Enzyme‐enzyme interactions and control analysis

Abstract

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 n, 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, (xi # l), the summation theorems are given byThe example of monomer-oligomer equilibria is used to illustrate non-additive behaviour and experimental methods for their study are suggested.In the classical study of the control of metabolism, two fundamental assumptions are usually made regarding the properties of the enzymes which constitute metabolic systems. The first is that the reaction rate of an isolated enzyme is first order with respect to enzyme concentration and the second assumption is that all enzymes are independently acting cataThe first assumption, that of additivity, (i.e. rate K E ) is based on the observations of the kinetics of a wide range of extracted enzymes. However, there are a number of instances where additivity may not apply [l]. For example, if an enzyme monomer-oligomer equilibrium exists and if the overall specific activity of the mix of monomer and homologous oligomer varies with the proportions of the two forms, then deviations from additivity will occur. Similar deviations could occur if the total concentration of a particular enzyme is partitioned between the free enzyme and enzyme bound to a catalytically inert substratum, such as a membrane or cytoskeleton, present in constant amount. If the bound enzyme has different kinetics from the free enzyme, then nonadditivity would be observed. Similar arguments apply to enzymes operating in cascades.The second assumption, that of independence, is usually represented by each enzyme catalysing one step without the enzyme associating with any other. Such associations between some enzymes, however, are known to take place. Nevertheless, there would be no functional consequences of such association if the catalytic activities of the enzymes in the heterologous complex were the same as those of the free lysts.

Sensitivity analysis approaches applied to systems biology models

“…p-elasticity coefficient (parameter-elasticity coefficient) the reaction rate v i the parameter p j [27,28] …”

Control theory of metabolic channelling

“…In ordinary (ideal) metabolic pathways there is a one-toone correspondence between the enzymes and reactions, and another definition for the control coefficient [5,6] compares a relative change of the local rate (Sv i /vi) through a reaction i with a variation (SJ/J) of the system's (steady-state) flux caused by a change in the rate L' The control coefficient defined in this manner is designated by CJi [8], and is referred to as the control coefficient with respect to the activity or rate of an enzyme to emphasize its relation to a 'local' rate, v i .A short-hand notation [5,6,7] for this definition reads: C J= (dJ/J)':v~ (2) v, (~v,/v,) ....…”

“…Assuming thermodynamic equilibrium between the separate enzymes and the complex they calculated the elasticities of partial reactions (i.e., proceeding in the bulk phase and in the channelled phase) with respect to the total enzyme concentrations. However, only under special conditions these elasticities which are referred to as protein (r 0 elasticities [8,33] depend only on the equilibrium constant and the total amounts of the enzymes. This approximation fails for the more general case of a dynamic channel of Fig.…”

“…Treating cellular metabolism as a network of enzyme reactions control analysis used to be based on the following important assumptions: Ill) the rate of any reaction is proportional to the concentration of enzyme (a property often termed additivity [8]), (2) different enzymes are independent catalysts, (3) the concentrations of enzyme-bound metabolites can be neglected as compared to their free concentrations (substitution of the latter by the total metabolite concentrations greatly simplifies control analysis [9,10]). …”

“…[8,[33][34][35][36]). However, no control theory dealing with the general case of partial channelling, dynamic and/or static, has been developed.…”