How a short double-stranded DNA bends.

A recent experiment using fluorescence microscopy showed that double-stranded DNA fragments shorter than 100 base pairs loop with the probabilities higher by the factor of 10(2)-10(6) than predicted by the worm-like chain (WLC) model [R. Vafabakhsh and T. Ha, Science 337, 1101(2012)]. Furthermore, the looping probabilities were found to be nearly independent of the loop size. The results signify a breakdown of the WLC model for DNA mechanics which works well on long length scales and calls for fundamental understanding for stressed DNA on shorter length scales. We develop an analytical, statistical mechanical model to investigate what emerges to the short DNA under a tight bending. A bending above a critical level initiates nucleation of a thermally induced bubble, which could be trapped for a long time, in contrast to the bubbles in both free and uniformly bent DNAs, which are either transient or unstable. The trapped bubble is none other than the previously hypothesized kink, which releases the bending energy more easily as the contour length decreases. It leads to tremendous enhancement of the cyclization probabilities, in a reasonable agreement with experiment.

Weak temporal signals can synchronize and accelerate the transition dynamics of biopolymers under tension.

In addition to thermal noise, which is essential to promote conformational transitions in biopolymers, the cellular environment is replete with a spectrum of athermal fluctuations that are produced from a plethora of active processes. To understand the effect of athermal noise on biological processes, we studied how a small oscillatory force affects the thermally induced folding and unfolding transition of an RNA hairpin, whose response to constant tension had been investigated extensively in both theory and experiments. Strikingly, our molecular simulations performed under overdamped condition show that even at a high (low) tension that renders the hairpin (un)folding improbable, a weak external oscillatory force at a certain frequency can synchronously enhance the transition dynamics of RNA hairpin and increase the mean transition rate. Furthermore, the RNA dynamics can still discriminate a signal with resonance frequency even when the signal is mixed among other signals with nonresonant frequencies. In fact, our computational demonstration of thermally induced resonance in RNA hairpin dynamics is a direct realization of the phenomena called stochastic resonance and resonant activation. Our study, amenable to experimental tests using optical tweezers, is of great significance to the folding of biopolymers in vivo that are subject to the broad spectrum of cellular noises.

Dynamic Release of Bending Stress in Short dsDNA by Formation of a Kink and Forks.

Bending with high curvature is one of the major mechanical properties of double-stranded DNA (dsDNA) that is essential for its biological functions. The emergence of a kink arising from local melting in the middle of dsDNA has been suggested as a mechanism of releasing the energy cost of bending. Herein, we report that strong bending induces two types of short dsDNA deformations, induced by two types of local melting, namely, a kink in the middle and forks at the ends, which we demonstrate using D-shaped DNA nanostructures. The two types of deformed dsDNA structures dynamically interconvert on a millisecond timescale. The transition from a fork to a kink is dominated by entropic contribution (anti-Arrhenius behavior), while the transition from a kink to a fork is dominated by enthalpic contributions. The presence of mismatches in dsDNA accelerates kink formation, and the transition from a kink to a fork is removed when the mismatch size is three base pairs.

An effective mesoscopic model of double-stranded DNA.

Watson and Crick's epochal presentation of the double helix structure in 1953 has paved the way to intense exploration of DNA's vital functions in cells. Also, recent advances of single molecule techniques have made it possible to probe structures and mechanics of constrained DNA at length scales ranging from nanometers to microns. There have been a number of atomistic scale quantum chemical calculations or molecular level simulations, but they are too computationally demanding or analytically unfeasible to describe the DNA conformation and mechanics at mesoscopic levels. At micron scales, on the other hand, the wormlike chain model has been very instrumental in describing analytically the DNA mechanics but lacks certain molecular details that are essential in describing the hybridization, nano-scale confinement, and local denaturation. To fill this fundamental gap, we present a workable and predictive mesoscopic model of double-stranded DNA where the nucleotides beads constitute the basic degrees of freedom. With the inter-strand stacking given by an interaction between diagonally opposed monomers, the model explains with analytical simplicity the helix formation and produces a generalized wormlike chain model with the concomitant large bending modulus given in terms of the helical structure and stiffness. It also explains how the helical conformation undergoes overstretch transition to the ladder-like conformation at a force plateau, in agreement with the experiment.

Effects of static and temporally fluctuating tensions on semiflexible polymer looping.

Biopolymer looping is a dynamic process that occurs ubiquitously in cells for gene regulation, protein folding, etc. In cellular environments, biopolymers are often subject to tensions which are either static or temporally fluctuating far away from equilibrium. We study the dynamics of semiflexible polymer looping in the presence of such tensions by using Brownian dynamics simulation combined with an analytical theory. We show a minute tension dramatically changes the looping time, especially for long chains. Considering a dichotomically flipping noise as a simple example of the nonequilibrium tension, we find the phenomenon of resonant activation, where the looping time can be the minimum at an optimal flipping time. We discuss our results in connection with recent experiments.

How a single stretched polymer responds coherently to a minute oscillation in fluctuating environments: an entropic stochastic resonance.

Within the cell, biopolymers are often situated in constrained, fluid environments, e.g., cytoskeletal networks, stretched DNAs in chromatin. It is of paramount importance to understand quantitatively how they, utilizing their flexibility, optimally respond to a minute signal, which is, in general, temporally fluctuating far away from equilibrium. To this end, we analytically study viscoelastic response and associated stochastic resonance in a stretched single semi-flexible chain to an oscillatory force or electric field. Including hydrodynamic interactions between chain segments, we evaluate dynamics of the polymer extension in coherent response to the force or field. We find power amplification factor of the response at a noise-strength (temperature) can attain the maximum that grows as the chain length increases, indicative of an entropic stochastic resonance (ESR). In particular for a charged chain under an electric field, we find that the maximum also occurs at an optimal chain length, a new feature of ESR. The hydrodynamic interaction is found to enhance the power amplification, representing unique polymer cooperativity which the fluid background imparts despite its overdamping nature. For the slow oscillatory force, the resonance behavior is explained by the chain undulation of the longest wavelength. This novel ESR phenomenon suggests how a biopolymer self-organizes in an overdamping environment, utilizing its flexibility and thermal fluctuations.

Polymer translocation under time-dependent driving forces: resonant activation induced by attractive polymer-pore interactions.

We study the driven translocation of polymers under time-dependent driving forces using N-particle Langevin dynamics simulations. We consider the force to be either sinusoidally oscillating in time or dichotomic noise with exponential correlation time, to mimic both plausible experimental setups and naturally occurring biological conditions. In addition, we consider both the case of purely repulsive polymer-pore interactions and the case with additional attractive polymer-pore interactions, typically occurring inside biological pores. We find that the nature of the interaction fundamentally affects the translocation dynamics. For the non-attractive pore, the translocation time crosses over to a fast translocation regime as the frequency of the driving force decreases. In the attractive pore case, because of a free energy well induced inside the pore, the translocation time can be a minimum at the optimal frequency of the force, the so-called resonant activation. In the latter case, we examine the effect of various physical parameters on the resonant activation, and explain our observations using simple theoretical arguments.

Direct synthesis of polymer nanocapsules: self-assembly of polymer hollow spheres through irreversible covalent bond formation.

A detailed study of the direct synthesis of polymer nanocapsules, which does not require any template, and core removal, is presented. Thiol-ene "click" reaction between a CB[6] derivative (1) with 12 allyloxy groups at the periphery and dithiols directly produced polymer nanocapsules with a highly stable structure and relatively narrow size distribution. Based on a number of observations including the intermediates detected by DLS, TEM, and SEM studies, a mechanism of the nanocapsule formation was proposed, which includes 2D oligomeric patches turning into a hollow sphere. A theoretical study supports that the formation of a hollow sphere from a disk-shaped intermediate can be thermodynamically favorable under certain conditions. In particular, the effects of various factors such as monomer concentration, reaction temperature, and medium on the formation of polymer nanocapsules have been investigated, which qualitatively agree with those predicted by our theoretical model. An interesting feature of the polymer nanocapsules was that the polymer shell made of a CB[6] derivative allows facile tailoring of its surface properties in a noncovalent and modular manner by virtue of the unique recognition properties of the accessible molecular cavities exposed on the surface. Furthermore, this approach appears to be applicable to any building unit with a flat core and multiple polymerizable groups at the periphery which can direct polymer growth in lateral directions. Other reactions, such as amide bond formation, can be used for the synthesis of polymer nanocapsules in this approach. This novel approach to polymer nanocapsules represents a rare example of self-assembly of molecular components into nanometer-scale objects with interesting structures, shapes, and morphology through irreversible covalent bond formation.

Polymer escape from a metastable Kramers potential: path integral hyperdynamics study.

We study the dynamics of flexible, semiflexible, and self-avoiding polymer chains moving under a Kramers metastable potential. Due to thermal noise, the polymers, initially placed in the metastable well, can cross the potential barrier, but these events are extremely rare if the barrier is much larger than thermal energy. To speed up the slow rate processes in computer simulations, we extend the recently proposed path integral hyperdynamics method to the cases of polymers. We consider the cases where the polymers' radii of gyration are comparable to the distance between the well bottom and the barrier top. We find that, for a flexible polymers, the crossing rate (R) monotonically decreases with chain contour length (L), but with the magnitude much larger than the Kramers rate in the globular limit. For a semiflexible polymer, the crossing rate decreases with L but becomes nearly constant for large L. For a fixed L, the crossing rate becomes maximum at an intermediate bending stiffness. For the self-avoiding chain, the rate is a nonmonotonic function of L, first decreasing with L, and then, above a certain length, increasing with L. These findings can be instrumental for efficient separation of biopolymers.

How topological constraints facilitate growth and stability of bubbles in DNA.

The bubbles in double-stranded DNA, essential for gene transcription and replication, occur in mechanically constrained situations. Through an elastic model incorporating topological constraint, we show that, when a stretched double helix is underwound above a critical value of twist, a bubble can spontaneously form, yielding extension and torque behaviors quantitatively in agreement with magnetic tweezers experiments. We find that, unlike thermal bubble in an unconstrained DNA, the bubbles in these constrained states can grow and stabilize, provided that tension and length of DNA are above critical values.

Charge density coordination and dynamics in a rodlike polyelectrolyte.

We study static and dynamic correlation functions of segmental charge density fluctuation on a rodlike polymer in ionic solutions. The polymer is described by an effective Hamiltonian which incorporates the Coulomb interaction between fluctuating charges screened by ionic fluid environment. We analytically calculate the correlation functions and discuss how charge distribution and dynamics are affected by counterion valency and concentration in electrolyte. We find that the charge correlation exhibits an underdamped oscillation with a wavelength comparable to the counterion size and with the amplitude increasing with the counterion valency. The dynamic correlation of charge density is shown to decay with a characteristic time varying with the counterion valency and concentration. The multivalency gives rise to faster decay of the correlation than that given by one dimensional diffusion.

Effects of Preferential Counterion Interactions on the Specificity of RNA Folding.

The real-time search for native RNA structure is essential for the operation of regulatory RNAs. We previously reported that a fraction of the Azoarcus ribozyme achieves a compact structure in less than a millisecond. To scrutinize the forces that drive initial folding steps, we used time-resolved SAXS to compare the folding dynamics of this ribozyme in thermodynamically isostable concentrations of different counterions. The results show that the size of the fast-folding population increases with the number of available counterions and correlates with the flexibility of initial RNA structures. Within 1 ms of folding, Mg2+ exhibits a smaller preferential interaction coefficient per charge, ΔΓ+/ Z, than Na+ or [Co(NH3)6]3+. The lower ΔΓ+/ Z corresponds to a smaller yield of folded RNA, although Mg2+ stabilizes native RNA more efficiently than other ions at equilibrium. These results suggest that strong Mg2+-RNA interactions impede the search for globally native structure during early folding stages.

Static and dynamic correlations in a charged membrane.

We study static and dynamic correlations of two fluctuations, the charge density fluctuation and height fluctuation (undulation), on a fluid membrane with a finite excess charge in a viscous fluid. For a planar and symmetrical membrane, we consider a model Hamiltonian inclusive of the fluctuations at the Gaussian level, and construct their equations of motion. Within the model, there exists no coupling, either static or dynamic, between the two fluctuations. The correlation function of the charge density has a short-range damped oscillation over the size of lipid heads due to Coulomb attraction between unlike-charged lipids. Its dynamic correlation function is shown to decay much faster in time than that in simple diffusion. The correlation function of height undulation, on the other hand, has a long-range damped oscillation (bud) over the membrane size, due to Coulomb repulsion among the excess charges. As the excess charge density increases to a critical value, a bending instability sets in, where a minute perturbation on the membrane can cause a large bud to form. Due to the excess charge, the dynamic correlation of the undulation decays slowly in time; at the critical density of the instability, the decay becomes infinitely slow.

Two conformational states in D-shaped DNA: Effects of local denaturation.

The bending of double-stranded(ds) DNA on the nano-meter scale plays a key role in many cellular processes such as nucleosome packing, transcription-control, and viral-genome packing. In our recent study, a nanometer-sized dsDNA bent into a D shape was formed by hybridizing a circular single-stranded(ss) DNA and a complementary linear ssDNA. Our fluorescence resonance energy transfer (FRET) measurement of D-DNA revealed two types of conformational states: a less-bent state and a kinked state, which can transform into each other. To understand the origin of the two deformed states of D-DNA, here we study the presence of open base-pairs in the ds portion by using the breathing-DNA model to simulate the system. We provide strong evidence that the two states are due to the emergence of local denaturation, i.e., a bubble in the middle and two forks at ends of the dsDNA portion. We also study the system analytically and find that the free-energy landscape is bistable with two minima representative of the two states. The kink and fork sizes estimated by the analytical calculation are also in excellent agreement with the results of the simulation. Thus, this combined experimental-simulation-analytical study corroborates that highly bent D-DNA reduces bending stress via local denaturation.

Effect of surface undulation on polymer adsorption.

We study the adsorption of a long, flexible polymer (ideal or self-avoiding chain) interacting with a rough surface via a finite-range attraction. Within the Edwards equation approach, we develop a variational method to find the segmental distribution and the free energy of an adsorbed chain. As adsorption becomes strong, the segments tend to be localized within the valleys rather than above the hills of the undulating surface, resulting in a decrease of adsorption thickness. Consequently, the surface undulation enhances adsorption in the case of a strongly adsorbed chain whereas the undulation suppresses it for a weakly adsorbed one, since the enhanced entropic repulsion is dominant over the attraction from the surface. Considering the surface with undulation characterized by a Gaussian correlation as an example, we find an optimal correlation length at which the adsorption becomes the strongest and a critical correlation length below which desorption is induced.

Conformation of local denaturation in double-stranded DNA.

Double-stranded DNA (dsDNA) undergoes a denaturing transition above which the strands unbind completely. At temperatures (including the physiological temperature) below the transition the base pairs tend to unbind locally, giving way to loops, i.e., locally denatured states. In the flexible-chain model, the imaginary time Schrödinger equation describes the interstrand distance distribution of dsDNA with the time variable replaced by the sequence number. We transform the equation to the Fokker-Planck equation (FPE), which provides a convenient and powerful analytical method and, via the equivalent Langevin equation, a simulation scheme. The temperature-dependent potential that emerges in the FPE manifests how the DNA conformation changes dramatically near the transition temperature. We present several simulation plots along with analytical results illustrating the order parameter (concentration of bound base pairs), base pair distance correlation function, and loop size distribution at different temperatures.

Hollow nanotubular toroidal polymer microrings.

Despite the remarkable progress made in the self-assembly of nano- and microscale architectures with well-defined sizes and shapes, a self-organization-based synthesis of hollow toroids has, so far, proved to be elusive. Here, we report the synthesis of polymer microrings made from rectangular, flat and rigid-core monomers with anisotropically predisposed alkene groups, which are crosslinked with each other by dithiol linkers using thiol-ene photopolymerization. The resulting hollow toroidal structures are shape-persistent and mechanically robust in solution. In addition, their size can be tuned by controlling the initial monomer concentrations, an observation that is supported by a theoretical analysis. These hollow microrings can encapsulate guest molecules in the intratoroidal nanospace, and their peripheries can act as templates for circular arrays of metal nanoparticles.

Enhanced bubble formation in looped short double-stranded DNA.

Recent experiments have shown the double-stranded (ds) DNAs readily bend and loop over the scale much shorter than their persistence length (50 nm). In an effort to unveil this seemingly surprising phenomenon, we study the emergence of bubbles in short ds DNA loops by simulating the breathing DNA model. We analyze the bubble size distributions and the melting curves for varying contour lengths, which are critically compared with those of linear DNA of the same lengths. We analytically evaluate the free energies associated with double-strand bending and single-strand bubble formation to explain the simulation data. It is found that in shorter looped DNA the bubbles are more easily initiated and formed to release the large bending energy, giving rise to melting at a lower temperature and a lower contour length.

Charge density and bending rigidity of a rodlike polyelectrolyte: effects of multivalent counterions.

We study line charge density and bending persistence length of a semiflexible polyelectrolyte rod typified by DNA in a z:1 electrolyte with or without pre-existing 1:1 salt. We use a wormlike chain model, where the effective Hamiltonian incorporates bending energy, as well as where the Coulomb interaction between charged segments is screened and mediated by the ions in the solution. By analytically evaluating the free energy associated with the contour undulation and charge density fluctuation affected by the adsorbed ions, we find renormalized mean line-charge-density and persistence length. Multivalent counterions bind to the polyelectrolyte more readily than monovalent counterions, due to electrostatic attraction dominant over the entropy. Also, our results show that at physiological conditions the electrostatic interaction gives no appreciable change on the persistence length from its bare value, against the implications of earlier studies. This is because the mean-field and charge fluctuation effects largely cancel each other in the rodlike conformation.