Optimal Placement of Origins for DNA Replication

DNA replication is an essential process in biology and its timing must be robust so that cells can divide properly. Random fluctuations in the formation of replication starting points, called origins, and the subsequent activation of proteins lead to variations in the replication time. We analyze these stochastic properties of DNA and derive the positions of origins corresponding to the minimum replication time. We show that under some conditions the minimization of replication time leads to the grouping of origins, and relate this to experimental data in a number of species showing origin grouping.

Figure 1

(a) Coordinate system for origin loci with $d_1$, $d_2$ being the distance from the left or right end of the chromosome, respectively. $x$ is the position coordinate along the chromosome. Replication forks travel at a speed $v$ away from the origins. The grey regions show the replicated DNA at time $t$. (b) Simulation results, showing optimal loci to achieve minimal $T_{\mathrm{rep}}$ for 2 loci with different competences, are shown for $p_1\mathrm{\text{−}}{p}_2$ combinations on a lattice grid. Color indicates $d_1$, $d_2=1/2$ (beige) or $d_1$, $d_2=1/4$ (brown). The two regimes are separated by a coexistence line matched by the condition Eq. (1) in red. (c) Optimal position of 2 loci with respect to their competence $p$ to minimize the replication time $T_{\mathrm{rep}}$ (circles) and $p=2/3$ (dashed line).

Figure 2

(a) Probability at which groups separate $p_c$ vs loci/group $n$. Shown are simulations (circles) and analytical prediction for $p_c=1-1/\sqrt[n]{9}$ (line). (b) Distribution of origin loci on yeast chromosome VI with known (grey) and unknown competences [2, 18]. The distribution results from our simulation in the search for minimum $T_{\mathrm{rep}}$ (only grey origins considered). The group in the middle of the chromosome with a low and highly competent locus was recovered.

Figure 3

(a) Origin position $x$ so that $T_{\mathrm{rep}}$ for 2 pMcms is minimal on a segment of unit length, when the standard deviation $\sigma$ for their activation time increases. (b) Inset: $T_{\mathrm{rep}}$ as a function of $\sigma$ for realistic parameters as given in the text. Origins are distributed in 4 equally spaced groups of 16 pMcms (blue [dark grey]); 8 groups of 8 pMcms (green [medium-dark grey]); 16 groups of 4 pMcms (red [medium grey]); 32 groups of 2 pMcms (cyan [light grey]); 64 single pMcms (magenta [medium-light grey]); 64 pMcms placed randomly (black). Main: zoom around realistic $\sigma \sim 8\min$. For $6<\sigma <20\min$ minimal $T_{\mathrm{rep}}$ is achieved for groups of 8 pMcms. (c) Center-center distribution from 3 experiments [9] (squares) and from simulations 5 min after replication started. The simulation is positioning groups of 4 pMcms every 6.3 kb (solid line), groups of 8 pMcms every 12.5 kb (circles), or all randomly (crosses). A small random amount was added to the group location of fixed distances which was picked from a Gaussian distribution with $\sigma \sim 16\%$ of group distances. The $\mathrm{pMcm}/\mathrm{length}$ ratio was fixed [cf. (b)]. (d) Phase diagram of the two-origin model to minimize replication time with changing competence and increasing the $\sigma$. Color indicates origin position relative to chromosome ends $d_1$, $d_2=1/2$ (beige) or $d_1$, $d_2=1/4$ (brown).