Mathematical Modelling of DNA Replication Reveals a Trade-off between Coherence of Origin Activation and Robustness against Rereplication

Eukaryotic genomes are duplicated from multiple replication origins exactly once per cell cycle. In Saccharomyces cerevisiae, a complex molecular network has been identified that governs the assembly of the replication machinery. Here we develop a mathematical model that links the dynamics of this network to its performance in terms of rate and coherence of origin activation events, number of activated origins, the resulting distribution of replicon sizes and robustness against DNA rereplication. To parameterize the model, we use measured protein expression data and systematically generate kinetic parameter sets by optimizing the coherence of origin firing. While randomly parameterized networks yield unrealistically slow kinetics of replication initiation, networks with optimized parameters account for the experimentally observed distribution of origin firing times. Efficient inhibition of DNA rereplication emerges as a constraint that limits the rate at which replication can be initiated. In addition to the separation between origin licensing and firing, a time delay between the activation of S phase cyclin-dependent kinase (S-Cdk) and the initiation of DNA replication is required for preventing rereplication. Our analysis suggests that distributive multisite phosphorylation of the S-Cdk targets Sld2 and Sld3 can generate both a robust time delay and contribute to switch-like, coherent activation of replication origins. The proposed catalytic function of the complex formed by Dpb11, Sld3 and Sld2 strongly enhances coherence and robustness of origin firing. The model rationalizes how experimentally observed inefficient replication from fewer origins is caused by premature activation of S-Cdk, while premature activity of the S-Cdk targets Sld2 and Sld3 results in DNA rereplication. Thus the model demonstrates how kinetic deregulation of the molecular network governing DNA replication may result in genomic instability

Bud-Localization of CLB2 mRNA Can Constitute a Growth Rate Dependent Daughter Sizer

Maintenance of cellular size is a fundamental systems level process that requires balancing of cell growth with proliferation. This is achieved via the cell division cycle, which is driven by the sequential accumulation and destruction of cyclins. The regulatory network around these cyclins, particularly in G1, has been interpreted as a size control network in budding yeast, and cell size as being decisive for the START transition. However, it is not clear why disruptions in the G1 network may lead to altered size rather than loss of size control, or why the S-G2-M duration also depends on nutrients. With a mathematical population model comprised of individually growing cells, we show that cyclin translation would suffice to explain the observed growth rate dependence of cell volume at START. Moreover, we assess the impact of the observed bud-localisation of the G2 cyclin CLB2 mRNA, and find that localised cyclin translation could provide an efficient mechanism for measuring the biosynthetic capacity in specific compartments: The mother in G1, and the growing bud in G2. Hence, iteration of the same principle can ensure that the mother cell is strong enough to grow a bud, and that the bud is strong enough for independent life. Cell sizes emerge in the model, which predicts that a single CDK-cyclin pair per growth phase suffices for size control in budding yeast, despite the necessity of the cell cycle network around the cyclins to integrate other cues. Size control seems to be exerted twice, where the G2/M control affects bud size through bud-localized translation of CLB2 mRNA, explaining the dependence of the S-G2-M duration on nutrients. Taken together, our findings suggest that cell size is an emergent rather than a regulatory property of the network linking growth and proliferation