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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]

Ion channels exhibit gating behavior, fluctuating between open and closed states, with the transmembrane voltage serving as one of the essential regulators of this process. Voltage gating is a fundamental functional aspect underlying the regulation of ion-selective, mostly α-helical, channels primarily found in excitable cell membranes. In contrast, there exists another group of larger, and less selective, β-barrel channels of a different origin, which are not directly associated with cell excitability. Remarkably, these channels can also undergo closing, or "gating", induced by sufficiently strong electric fields. Once the field is removed, the channels reopen, preserving a memory of the gating process. In this study, we explored the hypothesis that the voltage-induced closure of the β-barrel channels can be seen as a form of reversible protein denaturation by the high electric fields applied in model membranes experiments—typically exceeding twenty million volts per meter—rather than a manifestation of functional gating. Here, we focused on the bacterial outer membrane channel OmpF reconstituted into planar lipid bilayers and analyzed various characteristics of the closing-opening process that support this idea. Specifically, we considered the nearly symmetric response to voltages of both polarities, the presence of multiple closed states, the stabilization of the open conformation in channel clusters, the long-term gating memory, and the Hofmeister effects in closing kinetics. Furthermore, we contemplate the evolutionary aspect of the phenomenon, proposing that the field-induced denaturation of membrane proteins might have served as a starting point for their development into amazing molecular machines such as voltage-gated channels of nerve and muscle cells. [ABSTRACT FROM AUTHOR]

Using the framework of a continuous diffusion model based on the Smoluchowski equation, we analyze particle dynamics in the confinement of a transmembrane nanopore. We briefly review existing analytical results to highlight consequences of interactions between the channel nanopore and the translocating particles. These interactions are described within a minimalistic approach by lumping together multiple physical forces acting on the particle in the pore into a one-dimensional potential of mean force. Such radical simplification allows us to obtain transparent analytical results, often in a simple algebraic form. While most of our findings are quite intuitive, some of them may seem unexpected and even surprising at first glance. The focus is on five examples: (i) attractive interactions between the particles and the nanopore create a potential well and thus cause the particles to spend more time in the pore but, nevertheless, increase their net flux; (ii) if the potential well-describing particle-pore interaction occupies only a part of the pore length, the mean translocation time is a non-monotonic function of the well length, first increasing and then decreasing with the length; (iii) when a rectangular potential well occupies the entire nanopore, the mean particle residence time in the pore is independent of the particle diffusivity inside the pore and depends only on its diffusivity in the bulk; (iv) although in the presence of a potential bias applied to the nanopore the "downhill" particle flux is higher than the "uphill" one, the mean translocation times and their distributions are identical, i.e., independent of the translocation direction; and (v) fast spontaneous gating affects nanopore selectivity when its characteristic time is comparable to that of the particle transport through the pore. [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]

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]

Ligand- or voltage-driven stochastic gating--the structural rearrangements by which the channel switches between its open and closed states--is a fundamental property of biological membrane channels. Gating underlies the channel's ability to respond to different stimuli and, therefore, to be functionally regulated by the changing environment. The accepted understanding of the gating effect on the solute flux through the channel is that the mean flux is the product of the flux through the open channel and the probability of finding the channel in the open state. Here, using a diffusion model of channel-facilitated transport, we show that this is true only when the gating is much slower than the dynamics of solute translocation through the channel. If this condition breaks, the mean flux could differ from this simple estimate by orders of magnitude. [ABSTRACT FROM AUTHOR]

The steady-state flux through a singly occupied membrane channel is found for both discrete and continuum models of the solute dynamics in the channel. The former describes the dynamics as nearest-neighbor jumps between N sites, while the latter assumes that the molecule diffuses in a one-dimensional potential of mean force. For both models it is shown that the flux is the same as that for a simple two-site model with appropriately chosen rate constants, which contain all the relevant information about the more detailed dynamics. An interesting consequence of single occupancy is that the flux has a maximum as a function of the channel-solute interaction. If this interaction is too attractive, the molecule will never leave the channel, thus blocking it for the passage of other molecules. If it is too repulsive, the solute molecule will never enter the channel. Thus the flux vanishes in the two limits and, hence, has a maximum somewhere in-between. In the framework of the diffusion model, we find the optimal intrachannel potential of mean force that maximizes the flux using the calculus of variations. For a symmetric channel this potential is flat and occupies the entire channel. In the general case of an asymmetric channel, the optimal potential is obtained by tilting the optimal flat potential for the corresponding symmetric channel around the channel center, so that the solute is driven towards the reservoir with the lower solute concentration by a constant force. This implies that the flux is higher when the solute binding near the channel exit is stronger than that near the entrance. [ABSTRACT FROM AUTHOR]

Trapping by active sites on surfaces plays important roles in various chemical and biological processes, including catalysis, enzymatic reactions, and viral entry into host cells. However, the mechanisms of these processes remain not well understood, mostly because the existing theoretical descriptions are not fully accounting for the role of the surfaces. Here, we present a theoretical investigation on the dynamics of surface-assisted trapping by specific active sites. In our model, a diffusing particle can occasionally reversibly bind to the surface and diffuse on it before reaching the final target site. An approximate theoretical framework is developed, and its predictions are tested by Brownian dynamics computer simulations. It is found that the surface diffusion can be crucial in mediating trapping by active sites. Our theoretical predictions work reasonably well as long as the area of the active site is much smaller than the overall surface area. Potential applications of our approach are discussed. [ABSTRACT FROM AUTHOR]

Emergent rational drug design techniques explore individual properties of target biomolecules, small and macromolecule drug candidates, and the physical forces governing their interactions. In this minireview, we focus on the single-molecule biophysical studies of channel-forming bacterial toxins that suggest new approaches for their inhibition.We discuss several examples of blockage of bacterial pore-forming and AB-type toxins by the tailor-made compounds. In the concluding remarks, the most effective rationally designed pore-blocking antitoxins are compared with the small-molecule inhibitors of ion-selective channels of neurophysiology. [ABSTRACT FROM AUTHOR]

The article focuses on ion channel-forming bacterial toxins. The article discusses the channel-blocking and channel-forming toxins. It classifies the channel-forming toxins as endotoxins and exotoxins. It also discusses binary toxins. The article also focuses on the development of blockers of toxin pores.

We demonstrate that the cation-selective channel formedby gramicidinA can be used as a reliable sensor for studying the multivalent ionaccumulation at the surfaces of charged lipid membranes and the “chargeinversion” phenomenon. In asymmetrically charged membraneswith the individual leaflets formed from pure negative and positivelipids bathed by 0.1 M CsCl solutions the channel exhibits currentrectification, which is comparable to that of a typical n/p semiconductordiode. We show that even at these highly asymmetrical conditions thechannel conductance can be satisfactorily described by the electrodiffusionequation in the constant field approximation but, due to predictablelimitations, only when the applied voltages do not exceed 50 mV. Analysisof the changes in the voltage-dependent channel conductance upon additionof trivalent cations allows us to gauge their interactions with themembrane surface. The inversion of the sign of the effective surfacecharge takes place at the concentrations, which correlate with thecation size. Specifically, these concentrations are close to 0.05mM for lanthanum, 0.25 mM for hexaamminecobalt, and 4 mM for spermidine. [ABSTRACT FROM AUTHOR]

Abstract: Regulation of mitochondrial outer membrane (MOM) permeability has dual importance: in normal metabolite and energy exchange between mitochondria and cytoplasm, and thus in control of respiration, and in apoptosis by release of apoptogenic factors into the cytosol. However, the mechanism of this regulation involving the voltage-dependent anion channel (VDAC), the major channel of MOM, remains controversial. For example, one of the long-standing puzzles was that in permeabilized cells, adenine nucleotide translocase is less accessible to cytosolic ADP than in isolated mitochondria. Still another puzzle was that, according to channel-reconstitution experiments, voltage regulation of VDAC is limited to potentials exceeding 30mV, which are believed to be much too high for MOM. We have solved these puzzles and uncovered multiple new functional links by identifying a missing player in the regulation of VDAC and, hence, MOM permeability — the cytoskeletal protein tubulin. We have shown that, depending on VDAC phosphorylation state and applied voltage, nanomolar to micromolar concentrations of dimeric tubulin induce functionally important reversible blockage of VDAC reconstituted into planar phospholipid membranes. The voltage sensitivity of the blockage equilibrium is truly remarkable. It is described by an effective “gating charge” of more than ten elementary charges, thus making the blockage reaction as responsive to the applied voltage as the most voltage-sensitive channels of electrophysiology are. Analysis of the tubulin-blocked state demonstrated that although this state is still able to conduct small ions, it is impermeable to ATP and other multi-charged anions because of the reduced aperture and inversed selectivity. The findings, obtained in a channel reconstitution assay, were supported by experiments with isolated mitochondria and human hepatoma cells. Taken together, these results suggest a previously unknown mechanism of regulation of mitochondrial energetics, governed by VDAC interaction with tubulin at the mitochondria–cytosol interface. Immediate physiological implications include new insights into serine/threonine kinase signaling pathways, Ca2+ homeostasis, and cytoskeleton/microtubule activity in health and disease, especially in the case of the highly dynamic microtubule network which is characteristic of cancerogenesis and cell proliferation. In the present review, we speculate how these findings may help to identify new mechanisms of mitochondria-associated action of chemotherapeutic microtubule-targeting drugs, and also to understand why and how cancer cells preferentially use inefficient glycolysis rather than oxidative phosphorylation (Warburg effect). This article is part of a Special Issue entitled: VDAC structure, function, and regulation of mitochondrial metabolism. [Copyright &y& Elsevier]

Abstract: We study propagation of a particle that jumps between two states, in which it moves with different velocities and diffusion coefficients. To simplify analysis, in the main part of the paper we derive formulas assuming that in one of the states the particle is immobile. A generalization to the case when the particle is mobile in both states is given at the end of the paper. The formulas show how the effective drift velocity and effective diffusion coefficient depend on jump rates between the two states as well as on the particle velocities and diffusion coefficients in these states. Specifically, we find that the effective diffusion coefficient can exhibit a non-monotonic behavior as a function of the ratio of the jump rates. [Copyright &y& Elsevier]

Abstract: Driven by analogies with state vectors of quantum informatics and noise-based logic, we propose a general scheme and elements of neural circuitry for processing and addressing information in the brain. Specifically, we consider random (e.g., Poissonian) trains of finite-duration spikes, and, using the idealized concepts of excitatory and inhibitory synapses, offer a procedure for generating orthogonal vectors out of N partially overlapping trains (“neuro-bits”). We then show that these vectors can be used to construct different superpositions which represent the same number of logic values when carrying or routing information. In quantum informatics the above numbers are the same, however, the present logic scheme is more advantageous because it is deterministic in the sense that the presence of a vector in the spike train is detected by an appropriate coincidence circuit. For this reason it does not require time averaging or repeated measurements of the kind used in standard cross-correlation analysis or in quantum computing. [Copyright &y& Elsevier]

Abstract: We approach channel-facilitated membrane transport using a stochastic model based on considerations of particle diffusion inside the channel pore. This model allows us to rationalize the experimental observation that metabolite-specific biological channels exhibit affinities to their metabolites. We demonstrate that there is an optimal attractive interaction between the channel and the particle that maximizes the particle flux through the channel. A model in which the translocating solute jumps between neighboring binding sites is also analyzed. It is shown that the results predicted by the diffusion model can be recovered from the analysis of the binding-site model in a special limiting case. The binding-site model also describes the flux through a narrow channel where molecules cannot jump one over the other, and the regime of single-file diffusion is realized. [Copyright &y& Elsevier]

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]

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]

The membrane surface charge modifies the conductance of ion channels by changing the electric potential and redistributing the ionic composition in their vicinity. We have studied the effects of lipid charge on the conductance of a multi-state channel formed in planar lipid bilayers by the peptide antibiotic alamethicin. The channel conductance was measured in two lipids: in a neutral dioleoylphosphatidylethanolamine (DOPE) and a negatively charged dioleoylphosphatidylserine (DOPS). The charge state of DOPS was manipulated by the pH of the membrane-bathing solution. We find that at high salt concentrations (e.g., 2 M NaCl) the effect of the lipid charge is below the accuracy of our measurements. However, when the salt concentration in the membrane-bathing solution is decreased, the surface charge manifests itself as an increase in the conductance of the first two channel levels that correspond to the smallest conductive alamethicin aggregates. Our analysis shows that both the salt and pH dependence of the surface charge effect can be rationalized within the nonlinear Poisson-Boltzmann approach. Given channel conductance in neutral lipids, we use different procedures to account for the surface charge (e.g., introduce averaging over the channel aperture and take into account Na[sup +] adsorption to DOPS heads), but only one adjustable parameter: an effective distance from the nearest lipid charge to the channel mouth center. We show that this distance varies by 0.3–0.4 nm upon channel transition from the minimal conducting aggregate (level L0) to the next larger one (level L1). This conclusion is in accord with a simple geometrical model of alamethicin aggregation. [ABSTRACT FROM AUTHOR]

Attempts to discover the mechanism whereby malaria infected red blood cells uptake solutes, including anions, sugars, and amino acids. Study of the permeability of infected red blood cells using the whole-cell voltage-clamp method; Suggestion that an ion channel on the surface of infected red blood cells is responsible for the uptake.

The voltage-dependent anion channel (VDAC) is the primary regulating pathway of water-soluble metabolites and ions across the mitochondrial outer membrane. When reconstituted into lipid membranes, VDAC responds to sufficiently large transmembrane potentials by transitioning to gated states in which ATP/ADP flux is reduced and calcium flux is increased. Two otherwise unrelated cytosolic proteins, tubulin, and α-synuclein (αSyn), dock with VDAC by a novel mechanism in which the transmembrane potential draws their disordered, polyanionic C-terminal domains into and through the VDAC channel, thus physically blocking the pore. For both tubulin and αSyn, the blocked state is observed at much lower transmembrane potentials than VDAC gated states, such that in the presence of these cytosolic docking proteins, VDAC's sensitivity to transmembrane potential is dramatically increased. Remarkably, the features of the VDAC gated states relevant for bioenergetics—reduced metabolite flux and increased calcium flux—are preserved in the blocked state induced by either docking protein. The ability of tubulin and αSyn to modulate mitochondrial potential and ATP production in vivo is now supported by many studies. The common physical origin of the interactions of both tubulin and αSyn with VDAC leads to a general model of a VDAC inhibitor, facilitates predictions of the effect of post-translational modifications of known inhibitors, and points the way toward the development of novel therapeutics targeting VDAC. [ABSTRACT FROM AUTHOR]

Studies the application to biological ion channels of stochastic resonance in thermally activated reactions. Signal transduction properties of thermally activated reactions; Example of a time-dependent Poisson train of identical short pulses in the presence of a periodic modulation; Adiabatic approximation of signal and noise transfer.

Abstract Electrostatic potentials created by fixed or induced charges regulate many cellular phenomena including the rate of ion transport through proteinaceous ion channels. Nanometer-scale pores of these channels also play a critical role in the transport of charged and neutral macromolecules. We demonstrate here that, surprisingly, changing the charge state of a channel markedly alters the ability of nonelectrolyte polymers to enter the channel's pore. Specifically, we show that the partitioning of differently-sized linear nonelectrolyte polymers of ethylene glycol into the Staphylococcus aureus alpha-hemolysin channel is altered by the solution pH. Protonating some of the channel side chains decreases the characteristic polymer size (molecular weight) that can enter the pore by is similar to 25% but increases the ionic current by is similar to 15%. Thus, the "steric" and "electric" size of the channel change in opposite directions. The results suggest that effects due to polymer and channel hydration are crucial for polymer transport through such pores. [ABSTRACT FROM AUTHOR]

A spatial domain swept out by a spherical particle, whose center follows a Wiener trajectory, is referred to as a Wiener sausage. The present study focuses on the surface area of the Wiener sausage. Using intuitive arguments we derive the mean and variance of the surface area, as well as the asymptotic behavior of its probability density in the limits when the area tends to zero and infinity. [ABSTRACT FROM AUTHOR]

We study transitions of diffusing particles between the left and right ends of expanding and narrowing conical tubes. In an expanding tube, such transitions occur faster than in the narrowing tube of the same length and radius variation rate. This happens because the entropy potential pushes the particle towards the wide tube end, thus accelerating the transitions in the expanding tube and slowing them down in the narrowing tube. To gain deeper insight into how the transitions occur, we divide each trajectory into the direct-transit and looping segments. The former is the final part of the trajectory, where the particle starting from the left tube end goes to the right end without returning to the left one. The rest of the trajectory is the looping segment, where the particle, starting from the left tube end, returns to this end again and again until the direct transition happens. Our focus is on the durations of the two segments and their sum, which is the duration of the particle first passage between the left and right ends of the tube. We approach the problem using the one-dimensional description of the particle diffusion along the tube axis in terms of the modified Fick-Jacobs equation. This allows us to derive analytical expressions for the Laplace transforms of the probability densities of the firstpassage, direct-transit, and looping times, which we use to find the mean values of these random variables. Our results show that the direct transits are independent of the entropy potential and occur as in free diffusion. However, this "free diffusion" occurs with the effective diffusivity entering the modified Fick-Jacobs equation, which is smaller than the particle diffusivity in a cylindrical tube. This is the only way how the varying tube geometry manifests itself in the direct transits. Since direct-transit times are direction-independent, the difference in the first-passage times in the tubes of the two types is due to the difference in the durations of the looping segments in the expanding and narrowing tubes. Obtained analytical results are supported by three-dimensional Brownian dynamics simulations. [ABSTRACT FROM AUTHOR]

Recent experiments with single biological nanopores, as well as single-molecule fluorescence spectroscopy and pulling studies of protein and nucleic acid folding raised a number of questions that stimulated theoretical and computational investigations of barrier crossing dynamics. The present paper addresses a closely related problem focusing on trajectories of Brownian particles that escape from a cylindrical trap in the presence of a force F parallel to the cylinder axis. To gain new insights into the escape dynamics, we analyze the "fine structure" of these trajectories. Specifically, we divide trajectories into two segments: a looping segment, when a particle unsuccessfully tries to escape returning to the trap bottom again and again, and a direct-transit segment, when it finally escapes moving without touching the bottom. Analytical expressions are derived for the Laplace transforms of the probability densities of the durations of the two segments. These expressions are used to find the mean looping and direct-transit times as functions of the biasing force F. It turns out that the forcedependences of the two mean times are qualitatively different. The mean looping time monotonically increases as F decreases, approaching exponential F-dependence at large negative forces pushing the particle towards the trap bottom. In contrast to this intuitively appealing behavior, the mean directtransit time shows rather counterintuitive behavior: it decreases as the force magnitude, |F|, increases independently of whether the force pushes the particles to the trap bottom or to the exit from the trap, having a maximum at F = 0. [ABSTRACT FROM AUTHOR]

Channel-facilitated transport of metabolites across biological membranes results in excess noise in the current carried by small ions. This noise originates from fluctuations of the number of metabolite molecules in the channel due to their diffusion. We have carried out a theoretical study of particle number fluctuations in a cylindrical pore. First, we obtain the power spectral density of these fluctuations as a function of pore length and radius, as well as the diffusion constants of the particle in the pore and in the bulk, in the absence of particle-pore interactions. We then perform three-dimensional Brownian dynamics simulations that show excellent agreement with the analytical result. Finally, we demonstrate that explicit expressions for the low-frequency limit of the spectral density can be found even when the particle interacts with the pore. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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]

Introduces a class of non-dynamical and threshold-free systems that also exhibit stochastic resonance. The presentation and analysis of a general mathematical model for such systems; The demonstration that stochastic resonance can occur in a broad class of thermally driven physico-chemical systems; Examples of systems.

Describes the noise-induced enhancement or stochastic resonance of signal transduction across a system of voltage-dependent ion channels formed by the peptide alamethicin. Analysis of the alamethicin's signal transduction properties; Wave signal correlation in the power spectral density; Output signals from ion channels.

Discusses the use of conductance changes of a small electrolyte-filled capillary in observing the statistics and mechanics of flexible polymers moving within single-molecule structures. Function of the Coulter counter; Polymer-induced conductance fluctuations of a single alamethicin channel; Changes for the three states of the alamethicin channel; Polymer-generated excess noise.

Axial diffusion in a two-dimensional channel of smoothly varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with position-dependent effective diffusivity by means of the modified Fick-Jacobs equation. In this paper, Brownian dynamics simulations are used to study the range of applicability of such a description, as well as the accuracy of the expressions for the effective diffusivity proposed by different researchers. [ABSTRACT FROM AUTHOR]

This paper is devoted to bulk-mediated surface diffusion of a particle which can diffuse both on a flat surface and in the bulk layer above the surface. It is assumed that the particle is on the surface initially (at t = 0) and at time t, while in between it may escape from the surface and come back any number of times. We propose a new approach to the problem, which reduces its solution to that of a two-state problem of the particle transitions between the surface and the bulk layer, focusing on the cumulative residence times spent by the particle in the two states. These times are random variables, the sum of which is equal to the total observation time t. The advantage of the proposed approach is that it allows for a simple exact analytical solution for the double Laplace transform of the conditional probability density of the cumulative residence time spent on the surface by the particle observed for time t. This solution is used to find the Laplace transform of the particle mean square displacement and to analyze the peculiarities of its time behavior over the entire range of time. We also establish a relation between the double Laplace transform of the conditional probability density and the Fourier-Laplace transform of the particle propagator over the surface. The proposed approach treats the cases of both finite and infinite bulk layer thicknesses (where bulk-mediated surface diffusion is normal and anomalous at asymptotically long times, respectively) on equal footing. [ABSTRACT FROM AUTHOR]

In this paper, we study biased diffusion of point Brownian particles in a three-dimensional comb-like structure formed by a main cylindrical tube with identical periodic cylindrical dead ends. It is assumed that the dead ends are thin cylinders whose radius is much smaller than both the radius of the main tube and the distance between neighboring dead ends. It is also assumed that in the main tube, the particle, in addition to its regular diffusion, moves with a uniform constant drift velocity. For such a system, we develop a formalism that allows us to derive analytical expressions for the Laplace transforms of the first two moments of the particle displacement along the main tube axis. Inverting these Laplace transforms numerically, one can find the time dependences of the two moments for arbitrary values of both the drift velocity and the dead-end length, including the limiting case of infinitely long dead ends, where the unbiased diffusion becomes anomalous at sufficiently long times. The expressions for the Laplace transforms are used to find the effective drift velocity and diffusivity of the particle as functions of its drift velocity in the main tube and the tube geometric parameters. As might be expected from common-sense arguments, the effective drift velocity monotonically decreases from the initial drift velocity to zero as the dead-end length increases from zero to infinity. The effective diffusivity is a more complex, non-monotonic function of the dead-end length. As this length increases from zero to infinity, the effective diffusivity first decreases, reaches a minimum, and then increases approaching a plateau value which is proportional to the square of the particle drift velocity in the main tube. [ABSTRACT FROM AUTHOR]

Diffusion in a comb-like structure, formed by a main cylindrical tube with identical periodic dead ends of cylindrical shape, occurs slower than that in the same system without dead ends. The reason is that the particle, entering a dead end, interrupts its propagation along the tube axis. The slowdown becomes stronger and stronger as the dead end length increases, since the particle spends more and more time in the dead ends. In the limiting case of infinitely long dead ends, diffusion becomes anomalous with the exponent equal to 1/2. We develop a formalism which allows us to study the mean square displacement of the particle along the tube axis in such systems. The formalism is applicable for an arbitrary dead end length, including the case of anomalous diffusion in a tube with infinitely long dead ends. In particular, we demonstrate how intermediate anomalous diffusion arises when the dead ends are long enough. [ABSTRACT FROM AUTHOR]

The mean lifetime of a particle diffusing in a cylindrical cavity with a circular absorbing spot on the cavity wall is studied analytically as a function of the spot radius, its location on the wall, the particle initial position, and the cavity shape determined by its length and radius. When the spot radius tends to zero our formulas for the mean lifetime reduce to the result given by the solution of the narrow escape problem, according to which the mean lifetime is proportional to the ratio of the cavity volume to the spot radius and is independent of the cavity shape, the spot location on the cavity wall, and the particle starting point, assuming that this point is not too close to the spot. When the spot radius is not small enough, the asymptotic narrow escape formula for the mean lifetime fails, and one should use more general formulas derived in the present study. To check the accuracy and to establish the range of applicability of the formulas, we compare our theoretical predictions with the results of Brownian dynamics simulations. [ABSTRACT FROM AUTHOR]

The transport of many solutes across biological membranes happens with the help of specialized proteins that form water-filled channels traversing the membranes. Recent experimental and theoretical work demonstrates that solute translocation can be facilitated by attractive interactions between the channel and penetrating particle. Here we consider an important aspect of channel-facilitated passive transport, the average lifetimes in the channel for those particles that traverse the channel and those that return, as well as the total average lifetime of the particle in the channel. Exact expressions for the average lifetimes are derived in the framework of a one-dimensional diffusion model. The validity of our one-dimensional analysis is verified by good agreement of the theoretical predictions with the average lifetimes found in three-dimensional Brownian dynamics simulations. [ABSTRACT FROM AUTHOR]

The rate of a diffusion-controlled reaction with a buried binding site is smaller than the rate for the same site on the surface. We study the slowdown of the reaction rate when the site is hidden in a pore that connects two bulk media. On the assumption that the pore is cylindrical we derive an expression for the Laplace transform of the rate coefficient from which we infer the long-time limit of the reaction rate. This provides information on how the reaction rate depends on the channel radius, the location of the site, and the diffusion constant in the pore, which is allowed to differ from that in the bulk. The validity of approximations was checked by simulations that indicated excellent agreement between the analytical and and numerical results. [ABSTRACT FROM AUTHOR]

Transport of metabolites between cells and between subcellular compartments is facilitated by special protein channels that form aqueous pores traversing biological membranes. Accumulating evidence demonstrates that solute-specific channels display pronounced binding to the corresponding solutes. In this paper we rationalize this observation by showing that a wide and deep potential well inside the channel is able to greatly increase the transit probability of the particle through the channel. Using a one-dimensional diffusion model with radiation boundary conditions, we give exact analytical expressions for the particle translocation probabilities. We also run Brownian dynamics simulations to verify the model and the quantitative predictions of our theory. [ABSTRACT FROM AUTHOR]

Transport of solutes through membrane channels produces additional noise in the channel ion current because the number of solute molecules in the channel fluctuates. We obtain a general expression for the power spectral density of these fluctuations in a cylindrical channel in the presence of a binding site of arbitrary strength. The expression shows how the spectral density transforms from that in the case of no-binding to the Lorentzian spectral density corresponding to the strong-binding limit. Brownian dynamics simulations confirm our analytical results. [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]

Any trajectory of a diffusing particle making a transition between two end points of an interval can be divided into two segments, which we call direct-transit and looping parts. The former is the final segment of the trajectory, when the particle goes from one end point of the interval to the opposite end point, without retouching the starting point. The rest of the trajectory is the looping part. We study mean durations of the two parts in the presence of a symmetric linear cusp potential which, depending on the parameter values, forms either a barrier or a well between the end points. For the cusp barrier, we find that the mean direct-transit time decreases as the barrier height increases at a fixed interval length. This happens because the increase in the barrier height results in the increase of the magnitude of the force acting on the particle on both sides of the barrier. Interestingly, though the mean looping and direct-transit times are different in the case of the barrier and well potentials with equal height and depth, respectively, the mean first-passage times for the two cases are identical. [ABSTRACT FROM AUTHOR]

Understanding the role of noise at cellular and higher hierarchical levels depends on our knowledge of the physical mechanisms of its generation. Conversely, noise is a rich source of information about these mechanisms. Using channel-forming protein molecules reconstituted into artificial 5-nm-thick insulating lipid films, it is possible to investigate noise in single-molecule experiments and to relate its origins to protein function. Recent progress in this field is reviewed with an emphasis on how this experimental technique can be used to study low-frequency protein dynamics, including not only reversible ionization of sites on the channel-forming protein molecule, but also molecular mechanisms of 1/f-noise generation. Several new applications of the single-molecule noise analysis to membrane transport problem are also addressed. Among those is a study on antibiotic translocation across bacterial walls. High-resolution recording of ionic current through the single channel, formed by the general bacterial porin, OmpF, enables us to resolve single-molecule events of antibiotic translocation. [ABSTRACT FROM AUTHOR]

The article presents the study which focuses on partitioning of size-dependent forced polyethylene glycols (PEGs) into outer voltage-dependent anion channels, outer membrane protein C and bacterial channel-forming toxin alpha-hemolysin. Topics mentioned include the osmotic pressure of PEGs, effects of PEGs on electrolyte solution, and the ability of PEgs to reduce electrolyte conductivity.

It was previously shown that tubulin dimer interaction with the mitochondrial outer membrane protein voltage-dependent anion channel (VDAC) blocks traffic through the channel and reduces oxidative metabolism and that this requires the unstructured anionic C-terminal tail peptides found on both α- and β-tubulin subunits. It was unclear whether the α- and β-tubulin tails contribute equally to VDAC blockade and what effects might be due to sequence variations in these tail peptides or to tubulin post-translational modifications, which mostly occur on the tails. The nature of the contribution of the tubulin body beyond acting as an anchor for the tails had not been clarified either. Here we present peptide-protein chimeras to address these questions. These constructs allow us to easily combine a tail peptide with different proteins or combine different tail peptides with a particular protein. The results show that a single tail grafted to an inert protein is sufficient to produce channel closure similar to that observed with tubulin. We show that the β-tail is more than an order of magnitude more potent than the α-tail and that the lower α-tail activity is largely due to the presence of a terminal tyrosine. Detyrosination activates the α-tail, and activation is reversed by the removal of the glutamic acid penultimate to the tyrosine. Nitration of tyrosine reverses the tyrosine inhibition of binding and even induces prolonged VDAC closures. Our results demonstrate that small changes in sequence or post-translational modification of the unstructured tails of tubulin result in substantial changes in VDAC closure. [ABSTRACT FROM AUTHOR]