Metabolic regulation and mathematical models

Effects of cadmium on the control and internal regulation of oxidative phosphorylation in potato tuber mitochondria

The effect of cadmium on the distribution of control over oxidative phosphorylation in potato tuber mitochondria was quantified by measuring control coefficients using top-down metabolic control analysis. Oxidative phosphorylation was divided into three subsystems, namely substrate oxidation, the phosphorylation reactions and the proton leak. The control exerted by each of these subsystems over the system fluxes, the value of the protonmotive force and the effective P/O ratio was quantified in the presence of different concentrations of free cadmium (up to 21 microM). Cadmium is known to stimulate the proton leak and inhibit the substrate oxidation reactions, but it had little effect on the distribution of control over the system variables except to shift the pattern to lower rates. Control exerted by particular subsystems appeared to change or to stay the same as cadmium was varied, depending on whether the control coefficients were presented as a function of respiration rate or protonmotive force. The regulatory strength of protonmotive force on the system variables was also calculated, as partial internal response coefficients. These coefficients changed with ATP turnover rate and with cadmium concentration, showing how the internal regulation of oxidative phosphorylation shifts under different conditions. The values of control coefficients and partial internal response coefficients show where control lies and how intermediates regulate the system variables under different conditions of ATP demand and external effector (i.e. cadmium) concentration. However, they are not useful for identifying the sites of action of external effectors, for which elasticity and regulation analysis must be used.

Control theory of one enzyme

The analogue of metabolic control theory is developed for the control of reactions catalyzed by single enzymes. The control exerted by any of the elemental transitions of enzyme catalytic cycles on reaction rate and on concentrations (probabilities) of enzyme states is quantified in line with the principle of detailed balance. For enzyme reactions with arbitrary kinetic schemes, e.g., with several enzyme cycles, reflecting coupling and slipping of reactions, it is derived what the various sums of the control coefficients are equal to (cycle summation theorems). Total control on flux, state probability and ratios of branch fluxes are 1, 0 and 0, respectively. The general connectivity theorems are derived which indicate how control is determined by the kinetics of the elemental steps. In addition, for enzymes catalyzing single (or completely coupled) processes the control coefficients are expressed in terms of actual and standard free energy differences across the steps. The prevalent qualitative contention that the step with the smallest forward rate constant, or with the largest free energy drop is the step limiting the performance of the enzyme is shown to fail. The new theory should allow subtle analysis of the control of an enzyme catalyzed reaction.

The kinetics of facilitated diffusion followed by enzymatic conversion of the substrate

The uptake of a substrate that is transported into the cell by facilitated diffusion and subsequently converted in a series of enzymatic reactions, measured as a function of the external concentration, does not usually show the rectangular hyperbolic function characteristic of Michaelis-Menten kinetics. Instead, a seemingly biphasic curve is observed, consisting of Michaelis-Menten kinetics at low concentrations and no further uptake at higher levels. By combining the equations for facilitated diffusion and an enzymatic reaction, we have derived an equation that describes the overall rate of uptake and metabolism of a substrate that is transported across the plasma membrane by facilitated diffusion. Modelling based on this equation simulated the kinetics found experimentally, as long as the kinetic parameters of the carrier were chosen to render it asymmetric. The overall rate was influenced by the kinetics of both reactions over a wide range of concentrations, confirming the principles of the 'Control Analysis' theory in an independent manner.

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.

Coordination of catalytic activities within enzyme complexes

If two enzymes are physically and permanently associated as a bi-enzyme complex and if these enzymes catalyze non-consecutive chemical reactions, either of these reactions may inhibit or activate the other. If these reactions belong to two different metabolic cycles, the functioning of one of these cycles will control the fine tuning of the other. Thus simple kinetic considerations lead to the conclusion that, owing to the spatial organization of enzymes as multimolecular complexes, a fine tuning and a coordination of different metabolic networks, or cycles, may be exerted. It thus appears that channelling of reaction intermediates within a multienzyme complex does not represent the only functional advantage brought about by this type of spatial molecular organization.

Modular analysis of the control of complex metabolic pathways

The understanding of the functioning of the intact cell would be simplified appreciably if it were possible first to analyze particular modules of cell physiology separately, and then to integrate the information so as to yield understanding of the control structure in terms of the mutual regulation of the modules. Here we develop a quantitative method based on Metabolic Control Analysis that makes this possible: The relevant properties of the modules are contained in "overall" elasticity coefficients, which reflect the changes in fluxes in the module upon a small variation of the environment of the module, allowing the latter to attain steady state. We show how overall control coefficients, which reflect the control exerted by the processes catalyzed by each module, can be expressed into the overall elasticity coefficients. We derive corresponding summation and connectivity theorems. A number of possible divisions of physiological systems into modules is discussed. This work is a generalization of previous analyses of overall control properties in that it allows for multiple fluxes to connect the modules, and reaction stoichiometries of any complexity.

Metabolic engineering--methodologies and future prospects

Attempts to improve the productivity of cellular systems or to increase metabolite yield often require radical alteration of the flux through primary metabolic pathways. However, achieving the desired result often proves difficult because the control architectures at key branch points have evolved to resist flux changes. Identification and characterization of these metabolic nodes is a prerequisite to rational metabolic engineering.

Metabolic channelling and control of the flux

Metabolic control theory is extended to include channelled metabolism in general. A simple relationship between the flux control by the enzymes and the degree of metabolite channelling is derived. This relationship suggests experiments in which modulation of gene expression allows one to quantify channelling.

'Channelled' pathways can be more sensitive to specific regulatory signals

In 'simple' metabolic pathways the response to an external signal is readily described in terms of the effect of the signal on its receptor enzyme and the control exerted by that enzyme. We show here that in the response of 'channelled' pathways to such a signal, additional terms appear that reflect the direct enzyme-enzyme interactions. They tend to enhance the responsiveness of the pathway. The normalized value of the response is called the signal transduction coefficient. We show that in channelled pathways these coefficients are usually larger than in corresponding non-channelled (simple) pathways.

The sum of the control coefficients of all enzymes on the flux through a group-transfer pathway can be as high as two

In simple metabolic pathways the control exerted by enzyme concentrations on the pathway flux adds up to one when the control is quantified in terms of control coefficients. In this paper we demonstrate that this classical summation theorem has to be modified in pathways where the enzymes participate by transferring a group between each other. We derive the corresponding new control theorem and show how it is consistent with standard metabolic control analysis. In group-transfer pathways lacking enzyme complexes, the sum of the flux control by enzyme concentrations and by the donor and acceptor couples of the pathway, equals two. In group-transfer pathways with enzyme-enzyme interactions the flux control by the dissociation rate constants of the enzyme-enzyme complexes must be added to obtain this sum of two. In all cases, the sum of the controls by all reaction activities remains one. Both by using the new theorem and by numerical simulations, we then demonstrate that, in group-transfer pathways with or without enzyme interactions, the sum of the control of enzymes on the pathway flux is higher than one and can reach a value of two. The total control of all enzymes on the concentration of any intermediate either with or without the transferred group can be equal to one, rather than to the zero found in the classical case. Examples of group-transfer pathways are the bacterial phosphoenolpyruvate:sugar phosphotransferase system, the main pathway for uptake of sugars in Enterobacteriaceae, and the electron-transfer chain in free-energy transducing membranes.

The use of lac-type promoters in control analysis

For control analysis, it is necessary to modulate the activity of an enzyme around its normal level and measure the changes in steady-state fluxes or concentrations. We describe an improved method for effecting the modulation, as elaborated for Escherichia coli. The chromosomal gene, encoding the enzyme of interest, is put under the control of a lacUV5 or a tacI promoter. The alternative use of the two promoters leads to an expression range which should make it suitable for the use in control analysis of many enzymes. The lacUV5 promoter should be used when the wild-type expression level is low, the tacI promoter when the latter is high. The endogenous lac operon is placed under the control of a second copy of the lacUV5 promoter and a lacY7am mutation (eliminating lactose permease, the transport system for the inducer isopropyl-thio-beta-D- galactoside) is introduced. The method was demonstrated experimentally by constructing E. coli strains, in which the chromosomal atp operon is transcribed from the lacUV5 and the tacI promoter. We measured the concentration of the c subunit of H(+)-ATPase, and found that the expression of this enzyme could be modulated between non-detectable levels and up to five times the wild-type level. Thus, in the absence of inducer, no expression of atp genes could be detected when the atp operon was controlled by the lacUV5 promoter, and we estimate that the expression was less than 0.0025 times the wild-type level. We show that the introduction of a lacY mutation facilitated the attainment of steady induction levels of partially induced cells. The mutation also reduced positive cooperativity in the dependence of expression on the concentration of isopropyl-thio-beta-D-galactoside (the inducer) and shifted the concentration of inducer needed for half maximum induction to higher values. These properties should facilitate the experimental modulation of the enzyme activity by varying the concentration of the inducer.

Cellular and metabolic engineering. An overview

Metabolic engineering is defined as the purposeful modification of intermediary metabolism using recombinant DNA techniques. Cellular engineering, a more inclusive term, is defined as the purposeful modification of cell properties using the same techniques. Examples of cellular and metabolic engineering are divided into five categories: 1. Improved production of chemicals already produced by the host organism; 2. Extended substrate range for growth and product formation; 3. Addition of new catabolic activities for degradation of toxic chemicals; 4. Production of chemicals new to the host organism; and 5. Modification of cell properties. Over 100 examples of cellular and metabolic engineering are summarized. Several molecular biological, analytical chemistry, and mathematical and computational tools of relevance to cellular and metabolic engineering are reviewed. The importance of host selection and gene selection is emphasized. Finally, some future directions and emerging areas are presented.

Control of the metabolic flux in a system with high enzyme concentrations and moiety-conserved cycles. The sum of the flux control coefficients can drop significantly below unity

In a number of metabolic pathways enzyme concentrations are comparable to those of substrates. Recently it has been shown that many statements of the 'classical' metabolic control theory are violated if such a system contains a moiety-conserved cycle. For arbitrary pathways we have found: (a) the equation connecting coefficients CEiJ (obtained by varying the Ei concentration) and CviJ (obtained by varying the kicat), and (b) modified summation equations. The sum of the enzyme control coefficients (equal to unity under the 'classical' theory) appears always to be below unity in the systems considered. The relationships revealed were illustrated by a numerical example where the sum of coefficients CEiJ reached negative values. A method for experimental measurements of the above coefficients is proposed.

Evolutionary optimization of the catalytic efficiency of enzymes

1. The rate equation for a generalized Michaelian type of enzymic reaction mechanism has been analyzed in order to establish how the mechanism should be kinetically designed in order to optimize the catalytic efficiency of the enzyme for a given average magnitude of true and apparent first-order rate constants in the mechanism at given concentrations of enzyme, substrate and product. 2. As long as on-velocity constants for substrate and product binding to the enzyme have not reached the limiting value for a diffusion-controlled association process, the optimal state of enzyme operation will be characterized by forward (true and apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. The drop in free energy driving the catalysed reaction will occur to an equal extent for each reaction step in the mechanism. All internal equilibrium constants will be of equal magnitude and reflect only the closeness of the catalysed reaction to equilibrium conditions. 3. When magnitudes of on-velocity constants for substrate and product binding have reached their upper limits, the optimal kinetic design of the reaction mechanism becomes more complex and has to be established by numerical methods. Numerical solutions, calculated for triosephosphate isomerase, indicate that this particular enzyme may or may not be considered to exhibit close to maximal efficiency, depending on what value is assigned to the upper limit for a ligand association rate constant. 4. Arguments are presented to show that no useful information on the evolutionary optimization of the catalytic efficiency of enzymes can be obtained by previously taken approaches that are based on the application of linear free-energy relationships for rate and equilibrium constants in the reaction mechanism.

Oscillations in coupled enzymic reactions at high concentration of enzyme

The transient-state kinetic consequences of the coupling of a single-enzyme reaction to other metabolic reactions have been examined in generalized terms. Analytical data are presented which specify under what conditions such coupling may lead to an oscillatory transient rate behaviour of a reaction system involving an enzyme operating by a Michaelian mechanism. The results indicate that the presence of enzyme in concentrations comparable to those of substrate and product may represent a hitherto unforeseen possible source of weakly damped, or even sustained, oscillations in metabolic networks. This observation has some important implications with regard to the occurrence of oscillations in biochemical reaction systems and to transient-state kinetic modelling of metabolic systems.

The definitions of metabolic control analysis revisited

Various definitions of coefficients in metabolic control analysis are examined with respect to their theoretical consistency and practical applicability. We suggest agreement upon a definition for control coefficients which is clearly distinct from that for response coefficients, in such a way that the former describe inherent properties of the metabolic system while the latter refer to the influence of special parameters. Advantages and drawbacks of using normalized or non-normalized control coefficients are studied. It is shown that normalized control coefficients have the advantage of being invariant to a different rescaling of the particular fluxes. We demonstrate that some problems are easier to tackle if the consistency of time-independent control coefficients with their time-dependent counterparts is taken into account. It is shown that the matrix of flux control coefficients is an indempotent matrix. This allows an interpretation in terms of the transduction of the effect of parameter perturbations. Several aspects of the experimental measurement of control coefficients are discussed, with special reference to the different definitions.

Pharmacokinetics: philosophy of modeling

Generally speaking, there are two extremes of scientific personality types: sharpeners and levelers. Sharpeners, highly attuned to system differences and nuances, and always alert to distinctions, try hard to let nothing slip by them unnoticed. Levelers, on the other hand, attempt to submerge system differences, reveal uniform patterns, and condense disparate elements. This paper is one leveler's attempt to address the following philosophical questions confronting pharmacokinetic modelers: (1) What is the nature of reality? (2) What is a model? (3) Why do we model? (4) What are the different types of models? (5) How do we model? (6) What are the properties and characteristics of models? (7) How do we evaluate models? (8) What are some of the tricks and traps of modeling? And (9), what are some of the psychological characteristics of modelers?

Control theory of regulatory cascades

We have extended Metabolic Control Theory to include cascades consisting of several modules controlling each other solely via regulatory effects. We derive several theorems that determine how the control properties of a cascade derive from (1) the control properties of each module, taken in isolation and (2) the regulatory interactions between the modules. Two cases are treated explicitly. The first concerns cascades in the absence of feed-back: in this case the internal control behaviour of each module is unaffected by external regulatory interactions. The second includes one feed-back loop and gives a quantitative expression of how feed-back modifies control properties: the internal control matrix within one module can be calculated as if the elasticity matrix of this module was the sum of its intrinsic elasticity matrix and a cyclic regulation matrix. More complex cascades can be analysed recursively by subdividing them into simpler modules, which can be treated individually. The theoretical framework developed here should facilitate quantitative experimental analysis of the control of cell physiology where the latter involves regulatory cascades.

Lactate is not a major product of glucose metabolism in the respiring jejunum perfused in the recirculation mode in vitro

Yields of lactate from glucose absorbed from the luminal medium and extracted concurrently from the vascular medium of the perfused rat jejunum in vitro were half those previously reported from comparable glucose concentrations in the recirculated perfusion media. These low yields were obtained by maintaining perfusion medium flow rates and pressures pharmacologically at values found in vivo; permitting normal peristalsis; and restoring the depleted glyceric acid-2,3-bisphosphate and reduced deformability of out-dated blood-bank erythrocytes to normal physiological values before they were added to the vascular perfusion medium and equilibrated at 37 degrees C with air/CO2. Respiration rates are recorded for the first time in each perfusion experiment. A substantial fraction of glucose consumed in this and all earlier recirculation perfusion experiments in vitro has still to be accounted for.

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.

Physiological controls and regulation of ergot alkaloid formation

Innovation and technical development of ergot alkaloids (EA) has moved closer to scientific research. Circumstantial evidence presently links the initiation of EA metabolism to changes in a range of parameters--morphology, concentrations of enzymes and their substrates, nutrients and external stress. The biosynthesis of EA begins at the level of the genetic information apparatus and continues at the level of physiological expression. EA and their formation play a role in the physiology of the production organism. Insufficient insight into Claviceps physiology hampers the deployment of computers in the control and regulation of the EA process. Knowledge of physiological controls and genetic manipulation are the principal tools of modern EA production. In principle it is now possible to improve EA yields by a concerted breeding of the ergot fungus by sexual and parasexual genetic engineering.

Kinetic parameters of enzymatic reactions in states of maximal activity; an evolutionary approach

A theoretical investigation is presented which allows the calculation of states of maximal reaction rates for single enzymes and for unbranched enzymatic chains. As an extension to previous papers (Heinrich & Holzhütter, 1985, Biomed. biochim. Acta 44, 959-969; Heinrich et al., 1987, Bull. math. Biol. 49, 539-595) a detailed enzymatic mechanism was taken into consideration. Conclusions are drawn for the optimal values of the microscopic rate constants as well as of the maximal activities and Michaelis constants. Ten solutions are found which depend on the equilibrium constant as well as on the concentrations of substrates and products. It is shown that for high equilibrium constants one of the solutions applies to a very large range of the concentrations of the outer reactants. This solution is characterized by maximal values of the rate constants of all forward reactions and by non-maximal values of the rate constants of all backward reactions. In contrast to previous assumptions (Albery & Knowles, 1976b, Biochemistry 15, 5631-5640; Burbaum et al., 1989, Biochemistry 28, 9293-9305) states of maximal reaction rate are not always characterized by the highest possible values of the second-order rate constants which are related to the diffusion of the substrate and the product to the active site of the enzyme. Predictions are made concerning the ratios of maximal activities in optimal states as well as for the adaptation of the Michaelis constants to the concentrations of the outer reactants. Using metabolic control analysis it is shown that the solutions obtained for single enzymes may also be applied in multi-enzyme systems.

Identification of possible two-reactant sources of oscillations in the Calvin photosynthesis cycle and ancillary pathways

A systematic search for possible sources of experimentally observed oscillations in the photosynthetic reaction system has been performed by application of recent theoretical results characterizing the transient-state rate behaviour of metabolic reactions involving two independent concentration variables. All subsystems involving two independent reactants in metabolically fundamental parts of the Calvin cycle and the ancillary pathways of starch and sucrose synthesis have been examined in order to decide on basis of their kinetic and stoichiometric structure whether or not they may trigger oscillations. The results show that no less than 20 possible oscillators can be identified in the examined reaction system, only three of which have been previously considered as potential sources of experimentally observed oscillations. This illustrates the superiority of the method now applied over those previously used to identify possible two-reactant sources of metabolic oscillations and indicates that there should be no difficulty in complex metabolic pathways to point to a multitude of interactions that may trigger an oscillatory rate behaviour of the system.

Minimization of intermediate concentrations as a suggested optimality principle for biochemical networks. II. Time hierarchy, enzymatic rate laws, and erythrocyte metabolism

The multiobjective problem of minimizing all intermediate concentrations is solved for a model of glycolysis, the pentose monophosphate shunt and the glutathione system in human erythrocytes. It turns out that one solution out of four obtained corresponds qualitatively to the real system. Furthermore, it is shown that for any reaction system, the mentioned optimality principle implies distinct time hierarchy in that some reactions are infinitely fast and subsist in quasi-equilibrium. Finally, the relationships to the standard method of deriving enzymatic rate laws are discussed.

A method for testing the stability of a steady-state system during the calculation of a response to large changes in regulator concentrations

A modification of the 'finite decomposition' method (Crabtree and Newsholme (1985) Curr. Top. Cell. Regul. 25, 21-76) for calculating physiological responses from sensitivities is described, to enable the system to be tested for stability at each step of the procedure. Instability is indicated by a change of sign of the determinant of the square matrix (N) in the governing equation for the system. The method cannot be used to predict a change of sign of the determinant of the square matrix (N) in the governing equation for the system. The method cannot be used to predict responses beyond any step at which instability occurs.

Balancing of energy-consuming processes of rat hepatocytes

A method for the quantification of energy consuming processes described by Siems et al. for reticulocytes and by Müller et al. for ascites tumour cells was applied to balance the ATP-consumption of isolated rat hepatocytes. On the basis of decreased coupled respiration rates following the specific inhibition of energy-requiring reactions, the energy demands of protein turnover, nucleic acid synthesis, Na+/K(+)-ATPase and Ca2(+)-transport of hepatocytes in different incubation media were assessed. These processes together with urea synthesis account for about 60 per cent of the total energy consumption in a glucose and amino acid-enriched Eagle/Borsook medium. The metabolic flux rates of total ATP-consumption and ATP-consumption of single energy-requiring processes in hepatocytes are compared with those in reticulocytes and different tumour cell types.

Mathematical modelling of the purine metabolism of the rat liver

The regulation of the purine metabolism of the rat liver is studied on the basis of a mathematical model which comprises rate laws and kinetic constants of all physiologically relevant reactions. The computed stationary and time-dependent concentrations are in good accordance with experimental data obtained in the ischaemic rat liver and in isolated hepatocytes. In particular, model-based simulations of the adenine nucleotide metabolism have been performed for situations where ATP-deficient states of the cell (hypoxia, anoxia or ischaemia) of various length are followed by onset of ATP production (reoxygenation). These simulations confirm the experimentally observed incomplete recovery of ATP and of the total pool of adenine nucleotides within a few hours of reoxygenation after long-term ATP depletion. Therefore, it can be concluded that this phenomenon is an intrinsic regulatory property of the purine metabolism and not necessarily due to some irreversible changes in the activity of the enzymes involved.

Metabolic control analysis. The effects of high enzyme concentrations

Differing views have been given in the literature as to whether the presence in a pathway of an enzyme at a concentration comparable to that of its substrate affects the values of control coefficients and the theorems of metabolic control analysis. Here we argue in favour of one of those views: that there is no effect unless the enzyme sequesters a substrate that contains a conserved moiety. In this particular case, we derive both a general criterion for estimating whether such an effect will be of a significant magnitude, and equations for determining the changes in the flux control coefficients. The nature of the phenomenom and the application of the equations are illustrated with a numerical simulation.

Control analysis of photosynthetic CO2 fixation

The potential of control analysis to aid our understanding of regulation and control of photosynthetic carbon metabolism is investigated. Methods of metabolic control analysis are used to determine flux control coefficients of photosynthetic reactions from enzyme elasticities. Equations expressing control coefficients symbolically by enzyme elasticities are derived, and general properties of these expressions are analysed. Suggestions for experimental determination of flux control coefficients from enzyme elasticities are given. A simplified model of the Calvin-Benson cycle is used to illustrate interrelations between patterns of photosynthetic metabolites and that of control coefficients.

Effect of aging on the oxidative phosphorylation pathway

The proposed study was undertaken to investigate the effect of aging on control of the oxidative phosphorylation pathway. Flux control coefficients for adenine nucleotide translocase and cytochrome c oxidase were determined using the procedure of Groen et al. [J. Biol. Chem., 257 (1982) 137-144]. Hepatic mitochondrial fractions from Fischer 344 rats were isolated from control (average age 6.5 months), and aged (average age 27.3 months) groups. No aging-related changes in the extent of control of respiration by the oxidase were obtained, however, differences were observed for the translocase. For the control group of animals, the greatest regulation occurred at 80-85% maximal respiratory rates, and declined at higher rates. For the aged group, a similar flux control coefficient was obtained at 80-85% respiration, but was maintained as respiration increased to maximal rates. It is proposed that changes in the flux control coefficients at maximal respiratory rates are associated with an aging-related decrease in translocase activity. Evaluation of translocase content revealed no significant differences between the two groups supporting the concept that the decreased activity was not due to decreased content. During the course of these experiments, it also became apparent that there was a significant aging-related decrease in the rate of succinate oxidation providing an adequate supply of ADP was present. No significant changes in respiratory rates, or RCR, were evident at suboptimal concentrations of ADP as reported previously from this laboratory [Vorbeck, M.L. et al., Arch. Biochem. Biophys., 214 (1982) 67-79]. Since similar decreases in respiration were obtained upon addition of an uncoupler, the aging-related changes in respiration are attributed to differences at the level of the electron transport system, including its associated reactions. The aging-related differences in respiratory rates, and extent of control of respiration, were both observed under conditions of maximal stimulation of respiration. This suggests an inability of mitochondria from aged animals to respond to the increased demands of oxidation. Basic to these differences may be the lipid-membrane associated changes seen during aging.

Cellular concentrations of enzymes and their substrates

The activity of crude and pure enzyme preparations as well as the molecular weight of these enzymes were obtained from the literature for several organisms. From these data enzyme concentrations were calculated and compared to the concentration(s) of their substrates in the same organism. The data are expressed as molar ratios of metabolite concentration to enzyme site concentration. Of the 140 ratios calculated, 88% were one or greater, indicating that in general substrates exceed their cognate enzyme concentrations. Of the 17 cases where enzyme exceeds metabolite concentration, 16 were in glycolysis. The data in general justify the use of enzyme kinetic mechanisms determined in vitro in the construction of dynamic models which simulate in vivo metabolism.

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.

Enzyme-enzyme interactions and control analysis. 1. The case of non-additivity: monomer-oligomer associations

Two usual assumptions of the treatment of metabolism are: (a) the rates of isolated enzyme reactions are additive, i.e., that rate is proportional to enzyme concentration; (b) in a system, the rates of individual enzyme reactions are not influenced by interactions with other enzymes, i.e. that they are acting independently, except by being coupled through shared metabolites. On this basis, control analysis has established theorems and experimental methods for studying the distribution of control. These assumptions are not universally true and it is shown that the theorems can be modified to take account of such deviations. This is achieved by defining additional elasticity coefficients, designated by the symbol pi, which quantify the effects of homologous and heterologous enzyme interactions. Here we show that for the case of non-proportionality of rate with enzyme concentration, (pi ii not equal to 1), the summation theorems are given by (Formula: see text). The example of monomer-oligomer equilibria is used to illustrate non-additive behaviour and experimental methods for their study are suggested.

Metabolic dynamics in the human red cell. Part III--Metabolic reaction rates

The kinetics of the enzymatic reaction and transport rates that constitute the main metabolic pathways of the red cell metabolism are described. The red cell metabolic model consists of 33 dynamic mass balances that contain 41 enzymatic reaction rate laws and transmembrane processes. Our goal here is two-fold: the development of rate expressions for the individual biochemical reactions of the integrated red cell metabolism, and order of magnitudes estimates to gauge their dynamic properties in terms of response times and action scales of substrates, products and regulators.

The effects of generation and gender on the joint distributions of lipid and apolipoprotein phenotypes in the population at large

The generation and gender effects on the joint distributions of total plasma cholesterol (Total-C), ln triglycerides (lnTrig), HDL-cholesterol (HDL-C), LDL-cholesterol (LDL-C), apolipoproteins AI (Apo AI), AII (Apo AII), and E (lnApo E) were studied in 184 male grandparents (MGP), 242 female grandparents (FGP), 237 male parents (MP), 235 female parents (FP), 202 male children (MC), and 200 female children (FC). Homogeneity of variance tests revealed that lipid variances were gender and/or generation specific while apolipoprotein variances were homogeneous across strata. In the absence of heterogeneity of variance, significant heterogeneity in LDL:lnTrig and lnTrig:Apo AII covariation was found between genders in the parental generation. In the presence of heterogeneity of variance, significant heterogeneity of correlation between genders and/or across generations was found for the HDL-C:LDL-C, Total-C:LDL-C, Total-C:lnTrig, lnTrig:LDL-C, Total-C:lnApo E and HDL-C:lnApo E bivariate distributions. Analyses of principal components revealed that the generation and gender specific cohorts have similar eigenvalues but distinct eigenvectors for the first two principal components underlying the seven dimensional lipid and apolipoprotein distribution. We conclude that the amount of variability explained by the first two principal components is the same across cohorts but how the interindividual variability is distributed among the lipid and apolipoprotein traits is generation and gender specific. This study documents the role that variance and covariance might play in determining risk of disease for special subgroups of the population at large. It also demonstrates how variances and covariances between risk factors traits characterize life processes of aging and sexual dimorphism. This study argues that future biometrical genetic and epidemiological studies of coronary artery disease must take into account age and gender effects on interindividual variability and covariability of risk factors.