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.Author Summary: For a cell to divide into two daughter cells, its genetic information must be accurately duplicated. The large genomes in eukaryotic cells are copied from hundreds or thousands of replication origins to achieve the duplication of the entire DNA in a limited time span. Errors that result in incomplete or multiple copying of parts of the genome can cause cancer in humans. To avoid such errors, the replication origins must be activated coherently across the genome, and repeated firing of already activated origins must be strictly prevented. We developed a kinetic model of the biochemical network that governs the initiation of DNA replication in yeast to understand how these functional properties are realized through the interaction of multiple molecular players. Our computational analysis shows that optimized kinetic parameters are required for the biological functionality of the network, and such parameters indeed account for the measured kinetics of replication initiation. We predict that both the near-synchronous start of replication and the robustness against DNA rereplication are supported by time delays caused by multiple regulatory protein phosphorylations. Our analysis suggests that the kinetic design of the DNA replication network represents an adaptation to multiple, and partially conflicting, functional requirements.