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This study is devoted to the transport of neutral solutes through porous flat membranes, driven by the solute concentration difference in the reservoirs separated by the membrane. Transport occurs through membrane channels, which are assumed to be non-overlapping, identical, straight cylindrical pores connecting the reservoirs. The key quantities characterizing transport are membrane permeability and its diffusion resistance. Such transport problems arising in very different contexts, ranging from plant physiology and cell biology to chemical engineering, have been studied for more than a century. Nevertheless, an expression giving the permeability for a membrane of arbitrary thickness at arbitrary surface densities of the channel openings is still unknown. Here, we fill in the gap and derive such an expression. Since this expression is approximate, we compare its predictions with the permeability obtained from Brownian dynamics simulations and find good agreement between the two. [ABSTRACT FROM AUTHOR]

Using the gramicidin A channel as a molecular probe, we show that tubulin binding to planar lipid membranes changes the channel kinetics—seen as an increase in the lifetime of the channel dimer—and thus points towards modification of the membrane's mechanical properties. The effect is more pronounced in the presence of non-lamellar lipids in the lipid mixture used for membrane formation. To interpret these findings, we propose that tubulin binding redistributes the lateral pressure of lipid packing along the membrane depth, making it closer to the profile expected for lamellar lipids. This redistribution happens because tubulin perturbs the lipid headgroup spacing to reach the membrane's hydrophobic core via its amphiphilic α-helical domain. Specifically, it increases the forces of repulsion between the lipid headgroups and reduces such forces in the hydrophobic region. We suggest that the effect is reciprocal, meaning that alterations in lipid bilayer mechanics caused by membrane remodeling during cell proliferation in disease and development may also modulate tubulin membrane binding, thus exerting regulatory functions. One of those functions includes the regulation of protein–protein interactions at the membrane surface, as exemplified by VDAC complexation with tubulin. [ABSTRACT FROM AUTHOR]

Diffusive flux of solute molecules through a membrane channel driven by the solute concentration difference on the two sides of the membrane is inversely proportional to the channel diffusion resistance. We show that the intrinsic, channel proper, part of this resistance is the ratio of the sum of the mean first-passage times of the molecule between the channel ends and the molecule partition function in the channel. This is derived without appealing to any specific model of the channel and, therefore, is applicable to transport in channels of arbitrary shape and tortuosity and at arbitrary interaction strength of solute molecules with the channel walls. [ABSTRACT FROM AUTHOR]

In the one-dimensional description, the interaction of a solute molecule with the channel wall is characterized by the potential of mean force U(x), where the x-coordinate is measured along the channel axis. When the molecule can reversibly bind to certain amino acid(s) of the protein forming the channel, this results in a localized well in the potential U(x). Alternatively, this binding can be modeled by introducing a discrete localized site, in addition to the continuum of states along x. Although both models may predict identical equilibrium distributions of the coordinate x, there is a fundamental difference between the two: in the first model, the molecule passing through the channel unavoidably visits the potential well, while in the latter, it may traverse the channel without being trapped at the discrete site. Here, we show that when the two models are parameterized to have the same thermodynamic properties, they automatically yield identical translocation probabilities and mean translocation times, yet they predict qualitatively different shapes of the translocation time distribution. Specifically, the potential well model yields a narrower distribution than the model with a discrete site, a difference that can be quantified by the distribution's coefficient of variation. This coefficient turns out to be always smaller than unity in the potential well model, whereas it may exceed unity when a discrete trapping site is present. Analysis of the translocation time distribution beyond its mean thus offers a way to differentiate between distinct translocation mechanisms. [ABSTRACT FROM AUTHOR]

This paper deals with the escape of a charged blocker molecule from a voltage-biased membrane channel with a constriction zone which the molecule cannot pass through. Recently, we developed a two-site model of the blocker dynamics in such a system and applied it to analyze the escape kinetics. Here, we compare the decay of the blocker survival probability predicted by the two-site model with that for the survival probability given by a more accurate model which assumes continuum diffusion of the blocker molecule inside the channel. The main finding of the present work is that both models predict the same decay of the survival probability at long times. This result is of practical importance since only the long-time tail of the survival probability can be studied in single-channel experiments in which, due to a limited time resolution, only long-lasting individual events of channel blockades can be measured. [ABSTRACT FROM AUTHOR]

When a large solute molecule enters a membrane channel from the membrane-bathing electrolyte solution, it blocks the small-ion current flowing through the channel. If the molecule spends in the channel sufficiently long time, individual blockades can be resolved in single-channel experiments. In this paper, we develop an analytical theory of the blocker escape kinetics from the channel, assuming that a charged blocking molecule cannot pass through a constriction region (bottleneck). We focus on the effect of the external voltage bias on the blocker survival probability in the channel. The bias creates a potential well for the charged blocker in the channel with the minimum located near the bottleneck. When the bias is strong, the well is deep, and escape from the channel is a slow process that allows for time-resolved observation of individual blocking events. Our analysis is performed in the framework of a two-site model of the blocker dynamics in the channel. Importantly, the rate constants, fully determining this model, are derived from a more realistic continuum diffusion model. This is done by mapping the latter onto its two-site counterpart which, while being much simpler, captures the main features of the blocker escape kinetics at high biases. [ABSTRACT FROM AUTHOR]

We study trapping of particles diffusing in a spherical cavity with an absorbing wall containing small static spherical absorbers localized in a spherical region in the center of the cavity. The focus is on the competition between the absorbers and the cavity wall for diffusing particles. Assuming that the absorbers and, initially, the particles are uniformly distributed in the central region, we derive an expression for the particle trapping probability by the cavity wall. The expression gives this probability as a function of two dimensionless parameters: the transparency parameter, characterizing the efficiency of the particle trapping by the absorbers, and the ratio of the absorber-containing region radius to that of the cavity. This work is a generalization of a recent study by Krapivsky and Redner [J. Chem. Phys. 147, 214903 (2017)] who considered the case where the absorber-containing region occupies the entire cavity. The expression for the particle trapping probability is derived in the framework of a steady-state approach which, in our opinion, is much simpler than the time-dependent approach used in the above-mentioned study. [ABSTRACT FROM AUTHOR]