Sign-sensitivities for reaction networks: an algebraic approach
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Sign-sensitivities for reaction networks : an algebraic approach. / Feliu, Elisenda.
In: Mathematical Biosciences and Engineering, Vol. 16, No. 6, 11.09.2019, p. 8195-8213.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Sign-sensitivities for reaction networks
T2 - an algebraic approach
AU - Feliu, Elisenda
PY - 2019/9/11
Y1 - 2019/9/11
N2 - This paper presents an algebraic framework to study sign-sensitivities for reaction networks modeled by means of systems of ordinary differential equations. Specifically, we study the sign of the derivative of the concentrations of the species in the network at steady state with respect to a small perturbation on the parameter vector. We provide a closed formula for the derivatives that accommodates common perturbations, and illustrate its form with numerous examples. We argue that, mathematically, the study of the response to the system with respect to changes in total amounts is not well posed, and that one should rather consider perturbations with respect to the initial conditions. We find a sign-based criterion to determine, without computing the sensitivities, whether the sign depends on the steady state and parameters of the system. This is based on earlier results of so-called injective networks. Finally, we address systems with multiple steady states and the restriction to stable steady states.
AB - This paper presents an algebraic framework to study sign-sensitivities for reaction networks modeled by means of systems of ordinary differential equations. Specifically, we study the sign of the derivative of the concentrations of the species in the network at steady state with respect to a small perturbation on the parameter vector. We provide a closed formula for the derivatives that accommodates common perturbations, and illustrate its form with numerous examples. We argue that, mathematically, the study of the response to the system with respect to changes in total amounts is not well posed, and that one should rather consider perturbations with respect to the initial conditions. We find a sign-based criterion to determine, without computing the sensitivities, whether the sign depends on the steady state and parameters of the system. This is based on earlier results of so-called injective networks. Finally, we address systems with multiple steady states and the restriction to stable steady states.
U2 - 10.3934/mbe.2019414
DO - 10.3934/mbe.2019414
M3 - Journal article
C2 - 31698663
VL - 16
SP - 8195
EP - 8213
JO - Mathematical Biosciences and Engineering
JF - Mathematical Biosciences and Engineering
SN - 1547-1063
IS - 6
ER -
ID: 230140964