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 hi
gh 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.
We study stochastic copying schemes in which discrimination between a right and a wrong match is achieved via different kinetic barriers or different binding energies of the two matches. We demonstrate that, in single-step reactions, the two discrimi
nation mechanisms are strictly alternative and can not be mixed to further reduce the error fraction. Close to the lowest error limit, kinetic discrimination results in a diverging copying velocity and dissipation per copied bit. On the opposite, energetic discrimination reaches its lowest error limit in an adiabatic regime where dissipation and velocity vanish. By analyzing experimentally measured kinetic rates of two DNA polymerases, T7 and Pol{gamma}, we argue that one of them operates in the kinetic and the other in the energetic regime. Finally, we show how the two mechanisms can be combined in copying schemes implementing error correction through a proofreading pathway
The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model describin
g the competition of two species and incorporating all the above ingredients. We find that the presence of habitat preference --- generating spatial niches --- strongly stabilizes the coexistence of the two species. Eliminating habitat preference --- neutral dynamics --- the model generates patterns, such as distribution of population sizes, practically identical to those obtained in the presence of habitat preference, provided an higher immigration rate is considered. Notwithstanding the similarity in the population distribution, we show that invasibility properties depend on habitat preference in a non-trivial way. In particular, the neutral model results results more invasible or less invasible depending on whether the comparison is made at equal immigration rate or at equal distribution of population size, respectively. We discuss the relevance of these results for the interpretation of invasibility experiments and the species occupancy of preferred habitats.
