OPTIMAL PROTEIN SEPARATION

Gradient elution chromatography (GEC) is not only commonly used in lab oratory settings, but also increasingly used in separation and purific ation of biochemical and pharmaceutical products. These processes ofte n deal with very precious materials. Thus, it is extremely important t o obtain operational conditions so that the process efficiency is opti mum. However, this class of optimal control problems is highly nonstan dard, and hence cannot be solved using conventional optimal control te chniques. There are three specific characteristics associated with thi s class of optimal control problems: (i) the process contains a set of interrelated subprocesses with different time or space intervals; (ii ) the min-max objective function is not in the conventional form; and (iii) state dependent time lag appears in the control variables. This paper considers a related optimal control problem in which optimal con trol strategies of gradient elution linear chromatography (GELC) are t o be obtained for protein separations. The ionic strength, the gradien t of which affects the linear equilibrium constants in affinity chroma tography systems, is selected as the control variable. Using the contr ol parametrization technique, the control variables are approximated b y piecewise linear functions. Thus, a sequence of nonstandard optimal parameter selection problems is obtained. Each of these approximate pr oblems is then shown to be equivalent to a standard min-max optimizati on problem, and hence is solvable by existing optimization software. F or illustration, the proposed methodology is used in a case study.