Figure 1.
Model of DNA replication initiation.
(A) The molecular network of DNA replication initiation consists of four modules: licensing of replication origins (blue), activation of S-Cdk (orange), formation of the 11-3-2 activator (red), and origin firing (green), together with multiple mechanisms for inhibiting the relicensing of fired origins, as described in the text. (B) The firing rate f(t), total number of firing origins N, mean time to origin firing τ and the duration of origin firing Δ. (C) For each origin i, the replicon Ri is calculated using the simulated firing times ti, the origin positions xi derived from the measured distribution of inter-origin distances and the experimentally determined polymerase progression speed v (Text S3).
Figure 2.
Optimized parameter sets required for rapid and coherent origin activation.
(A) Admissible parameter sets (n = 109) show synchronous activation of replication origins without rereplication (red curve, reference parameter set as given in Table S2). (B) Correlation of the duration of origin firing Δ and the mean time to firing τ. (C) The distribution of firing times for the early replication origins predicted by the model (red bars, reference parameter set) closely matches the measured replication profile of potential early replication origins in budding yeast (black bars, redrawn from Fig 5, +HU, Yabuki et al. [11]). The simulated distribution was scaled to the same total number of fired origins as in the experiment. (D) Typical kinetics of the model (reference parameter set): activation time course of G1-Cdk as an input function (blue curve), followed by delayed activation of S-Cdk (orange curve). S-Cdk triggers formation of the 11-3-2 activator (red curve) and the firing of replication origins (black curve). (E) Mean affinities for binding reactions (both binding partners indicated) in the admissible parameter sets. The rather high binding affinities of Cdc45, the 11-3-2 activator and the GINS/DNA polymerase complex to the origins as well as those of phospho-Sld2 and phospho-Sld3 to Dpb11 support fast origin firing. There is hierarchy in regulatory phosphorylations by S-Cdk, with rather high S-Cdk affinity for Sld2 (mean Kd = 250 nM), and lower for Orc6 (mean Kd = 1.18 µM). The affinity of the phosphatase for Sld2 and Sld3, counteracting origin firing, is also moderate (mean Kd = 3.36 µM).
Figure 3.
Sensitivity to variations in protein concentrations.
(A) Control coefficients for the total number of fired origins N, the mean time to firing t, the duration of firing Δ, and the number of rereplicating origins ρ, calculated for the concentration of each protein component (mean value and standard deviation for admissible parameter sets). (B) Total number of firing origins N, mean time to firing τ and the duration of firing Δ are robust network responses, whereas the number of rereplicating origins ρ is very vulnerable against fluctuations in the protein concentrations. (C) Fast origin activation increases the probability for rereplication. Colour code indicates the vulnerability to rereplication.
Figure 4.
Deregulation of S-Cdk activity reduces origin firing and causes rereplication.
(A) Rapid activation of S-Cdk (upper panel) causes coherent origin firing (lower panel, red curve). Blue and green curves show the kinetics of pre-replicative and pre-initiation complexes. (B) Distribution of replicon size corresponding to the firing kinetics in (A). (C) Slow activation of S-Cdk (upper panel) due to a slow Sic1 degradation, as observed under suboptimal growth conditions, causes delayed origin firing (lower panel, red curve). (D) Distribution of replicon size corresponding to the firing kinetics in (C). (E) Premature and reduced activation of S-Cdk, as suggested for the Δsic1 mutant (upper panel) causes reduced origin licensing and premature origin firing (lower panel). (F) The distribution of replicon sizes corresponding to firing kinetics of (E) is broadened and large replicons (>120 kb) can occur. (G) A constitutive 11-3-2 activator together can bypass the requirement for S-Cdk (using a non-degradable mutant form of Sic1, sic1ΔNT) in replication initiation but causes asynchronous firing and considerable rereplication. (H) Distribution of replicon size corresponding to the firing kinetics in (G). (I) Quantification of the kinetics of origin firing for the conditions shown in (A)–(H). All simulations with reference parameter set; parameter changes for (C)–(H) specified in Text S2.
Figure 5.
Optimal S-Cdk activity for efficient origin firing without rereplication.
(A) Number of rereplicating origins ρ, (B) mean time to firing τ, (C) number of fired origins N, and (D) the duration of firing Δ, each versus number of active S-Cdk molecules. Black curve, median of all admissible parameter sets; gray area, 68% quantile; red curve, reference parameter set.
Figure 6.
Mechanism of multisite protein phosphorylation.
(A) Mixed random-sequential phosphorylation of Sld2: six Ser/Thr residues are phosphorylated randomly, giving rise to a large number of possible phosphorylation pathways (states 0: unphosphorylated and 1: phosphorylated). Together, these phosphorylations cause a conformational change that allows phosphorylation of the essential Thr84 (state indicated in red), the docking site for Dpb11. (B) In agreement with experimental data [38], the model gives rise to hyperbolic time course for each of the initial six Ser/Thr residues (black curve), while Thr84 (red curve) is phosphorylated with a time delay. To mirror the in-vitro assay conditions, the model simulation was performed without phosphatase activity. (C) The mean time for complete phosphorylation rises with the number of phosphorylation sites (the increase is less than linear because of the random phosphorylation mechanism), while (D) the temporal coherence of phosphorylation increases (decreasing Δ/τ). (E) The robustly high temporal coherence of protein activation by multisite phosphorylation (low Δ/τ) contrasts with the strong dependence of single-site phosphorylation on the activation time of the input kinase, σ (see upper panel).
Figure 7.
Multisite phosphorylation of Sld2 functions supports coherent origin firing without rereplication.
(A) Effects of hypothetical single phosphorylation of Sic1 for its fast degradation: less coherent S-Cdk activation (upper panel) but unaffected kinetics of origin firing (lower panel; red curve, reference parameter set; black curves, other admissible parameter sets). (B) The effect of reducing the number of phosphorylation sites in Sld2 to a single site is more pronounced. Origin firing starts earlier and the number of rereplicating origins is increased (lower panel) for all parameter sets. (C) Number of rereplicating origins ρ, mean time to firing τ, duration of firing Δ, and the length of S phase computed for the reference parameter set (red curves in (A) and (B)). Mean values and standard deviations for all admissible parameter sets (black curves in (A) and (B)) are given in brackets. (D) A hypothetical reduction in the number of phosphorylation events required to activate Sld2 strongly affects origin firing (rereplicating origins ρ, firing duration Δ, mean time to firing τ). There is an additional effect of the reduction of required Sld3 phosphorylation steps (from two to one), whereas a reduction in the required Sic1 phosphorylation steps (from six to one) has no additional impact.