  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.
