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Register a new userA Linear Programming Approach to Dynamical Equivalence, Linear Conjugacy, and the Deficiency One Theorem
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Matthew D. Johnston
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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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A numerically effective procedure for determining weakly reversible chemical reaction networks that are linearly conjugate to a known reaction network is proposed in this paper. The method is based on translating the structural and algebraic characteristics of weak reversibility to logical statements and solving the obtained set of linear (in)equalities in the framework of mixed integer linear programming. The unknowns in the problem are the reaction rate coefficients and the parameters of the linear conjugacy transformation. The efficacy of the approach is shown through numerical examples.
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