Thermodynamics of Error Correction

TL;DR

This paper presents a universal thermodynamic framework for understanding error rates in molecular information copying, revealing three operational regimes and the fundamental limits imposed by chemical driving and work dissipation.

Contribution

It derives a universal expression linking copy error to entropy production, applicable to any molecular copying system, and characterizes three distinct thermodynamic regimes of error correction.

Findings

Error rate depends on entropy production and work dissipated.

Copying can operate in regimes of error increase, decrease, or work extraction.

Error reduction is limited by chemical driving of proofreading reactions.

Abstract

Information processing at the molecular scale is limited by thermal fluctuations. This can cause undesired consequences in copying information since thermal noise can lead to errors that can compromise the functionality of the copy. For example, a high error rate during DNA duplication can lead to cell death. Given the importance of accurate copying at the molecular scale, it is fundamental to understand its thermodynamic features. In this paper, we derive a universal expression for the copy error as a function of entropy production and {\cred work dissipated by the system during wrong incorporations}. Its derivation is based on the second law of thermodynamics, hence its validity is independent of the details of the molecular machinery, be it any polymerase or artificial copying device. Using this expression, we find that information can be copied in three different regimes. In two of them, work is dissipated to either increase or decrease the error. In the third regime, the protocol extracts work while correcting errors, reminiscent of a Maxwell demon. As a case study, we apply our framework to study a copy protocol assisted by kinetic proofreading, and show that it can operate in any of these three regimes. We finally show that, for any effective proofreading scheme, error reduction is limited by the chemical driving of the proofreading reaction.