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A02 SAKAUE, Takahiro |Proposed Research Projects (2016-2017)

Paper | Original Paper

2017

Yumino Hayase, Takahiro Sakaue and Hiizu Nakanishi,
Compressive response and helix formation of a semiflexible polymer confined in a nanochannel,
Physical Review E 95, 052502/1-6 (2017).

[Summary] Configurations of a single semiflexible polymer is studied when it is pushed into a nanochannel in the case where the polymer persistence length lp is much longer than the channel diameter D:lp/D≫1. Using numerical simulations, we show that the polymer undergoes a sequence of recurring structural transitions upon longitudinal compression: random deflection along the channel, a helix going around the channel wall, double-fold random deflection, double-fold helix, etc. We find that the helix transition can be understood as buckling of deflection segments, and the initial helix formation takes place at very small compression with no appreciable weak compression regime of the random deflection polymer.

*Takuya Saito and Takahiro Sakaue,
Complementary mode analyses between sub-and superdiffusion,
Physical Review E 95, 042143 (2017).

[Summary] Several subdiffusive stochastic processes in nature, e.g., the motion of a tagged monomer in polymers, the height fluctuation of interfaces, particle dynamics in single-file diffusion, etc., can be described rigorously or approximately by the superposition of various modes whose relaxation times are broadly distributed. In this paper, we propose a mode analysis generating superdiffusion, which is paired with or complementary to subdiffusion. The key point in our discussion lies in the identification of a pair of conjugated variables, which undergo sub- and superdiffusion, respectively. We provide a simple interpretation for the sub- and superdiffusion duality for these variables using the language of polymer physics. The analysis also suggests the usefulness of looking at the force fluctuation in experiments, where a polymer is driven by a constant velocity.

*Takahiro Sakaue, Jean-Charles Walter, Enrico Carlon and Carlo Vanderzande,
Non-Markovian dynamics of reaction coordinate in polymer folding,
Soft Matter 13, 3174-3181 (2017).

[Summary] We develop a theoretical description of the critical zipping dynamics of a self-folding polymer. We use tension propagation theory and the formalism of the generalized Langevin equation applied to a polymer that contains two complementary parts which can bind to each other. At the critical temperature, the (un)zipping is unbiased and the two strands open and close as a zipper. The number of broken base pairs n(t) displays a subdiffusive motion characterized by a variance growing as 〈Δn2(t)〉 ∼ tα with α < 1 at long times. Our theory provides an estimate of both the asymptotic anomalous exponent α and of the subleading correction term, which are both in excellent agreement with numerical simulations. The results indicate that the tension propagation theory captures the relevant features of the dynamics and shed some new insights on related polymer problems characterized by anomalous dynamical behavior.

*Takahiro Sakaue, Takuya Saito,
Active diffusion of model chromosomal loci driven by athermal noise,
Soft Matter 13, 81-87 (2017).

[Summary] Active diffusion, i.e., fluctuating dynamics driven by athermal noise, is found in various out-of-equilibrium systems. Here we discuss the nature of the active diffusion of tagged monomers in a flexible polymer. A scaling argument based on the notion of tension propagation clarifies how the polymeric effect is reflected in the anomalous diffusion exponent, which may be of relevance to the dynamics of chromosomal loci in living cells.

2016

*Takahiro Sakaue,
Dynamics of polymer translocation: a short review with an introduction of weakly-driven regime,
Polymers 8, 424:1-12 (2016).

[Summary] As emphasized in a recent review (by V.V. Palyulin, T. Ala-Nissila, R. Metzler), theoretical understanding of the unbiased polymer translocation lags behind that of the (strongly) driven translocation. Here, we suggest the introduction of a weakly-driven regime, as described by the linear response theory to the unbiased regime, which is followed by the strongly-driven regime beyond the onset of nonlinear response. This provides a concise crossover scenario, bridging the unbiased to strongly-driven regimes.

Kyohei Shitara and *Takahiro Sakaue,
Shear modulus of structured electro-rheological fluid mixtures,
Physical Review E 93, 052603/1-7 (2016).

[Summary] Some immiscible blends under a strong electric field often exhibit periodic structures, bridging the gap between two electrodes. Upon shear, the structures tilt, and exhibit an elastic response which is mostly governed by the electric energy. Assuming a two-dimensional stripe structure, we calculate the Maxwell stress, and derive an expression for the shear modulus, demonstrating how it depends on the external electric field, the composition, and the dielectric properties of the blend. We also suggest the notion of effective interfacial tension, which renormalizes the effect of the electric field. This leads to a simple derivation of the scaling law for the selection of the wavelength of the structure formed under an electric field.

*Takahiro Sakaue, and Chihiro H. Nakajima,
Miscibility Phase Diagram of Ring Polymer Blends: A Topological Effect,
Physical Review E 93, 042502/1-9 (2016).

[Summary] The miscibility of polymer blends, a classical problem in polymer science, may be altered, if one or both of the component do not have chain ends. Based on the idea of topological volume, we propose a mean-field theory to clarify how the topological constraints in ring polymers affect the phase behavior of the blends. While the large enhancement of the miscibility is expected for ring-linear polymer blends, the opposite trend toward demixing, albeit comparatively weak, is predicted for ring-ring polymer blends. Scaling formulas for the shift of critical point for both cases are derived. We discuss the valid range of the present theory, and the crossover to the linear polymer blends behaviors, which is expected for short chains. These analyses put forward a view that the topological constraints could be represented as an effective excluded-volume effects, in which the topological length plays a role of the screening factor.

Ahmed Khorshid, Susan Amin, Zhiyue Zhang, Takahiro Sakaue, *Walter Reisner,
Non-Equilibrium Dynamics of Nanochannel Confined DNA,
Macromolecules 49(5), 1933–1940 (2016).

[Summary] We show that the dynamic non-equilibrium segmental concentration profile of a single nanochannel confined DNA molecule can be described via a partial differential evolution equation based on nonlinear diffusion, using an approach analogous to that used in the description of many-molecule systems such as polymer solutions. This equation can describe the segmental concentration profile of a single polymer along the nanochannel as a function of time for chain behavior ranging from states of high compression to equilibrium. In particular, to demonstrate the generality of our approach, we show that our model can describe two distinct types of experimental behavior generated via a sliding bead assay, symmetric relaxation resulting from free expansion of the polymer after compression, and the evolution of DNA concentration “shock waves” as a molecule is driven from equilibrium to a compressed state.