A quantitative model of the initiation of DNA replication in Saccharomyces cerevisiae predicts the effects of system perturbations

An autonomous mathematical model for the mammalian cell cycle

A mathematical model for the mammalian cell cycle is developed as a system of 13 coupled nonlinear ordinary differential equations. The variables and interactions included in the model are based on detailed consideration of available experimental data. A novel feature of the model is inclusion of cycle tasks such as origin licensing and initiation, nuclear envelope breakdown and kinetochore attachment, and their interactions with controllers (molecular complexes involved in cycle control). Other key features are that the model is autonomous, except for a dependence on external growth factors; the variables are continuous in time, without instantaneous resets at phase boundaries; mechanisms to prevent rereplication are included; and cycle progression is independent of cell size. Eight variables represent cell cycle controllers: the Cyclin D1-Cdk4/6 complex, APC^Cdh1, SCF^βTrCP, Cdc25A, MPF, NuMA, the securin-separase complex, and separase. Five variables represent task completion, with four for the status of origins and one for kinetochore attachment. The model predicts distinct behaviors corresponding to the main phases of the cell cycle, showing that the principal features of the mammalian cell cycle, including restriction point behavior, can be accounted for in a quantitative mechanistic way based on known interactions among cycle controllers and their coupling to tasks. The model is robust to parameter changes, in that cycling is maintained over at least a five-fold range of each parameter when varied individually. The model is suitable for exploring how extracellular factors affect cell cycle progression, including responses to metabolic conditions and to anti-cancer therapies.

Stochasticity of replication forks' speeds plays a key role in the dynamics of DNA replication

Eukaryotic DNA replication is elaborately orchestrated to duplicate the genome timely and faithfully. Replication initiates at multiple origins from which replication forks emanate and travel bi-directionally. The complex spatio-temporal regulation of DNA replication remains incompletely understood. To study it, computational models of DNA replication have been developed in S. cerevisiae. However, in spite of the experimental evidence of forks’ speed stochasticity, all models assumed that forks’ speeds are the same. Here, we present the first model of DNA replication assuming that speeds vary stochastically between forks. Utilizing data from both wild-type and hydroxyurea-treated yeast cells, we show that our model is more accurate than models assuming constant forks’ speed and reconstructs dynamics of DNA replication faithfully starting both from population-wide data and data reflecting fork movement in individual cells. Completion of replication in a timely manner is a challenge due to its stochasticity; we propose an empirically derived modification to replication speed based on the distance to the approaching fork, which promotes timely completion of replication. In summary, our work discovers a key role that stochasticity of the forks’ speed plays in the dynamics of DNA replication. We show that without including stochasticity of forks’ speed it is not possible to accurately reconstruct movement of individual replication forks, measured by DNA combing.

DNA replication in eukaryotes starts from multiple sites termed replication origins. Replication timing at individual sites is stochastic, but reproducible population-wide. Complex and not yet completely understood mechanisms ensure that genome is replicated exactly once and that replication is finished in time. This complex spatio-temporal organization of DNA replication makes computational modeling a useful tool to study replication mechanisms. For simplicity, all previous models assumed constant replication forks’ speed. Here, we show that such models are incapable of accurately reconstructing distances travelled by individual replication forks. Therefore, we propose a model assuming that replication speed varies stochastically between forks. We show that such model reproduces faithfully distances travelled by individual replication forks. Moreover, our model is simpler than previous model and thus avoids over-learning (fitting noise). We also discover how replication speed may be attuned to timely complete replication. We propose that forks’ speed increases with diminishing distance to the approaching fork, which we show promotes timely completion of replication. Such speed up can be e.g. explained by a synergy effect of chromatin unwinding by both forks. Our model can be used to simulate phenomena beyond replication, e.g. DNA double-strand breaks resulting from broken replication forks.

A variable fork rate affects timing of origin firing and S phase dynamics in Saccharomyces cerevisiae

Activation (in the following referred to as firing) of replication origins is a continuous and irreversible process regulated by availability of DNA replication molecules and cyclin-dependent kinase activities, which are often altered in human cancers. The temporal, progressive origin firing throughout S phase appears as a characteristic replication profile, and computational models have been developed to describe this process. Although evidence from yeast to human indicates that a range of replication fork rates is observed experimentally in order to complete a timely S phase, those models incorporate velocities that are uniform across the genome. Taking advantage of the availability of replication profiles, chromosomal position and replication timing, here we investigated how fork rate may affect origin firing in budding yeast. Our analysis suggested that patterns of origin firing can be observed from a modulation of the fork rate that strongly correlates with origin density. Replication profiles of chromosomes with a low origin density were fitted with a variable fork rate, whereas for the ones with a high origin density a constant fork rate was appropriate. This indeed supports the previously reported correlation between inter-origin distance and fork rate changes. Intriguingly, the calculated correlation between fork rate and timing of origin firing allowed the estimation of firing efficiencies for the replication origins. This approach correctly retrieved origin efficiencies previously determined for chromosome VI and provided testable prediction for other chromosomal origins. Our results gain deeper insights into the temporal coordination of genome duplication, indicating that control of the replication fork rate is required for the timely origin firing during S phase.