Chargaff's second parity rule and the kinetics of DNA replication

TL;DR

The paper addresses why Chargaff's second parity rule emerges within single DNA strands by modeling DNA replication as a template-directed, stochastic process governed by polymerase kinetics. It combines Gillespie simulations across multiple polymerases and concentrations with a matrix-analytic theory showing that successive replications drive mononucleotide and oligonucleotide fractions toward $A\approx T$ and $C\approx G$, with deviations of order the polymerase error probability $\eta$. The main contributions include (i) a detailed kinetic framework linking replication dynamics to intrastrand symmetry, (ii) explicit asymptotic expressions showing why complementarity dominates despite rate asymmetries, and (iii) extensions to memory-dependent kinetics and proofreading, demonstrating the robustness of the mechanism. The findings suggest a universal, physics-based explanation for Chargaff's second parity rule and imply that genome composition reflects the integrated activity of polymerases and intracellular nucleotide pools, with practical implications for interpreting genomic compositions and designing experiments to test multi-replication dynamics.

Abstract

A model of DNA replication is investigated, which is based on the biochemical kinetics of DNA polymerases, copying a DNA strand into its complement, except for rare point-like mutations due to nucleotide substitutions. Numerical simulations of many successive replications starting from an initial DNA sequence show that the fractions of mono- and oligonucleotides converge toward compliance with Chargaff's second parity rule. The theory of this multireplication process reveals that the approximate equalities between the fractions of complementary nucleotides are the consequence of (1) the dominant role of complementarity in the DNA replication kinetic process and (2) the smallness of the polymerase error probability. These two features lead to a robust mechanism underlying Chargaff's second parity rule.

Figures (5)

• Figure 1: Schematic representation of many successive DNA replications $r=1,2,3,\dots$. Some DNA polymerase (pol) is depicted at time $t=0$ at the beginning of the replication of the template $r=0$ into its copy $r=1$, which is further replicated into the copies $r=2,3,\dots$. Every replication proceeds from the $3'$ to the $5'$ chain end of the template, hence the zigzag progress of the successive replications. Replication errors may happen substituting a few nucleotides into non-complementary ones (in bold). The successive replications may be achieved by several DNA polymerases of the same type.
• Figure 2: Fractions of the mononucleotides A (open squares), T (filled squares), C (open circles), G (filled circles), binucleotides AT (open diamonds), TA (filled diamonds), AC (pluses), GT (times), and trinucleotides ATA (open triangles), TAT (filled triangles), CTA (open pentagons), TAG (stars), versus the even values of the replication number $r$ in DNA strands generated by the DNA polymerase Dpo1 from the archaeon Sulfolobus solfataricus P2 in a solution with the nucleotide concentrations (\ref{['conc-II']}). The initial DNA strand has equal mononucleotide fractions $A_0=C_0=G_0=T_0=25\%$. The data points showing the results of the numerical simulation with Gillespie's algorithm are plotted every 200 replications. The solid lines depict the fractions predicted by theory. The asymptotic values of the fractions are given by $A=T=43.8\%$, $C=G=6.2\%$, $AT=TA=19.2\%$, $AC=GT=2.7\%$, $ATA=TAT=8.4\%$, and $CTA=TAG=1.2\%$, as obtained by averaging their values between the replications $r=9900$ and $r=10000$.
• Figure 3: Fractions of the mononucleotides A (open squares), T (filled squares), C (open circles), G (filled circles), binucleotides AT (open diamonds), TA (filled diamonds), AC (pluses), GT (times), and trinucleotides ATA (open triangles), TAT (filled triangles), CTA (open pentagons), TAG (stars), versus the even values of the replication number $r$ in DNA strands generated by the DNA polymerase Dpo1 from the archaeon Sulfolobus solfataricus P2 in a solution with the nucleotide concentrations (\ref{['conc-II']}). The initial DNA strand has the unequal mononucleotide fractions $A_0=70\%$, $C_0=15\%$, $G_0=10\%$, and $T_0=5\%$. The data points showing the results of the numerical simulation with Gillespie's algorithm are plotted every 200 replications. The solid lines depict the fractions predicted by theory. The asymptotic values of the fractions are given by $A=T=43.8\%$, $C=G=6.2\%$, $AT=TA=19.2\%$, $AC=GT=2.7\%$, $ATA=TAT=8.4\%$, and $CTA=TAG=1.2\%$, as obtained by averaging their values between the replications $r=9900$ and $r=10000$.
• Figure 4: Fractions of the mononucleotides A (open squares), T (filled squares), C (open circles), G (filled circles), binucleotides AT (open diamonds), TA (filled diamonds), AC (pluses), GT (times), and trinucleotides ATA (open triangles), TAT (filled triangles), CTA (open pentagons), TAG (stars), versus the even values of the replication number $r$ in DNA strands generated by the DNA polymerase Dpo1 from the archaeon Sulfolobus solfataricus P2 in a solution with the nucleotide concentrations (\ref{['conc-II']}), here, for the kinetics depending on the previously incorporated nucleotide with the constants (\ref{['kp-cc-ci-M']}) and (\ref{['K-cc-ci-M']}). The initial DNA strand has equal mononucleotide fractions $A_0=C_0=G_0=T_0=25\%$. The data points showing the results of the numerical simulation with Gillespie's algorithm are plotted every 200 replications. The solid lines depict the fractions predicted by theory. The asymptotic values of the fractions are given by $A=T=43.8\%$, $C=G=6.2\%$, $AT=TA=19.2\%$, $AC=GT=2.7\%$, $ATA=TAT=8.4\%$, and $CTA=TAG=1.2\%$, as obtained by averaging their values between the replications $r=9900$ and $r=10000$.
• Figure 5: Fractions of the mononucleotides A (open squares), T (filled squares), C (open circles), G (filled circles), binucleotides AT (open diamonds), TA (filled diamonds), AC (pluses), GT (times), and trinucleotides ATA (open triangles), TAT (filled triangles), CTA (open pentagons), TAG (stars), versus the even values of the replication number $r$ in DNA strands generated by the DNA polymerase Dpo1 from the archaeon Sulfolobus solfataricus P2 in a solution with the nucleotide concentrations (\ref{['conc-II']}), here, for the kinetics depending on the previously incorporated nucleotide with the constants (\ref{['kp-cc-ci-M']}) and (\ref{['K-cc-ci-M']}). The initial DNA strand has the unequal mononucleotide fractions $A_0=70\%$, $C_0=15\%$, $G_0=10\%$, and $T_0=5\%$. The data points showing the results of the numerical simulation with Gillespie's algorithm are plotted every 200 replications. The solid lines depict the fractions predicted by theory. The asymptotic values of the fractions are given by $A=T=43.8\%$, $C=G=6.2\%$, $AT=TA=19.2\%$, $AC=GT=2.7\%$, $ATA=TAT=8.4\%$, and $CTA=TAG=1.2\%$, as obtained by averaging their values between the replications $r=9900$ and $r=10000$.