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A linear programming approach to dynamical equivalence, linear conjugacy, and the Deficiency One Theorem

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Abstract

The well-known Deficiency One Theorem gives structural conditions on a chemical reaction network under which, for any set of parameter values, the steady states of the corresponding mass action system may be easily characterized. It is also known, however, that mass action systems are not uniquely associated with reaction networks and that some representations may satisfy the Deficiency One Theorem while others may not. In this paper we present a mixed-integer linear programming framework capable of determining whether a given mass action system has a dynamically equivalent or linearly conjugate representation which has an underlying network satisfying the Deficiency One Theorem. This extends recent computational work determining linearly conjugate systems which are weakly reversible and have a deficiency of zero.

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Acknowledgments

The author gratefully thanks San José State University for its financial and logistic support, and Lake Tahoe for the serenity which lead to the conception of this project. The author also thanks the reviewers for their insightful and helpful suggestions.

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  1. Department of Mathematics, San José State University, One Washington Square, San José, CA, 95192, USA

    Matthew D. Johnston

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  1. Matthew D. Johnston
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Correspondence to Matthew D. Johnston.

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Johnston, M.D. A linear programming approach to dynamical equivalence, linear conjugacy, and the Deficiency One Theorem. J Math Chem 54, 1612–1631 (2016). https://doi.org/10.1007/s10910-016-0640-9

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