Seminar in PSA 107

ABSTRACT

Title:  Canonical Model of Cascades of mediating Molecules in Cellular Metabolic
          Pathways and Regulation of Stable Gene Expression States in Cellular Circuits.

By:    John Burke, ASU Department of Mathematics & Statistics

Abstract: 

Metabolic linear cascades of molecules passing from a challenge at the cell membrane to gene expression with multiple gene expression states are derived and investigated.

Dynamical systems derived from mass balance equations of biochemical reactions of mediating molecules in cellular metabolic pathways are used to derive canonical models for cascades of signaling molecules. Analysis of relative reaction rates leads to a dynamical system with three time scales. Applying singular perturbation techniques to the system yields an analytic approximation of signal molecule concentrations; this enables us to estimate amplification and timing of pulses in the cascade.

Biochemical reactions of autoregulatory gene transcription factors, their promoter sites, and products, are modeled using mass balance dynamical systems to describe autoactivation of gene transcription by dimers at multiple
promoter sites. Under biologically feasible assumptions, the system is analyzed using quasi-static approximation techniques. This results in a scalar ODE of codimesion greater than two. Bifurcation theory is used to investigate multiple stable gene expression states, and possible mechanisms for switching between them.