Mathematical modeling of genome replication

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.

Dual DNA replication modes: varying fork speeds and initiation rates within the spatial replication program in Xenopus

Large vertebrate genomes duplicate by activating tens of thousands of DNA replication origins, irregularly spaced along the genome. The spatial and temporal regulation of the replication process is not yet fully understood. To investigate the DNA replication dynamics, we developed a methodology called RepliCorr, which uses the spatial correlation between replication patterns observed on stretched single-molecule DNA obtained by either DNA combing or high-throughput optical mapping. The analysis revealed two independent spatiotemporal processes that regulate the replication dynamics in the Xenopus model system. These mechanisms are referred to as a fast and a slow replication mode, differing by their opposite replication fork speed and rate of origin firing. We found that Polo-like kinase 1 (Plk1) depletion abolished the spatial separation of these two replication modes. In contrast, neither replication checkpoint inhibition nor Rap1-interacting factor (Rif1) depletion affected the distribution of these replication patterns. These results suggest that Plk1 plays an essential role in the local coordination of the spatial replication program and the initiation-elongation coupling along the chromosomes in Xenopus, ensuring the timely completion of the S phase.

Mathematical model for the distribution of DNA replication origins

DNA replication in yeast and in many other organisms starts from well-defined locations on the DNA known as replication origins. The spatial distribution of these origins in the genome is particularly important in ensuring that replication is completed quickly. Cells are more vulnerable to DNA damage and other forms of stress while they are replicating their genome. This raises the possibility that the spatial distribution of origins is under selection pressure. In this paper we investigate the hypothesis that natural selection favors origin distributions leading to shorter replication times. Using a simple mathematical model, we show that this hypothesis leads to two main predictions about the origin distributions: that neighboring origins that are inefficient (less likely to fire) are more likely to be close to each other than efficient origins; and that neighboring origins with larger differences in firing times are more likely to be close to each other than origins with similar firing times. We test these predictions using next-generation sequencing data, and show that they are both supported by the data.

An evolutionary model identifies the main evolutionary biases for the evolution of genome-replication profiles

Recent results comparing the temporal program of genome replication of yeast species belonging to the Lachancea clade support the scenario that the evolution of the replication timing program could be mainly driven by correlated acquisition and loss events of active replication origins. Using these results as a benchmark, we develop an evolutionary model defined as birth-death process for replication origins and use it to identify the evolutionary biases that shape the replication timing profiles. Comparing different evolutionary models with data, we find that replication origin birth and death events are mainly driven by two evolutionary pressures, the first imposes that events leading to higher double-stall probability of replication forks are penalized, while the second makes less efficient origins more prone to evolutionary loss. This analysis provides an empirically grounded predictive framework for quantitative evolutionary studies of the replication timing program.

Stochasticity of replication forks' speeds plays a key role in the dynamics of DNA replication

Eukaryotic DNA replication is elaborately orchestrated to duplicate the genome timely and faithfully. Replication initiates at multiple origins from which replication forks emanate and travel bi-directionally. The complex spatio-temporal regulation of DNA replication remains incompletely understood. To study it, computational models of DNA replication have been developed in S. cerevisiae. However, in spite of the experimental evidence of forks’ speed stochasticity, all models assumed that forks’ speeds are the same. Here, we present the first model of DNA replication assuming that speeds vary stochastically between forks. Utilizing data from both wild-type and hydroxyurea-treated yeast cells, we show that our model is more accurate than models assuming constant forks’ speed and reconstructs dynamics of DNA replication faithfully starting both from population-wide data and data reflecting fork movement in individual cells. Completion of replication in a timely manner is a challenge due to its stochasticity; we propose an empirically derived modification to replication speed based on the distance to the approaching fork, which promotes timely completion of replication. In summary, our work discovers a key role that stochasticity of the forks’ speed plays in the dynamics of DNA replication. We show that without including stochasticity of forks’ speed it is not possible to accurately reconstruct movement of individual replication forks, measured by DNA combing.

DNA replication in eukaryotes starts from multiple sites termed replication origins. Replication timing at individual sites is stochastic, but reproducible population-wide. Complex and not yet completely understood mechanisms ensure that genome is replicated exactly once and that replication is finished in time. This complex spatio-temporal organization of DNA replication makes computational modeling a useful tool to study replication mechanisms. For simplicity, all previous models assumed constant replication forks’ speed. Here, we show that such models are incapable of accurately reconstructing distances travelled by individual replication forks. Therefore, we propose a model assuming that replication speed varies stochastically between forks. We show that such model reproduces faithfully distances travelled by individual replication forks. Moreover, our model is simpler than previous model and thus avoids over-learning (fitting noise). We also discover how replication speed may be attuned to timely complete replication. We propose that forks’ speed increases with diminishing distance to the approaching fork, which we show promotes timely completion of replication. Such speed up can be e.g. explained by a synergy effect of chromatin unwinding by both forks. Our model can be used to simulate phenomena beyond replication, e.g. DNA double-strand breaks resulting from broken replication forks.

Molecular Mechanisms of DNA Replication and Repair Machinery: Insights from Microscopic Simulations

Reproduction, the hallmark of biological activity, requires making an accurate copy of the genetic material to allow the progeny to inherit parental traits. In all living cells, the process of DNA replication is carried out by a concerted action of multiple protein species forming a loose protein-nucleic acid complex, the replisome. Proofreading and error correction generally accompany replication but also occur independently, safeguarding genetic information through all phases of the cell cycle. Advances in biochemical characterization of intracellular processes, proteomics and the advent of single-molecule biophysics have brought about a treasure trove of information awaiting to be assembled into an accurate mechanistic model of the DNA replication process. In this review, we describe recent efforts to model elements of DNA replication and repair processes using computer simulations, an approach that has gained immense popularity in many areas of molecular biophysics but has yet to become mainstream in the DNA metabolism community. We highlight the use of diverse computational methods to address specific problems of the fields and discuss unexplored possibilities that lie ahead for the computational approaches in these areas.

Bayesian inference of origin firing time distributions, origin interference and licencing probabilities from Next Generation Sequencing data

DNA replication is a stochastic process with replication forks emanating from multiple replication origins. The origins must be licenced in G1, and the replisome activated at licenced origins in order to generate bi-directional replication forks in S-phase. Differential firing times lead to origin interference, where a replication fork from an origin can replicate through and inactivate neighbouring origins (origin obscuring). We developed a Bayesian algorithm to characterize origin firing statistics from Okazaki fragment (OF) sequencing data. Our algorithm infers the distributions of firing times and the licencing probabilities for three consecutive origins. We demonstrate that our algorithm can distinguish partial origin licencing and origin obscuring in OF sequencing data from Saccharomyces cerevisiae and human cell types. We used our method to analyse the decreased origin efficiency under loss of Rat1 activity in S. cerevisiae, demonstrating that both reduced licencing and increased obscuring contribute. Moreover, we show that robust analysis is possible using only local data (across three neighbouring origins), and analysis of the whole chromosome is not required. Our algorithm utilizes an approximate likelihood and a reversible jump sampling technique, a methodology that can be extended to analysis of other mechanistic processes measurable through Next Generation Sequencing data.

Rapid high-resolution measurement of DNA replication timing by droplet digital PCR

Genomes are replicated in a reproducible temporal pattern. Current methods for assaying allele replication timing are time consuming and/or expensive. These include high-throughput sequencing which can be used to measure DNA copy number as a proxy for allele replication timing. Here, we use droplet digital PCR to study DNA replication timing at multiple loci in budding yeast and human cells. We establish that the method has temporal and spatial resolutions comparable to the high-throughput sequencing approaches, while being faster than alternative locus-specific methods. Furthermore, the approach is capable of allele discrimination. We apply this method to determine relative replication timing across timing transition zones in cultured human cells. Finally, multiple samples can be analysed in parallel, allowing us to rapidly screen kinetochore mutants for perturbation to centromere replication timing. Therefore, this approach is well suited to the study of locus-specific replication and the screening of cis- and trans-acting mutants to identify mechanisms that regulate local genome replication timing.

Origins Left, Right, and Centre: Increasing the Number of Initiation Sites in the Escherichia coli Chromosome

The bacterium Escherichia coli contains a single circular chromosome with a defined architecture. DNA replication initiates at a single origin called oriC. Two replication forks are assembled and proceed in opposite directions until they fuse in a specialised zone opposite the origin. This termination area is flanked by polar replication fork pause sites that allow forks to enter, but not to leave. Thus, the chromosome is divided into two replichores, each replicated by a single replication fork. Recently, we analysed the replication parameters in E. coli cells, in which an ectopic origin termed oriZ was integrated in the right-hand replichore. Two major obstacles to replication were identified: (1) head-on replication⁻transcription conflicts at highly transcribed rrn operons, and (2) the replication fork trap. Here, we describe replication parameters in cells with ectopic origins, termed oriX and oriY, integrated into the left-hand replichore, and a triple origin construct with oriX integrated in the left-hand and oriZ in the right-hand replichore. Our data again highlight both replication⁻transcription conflicts and the replication fork trap as important obstacles to DNA replication, and we describe a number of spontaneous large genomic rearrangements which successfully alleviate some of the problems arising from having an additional origin in an ectopic location. However, our data reveal additional factors that impact efficient chromosome duplication, highlighting the complexity of chromosomal architecture.

Analysis of Replicative Polymerase Usage by Ribonucleotide Incorporation

Mapping the usage of replicative DNA polymerases has previously proved to be technically challenging. By exploiting mutant polymerases that incorporate ribonucleotides into the DNA with a significantly higher proficiency than their wild-type counterparts, we and others have developed methods that can identify what proportion of each DNA strand (i.e., the Watson and Crick strands) is replicated by a specific DNA polymerase. The incorporation of excess ribonucleotides by a mutated polymerase effectively marks, in each individual cells, the DNA strand that is replicated by that specific mutated polymerase. Changes to DNA polymerase usage can be examined at specific loci by Southern blot analysis while a global analysis of polymerase usage can be achieved by applying next-generation sequencing. This genome-wide data also provides a direct measure of replication origin efficiency and can be used to indirectly calculate replication timing.

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.

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

Eukaryotic cells initiate DNA synthesis by sequential firing of hundreds of origins. This ordered replication is described by replication profiles, which measure the DNA content within a cell population. Here, we show that replication dynamics can be deduced from replication profiles of free-cycling cells. While such profiles lack explicit temporal information, they are sensitive to fork velocity and initiation capacity through the passive replication pattern, namely the replication of origins by forks emanating elsewhere. We apply our model-based approach to a compendium of profiles that include most viable budding yeast mutants implicated in replication. Predicted changes in fork velocity or initiation capacity are verified by profiling synchronously replicating cells. Notably, most mutants implicated in late (or early) origin effects are explained by global modulation of fork velocity or initiation capacity. Our approach provides a rigorous framework for analyzing DNA replication profiles of free-cycling cells.

Mapping ribonucleotides in genomic DNA and exploring replication dynamics by polymerase usage sequencing (Pu-seq)

Ribonucleotides are frequently misincorporated into DNA during replication, and they are rapidly repaired by ribonucleotide excision repair (RER). Although ribonucleotides in template DNA perturb replicative polymerases and can be considered as DNA damage, they also serve positive biological functions, including directing the orientation of mismatch repair. Here we describe a method for ribonucleotide identification by high-throughput sequencing that allows mapping of the location of ribonucleotides across the genome. When combined with specific mutations in the replicative polymerases that incorporate ribonucleotides at elevated frequencies, our ribonucleotide identification method was adapted to map polymerase usage across the genome. Polymerase usage sequencing (Pu-seq) has been used to define, in unprecedented detail, replication dynamics in yeasts. Although other methods that examine replication dynamics provide direct measures of replication timing and indirect estimates of origin efficiency, Pu-seq directly ascertains origin efficiency. The Pu-seq protocol can be completed in 12-14 d.

A global profile of replicative polymerase usage

Three eukaryotic DNA polymerases are essential for genome replication. Polymerase (Pol) α-primase initiates each synthesis event and is rapidly replaced by processive DNA polymerases: Polɛ replicates the leading strand, whereas Polδ performs lagging-strand synthesis. However, it is not known whether this division of labor is maintained across the whole genome or how uniform it is within single replicons. Using Schizosaccharomyces pombe, we have developed a polymerase usage sequencing (Pu-seq) strategy to map polymerase usage genome wide. Pu-seq provides direct replication-origin location and efficiency data and indirect estimates of replication timing. We confirm that the division of labor is broadly maintained across an entire genome. However, our data suggest a subtle variability in the usage of the two polymerases within individual replicons. We propose that this results from occasional leading-strand initiation by Polδ followed by exchange for Polɛ.

Dynamics and control of DNA sequence amplification

DNA amplification is the process of replication of a specified DNA sequence in vitro through time-dependent manipulation of its external environment. A theoretical framework for determination of the optimal dynamic operating conditions of DNA amplification reactions, for any specified amplification objective, is presented based on first-principles biophysical modeling and control theory. Amplification of DNA is formulated as a problem in control theory with optimal solutions that can differ considerably from strategies typically used in practice. Using the Polymerase Chain Reaction as an example, sequence-dependent biophysical models for DNA amplification are cast as control systems, wherein the dynamics of the reaction are controlled by a manipulated input variable. Using these control systems, we demonstrate that there exists an optimal temperature cycling strategy for geometric amplification of any DNA sequence and formulate optimal control problems that can be used to derive the optimal temperature profile. Strategies for the optimal synthesis of the DNA amplification control trajectory are proposed. Analogous methods can be used to formulate control problems for more advanced amplification objectives corresponding to the design of new types of DNA amplification reactions.

Different rates of DNA replication at early versus late S-phase sections: multiscale modeling of stochastic events related to DNA content/EdU (5-ethynyl-2'deoxyuridine) incorporation distributions

Mathematical modeling allows relating molecular events to single-cell characteristics assessed by multiparameter cytometry. In the present study we labeled newly synthesized DNA in A549 human lung carcinoma cells with 15-120 min pulses of EdU. All DNA was stained with DAPI and cellular fluorescence was measured by laser scanning cytometry. The frequency of cells in the ascending (left) side of the "horseshoe"-shaped EdU/DAPI bivariate distributions reports the rate of DNA replication at the time of entrance to S phase while their frequency in the descending (right) side is a marker of DNA replication rate at the time of transition from S to G2 phase. To understand the connection between molecular-scale events and scatterplot asymmetry, we developed a multiscale stochastic model, which simulates DNA replication and cell cycle progression of individual cells and produces in silico EdU/DAPI scatterplots. For each S-phase cell the time points at which replication origins are fired are modeled by a non-homogeneous Poisson Process (NHPP). Shifted gamma distributions are assumed for durations of cell cycle phases (G1, S and G2 M), Depending on the rate of DNA synthesis being an increasing or decreasing function, simulated EdU/DAPI bivariate graphs show predominance of cells in left (early-S) or right (late-S) side of the horseshoe distribution. Assuming NHPP rate estimated from independent experiments, simulated EdU/DAPI graphs are nearly indistinguishable from those experimentally observed. This finding proves consistency between the S-phase DNA-replication rate based on molecular-scale analyses, and cell population kinetics ascertained from EdU/DAPI scatterplots and demonstrates that DNA replication rate at entrance to S is relatively slow compared with its rather abrupt termination during S to G2 transition. Our approach opens a possibility of similar modeling to study the effect of anticancer drugs on DNA replication/cell cycle progression and also to quantify other kinetic events that can be measured during S-phase.

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.

The dynamics of genome replication using deep sequencing

Eukaryotic genomes are replicated from multiple DNA replication origins. We present complementary deep sequencing approaches to measure origin location and activity in Saccharomyces cerevisiae. Measuring the increase in DNA copy number during a synchronous S-phase allowed the precise determination of genome replication. To map origin locations, replication forks were stalled close to their initiation sites; therefore, copy number enrichment was limited to origins. Replication timing profiles were generated from asynchronous cultures using fluorescence-activated cell sorting. Applying this technique we show that the replication profiles of haploid and diploid cells are indistinguishable, indicating that both cell types use the same cohort of origins with the same activities. Finally, increasing sequencing depth allowed the direct measure of replication dynamics from an exponentially growing culture. This is the first time this approach, called marker frequency analysis, has been successfully applied to a eukaryote. These data provide a high-resolution resource and methodological framework for studying genome biology.

High-resolution replication profiles define the stochastic nature of genome replication initiation and termination

Eukaryotic genome replication is stochastic, and each cell uses a different cohort of replication origins. We demonstrate that interpreting high-resolution Saccharomyces cerevisiae genome replication data with a mathematical model allows quantification of the stochastic nature of genome replication, including the efficiency of each origin and the distribution of termination events. Single-cell measurements support the inferred values for stochastic origin activation time. A strain, in which three origins were inactivated, confirmed that the distribution of termination events is primarily dictated by the stochastic activation time of origins. Cell-to-cell variability in origin activity ensures that termination events are widely distributed across virtually the whole genome. We propose that the heterogeneity in origin usage contributes to genome stability by limiting potentially deleterious events from accumulating at particular loci.

•

Deep sequencing reveals a high-resolution view of genome replication dynamics

•

Genome-wide modeling and single-cell imaging reveal stochastic origin activity

•

Origin activity determines the location of replication termination events

•

Termination events are widely distributed across the whole genome

Stochastic association of neighboring replicons creates replication factories in budding yeast

Inside the nucleus, DNA replication is organized at discrete sites called replication factories, consisting of DNA polymerases and other replication proteins. Replication factories play important roles in coordinating replication and in responding to replication stress. However, it remains unknown how replicons are organized for processing at each replication factory. Here we address this question using budding yeast. We analyze how individual replicons dynamically organized a replication factory using live-cell imaging and investigate how replication factories were structured using super-resolution microscopy. Surprisingly, we show that the grouping of replicons within factories is highly variable from cell to cell. Once associated, however, replicons stay together relatively stably to maintain replication factories. We derive a coherent genome-wide mathematical model showing how neighboring replicons became associated stochastically to form replication factories, which was validated by independent microscopy-based analyses. This study not only reveals the fundamental principles promoting replication factory organization in budding yeast, but also provides insight into general mechanisms by which chromosomes organize sub-nuclear structures.

A variable fork rate affects timing of origin firing and S phase dynamics in Saccharomyces cerevisiae

Activation (in the following referred to as firing) of replication origins is a continuous and irreversible process regulated by availability of DNA replication molecules and cyclin-dependent kinase activities, which are often altered in human cancers. The temporal, progressive origin firing throughout S phase appears as a characteristic replication profile, and computational models have been developed to describe this process. Although evidence from yeast to human indicates that a range of replication fork rates is observed experimentally in order to complete a timely S phase, those models incorporate velocities that are uniform across the genome. Taking advantage of the availability of replication profiles, chromosomal position and replication timing, here we investigated how fork rate may affect origin firing in budding yeast. Our analysis suggested that patterns of origin firing can be observed from a modulation of the fork rate that strongly correlates with origin density. Replication profiles of chromosomes with a low origin density were fitted with a variable fork rate, whereas for the ones with a high origin density a constant fork rate was appropriate. This indeed supports the previously reported correlation between inter-origin distance and fork rate changes. Intriguingly, the calculated correlation between fork rate and timing of origin firing allowed the estimation of firing efficiencies for the replication origins. This approach correctly retrieved origin efficiencies previously determined for chromosome VI and provided testable prediction for other chromosomal origins. Our results gain deeper insights into the temporal coordination of genome duplication, indicating that control of the replication fork rate is required for the timely origin firing during S phase.