A generic rate equation for catalysed, template-directed polymerisation and its use in computational systems biology

[摘要] ENGLISH ABSTRACT: Progress in computational systems biology depends crucially on the availabilityof generic rate equations that accurately describe the behaviourand regulation of catalysed processes over a wide range of conditions.Such equations for ordinary enzyme-catalysed reactions have been developedin our group and have proved extremely useful in modellingmetabolic networks. However, these networks link to growth and reproductionprocesses through template-directed synthesis of macromoleculessuch as polynucleotides and polypeptides. Lack of an equation thatcaptures such a relationship led us to derive a generic rate equation thatdescribes catalysed, template-directed polymerisation reactions with varyingmonomer stoichiometry and varying chain length. A model describingthe mechanism of a generic template-directed polymerisation processin terms of elementary reactions with mass action kinetics was developed.Maxima, a computational algebraic solver, was used to determineanalytical expressions for the steady-state concentrations of the speciesin the equation system from which a steady-state rate equation could bederived. Using PySCeS, a numerical simulation platform developed inour group, we calculated the time-dependent evolution and the steadystatesof the species in the catalytic mechanisms used in the derivationof the rate equations. The rate equation was robust in terms of beingaccurately derived, and in comparison with the rates determined withPySCeS. Addition of more elongation steps to the mechanism allowed thegeneralisation of the rate equation to an arbitrary number of elongationssteps and an arbitrary number of monomer types. To test the regulatorydesign of the system we incorporated the generic rate equation in a computationalmodel describing a metabolic system consisting of multiplemonomer supplies linked by a template-directed demand reaction. Ratecharacteristics were chosen to demonstrate the utility of the simplifiedgeneric rate equation. The rate characteristics provided a visual representationof the control and regulation profile of the system and showedhow this profile changes under varying conditions.

[发布机构] Stellenbosch University