  We study biochemical reaction networks capable of product discrimination
inspired by biological proofreading mechanisms. At equilibrium, product
discrimination, the selective formation of a "correct" product with respect to
an "incorrect product", is fundamentally limited by the free energy difference
between the two products. However, biological systems often far exceed this
limit, by using discriminatory networks that expend free energy to maintain
non-equilibrium steady states. Non-equilibrium systems are notoriously
difficult to analyze and no systematic methods exist for determining parameter
regimes which maximize discrimination. Here we introduce a measure that can be
computed directly from the biochemical rate constants and which provides a
necessary condition for proofreading. Non-equilibrium systems can discriminate
using binding energy (energetic) differences or using activation energy
(kinetic) differences, but in both cases, proofreading is optimal when
dissipation is maximized, so long as the necessary condition we introduce is
satisfied. We show that these constraints can be in opposition and that this
explains why the error rate is a non-monotonic function of the irreversible
drive in the original proofreading scheme of Hopfield and Ninio. Finally, we
introduce mixed networks, in which one product is favored energetically and the
other kinetically. In such networks, sensitive product switching can be
achieved simply by spending free energy. Biologically, this corresponds to the
ability to select between products by driving a single reaction without network
fine tuning. This may be used to explore alternate product spaces in
challenging environments.
