at the

American Institute of Mathematics, Palo Alto, California

organized by

Alicia Dickenstein, Jeremy Gunawardena, and Anne Shiu

This workshop, sponsored by AIM and the NSF, will be devoted to the mathematical analysis of biochemical reaction networks arising in systems biology. Specifically, we are interested in classes of nonlinear dynamical systems that arise from biologically-relevant networks of chemical reactions, parametrized by rate constants that are usually unknown and difficult to measure. The nonlinearities in these systems have hindered mathematical analysis of network behavior, which has largely been studied by numerical simulation.

Recent developments have suggested that mathematical analysis of such networks may be feasible, using methods from computational algebra, algebraic geometry and dynamical systems. For instance, one class of dynamical systems, coming from mass-action kinetics, gives rise to polynomial dynamical systems. Here, the biologically-relevant steady states are the positive real solutions to a system of polynomial equations and from computational algebra and algebraic geometry have been used to shed light on steady-state behaviour. Difficult questions still remain regarding the transient dynamics and generalisations to non mass-action systems.

The primary aim of this workshop is to bring together mathematicians as well as researchers who are closer to the experimental side of systems biology, in order to formulate precise open problems and to explore appropriate mathematical methods to tackle them. We hope to sustain an open dialogue between theory and experiment, so that they may continue to stimulate each other. Among the problems we may consider initially are the following.

- Decomposition of parameter spaces according to qualitative dynamical behaviour.
- Computation of steady state polynomial invariants.
- The Global Attractor Conjecture.
- Elimination theory and the QSSA (quasi-steady state approximation) approach.
- Extension of mass-action kinetics results to more general kinetics.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email *workshops@aimath.org*

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