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SIAM J. APPL. MATH. c 2009 Society for Industrial and Applied Mathematics
Vol. 69, No. 4, pp. 977998
SENSITIVITY AND ROBUSTNESS IN CHEMICAL REACTION
GUY SHINAR, URI ALON, AND MARTIN FEINBERG
Abstract. For a wide class of chemical reaction networks, including all those governed by
detailed balanced mass-action kinetics, we examine the robustness of equilibrium species concentra-
tions against fluctuations in the overall reactant supply. In particular, we present lower bounds on
the individual species-concentration sensitivities that derive from reaction network structure alone,
independent of kinetic parameters or even of the particular equilibrium state at which sensitivities
are calculated. These bounds suggest that, in the class of reaction networks considered here, very
high robustness (i.e., very low sensitivities) should be expected only when the various molecules are
constructed from a large number of distinct elemental building blocks that appear in high multiplicity
or that combine gregariously. This situation is often encountered in biology.
Key words. equilibrium points, chemical reaction networks, sensitivity, robustness, systems
AMS subject classifications. 80A30, 37C05, 37C25, 92C45