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Coarse-graining biochemical complexity

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Ilya Nemenman, Los Alamos National Lab
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To decrease the complexity involved in analysis of large stochastic
biochemical networks, one often coarse-grains them to a level of
effective deterministic reactions (such as the famous Hill law),
sometimes infused with Poisson/Langevin noise. When is such
description fair? To understand this, we developed a novel technique,
which has its roots in statistical field theory and adiabatic quantum
mechanics. The technique allows us to derive rigorous laws describing
coarse-grained, effective stochastic dynamics. We found that, for
complex reactions, stochasticity results in corrections to the mean
reaction rates, which are intimately related to stochastic pumping
effect, and to the Berry phase in quantum mechanics. Additionally,
the noise variance for coarse-grained reactions differs substantially
from the usual Poisson statistics, and both effects must be accounted
for in careful analytical or numerical studies. I will illustrate
these points using a simple example of a Michaelis-Menten enzyme.