Information management in DNA replication modeled by directional, stochastic chains with memory

Stochastic chains represent a key variety of phenomena in many branches of science within the context of information theory and thermodynamics. They are typically approached by a sequence of independent events or by a memoryless Markov process. Stochastic chains are of special significance to molecular biology, where genes are conveyed by linear polymers made up of molecular subunits and transferred from DNA to proteins by specialized molecular motors in the presence of errors. Here, we demonstrate that when memory is introduced, the statistics of the chain depends on the mechanism by which objects or symbols are assembled, even in the slow dynamics limit wherein friction can be neglected. To analyze these systems, we introduce a sequence-dependent partition function, investigate its properties, and compare it to the standard normalization defined by the statistical physics of ensembles. We then apply this theory to characterize the enzyme-mediated information transfer involved in DNA replication under th...