How do proteins search for their specific sites on coiled or globular DNA

It is known since the early days of molecular biology that proteins locate their specific targets on DNA up to two orders of magnitude faster than the Smoluchowski 3D diffusion rate. It was the idea due to Delbruck that they are non-specifically adsorbed on DNA, and sliding along DNA provides for the faster 1D search. Surprisingly, the role of DNA conformation was never considered in this context. In this article, we explicitly address the relative role of 3D diffusion and 1D sliding along coiled or globular DNA and the possibility of correlated re-adsorbtion of desorbed proteins. We have identified a wealth of new different scaling regimes. We also found the maximal possible acceleration of the reaction due to sliding, we found that the maximum on the rate-versus-ionic strength curve is asymmetric, and that sliding can lead not only to acceleration, but in some regimes to dramatic deceleration of the reaction.Comment: 16 pages, 5 figure

Evidence for Sequential and Increasing Activation of Replication Origins along Replication Timing Gradients in the Human Genome

Genome-wide replication timing studies have suggested that mammalian chromosomes consist of megabase-scale domains of coordinated origin firing separated by large originless transition regions. Here, we report a quantitative genome-wide analysis of DNA replication kinetics in several human cell types that contradicts this view. DNA combing in HeLa cells sorted into four temporal compartments of S phase shows that replication origins are spaced at 40 kb intervals and fire as small clusters whose synchrony increases during S phase and that replication fork velocity (mean 0.7 kb/min, maximum 2.0 kb/min) remains constant and narrowly distributed through S phase. However, multi-scale analysis of a genome-wide replication timing profile shows a broad distribution of replication timing gradients with practically no regions larger than 100 kb replicating at less than 2 kb/min. Therefore, HeLa cells lack large regions of unidirectional fork progression. Temporal transition regions are replicated by sequential activation of origins at a rate that increases during S phase and replication timing gradients are set by the delay and the spacing between successive origin firings rather than by the velocity of single forks. Activation of internal origins in a specific temporal transition region is directly demonstrated by DNA combing of the IGH locus in HeLa cells. Analysis of published origin maps in HeLa cells and published replication timing and DNA combing data in several other cell types corroborate these findings, with the interesting exception of embryonic stem cells where regions of unidirectional fork progression seem more abundant. These results can be explained if origins fire independently of each other but under the control of long-range chromatin structure, or if replication forks progressing from early origins stimulate initiation in nearby unreplicated DNA. These findings shed a new light on the replication timing program of mammalian genomes and provide a general model for their replication kinetics

Modeling Inhomogeneous DNA Replication Kinetics

In eukaryotic organisms, DNA replication is initiated at a series of chromosomal locations called origins, where replication forks are assembled proceeding bidirectionally to replicate the genome. The distribution and firing rate of these origins, in conjunction with the velocity at which forks progress, dictate the program of the replication process. Previous attempts at modeling DNA replication in eukaryotes have focused on cases where the firing rate and the velocity of replication forks are homogeneous, or uniform, across the genome. However, it is now known that there are large variations in origin activity along the genome and variations in fork velocities can also take place. Here, we generalize previous approaches to modeling replication, to allow for arbitrary spatial variation of initiation rates and fork velocities. We derive rate equations for left- and right-moving forks and for replication probability over time that can be solved numerically to obtain the mean-field replication program. This method accurately reproduces the results of DNA replication simulation. We also successfully adapted our approach to the inverse problem of fitting measurements of DNA replication performed on single DNA molecules. Since such measurements are performed on specified portion of the genome, the examined DNA molecules may be replicated by forks that originate either within the studied molecule or outside of it. This problem was solved by using an effective flux of incoming replication forks at the model boundaries to represent the origin activity outside the studied region. Using this approach, we show that reliable inferences can be made about the replication of specific portions of the genome even if the amount of data that can be obtained from single-molecule experiments is generally limited

Replication Fork Polarity Gradients Revealed by Megabase-Sized U-Shaped Replication Timing Domains in Human Cell Lines

In higher eukaryotes, replication program specification in different cell types remains to be fully understood. We show for seven human cell lines that about half of the genome is divided in domains that display a characteristic U-shaped replication timing profile with early initiation zones at borders and late replication at centers. Significant overlap is observed between U-domains of different cell lines and also with germline replication domains exhibiting a N-shaped nucleotide compositional skew. From the demonstration that the average fork polarity is directly reflected by both the compositional skew and the derivative of the replication timing profile, we argue that the fact that this derivative displays a N-shape in U-domains sustains the existence of large-scale gradients of replication fork polarity in somatic and germline cells. Analysis of chromatin interaction (Hi-C) and chromatin marker data reveals that U-domains correspond to high-order chromatin structural units. We discuss possible models for replication origin activation within U/N-domains. The compartmentalization of the genome into replication U/N-domains provides new insights on the organization of the replication program in the human genome

A Dynamic Stochastic Model for DNA Replication Initiation in Early Embryos

Background: Eukaryotic cells seem unable to monitor replication completion during normal S phase, yet must ensure a reliable replication completion time. This is an acute problem in early Xenopus embryos since DNA replication origins are located and activated stochastically, leading to the random completion problem. DNA combing, kinetic modelling and other studies using Xenopus egg extracts have suggested that potential origins are much more abundant than actual initiation events and that the time-dependent rate of initiation, I(t), markedly increases through S phase to ensure the rapid completion of unreplicated gaps and a narrow distribution of completion times. However, the molecular mechanism that underlies this increase has remained obscure.Methodology/Principal Findings: Using both previous and novel DNA combing data we have confirmed that I(t) increases through S phase but have also established that it progressively decreases before the end of S phase. To explore plausible biochemical scenarios that might explain these features, we have performed comparisons between numerical simulations and DNA combing data. Several simple models were tested: i) recycling of a limiting replication fork component from completed replicons; ii) time-dependent increase in origin efficiency; iii) time-dependent increase in availability of an initially limiting factor, e. g. by nuclear import. None of these potential mechanisms could on its own account for the data. We propose a model that combines time-dependent changes in availability of a replication factor and a fork-density dependent affinity of this factor for potential origins. This novel model quantitatively and robustly accounted for the observed changes in initiation rate and fork density.Conclusions/Significance: This work provides a refined temporal profile of replication initiation rates and a robust, dynamic model that quantitatively explains replication origin usage during early embryonic S phase. These results have significant implications for the organisation of replication origins in higher eukaryotes

Mathematical Modelling of DNA Replication Reveals a Trade-off between Coherence of Origin Activation and Robustness against Rereplication

Eukaryotic genomes are duplicated from multiple replication origins exactly once per cell cycle. In Saccharomyces cerevisiae, a complex molecular network has been identified that governs the assembly of the replication machinery. Here we develop a mathematical model that links the dynamics of this network to its performance in terms of rate and coherence of origin activation events, number of activated origins, the resulting distribution of replicon sizes and robustness against DNA rereplication. To parameterize the model, we use measured protein expression data and systematically generate kinetic parameter sets by optimizing the coherence of origin firing. While randomly parameterized networks yield unrealistically slow kinetics of replication initiation, networks with optimized parameters account for the experimentally observed distribution of origin firing times. Efficient inhibition of DNA rereplication emerges as a constraint that limits the rate at which replication can be initiated. In addition to the separation between origin licensing and firing, a time delay between the activation of S phase cyclin-dependent kinase (S-Cdk) and the initiation of DNA replication is required for preventing rereplication. Our analysis suggests that distributive multisite phosphorylation of the S-Cdk targets Sld2 and Sld3 can generate both a robust time delay and contribute to switch-like, coherent activation of replication origins. The proposed catalytic function of the complex formed by Dpb11, Sld3 and Sld2 strongly enhances coherence and robustness of origin firing. The model rationalizes how experimentally observed inefficient replication from fewer origins is caused by premature activation of S-Cdk, while premature activity of the S-Cdk targets Sld2 and Sld3 results in DNA rereplication. Thus the model demonstrates how kinetic deregulation of the molecular network governing DNA replication may result in genomic instability