Bridging algorithms are global Monte Carlo moves which allow for an efficient sampling of single polymer chains. In this manuscript we discuss the adaptation of three bridging algorithms from lattice to continuum models, and give details on the corrections to the acceptance rules which are required to fulfill detailed balance. For the first time we are able to compare the efficiency of the moves by analyzing the occurrence of knots in globular states. For a flexible homopolymer chain of length N=1000, independent configurations can be generated up to two orders of magnitude faster than with slithering snake moves.
The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter depending on the knot kind is an amplitude such that relative probabilities of knots do not vary with the temperature $T$, in the limit of long chains. We arrive at this conclusion by simulating interacting self-avoiding rings at low $T$ on the cubic lattice, both with unrestricted topology and with setups where the globule is divided by a slip link in two loops…
Macroscopic properties of suspensions, such as those composed of globular particles (e.g., colloidal or macromolecular), can be tuned by controlling the equilibrium aggregation of the particles. We examine how aggregation -- and, hence, macroscopic properties -- can be controlled in a system composed of both globular particles and long, flexible polymer chains that reversibly bind to one another. We base this on a minimal statistical mechanical model of a single aggregate in which the polymer chain is treated either as ideal or self-avoiding, and, in addition, the globular particles are taken …
Recent experimental results suggest that the E. coli chromosome feels a self-attracting interaction of osmotic origin, and is condensed in foci by bridging interactions. Motivated by these findings, we explore a generic modeling framework combining solely these two ingredients, in order to characterize their joint effects. Specifically, we study a simple polymer physics computational model with weak ubiquitous short-ranged self attraction and stronger sparse bridging interactions. Combining theoretical arguments and simulations, we study the general phenomenology of polymer collapse induced by…
There are many proteins or protein complexes which have multiple DNA binding domains. This allows them to bind to multiple points on a DNA molecule (or chromatin fibre) at the same time. There are also many proteins which have been found to be able to compact DNA in vitro, and many others have been observed in foci or puncta when fluorescently labelled and imaged in vivo. In this work we study, using coarse-grained Langevin dynamics simulations, the compaction of polymers by simple model proteins and a phenomenon known as the "bridging-induced attraction". The latter is a mechanism observed in…
Topological constraints can affect both equilibrium and dynamic properties of polymer systems, and can play a role in the organization of chromosomes. Despite many theoretical studies, the effects of topological constraints on the equilibrium state of a single compact polymer have not been systematically studied. Here we use simulations to address this longstanding problem. We find that sufficiently long unknotted polymers differ from knotted ones in the spatial and topological states of their subchains. The unknotted globule has subchains that are mostly unknotted and form asymptotically comp…
Ferrogels and magnetic elastomers differentiate themselves from other materials by their unique capability of reversibly changing shape and mechanical properties under the influence of an external magnetic field. A crucial issue in the study of these outstanding materials is the interaction between the mesoscopic magnetic particles and the polymer matrix in which they are embedded. Here we analyze interactions between two such particles connected by a polymer chain, a situation representative for particle-crosslinked magnetic gels. To make a first step towards a scale-bridging description of t…
Swollen Micelles Plus Hydrophobically Modified Hydrosoluble Polymers in Aqueous Solutions: Decoration Versus Bridging. a Small Angle Neutron Scattering Study
在本文中，我们研究了水包油微乳液的液滴之间引入的有效相互作用后，逐步加入疏水改性的水溶性聚（环氧乙烷）-PEO基本上使用小角中子散射。为了讨论装饰和桥接的液滴的相对重要性，我们比较了类似的样品与添加的PEO接枝在两端与疏水C12 H 25链（PEO-2 m）或添加的PEO接枝在一端仅与C12 H 25链（PEO-m）。PEO-m或PEO-2 m通过它们的疏水末端吸附到液滴上，并且发现当每个液滴添加多达40个疏水C12 H25链时，液滴保持它们的形式和尺寸。当液滴体积分数小于10%时，PEO-m和PEO-2 m引入的有效相互作用有很大的不同：PEO-m引入的是排斥相互作用，而PEO-2 m引入的是吸引相互作用。当加入足够量的PEO-2 m时，这种有吸引力的相互作用导致在低体积分数范围内的缔合相分离。
Understanding the transmission of nanoscale forces in the pico-to-nanonewton range is important in polymer physics. While physical approaches have limitations in analyzing the local force distribution in condensed environments, chemical analysis using force probes is promising. However, there are stringent requirements for probing the local forces generated before structural damage. The magnitude of those forces corresponds to the range below covalent bond scission (from 200 pN to several nN) and above thermal fluctuation (several pN). Here, we report a conformationally flexible dual-fluoresce…
We introduce a powerful Monte Carlo (MC) algorithm for the atomistic simulation of bulk models of oligo- and poly-thiophenes by redesigning MC moves originally developed for considerably simpler polymer structures and architectures, such as linear and branched polyethylene, to account for the ring structure of the thiophene monomer. Elementary MC moves implemented include bias reptation of an end thiophene ring, flip of an internal thiophene ring, rotation of an end thiophene ring, concerted rotation of three thiophene rings, rigid translation of an entire molecule, rotation of an entire molec…
The widely used double-bridging hybrid (DBH) method for equilibrating simulated entangled polymer melts [R. Auhl et al., J. Chem. Phys. v. 119, p. 12718, 2003] loses its effectiveness as chain stiffness increases into the semiflexible regime because the energy barriers associated with double-bridging Monte Carlo moves become prohibitively high. Here we overcome this issue by combining DBH with the use of core-softened pair potentials. This reduces the energy barriers substantially, allowing us to equilibrate melts with $N \simeq 40 N_e$ and chain stiffnesses all the way up to the isotropic-nem…
Via molecular dynamics simulation with Langevin thermostat we study the structure and dynamics of a flexible bead-spring active polymer model after a quench from good to poor solvent conditions. The self propulsion is introduced via a Vicsek-like alignment activity rule which works on each individual monomer in addition to the standard attractive and repulsive interactions among the monomeric beads. We observe that the final conformations are in the globular phase for the passive as well as for all the active cases. By calculating the bond length distribution, radial distribution function, etc…
We study the behavior of a flexible polymer chain in the presence of a low-molecular weight solvent in the vicinity of a liquid-gas critical point within the framework of a self-consistent field theory. The total free energy of the dilute polymer solution is expressed as a function of the radius of gyration of the polymer and the average solvent number density within the gyration volume at the level of the mean-field approximation. Varying the strength of attraction between polymer and solvent we show that two qualitatively different regimes occur at the liquid-gas critical point. In case of w…
Molecular dynamics simulations have been performed on pure liquid water, aqueous solutions of sodium chloride, and polymer solutions exposed to a strong external electric field with the goal to gain molecular insight into the structural response to the field. Several simulation methodologies have been used to elucidate the molecular mechanisms of the processes leading to the formation of liquid bridges and jets (in the production of nanofibers). It is shown that in the established nanoscale structures, the molecules form a chain with their dipole moments oriented parallel to the applied field …
Polymer brushes normally swell in a good solvent and collapse in a poor solvent. An abnormal response of polymer brushes, so-called co-nonsolvency, is the phenomenon where the brush counter-intuitively collapses in a good solvent mixture. In this work, we employed molecular dynamics simulations to investigate the structural properties of the grafted polymers on the occurrence of co-nonsolvency. Brushes with various grafting densities were considered to study the effect of topological excluded volumes on the co-nonsolvency. We found that the brush height follows a novel scaling behavior of the …
Polymer materials have the characteristic feature that they are multiscale systems by definition. Already the description of a single molecules involves a multitude of different scales, and cooperative processes in polymer assemblies are governed by the interplay of these scales. Polymers have been among the first materials for which systematic multiscale techniques were developed, yet they continue to present extraordinary challenges for modellers. In this perspective, we review popular models that are used to describe polymers on different scales and discuss scale bridging strategies such as…
We model the environment of eukaryotic nuclei by representing macromolecules by only their entropic properties, with globular molecules represented by spherical colloids and flexible molecules by polymers. We put particular focus on proteins with both globular and intrinsically disordered regions, which we represent with `tadpole' constructed by grafting single polymers and colloids together. In Monte Carlo simulations we find these tadpoles support phase separation via depletion flocculation, and demonstrate several surfactant behaviours, including being found preferentially at interfaces and…
By means of molecular dynamics simulations we investigate the formation of single-chain nanoparticles through intramolecular cross-linking of polymer chains, in the presence of their precursors acting as purely steric crowders in concentrated solution. In the case of the linear precursors, the structure of the resulting SCNPs is weakly affected by the density at which the synthesis is performed. Crowding has significant effects if ring precursors are used: higher concentrations lead to the formation of SCNPs with more compact and spherical morphologies. Such SCNPs retain in the swollen state (…
We study the lower critical solution temperature (LCST) in thermoresponsive polymer solutions by means of a coarse grained single polymer chain simulation and a theoretical approach. The simulation model includes solvent explicitly and thus accounts for solvent interactions and entropy directly. The theoretical model consists of a single chain polymer in an implicit solvent where the effect of solvent is included through the intra-polymer solvophobic potential proposed by Kolomeisky and Widom. Our results indicate that the LCST behavior is determined by the competition between the mean energy …
Collapse of the polymer chain upon the sharp decrease of solvent quality is studied. During collapse, any pair of polymer units appearing in a sufficiently close vicinity in space has the possibility with a certain probability to form an irreversible crosslink, thereby preventing the interpenetration of chain material between the forming clusters. Globular structures having different spatial chain packing at various scales are obtained by computer simulations. It is shown that the dependence of probability of contact between two monomers in space , where s is a distance between monomers along …
We study the Brownian dynamics of flexible and semiflexible polymer chains densely grafted on a flat substrate, upon rapid quenching of the system when the quality of solvent becomes poor and chains attempt collapse into a globular state. The collapse process of such a polymer brush differs from individual chains, both in its kinetics and its structural morphology. We find that the resulting collapsed brush does not form a homogeneous dense layer, in spite of all chain monomers equally attracting each other via a model Lennard-Jones potential. Instead, a very distinct inhomogeneous density dis…
We review the mechanism and consequences of the "bridging-induced attraction", a generic biophysical principle which underpins some existing models for chromosome organisation in 3-D. This attraction, which was revealed in polymer physics-inspired computer simulations, is a generic clustering tendency arising in multivalent chromatin-binding proteins, and it provides an explanation for the biogenesis of nuclear bodies and transcription factories via microphase separation. Including post-translational modification reactions involving these multivalent proteins can account for the fast dynamics …
Single-chain nanoparticles (SCNPs) are a new class of macromolecular objects, synthesized through purely intramolecular cross-linking of single polymer chains. We use a multi-scale hydrodynamics simulation approach to study, for the first time, SCNPs under shear flow. We investigate the case of irreversible SCNPs (permanent cross-links) in dilute solution. SCNPs emerge as a novel class of macromolecular objects with response to shear distinct from other systems such as linear chains, star polymers, rings or dendrimers. This is evidenced by the observed set of scaling exponents for the shear ra…
In the paper we investigate statistical and topological properties of fractional Brownian polymer chains, equipped with the short-range volume interactions. The attention is paid to statistical properties of collapsed conformations with the fractal dimension $D_f\ge 2$ in the three-dimensional space, which are analyzed both numerically and \textit{via} the mean-field Flory approach. Our study is motivated by an attempt to mimic the conformational statistics of collapsed unknotted polymer rings, which are known to form compact hierarchical crumpled globules (CG) with $D_f=3$ at large scales. Re…
By means of Langevin dynamics simulations, we investigate the gel formation of randomly functionalized polymers in solution, with the ability to form both intra- and intermolecular reversible bonds. Under highly dilute conditions, these polymers form soft nano-objects (so-called single-chain nanoparticles, SCNPs), resulting from the purely intramolecular cross-linking of the reactive functional groups. Here we show that the competition between intra- and intermolecular bonds at finite concentration is governed by a delicate balance of various entropic contributions and leads to a density depen…
Polymeric single-chain nanoparticles (SCNPs) are soft nano-objects synthesized by purely intramolecular cross-linking of single polymer chains. By means of computer simulations, we investigate the conformational properties of SCNPs as a function of the bending stiffness of their linear polymer precursors. We investigate a broad range of characteristic ratios from the fully flexible case to those typical of bulky synthetic polymers. Increasing stiffness hinders bonding of groups separated by short contour distances and increases looping over longer distances, leading to more compact nanoparticl…
We perform simulations of a system containing simple model proteins and a polymer representing chromatin. We study the interplay between protein-protein and protein-chromatin interactions, and the resulting condensates which arise due to liquid-liquid phase separation, or a via a 'bridging-induced attraction' mechanism. For proteins which interact multivalently, we obtain a phase diagram which includes liquid-like droplets, droplets with absorbed polymer, and coated polymer regimes. Of particular interest is a regime where protein droplets only form due to interaction with the polymer; here, u…
One of the most important problems in development is how epigenetic domains can be first established, and then maintained, within cells. To address this question, we propose a framework which couples 3D chromatin folding dynamics, to a "recolouring" process modelling the writing of epigenetic marks. Because many intra-chromatin interactions are mediated by bridging proteins, we consider a "two-state" model with self-attractive interactions between two epigenetic marks which are alike (either active or inactive). This model displays a first-order-like transition between a swollen, epigeneticall…
