Stochastic modeling of regulated enzymes

Abstract

The stochastic model of the allosterically regulated enzyme aspartate transcarbamylase uses a Markov process to describe the rate of reaction of substrate binding given various concentration levels. The enzymatic process may be viewed as an M/M/2 queueing system where two different types of arrivals are necessary for a service. There are two servers and a capacity of four customers in the system, two of each type. Arrival rates at a particular server are dependent on the state of the other server. In addition, two other types of customers may enter the system. These do not enter the service facility but do influence the arrival rates of the former type of customers. This research also develops a numerical solution procedure for obtaining the rate of reaction under given concentrations of the ligands. Finally, a method is described which utilizes a least-squares criterion for obtaining estimates for various unknown parameters. In this method, a Marquardt optimization procedure includes analytical expressions for the partial derivatives of the steady-state probabilities with respect to the unknown parameters.