Chromatin phase separated nanoregions explored by polymer cross-linker models and reconstructed from single particle trajectories.

Phase separated domains (PSDs) are ubiquitous in cell biology, representing nanoregions of high molecular concentration. PSDs appear at diverse cellular domains, such as neuronal synapses but also in eukaryotic cell nucleus, limiting the access of transcription factors and thus preventing gene expression. We develop a generalized cross-linker polymer model, to study PSDs: we show that increasing the number of cross-linkers induces a polymer condensation, preventing access of diffusing molecules. To investigate how the PSDs restrict the motion of diffusing molecules, we compute the mean residence and first escaping times. Finally, we develop a method based on mean-square-displacement of single particle trajectories to reconstruct the properties of PSDs from the continuum range of anomalous exponents. We also show here that PSD generated by polymers do not induces a long-range attracting field (potential well), in contrast with nanodomains at neuronal synapses. To conclude, PSDs can result from condensed chromatin organization, where the number of cross-linkers controls molecular access.

Multi-feature clustering of CTCF binding creates robustness for loop extrusion blocking and Topologically Associating Domain boundaries.

Topologically Associating Domains (TADs) separate vertebrate genomes into insulated regulatory neighborhoods that focus genome-associated processes. TADs are formed by Cohesin-mediated loop extrusion, with many TAD boundaries consisting of clustered binding sites of the CTCF insulator protein. Here we determine how this clustering of CTCF binding contributes to the blocking of loop extrusion and the insulation between TADs. We identify enrichment of three features of CTCF binding at strong TAD boundaries, consisting of strongly bound and closely spaced CTCF binding peaks, with a further enrichment of DNA-binding motifs within these peaks. Using multi-contact Nano-C analysis in cells with normal and perturbed CTCF binding, we establish that individual CTCF binding sites contribute to the blocking of loop extrusion, but in an incomplete manner. When clustered, individual CTCF binding sites thus create a stepwise insulation between neighboring TADs. Based on these results, we propose a model whereby multiple instances of temporal loop extrusion blocking create strong insulation between TADs.

Data-driven multiscale dynamical framework to control a pandemic evolution with non-pharmaceutical interventions.

Before the availability of vaccines, many countries have resorted multiple times to drastic social restrictions to prevent saturation of their health care system, and to regain control over an otherwise exponentially increasing COVID-19 pandemic. With the advent of data-sharing, computational approaches are key to efficiently control a pandemic with non-pharmaceutical interventions (NPIs). Here we develop a data-driven computational framework based on a time discrete and age-stratified compartmental model to control a pandemic evolution inside and outside hospitals in a constantly changing environment with NPIs. Besides the calendrical time, we introduce a second time-scale for the infection history, which allows for non-exponential transition probabilities. We develop inference methods and feedback procedures to successively recalibrate model parameters as new data becomes available. As a showcase, we calibrate the framework to study the pandemic evolution inside and outside hospitals in France until February 2021. We combine national hospitalization statistics from governmental websites with clinical data from a single hospital to calibrate hospitalization parameters. We infer changes in social contact matrices as a function of NPIs from positive testing and new hospitalization data. We use simulations to infer hidden pandemic properties such as the fraction of infected population, the hospitalisation probability, or the infection fatality ratio. We show how reproduction numbers and herd immunity levels depend on the underlying social dynamics.

Nanorheology of active-passive polymer mixtures differentiates between linear and ring polymer topology.

We study the motion of dispersed nanoprobes in entangled active-passive polymer mixtures. By comparing the two architectures of linear vs. unconcatenated and unknotted circular polymers, we demonstrate that novel, rich physics emerge. For both polymer architectures, nanoprobes of size smaller than the entanglement threshold of the solution move faster as activity is increased and more energy is pumped in the system. For larger nanoprobes, a surprising phenomenon occurs: while in linear solutions they move qualitatively as before, in active-passive ring solutions nanoprobes decelerate with respect to the purely passive conditions. We rationalize this effect in terms of the non-equilibrium, topology-dependent association (clustering) of nanoprobes to the cold component of the ring mixture reminiscent of the recently discovered [Weber et al., Phys. Rev. Lett., 2016, 116, 058301] phase separation in scalar active-passive mixtures. We conclude with a potential connection to the microrheology of the chromatin in the nuclei of the cells.

Chromatin stability generated by stochastic binding and unbinding of cross-linkers at looping sites revealed by Markov models.

Chromatin loops inside the nucleus can be stable for a very long time, which remains poorly understood. Such a time is crucial for chromatin organization maintenance and stability. We explore here several physical scenarios, where loop maintenance is due to diffusing cross-linkers (cohesin stabilized by two CTCF molecules) that can bind and unbind at the base of chromatin loops. Using a Markov chain approach to coarse-grain the binding and unbinding, we consider that a stable loop disappears when the last cross-linker is unbound. We derive expressions for this last passage time that we use to quantify the loop stability for various parameters, such as the chemical rate constant or the number of cross-linkers. The present analysis suggests that the balance between binding and unbinding events regulates the number of cross-linkers in place, based on a positive feed-back mechanism that stabilizes the loop over long-time. To conclude, we found that short- and long-lasting stable loops can vary from minutes to the entire cell cycle lifetime, when the number of cross-linkers increases from 1 to 10. This result suggests that a large spectrum of loop time scales is expected with such a few numbers of cross-linkers per local binding sites.

Microrheology of interphase chromosomes with spatial constraints: a computational study.

Chromatin fibers within the interior of the nucleus of the cell make stable interactions with the nucleoskeleton, an ensemble of 'extra-chromatin' structures which help ensuring genome stability. Although the role of these interactions appears crucial to the correct behavior of the cell, their impact on chromatin structure and dynamics remains to be elucidated. In order to tackle this important issue, in this work we introduce a simple polymer model for chromatin fibers in interphase which takes into account the two generic properties of chain-versus-chain mutual uncrossability and the presence of stable binding interactions to an extra-chromatin nuclear matrix. To study how these constraints affect chromatin structure from small to large scales, we employ extensive molecular dynamics computer simulations and we monitor the motion of nanoprobes of different sizes embedded within the polymer medium. Our results demonstrate that nanoprobes show hampered motion whenever their linear size becomes larger than chromatin stiffness. This transition is also displaying features which usually belong to the realm of glassy systems, namely long-tail correlations in the distribution functions of nanoprobe spatial displacements and heterogeneous behavior accompanied by ergodicity breaking.

The Ising model in swollen vs. compact polymers: Mean-field approach and computer simulations.

We study the properties of the classical Ising model with nearest-neighbor interaction for spins located at the monomers of long polymer chains in 2 and 3 dimensions. We compare results for two ensembles of polymers with very different single chain properties: 1) swollen, self-avoiding linear polymer chains in good solvent conditions and 2) compact, space-filling randomly branching polymers in melt. By employing a mean-field approach and Monte Carlo computer simulations, we show that swollen polymers cannot sustain an ordered phase. On the contrary, compact polymers may indeed produce an observable phase transition. Finally, we briefly consider the statistical properties of the ordered phase by comparing polymer chains within the same universality class but characterized by very different shapes.