Kinetic model of DNA replication in eukaryotic organisms

DNA replication timing reveals genome-wide features of transcription and fragility

DNA replication in humans requires precise regulation to ensure accurate genome duplication and maintain genome integrity. A key indicator of this regulation is replication timing, which reflects the interplay between origin firing and fork dynamics. We present a high-resolution (1-kilobase) mathematical model that infers firing rate distributions from Repli-seq timing data across multiple cell lines, enabling a genome-wide comparison between predicted and observed replication. Notably, regions where the model and data diverge often overlap fragile sites and long genes, highlighting the influence of genomic architecture on replication dynamics. Conversely, regions of strong concordance are associated with open chromatin and active promoters, where elevated firing rates facilitate timely fork progression and reduce replication stress. In this work, we provide a valuable framework for exploring the structural interplay between replication timing, transcription, and chromatin organisation, offering insights into the mechanisms underlying replication stress and its implications for genome stability and disease.

Chromatin as a Coevolutionary Graph: Modeling the Interplay of Replication with Chromatin Dynamics

Modeling DNA replication poses significant challenges due to the intricate interplay of biophysical processes and the need for precise parameter optimization. In this study, we explore the interactions among three key biophysical factors that influence chromatin folding: replication, loop extrusion, and compartmentalization. Replication forks, known to act as barriers to the motion of loop extrusion factors, also correlate with the phase separation of chromatin into A and B compartments. Our approach integrates three components: (1) a numerical model that takes into advantage single-cell replication timing data to simulate replication fork propagation; (2) a stochastic Monte Carlo simulation that captures the interplay between the biophysical factors, with loop extrusion factors binding, unbinding, and extruding dynamically, while CTCF barriers and replication forks act as static and moving barriers, and a Potts Hamiltonian governs the spreading of epigenetic states driving chromatin compartmentalization; and (3) a 3D OpenMM simulation that reconstructs the chromatin's 3D structure based on the states generated by the stochastic model. To our knowledge, this is the first framework to dynamically integrate and simulate these three biophysical factors, enabling insights into chromatin behavior during replication. Furthermore, we investigate how replication stress alters these dynamics and affects chromatin structure.

Rif1 restrains the rate of replication origin firing in Xenopus laevis

Metazoan genomes are duplicated by the coordinated activation of clusters of replication origins at different times during S phase, but the underlying mechanisms of this temporal program remain unclear during early development. Rif1, a key replication timing factor, inhibits origin firing by recruiting protein phosphatase 1 (PP1) to chromatin counteracting S phase kinases. We have previously described that Rif1 depletion accelerates early Xenopus laevis embryonic cell cycles. Here, we find that in the absence of Rif1, patterns of replication foci change along with the acceleration of replication cluster activation. However, initiations increase only moderately inside active clusters. Our numerical simulations suggest that the absence of Rif1 compresses the temporal program towards more homogeneity and increases the availability of limiting initiation factors. We experimentally demonstrate that Rif1 depletion increases the chromatin-binding of the S phase kinase Cdc7/Drf1, the firing factors Treslin, MTBP, Cdc45, RecQL4, and the phosphorylation of both Treslin and MTBP. We show that Rif1 globally, but not locally, restrains the replication program in early embryos, possibly by inhibiting or excluding replication factors from chromatin.

f = m*a: A Framework for Investigating the Regulation of Replication Timing

Stochastic models of replication timing posit that origin firing timing is regulated by origin firing probability, with early-firing origins having a high probability of firing and late-firing origins having a lower probability. However, they offer no insight into why one origin should have a higher firing probability than another. Here, a simple framework is suggested for how to approach the question by noting that the firing probability (f) must be the product of the stoichiometry of the MCM replicative helicase loaded at the origin (m) and the probability with which that MCM is activated (a). This framework emphasizes that mechanistic understanding of replication timing must focus on MCM loading and activation and can be simplified to the equation f = m*a.

Organization of DNA Replication Origin Firing in Xenopus Egg Extracts: The Role of Intra-S Checkpoint

During cell division, the duplication of the genome starts at multiple positions called replication origins. Origin firing requires the interaction of rate-limiting factors with potential origins during the S(ynthesis)-phase of the cell cycle. Origins fire as synchronous clusters which is proposed to be regulated by the intra-S checkpoint. By modelling the unchallenged, the checkpoint-inhibited and the checkpoint protein Chk1 over-expressed replication pattern of single DNA molecules from Xenopus sperm chromatin replicated in egg extracts, we demonstrate that the quantitative modelling of data requires: (1) a segmentation of the genome into regions of low and high probability of origin firing; (2) that regions with high probability of origin firing escape intra-S checkpoint regulation and (3) the variability of the rate of DNA synthesis close to replication forks is a necessary ingredient that should be taken in to account in order to describe the dynamic of replication origin firing. This model implies that the observed origin clustering emerges from the apparent synchrony of origin firing in regions with high probability of origin firing and challenge the assumption that the intra-S checkpoint is the main regulator of origin clustering.

Dynamics of DNA replication in a eukaryotic cell

Each genomic locus in a eukaryotic cell has a distinct average time of replication during S phase that depends on the spatial and temporal pattern of replication initiation events. Replication timing can affect genomic integrity because late replication is associated with an increased mutation rate. For most eukaryotes, the features of the genome that specify the location and timing of initiation events are unknown. To investigate these features for the fission yeast, Schizosaccharomyces pombe, we developed an integrative model to analyze large single-molecule and global genomic datasets. The model provides an accurate description of the complex dynamics of S. pombe DNA replication at high resolution. We present evidence that there are many more potential initiation sites in the S. pombe genome than previously identified and that the distribution of these sites is primarily determined by two factors: the sequence preferences of the origin recognition complex (ORC), and the interference of transcription with the assembly or stability of prereplication complexes (pre-RCs). We suggest that in addition to directly interfering with initiation, transcription has driven the evolution of the binding properties of ORC in S. pombe and other eukaryotic species to target pre-RC assembly to regions of the genome that are less likely to be transcribed.

On the Interplay of the DNA Replication Program and the Intra-S Phase Checkpoint Pathway

DNA replication in eukaryotes is achieved by the activation of multiple replication origins which needs to be precisely coordinated in space and time. This spatio-temporal replication program is regulated by many factors to maintain genome stability, which is frequently threatened through stresses of exogenous or endogenous origin. Intra-S phase checkpoints monitor the integrity of DNA synthesis and are activated when replication forks are stalled. Their activation leads to the stabilization of forks, to the delay of the replication program by the inhibition of late firing origins, and the delay of G2/M phase entry. In some cell cycles during early development these mechanisms are less efficient in order to allow rapid cell divisions. In this article, we will review our current knowledge of how the intra-S phase checkpoint regulates the replication program in budding yeast and metazoan models, including early embryos with rapid S phases. We sum up current models on how the checkpoint can inhibit origin firing in some genomic regions, but allow dormant origin activation in other regions. Finally, we discuss how numerical and theoretical models can be used to connect the multiple different actors into a global process and to extract general rules.

The eukaryotic bell-shaped temporal rate of DNA replication origin firing emanates from a balance between origin activation and passivation

The time-dependent rate I(t) of origin firing per length of unreplicated DNA presents a universal bell shape in eukaryotes that has been interpreted as the result of a complex time-evolving interaction between origins and limiting firing factors. Here, we show that a normal diffusion of replication fork components towards localized potential replication origins (p-oris) can more simply account for the I(t) universal bell shape, as a consequence of a competition between the origin firing time and the time needed to replicate DNA separating two neighboring p-oris. We predict the I(t) maximal value to be the product of the replication fork speed with the squared p-ori density. We show that this relation is robustly observed in simulations and in experimental data for several eukaryotes. Our work underlines that fork-component recycling and potential origins localization are sufficient spatial ingredients to explain the universality of DNA replication kinetics.

Before a cell can divide, it must duplicate its DNA. In eukaryotes – organisms such as animals and fungi, which store their DNA in the cell’s nucleus – DNA replication starts at specific sites in the genome called replication origins. At each origin sits a protein complex that will activate when it randomly captures an activating protein that diffuses within the nucleus. Once a replication origin activates or “fires”, the complex then splits into two new complexes that move away from each other as they duplicate the DNA. If an active complex collides with an inactive one at another origin, the latter is inactivated – a phenomenon known as origin passivation. When two active complexes meet, they release the activating proteins, which diffuse away and eventually activate other origins in unreplicated DNA.

The number of origins that activate each minute divided by the length of unreplicated DNA is referred to as the “rate of origin firing”. In all eukaryotes, this rate – also known as I(t) – follows the same pattern. First, it increases until more than half of the DNA is duplicated. Then it decreases until everything is duplicated. This means that, if plotted out, the graph of origin firing rate would always be a bell-shaped curve, even for organisms with genomes of different sizes that have different numbers of origins. The reason for this universal shape remained unclear.

Scientists had tried to create numerical simulations that model the rate of origin firing. However, for these simulations to reproduce the bell-shape curve, a number of untested assumptions had to be made about how DNA replication takes place. In addition, these models ignored the fact that it takes time to replicate the DNA between origins.

To take this time into account, Arbona et al. instead decided to model the replication origins as discrete and distinct entities. This way of building the mathematical model succeeded in reproducing the universal bell curve shape without additional assumptions. With this simulation, the balance between origin activation and passivation is enough to achieve the observed pattern.

The new model also predicts that the maximum rate of origin firing is determined by the speed of DNA replication and the density of origins in the genome. Arbona et al. verified this prediction in yeast, fly, frog and human cells – organisms with different sized genomes that take between 20 minutes and 8 hours to replicate their DNA. Lastly, the prediction also held true in yeast treated with hydroxyurea, an anticancer drug that slows DNA replication.

A better understanding of DNA replication can help scientists to understand how this process is perturbed in cancers and how drugs that target DNA replication can treat these diseases. Future work will explore how the 3D organization of the genome affects the diffusion of activating proteins within the cell nucleus.

Cell-to-cell variability and robustness in S-phase duration from genome replication kinetics

Genome replication, a key process for a cell, relies on stochastic initiation by replication origins, causing a variability of replication timing from cell to cell. While stochastic models of eukaryotic replication are widely available, the link between the key parameters and overall replication timing has not been addressed systematically. We use a combined analytical and computational approach to calculate how positions and strength of many origins lead to a given cell-to-cell variability of total duration of the replication of a large region, a chromosome or the entire genome. Specifically, the total replication timing can be framed as an extreme-value problem, since it is due to the last region that replicates in each cell. Our calculations identify two regimes based on the spread between characteristic completion times of all inter-origin regions of a genome. For widely different completion times, timing is set by the single specific region that is typically the last to replicate in all cells. Conversely, when the completion time of all regions are comparable, an extreme-value estimate shows that the cell-to-cell variability of genome replication timing has universal properties. Comparison with available data shows that the replication program of three yeast species falls in this extreme-value regime.

Cell-size distribution and scaling in a one-dimensional Kolmogorov-Johnson-Mehl-Avrami lattice model with continuous nucleation

The Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth model is considered on a one-dimensional (1D) lattice. Cells can grow with constant speed and continuously nucleate on the empty sites. We offer an alternative mean-field-like approach for describing theoretically the dynamics and derive an analytical cell-size distribution function. Our method reproduces the same scaling laws as the KJMA theory and has the advantage that it leads to a simple closed form for the cell-size distribution function. It is shown that a Weibull distribution is appropriate for describing the final cell-size distribution. The results are discussed in comparison with Monte Carlo simulation data.

Deciphering DNA replication dynamics in eukaryotic cell populations in relation with their averaged chromatin conformations

We propose a non-local model of DNA replication that takes into account the observed uncertainty on the position and time of replication initiation in eukaryote cell populations. By picturing replication initiation as a two-state system and considering all possible transition configurations, and by taking into account the chromatin’s fractal dimension, we derive an analytical expression for the rate of replication initiation. This model predicts with no free parameter the temporal profiles of initiation rate, replication fork density and fraction of replicated DNA, in quantitative agreement with corresponding experimental data from both S. cerevisiae and human cells and provides a quantitative estimate of initiation site redundancy. This study shows that, to a large extent, the program that regulates the dynamics of eukaryotic DNA replication is a collective phenomenon that emerges from the stochastic nature of replication origins initiation.

Tight Chk1 Levels Control Replication Cluster Activation in Xenopus

DNA replication in higher eukaryotes initiates at thousands of origins according to a spatio-temporal program. The ATR/Chk1 dependent replication checkpoint inhibits the activation of later firing origins. In the Xenopus in vitro system initiations are not sequence dependent and 2-5 origins are grouped in clusters that fire at different times despite a very short S phase. We have shown that the temporal program is stochastic at the level of single origins and replication clusters. It is unclear how the replication checkpoint inhibits late origins but permits origin activation in early clusters. Here, we analyze the role of Chk1 in the replication program in sperm nuclei replicating in Xenopus egg extracts by a combination of experimental and modelling approaches. After Chk1 inhibition or immunodepletion, we observed an increase of the replication extent and fork density in the presence or absence of external stress. However, overexpression of Chk1 in the absence of external replication stress inhibited DNA replication by decreasing fork densities due to lower Cdk2 kinase activity. Thus, Chk1 levels need to be tightly controlled in order to properly regulate the replication program even during normal S phase. DNA combing experiments showed that Chk1 inhibits origins outside, but not inside, already active clusters. Numerical simulations of initiation frequencies in the absence and presence of Chk1 activity are consistent with a global inhibition of origins by Chk1 at the level of clusters but need to be combined with a local repression of Chk1 action close to activated origins to fit our data.

Replicon: a software to accurately predict DNA replication timing in metazoan cells

Eukaryotic DNA replication follows a strict temporal program where genomic loci are replicated at precise times during the S phase of the cell cycle. Yet, the mechanism in control of the timing program in metazoan cells is poorly understood. In a recent publication, the authors proposed an intuitive stochastic model of DNA replication and showed that it predicts replication timing with an accuracy approaching the level of experimental biological repeats. Here, we discuss an extended software implementation of the mechanistic model: Replicon. This package allows interested researchers to predict the global replication timing program in human cells from chromatin data.

A chromatin structure-based model accurately predicts DNA replication timing in human cells

The metazoan genome is replicated in precise cell lineage‐specific temporal order. However, the mechanism controlling this orchestrated process is poorly understood as no molecular mechanisms have been identified that actively regulate the firing sequence of genome replication. Here, we develop a mechanistic model of genome replication capable of predicting, with accuracy rivaling experimental repeats, observed empirical replication timing program in humans. In our model, replication is initiated in an uncoordinated (time‐stochastic) manner at well‐defined sites. The model contains, in addition to the choice of the genomic landmark that localizes initiation, only a single adjustable parameter of direct biological relevance: the number of replication forks. We find that DNase‐hypersensitive sites are optimal and independent determinants of DNA replication initiation. We demonstrate that the DNA replication timing program in human cells is a robust emergent phenomenon that, by its very nature, does not require a regulatory mechanism determining a proper replication initiation firing sequence.

Inferring the spatiotemporal DNA replication program from noisy data

We generalize a stochastic model of DNA replication to the case where replication-origin-initiation rates vary locally along the genome and with time. Using this generalized model, we address the inverse problem of inferring initiation rates from experimental data concerning replication in cell populations. Previous work based on curve fitting depended on arbitrarily chosen functional forms for the initiation rate, with free parameters that were constrained by the data. We introduce a nonparametric method of inference that is based on Gaussian process regression. The method replaces specific assumptions about the functional form of the initiation rate with more general prior expectations about the smoothness of variation of this rate, along the genome and in time. Using this inference method, we recover, with high precision, simulated replication schemes from noisy data that are typical of current experiments.

A personal reflection on the replicon theory: from R1 plasmid to replication timing regulation in human cells

Fifty years after the Replicon Theory was originally presented, detailed mechanistic insight into prokaryotic replicons has been obtained and rapid progress is being made to elucidate the more complex regulatory mechanisms of replicon regulation in eukaryotic cells. Here, I present my personal perspectives on how studies of model replicons have contributed to our understanding of the basic mechanisms of DNA replication as well as the evolution of replication regulation in human cells. I will also discuss how replication regulation contributes to the stable maintenance of the genome and how disruption of replication regulation leads to human diseases.

From simple bacterial and archaeal replicons to replication N/U-domains

The Replicon Theory proposed 50 years ago has proven to apply for replicons of the three domains of life. Here, we review our knowledge of genome organization into single and multiple replicons in bacteria, archaea and eukarya. Bacterial and archaeal replicator/initiator systems are quite specific and efficient, whereas eukaryotic replicons show degenerate specificity and efficiency, allowing for complex regulation of origin firing time. We expand on recent evidence that ~50% of the human genome is organized as ~1,500 megabase-sized replication domains with a characteristic parabolic (U-shaped) replication timing profile and linear (N-shaped) gradient of replication fork polarity. These N/U-domains correspond to self-interacting segments of the chromatin fiber bordered by open chromatin zones and replicate by cascades of origin firing initiating at their borders and propagating to their center, possibly by fork-stimulated initiation. The conserved occurrence of this replication pattern in the germline of mammals has resulted over evolutionary times in the formation of megabase-sized domains with an N-shaped nucleotide compositional skew profile due to replication-associated mutational asymmetries. Overall, these results reveal an evolutionarily conserved but developmentally plastic organization of replication that is driving mammalian genome evolution.

Replication dynamics: biases and robustness of DNA fiber analysis

The factors that govern replication programs are still poorly identified in metazoans, especially in mammalian cells. Thanks to molecular combing, the dynamics of DNA replication can be assessed at the genome-scale level from the cumulative analysis of single DNA fibers. This technique notably enables measurement of replication fork speed and fork asymmetry and that of distances separating either initiation or termination events. The results presented here aim to evaluate requirements critical to accurate measurement of replication parameters by molecular combing. We show that sample size, fiber length and DNA counterstaining are crucial to gain robust information concerning replication dynamics. Our results thus provide a methodological frame to investigate the DNA replication program through molecular combing analyses.

A general approach to break the concentration barrier in single-molecule imaging

Single-molecule fluorescence imaging is often incompatible with physiological protein concentrations, as fluorescence background overwhelms an individual molecule's signal. We solve this problem with a new imaging approach called PhADE (PhotoActivation, Diffusion and Excitation). A protein of interest is fused to a photoactivatable protein (mKikGR) and introduced to its surface-immobilized substrate. After photoactivation of mKikGR near the surface, rapid diffusion of the unbound mKikGR fusion out of the detection volume eliminates background fluorescence, whereupon the bound molecules are imaged. We labeled the eukaryotic DNA replication protein flap endonuclease 1 with mKikGR and added it to replication-competent Xenopus laevis egg extracts. PhADE imaging of high concentrations of the fusion construct revealed its dynamics and micrometer-scale movements on individual, replicating DNA molecules. Because PhADE imaging is in principle compatible with any photoactivatable fluorophore, it should have broad applicability in revealing single-molecule dynamics and stoichiometry of macromolecular protein complexes at previously inaccessible fluorophore concentrations.

Replication timing and its emergence from stochastic processes

The temporal organization of DNA replication has puzzled cell biologists since before the mechanism of replication was understood. The realization that replication timing correlates with important features, such as transcription, chromatin structure and genome evolution, and is misregulated in cancer and aging has only deepened the fascination. Many ideas about replication timing have been proposed, but most have been short on mechanistic detail. However, recent work has begun to elucidate basic principles of replication timing. In particular, mathematical modeling of replication kinetics in several systems has shown that the reproducible replication timing patterns seen in population studies can be explained by stochastic origin firing at the single-cell level. This work suggests that replication timing need not be controlled by a hierarchical mechanism that imposes replication timing from a central regulator, but instead results from simple rules that affect individual origins.

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.

Optimal placement of origins for DNA replication

DNA replication is an essential process in biology and its timing must be robust so that cells can divide properly. Random fluctuations in the formation of replication starting points, called origins, and the subsequent activation of proteins lead to variations in the replication time. We analyze these stochastic properties of DNA and derive the positions of origins corresponding to the minimum replication time. We show that under some conditions the minimization of replication time leads to the grouping of origins, and relate this to experimental data in a number of species showing origin grouping.

Consecutive incorporation of fluorophore-labeled nucleotides by mammalian DNA polymerase beta

In the present study, we investigated mammalian polymerases that consecutively incorporate various fluorophore-labeled nucleotides. We found that rat DNA polymerase beta (pol beta) consecutively incorporated fluorophore-labeled nucleotides to a greater extent than four bacterial polymerases, Sequenase Version 2.0, Vent(R) (exo-), DNA polymerase IIIalpha and the Klenow fragment, and the mammalian polymerases DNA polymerase alpha and human DNA polymerase delta, under mesophilic conditions. Furthermore, we investigated the kinetics of correct or mismatched incorporation with labeled nucleotides during synthesis by rat pol beta. The kinetic parameters K(m) and k(cat) were measured and used for evaluating: (i) the discrimination against correct pair incorporation of labeled nucleotides relative to unlabeled nucleotides; and (ii) the fidelity for all nucleotide combinations of mismatched pairs in the presence of labeled or unlabeled nucleotides. We also investigated the effect of fluorophore-labeled nucleotides on terminal deoxynucleotidyl transferase activity of rat pol beta. We have demonstrated for the first time that mammalian pol beta can consecutively incorporate various fluorophore-labeled dNTPs. These findings suggest that pol beta is useful for high-density labeling of DNA probes and single-molecule sequencing for high-speed genome analysis.

S-phase progression in mammalian cells: modelling the influence of nuclear organization

The control of DNA replication is of fundamental importance as cell proliferation demands that identical copies of the genetic material are passed to the two daughter cells that form during mitosis. These genetic copies are generated in the preceding S phase, where the entire DNA complement of the mother cell must be copied exactly once. As part of this process, it is known that different regions of mammalian genomes are replicated at specific times of a temporally defined replication programme. The key feature of this programme is that active genes in euchromatin are replicated before inactive ones in heterochromatin. This separation of S phase into periods where different classes of chromatin are duplicated is important in maintaining changes in gene expression that define individual cell types. Recent attempts to understand the structure of the S-phase timing programme have focused on the use of genome-wide strategies that inevitably use DNA isolated from large cell populations for analysis. However, this approach provides a composite view of events that occur within a population without knowledge of the cell-to-cell variability across the population. In this review, we attempt to combine information generated using genome-wide and single cell strategies in order to develop a coherent molecular understanding of S-phase progression. During this integration, we have explored how available information can be introduced into a modelling environment that best describes S-phase progression in mammalian cells.

Mathematical modelling of eukaryotic DNA replication

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 population-averaged spatiotemporal patterns of DNA replication in several organisms. On the other hand, single-molecule 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.

Defects and DNA replication

We introduce a rate-equation formalism to study DNA replication kinetics in the presence of defects resulting from DNA damage and find a crossover between two regimes: a normal regime, where the influence of defects is local, and an initiation-limited regime. In the latter, defects have a global impact on replication, whose progress is set by the rate at which origins of replication are activated, or initiated. Normal, healthy cells have defect densities in the normal regime. Our model can explain an observed correlation between interorigin separation and rate of DNA replication.

Universal temporal profile of replication origin activation in eukaryotes

Although replication proteins are conserved among eukaryotes, the sequence requirements for replication initiation differ between species. In all species, however, replication origins fire asynchronously throughout S phase. The temporal program of origin firing is reproducible in cell populations but largely probabilistic at the single-cell level. The mechanisms and the significance of this program are unclear. Replication timing has been correlated with gene activity in metazoans but not in yeast. One potential role for a temporal regulation of origin firing is to minimize fluctuations in replication end time and avoid persistence of unreplicated DNA in mitosis. Here, we have extracted the population-averaged temporal profiles of replication initiation rates for S. cerevisiae, S. pombe, D. melanogaster, X. laevis and H. sapiens from genome-wide replication timing and DNA combing data. All the profiles have a strikingly similar shape, increasing during the first half of S phase then decreasing before its end. A previously proposed minimal model of stochastic initiation modulated by accumulation of a recyclable, limiting replication-fork factor and fork-promoted initiation of new origins, quantitatively described the observed profiles without requiring new implementations.

The selective pressure for timely completion of genome replication and optimal usage of replication proteins that must be imported into the cell nucleus can explain the generic shape of the profiles. We have identified a universal behavior of eukaryotic replication initiation that transcends the mechanisms of origin specification. The population-averaged efficiency of replication origin usage changes during S phase in a strikingly similar manner in a highly diverse set of eukaryotes. The quantitative model previously proposed for origin activation in X. laevis can be generalized to explain this evolutionary conservation.

Control of DNA replication by anomalous reaction-diffusion kinetics

We propose a simple model for the control of DNA replication in which the rate of initiation of replication origins is controlled by protein-DNA interactions. Analyzing recent data from Xenopus frog embryos, we find that the initiation rate is reaction limited until nearly the end of replication, when it becomes diffusion limited. Initiation of origins is suppressed when the diffusion-limited search time dominates. To fit the experimental data, we find that the interaction between DNA and the rate-limiting protein must be subdiffusive.

Computational methods to study kinetics of DNA replication

New technologies such as DNA combing have led to the availability of large quantities of data that describe the state of DNA while undergoing replication in S phase. In this chapter, we describe methods used to extract various parameters of replication--fork velocity, origin initiation rate, fork density, numbers of potential and utilized origins--from such data. We first present a version of the technique that applies to "ideal" data. We then show how to deal with, a number of real-world complications, such as the asynchrony of starting times of a population of cells, the finite length of fragments used in the analysis, and the finite amount of DNA in a chromosome.

Introduction to molecular combing: genomics, DNA replication, and cancer

The sequencing of the human genome inaugurated a new era in both fundamental and applied genetics. At the same time, the emergence of new technologies for probing the genome has transformed the field of pharmaco-genetics and made personalized genomic profiling and high-throughput screening of new therapeutic agents all but a matter of routine. One of these technologies, molecular combing, has served to bridge the technical gap between the examination of gross chromosomal abnormalities and sequence-specific alterations. Molecular combing provides a new perspective on the structure and dynamics of the human genome at the whole genome and sub-chromosomal levels with a resolution ranging from a few kilobases up to a megabase and more. Originally developed to study genetic rearrangements and to map genes for positional cloning, recent advances have extended the spectrum of its applications to studying the real-time dynamics of the replication of the genome. Understanding how the genome is replicated is essential for elucidating the mechanisms that both maintain genome integrity and result in the instabilities leading to human genetic disease and cancer. In the following, we will examine recent discoveries and advances due to the application of molecular combing to new areas of research in the fields of molecular cytogenetics and cancer genomics.

How Xenopus laevis embryos replicate reliably: investigating the random-completion problem

DNA synthesis in Xenopus frog embryos initiates stochastically in time at many sites (origins) along the chromosome. Stochastic initiation implies fluctuations in the time to complete and may lead to cell death if replication takes longer than the cell cycle time ( approximately 25 min) . Surprisingly, although the typical replication time is about 20 min , in vivo experiments show that replication fails to complete only about 1 in 300 times. How is replication timing accurately controlled despite the stochasticity? Biologists have proposed two solutions to this "random-completion problem." The first solution uses randomly located origins but increases their rate of initiation as S phase proceeds, while the second uses regularly spaced origins. In this paper, we investigate the random-completion problem using a type of model first developed to describe the kinetics of first-order phase transitions. Using methods from the field of extreme-value statistics, we derive the distribution of replication-completion times for a finite genome. We then argue that the biologists' first solution to the problem is not only consistent with experiment but also nearly optimizes the use of replicative proteins. We also show that spatial regularity in origin placement does not alter significantly the distribution of replication times and, thus, is not needed for the control of replication timing.

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.

Cell cycle regulation of DNA replication

Eukaryotic DNA replication is regulated to ensure all chromosomes replicate once and only once per cell cycle. Replication begins at many origins scattered along each chromosome. Except for budding yeast, origins are not defined DNA sequences and probably are inherited by epigenetic mechanisms. Initiation at origins occurs throughout the S phase according to a temporal program that is important in regulating gene expression during development. Most replication proteins are conserved in evolution in eukaryotes and archaea, but not in bacteria. However, the mechanism of initiation is conserved and consists of origin recognition, assembly of prereplication (pre-RC) initiative complexes, helicase activation, and replisome loading. Cell cycle regulation by protein phosphorylation ensures that pre-RC assembly can only occur in G1 phase, whereas helicase activation and loading can only occur in S phase. Checkpoint regulation maintains high fidelity by stabilizing replication forks and preventing cell cycle progression during replication stress or damage.

A Cdc7 kinase inhibitor restricts initiation of DNA replication and has antitumor activity

Cdc7 is an essential kinase that promotes DNA replication by activating origins of replication. Here, we characterized the potent Cdc7 inhibitor PHA-767491 (1) in biochemical and cell-based assays, and we tested its antitumor activity in rodents. We found that the compound blocks DNA synthesis and affects the phosphorylation of the replicative DNA helicase at Cdc7-dependent phosphorylation sites. Unlike current DNA synthesis inhibitors, PHA-767491 prevents the activation of replication origins but does not impede replication fork progression, and it does not trigger a sustained DNA damage response. Treatment with PHA-767491 results in apoptotic cell death in multiple cancer cell types and tumor growth inhibition in preclinical cancer models. To our knowledge, PHA-767491 is the first molecule that directly affects the mechanisms controlling initiation as opposed to elongation in DNA replication, and its activities suggest that Cdc7 kinase inhibition could be a new strategy for the development of anticancer therapeutics.

Global regulation of genome duplication in eukaryotes: an overview from the epifluorescence microscope

In eukaryotes, DNA replication is initiated along each chromosome at multiple sites called replication origins. Locally, each replication origin is "licensed" or specified at the end of the M and the beginning of the G1 phases of the cell cycle. During the S phase when DNA synthesis takes place, origins are activated in stages corresponding to early and late-replicating domains. The staged and progressive activation of replication origins reflects the need to maintain a strict balance between the number of active replication forks and the rate at which DNA synthesis proceeds. This suggests that origin densities (frequency of initiation) and replication fork movement (rates of elongation) must be coregulated to guarantee the efficient and complete duplication of each subchromosomal domain. Emerging evidence supports this proposal and suggests that the ATM/ATR intra-S phase checkpoint plays an important role in the coregulation of initiation frequencies and rates of elongation. In this paper, we review recent results concerning the mechanisms governing the global regulation of DNA replication and discuss the roles these mechanisms play in maintaining genome stability during both a normal and perturbed S phase.

DNA combing reveals intrinsic temporal disorder in the replication of yeast chromosome VI

It is generally believed that DNA replication in most eukaryotes proceeds according to a precise program in which there is a defined temporal order by which each chromosomal region is duplicated. However, the regularity of this program at the level of individual chromosomes, in terms of both the relative timing and the size of the DNA domain, has not been addressed. Here, the replication of chromosome VI from synchronized budding yeast was studied at a resolution of approximately 1 kb with DNA combing and fluorescence microscopy. Contrary to what would be expected from cells following a rigorous temporal program, no two molecules exhibited the same replication pattern. Moreover, a direct evaluation of the extent to which the replication of distant chromosomal segments was coordinated indicates that the overwhelming majority of these segments were replicated independently. Importantly, averaging the patterns of all the fibers examined recapitulates the ensemble-averaged patterns obtained from population studies of the replication of chromosome VI. Thus, rather than an absolutely defined temporal order of replication, replication timing appears to be essentially probabilistic within individual cells, exhibiting only temporal tendencies within extended domains.

Ribonucleotide reductase and the regulation of DNA replication: an old story and an ancient heritage

All organisms that synthesize their own DNA have evolved mechanisms for maintaining a constant DNA/cell mass ratio independent of growth rate. The DNA/cell mass ratio is a central parameter in the processes controlling the cell cycle. The co-ordination of DNA replication with cell growth involves multiple levels of regulation. DNA synthesis is initiated at specific sites on the chromosome termed origins of replication, and proceeds bidirectionally to elongate and duplicate the chromosome. These two processes, initiation and elongation, therefore determine the total rate of DNA synthesis in the cell. In Escherichia coli, initiation depends on the DnaA protein while elongation depends on a multiprotein replication factory that incorporates deoxyribonucleotides (dNTPs) into the growing DNA chain. The enzyme ribonucleotide reductase (RNR) is universally responsible for synthesizing the necessary dNTPs. In this review we examine the role RNR plays in regulating the total rate of DNA synthesis in E. coli and, hence, in maintaining constant DNA/cell mass ratios during normal growth and under conditions of DNA stress.

How Xenopus laevis replicates DNA reliably even though its origins of replication are located and initiated stochastically

DNA replication in Xenopus laevis is extremely reliable, failing to complete before cell division no more than once in 10 000 times; yet replication origin sites are located and initiated stochastically. Using a model based on 1D theories of nucleation and growth and using concepts from extreme-value statistics, we derive the distribution of replication times given a particular initiation function. We show that the experimentally observed initiation strategy for Xenopus laevis meets the reliability constraint and is close to the one that requires the fewest resources of a cell.

DNA replication timing: random thoughts about origin firing

Regions of metazoan genomes replicate at defined times within S phase. This observation suggests that replication origins fire with a defined timing pattern that remains the same from cycle to cycle. However, an alterative model based on the stochastic firing of origins may also explain replication timing. This model assumes varying origin efficiency instead of a strict origin-timing programme. Here, we discuss the evidence for both models.

Invasive advance of an advantageous mutation: Nucleation theory

For sedentary organisms with localized reproduction, spatially clustered growth drives the invasive advance of a favorable mutation. We model competition between two alleles where recurrent mutation introduces a genotype with a rate of local propagation exceeding the resident's rate. We capture ecologically important properties of the rare invader's stochastic dynamics by assuming discrete individuals and local neighborhood interactions. To understand how individual-level processes may govern population patterns, we invoke the physical theory for nucleation of spatial systems. Nucleation theory discriminates between single-cluster and multi-cluster dynamics. A sufficiently low mutation rate, or a sufficiently small environment, generates single-cluster dynamics, an inherently stochastic process; a favorable mutation advances only if the invader cluster reaches a critical radius. For this mode of invasion, we identify the probability distribution of waiting times until the favored allele advances to competitive dominance, and we ask how the critical cluster size varies as propagation or mortality rates vary. Increasing the mutation rate or system size generates multi-cluster invasion, where spatial averaging produces nearly deterministic global dynamics. For this process, an analytical approximation from nucleation theory, called Avrami's Law, describes the time-dependent behavior of the genotype densities with remarkable accuracy.

Reconstructing DNA replication kinetics from small DNA fragments

In higher organisms, DNA replicates simultaneously from many origins. Recent in vitro experiments have yielded large amounts of data on the state of replication of DNA fragments. From measurements of the time dependence of the average size of replicated and nonreplicated domains, one can estimate the rate of initiation of DNA replication origins, as well as the average rate at which DNA bases are copied. One problem in making such estimates is that, in the experiments, the DNA is broken up into small fragments, whose finite size can bias downward the measured averages. Here, we present a systematic way of accounting for this bias by deriving theoretical relationships between the original domain-length distributions and fragment-domain length distributions. We also derive unbiased average-domain-length estimators that yield accurate results, even in cases where the replicated (or nonreplicated) domains are larger than the average DNA fragment. Then we apply these estimators to previously obtained experimental data to extract improved estimates of replication kinetics parameters.

DNA replication origins fire stochastically in fission yeast

DNA replication initiates at discrete origins along eukaryotic chromosomes. However, in most organisms, origin firing is not efficient; a specific origin will fire in some but not all cell cycles. This observation raises the question of how individual origins are selected to fire and whether origin firing is globally coordinated to ensure an even distribution of replication initiation across the genome. We have addressed these questions by determining the location of firing origins on individual fission yeast DNA molecules using DNA combing. We show that the firing of replication origins is stochastic, leading to a random distribution of replication initiation. Furthermore, origin firing is independent between cell cycles; there is no epigenetic mechanism causing an origin that fires in one cell cycle to preferentially fire in the next. Thus, the fission yeast strategy for the initiation of replication is different from models of eukaryotic replication that propose coordinated origin firing.

Spatial dynamics of invasion: the geometry of introduced species

Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyse this phenomenon, we note that invaders often cluster spatially when rare, and consequently an introduced exotic's population dynamics should depend on locally structured interactions. Ecological theory for spatially structured invasion relies on deterministic approximations, and determinism does not address the observed uncertainty of the exotic-introduction process. We take a new approach to the population dynamics of invasion and, by extension, to the general question of invasibility in any spatial ecology. We apply the physical theory for nucleation of spatial systems to a lattice-based model of competition between plant species, a resident and an invader, and the analysis reaches conclusions that differ qualitatively from the standard ecological theories. Nucleation theory distinguishes between dynamics of single- and multi-cluster invasion. Low introduction rates and small system size produce single-cluster dynamics, where success or failure of introduction is inherently stochastic. Single-cluster invasion occurs only if the cluster reaches a critical size, typically preceded by a number of failed attempts. For this case, we identify the functional form of the probability distribution of time elapsing until invasion succeeds. Although multi-cluster invasion for sufficiently large systems exhibits spatial averaging and almost-deterministic dynamics of the global densities, an analytical approximation from nucleation theory, known as Avrami's law, describes our simulation results far better than standard ecological approximations.

Models of cell signaling pathways

Cellular signaling circuits handle an enormous range of computations. Beyond the housekeeping, replicating and other functions of individual cells, signaling circuits must implement the immensely complex logic of development and function of multicellular organisms. Computer models are useful tools to understand this complexity. Recent studies have extended such models to include electrical, mechanical and spatial details of signaling, and to address the stochastic effects that arise when small numbers of molecules interact. Increasing numbers of models have been developed in close conjunction with experiments, and this interplay gives a deeper and more reliable insight into signaling function.