Hard Bounds on Molecular Fluctuations in Stochastic Reaction Systems*

The probabilistic nature of single chemical events spontaneously creates fluctuations in molecule concentrations in cells. A major challenge to analyze such intracellular noise is that most dynamical phenomena in biology do not depend on the expression pattern of any single gene on its own, but on the interactions between proteins, mRNA, DNA, and other components in the cells. In principle, fluctuations in each component may propagate to other components and to the whole genetic regulatory network. I will present fundamental limits on suppressing such molecular fluctuations in a general stochastic reaction systems which allow arbitrary regulatory topologies and control functions. The results, briefly, indicate that to reduce the fluctuation in one component will inevitably increase fluctuations of other components. I will also discuss how such trade-off of noise suppression relates to information theory.