Fig. 1.
Free-energy landscapes for simple examples of (A) TSA, in which the monomers remain bound to the template during the copy process and (B) persistent copying, in which the monomers detach from the template after they have been incorporated into the polymer. Both diagrams show the addition of three monomers to a growing polymer, driven by a chemical free energy of backbone polymerization . In each subfigure, two scenarios are considered: the addition of two incorrect monomers, followed by a correct one (Top), and the addition of three correct monomers (Bottom). Local minima in the landscape represent macrostates following complete incorporation of monomers; intermediate configurations, illustrated schematically for the first transition, are part of the effective barriers. In TSA, the chemical free-energy cost of previously incorporated mismatches is retained as the daughter grows (20–25). Thus, in A, each mismatch in the daughter increases the chemical free energy by relative to the perfect match. In persistent copying (in B), the chemical free-energy penalty for incorporating wrong monomers is only temporary; it arises when the incorrect monomer is added to the growing polymer, but is lost when that monomer subsequently detaches from the template. As a result, the overall chemical free-energy change of creating an incorrect polymer is the same as that for a correct one. Analyzing the consequences of this constraint, which is a generic feature of copying but does not arise in TSA, is the essence of this work. The figure also shows that, in our specific model, incorporating a wrong monomer after a correct one tends to reduce the chemical free-energy drop to , and incorporating a correct monomer after an incorrect one tends to increase it to ; however, adding a wrong monomer to a wrong one, and adding a correct monomer to a correct one, does not change the free-energy drop .