Mathematical modelling of eukaryotic DNA replication

Abstract

Eukaryotic DNA replication is a complex process. Replication starts at thousand origins that are activated at different times in S phase and terminates when converging replication forks meet. Potential origins are much more abundant than actually fire within a given S phase. The choice of replication origins and their time of activation is never exactly the same in any two cells. Individual origins show different efficiencies and different firing time probability distributions, conferring stochasticity to the DNA replication process. High-throughput microarray and sequencing techniques are providing increasingly huge datasets on the populationaveraged spatiotemporal patterns of DNA replication in several organisms. On the other hand, singlemolecule replication mapping techniques such as DNA combing provide unique information about cell-to-cell variability in DNA replication patterns. Mathematical modelling is required to fully comprehend the complexity of the chromosome replication process and to correctly interpret these data. Mathematical analysis and computer simulations have been recently used to model and interpret genome-wide replication data in the yeast Saccharomyces cerevisiae and Schizosaccharomyces pombe, in Xenopus egg extracts and in mammalian cells. These works reveal how stochasticity in origin usage confers robustness and reliability to the DNA replication process.

Model-based analysis of DNA replication profiles: predicting replication fork velocity and initiation rate by profiling free-cycling cells

“…4B). Based on this pattern around well-characterized origins, we estimated wild-type fork velocity to be 2.3 kb/min, consistent with previous estimates (1.6-3 kb/min) (Raghuraman et al 2001;Yabuki et al 2002;Hyrien and Goldar 2010;Sekedat et al 2010;Yang et al 2010). To estimate Figure 2.…”

“…To better understand the consequences of perturbing different replication parameters, we formulated a model of DNA replication that enables simulating three types of perturbations: change in the efficiency of individual origins, change in fork velocity, and change in the overall initiation capacity (Supplemental Material). Following the formulation used in previous models (Jun and Bechhoefer 2005;Lygeros et al 2008;Brümmer et al 2010;Hyrien and Goldar 2010;Rhind et al 2010;Koutroumpas and Lygeros 2011;Bechhoefer and Rhind 2012), we simulated genome replication in a straightforward manner Baker and Bechhoefer 2014): Given fork velocity, v, initiation capacity, I, and origin-specific parameters (chromosomal positions and relative firing probabilities of all replication origins, x i and n i ), we compute the temporal increase in DNA content across the genome. The replication profile of free-cycling cells is obtained by averaging the DNA contents over the simulated times.…”

“…It is less well suited for characterizing wild-type cells, primarily because the SVD projections are not intuitive and do not provide explicit information about the parameters controlling replication. Curve-fitting methods that attempt to more directly model the full replication profile are better suited for characterizing the wild-type profiles and were indeed applied to multiple systems ranging from a Xenopus embryo (Goldar et al 2008;Yang and Bechhoefer 2008;Gauthier and Bechhoefer 2009), budding yeast (Brümmer et al 2010;de Moura et al 2010;Yang et al 2010;Retkute et al 2011), regions of human cells (Gindin et al 2014), and others (Hyrien and Goldar 2010;Koutroumpas and Lygeros 2011;Retkute et al 2012;Baker and Bechhoefer 2014). These methods are labor-intensive and require an expert user to set up.…”

Linking the DNA strand asymmetry to the spatio-temporal replication program

“…Altogether these results enlighten the fundamental role of these "islands" of open chromatin observed at U-domains borders: at the heart of a compartmentalization of chromosomes into chromatin units of independent replication and of coordinated gene transcription, they likely are the corner stone of a highly paralleled spatio-temporal replication program in the human genome and more generally in mammalian genomes [20,39]. Altogether these results open new perspectives in the modeling of the replication program in higher eukaryotes [50,51] possibly differing from those proposed in yeast [52][53][54] where the existence of a replication-associated skew has been recently demonstrated [55]. In that context, a dynamic model has been recently proposed [35,39] in which replication first initiates at replication timing U-domains borders followed by a chromatin gradient-mediated succession of secondary origin activations.…”

Optimal Placement of Origins for DNA Replication

“…The location of the origins is one of the crucial factors determining the replication time of cells, and it is reasonable to expect that the loci have been selected by evolution such that the replication time is minimized. There are a number of recent theoretical and modeling works on the dynamics of DNA replication (reviewed in [3]). Previous theoretical works on S. cerevisiae have used the experimentally determined loci as given parameters, without attempting to understand why the origins are located where they are [2,[4][5][6].…”