Optimization Based Design of Robust Synthetic

1. Optimization Based Design of Robust Synthetic Switches in Biological Networks Rajwant S. Bedi, Nael H. El-Farra Department of Chemical Engineering & Materials Science University of California, Davis, 95616 Understanding DNA and its genes have created valuable advances in medicine. Furthering this knowledge rests on understanding the dynamic behavior of these genes as well as interaction of genes with one another. Integration of biology and engineering generates the possibility of modeling and quantification of genetic networks. Construction of synthetic networks enhances our understanding of real systems, and it is a first step towards cellular control. This work presents an optimization-based methodology for the analysis and design of robust synthetic switches in biological networks. We initially derive a general performance functional that measures several robustness criteria and captures the tradeoffs between them. These criteria include the separation between the steady-states, the switching time and the energy gap between the two stable states, which measures the uncertainty of transition between those states. We use Lyapunov-based techniques to link the robustness criteria in the cost functional and the network states and parameters. To find the most efficient switch, the cost functional is minimized. We analyze the behavior of the switch with the aid of general nonlinear model of synthetic switches along variations in the model parameters, initial conditions and the induced energies. This identifies tunable parameters that can serve as decision variables in the optimization formulation. Finally, we optimize the performance measure through parameter tuning using Sequential Quadratic Programming (SQP) algorithm. The efficacy of the proposed optimization method is demonstrated through computer simulation studies using models of the bacteriophage lambda switch system.