed as elasticity coefficients). This paper describes a non-algebraic diagrammatic method which generates the mathematical expressions for flux or concentration-control coefficients in terms of elasticity coefficients. According to a set of simple rules, 'flux-control patterns' or 'concentration-control patterns' are drawn on a metabolic diagram. Each control pattern represents a product of elasticity coefficients that occurs as a term in the expression for a control coefficient. The rules also generate the correct sign that precedes each term. The control patterns are then used to build the expressions for control coefficients. The procedure was developed in such a way that each control pattern can be understood in terms of a 'chain of local effects' which shows how a perturbation in the activity of an enzyme is propagated through the metabolic pathway.

Biological Transport↗
PubMed1986

Metabolic control analysis of moiety-conserved cycles.

Moiety-conserved cycles are metabolic structures that interconvert different forms of a chemical moiety (such as ATP-ADP-AMP, the different forms of adenylate), while the sum of these forms remains constant. Their metabolic behaviour is treated within the framework of control analysis [Kacser, H. & Burns, J.A. (1973) Symp. Soc. Exp. Biol 27, 65-104]. To explain the importance of the conserved sum of cycle metabolites as a parameter of the system, the cycle is first regarded as a 'black box'. The interactions of the cycle with the rest of the system are expressed in terms of 'cycle elasticities' and 'cycle control coefficients' by the usual connectivity properties. The conserved sum is seen to be an 'external' parameter in the sense that its effect is described by a combined response expression. All cycle coefficients can be written in terms of elasticities and concentrations of cycle metabolites. The treatment shows how connectivity expressions should be modified when moiety-conserved cycles are present and establishes new summation and connectivity properties. The analysis is applied to a two-member moiety-conserved cycle and its general application is discussed.

Catalysis↗
PubMed1986

Inhibition of pyruvate dehydrogenase complex by moniliformin.

The mechanism for the inhibition of pyruvate dehydrogenase complex from bovine heart by moniliformin was investigated. Thiamin pyrophosphate proved to be necessary for the inhibitory action of moniliformin. The inhibition reaction was shown to be time-dependent and to follow first-order and saturation kinetics. Pyruvate protected the pyruvate dehydrogenase complex against moniliformin inactivation. Extensive dialysis of the moniliformin-inactivated complex only partially reversed inactivation. Moniliformin seems to act by inhibition of the pyruvate dehydrogenase component of the enzyme complex and not by acting on the dihydrolipoamide transacetylase or dehydrogenase components, as shown by monitoring the effect of moniliformin on each component individually. On the basis of these results, a suicide inactivator mechanism for moniliformin on pyruvate dehydrogenase is proposed.

Cyclobutanes↗
PubMed1986

Steady-state modelling of metabolic pathways: a guide for the prospective simulator.

Steady-state modelling and control analysis by means of computer simulation provides valuable insight into the behavior of metabolic pathways. This review, which is aimed at the newcomer to this field, discusses the objectives of steady-state modelling and the steady-state properties of the four basic metabolic structures, namely linear and branched chains, loops and cycles. It is shown how the model definition in terms of stoichiometric reactions and rate equations leads to a set of balance equations from which the conservation constraints and flux relationships can be deduced, either informally or through a rigorous analysis of the stoichiometric matrix. The initial analysis of a steady-state metabolic model is summarized in an algorithm. Key references to the literature on metabolic modelling are given.

Computer Simulation↗
PubMed1986

METAMOD: software for steady-state modelling and control analysis of metabolic pathways on the BBC microcomputer.

METAMOD, a BBC microcomputer-based software package for steady-state modelling and control analysis of model metabolic pathways, is described, The package consists of two programs. METADEF allows the user to define the pathway in terms of reactions, rate equations and initial concentrations of metabolites. METACAL uses one of two algorithms to calculate the steady-state concentrations and fluxes. One algorithm uses the current ratio of production and consumption rates of variable metabolites to adjust iteratively their concentrations in such a way that they converge towards the steady state. The other algorithm solves the roots of the system equations by means of a quasi-Newtonian procedure. Control analysis allows the calculation of elasticity, control and response coefficients, by means of finite difference approximation. METAMOD is interactive and easy to use, and suitable for teaching and research purposes.

Algorithms↗