Inferring the spatiotemporal DNA replication program from noisy data

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.

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.

Genome replication in asynchronously growing microbial populations

Biological cells replicate their genomes in a well-planned manner. The DNA replication program of an organism determines the timing at which different genomic regions are replicated, with fundamental consequences for cell homeostasis and genome stability. In a growing cell culture, genomic regions that are replicated early should be more abundant than regions that are replicated late. This abundance pattern can be experimentally measured using deep sequencing. However, a general quantitative theory linking this pattern to the replication program is still lacking. In this paper, we predict the abundance of DNA fragments in asynchronously growing cultures from any given stochastic model of the DNA replication program. As key examples, we present stochastic models of the DNA replication programs in budding yeast and Escherichia coli. In both cases, our model results are in excellent agreement with experimental data and permit to infer key information about the replication program. In particular, our method is able to infer the locations of known replication origins in budding yeast with high accuracy. These examples demonstrate that our method can provide insight into a broad range of organisms, from bacteria to eukaryotes.

Neural network and kinetic modelling of human genome replication reveal replication origin locations and strengths

In human and other metazoans, the determinants of replication origin location and strength are still elusive. Origins are licensed in G1 phase and fired in S phase of the cell cycle, respectively. It is debated which of these two temporally separate steps determines origin efficiency. Experiments can independently profile mean replication timing (MRT) and replication fork directionality (RFD) genome-wide. Such profiles contain information on multiple origins' properties and on fork speed. Due to possible origin inactivation by passive replication, however, observed and intrinsic origin efficiencies can markedly differ. Thus, there is a need for methods to infer intrinsic from observed origin efficiency, which is context-dependent. Here, we show that MRT and RFD data are highly consistent with each other but contain information at different spatial scales. Using neural networks, we infer an origin licensing landscape that, when inserted in an appropriate simulation framework, jointly predicts MRT and RFD data with unprecedented precision and underlies the importance of dispersive origin firing. We furthermore uncover an analytical formula that predicts intrinsic from observed origin efficiency combined with MRT data. Comparison of inferred intrinsic origin efficiencies with experimental profiles of licensed origins (ORC, MCM) and actual initiation events (Bubble-seq, SNS-seq, OK-seq, ORM) show that intrinsic origin efficiency is not solely determined by licensing efficiency. Thus, human replication origin efficiency is set at both the origin licensing and firing steps.

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.

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.

Inferring the Forces Controlling Metaphase Kinetochore Oscillations by Reverse Engineering System Dynamics

Kinetochores are multi-protein complexes that mediate the physical coupling of sister chromatids to spindle microtubule bundles (called kinetochore (K)-fibres) from respective poles. These kinetochore-attached K-fibres generate pushing and pulling forces, which combine with polar ejection forces (PEF) and elastic inter-sister chromatin to govern chromosome movements. Classic experiments in meiotic cells using calibrated micro-needles measured an approximate stall force for a chromosome, but methods that allow the systematic determination of forces acting on a kinetochore in living cells are lacking. Here we report the development of mathematical models that can be fitted (reverse engineered) to high-resolution kinetochore tracking data, thereby estimating the model parameters and allowing us to indirectly compute the (relative) force components (K-fibre, spring force and PEF) acting on individual sister kinetochores in vivo. We applied our methodology to thousands of human kinetochore pair trajectories and report distinct signatures in temporal force profiles during directional switches. We found the K-fibre force to be the dominant force throughout oscillations, and the centromeric spring the smallest although it has the strongest directional switching signature. There is also structure throughout the metaphase plate, with a steeper PEF potential well towards the periphery and a concomitant reduction in plate thickness and oscillation amplitude. This data driven reverse engineering approach is sufficiently flexible to allow fitting of more complex mechanistic models; mathematical models of kinetochore dynamics can therefore be thoroughly tested on experimental data for the first time. Future work will now be able to map out how individual proteins contribute to kinetochore-based force generation and sensing.

To achieve proper cell division, newly duplicated chromosomes must be segregated into daughter cells with high fidelity. This occurs in mitosis where during the crucial metaphase stage chromosomes are aligned on an imaginary plate, called the metaphase plate. Chromosomes are attached to a structural scaffold—the mitotic spindle, which is composed of dynamic fibres called microtubules—by protein machines called kinetochores. Observation of kinetochores during metaphase reveals they undergo a series of forward and backward movements. The mechanical system generating this oscillatory motion is not well understood. By tracking kinetochores in live cell 3D confocal microscopy and reverse engineering their trajectories we decompose the forces acting on kinetochores into the three main force generating components. Kinetochore dynamics are dominated by K-fibre forces, although changes in the minor spring force over time suggests an important role in controlling directional switching. In addition, we show that the strength of forces can vary both spatially within cells throughout the plate and between cells.