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 induced by adsorption

We study the translocation of a flexible polymer through a pore in a membrane induced by its adsorption on \trans side of the membrane. When temperature $T$ is higher than $T_c$, the adsorption-desorption transition temperature, attractive interaction between polymer and membrane plays little role in affecting polymer conformation, leading to translocation time that scales as $\tau\sim L^3$ where $L$ is the polymer contour length. When $T < T_c$, however, the translocation time undergoes a sharp crossover to $\tau\sim L^2$ for sufficiently long polymers, following the second order conformational (adsorption) transition. The translocation time is found to exhibit the crossover around $T=T_c'$, which is lower than $T_c$ for polymers shorter than a critical length($N<N_c$).Comment: 19 pages RevTeX, 5 postscript figures, to be published in J. Chem. Phys. 108(7), 3013 (1998

Scaling theory of driven polymer translocation

We present a theoretical argument to derive a scaling law between the mean translocation time $\tau$ and the chain length $N$ for driven polymer translocation. This scaling law explicitly takes into account the pore-polymer interactions, which appear as a correction term to asymptotic scaling and are responsible for the dominant finite size effects in the process. By eliminating the correction-to-scaling term we introduce a rescaled translocation time and show, by employing both the Brownian Dynamics Tension Propagation theory [Ikonen {\it et al.}, Phys. Rev. E {\bf 85}, 051803 (2012)] and molecular dynamics simulations that the rescaled exponent reaches the asymptotic limit in a range of chain lengths that is easily accessible to simulations and experiments. The rescaling procedure can also be used to quantitatively estimate the magnitude of the pore-polymer interaction from simulations or experimental data. Finally, we also consider the case of driven translocation with hydrodynamic interactions (HIs). We show that by augmenting the BDTP theory with HIs one reaches a good agreement between the theory and previous simulation results found in the literature. Our results suggest that the scaling relation between $\tau$ and $N$ is retained even in this case.Comment: 5 pages, 4 figure

Polymer Release out of a Spherical Vesicle through a Pore

Translocation of a polymer out of curved surface or membrane is studied via mean first passage time approach. Membrane curvature gives rise to a constraint on polymer conformation, which effectively drives the polymer to the outside of membrane where the available volume of polymer conformational fluctuation is larger. Considering a polymer release out of spherical vesicle, polymer translocation time $\tau$ is changed to the scaling behavior $\tau\sim L^2$ for $R<R_G$, from $\tau\sim L^3$ for $R\gg R_G$, where $L$ is the polymer contour length and $R$, $R_G$ are vesicle radius and polymer radius of gyration respectively. Also the polymer capture into a spherical budd is studied and possible apparatus for easy capture is suggested.Comment: 14 pages RevTeX, 6 postscript figures, published in Phys. Rev. E 57, 730 (1998

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.Comment: 7 pages, 8 figures, accepted in the Journal of Chemical Physic

How dsDNA breathing enhances its flexibility and instability on short length scales

We study the unexpected high flexibility of short dsDNA which recently has been reported by a number of experiments. Via the Langevin dynamics simulation of our Breathing DNA model, first we observe the formation of bubbles within the duplex and also forks at the ends, with the size distributions independent of the contour length. We find that these local denaturations at a physiological temperature, despite their rare and transient presence, can lower the persistence length drastically for a short DNA segment in agreement with experiment

Stochastic Resonance of a Flexible Chain Crossing over a Barrier

We study the stochastic resonance (SR) of a flexible polymer surmounting a bistable-potential barrier. Due to the flexibility that can enhance crossing rate and change chain conformations at the barrier, the SR behaviors manifest many features of an entropic SR of a new kind, such as the power amplification peaks at optimal chain lengths and elastic constants as well as the optimal noise strengths. The pronounced peaks that emerge depending on the chain lengths and conformation states suggest novel means of manipulating biopolymers, such as efficient separation methods, within undulating channels.Comment: 13 pages, 9 figure

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.Peer reviewe