Generic kinetic equations for modelling multisubstrate reactions in computational systems biology

[摘要] Systems biology is a rapidly developing field, studying biological systems by methodically perturbingthem either chemically, genetically or biologically. The system response is observedand incorporated into mathematical models. These computational models describe the systemstructure, predicting its behaviour in response to individual perturbations. Metabolic networksare examples of such systems and are modelled in silico as kinetic models. These kinetic modelsconsist of the constituent enzyme reactions that make up the different pathways of a metabolicnetwork. Each enzyme reaction is represented as a mathematical equation. The main focus of akinetic model is to portray as realistically as possible a view in silico of physiological behaviour.The equations used to describe model reactions therefore need to make accurate predictions ofenzyme behaviour.Numerous enzymes in metabolic networks are cooperative enzymes and many equations havebeen put forward to describe these reactions. Examples of equations used to model cooperativeenzymes are the Adair equation, the uni-reactant Monod, Wyman and Changeux model, Hillequation, and the recently derived reversible Hill equation. Hill equations fit the majority ofexperimental data very well and have many advantages over their uni-substrate counterparts.In contrast to the abovementioned equations, the majority of enzyme reactions in metabolismare of a multisubstrate nature. Moreover, these multisubstrate reactions should be modelled asreversible reactions, as the contribution of the reverse reaction rate on the net conversion rate cannot be ignored [1]. To date, only the bi-substrate reversible MWC equation has been formulatedto describe cooperativity for a reversible reaction of more than one substrate. It is, however,difficult to use as a result of numerous parameters, not all of which have clear operationalmeaning. Moreover, MWC equations do not predict realistic allosteric modifier behaviour [2, 3].Hofmeyr & Cornish-Bowden [3] showed how the uni-reactant reversible Hill equation succeeds inpredicting realistic allosteric inhibitor behaviour, compared to the uni-reactant MWC equation,which does not. The aim of this study was to therefore derive a reversible Hill equation that candescribe multisubstrate cooperative reactions and predicts realistic allosteric modifier behaviour.In this work, we present a generalised multisubstrate reversible Hill (GRH) equation. The bi-substrate and three substrate cases of this equation were also extended to incorporate anynumber of independently binding allosteric modifiers. The derived GRH equation is evaluatedagainst the above mentioned cooperative models and shows good correlation. Moreover, thepredicted behaviour of the bi-substrate reversible Hill equation with one allosteric inhibitor iscompared to the MWC equation with one allosteric inhibitor in silico. This showed how thebi-substrate reversible Hill equation is able to account for substrate-modifier saturation, unlikethe MWC equation, which does not. Additionally, the bi-substrate reversible Hill equation behaviourwas evaluated against in vitro data from a cooperative bi-substrate enzyme which wasallosterically inhibited. The experimental data confirm the validity of the behaviour predictedby the bi-substrate reversible Hill equation. Furthermore, we also present here reversible Hillequations for two substrates to one product and one substrate to two products reactions. Reactionsof this nature are often found in metabolism and the need to accurately describe theirbehaviour is as important as reactions with equal substrates and products.The proposed reversible Hill equations are all independent of underlying enzyme mechanism,they contain parameters that have clear operational meaning and all of the newly derived equationscan be transformed to non-cooperative equations by setting the Hill coefficient equal toone. These equations are of great use in computational models, enabling the modeller to accuratelydescribe the behaviour of a vast number of cooperative and non-cooperative enzymereactions with only a few equations.

[发布机构] Stellenbosch University