Blockage coefficient of cylindrical blocker and diffusion resistance of membrane channels.

This study deals with potential flow of ideal fluid in an infinite cylindrical tube in the presence of a blocking object. The blockage effect of the object on the flow can be characterized by a lump parameter, blockage coefficient, which accounts for the object shape and size. For a cylindrical blocking object, analytical results for the blockage coefficient are known only in three limiting cases: for a long thin cylinder and for small and large blocking disks. We propose a simple analytical expression for the blockage coefficient of a cylindrical blocker of arbitrary length and radius that reduces to the known asymptotic results in the corresponding limits.

Probing sugar translocation through maltoporin at the single channel level.

Sugar permeation through maltoporin of Escherichia coli, a trimer protein that facilitates maltodextrin translocation across outer bacterial membranes, was investigated at the single channel level. For large sugars, such as maltohexaose, elementary events of individual sugar molecule penetration into the channel were readily observed. At small sugar concentrations an elementary event consists of maltoporin channel closure by one third of its initial conductance in sugar-free solution. Statistical analysis of such closures at higher sugar concentrations shows that all three pores of the maltoporin channel transport sugars independently. Interestingly, while channel conductance is only slightly asymmetric showing about 10% higher values at -200 mV than at +200 mV (from the side of protein addition), asymmetry in dependence of the sugar binding constant on the voltage polarity is about 20 times higher. Combining our data with observations made with bacteriophage-lambda we conclude that the sugar residence time is much more sensitive to (and is decreased by) voltages that are negative from the intra-cell side of the bacterial membrane.

Watching small molecules move: interrogating ionic channels using neutral solutes.

Whether they are small enough to wriggle through the current-carrying part of an ionic channel or big enough to be kept outside and thus able to exert an osmotic stress on the channel space, polymers interact with channels in several instructive ways. The osmotic stress of excluded polymers allows one to measure the number of water molecules that come out of the channel in transitions between various "open" to "closed" states. The loss of osmotic activity, due to the partial or completely unrestricted admission of small polymers becomes a measure of the transfer probabilities of polymers from solution to small cavities; it provides an opportunity to study polymer conformation in a perfectly sieved preparation. Current fluctuations due to the partial blockage by a transient polymer are converted into estimates of times of passage and diffusion constants of polymers in channels. These estimates show how a channel whose functional states last for milliseconds is able to average over the interactions with polymers, interactions that last only microseconds. One sees clearly that in this averaging, the macromolecular channel is large enough to react like a macroscopic object to the chemical potentials of the species that modulate its activity.

[Fluctuation in the electric conductivity of lipid bilayers after one-sided application of polyene antibiotics]. / Fluktuatsiia élektroprovodnosti lipidnykh bisloev pri odnostoronnem deistvii polienovykh antibiotikov.

It is shown that the fluctuation spectrum of the lipid bilayer conductance induced by one-sided application of polyene antibiotics has a profound l/f component with a magnitude being proportional to the single-channel conductance. The observed component is thought to be caused by the channel mobility increasing at one-sided polyene application in a comparison with two-sided application where a Lorentzian spectrum of fluctuations was found earlier.

Brownian motion in confined geometries.

In a great number of technologically and biologically relevant cases, transport of micro- or nanosized objects is governed by both omnipresent thermal fluctuations and confining walls or constrictions limiting the available phase space. The present Topical Issue covers the most recent applications and theoretical findings devoted to studies of Brownian motion under confinement of channel-like geometries.

Diffusion in a tube of varying cross section: numerical study of reduction to effective one-dimensional description.

Brownian dynamics simulations of the particle diffusing in a long conical tube (the length of the tube is much greater than its smallest radius) are used to study reduction of the three-dimensional diffusion in tubes of varying cross section to an effective one-dimensional description. The authors find that the one-dimensional description in the form of the Fick-Jacobs equation with a position-dependent diffusion coefficient, D(x), suggested by Zwanzig [J. Phys. Chem. 96, 3926 (1992)], with D(x) given by the Reguera-Rubi formula [Phys. Rev. E 64, 061106 (2001)], D(x)=D/sq rt1+R'(x)2, where D is the particle diffusion coefficient in the absence of constraints, and R(x) is the tube radius at x, is valid when |R'(x)|1, higher spatial derivatives of the one-dimensional concentration in the effective diffusion equation cannot be neglected anymore as was indicated by Kalinay and Percus [J. Chem. Phys. 122, 204701 (2005)]. Thus the reduction to the effective one-dimensional description is a useful tool only when |R'(x)|

Analytical theory of hysteresis in ion channels: two-state model.

Channel-forming proteins in a lipid bilayer of a biological membrane usually respond to variation of external voltage by changing their conformations. Periodic voltages with frequency comparable with the inverse relaxation time of the protein produce hysteresis in the occupancies of the protein conformations. If the channel conductance changes when the protein jumps between these conformations, hysteresis in occupancies is observed as hysteresis in ion current through the channel. We develop an analytical theory of this phenomenon assuming that the channel conformational dynamics can be described in terms of a two-state model. The theory describes transient behavior of the channel after the periodic voltage is switched on as well as the shape and area of the hysteretic loop as functions of the frequency and amplitude of the applied voltage. The area vanishes as the voltage period T tends to zero and infinity. Asymptotic behaviors of the loop area A in the high- and low-frequency regimes, respectively, are A approximately T and A approximately T(-1).

Probing alamethicin channels with water-soluble polymers. Effect on conductance of channel states.

Channel access resistance has been measured to estimate the characteristic size of a single ion channel. We compare channel conductance in the presence of nonpenetrating water-soluble polymers with that obtained for polymer-free electrolyte solution. The contribution of the access resistance to the total alamethicin channel resistance is approximately 10% for first three open channel levels. The open alamethicin channel radii inferred for these first three levels from the access resistance are 6.3, 10.3, and 11.4 A. The dependence of channel conductance on polymer molecular weight also allows evaluation of the channel dimensions from polymer exclusion. Despite varying conductance, it was shown that steric radii of the alamethicin channel at different conductance levels remain approximately unchanged. These results support a model of the alamethicin channel as an array of closely packed parallel pores of nearly uniform diameter.

Hofmeister effect in ion transport: reversible binding of halide anions to the roflamycoin channel.

We have studied the anion-dependent gating of roflamycoin ion channels using spectral analysis of noise in currents through multichannel planar lipid bilayers. We have found that in addition to low frequency current fluctuations that may be attributed to channel switching between open and closed conformations, roflamycoin channels exhibit a pronounced higher frequency noise indicating that the open channel conductance has substates with short lifetimes. This noise is well described by a Lorentzian spectrum component with a characteristic cutoff frequency that depends on the type of halide anions according to their position in the Hofmeister series. It is suggested that transitions between the substates correspond to a reversible ionization of the channel by a penetrating anion that binds to the channel structure, more chaotropic anions being bound for longer times. Within a framework of a two-substate model, the duration of the substate with reduced electrostatic barrier for cation current varies exponentially with anion electron polarizability. This explains two features of the roflamycoin channel reported earlier: the increase in apparent single-channel conductance along the series F- < Cl- < Br- < I- and the reverse of channel selectivity from anionic for KF to cationic for KI.

Alamethicin channel conductance modified by lipid charge.

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+ 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.

Stochastic resonance in non-dynamical systems without response thresholds.

The addition of noise to a system can sometimes improve its ability to transfer information reliably. This phenomenon--known as stochastic resonance--was originally proposed to account for periodicity in the Earth's ice ages, but has now been shown to occur in many systems in physics and biology. Recent experimental and theoretical work has shown that the simplest system exhibiting 'stochastic resonance' consists of nothing more than signal and noise with a threshold-triggered device (when the signal plus noise exceeds the threshold, the system responds momentarily, then relaxes to equilibrium to await the next triggering event). Here we introduce a class of non-dynamical and threshold-free systems that also exhibit stochastic resonance. We present and analyse a general mathematical model for such systems, in which a sequence of pulses is generated randomly with a probability (per unit time) that depends exponentially on an input. When this input is a sine-wave masked by additive noise, we observe an increase in the output signal-to-noise ratio as the level of noise increases. This result shows that stochastic resonance can occur in a broad class of thermally driven physico-chemical systems, such as semiconductor p-n junctions, mesoscopic electronic devices and voltage-dependent ion channels, in which reaction rates are controlled by activation barriers.

Signal transduction across alamethicin ion channels in the presence of noise.

We have studied voltage-dependent ion channels of alamethicin reconstituted into an artificial planar lipid bilayer membrane from the point of view of electric signal transduction. Signal transduction properties of these channels are highly sensitive to the external electric noise. Specifically, addition of bandwidth-restricted "white" noise of 10-20 mV (r.m.s.) to a small sine wave input signal increases the output signal by approximately 20-40 dB conserving, and even slightly increasing, the signal-to-noise ratio at the system output. We have developed a small-signal adiabatic theory of stochastic resonance for a threshold-free system of voltage-dependent ion channels. This theory describes our main experimental findings giving good qualitative understanding of the underlying mechanism. It predicts the right value of the output signal-to-noise ratio and provides a reliable estimate for the noise intensity corresponding to its maximum. Our results suggest that the alamethicin channel in a lipid bilayer is a good model system for studies of mechanisms of primary electrical signal processing in biology showing an important feature of signal transduction improvement by a fluctuating environment.

The charge state of an ion channel controls neutral polymer entry into its pore.

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 approximately 25% but increases the ionic current by approximately 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.

Examining noise sources at the single-molecule level: 1/f noise of an open maltoporin channel.

We have studied the phenomenological origin of 1/f noise in a solute-specific bacterial ion channel, maltoporin. We show that after excision of small, but resolvable stepwise changes in the recordings of the current through a single open channel, the 1/f noise component disappears and the channel exhibits noise that is "white" below 100 Hz. Combined with results of a recent noise study of several bacterial porins, our observations suggest that 1/f noise is caused by the equilibrium conductance fluctuations related to the conformational flexibility of the channel pore structural constituents.

Noise-induced enhancement of signal transduction across voltage-dependent ion channels.

The presence of noise in a signal transduction system usually interferes with its ability to transfer information reliably. But many nonlinear systems can use noise to enhance performance, and this phenomenon, called stochastic resonance, may underlie the extraordinary ability of some biological systems to detect and amplify small signals in noisy environments. Previous work has demonstrated the occurrence of stochastic resonance in a complex system of biological transducers and neural signal pathways, but the possibility that it could occur at the sub-cellular level has remained open. Here we report the observation of stochastic resonance in a system of voltage-dependent ion channels formed by the peptide alamethicin. A hundred-fold increase in signal transduction induced by external noise is accompanied by a growth in the output signal-to-noise ratio. The system of ion channels considered here represents the simplest biological system yet known to exhibit stochastic resonance.

Protonation dynamics of the alpha-toxin ion channel from spectral analysis of pH-dependent current fluctuations.

To probe protonation dynamics inside the fully open alpha-toxin ion channel, we measured the pH-dependent fluctuations in its current. In the presence of 1 M NaCl dissolved in H2O and positive applied potentials (from the side of protein addition), the low frequency noise exhibited a single well defined peak between pH 4.5 and 7.5. A simple model in which the current is assumed to change by equal amounts upon the reversible protonation of each of N identical ionizable residues inside the channel describes the data well. These results, and the frequency dependence of the spectral density at higher frequencies, allow us to evaluate the effective pK = 5.5, as well as the rate constants for the reversible protonation reactions: kon = 8 x 10(9) M-1 s-1 and koff = 2.5 x 10(4) s-1. The estimate of kon is only slightly less than the diffusion-limited values measured by others for protonation reactions for free carboxyl or imidazole residues. Substitution of H2O by D2O caused a 3.8-fold decrease in the dissociation rate constant and shifted the pK to 6.0. The decrease in the ionization rate constants caused by H2O/D2O substitution permitted the reliable measurement of the characteristic relaxation time over a wide range of D+ concentrations and voltages. The dependence of the relaxation time on D+ concentration strongly supports the first order reaction model. The voltage dependence of the low frequency spectral density suggests that the protonation dynamics are virtually insensitive to the applied potential while the rate-limiting barriers for NaCl transport are voltage dependent. The number of ionizable residues deduced from experiments in H2O (N = 4.2) and D2O (N = 4.1) is in good agreement.

ATP transport through a single mitochondrial channel, VDAC, studied by current fluctuation analysis.

The "molecular Coulter counter" concept has been used to study transport of ATP molecules through the nanometer-scale aqueous pore of the voltage-dependent mitochondrial ion channel, VDAC. We examine the ATP-induced current fluctuations and the change in average current through a single fully open channel reconstituted into a planar lipid bilayer. At high salt concentration (1 M NaCl), the addition of ATP reduces both solution conductivity and channel conductance, but the effect on the channel is several times stronger and shows saturation behavior even at 50 mM ATP concentration. These results and simple steric considerations indicate pronounced attraction of ATP molecules to VDAC's aqueous pore and permit us to evaluate the effect of a single ATP molecule on channel conductance. ATP addition also generates an excess noise in the ionic current through the channel. Analysis of this excess noise shows that its spectrum is flat in the accessible frequency interval up to several kilohertz. ATP exchange between the pore and the bulk is fast enough not to display any dispersion at these frequencies. By relating the low-frequency spectral density of the noise to the equilibrium diffusion of ATP molecules in the aqueous pore, we calculate a diffusion coefficient D = (1.6-3.3)10(-11) m2/s. This is one order of magnitude smaller than the ATP diffusion coefficient in the bulk, but it agrees with recent results on ATP flux measurements in multichannel membranes using the luciferin/luciferase method.

Probing alamethicin channels with water-soluble polymers. Size-modulated osmotic action.

Contrary to expectations based on heightened solution viscosity, alamethicin channels appear to speed up in the presence of water soluble polyethylene glycols (PEGs) and dextrans. Specifically, added polymers reduce the probabilities of transition to higher-conductance states but do not change channel lifetimes. They thereby shorten the duration of current "bursts." These modified probabilities and kinetics reveal the action of polymer osmotic stress to suppress channel formation. The osmotic action of large, fully excluded polymers shows that some 3,000 A3 of water are taken up by the channel from the solution upon each transition to an adjacent higher-conductance state. The partial osmotic action of incompletely excluded polymers reveals the extent of exclusion for different-size polymers. The partial exclusion thus measured agrees remarkably well with estimates using data on reduction of single-channel conductance by current-impeding polymers. One can relate the degree of each polymer's exclusion to its size and to the radius of the channel pore.

A voltage-dependent channel involved in nutrient uptake by red blood cells infected with the malaria parasite.

Growth of the malaria parasite in human red blood cells (RBCs) is accompanied by an increased uptake of many solutes including anions, sugars, purines, amino acids and organic cations. Although the pharmacological properties and selectivity of this uptake suggest that a chloride channel is involved, the precise mechanism has not been identified. Moreover, the location of this uptake in the infected RBC is unknown because tracer studies are complicated by possible uptake through fluid-phase pinocytosis or membranous ducts. Here we have studied the permeability of infected RBCs using the whole-cell voltage-clamp method. With this method, uninfected RBCs had ohmic whole-cell conductances of less than 100 pS, consistent with their low tracer permeabilities. In contrast, trophozoite-infected RBCs exhibited voltage-dependent, non-saturating currents that were 150-fold larger, predominantly carried by anions and abruptly abolished by channel blockers. Patch-clamp measurements and spectral analysis confirmed that a small (< 10 pS) ion channel on the infected RBC surface, present at about 1,000 copies per cell, is responsible for these currents. Because its pharmacological properties and substrate selectivities match those seen with tracer studies, this channel accounts for the increased uptake of small solutes in infected RBCs. The surface location of this new channel and its permeability to organic solutes needed for parasite growth indicate that it may have a primary role in a sequential diffusive pathway for parasite nutrient acquisition.

Counting polymers moving through a single ion channel.

The change in conductance of a small electrolyte-filled capillary owing to the passage of sub-micrometre-sized particles has long been used for particle counting and sizing. A commercial device for such measurements, the Coulter counter, is able to detect particles of sizes down to several tenths of a micrometre. Nuclepore technology (in which pores are etched particle tracks) has extended the lower limit of size detection to 60-nm particles by using a capillary of diameter 0.45 micron (ref. 4). Here we show that natural channel-forming peptides incorporated into a bilayer lipid membrane can be used to detect the passage of single molecules with gyration radii as small as 5-15 A. From our experiments with alamethicin pores we infer both the average number and the diffusion coefficients of poly(ethylene glycol) molecules in the pore. Our approach provides a means of observing the statistics and mechanics of flexible polymers moving within the confines of precisely defined single-molecule structures.