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The Random First-Order Transition (RFOT) theory predicts that transport proceeds by the cooperative movement of particles in domains, whose sizes increase as a liquid is compressed above a characteristic volume fraction, ϕd. The rounded dynamical transition around ϕd, which signals a crossover to activated transport, is accompanied by a growing correlation length that is predicted to diverge at the thermodynamic glass transition density (>ϕd). Simulations and imaging experiments probed the single particle dynamics of mobile particles in response to pinning all the particles in a semi-infinite space or randomly pinning (RP) a fraction of particles in a liquid at equilibrium. The extracted dynamic length increases non-monotonically with a peak around ϕd, which not only depends on the pinning method but is also different from ϕd of the actual liquid. This finding is at variance with the results obtained using the small wavelength limit of a four-point structure factor for unpinned systems. To obtain a consistent picture of the growth of the dynamic length, one that is impervious to the use of RP, we introduce a multiparticle structure factor, Smpc(q,t), that probes collective dynamics. The collective dynamical length, calculated from the small wave vector limit of Smpc(q,t), increases monotonically as a function of the volume fraction in a glass-forming binary mixture of charged colloidal particles in both unpinned and pinned systems. This prediction, which also holds in the presence of added monovalent salt, may be validated using imaging experiments. 

Local stresses in a tissue, a collective property, links cell division and dynamics. 

Understanding the biophysical basis of protein aggregation is important in biology because of the potential link to several misfolding diseases. Although experiments have shown that protein aggregates adopt a variety of morphologies, the dynamics of their formation are less well characterized. Here, we introduce a minimal model to explore the dependence of the aggregation dynamics on the structural and sequence features of the monomers. Using simulations, we demonstrate that sequence complexity (codified in terms of word entropy) and monomer rigidity profoundly influence the dynamics and morphology of the aggregates. Flexible monomers with low sequence complexity (corresponding to repeat sequences) form liquid-like droplets that exhibit ergodic behavior. Strikingly, these aggregates abruptly transition to more ordered structures, reminiscent of amyloid fibrils, when the monomer rigidity is increased. In contrast, aggregates resulting from monomers with high sequence complexity are amorphous and display nonergodic glassy dynamics. The heterogeneous dynamics of the low and high-complexity sequences follow stretched exponential kinetics, which is one of the characteristics of glassy dynamics. Importantly, at nonzero values of the bending rigidities, the aggregates age with the relaxation times that increase with the waiting time. Informed by these findings, we provide insights into aging dynamics in protein condensates and contrast the behavior with the dynamics expected in RNA repeat sequences. Our findings underscore the influence of the monomer characteristics in shaping the morphology and dynamics of protein aggregates, thus providing a foundation for deciphering the general rules governing the behavior of protein condensates. 

Repeat RNA sequences self-associate to form condensates. Simulations of a coarse-grained single-interaction site model for (CAG)n (n = 30 and 31) show that the salt-dependent free energy gap, ΔGS, between the ground (perfect hairpin) and the excited state (slipped hairpin (SH) with one CAG overhang) of the monomer for (n even) is the primary factor that determines the rates and yield of self-assembly. For odd n, the free energy (GS) of the ground state, which is an SH, is used to predict the self-association kinetics. As the monovalent salt concentration, CS, increases, ΔGS and GS increase, which decreases the rates of dimer formation. In contrast, ΔGS for shuffled sequences, with the same length and sequence composition as (CAG)31, is larger, which suppresses their propensities to aggregate. Although demonstrated explicitly for (CAG) polymers, the finding of inverse correlation between the free energy gap and RNA aggregation is general. 

Compartment formation in interphase chromosomes is a result of spatial segregation between euchromatin and heterochromatin on a few megabase pairs (Mbp) scale. On the sub-Mbp scales, topologically associating domains (TADs) appear as interacting domains along the diagonal in the ensemble averaged Hi-C contact map. Hi-C experiments showed that most of the TADs vanish upon deleting cohesin, while the compartment structure is maintained, and perhaps even enhanced. However, closer inspection of the data reveals that a non-negligible fraction of TADs is preserved (P-TADs) after cohesin loss. Imaging experiments show that, at the single-cell level, TAD-like structures are presenteven without cohesin. To provide a structural basis for these findings, we first used polymer simulations to show that certain TADs with epigenetic switches across their boundaries survive after depletion of loops. More importantly, the three-dimensional structures show that many of the P-TADs have sharp physical boundaries. Informed by the simulations, we analyzed the Hi-C maps (with and without cohesin) in mouse liver and human colorectal carcinoma cell lines, which affirmed that epigenetic switches and physical boundaries (calculated using the predicted 3D structures using the data-driven HIPPS method that uses Hi-C as the input) explain the origin of the P-TADs. Single-cell structures display TAD-like features in the absence of cohesin that are remarkably similar to the findings in imaging experiments. Some P-TADs, with physical boundaries, are relevant to the retention of enhancer–promoter/promoter–promoter interactions. Overall, our study shows that preservation of a subset of TADs upon removing cohesin is a robust phenomenon that is valid across multiple cell lines. 

DNA−protein interactions are pervasive in a number of biophysical processes ranging from transcription and gene expression to chromosome folding. To describe the structural and dynamic properties underlying these processes accurately, it is important to create transferable computational models. Toward this end, we introduce Coarse-grained Force Field for Energy Estimation, COFFEE, a robust framework for simulating DNA− protein complexes. To brew COFFEE, we integrated the energy function in the self-organized polymer model with side-chains for proteins and the three interaction site model for DNA in a modular fashion, without recalibrating any of the parameters in the original force-fields. A unique feature of COFFEE is that it describes sequence−specific DNA−protein interactions using a statistical potential (SP) derived from a data set of high-resolution crystal structures. The only parameter in COFFEE is the strength (λDNAPRO) of the DNA−protein contact potential. For an optimal choice of λDNAPRO, the crystallographic B-factors for DNA−protein complexes with varying sizes and topologies are quantitatively reproduced. Without any further readjustments to the force-field parameters, COFFEE predicts scattering profiles that are in quantitative agreement with small-angle X-ray scattering experiments, as well as chemical shifts that are consistent with NMR. We also show that COFFEE accurately describes the salt-induced unraveling of nucleosomes. Strikingly, our nucleosome simulations explain the destabilization effect of ARG to LYS mutations, which do not alter the balance of electrostatic interactions but affect chemical interactions in subtle ways. The range of applications attests to the transferability of COFFEE, and we anticipate that it would be a promising framework for simulating DNA−protein complexes at the molecular length-scale. 

We compute the free energy of confinement F for a wormlike chain (WLC), with persistence length lp, that is confined to the surface of a cylinder of radius R under an external tension f using a mean field variational approach. For long chains, we analytically determine the behavior of the chain in a variety of regimes, which are demarcated by the interplay of lp, the Odijk deflection length (ld = (R2lp)1/3), and the Pincus length (lf = kBT/f, with kBT being the thermal energy). The theory accurately reproduces the Odijk scaling for strongly confined chains at f = 0, with F ∼ Ll−1/3p R−2/3. For moderate values of f, the Odijk scaling is discernible only when lp   R for strongly confined chains. Confinement does not significantly alter the scaling of the mean extension for sufficiently high tension. The theory is used to estimate unwrapping forces for DNA from nucleosomes.