It was observed by Jacob and Monod in the 1960's that gene regulatory networks could have arbitrarily complicated interaction structures and behaviour. Rod Edwards from the University of Victoria will give a talk of interest to anybody working on modelling of large and complex network models.
 Rod Edwards |
Place: AUN, Biotechnology Building, room BT3A-11
Speaker: Prof. Rod Edwards, Dept. of Mathematics and Statistics, University of Victoria, Canada
Recent advances in genomics research have begun to allow exploration of particular gene regulation pathways but it is also worthwhile to consider the range of possible dynamical behaviours in networks of this sort. One approach to the problem of understanding the dynamical possibilities has been to concentrate on structural classes and activation/repression switching dynamics by means of a `hard switching' limit. This active/inactive idealization may capture the behaviour of more realistic models with linear terms that don't contribute essentially to the switching dynamics. The resulting equations are mathematically tractable due to their piecewise-linear nature, and it has been shown that even in quite small (n=4) networks, there is a rich variety of stable dynamics, including multistability (crucial to cell differentiation, for example), periodic orbits (e.g. the cell cycle) and chaos. Prof. Edwards will present some examples of the impressive variety of types of dynamics that can arise in such networks, and show how analysis can be used to determine their dynamics and to elucidate more general structural principles.
In addition to his work on gene networks, prof. Edwards has also been
engaged in analysis of neural networks and in mathematical modelling
and analysis of tremor in patients with Parkinson's disease. Even
though his talk will be focused on a very specific mathematical
framework of non-linear ordinary differential equations - piecewise
linear equations which are developed to model gene networks - his
approach and methods should be of interest to anybody working on
modelling of large and complex network models.
For more information on Rod Edwards, please see http://www.math.uvic.ca/faculty/edwards/
