Fatty acid droplet self-division driven by a chemical reaction.

Division of a millimeter-sized and compartmentalized fatty acid droplet is triggered by a chemical pH clock reaction operating on the ten-second time scale. The autonomous pH change inside the compartment translates into the deprotonation of the fatty acid molecules, leading to a negative interfacial tension at the water-oil interface inside the droplet. This phenomenon induces the expansion of the droplet, which is followed by its division into daughter droplets governed by the Plateau-Rayleigh instability.

Spectra of "real-world" graphs: beyond the semicircle law.

Many natural and social systems develop complex networks that are usually modeled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semicircle law is known to describe the spectral densities of uncorrelated random graphs, much less is known about the spectra of real-world graphs, describing such complex systems as the Internet, metabolic pathways, networks of power stations, scientific collaborations, or movie actors, which are inherently correlated and usually very sparse. An important limitation in addressing the spectra of these systems is that the numerical determination of the spectra for systems with more than a few thousand nodes is prohibitively time and memory consuming. Making use of recent advances in algorithms for spectral characterization, here we develop methods to determine the eigenvalues of networks comparable in size to real systems, obtaining several surprising results on the spectra of adjacency matrices corresponding to models of real-world graphs. We find that when the number of links grows as the number of nodes, the spectral density of uncorrelated random matrices does not converge to the semicircle law. Furthermore, the spectra of real-world graphs have specific features, depending on the details of the corresponding models. In particular, scale-free graphs develop a trianglelike spectral density with a power-law tail, while small-world graphs have a complex spectral density consisting of several sharp peaks. These and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks.

Towards a chemically driven molecular electron pump.

Charge can be pumped through a tiny gated portal from a reservoir at low electrochemical potential to one at the same or higher electrochemical potential by cyclically modulating the portal and gate energies. A theoretically and experimentally well established mechanism is Thouless adiabatic pumping, achieved by a precisely timed out-of-phase modulation of at least two parameters of the system. Here we show that stochastic modulation between two configurations of gate and portal energies can drive efficient pumping by a different, nonadiabatic, mechanism that may provide a basis for chemically driven electron pumping through a molecular wire.

Nonlinearly coupled flows.

We study energy flows that are coupled at a higher than linear order. A number of examples are presented where a force brings about a flow in the perpendicular direction. In some cases the symmetry of the system is such that coupling can only take place at even orders. We apply the theory to recently proposed two-dimensional devices that separate colloidal particles by ratcheting the different particles in different directions.

A chemically reversible Brownian motor: application to kinesin and Ncd.

Kinesin and nonclaret disjunctional protein (ncd) are two microtubule-based molecular motors that use energy from ATP hydrolysis to drive motion in opposite directions. They are structurally very similar and bind with similar orientations on microtubule. What is the origin of the different directionality? Is it some subtle feature of the structure of the motor domains, not apparent in x-ray diffraction studies, or possibly some difference near the neck regions far from the microtubule binding site? Perhaps because the motors function as dimers, the explanation involves differences in the strength of the interaction between the two motor monomers themselves. Here we present another possibility, based on a Brownian ratchet, in which the direction of motion of the motor is controlled by the chemical mechanism of ATP hydrolysis and is an inherent property of a single head. In contrast to conventional power stroke models, dissociation of the individual heads is not obligatory in the chemomechanical cycle, and the steps during which motion and force generation occurs are best described as one-dimensional thermally activated transitions that take place while both heads are attached to the microtubule. We show that our model is consistent with experiments on kinesin in which the velocity is measured as a function of external force and with the observed stiochiometry of one ATP/8-nm step at low load. Further, the model provides a way of understanding recent experiments on the ATP dependence of the variance (randomness) of the distance moved in a given time.

Intrawell relaxation of overdamped Brownian particles.

We consider an overdamped Brownian particle in a well. When the particle escapes, it does so as an instanton, i.e., in one run and without dwelling anywhere on the way from the bottom of the well to the top of the barrier. For a sufficiently steep slope the instanton time equals the time it takes the particle to deterministically slide down the same slope. We show that the instanton time is also the relaxation time for the escape rate after the barrier changes shape.

Efficiency of Brownian heat engines.

We study the efficiency of one-dimensional thermally driven Brownian ratchets or heat engines. We identify and compare the three basic setups characterized by the type of the connection between the Brownian particle and the two heat reservoirs: (i) simultaneous, (ii) alternating in time, and (iii) position dependent. We make a clear distinction between the heat flow via the kinetic and the potential energy of the particle, and show that the former is always irreversible and it is only the third setup where the latter is reversible when the engine works quasistatically. We also show that in the third setup the heat flow via the kinetic energy can be reduced arbitrarily, proving that even for microscopic heat engines there is no fundamental limit of the efficiency lower than that of a Carnot cycle.

Fluctuation driven transport and models of molecular motors and pumps.

Non-equilibrium fluctuations can drive vectorial transport along an anisotropic structure in an isothermal medium by biasing the effect of thermal noise (kBT). Mechanisms based on this principle are often called Brownian ratchets and have been invoked as a possible explanation for the operation of biomolecular motors and pumps. We discuss the thermodynamics and kinetics for the operation of microscopic ratchet motors under conditions relevant to biology, showing how energy provided by external fluctuations or a non-equilibrium chemical reaction can cause unidirectional motion or uphill pumping of a substance. Our analysis suggests that molecular pumps such as Na,K-ATPase and molecular motors such as kinesin and myosin may share a common underlying mechanism.

Collective transport in locally asymmetric periodic structures.

In this paper we give an overview of the cooperative effects in fluctuation driven transport arising from the interaction of a large number of particles. (i) First, we study a model with finite-sized, overdamped Brownian particles interacting via hard-core repulsion. Computer simulations and theoretical calculations reveal a number of novel cooperative transport phenomena in this system, including the reversal of direction of the net current as the particle density is increased, and a very strong and complex dependence of the average velocity on both the size and the average distance of the particles. (ii) Next, we consider the cooperation of a collection of motors rigidly attached to a backbone. This system possesses dynamical phase transition allowing spontaneous directed motion even if the system is spatially symmetric. (iii) Finally, we report on an experimental investigation exploring the horizontal transport of granular particles in a vertically vibrated system whose base has a sawtooth-shaped profile. The resulting material flow exhibits complex collective behavior, both as a function of the number of layers of particles and the driving frequency; in particular, under certain conditions, increasing the layer thickness leads to a reversal of the current, while the onset of transport as a function of frequency occurs gradually in a manner reminiscent of a phase transition. (c) 1998 American Institute of Physics.

The kinesin walk: a dynamic model with elastically coupled heads.

Recently individual two-headed kinesin molecules have been studied in in vitro motility assays revealing a number of their peculiar transport properties. In this paper we propose a simple and robust model for the kinesin stepping process with elastically coupled Brownian heads that show all of these properties. The analytic and numerical treatment of our model results in a very good fit to the experimental data and practically has no free parameters. Changing the values of the parameters in the restricted range allowed by the related experimental estimates has almost no effect on the shape of the curves and results mainly in a variation of the zero load velocity that can be directly fitted to the measured data. In addition, the model is consistent with the measured pathway of the kinesin ATPase.