Dr. Tomas Gedeon (Dept. of Mathematical Sciences, MSU) 

3/3/2022  3:10pm

Abstract:

Transcription and translation retrieve and operationalize gene encoded information in cells. These processes are not instantaneous and incur significant delays. We briefly discuss justification and derivation of the model, analysis of the appropriate setting of the corresponding dynamical system, and extenive numerical analysis of its dynamics. Comparison with constant delay models shows significant differences in dynamics that include existence of stable periodic orbits in inducible systems and multistability in repressible systems. A combination of parameter space exploration, numerics, analysis of steady state linearization and bifurcation theory indicates the likely presence of Shilnikov-type homoclinic bifurcations in the repressible operon model.