Compression and Stretching of Confined Linear and Ring Polymers by Applying Force

We use Langevin dynamics to study the deformations of linear and ring polymers in different confinements by applying compression and stretching forces on their two sides. Our results show that the compression deformations are the results of an interplay among of polymer rigidity, degree of confinement, and force applied. When the applied force is beyond the threshold required for the buckling transition, the semiflexible chain under the strong confinement firstly buckles; then comes helical deformation. However, under the same force loading, the semiflexible chain under the weaker confinement exhibits buckling instability and shrinks from the folded ends/sides until it becomes three-folded structures. This happens because the strong confinement not only strongly reduces the buckling wavelength, but also increases the critical buckling force threshold. For the weakly confined polymers, in compression process, the flexible linear polymer collapses into condensed states under a small external force, whereas the ring polymer only shows slight shrinkage, due to the excluded volume interactions of two strands in the crowded states. These results are essential for understanding the deformations of the ring biomacromolecules and polymer chains in mechanical compression or driven transport.

Minimalistic 3D Chromatin Models: Sparse Interactions in Single Cells Drive the Chromatin Fold and Form Many-Body Units

Computational modeling of 3D chromatin plays an important role in understanding the principles of genome organization. We discuss methods for modeling 3D chromatin structures, with focus on a minimalistic polymer model which inverts population Hi-C into high-resolution, high-coverage single-cell chromatin conformations. Utilizing only basic physical properties such as nuclear volume and no adjustable parameters, this model uncovers a few specific Hi-C interactions (15-35 for enhancer-rich loci in human cells) that can fold chromatin into individual conformations consistent with single-cell imaging, Dip-C, and FISH-measured genomic distance distributions. Aggregating an ensemble of conformations also reproduces population Hi-C interaction frequencies. Furthermore, this single-cell modeling approach allows quantification of structural heterogeneity and discovery of specific many-body units of chromatin interactions. This minimalistic 3D chromatin polymer model has revealed a number of insights: 1) chromatin scaling rules are a result of volume-confined polymers; 2) TADs form as a byproduct of 3D chromatin folding driven by specific interactions; 3) chromatin folding at many loci is driven by a small number of specific interactions; 4) cell subpopulations equipped with different chromatin structural scaffolds are developmental stage-dependent; and 5) characterization of the functional landscape and epigenetic marks of many-body units which are simultaneously spatially co-interacting within enhancer-rich, euchromatic regions. The implications of these findings in understanding the genome structure-function relationship are also discussed.

Using Monte Carlo to Simulate Complex Polymer Systems: Recent Progress and Outlook

Metropolis Monte Carlo has been employed with remarkable success over the years to simulate the dense phases of polymer systems. Owing, in particular, to the freedom it provides to accelerate sampling in phase space through the clever design and proper implementation of even unphysical moves that take the system completely away from its natural trajectory, and despite that it cannot provide any direct information about dynamics, it has turned to a powerful simulation tool today, often viewed as an excellent alternative to the other, most popular method of Molecular Dynamics. In the last years, Monte Carlo has advanced considerably thanks to the design of new moves or to the efficient implementation of existing ones to considerably more complex systems than those for which these were originally proposed. In this short review, we highlight recent progress in the field (with a clear emphasis in the last 10 years or so) by presenting examples from applications of the method to several systems in Soft Matter, such as polymer nanocomposites, soft nanostructured materials, confined polymers, polymer rings and knots, hydrogels and networks, crystalline polymers, and many others. We highlight, in particular, extensions of the method to non-equilibrium systems (e.g., polymers under steady shear flow) guided by non-equilibrium thermodynamics and emphasize the importance of hybrid modeling schemes (e.g., coupled Monte Carlo simulations with field theoretic calculations). We also include a short section discussing some key remaining challenges plus interesting future opportunities.