Dimitri Loutchko, Yuki Sughiyama, Tetsuya J. Kobayashi
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Cramer-Rao bound and absolute sensitivity in chemical reaction networks
Chemical reaction networks (CRN) comprise an important class of models to
understand biological functions such as cellular information processing, the
robustness and control of metabolic pathways, circadian rhythms, and many more.
However, any CRN describing a certain function does not act in isolation but is
a part of a much larger network and as such is constantly subject to external
changes. In [Shinar, Alon, and Feinberg. "Sensitivity and robustness in
chemical reaction networks." SIAM J App Math (2009): 977-998.], the responses
of CRN to changes in the linear conserved quantities, called sensitivities,
were studied in and the question of how to construct absolute, i.e.,
basis-independent, sensitivities was raised. In this article, by applying
information geometric methods, such a construction is provided. The idea is to
track how concentration changes in a particular chemical propagate to changes
of all the other chemicals within a steady state. This is encoded in the matrix
of absolute sensitivites. A linear algebraic characterization of the matrix of
absolute sensitivities for quasi-thermostatic CRN is derived via a Cramer-Rao
bound for CRN, which is based on the the analogy between quasi-thermostatic
steady states and the exponential family of probability distributions.