Mathematics Seminar 04/21/23

Abstract:  In recent years, gene regulatory networks (GRNs) have attracted a lot of interest as they play a crucial role in modeling the protein regulation processes. In this work, we construct and analyze a new second-order partitioned exponential method for simulating genetic regulatory systems. For such systems with highly nonlinearities, a novel splitting technique is proposed to improve the stability and thus further increase accuracy and efficiency of the method. Alternatively, one can perform dynamic linearization of the system. In particular, we additionally suggest a second- and fourth-order exponential methods for such systems depending on their structure and properties. The linear stability analysis of the proposed methods is also presented. Finally, we present numerical experiments on various models, including a 2-gene and 3-gene repressilator models and a 13-dimensional budding yeast cell cycle model, to demonstrate the effectiveness of our proposed methods.

This is joint work with Vu Thai Luan and Julius Ehigie.