Kinetic Signature of Cooperativity in the Irreversible Collapse of a Polymer

A mean-field theory for predicting single polymer collapse induced by neutral crowders

Macromolecular crowding can induce the collapse of a single long polymer into a globular form due to depletion forces of entropic nature. This phenomenon has been shown to play a significant role in compacting the genome within the bacterium Escherichia coli into a well-defined region of the cell known as the nucleoid. Motivated by the biological significance of this process, numerous theoretical and computational studies have searched for the primary determinants of the behavior of polymer-crowder phases. However, our understanding of this process remains incomplete and there is debate on a quantitatively unified description. In particular, different simulation studies with explicit crowders have proposed different order parameters as potential predictors for the collapse transition. In this work, we present a comprehensive analysis of published simulation data obtained from different sources. Based on the common behavior we find in this data, we develop a unified phenomenological model that we show to be predictive. Finally, to further validate the accuracy of the model, we conduct new simulations on polymers of various sizes, and investigate the role of jamming of the crowders.

Transcription-induced domains form the elementary constraining building blocks of bacterial chromosomes

Transcription generates local topological and mechanical constraints on the DNA fiber, leading to the generation of supercoiled chromosome domains in bacteria. However, the global impact of transcription on chromosome organization remains elusive, as the scale of genes and operons in bacteria remains well below the resolution of chromosomal contact maps generated using Hi-C (~5-10 kb). Here we combined sub-kb Hi-C contact maps and chromosome engineering to visualize individual transcriptional units. We show that transcriptional units form discrete three-dimensional transcription-induced domains that impose mechanical and topological constraints on their neighboring sequences at larger scales, modifying their localization and dynamics. These results show that transcriptional domains constitute primary building blocks of bacterial chromosome folding and locally impose structural and dynamic constraints.

Karyotype engineering reveals spatio-temporal control of replication firing and gene contacts

Eukaryotic genomes vary in terms of size, chromosome number, and genetic complexity. Their temporal organization is complex, reflecting coordination between DNA folding and function. Here, we used fused karyotypes of budding yeast to characterize the effects of chromosome length on nuclear architecture. We found that size-matched megachromosomes expand to occupy a larger fraction of the enlarged nucleus. Hi-C maps reveal changes in the three-dimensional structure corresponding to inactivated centromeres and telomeres. De-clustering of inactive centromeres results in their loss of early replication, highlighting a functional correlation between genome organization and replication timing. Repositioning of former telomere-proximal regions on chromosome arms exposed a subset of contacts between flocculin genes. Chromatin reorganization of megachromosomes during cell division remained unperturbed, and it revealed that centromere-rDNA contacts in anaphase, extending over 0.3 Mb on wild-type chromosome, cannot exceed ∼1.7 Mb. Our results highlight the relevance of engineered karyotypes to unveiling relationships between genome organization and function.

Kinetics of charged polymer collapse in poor solvents

Extensive molecular dynamics simulations, using simple charged polymer models, have been employed to probe the collapse kinetics of a single flexible polyelectrolyte (PE) chain under implicit poor solvent conditions. We investigate the role of the charged nature of PE chain (A), valency of counterions (Z) on the kinetics of such PE collapse. Our study shows that the collapse kinetics of charged polymers are significantly different from those of the neutral polymer and that the finite-size scaling behavior of PE collapse times does not follow the Rouse scaling as observed in the case of neutral polymers. The critical exponent for charged PE chains is found to be less than that of neutral polymers and also exhibits dependence on counterion valency. The coarsening of clusters along the PE chain suggests a multi-stage collapse and exhibits opposite behavior of exponents compared to neutral polymers: faster in the early stages and slower in the later stages of collapse.

Learning heterogenous reaction rates from stochastic simulations

Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by complex dynamical systems reproducing spatial movements of molecules and their collisions. Such molecular dynamics systems may implicitly capture intricate phenomena that affect reaction rates but are not accounted for in the macroscopic models. In this work we present a data assimilation procedure for learning nonhomogeneous kinetic parameters from molecular simulations with many simultaneously reacting species. The learned parameters can then be plugged into the deterministic reaction rate equations to predict long time evolution of the macroscopic system. In this way, our procedure discovers an effective differential equation for reaction kinetics. To demonstrate the procedure, we upscale the kinetics of a molecular system that forms a complex covalently bonded network severely interfering with the reaction rates. Incidentally, we report that the kinetic parameters of this system feature peculiar time and temperature dependences, whereas the probability of a network strand to close a cycle follows a universal distribution.

Supercoiled DNA and non-equilibrium formation of protein complexes: A quantitative model of the nucleoprotein ParBS partition complex

ParABS, the most widespread bacterial DNA segregation system, is composed of a centromeric sequence, parS, and two proteins, the ParA ATPase and the ParB DNA binding proteins. Hundreds of ParB proteins assemble dynamically to form nucleoprotein parS-anchored complexes that serve as substrates for ParA molecules to catalyze positioning and segregation events. The exact nature of this ParBS complex has remained elusive, what we address here by revisiting the Stochastic Binding model (SBM) introduced to explain the non-specific binding profile of ParB in the vicinity of parS. In the SBM, DNA loops stochastically bring loci inside a sharp cluster of ParB. However, previous SBM versions did not include the negative supercoiling of bacterial DNA, leading to use unphysically small DNA persistences to explain the ParB binding profiles. In addition, recent super-resolution microscopy experiments have revealed a ParB cluster that is significantly smaller than previous estimations and suggest that it results from a liquid-liquid like phase separation. Here, by simulating the folding of long (≥ 30 kb) supercoiled DNA molecules calibrated with realistic DNA parameters and by considering different possibilities for the physics of the ParB cluster assembly, we show that the SBM can quantitatively explain the ChIP-seq ParB binding profiles without any fitting parameter, aside from the supercoiling density of DNA, which, remarkably, is in accord with independent measurements. We also predict that ParB assembly results from a non-equilibrium, stationary balance between an influx of produced proteins and an outflux of excess proteins, i.e., ParB clusters behave like liquid-like protein condensates with unconventional “leaky” boundaries.

In bacteria, faithful genome inheritance requires the two replicated DNA molecules to be segregated at the opposite halves of the cell. ParABS, the most widespread bacterial DNA segregation system, is composed of a centromere sequence, parS, and two proteins, the ParA ATPase and the ParB DNA binding protein. Hundreds of ParB assemble dynamically to form clusters around parS, which then serve as substrates for ParA molecules to catalyze the positioning and segregation events. The nature of these clusters and their interaction with DNA have remained elusive. Here, we propose a realistic minimal model that captures quantitatively the peculiar DNA binding profile of ParB in the vicinity of parS in Escherichia coli. From the viewpoint of DNA, the only fitting parameter is the in vivo supercoiling density resulting from the removal of DNA helices by toposiomerases, which is in accord with previous independent estimations. From the viewpoint of ParB clusters, we predict that they behave like liquid-like protein condensates with unconventional boundaries. Namely, we predict boundaries to be leaky (i.e. not sharp) as a result of the non-equilibrium protein production, diffusion and dilution. Altogether, our work provides novel insights into bacterial DNA organization and intracellular liquid-liquid phase separation.

Cross-linker mediated compaction and local morphologies in a model chromosome

Chromatin and associated proteins constitute the highly folded structure of chromosomes. We consider a self-avoiding polymer model of the chromatin, segments of which may get cross-linked via protein binders that repel each other. The binders cluster together via the polymer mediated attraction, in turn, folding the polymer. Using molecular dynamics simulations, and a mean field description, we explicitly demonstrate the continuous nature of the folding transition, characterized by unimodal distributions of the polymer size across the transition. At the transition point the chromatin size and cross-linker clusters display large fluctuations, and a maximum in their negative cross-correlation, apart from a critical slowing down. Along the transition, we distinguish the local chain morphologies in terms of topological loops, inter-loop gaps, and zippering. The topologies are dominated by simply connected loops at the criticality, and by zippering in the folded phase.

Pearl-Necklace-Like Local Ordering Drives Polypeptide Collapse

The collapse of the polypeptide backbone is an integral part of protein folding. Using polyglycine as a probe, we explore the nonequilibrium pathways of protein collapse in water. We find that the collapse depends on the competition between hydration effects and intrapeptide interactions. Once intrapeptide van der Waal interactions dominate, the chain collapses along a nonequilibrium pathway characterized by formation of pearl-necklace-like local clusters as intermediates that eventually coagulate into a single globule. By describing this coarsening through the contact probability as a function of distance along the chain, we extract a time-dependent length scale that grows in a linear fashion. The collapse dynamics is characterized by a dynamical critical exponent z ≈ 0.5 that is much smaller than the values of z = 1–2 reported for nonbiological polymers. This difference in the exponents is explained by the instantaneous formation of intrachain hydrogen bonds and local ordering that may be correlated with the observed fast folding times of proteins.

Improved inference of chromosome conformation from images of labeled loci

We previously published a method that infers chromosome conformation from images of fluorescently-tagged genomic loci, for the case when there are many loci labeled with each distinguishable color.  Here we build on our previous work and improve the reconstruction algorithm to address previous limitations.  We show that these improvements 1) increase the reconstruction accuracy and 2) allow the method to be used on large-scale problems involving several hundred labeled loci.  Simulations indicate that full-chromosome reconstructions at 1/2 Mb resolution are possible using existing labeling and imaging technologies.  The updated reconstruction code and the script files used for this paper are available at:  https://github.com/heltilda/align3d.

DamC reveals principles of chromatin folding in vivo without crosslinking and ligation

Current understanding of chromosome folding largely relies on chromosome conformation capture (3C)-based experiments, where chromosomal interactions are detected as ligation products after chromatin crosslinking. To measure chromosome structure in vivo, quantitatively and without crosslinking and ligation, we implemented a modified version of DamID named DamC, which combines DNA-methylation based detection of chromosomal interactions with next-generation sequencing and biophysical modelling of methylation kinetics. DamC performed in mouse embryonic stem cells provides the first in vivo validation of the existence of topologically associating domains (TADs), CTCF loops and confirms 3C-based measurements of the scaling of contact probabilities. Combining DamC with transposon-mediated genomic engineering shows that new loops can be formed between ectopic and endogenous CTCF sites, which redistributes physical interactions within TADs. DamC provides the first crosslinking- and ligation-free demonstration of the existence of key structural features of chromosomes and provides novel insights into how chromosome structure within TADs can be manipulated.