Hirofumi Wada

Helical flow of surface protein required for bacterial gliding motility

Cells of Flavobacterium johnsoniae and of many other members of the phylum Bacteroidetes exhibit rapid gliding motility over surfaces by a unique mechanism. These cells do not have flagella or pili; instead, they rely on a novel motility apparatus composed of Gld and Spr proteins. SprB, a 669-kDa cell-surface adhesin, is required for efficient gliding. SprB was visualized by electron microscopy as thin 150-nm-long filaments extending from the cell surface. Fluorescence microscopy revealed movement of SprB proteins toward the poles of the cell at ∼2 μm/s. The fluorescent signals appeared to migrate around the pole and continue at the same speed toward the opposite pole along an apparent left-handed helical closed loop. Movement of SprB, and of cells, was rapidly and reversibly blocked by the addition of carbonyl cyanide m-chlorophenylhydrazone, which dissipates the proton gradient across the cytoplasmic membrane. In a gliding cell, some of the SprB protein appeared to attach to the substratum. The cell body moved forward and rotated with respect to this point of attachment. Upon reaching the rear of the cell, the attached SprB often was released from the substratum, and apparently recirculated to the front of the cell along a helical path. The results suggest a model for Flavobacterium gliding, supported by mathematical analysis, in which adhesins such as SprB are propelled along a closed helical loop track, generating rotation and translation of the cell body.

Non-equilibrium hydrodynamics of a rotating filament

The nonlinear dynamics of an elastic filament that is forced to rotate at its base is studied by hydrodynamic simulation techniques; coupling between stretch, bend, twist elasticity and thermal fluctuations is included. The twirling-overwhirling transition is located and found to be strongly discontinuous. For finite bend and twist persistence length, thermal fluctuations lower the threshold rotational frequency, for infinite persistence length the threshold agrees with previous analytical predictions.

Discrete elastic model for stretching-induced flagellar polymorphs

Force-induced reversible transformations between coiled and normal polymorphs of bacterial flagella have been observed in recent optical-tweezer experiment. We introduce a discrete elastic rod model with two competing helical states governed by a fluctuating spin-like variable that represents the underlying conformational states of flagellin monomers. Using hybrid Brownian dynamics Monte Carlo simulations, we show that a helix undergoes shape transitions dominated by domain wall nucleation and motion in response to externally applied uniaxial tension. A scaling argument for the critical force is presented in good agreement with experimental and simulation results. Stretching-rate-dependent elasticity including a buckling instability are found, also consistent with the experiment.

Dragging a polymer in a viscous fluid: Steady state and transient

We study the conformation and dynamics of a single polymer chain that is pulled by a constant force applied at its one end with the other end free. Such a situation is relevant to the growing technology of manipulating individual macromolecules, which offers a paradigm research for probing far-from-equilibrium responses of long flexible biological polymers. We first analyze the Rouse model for the Gaussian chains for which the exact analytical results can be obtained. More realistic features such as the finite extensibility, the excluded volume, and the hydrodynamic interactions are taken into account with the help of the scaling argument, which leads to various nontrivial predictions such as the force-dependent friction constants. We elucidate (i) generalized dynamical equations of state describing extension and friction laws in steady-state and (ii) the tension propagation laws in the transient process. We point out that the time evolutions of the dynamic friction in the transient process crucially depend on the experimental protocol, i.e., either constant force or constant velocity ensemble. These predictions could be verified in experiments using giant DNAs and chromosomes.

Stretching helical nano-springs at finite temperature

Using dynamic simulations and analytic methods, we study the elastic response of a helical filament subject to uniaxial tension over a wide range of bend and twist persistence length. A low-pitch helix at low temperatures exhibits a stretching instability and the force-extension curve consists of a sequence of spikes. At elevated temperature (i.e. small persistence lengths) the helix melts and a pronounced force plateau is obtained in the fixed-extension ensemble. The torque boundary condition significantly affects the resulting elastic properties.

Universal bond correlation function for two-dimensional polymer rings

The bond orientational correlation function (BCF) of a semiflexible ring polymer on a flat surface is studied theoretically. For a stiff chain, we give an exact analytic form of BCF with perturbation calculations. For a chain sufficiently longer than its persistence length, the conventional exponential decay vanishes and a long-range order along the chain contour appears. We demonstrate that the bond orientational correlation satisfies the scaling properties, and construct an interpolating formula for its universal curve that encompasses the short- and large-distance behaviors. Our analytical findings are confirmed by extensive Langevin dynamics simulations, and are in excellent agreement with recent experimental data obtained from DNA molecules imaged by atomic force microscopy without any fitting parameters.

Anomalous pressure in fluctuating shear flow.

We investigate how the pressure in fluctuating shear flow depends on the shear rate S and on the system size L by studying fluctuating hydrodynamics under shear conditions. We derive anomalous forms of the pressure for two limiting values of the dimensionless parameter lambda=SL(2)/nu, where nu is the kinematic viscosity. In the case lambda << 1, the pressure is not an intensive quantity because of the influence of the long-range spatial correlations of momentum fluctuations. In the other limit lambda >> 1, the long-range correlations are suppressed at large distances, and the pressure is intensive. In this case, however, there is the interesting effect that the nonequilibrium correction to the pressure is proportional to S(3/2), which was previously obtained with the projection operator method [K. Kawasaki and J. D. Gunton, Phys. Rev. A 8, 2048 (1973)].

Dynamic force spectroscopy of a single condensed DNA

The dynamic force vs. the extension relationship of single DNA molecules in the presence of trivalent cation, spermidine, is studied using optical tweezers. A hysteresis between the stretching and relaxing cycles increases with increasing operating speed. The rate-dependent hysteresis is manifested due to the dissipative stretching and the delay of DNA condensation in the relaxing process. Effective friction inside a DNA condensate is estimated quantitatively, and its physical origin is discussed based on the Kramers-type kinetic theory.

Instabilities and turbulence-like dynamics in an oppositely driven binary particle mixture

Using extensive particle-based simulations, we investigate out-of-equilibrium pattern dynamics in an oppositely driven binary particle system in two dimensions. A surprisingly rich dynamical behavior including lane formation, jamming, oscillation and turbulence-like dynamics is found. The ratio of two friction coefficients is a key parameter governing the stability of lane formation. When the friction coefficient transverse to the external force direction is sufficiently small compared to the longitudinal one, the lane structure becomes unstable to shear-induced disturbances, and the system eventually exhibits a dynamical transition into a novel turbulence-like phase characterized by random convective flows. We numerically construct an out-of-equilibrium phase diagram. Statistical analysis of complex spatio-temporal dynamics of the fully nonlinear turbulence-like phase suggests its apparent reminiscence to the swarming dynamics in certain active matter systems.

Nonlinear elasticity of single collapsed polyelectrolytes

Nonlinear elastic responses of short and stiff polyelectrolytes are investigated by dynamic simulations on a single-molecule level. When a polyelectrolyte condensate undergoes a mechanical unfolding, two types of force-extension curves--i.e., a force plateau and a stick-release pattern--are observed depending on the strength of the electrostatic interaction. We provide a physical interpretation of such force-extension behavior in terms of intramolecular structures of the condensates. We also describe charge distributions of counterions condensed onto a polyelectrolyte, which clarify formation of one-dimensional strongly correlated liquid at large Coulomb coupling regime. These findings may provide significant insights into the relationship between a molecular elasticity and a molecular mechanism of like-charge attractions observed in a wide range of charged biopolymer systems.