Processive and distributive non-equilibrium networks discriminate in alternate limits

Abstract

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 which provides a condition for proofreading in a broad class of models, making it a useful objective function for optimizing discrimination schemes. Our results suggest that this measure is related to whether a network is processive or distributive. Processive networks are those that have a single dominant pathway for reaction progression, such as a protein complex that must be assembled sequentially. While distributive networks are those that have many effective pathways from the reactant to the product state; e.g. a protein complex in which the subunits can associate in any order. Non-equilibrium systems can discriminate using either binding energy (energetic) differences or activation energy (kinetic) differences. In both cases, proofreading is optimal when dissipation is maximized. In this work, we show that for a general class of proofreading networks, energetic discrimination requires processivity and kinetic discrimination requiring distributivity. Optimal discrimination thus requires both maximizing dissipation and being in the correct processive/distributive limit. Sometimes, adjusting a single rate may put these requirements in opposition and in these cases, the error may be a non-monotonic function of that rate. This provides an explanation for the observation that the error 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 to drive the network toward either the processive limit or the distributive limit. 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.