Reaction kinetics of catalyzed competitive heteropolymer cleavage.

A theoretical formulation for complete heteropolymer degradation is developed in terms of Michaelis-Menten reaction kinetics under the quasi-steady-state approximation. This allows the concentration of the entire intermediate decomposition cascade to be accounted for as well as each species of emerging final product. The formulation is implemented computationally and results in stable reaction kinetics across a range of orders of magnitude for K(M) and k(cat). The model is compared with experiment, specifically in vitro HIV-1 protease-catalyzed retroviral Gag-polyprotein processing. Using an experimentally determined cleavage-polypeptide parameter set, good qualitative agreement is reached with Gag degradation kinetics, given the difference in experimental conditions. A parameter search within 1 order of magnitude of variation of the experimental set results in the determination of an optimal parameter set in complete agreement with experiment which allows the time evolution of each individual as well as intermediate species in Gag to be accurately followed. Future investigations that determine the required enzymatic parameters to populate such a scheme will allow for the model to be refined in order to track the time for viral maturation and infectivity.