A COMPUTER MODEL OF THE L-ARABINOSE GENE-ENZYME COMPLEX OF ESCHERICHIA COLI WITH AN ANALYSIS OF ITS CONTROL METHODOLOGY

This research investigated mathematically aspects of the "Demand Theory of Gene Regulation," which relates the evolution of control of gene activity to the environmental pressure upon the organism. The specific goal was to utilize an engineering systems approach to quantify some portions of this theory and examine the energy cost to the organism of alternative strategies of genetic control.;A systems theory approach was taken to represent the biological system by a linear time invariant realization. The L-arabinose gene-enzyme complex of E. coli was simulated on the computer using an eight state space model. This operon is regulated by both a repressor and an activator thus combining both negative and positive control. The first six states of the model represented protein/DNA interactions, while the final two states represented the concentrations of the repressor and activator proteins. All inputs to the system (RNAP, cAMP and L-arabinose) were considered as step inputs. The output (L-arabinose isomerase specific activity) was related directly to the activity of the DNA in the biological system. The stability, controllability, frequency response and state space relationships of the system model were studied. Coefficients in the system's equations were optimized based upon least square error criteria using as expected values the uninduced and induced values of L-arabinose isomerase specific activity as reported in the literature. Four models were developed and then compared to published biological data. Residual analysis on a set of biological variables was used to differentiate among the models and select the model of best fit.;A model utilizing repressor only control was also developed for the L-arabinose system. The resulting five state model was optimized and tested against reported data utilizing residual analysis.;A quadratic cost function was used to compare alternative control methodologies. Cost comparisons were made between the five state and eight state models. The energy cost to the cell was assumed to be proportional to the protein/DNA associations and the concentrations of the repressor and activator proteins. Results of the cost analysis show that a dual control system is more cost effective under most environmental conditions for this specific gene-enzyme complex.