The machinery of the eukaryotic cell cycle has been extensively dissected and described, in both simple and complex organisms. Proliferation hinges on the cell’s ability to replicate the genome with high fidelity, segregate the chromosomes equally, and ultimately divide into two genetically identical cells. A fundamental process in the regulation of DNA replication is the step-wise assembly of the pre-replicative complex (pre-RC) at origins of replication. The pre-RC is a congregation of proteins each performing a specific role. Its formation is facilitated by the six-subunit origin recognition complex (ORC), which, in the budding yeast Saccharomyces cerevisiae,
binds an 11
bp consensus sequence [1
]. ORC then recruits Cdc6, which, like ORC, exhibits ATPase activity [4
]. The co-import of Cdt1 and the Mcm2-7 complex (MCM) into the nucleus follows [7
], and the MCM·Cdt1 heptamer is then targeted to origins by an interaction between Cdt1 and Orc6 [8
]. Initial loading of an MCM ring at the origin requires Cdc6 ATP-hydrolysis. Reiterative loading of an additional MCM molecule occurs via ORC ATP-hydrolysis [10
], resulting in two rings at each origin [11
]. At this point origins are said to be licensed. In late G1 phase, a burst of Dbf4 synthesis activates the Dbf4-dependent kinase Cdc7 (DDK), which then phosphorylates multiple MCM subunits [14
], bringing about a conformational change that stimulates MCM helicase activity. Dbf4 levels decrease over the course of S-phase and, starting at the metaphase/anaphase transition, Dbf4 is actively degraded by the anaphase promoting complex (APC) and its activating co-factor, Cdc20 [19
]. In this way, Dbf4 levels are prevented from rising until the next G1/S transition.
The phosphorylation of MCM by DDK is coincident with the phosphorylation of the protein factors Sld2 and Sld3 by Clb5-Cdc28, a cyclin-dependent kinase (CDK) complex, the activity of which rises just prior to S-phase entry. The Sld proteins, once phosphorylated, are stabilized as a complex with the adaptor protein Dpb11 and the tetrameric GINS complex, forming a module that interacts with Cdc45. The latter acts as a scaffold for this module, which is then competent to associate with the pre-RC and attract DNA polymerase [15
]. A recent study shows that the end result is the tight association of Cdc45, MCM and GINS (collectively known as CMG) with origins, allowing the unwinding of DNA and processive replication by DNA polymerase [27
]. This represents the essential role of CDK in stabilizing polymerase at the moving replication fork and switching the system from a pre-replicative state to a replicative one. From this point until late in mitosis, CDK levels remain high. This continued CDK activity prevents re-establishment of pre-RCs at origins that have already fired through a number of mechanisms. Firstly, CDK phosphorylates Cdc6, thus causing the SCFcdc4
complex to target Cdc6 to the proteasome for degradation [28
]. Secondly, Orc2 and Orc6 are phosphorylated by CDK [32
], with the phosphorylation of Orc6 rendering it refractory to interaction with Cdt1 [35
], thereby preventing further MCM loading. Finally, CDK facilitates the nuclear export of both MCM and Cdt1, at different time points. Just prior to initiation, Cdt1 exits via a CDK-dependent mechanism, while MCM proteins fall off the DNA upon fork termination and are then exported in a CDK-dependent manner [7
]. Thus, while CDK initiates replication, it subsequently prevents pre-RC reassembly. This illustrates its dual role in triggering initiation through formation of CMG, then preventing re-initiation by inhibiting pre-RC reformation.
Mathematical modeling has been successfully used in the past to address various aspects of the cell cycle. Early models (e.g. [39
]) did not incorporate specific biochemical mechanisms; they were hypothetical representations of periodic cellular activity. As the molecular mechanisms driving the cell cycle were revealed, models appeared that incorporated these findings (e.g. [40
]). For S. cerevisiae
in particular, multiple modeling approaches have been applied, based both on network descriptions [44
] and on specific molecular details such as gene expression and biochemical kinetics [45
] (reviewed in [48
]). Some modeling efforts have been comprehensive, such as the Tyson group’s ordinary differential equation (ODE)-based models [45
], while others address specific cell-cycle phenomena, such as the links between cell size and cycle progression [49
]. Spiesser et al. [51
] developed a model of chromosomal replication, which reproduced the spatio-temporal replication profile of yeast chromosomes. Origin firing was also described in [52
] wherein the authors used a stochastic model to describe these origin-specific features of replication.
A recent report [54
] presented an ODE-based model describing the initiation of DNA replication, incorporating origin licensing, firing and the network of regulatory phosphorylation events. The model parameters were partly calibrated against experimental data, but largely selected through an optimization routine designed to attain an idealized function, resulting in a model that is particularly suited to exploring events specifically at the G1/S transition.
Here, we present a new model of the initiation of DNA replication. In contrast to the work of Brümmer et al. [54
], we took a ‘bottom-up’ approach and began by gathering in vivo
data for precise protein levels at specific cell cycle time-points, then calibrated our model against these values. Rather than limiting ourselves to the observation of firing near the G1/S transition and fitting to DNA-specific replication profiles, we validated our model against the behaviour of the constituent protein complexes throughout the entire cell cycle. To facilitate the use of our model in a comprehensive description of the cell cycle, we designed it to integrate easily with the model of Chen et al. [45
]. Finally, we validated the model by comparing in silico
predictions to experimental observations, using both our own knockdown experiments and results from the literature. The model presented here consolidates the known interactions between DNA replication initiation proteins and the mechanisms that allow them to drive genome duplication. Additionally, regulatory aspects of the system, which ensure that re-replication does not occur, have been modeled. The model’s behaviour provides a falsifiable hypothesis regarding the dynamics of DNA replication initiation. Furthermore, it accurately predicts the phenotypes of known experimental cell cycle mutants as well as those arising through in vivo
perturbations to proteins in the network. Because our model is constrained only by the fluctuating levels of replication factors, it provides a unique understanding of the kinetics governing the reactions between them. Successful integration into a whole cell cycle model allows the initiation of DNA replication to be explored in a broader quantitative context.