Entropy Involved in Fidelity of DNA Replication

J Ricardo Arias-Gonzalez,Gonzalo G De Polavieja

doi:10.1371/journal.pone.0042272

Abstract

Information has an entropic character which can be analyzed within the framework of the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is performed sufficiently slowly. Structural and recent single-molecule assays have provided dynamic details of polymerase machinery with insight into information processing. Here, we introduce a rigorous characterization of Shannon Information in biomolecular systems and apply it to DNA replication in the limit of no dissipation. Specifically, we devise an equilibrium pathway in DNA replication to determine the entropy generated in copying the information from a DNA template in the absence of friction. Both the initial state, the free nucleotides randomly distributed in certain concentrations, and the final state, a polymerized strand, are mesoscopic equilibrium states for the nucleotide distribution. We use empirical stacking free energies to calculate the probabilities of incorporation of the nucleotides. The copied strand is, to first order of approximation, a state of independent and non-indentically distributed random variables for which the nucleotide that is incorporated by the polymerase at each step is dictated by the template strand, and to second order of approximation, a state of non-uniformly distributed random variables with nearest-neighbor interactions for which the recognition of secondary structure by the polymerase in the resultant double-stranded polymer determines the entropy of the replicated strand. Two incorporation mechanisms arise naturally and their biological meanings are explained. It is known that replication occurs far from equilibrium and therefore the Shannon entropy here derived represents an upper bound for replication to take place. Likewise, this entropy sets a universal lower bound for the copying fidelity in replication.

Highlights

Many of the proteins in the cell are molecular motors which move along a molecular track and develop a mechanical work
From a thermodynamic point of view, the initial and final states are mesoscopic equilibrium states as we study later in this article, the final state is different if the copying process occurs in or out of equilibrium [22]
The entropy in Eq 3 does depend on the number l of nucleotides that are imposed by the fitting length of the polymerase to the DNA template and on the supervising mechanism that the polymerase establishes by its architecture

Summary

Introduction

Many of the proteins in the cell are molecular motors which move along a molecular track and develop a mechanical work. DNA/RNA polymerase works as both a Turing Machine and a Maxwell’s Demon [3,4,5,6]: it is capable of successively reading one nucleotide at a time, identifying a complementary nucleotide in the environment and writing the information by catalyzing a phosphodiester bond in the nascent replicated strand. It is capable of identifying errors in the copied strand by recognizing the secondary structure of the resulting doublestranded polymer [7,8,9]. The pairing process follows spontaneously by hydrogen bonding and the emerging helical structure of the double-stranded polymer is mainly the result of the stacking interactions between the new base-pair and its immediate previous neighbor in the polymer chain [12]

Results

Discussion

Conclusion