Information-to-energy trade-offs and the optimal alphabet of polymer replication

We analyze information transmission in a recently proposed coarse-grained model of polymer replication by framing it as a communication channel between templates and copies. By calculating the mutual information in the steady-state limit of long chains, we recover the accurate-random phase diagram and establish that the information per-monomer depends solely on template specificity within the accurate regime. Crucially, even in the accurate region, small error fractions lead to substantial information loss due to the nonlinear relationship between errors and mutual information. Examining the information-to-energy cost ratio reveals non-monotonic behavior as a function of monomer alphabet size, with an optimum determined primarily by the per-monomer assembly free energy. For DNA's four-base alphabet, we find that the observed effective assembly energy (at least $14\,k_B T$) places the system far from the information-transmission optimum, suggesting that biological replication may prioritize the suppression of spontaneous random assembly over information-to-energy efficiency. We also characterize achievable rate-fidelity trade-offs using Shannon bounds, providing a theoretical framework for evaluating future proofreading mechanisms in ensemble models.