Theory of Semi-discontinuous DNA Replication

TL;DR

This work develops a framework to investigate the semi-discontinuous replication by incorporating stochastic dynamics of the lagging-strand polymerase and reveals that the collisions of lagging-strand polymerase with pre-synthesised Okazaki fragments primarily trigger its dissociation from the lagging strand.

Abstract

In biological cells, DNA replication is carried out by the replisome, a protein complex encompassing multiple DNA polymerases. DNA replication is semi-discontinuous: a DNA polymerase synthesizes one (leading) strand of the DNA continuously, and another polymerase synthesizes the other (lagging) strand discontinuously. Complex dynamics of the lagging-strand polymerase within the replisome result in the formation of short interim fragments, known as Okazaki fragments, and gaps between them. Although the semi-discontinuous replication is ubiquitous, a detailed characterization of it remains elusive. In this work, we develop a framework to investigate the semi-discontinuous replication by incorporating stochastic dynamics of the lagging-strand polymerase. Computing the size distribution of Okazaki fragments and gaps, we uncover the significance of the polymerase dissociation in shaping them. We apply the method to the previous experiment on the T4 bacteriophage replication system and identify the key parameters governing the polymerase dynamics. These results reveal that the collisions of lagging-strand polymerase with pre-synthesised Okazaki fragments primarily trigger its dissociation from the lagging strand.

Figures (5)

• Figure 1: A schematic view of our model for replisome carrying out semi-discontinuous replication.
• Figure 2: Effect of polymerase dissociation by collision on the OF sizes: (a)-(c) The size distributions of the OFs (Eq. \ref{['eqn:prob-of']}) make a transition from monotonic to non-monotonic form as $p$ increases from $p=1$ to $p>1$. (d) The fraction of dissociations by collision (Eq. \ref{['eq:eq2']}) increases, and (e) the mean OF size (Eq. \ref{['eq:eq3']}) decreases as with $p$. Symbols represent the results of the Monte-Carlo simulation. In simulations, we fixed $\epsilon=0.05 \,{\rm sec^{-1}}$ and $v=400 \,{\rm bp \cdot sec^{-1}}$. We chose $\pi=0.05 \, {\rm sec^{-1}}$, $\pi=1 \, {\rm sec^{-1}}$, and $\pi=5 \, {\rm sec^{-1}}$ in (a), (b), and (c), respectively. In (d) and (e), the range of $\pi$ is from $0.005\, {\rm sec^{-1}}$ to $8.5\, {\rm sec^{-1}}$, chosen in such a way that they are close to the experimental data, see Table \ref{['table:optimal rates']} and dashed line in (d). We show $f_c$ and $\langle z \rangle$ corresponding to (a)-(c) in (d) and (e), respectively, using the same but enlarged symbols.
• Figure 3: OF size distribution of T4 bacteriophage: Symbols represents the experimental data obtained from chastain2000analysis for $8\,{\rm nM}$ (left) and $64\,{\rm nM}$ (right) primase concentrations. The error bars represent the standard error, see Appendix. B for details. The solid line is for Eq. \ref{['eqn:prob-of']} with the optimal parameter values reported in Table \ref{['table:optimal rates']}.
• Figure 4: Predicted size distributions of gaps in T4 bacteriophage for $8\,{\rm nM}$ (circles) and $64\,{\rm nM}$ (squares) primase concentrations: Symbols represent the simulation results, and the solid line is from Eq. \ref{['eqn:gapsize']} for the parameters given in Table \ref{['tab:optimalvalue']}. The kink at $g=0$ (shown in insets) is due to the zero-sized gaps and its strength is $f_c$ as shown in the coefficient of the delta function in Eq. \ref{['eqn:gapsize']}.
• Figure 5: Schematic representation of (a) the transition probability, $W(z,g|z',g')$, given in Eq. \ref{['eq:eq9']} and (b) the random walk analogy for the OF size synthesis given in Eq. \ref{['eq:CKZS']}.