(125f) Systematic Reduction of Models of Mechanistic Template Polymerization Processes and Applications to Genetic Networks

The engineering of gene regulatory circuits necessitates the use of systematic mathematical modeling to provide guidelines and make quantitative predictions. The components of such circuits pose exceedingly diverse and rich forms of interactions, it is therefore indispensable that mathematical models incorporate the essential details of the processes involved for making accurate predictions.

It has been shown that incorporating time delays in reduced models of gene networks is often essential to capture the whole range of behavior. From a mechanistic model for protein translation in the form of a large system of ordinary differential equations (ODEs), we systematically derive a reduced time-delay model by performing systematic approximations on the ODE system. We find quantitative agreement in protein synthesis rates and ribosome density on the messages between the two models. The region in parameter space where self-sustained oscillations exist is found, via bifurcation analysis, for both the reduced model obtained and a heuristic model proposed else- where. Qualitative differences are found between the models and explained in terms of the undergoing biological process.