A. W. C. Lau

State-Dependent Diffusion: Thermodynamic Consistency and its Path Integral Formulation

The friction coefficient of a particle can depend on its position, as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show that the requirement that a particles distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number of examples with spatially varying diffusion coefficients. We also derive a path integral representation for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.

Fluctuation theorem and large deviation function for a solvable model of a molecular motor

We study a discrete stochastic model of a molecular motor. This discrete model can be viewed as a minimal ratchet model. We extend our previous work on this model, by further investigating the constraints imposed by the fluctuation theorem on the operation of a molecular motor far from equilibrium. In this work, we show the connections between different formulations of the fluctuation theorem. One formulation concerns the generating function of the currents while another one concerns the corresponding large deviation function, which we have calculated exactly for this model. A third formulation concerns the ratio of the probability of observing a velocity v to the same probability of observing a velocity -v . Finally, we show that all the formulations of the fluctuation theorem can be understood from the notion of entropy production.

Elongation and Fluctuations of Semiflexible Polymers in a Nematic Solvent

We directly visualize single polymers with persistence lengths l(p), ranging from 0.05 to 16 microm, dissolved in the nematic phase of rodlike fd virus. Polymers with a sufficiently large persistence length undergo a coil-rod transition at the isotropic-nematic transition of the background solvent. We quantitatively analyze the transverse fluctuations of the semiflexible polymers and show that at long wavelengths they are driven by the fluctuating nematic background. We extract the Odijk deflection length and the elastic constant of the background nematic phase from the data.

Nonequilibrium fluctuations and mechanochemical couplings of a molecular motor.

We investigate theoretically the violations of Einstein and Onsager relations and the thermodynamic efficiency for a single processive motor operating far from equilibrium using an extension of the two-state model introduced by Kafri et al. [Biophys. J. 86, 3373 (2004)10.1529/biophysj.103.036152]. With the aid of the Fluctuation Theorem, we analyze the general features of these violations and this efficiency and link them to mechanochemical couplings of motors. In particular, an analysis of the experimental data of kinesin using our framework leads to interesting predictions that may serve as a guide for future experiments.

Condensation of isolated semi-flexible filaments driven by depletion interactions

Using fluorescence microscopy, we directly visualize the condensed structures of individual semi-flexible actin filaments in a poor solvent. The condensation of filaments into either ring-like or racquet-like structures is driven by non-adsorbing polymers which induce attractive interactions between filaments via the well-known depletion mechanism. A quantitative analysis of the racquet structures yields a direct measurement of the adhesion strength between a pair of filaments. We also compare our experimental data with a theoretical model, demonstrating that in the limit of weak binding, thermal fluctuations can renormalize the effective strength of the attractive depletion interactions. Our experimental methods can be applied to other filamentous structures to directly measure their attractive intermolecular potentials.

Electrostatic attraction of coupled Wigner crystals: finite temperature effects.

In this paper we present a unified physical picture for the electrostatic attraction between two coupled planar Wigner crystals at finite temperature. This model may facilitate our conceptual understanding of counterion-mediated attractions between (highly) similarly charged planes. By adopting an elastic theory, we show that the total attractive force between them can be (approximately) decomposed into a short-ranged and a long-ranged component. They are evaluated below the melting temperature of the Wigner crystals. In particular, we analyze the temperature dependence of the short-ranged attraction, arising from ground-state configuration, and we argue that thermal fluctuations may drastically reduce its strength. Also, the long-range force agrees exactly with that based on the charge-fluctuation approach. Furthermore, we take quantum contributions to the long-ranged (fluctuation-induced) attraction into account and show how the fractional power law, which scales as d(-7/2) for large interplanar distance d at zero temperature, crosses over to the classical regime d(-3) via an intermediate regime of d(-2).

Spreading of latex particles on a substrate

We have investigated both experimentally and theoretically the spreading behavior of latex particles deposited on solid substrates. These particles, which are composed of cross-linked polymer chains, have an intrinsic elastic modulus. We show that the elasticity must be considered to account for the observed contact angle between the particle and the solid substrate, as measured through atomic-force microscopy techniques. In particular, the work of adhesion computed within our model can be significantly larger than that from the classical Dupre formula.

Binding of oppositely charged membranes and membrane reorganization

Abstract:We consider the electrostatic interaction between two rigid membranes, with different surface charge densities of opposite sign, across an aqueous solution without added salt. Exact solutions to the nonlinear Poisson-Boltzmann equation are obtained and their physical meaning discussed. We also calculate the electrostatic contribution to the free energy and discuss the renormalization of the area per head group of the charged lipids arising from the Coulomb interaction.

CHARGE-FLUCTUATION-INDUCED NONANALYTIC BENDING RIGIDITY

In this Letter, we consider a neutral system of mobile positive and negative charges confined on the surface of curved films. This may be an appropriate model for: i) a highly charged membrane whose counterions are confined to a sheath near its surface; ii) a membrane composed of an equimolar mixture of anionic and cationic surfactants in aqueous solution. We find that the charge fluctuations contribute a non-analytic term to the bending rigidity that varies logarithmically with the radius of curvature. This may lead to spontaneous vesicle formation, which is indeed observed in similar systems.

Entropic interactions in suspensions of semiflexible rods: short-range effects of flexibility.

We compute the entropic interactions between two colloidal spheres immersed in a dilute suspension of semiflexible rods. Our model treats the semiflexible rod as a bent rod at fixed angle, set by the rod contour and persistence lengths. The entropic forces arising from this additional rotational degree of freedom are captured quantitatively by the model, and account for observations at short range in a recent experiment. Global fits to the interaction potential data suggest the persistence length of the fd virus is about two to three times smaller than the commonly used value of 2.2 microm.