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 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.
- Received 23 April 2015
DOI:https://doi.org/10.1103/PhysRevX.5.041039
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Published by the American Physical Society
Popular Summary
From the operation of digital computers to the duplication of genetic material, accurate copying of information is crucial for the functioning of complex organisms and devices. A common feature of all copying machines is that they consume energy to operate at a finite speed, making copying a thermodynamically irreversible process. Our work reveals the existence of a universal relation between irreversibility and accuracy, which is independent of the specific system and the copying protocol. We apply this relation to study kinetic proofreading, an important error-correction mechanism employed by biological systems. We find that, in addition to increasing precision, proofreading can also extract work while correcting errors.
Thermal fluctuations affect copying on the molecular level, and significant deleterious effects can result from, for example, errors associated with DNA copying. Here, we focus on the second law of thermodynamics and how thermodynamics affects the accuracy of copying. We examine how a polymer strand with two different kinds of monomers is copied when free monomers are selected for the copying process. We recover an equilibrium error rate and three copying regimes, all of which are possible in nature. We note that the microscopic details of the copying process are important; they determine both the error rate and thermodynamic quantities such as dissipated work. Although each of these quantities is detail dependent, there are relations among these quantities that are independent of the details.
We expect that our findings will pave the way for future studies of other cellular information-processing tasks (e.g., chemosensing).