Modelling the DNA replication program in eukaryotes

DNA replication in higher organisms starts at many places across the genome and throughout S (synthesis) phase. In order to understand replication in eukaryotes, one needs to know not only how the replicative machinery functions on the molecular level but also how the machinery is organized genome wide to ensure complete duplication. Over the past fifteen years, advances in technology have allowed researchers to perform genome-wide experiments that probe the state of replication in many organisms. These datasets make possible quantitative modelling of the replication process. The kinetics of DNA replication is formally analogous to a physical phase-transformation process. In replication, the DNA is transformed from a "non-replicated'' phase to a "replicated'' phase, just as freezing water is transformed from a liquid phase to a solid phase. Using this analogy, we map the replication process onto a stochastic nucleation-and-growth model introduced in statistical physics to describe first-order phase transitions. Extending the model, we develop a mathematical framework that is flexible enough to describe the kinetics of replication in eukaryotes. We present three applications of our theory: 1) We apply the theory to a recent dataset on budding yeast to extract its genome-wide replication program. Based on this study, we give the first proposal to explain how the temporal aspect of the replication program can be controlled mechanistically. 2) We address the "random-completion problem,'' which asks how replication-completion times can be controlled when replication starts at random places and times. We find that the strategy adopted in frog embryos to solve the problem also nearly minimizes the use of certain replicative machinery. 3) We study possible ways to extract information from a popular technique used to probe replication in multicellular eukaryotes, ranging from worms to humans. We show preliminary results that can be extended to real experiments in the near future.