Molecular Modelling of Gene Circuits

10:00am - 10:30am Tea and Coffee, The Street, Zeeman Building.

10:30am - 11:30am Molecular Foundations of Genetics and Modelling. Markus Kirkilionis, Warwick

11:30am - 12:30am Molecular Systems with Infinite and Finite State Spaces I. Luca Sbano, Rome.

12:30am - 1:30pm Lunch Break, The Street, Zeeman Building.

1:30pm - 3:00pm Molecular Systems with Infinite and Finite State Spaces II. Luca Sbano, Rome.

3:00pm - 3:30pm Tea Break, The Street, Zeeman Building.

3:30pm - 5:00 Reserved for talks by participants.

Luca Sbano, Molecular Systems with Infinite and Finite State Spaces I+II.

Abstract:
This talk aims to present a general approach to study stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger macro-molecules, finite and small in numbers per cell (like protein complexes), with smaller, very abundant molecules, for example metabolites. We study the construction of the continuum approximation of the associated Master Equation (ME) by using the Trotter approximation. The continuum limit shows regimes where the finite states evolve faster
than the ones that admit a continuum description. Then we develop a rigourous asymptotic adiabatic theory upon the condition that the jump process arising from the finite states of the Markov Chain (MC, typically describing conformational changes of the macro-molecules) occurs with large frequency.
This approach will be illustrated through several examples, in particular the modelling of a genetic clock
formed by two interacting genes.