### Mathematical Biosciences and Engineering

2019, Issue 6: 8195-8213. doi: 10.3934/mbe.2019414
Research article Special Issues

# Sign-sensitivities for reaction networks: an algebraic approach

• Received: 30 April 2019 Accepted: 26 August 2019 Published: 11 September 2019
• 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.

Citation: Elisenda Feliu. Sign-sensitivities for reaction networks: an algebraic approach[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 8195-8213. doi: 10.3934/mbe.2019414

### Related Papers:

• 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.

• © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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