Edge-effects dominate copying thermodynamics for finite-length molecular oligomers

Abstract

A signature feature of living systems is their ability to produce copies of information-carrying molecular templates such as DNA. These copies are made by assembling a set of monomer molecules into a linear macromolecule with a sequence determined by the template. The copies produced have a finite length - they are often 'oligomers', or short polymers - and must eventually detach from their template. We explore the role of the resultant initiation and termination of the copy process in the thermodynamics of copying. By splitting the free-energy change of copy formation into informational and chemical terms, we show that, surprisingly, copy accuracy plays no direct role in the overall thermodynamics. Instead, finite-length templates function as highly-selective engines that interconvert chemical and information-based free energy stored in the environment; it is thermodynamically costly to produce outputs that are more similar to the oligomers in the environment than sequences obtained by randomly sampling monomers. In contrast to previous work that neglects separation, any excess free energy stored in correlations between copy and template sequences is lost when the copy fully detaches and mixes with the environment; these correlations therefore do not feature in the overall thermodynamics. Previously-derived constraints on copy accuracy therefore only manifest as kinetic barriers experienced while the copy is template attached; these barriers are easily surmounted by shorter oligomers.