Influence of enzyme production dynamics on the optimal control of a linear unbranched chemical process

In this paper we consider the classic kinetic problem of the minimization of the operation time in which a substrate is transformed into a product in multi-step enzymatic reactions. We propose a realistic formulation that incorporates the enzyme dynamics, and present a method for obtaining the solution for an unbranched scheme and bi-linear kinetic model in an almost exclusively analytical way. The solution, which involves the exponential integral, is illustrated with several examples.