Speaker
Peter Sollich
(Kings College London)
Description
In systems biology we are encouraged to think in terms of
networks to try and understand the complex behaviour of
cells. There is much uncertainty in the identification process
of proteins, so often the complete network of reactions in a
protein interaction network (PIN) is unknown. Even in cases
where the whole network is known relatively accurately, it
is typically very large and therefore the dynamics hard to
analyse in detail; also reliable information on the requisite
reaction rates is difficult to obtain. Finally, experimental
measurements of the dynamics of protein concentrations,
e.g. using optical techniques, are typically possible only for a
limited number of protein species simultaneously.
These considerations motivate us to try to find descriptions
for the dynamics of moderately sized subnetworks of much
larger ("bulk") reaction networks. Eventually we would like
to solve the inverse problem, i.e. infer from observed
subnetwork dynamics something about the bulk network
properties. As a first step towards this, we address the
question of what form the dynamical equations for a
subnetwork should take. We propose to use the Mori-
Zwanzig projection formalism, which allows one to derive a
set of dynamical equations for selected variables from a
network using information from the whole network. We
point out some ways in which this differs from more familiar
applications of projection techniques in mode coupling
theory, and give some toy examples to illustrate the
approach.
