This is the third of three pages containing the abstracts of the papers in the Special Issue of the Journal of Theoretical Biology 182, pp. 193-457 (1996) in honour of Henrik Kacser
Arthur R. Peacocke (Exeter College, Oxford OX1 3DP, England)
EDITOR'S NOTE: This article is reproduced, with minor modifications, from pp. 119-124 of A. R. Peacocke, An Introduction to the Physical Chemistry of Biological Organization, Clarendon Press, Oxford, 1983. As it was not written as a stand-alone article it has no abstract. The following brief summary was written by ACB and does not form part of the published issue of the Journal of Theoretical Biology.
In the chapter from which this extract is taken, Dr Peacocke discusses the origins of modern ideas of how the behaviour of living organisms can be explained in terms of chemical kinetics. After discussing the importance of the ideas of Hinshelwood and colleagues from the 1930s onwards (not reproduced in the extract), he credits Kacser with the awareness that living organisms have systemic properties that depend on organization and functional relationships, so that they cannot simply be treated as the result of an "additive" combination of their constituents. In contrast to Hinshelwood and his school, who worked up from physical chemistry to cell organization, Kacser started from a much more biological perspective. He drew attention to the differences between closed and open thermodynamic systems, and showed how various properties of living organisms could be correlated with properties of open systems. In more detailed examples, Kacser showed how model systems could exhibit such properties as multiple steady states and the formation of diverse cell patterns during embryonic development. The later parts of the chapter (not reproduced in the extract) deal in particular with oscillatory behaviour. [Index]
J. W. Porteous (Department of Molecular and Cell Biology, University of Aberdeen, Marischal College, Aberdeen AB9 1AS, Scotland, U.K.; email d.mcb@aberdeen.ac.uk)
In The Molecular Basis of Dominance, Kacser & Burns (1981) demonstrated that dominance in diploids and polyploids, and pleiotropy in all organisms, were biochemical phenomena; they were the consequences of the response of a metabolic system to a genetically specified change in the activity of any one enzyme within the system. Epistasis was similarly explicable when each of at least two enzyme activities suffered a change. The significance of this achievement by Kacser & Burns (1981) for biochemistry, genetics, molecular biology and biotechnology is best seen against the background of 115 years of attempts to explain the origins of dominance. [Index]
Mark Salter (Wellcome Research Laboratories, Langley Court, Beckenham, Kent, BR3 3BS, UK; email ms43210@ggr.co.uk)
The flux control coefficient of nitric oxide synthase (NOS), for the in vivo synthesis of the key biological mediator nitric oxide (NO), was determined in four rat brain regions with varying NOS activities (cerebral cortex, hippocampus, amygdala and cerebellum) using metabolic control theory. Flux control coefficients were calculated from the ratio of the initial slopes of the fractional effect of the NOS inhibitor N-*gkomega-nitro-L-arginine (L-NA) on NO pathway flux and NOS activity. Under conditions of normal behaviour in the rat, NOS had a flux control coefficient not significantly different from 1 in all regions examined. These data demonstrate that the large majority of flux control for the synthesis of NO in the brain resides in NOS itself and not in the transport of its amino acid precursor, L-arginine, across the blood-brain or neuronal cell membranes. This paper describes the first example in which the control of metabolic flux has been quantified in a mammalian system in vivo and demonstrates the power of metabolic control theory to elucidate the distribution of control within a metabolic pathway in vivo. [Index]
Arthur R. Schulz (Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, Indianapolis, Indiana 46202-5122, USA; email via Nic Steussy at itof500@indyvax.iupui.edu) and Janos Südi (Institut für Toxikologie, Christian Albrechts Universität, D-24105 Kiel, Germany)
Single-enzyme reactions involving abortive complexes, and random sequences, respectively, are subjected to control analysis. Explicit analytical expressions are presented which cover these kinetic behaviors. The latter are based 1) on the concept of control coefficients which measure the sensitivity of flux with respect to rate constants, and 2) on the classical steady state rate equations. The methods include both a graph theoretic approach and computer-aided derivation of algebraic expressions. Some conclusions are derived from the analysis of simple models. It is demonstrated 1) that abortive complexes exert no kinetic (as opposed to equilibrium) control over steady state flux. 2) The sum of the paired flux control coefficients for each step in the catalytic cycle, as well as the sum of the flux control coefficients for the unidirectional steps which emanate from each enzyme species, is equal to unity in a random sequence. 3) In the case of a random reaction sequence, the numerator terms of the rate equation exert an effect in the paired flux control coefficients for those steps in the random portion of the reaction sequence. [Index]
Stefan Schuster (Institute of Biology, Section of Theoretical Biophysics Humboldt University Berlin, Invalidenstr. 42, D-10115 Berlin, Germany; email Stefan=Schuster@rz.hu-berlin.de; home page)
Metabolic Control Analysis had originally been devised to quantify the effect of changes in enzyme concentrations on steady-state fluxes and metabolite concentrations. In many situations, fluxes and concentrations are not the only relevant variables. For example, models of oxidative phosphorylation often include the proton-motive force as a state variable. A formalism is presented by which the control of generalized variables characterizing biochemical systems can be described. The concepts of "state variables" and "response variables" are introduced. Formulas linking generalized control coefficients to generalized elasticities are established. From these, unified summation and connectivity theorems are derived. These formulas result in well-known equations of Metabolic Control Analysis as special cases when the variables are specified to concentrations or fluxes.
It is shown that if the response variables only depend on the state variables or the reaction rates or both, control coefficients do not depend on the special choice of the perturbation parameters.
This analysis includes the treatment of proton-motive force, energy charge, cell volume and many other variables as special cases. We illustrate the analysis by specifying it to the treatment of concentration ratios, free-energy differences and transition times. [Index]
Asok K. Sen (Department of Mathematical Sciences, Purdue University School of Science, 402 N. Blackford Street, Indianapolis, IN 46202, USA; email ixyl100@indyvax.iupui.edu); home page
The sign of a flux (concentration) control coefficient of an enzyme determines if the metabolic flux (metabolite concentration) will increase or decrease when the enzyme concentration is increased/decreased. In general, the sign of a control coefficient depends on the magnitudes of the enzyme elasticities, fluxes etc. It is shown that in many pathways some (or all) of the control coefficients may have fixed signs irrespective of the magnitudes of the elasticities and fluxes. The remaining control coefficients are sign-indeterminate. The enzymes and metabolites whose control coefficients are sign-indeterminate can be identified in a heuristic fashion directly from the topology of the metabolic pathway, i.e., location of feedback/feedforward loops, location of branches, presence of isoenzymes etc. In other pathways such as those containing a substrate cycle, none of the control coefficients of the enzymes can have a fixed sign; a control coefficient may be positive, negative or zero depending on the actual magnitudes of the elasticities and velocities. [Index]
Stefan E. Szedlacsek, Alexandru R. Aricescu (Institute of Biochemistry, Department of Enzymology, Bucharest, Romania; Szedlacsek email stefan@linux.biochim.ro) and Bent H. Havsteen (Biochemisches Institut "Christian-Albrechts Universität" zu Kiel, Germany)
The expression of elasticity coefficients for time-dependent enzyme inhibition/activation by an external effector was initially derived. Only a limited number of restrictive assumptions were used, like the enzyme was considered to obey the Michaelis-Menten kinetics and effectors were supposed to be competitive ones. Then, a simple metabolic system under the control of a time-dependent effector (inhibitor or activator) was analysed and the expressions of the control coefficients were obtained. In addition, two numerical examples were used to represent the control coefficients as functions of time and effector concentration. The results indicate that the control coefficients vary in a relatively limited range of values; however, for certain intervals of time and of effector concentration local minima or major modifications of the coefficients may be recorded. The physiological importance of non-steady state analysis of metabolic systems controlled by external effectors was also discussed. It was stressed that the non-steady state treatment may contribute to create a more realistic image of the metabolic control processes. [Index]
Simon Thomas and David A. Fell (School of Biological and Molecular Sciences, Oxford Brookes University, Headington, Oxford, OX3 OBP, UK; Fell email daf@bms.brookes.ac.uk; ftp site)
Metabolic Control Analysis has invalidated many traditional biochemical concepts of control, in particular the rate-limiting step. However, it has not been used to question the mechanisms by which pathway flux is thought to be controlled, such as the action of allosteric effectors or of covalent modification mechanisms. Here we use Control Analysis and computer simulation to examine the response of pathway segments to changes in flux imposed by action on an enzyme outside the segment. Whether these segments contain near-equilibrium enzyme-catalysed reactions, cooperative enzymes, feedforward activation loops or feedback inhibiton loops, their responses are significantly different from those observed in vivo. In particular they do not exhibit the remarkable degrees of metabolite homoeostasis during large flux changes that have frequently been observed experimentally. On the other hand, near-constant levels of metabolites in spite of large changes of flux are consistent with our recent proposal that multi-site modulation – simultaneous activation of many pathway steps – is the normal method by which metabolism is controlled. [Index]
Néstor V. Torres (Grupo de Control Metabólico, Departamento de Bioquímica y Biología Molecular, Facultad de Biología, Universidad de La Laguna, 38206 La Laguna, Tenerife, Canary Islands, Spain; email ntorres@ull.es)
Based on a simplified model of a linear metabolic pathway (Kacser and Burns, 1973), and on the principles of Metabolic Control Analysis, an equation useful for predicting the maximum flux through a system after removing inhibitory feedback interaction is presented. The analysis shows that only when the flux control coefficient of the inhibited enzyme is significant (greater than 0.5) is it worthwhile to act on the regulatory features of the feedback interaction. The approach is then applied to a case study and the magnitude of the flux increase and the quality of the prediction studied in two different profiles of flux control coeffients. [Index]
Hans V. Westerhoff (Mathematical Biochemistry, University of Amsterdam, BioCentrum Amsterdam, and MicroPhysiology, Free University, BioCentrum Amsterdam, De Boelelaan 1081, NL-1087 HV Amsterdam, The Netherlands; email hw@bio.vu.nl; home page) and Douglas B. Kell (Institute of Biological Sciences, Edward Llwyd Building, University of Wales, Aberystwyth SY23 3DA, UK; email dbk@aber.ac.uk; home page)
Qualitative, trial-and-error methods designed to increase the flux to desirable biotechnological products have led to new technologies and vast improvements in existing ones. However, these methods now appear in many cases to have approached their limit. In addition, there is a strong feeling in industry that much of the recent boom in academic knowledge of biochemistry and molecular biology passes biotechnology by, simply because one cannot evaluate the implications of molecular kinetics for the functioning of the producer organisms as a whole. New methods, or more rational methods are called for.
We here review what has become of the insights of Henrik Kacser into how Metabolic Control Analysis (MCA) provides the necessary rational approach to bioengineering. The control coefficients point at the enzymes that need to be amplified to increase a desired flux, yield or concentration. Kinetic properties, called elasticity coefficients, can be used to calculate the control coefficients, and a variety of experimental methods have been developed for the direct measurements of the latter. MCA can further be used to calculate the combination of changes in enzyme activities that should be engineered in order to fulfil a requirement of a number of simultaneous changes. MCA is no longer limited to "ideal", "academic" metabolic pathways: signal transduction, regulated gene expression, metabolite channelling and cellular dynamics are all within reach. In the "universal method" as developed by Kacser and co-workers, this approach is not necessarily limited to very small changes. We here elaborate this method somewhat.
Where the previous MCA-based engineering principles focused on the modulation of enzyme concentrations, we here describe a strategy using site-directed mutagenesis. This strategy aims at increasing specifically the concentration of certain metabolites or certain fluxes without causing changes in any other metabolite or flux, hence safeguarding cellular homeostasis. The approach could also be useful when large changes are desired.
The principles of MCA are ready for industry, but how ready is industry for this rational approach to bioengineering? [Index]
Barbara E. Wright, Angelika Longacre and Jacqueline Reimers (University of Montana, Division of Biological Sciences, Missoula, MT 59812, USA; Wright email bewright@selway.umt.edu)
A flux analysis of glucose metabolism in Rhizopus oryzae was achieved
using [
]-labeled glucose and acetate. The rates of glucose
utilization and end product production were estimated, and metabolite pool sizes
and specific radioactivities were determined. These data were analyzed using
a specific radioactivity curve-matching program called TFLUX.
The analysis is consistent with the existence of separate mitochondrial and cytosolic
pools of pyruvate, malate and fumarate. [Index]