Different time scales in dynamic systems with multiple outcomes.

Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each specific outcome, effectively corresponding to a single-exit process and assuming the independence of each exit process. However, the presence of other exits influences the statistical properties and dynamics measured at any specific exit. Here, we present theoretical arguments to explicitly show the existence of different time scales, such as mean exit times and inverse exit fluxes, for dynamic processes with multiple exits. This implies that the statistics of any specific exit dynamics cannot be considered without taking into account the presence of other exits. Several illustrative examples are described in detail using analytical calculations, mean-field estimates, and kinetic Monte Carlo computer simulations. The underlying microscopic mechanisms for the existence of different time scales are discussed. The results are relevant for understanding the mechanisms of various biological, chemical, and industrial processes, including transport through channels and pores.

Crowding effects in non-equilibrium transport through nano-channels.

Transport through nano-channels plays an important role in many biological processes and industrial applications. Gaining insights into the functioning of biological transport processes and the design of man-made nano-devices requires an understanding of the basic physics of such transport. A simple exclusion process has proven to be very useful in explaining the properties of several artificial and biological nano-channels. It is particularly useful for modeling the influence of inter-particle interactions on transport characteristics. In this paper, we explore several models of the exclusion process using a mean field approach and computer simulations. We examine the effects of crowding inside the channel and in its immediate vicinity on the mean flux and the transport times of single molecules. Finally, we discuss the robustness of the theory's predictions with respect to the crucial characteristics of the hindered diffusion in nano-channels that need to be included in the model.

Effects of jamming on nonequilibrium transport times in nanochannels.

Many biological channels perform highly selective transport without direct input of metabolic energy and without transitions from a "closed" to an "open" state during transport. Mechanisms of selectivity of such channels serve as an inspiration for creation of artificial nanomolecular sorting devices and biosensors. To elucidate the transport mechanisms, it is important to understand the transport on the single molecule level in the experimentally relevant regime when multiple particles are crowded in the channel. In this Letter we analyze the effects of interparticle crowding on the nonequilibrium transport times through a finite-length channel by means of analytical theory and computer simulations.

Solitary modes of bacterial culture in a temperature gradient.

We study the behavior of a bacterial culture in a one-dimensional temperature gradient. The bacteria first accumulate near their natural temperature due to thermotaxis. The maximum of the bacterial density profile then drifts to lower temperature with a velocity proportional to the initial concentration of bacteria (typical velocity 0.5 microm/sec). Above a critical concentration of 10(8) cells/cm(3), a new mode develops from the initial accumulation in the form of a sharp pulse moving at a faster velocity ( approximately 3.5 microm/sec). The time of development of this mode diverges as the concentration approaches its critical value. This mode is a result of a positive feedback mechanism provided by interbacterial communication. A theoretical model shows good agreement with the experimental results.

Hydrodynamics of confined membranes.

We calculate the hydrodynamic interaction Lambdak (Oseen interaction kernel) and relaxation frequency omegak for the fluctuations of a membrane that is harmonically bounded to a permeable or impermeable wall. We show that due to the confining wall there is an increase in the effective viscosity of the fluid surrounding the membrane. This has been observed in experiments on confined membranes, such as lamellar phases and the red-blood cell membrane. Our results allow a quantitative analysis of these experiments, in terms of the strength of the membrane confining potential and dislocations.

Temperature dependence of the thermodynamics and kinetics of micellar solutions.

We predict theoretically the thermodynamics and relaxation kinetics of solutions of cylindrical branched micelles. Using a recently developed theory in combination with the experimental data, we explain the unusual, inverted temperature dependence of the phase separation observed in wormlike micelles and dilute microemulsions. We extend the model to treat the temperature dependence of the relaxation kinetics and explain the observations.

Entropic phase separation in polymer-microemulsion networks.

We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first-order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and the configurational entropy of the polymer connections between them. Because it is dominated by entropic effects, the phase behavior of the system is extremely robust and is independent of the detailed properties of either polymers or drops.

Cytoskeleton confinement and tension of red blood cell membranes.

We analyze theoretically both the static and dynamic fluctuation spectra of the red blood cell in a unified manner, using a simple model of the composite membrane. In this model, the two-dimensional spectrin network that forms the cytoskeleton is treated as a rigid shell, located at a fixed, average distance from the lipid bilayer. The cytoskeleton thereby confines both the static and dynamic fluctuations of the lipid bilayer. The sparse connections of the cytoskeleton and bilayer induce a surface tension, for wavelengths larger than the bilayer persistence length. The predictions of the model give a consistent account for both the wave vector and frequency dependence of the experimental data.

Thermodynamics and structure of self-assembled networks.

We study a generic model of self-assembling chains that can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micelles, dipolar fluids, and microemulsions. The model maps the partition function of a solution of branched, self-assembling, mutually avoiding clusters onto that of a Heisenberg magnet in the mathematical limit of zero spin components. As for the calculation of thermodynamic properties as well as the scattering structure factor, the mapping rigorously accounts for all possible cluster configurations, except for closed rings. The model is solved in the mean-field approximation. It is found that despite the absence of any specific interaction between the chains, the presence of the junctions induces an effective attraction between the monomers, which in the case of threefold junctions leads to a first-order reentrant phase separation between a dilute phase consisting mainly of single chains, and a dense network, or two network phases. The model is then modified to predict the structural properties at the mean-field level. Independent of the phase separation, we predict a percolation (connectivity) transition at which an infinite network is formed. The percolation transition partially overlaps with the first-order transition, and is a continuous, nonthermodynamic transition that describes a change in the topology of the system. Our treatment that predicts both the thermodynamic phase equilibria as well as the spatial correlations in the system allows us to treat both the phase separation and the percolation threshold within the same framework. The density-density correlation has the usual Ornstein-Zernicke form at low monomer densities. At higher densities, a peak emerges in the structure factor, signifying the onset of medium-range order in the system. Implications of the results for different physical systems are discussed.