# Critical lack of equilibrium in stochastic kinetic proofreading

## TL;DR

This paper investigates how the absence of detailed balance in stochastic kinetic proofreading models influences their ability to discriminate between ligands, revealing a critical threshold necessary for high specificity.

## Contribution

It establishes a critical level of detailed balance violation required for strong ligand discrimination and shows that exceeding this threshold does not guarantee improved specificity.

## Key findings

- Existence of a critical lack of detailed balance for high specificity
- Models with similar lack of detailed balance can differ in discrimination ability
- Strong discrimination is not solely determined by the degree of detailed balance violation

## Abstract

In this paper we study the relation between the property of detailed balance and the ability of discriminating between different ligands for a class of stochastic models of kinetic proofreading. We prove the existence of a critical amount of lack of detailed balance that the kinetic proofreading models must have in order to have strong specificity for a value of the binding energy $\sigma$. We also prove that the fact that a kinetic proofreading model has a lack of detailed balance that is larger than the critical one does not necessarily yield strong discrimination properties. Indeed, there exist different sets of chemical rates, leading to the same amount of lack of detailed balance, that have strong discrimination property in some cases and not in others.