Mathematical Modelling of DNA Replication

Before a cell divides into two daughter cells, its entire genetic material has to be copied without errors and exactly once. In eukaryotic cells, a vast amount of replication origins exists that enable the replication of the DNA to initiate simultaneously from many origins in parallel, thereby contributing to a relatively rapid duplication of the genome. The initiation of DNA replication from the replication origins is a tightly controlled process. The molecular machinery involved in this process in budding yeast has been identified in the past decades, but questions remain concerning their precise dynamical behavior and interactions. In order to restrict the initiation of DNA replication to once per cell cycle, the activation of the origins proceeds in two temporally separated phases, the licensing and the firing phase. A part of the replication machinery, including the presumptive DNA helicase, is assembled at the origins in the first phase, and is completed by loading of DNA polymerases in the second phase. The temporal separation of origin licensing and firing is tightly regulated by the activity of cyclin-dependent kinases (Cdks). In this work, a mathematical model for DNA replication in budding yeast is provided. Based on a multitude of experimental studies, a molecular interaction network is constructed and translated into balance equations for all molecule complexes assembled at the replication origins, free molecule complexes and all phosphorylation states. Initial protein concentrations could be taken from measurements. The kinetic parameters of the mathematical model are determined by using an optimization approach. Firstly, the biological functionality of the system is defined by means of four functional systems properties, the fraction of activated origins, the number of rereplicating origins and the rate of origin activation, measured by its mean time and duration. Secondly, the biological functionality of the entire system is maximized as a function of its kinetic parameters. The parameterized model accounts for the experimentally observed distribution of activation times of early replication origins and at the same time realizes the strict inhibition of DNA rereplication. Analysis of the kinetics of origin firing revealed that the prevention of DNA rereplication relies on a time delay between the licensing and firing of replication origins, which, however, limits the rate of origin activation. The multisite phosphorylation of two target proteins of the S phase cyclin-dependent kinase (S-Cdk), Sld2 and Sld3, is essential for creating a robust time delay before the activation of replication origins and at the same time in contributing to a synchronous initiation of DNA replication at several replication origins. The mathematical model rationalizes experimentally realized deregulations in the activity of Cdks and quantifies the resulting disorders in the kinetics of origin activation. Furthermore, the kinetics of origin activation calculated with the mathematical model is utilized to predict the consequences of specific deregulations in the activation of replication origins on the process of DNA replication during S phase, which is quantified by the duration of the DNA synthesis period and the distribution of DNA replicon sizes. In summary, a consistent model for DNA replication in budding yeast is developed and analyzed extensively. The connection of the initiation kinetics of DNA replication and its dynamics during S phase of the cell cycle, allows to comprehensively study the potential sources of chromosomal rearrangements.