Folding/unfolding kinetics on a semiflexible polymer chain (original) (raw)

Folding and unfolding kinetics of a single semiflexible polymer

Physical review. E, Statistical, nonlinear, and soft matter physics, 2008

We investigate theoretically the kinetics of the folding transition of a single semiflexible polymer. In the folding transition, the growth rate decreases with an increase in the number of monomers in the collapsed domain, suggesting that the main contribution to dissipation is from the motion of the domain. In the unfolding transition, the dynamic scaling exponents 1/8 and 1/4 were determined for the disentanglement and relaxation steps, respectively. We performed Langevin dynamics simulations to test our theory. It is found that our theory is in good agreement with simulations. We also propose the kinetics of the transitions in the presence of a hydrodynamic interaction.

Morphological variation in a toroid generated from a single polymer chain

The Journal of Chemical Physics, 2005

A single semiflexible polymer chain folds into a toroidal object under poor solvent conditions. In this study, we examined the morphological change in such a toroidal state as a function of the width and stiffness of the chain together with the surface energy, which characterizes the segmental interaction parameter. Change s in the thickness and outer/inner radius are interpreted in terms of these parameters. Our theoretical expectation corresponds to the actual morphological changes i n a single giant DNA molecule as observed by electron microscopy.

Different pathways in mechanical unfolding/folding cycle of a single semiflexible polymer

The European Physical Journal E, 2005

Kinetics of conformational change of a semiflexible polymer under mechanical external field were investigated with Langevin dynamics simulations. It is found that a semiflexible polymer exhibits large hysteresis in mechanical folding/unfolding cycle even with a slow operation, whereas in a flexible polymer, the hysteresis almost disappears at a sufficiently slow operation. This suggests that the essential features of the structural transition of a semiflexible polymer should be interpreted at least on a two-dimensional phase space. The appearance of such large hysteresis is discussed in relation to different pathways in the loading and unloading processes. By using a minimal twovariable model, the hysteresis loop is described in terms of different pathways on the transition between two stable states. 87.15.La,05.70.Fh

“Raindrop” Coalescence of Polymer Chains during Coil–Globule Transition

Macromolecules, 2013

We approach the problem of coil−globule transition dynamics numerically by Brownian dynamics simulations. This method allows us to study the behavior of polymer chains of varying stiffness and the effects of bending stiffness on chain morphology during the process of coil− globule collapse, imitating globule formation in poor solvent conditions. We record and analyze a three-stage process of globule formation for flexible chains: (1) nucleation, (2) coalescence of nuclei, and (3) collapsed globule formation. Stiffer chains undergo similar formation stages; however, the "raindrops" formed by these chains are elongated (unlike spherical structures formed by flexible chains) and exhibit regular packing of chains into antiparallel hairpin structures. In order to assess the transition dynamics quantitatively, polymer chain configurations were analyzed by generating contact maps and contact frequency histograms for all given configurations. These clusters are initial-configuration-dependent, and their growth and intercluster contacts have direct analogy with the process of raindrop coalescence.

Maximum Compaction Density of Folded Semiflexible Polymers

Macromolecules, 2013

We study the dynamics of polymer chain collapse into a globular state in poor solvent, as a function of chain flexibility. We examine the compactness of the folded globule assessing the direct contact and a larger length-scale structural characteristics at various persistence lengths l p. We discover that semiflexible polymer chains with a specific stiffness * I think it is easier to delete (l p ≈ 8 monomers) than add more discussion-I do not think that this statement is worth a set of simulations for shorter and longer chains* form the most densely folded structuresa phenomenon due to nematic-like hairpin formation and stacking of hairpin segments in the most compact state. Even in this most compactly folded state, the number of contacts between monomers (accounting for covalent bonds as well as non-covalent physical interactions) is still low and the globule is only just above the marginal stability threshold. We identify morphological changes associated with the dynamics of semiflexible chain collapse: flexible chains fold into globules, less flexible form rod-like structures, followed by toroidal structures of different geni, and finally, even stiffer chains form highly elongated rods. We also study the time of collapse as a function of persistence length, which shows that stiff chains take much longer to * To whom correspondence should be addressed 1 reach their elongated lowest energy state. We propose that polymer chain stiffness, as a regulator of both local and global chain compactness, is highly important in biological systems and in the dynamics of DNA-and protein folding.

Low-energy states of a semiflexible polymer chain with attraction and the whip-toroid transitions

The Journal of Chemical Physics, 2006

We establish a general model for the whip-toroid transitions of a semiflexible homopolymer chain using the path integral method and the O(3) nonlinear sigma model on a line segment with the local inextensibility constraint. We exactly solve the energy levels of classical solutions, and show that some of its classical configurations exhibit toroidal forms, and the system has phase transitions from a whip to toroidal states with a conformation parameter c = W 2l L 2π 2. We also discuss the stability of the toroid states and propose the low-energy effective Green function. Finally, with the finite size effect on the toroid states, predicted toroidal properties are successfully compared to experimental results of DNA condensation.

All-or-none folding of a flexible polymer chain in cylindrical nanoconfinement

Journal of Chemical Physics, 2020

Geometric confinement of a polymer chain results in a loss of conformational entropy. For a chain that can fold into a compact native state via a first-order-like transition, as is the case for many small proteins, confinement typically provides an entropic stabilization of the folded state, thereby shifting the location of the transition. This allows for the possibility of confinement (entropy) driven folding. Here, we investigate such confinement effects for a flexible square-well-sphere N-mer chain (monomer diameter σ) confined within a long cylindrical pore (diameter D) or a closed cylindrical box (height H = D). We carry out Wang-Landau simulations to construct the density of states, which provides access to the complete thermodynamics of the system. For a wide pore, an entropic stabilization of the folded state is observed. However, as the pore diameter approaches the size of the folded chain (D ∼ N 1/3 σ), we find a destabilization effect. For pore diameters smaller than the native ground-state, the chain folds into a different, higher energy, ground state ensemble and the T vs D phase diagram displays non-monotonic behavior as the system is forced into different ground states for different ranges of D. In this regime, isothermal reduction of the confinement dimension can induce folding, unfolding, or crystallite restructuring. For the cylindrical box, we find a monotonic stabilization effect with decreasing D. Scaling laws for the confinement free energy in the athermal limit are also investigated.

Morphological variation in a collapsed single homopolymer chain

The Journal of Chemical Physics, 1998

We studied the thermodynamics in a single homopolymer chain using a multicanonical Monte Carlo simulation. A polymer chain that exhibits an elongated coil state in a good solvent, or at high temperatures, collapses into a condensed state, i.e., coil-globule transition. For flexible polymer chains, as the temperature decreases, the coil state changes into a liquidlike spherical globule, and this liquid state then changes into a solidlike spherical globule; these are similar to the transitions between gas and liquid and between liquid and solid, respectively. For stiff polymer chains, the coil state changes into a crystalline state without the appearance of an intermediate liquidlike state, to give a product with toroidal morphology. For chains intermediate between stiff and flexible, the coil state changes into a state in which toroid and rod shapes coexist, and this state changes into a single solidlike state in which only the rod shape is present. These calculational results correspond well to experimental findings for the products of the collapse of single long DNA chains.

From toroidal to rod-like condensates of semiflexible polymers

The Journal of Chemical Physics, 2014

The competition between toroidal and rod-like conformations as possible ground states for DNA condensation is studied as a function of the stiffness, the length of the DNA and the form of the long-range interactions between neighboring molecules, using analytical theory supported by Monte Carlo simulations. Both conformations considered are characterized by a local nematic order with hexagonal packing symmetry of neighboring DNA molecules, but differ in global configuration of the chain and the distribution of its curvature as it wraps around to form a condensate. The long-range interactions driving the DNA condensation are assumed to be of the form pertaining to the attractive depletion potential as well as the attractive counterion induced soft potential. In the stiffness-length plane we find a transition between rod-like to toroid condensate for increasing stiffness at a fixed chain length L. Strikingly, the transition line is found to have a L 1/3 dependence irrespective of the details of the long-range interactions between neighboring molecules. When realistic DNA parameters are used, our description reproduces rather well some of the experimental features observed in DNA condensates. arXiv:1401.4300v1 [cond-mat.soft]