We investigate a flexible polymer chain made up of chiral active Brownian particles in two dimensions using computer simulations. In the presence of chiral active Brownian forces, the radius of gyration of the chain reduces significantly. We further identify the formation of spirals using the tangent-tangent correlation to characterize the internal structure of the chain. The polymer chain forms a pair of spirals with opposite spiral turns on both ends of the polymer. We compute the number of turns of both spirals, and find that the total number of turns increases with angular frequency as well as P{é}clet number. However, the spirals become weak and the number of turns decreases at a very high P{é}clet number. We draw a phase diagram using the turn number. The end-to-end correlation displays oscillatory behavior, which signifies the rotational dynamics of the chain. We quantify the rotation frequency from the end-to-end vector, which follows a power law behavior with exponent $3/2$. We also provide a scaling relation between the radius of gyration and the chain length, and the exponent decreases significantly in the presence of chiral active forces.
Elucidating versatile configurations of spiral folding, and investigating the deployment performance is of relevant interest to extend the applicability of deployable membranes towards large-scale and functional configurations. In this paper we propose new schemes to package flat and curved membranes of finite thickness by using multiple spirals, whose governing equations render folding lines by juxtaposing spirals and by accommodating membrane thickness. Our experiments using a set of topologically distinct flat and curved membranes deployed by tensile forces applied in the radial and circumf…
By simulating the first order globule-crystal transition of a flexible homopolymer chain, both by collision dynamics and Monte Carlo with non-kinetic moves, we show that the effective and the thermodynamic transition temperatures are different and we propose a way of quantifying the kinetic hindering. We then also observe that the top eigenvalue in the spectrum of the dynamical (contact or adjacency) matrix provides insight into the ensembles of folding and unfolding trajectories, and may be a suitable additional reaction coordinate for the folding transition of chain molecules.
Worm-like filaments that are propelled homogeneously along their tangent vector are studied by Brownian dynamics simulations. Systems in two dimensions are investigated, corresponding to filaments adsorbed to interfaces or surfaces. A large parameter space covering weak and strong propulsion, as well as flexible and stiff filaments is explored. For strongly propelled and flexible filaments, the free-swimming filaments spontaneously form stable spirals. The propulsion force has a strong impact on dynamic properties, such as the rotational and translational mean square displacement and the rate …
In recent past, experiments and simulations have suggested that apart from the solvent friction, friction arising from the protein itself plays an important role in protein folding by affecting the intra-chain loop formation dynamics. This friction is termed as internal friction in the literature. Using a flexible Gaussian chain with internal friction we analyze the intra- chain reconfiguration and loop formation times for all three topology classes namely end-to- end, end-to-interior and interior-to-interior. In a nutshell, bypassing expensive simulations we show how simple models like that o…
Many small proteins fold via a first-order "all-or-none" transition directly from an expanded coil to a compact native state. Here we study an analogous direct freezing transition from an expanded coil to a compact crystallite for a simple flexible homopolymer. Wang-Landau sampling is used to construct the 1D density of states for square-well chains of length 128. Analysis within both the micro-canonical and canonical ensembles shows that, for a chain with sufficiently short-range interactions, the usual polymer collapse transition is preempted by a direct freezing or "folding" transition. A 2…
Coarse-grained (lattice-) models have a long tradition in aiding efforts to decipher the physical or biological complexity of proteins. Despite the simplicity of these models, however, numerical simulations are often computationally very demanding and the quest for efficient algorithms is as old as the models themselves. Expanding on our previous work [T. Wüst and D. P. Landau, Phys. Rev. Lett. 102, 178101 (2009)], we present a complete picture of a Monte Carlo method based on Wang-Landau sampling in combination with efficient trial moves (pull, bond-rebridging and pivot moves) which is partic…
We study the dynamics of self-propelled chains with the excluded volume interaction via the Brownian dynamics simulation, in which the bending elasticity of chains is varied. The changes of the bending elasticity lead to various characteristics of the clustering behavior in the short-chain-only system. When a long self-propelled chain is mixed with these short chains, it can fold into the spiral-coil, a steadily rotating spiral conformation, either at a high density of short chains or at a low density if the long chain itself is sufficiently flexible. Our results qualitatively support the spec…
We investigate the crystallization mechanism of a single, flexible homopolymer chain with short range attractions. For a sufficiently narrow attractive well, the system undergoes a first-order like freezing transition from an expanded disordered coil to a compact crystalline state. Based on a maximum likelihood analysis of committor values computed for configurations obtained by Wang-Landau sampling, we construct a non-linear string reaction coordinate for the coil-to-crystal transition. In contrast to a linear reaction coordinate, the string reaction coordinate captures the effect of differen…
We investigate the crystallization of a single, flexible homopolymer chain using transition path sampling (TPS). The chain consists of N identical spherical monomers evolved according to Langevin dynamics. While neighboring monomers are coupled via harmonic springs, the non-neighboring monomers interact via a hard core and a short-ranged attractive potential. For a sufficiently small interaction range λ, the system undergoes a first-order freezing transition from an expanded, disordered phase to a compact crystalline state. Using a new shooting move tailored to polymers combined with a committ…
Despite their considerable practical and biological applications, the link between molecular properties, assembly conditions and self-organized structure in confined polymer solutions remains elusive. Here, we explore the lyotropic nematic ordering of semi-flexible chains in spherical confinement for multiple contour lengths across a wide regime of concentrations. We uncover an original crossover from two distinct quadrupolar states, both characterized by regular tetrahedral patterns of surface topological defects, to either longitudinal, latitudinal or spontaneously-twisted bipolar structures…
The motion of active polymers in a porous medium is shown to depend critically on flexibilty, activity and degree of polymerization. For given Peclet number, we observe a transition from localisation to diffusion as the stiffness of the chains is increased. Whereas stiff chains move almost unhindered through the porous medium, flexible ones spiral and get stuck. Their motion can be accounted for by the model of a continuous time random walk with a renewal process corresponding to unspiraling. The waiting time distribution is shown to develop heavy tails for decreasing stiffness, resulting in s…
We map out the solid-state morphologies formed by model soft-pearl-necklace polymers as a function of bending stiffness $k_b$ spanning the range from fully flexible to rodlike chains. The ratio of Kuhn length to bead diameter ($l_K/r_0$) increases monotonically with increasing $k_b$ and yields a one-parameter model that relates chain shape to bulk morphology and yields insights into the packing of anisotropic particles. In the flexible limit, monomers occupy the sites of close-packed crystallites while chains retain random-walk-like order. In the rodlike limit, nematic chain ordering typical o…
The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping-unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slow down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive e…
We systematically explore the self-assembly of semi-flexible polymers in deformable spherical confinement across a wide regime of chain stiffness, contour lengths and packing fractions by means of coarse-grained molecular dynamics simulations. Compliant, DNA-like filaments are found to undergo a continuous crossover from two distinct surface-ordered quadrupolar states, both characterized by tetrahedral patterns of topological defects, to either longitudinal or latitudinal bipolar structures with increasing polymer concentrations. These transitions, along with the intermediary arrangements that…
Using data from contact maps of the DNA-polymer of $E. Coli$ (at kilobase pair resolution) as an input to our model, we introduce cross-links between monomers in a bead-spring model of a ring polymer at very specific points along the chain. By suitable Monte Carlo Simulations, we show that the presence of these cross-links leads to a particular architecture and organization of the chain at large (micron) length scales of the DNA. We also investigate the structure of a ring polymer with an equal number of cross-links at random positions along the chain. We find that though the polymer does get …
We study the equilibrium properties of a single flexible homopolymers where consecutive monomers are represented by impenetrable hard spherical beads tangential to each other, and non-consecutive monomers interact via a square-well potential. To this aim, we use both replica exchange canonical simulations and micro-canonical Wang-Landau techniques. We perform a close comparative analysis of the corresponding results, and find perfect agreement between the two methods as well as the past results. The model is then refined in two different directions. By allowing partial overlapping between cons…
