The control of cell metabolism for homogeneous vs. heterogeneous enzyme systems

Effect of enzyme organization on the stability of Yates-Pardee pathways

Yates-Pardee-type metabolic pathways in a heterogeneous cell milieu are modeled as a system of coupled non-linear partial differential equations. A numerical solution to this system is described and some properties of such a physiological system are studied. Confinement with and without a membrane is considered and it is shown how confinement results in an increase in the stability of the metabolite concentrations. These results suggest that the enzyme organization may contribute to the stability of the cellular metabolism.

Why and when channelling can decrease pool size at constant net flux in a simple dynamic channel

Cornish-Bowden and Cárdenas (Cornish-Bowden, A. and Cárdenas M.L. (1993) Eur. J. Biochem. 213, 87-92) have suggested that simulation results peviously published by us (Mendes, P., Kell, D.B. and Westerhoff, H.V. (1992) Eur. J. Biochem. 204, 255-266) which had demonstrated that large reductions of intermediate pool sizes could be accompanied by increasing channel flux in a model metabolic pathway, were an artefact of changes in the pathway's overall flux of the order of 0.0075%, or of inappropriate alterations of enzyme activities. They also asserted to prove that the "channelling of an intermediate cannot affect its free concentration at constant net flux". We consider the co-response of the intermediate metabolite concentration ('pool') and the channel flux to changes in kinetic (or thermodynamic) parameters. Both by analytical proofs and by numerical examples we show that this co-response can be positive, negative or null, depending on the parameter change. In particular, we prove that there is always a number of ways of changing parameters such that the intermediate metabolite concentration decreases with increasing channel flux, whether the total flux varies or is constant. We also show that increased stability of the (dynamic) enzyme-intermediate-enzyme complex, as well as a single parameter change that similarly displays no cross-over effects, can lead to decreased intermediate metabolite concentration and increased channel flux at constant total flux. In general, a non-zero co-response of the intermediate metabolite concentration ('pool') and the channel flux to changes in kinetic (or other) parameters is the rule rather than the exception. More specifically: (i) The algebraic analysis ('general proof') given in Cornish-Bowden and Cárdenas (1993) contains the constraint that the elasticities of various steps to the modulation parameters which were used to vary the channel flux at constant net flux were unity. This is an unfortunate and unnecessary constraint which, when lifted, means that the concentration of the pool in the general case can indeed change at constant net flux. A 'simplified proof' given in Cornish-Bowden and Cárdenas (1993) also fails, due in addition to the consequent failure to include mass conservation relations for some of the enzymes. (ii) In the systems studied by Cornish-Bowden and Cárdenas (1993), flux is properly to be considered as a variable (since it varies during the transition to the steady state), and not a parameter, and as such cannot per se affect the magnitude of other variables in the steady state. (iii) By relaxing the constraint referred to in (i), above, and by making dual modulations (i.e., of more than one parameter at once) which are different from those carried out in Cornish-Bowden and Cárdenas (1993) we find many instances in which channelling (described by a parameter p) does significantly affect the concentration of the pool intermediate C at constant total flux. (iv) In the same pathways, but in which the flux is held constant by setting it via a zero-order flux-generating reaction, the addition of a channel is also able to significantly to modulate the size of the pool at constant total flux. Our results show that the effectiveness of channelling in decreasing a pool, even at constant flux, is very much a reality.

Control in channelled pathways. A matrix method calculating the enzyme control coefficients

The usual equations expressing the enzyme control coefficients (quantitative indicators of 'global' control properties of a pathway) via the elasticity coefficients (reflecting local kinetic properties of an enzyme reaction), cannot be applied to a variety of 'non-ideal' pathways, in particular to pathways with metabolic channelling. Here we show that the relationship between the control and elasticity coefficients can be obtained by considering such a metabolic pathway as a network of elemental chemical conversions (steps). To calculate the control coefficients of enzymes one should first determine the elasticity coefficients of such elemental steps and then take their appropriate combinations. Although the method is illustrated for a channelled pathway it can be used for any non-ideal pathway including those with high enzyme concentrations where the sequestration of metabolites by enzymes cannot be neglected.

Comparison of the kinetic properties of MGDG synthase in mixed micelles and in envelope membranes from spinach chloroplast

We have applied the 'membrane partition' kinetic modelling approach proposed by Heirwegh et al. [(1988) Biochem. J. 254, 101-108] to MGDG synthase in isolated envelope vesicles. Comparison of the kinetic parameters obtained for MGDG synthase assayed in purified envelope membranes and in mixed-micelles demonstrates that the latter are relevant to the situation in envelope membranes and that MGDG synthase has a very high affinity for dilinoleoylglycerol. Our results provide additional evidence for the hypothesis that the high affinity of the envelope MGDG synthase for dilinoleoylglycerol could be responsible for the presence of C18 fatty acids at both the sn-1 and sn-2 position of the glycerol backbone in MGDG.

Kinetic selectivity of cholinephosphotransferase in mouse liver: the Km for CDP-choline depends on diacylglycerol structure

The effects of different 1,2-diacyl-sn-glycerols on the kinetic properties of CDP-choline:1,2-diacylglycerol cholinephosphotransferase (EC 2.7.8.2) from mouse liver microsomes have been studied. Initial-velocity experiments were carried out with various concentrations of several species of diacylglycerol at different fixed concentrations of CDP-choline. Kinetic analysis of these data showed a family of intersecting lines consistent with a sequential kinetic mechanism of catalysis. The Km and Vmax. values derived from rate data revealed a pronounced effect of diacylglycerol species utilization on the Km value for CDP-choline. There was a biphasic relationship between diacylglycerol chain length and the Km for CDP-choline. Substitution of an unsaturated fatty acid in the sn-2 position of distearin also dramatically increased the CDP-choline Km value as well as the Vmax. 1,2-Dipalmitoyl-sn-glycerol was the preferred substrate over other disaturated species, but 1,2-dihexanoyl-sn-glycerol could not be utilized. These results demonstrate the kinetic mechanism of in vitro catalysis and suggest a regulatory role for CDP-choline concentration in the diacylglycerol species selectivity of cholinephosphotransferase resulting in the de novo biosynthesis of different molecular species of phosphatidylcholine.

Local probes and heterogeneous catalysis: a case study of a mitochondria-luciferase-hexokinase coupled system

Biological systems are characterized by a high degree of structural organization. In the intracellular context, this introduces physical constraints which are not considered in the standard biochemical analysis of isolated systems, aimed towards mechanistic studies. A major challenge in cellular biology is thus to integrate the structural and mechanistic information and reach an adequate representation of the modes of operation in situ. We present an approach to this problem which takes advantage of a localized probe to study heterogeneous coupled system, as minimal models for cellular operation. The system consists of ATP production at the surface of mitochondria, and ATP consumption in solution by the hexokinase reaction. Soluble or biologically localized firefly luciferase is used to continuously monitor ATP concentration either in the bulk solution or at the surface of the organelle, respectively. The general system of a surface source and a bulk sink is mathematically modeled, and an analytic steady-state solution for local and bulk ATP is presented. The results are validated by experiment and differ from the expected behavior of an equivalent homogeneous system in solution. The model is further adapted to evaluate the effect of mixing. In addition, two limiting cases of heterogeneous distribution of hexokinase are analyzed, in which the soluble enzyme adsorbs non-specifically to mitochondria, or binds selectively to the site of ATP appearance on the membrane. The results are discussed in terms of their significance to the analysis of bulk measurements in vitro and their relevance to better description of cellular situations.

Metabolic control analysis: a survey of its theoretical and experimental development

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Algorithms for the derivation of Flux and Concentration Control Coefficients

A computer program is described that derives the Flux and Concentration Control Coefficients for linear and branched metabolic pathways. The program prompts the user to enter a concise description of the metabolic pathway. From this description, the program constructs the appropriate equations in matrix form. The algorithm employed to obtain the symbolic determinants is described, and this algorithm also provides a convenient method for manual derivation of the Control Coefficients. The computer-based method will accommodate unlimited feed-forward and feed-backward loops and a maximum of two branches from each metabolite on the main pathway. The utility of the method is illustrated with a linear path with feed-forward and feed-backward loops, and with a substrate cycle as an example of a path with two branches.

In vivo channeling of substrates in an enzyme aggregate for beta-carotene biosynthesis

The existence and the mode of operation of certain enzyme aggregates may be established from the concentrations of intermediates measured in the presence of specific inhibitors. beta-Carotene, the most abundant carotenoid pigment in the fungus Phycomyces blakesleeanus, arises from ring formation at both ends of lycopene. The inhibitors nicotine, imidazole, alpha-picoline, and 2-(4-chlorophenylthio)triethylamine lead to the simultaneous accumulation of lycopene, beta-carotene, and the one-ring intermediate gamma-carotene. The quantitative analytical values obey precise mathematical relationships: those expected from the operation of an enzyme aggregate with two cyclases equally sensitive to the inhibitors. The intermediates lycopene and gamma-carotene rejected by chemically inhibited enzymes may be readmitted to other cyclases in the wild type but not in heterokaryons containing a carA mutation. We have calculated the fraction of inhibited cyclase under each condition, the affinity constant of each inhibitor for the cyclase, and the probability that a rejected intermediate molecule will be readmitted and further metabolized. The probabilities for lycopene and gamma-carotene are identical and independent of the inhibitor responsible for the rejection. Our calculations suggest that each rejected intermediate molecule is readmitted to the enzyme aggregates two or three times on the average.

Enzyme-enzyme interactions and their metabolic role

There are continuing reports on the existence of complexes of sequential metabolic enzymes. New techniques for their detection have been described and include affinity electrophoresis and the use of anti-idiotypic antibodies. Channeling of substrates has been reported for several systems as well as direct substrate transfer through dynamic enzyme associations. Kinetic parameters of metabolic control of organized systems have been formulated and tested in several systems. These recent results are expanding our understanding of metabolic processes and their control.

A microcompartmentation analysis of intermediate leakage response to substrate excess in a membrane-bound bifunctional enzyme: local control of hydroxyprogesterone channeling efficiency during cytochrome P450XVII-catalysed androgen biosynthesis

Evidence is presented for the first time that the cytochrome P450XVII-catalysed androgen formation from progesterone (P) in rat testicular microsomal membranes represents a metabolic sequence that exhibits the ability of intrinsic regulation of intermediate transfer and product formation efficiency. Exposure of this system, which catalyses a hydroxylation and oxidative cleavage reaction sequence, to increasing P concentration results in a decreased specific retention of the putative intermediate, 17 alpha-hydroxyprogesterone (HP) in the membrane compartment, and in a decreased HP conversion to androgens in favour of increasing HP transfer into the extramembrane space. This behaviour results in a decreased ratio of product vs. intermediate formation rates, which is interpreted as a partial "uncoupling" of the normal hydroxylation and cleavage reaction sequence catalysed by P450XVII. A similar pattern can likewise be observed in isolated testicular Leydig cells after exposure to increasing P concentrations under more physiological continuous-flow conditions. Further calculations indirectly indicate that the specific retention of HP in the membrane compartment can partially be attributed to its specific association with the P450XVII during catalysis. The results strongly suggest the existence of a local "channel" that becomes more leaky and therefore less effective if loaded with high influx rates. This pattern may be related to significant but incomplete competition of exogenously entering P and endogenously formed and transiently bound HP for oxygen attack at the P450XVII active site.

Enzyme-enzyme interactions and control analysis. 2. The case of non-independence: heterologous associations

The association of different enzymes into a complex may induce changes in the kinetic parameters of its component enzymes. This implies that they cannot be treated as independent catalysts. It will affect the formulations and theorems of control analysis and necessitates the introduction of additional elasticities reflecting the effect of one enzyme on the rate of another. We show how this is achieved as an extension of the classical treatment. We present modified summation and connectivity theorems incorporating both homologous and heterologous interactions. The case of channelling of metabolites in such complexes is considered and an experimental method for its detection is suggested.

A comparison of variant theories of intact biochemical systems. I. Enzyme-enzyme interactions and biochemical systems theory

The need for a well-structured theory of intact biochemical systems becomes increasingly evident as one attempts to integrate the vast knowledge of individual molecular constituents, which has been expanding for several decades. In recent years, several apparently different approaches to the development of such a theory have been proposed. Unfortunately, the resulting theories have not been distinguished from each other, and this has led to considerable confusion with numerous duplications and rediscoveries. Detailed comparisons and critical tests of alternative theories are badly needed to reverse these unfortunate developments. In this paper we (1) characterize a specific system involving enzyme-enzyme interactions for reference in comparing alternative theories, and (2) analyze the reference system by applying the explicit S-system variant within biochemical systems theory (BST), which represents a fundamental framework based upon the power-law formalism and includes several variants. The results provide the first complete and rigorous numerical analysis within the power-law formalism of a specific biochemical system and further evidence for the accuracy of the explicit S-system variant within BST. This theory is shown to represent enzyme-enzyme interactions in a systematically structured fashion that facilitates analysis of complex biochemical systems in which these interactions play a prominent role. This representation also captures the essential character of the underlying nonlinear processes over a wide range of variation (on average 20-fold) in the independent variables of the system. In the companion paper in this issue the same reference system is analyzed by other variants within BST as well as by two additional theories within the same power-law formalism--flux-oriented and metabolic control theories. The results show how all these theories are related to one another.

Metabolic control therapy and biochemical systems theory: different objectives, different assumptions, different results

The claim by Savageau et al. (1987 a, b, Math. Biosci. 86, 127-145, 147-167) that the theory of metabolic control associated with Kacser & Burns (1973, Symp. Soc. Exp. Biol. 27, 65-104) and with Heinrich & Rapoport (1974, Eur. J. Biochem. 42, 89-102) is no more than a special case of the biochemical systems theory of Savageau and colleagues is examined. It is shown to be based on a misconception of the objectives and assumptions of metabolic control theory. In particular, the control and elasticity coefficients that play a central role in metabolic control theory are not constants and cannot be treated as constants. Consequently they cannot in general be equated with the kinetic orders that appear in biochemical systems theory, though they do correspond at the point where the two theories are tangential to one another.

Specific accumulation of 17 alpha-hydroxyprogesterone in microsomal membranes during the process of cytochrome P-450(C-17)-catalysed androgen biosynthesis. A dynamic study of intermediate formation and turnover

A complete dynamic analysis of cytochrome P-450(C-17)-catalysed androgen biosynthesis from a single dose of progesterone and 17 alpha-hydroxyprogesterone in a double-label double-substrate experiment was performed in order to elucidate the controversial intermediacy of 17 alpha-hydroxyprogesterone. Label distribution within the steroid fractions as well as in the membrane and buffer compartments yields direct evidence that the endogenously formed 17 alpha-hydroxyprogesterone (which is in an 'intermediate state') accumulates to a higher degree in microsomal membranes than does the exogenously added 17 alpha-hydroxyprogesterone (which is in a 'substrate state') under certain conditions. It is also demonstrated that endogenously formed 17 alpha-hydroxyprogesterone may partly leave the membrane compartment (in terms of a 'leakage' or 'overflow' phenomenon) and is then able to equilibrate with the pool of exogenously added 17 alpha-hydroxyprogesterone. Since only the label distribution in the membrane-associated (but not always in the aqueous) 17 alpha-hydroxyprogesterone pool corresponds to the label distribution in the androgen fraction, it is concluded that only the membrane-associated 17 alpha-hydroxyprogesterone pool is directly accessible to cytochrome P-450(C-17)-catalysed conversion into androgens.

The perfection of substrate-channelling in interacting enzyme systems: energetics and evolution

Some implications of substrate channelling in interacting enzyme systems are considered, with regard to the energetics and evolution of enzyme action. The transient time, a key analytical parameter relating to the phenomenon of channelling, is the basis of our kinetic study. Bounds on the kinetics of multienzyme complexes are established using (apparent) rate constants emanating from the transient-time formulation of coupled reactions. From a transition state representation of the rate process, it is shown how dynamically and statically organized enzyme systems lead to the modification of current ideas on the evolutionary optimization of the energy profile of enzyme catalysis in situ.