  Mass-action kinetics is frequently used in systems biology to model the
behaviour of interacting chemical species. Many important dynamical properties
are known to hold for such systems if they are weakly reversible and have a low
deficiency. In particular, the Deficiency Zero and Deficiency One Theorems
guarantee strong regularity with regards to the number and stability of
positive equilibrium states. It is also known that chemical reaction networks
with disparate reaction structure can exhibit the same qualitative dynamics.
The theory of linear conjugacy encapsulates the cases where this relationship
is captured by a linear transformation. In this paper, we propose a
mixed-integer linear programming algorithm capable of determining weakly
reversible reaction networks with a minimal deficiency which are linearly
conjugate to a given reaction network.
