Current noise around steady states in discrete transport systems

Subject of this paper is the transport noise in discrete systems. The transport systems are given by a number (n) of binding sites separated by energy barriers. These binding sites may be in contact with constant outer reservoirs. The state of the system is characterized by the occupation numbers of particles (current carriers) at these binding sites. The change in time of the occupation numbers is generated by individual “jumps” of particles over the energy barriers, building up the flux matter (for charged particles: the electric current). In the limit n → ∞ continuum processes as e.g. usual diffusion are included in the transport model. The fluctuations in occupation numbers and other quantities linearly coupled to the occupation numbers may be treated with the usual master equation approach. The treatment of the fluctuations in fluxes (current) makes necessary a different theoretical approach which is presented in this paper under the assumption of vanishing interactions between the particles. This approach may be applied to a number of different transport systems in biology and physics (ion transport through porous channels in membranes, carrier mediated ion transport through membranes, jump diffusion e.g. in superionic conductors). As in the master equation approach the calculation of correlations and noise spectra may be reduced to the solution of the macroscopic equations for the occupation numbers. This result may be regarded as a generalization to non-equilibrium current fluctuations of the usual Nyquist theorem relating the current (voltage) noise spectrum in thermal equilibrium to the macroscopic frequency dependent admittance.The validity of the general approach is demonstrated by the calculation of the autocorrelation function and spectrum of current noise for a number of special examples (e.g, pores in membrances, carrier mediated ion transport).     

A channel mechanism for electrogenic ion pumps

A model of active ion transport is analyzed in which an essential part of the pump molecule is an ion channel. Ion translocation in the channel is described as a series of jumps between binding sites which are separated by energy barriers. Pumping action results from a transient energy-dependent modification of the barrier structure of the channel and requires only minor conformational changes of the pump molecule. This model is applied to the lightdriven proton pump of Halobacterium and to redox-coupled proton pumps in the mitochondrial respiratory chain. Similar considerations may be used to describe ATP-dependent ion transport.     

Energy-dependent masking of substrate binding sites of the lactose permease of Escherichia coli

A method was devised to measure the number of specific substrate binding sites of lactose permease in membrane preparations derived from mechanically disrupted Escherichia coli.The method consists of incubation with radioactive thiodigalactoside (galactosyl β-d-thiogalactoside, TDG) followed by precipitation with 80% saturated (NH₄)₂SO₄ and washing with the same solution.The measurement gave reproducible results, easy to correct for a moderate nonspecific binding, but active transport, when it occurred, resulted in excess counts.The radioactivity bound to the pellet was shown to depend on the presence of intact lac y gene product.Addition of ascorbate and phenazine methosulfate (PMS) stimulated active transport into the membrane vesicles. This could be inhibited by cyanide and by uncoupling agents and under these conditions the number of available binding sites was strongly diminished, while the inhibitors alone did not bring about a similar decrease.The decrease of available substrate binding sites was reversed by removal of oxygen or by washing out the respiratory substrates.The decrease in available binding sites is interpreted as reflecting one of the energy coupling steps which during in vivo active transport prevents the mobile carrier from being available for outflux, but the detailed interpretation of the reported results raises a number of problems connected with the energy cycle of active transport     

Unidirectional fluxes in saturated single-file pores of biological and artificial membranes I. Pores containing no more than one vacancy

A theoretical treatment of isotope fluxes in filled single-file pores is given. The treatment is confined to pores permitting only one vacancy at a time. Tracer flux, unidirectional fluxes and net flux are calculated. The exponent n which is obtained by representing the ratio of unidirectional fluxes as a power of the electrochemical activity-ratio proves to be closely related with m, the number of sites per pore. The minimum and maximum values of n are m?1 and m. It is shown that measurement of n provides sufficient information to determine m if the energetic properties of sites and barriers do not change too much with varying concentrations. Unlike the unidirectional fluxes, the net fluxes yield no direct information about the number of sites. The concentration dependence of the net fluxes, however, can be used to discriminate between the two limiting cases, n = m?1 and n = m. It is interesting with regard to the instantaneous potassium currents of nerve membranes that a suitable choice of the energetic parameters of a filled pore leads to a quasi-linearity of the net flux-voltage curves, which is only slightly affected by variation of the external concentration.     

Determination of membrane potential with lipophilic cations. Comparison of estimated values with various phosphonium ions

The binding of lipophilic ions to the membrane of envelope vesicles from Halobacterium halobium was examined. The lipophilic ions used constitute a homologous series of (Phe)₃-P⁺-(CH₂)_n-CH₃ (n = 0–5) and tetraphenylphosphonium (TPP⁺). In the absence of membrane potential, the binding of probes to the membrane was measured. For the probes of n = 0 and n = 1, and for TPP⁺, binding followed the Langmuir adsorption isotherm. For other probes, analysis revealed the presence of two, high- and low-affinity, binding sites. Upon illumination, which generated the membrane potential, the probe molecules were accumulated into the vesicles. If we ignore the membrane-potential-dependent binding of the probe molecules, the estimated values are larger when the probe used is more hydrophobic. We have tested some models describing the amount of probe bound on membranes in terms of concentration of free probe inside and outside the vesicles. No model has fulfilled the criterion of valid estimation that the membrane potentials estimated are independent of probes used. An experimental method for the estimation of true membrane potential is proposed. Effects of tetraphenylboron on the estimation of membrane potential and on the transport rate of phosphonium cations were examined.     

Modulation of serotonin binding in rat brain by membrane fluidity

Preincubation of rat brain homogenates with increasing concentrations of n-hexanol reduced specific serotonin (5-HT) binding and increased membrane fluidity as measured by fluorescence depolarization using 1,6-diphenyl-1,3,5-hexatriene (DPH) as a probe. At 5 mM ascorbate maximal reductions of both membrane fluidity and specific 5-HT binding were observed. Both effects were enhanced in the presence of ferrous sulphate and oxygen. In the presence of ascorbate (5.7 mM) only one 5-HT binding site was observed in contrast with high and low affinity binding sites (K_D1 = 0.08 ± 0.04 nM, K_D2 = 28.8 ± 1.3 nM) found in the absence of ascorbate. The ascorbate induced decrease of specific 5-HT binding may be explained by lipid peroxidation, which decreases membrane fluidity, and by ascorbate's reducing properties. Since different correlations were found between membrane fluidity and specific 5-HT binding depending upon the presence of ascorbate or n-hexanol, the results suggest that membrane fluidity is a critical factor, however, just one of several determinants in 5-HT binding studies.     

Dynamics of the TOM Complex of Mitochondria during Binding and Translocation of Preproteins

Translocation of preproteins across the mitochondrial outer membrane is mediated by the TOM complex. This complex consists of receptor components for the initial contact with preproteins at the mitochondrial surface and membrane-embedded proteins which promote transport and form the translocation pore. In order to understand the interplay between the translocating preprotein and the constituents of the TOM complex, we analyzed the dynamics of the TOM complex of Neurospora crassa and Saccharomyces cerevisiae mitochondria by following the structural alterations of the essential pore component Tom40 during the translocation of preproteins. Tom40 exists in a homo-oligomeric assembly and dynamically interacts with Tom6. The Tom40 assembly is influenced by a block of negatively charged amino acid residues in the cytosolic domain of Tom22, indicating a cross-talk between preprotein receptors and the translocation pore. Preprotein binding to specific sites on either side of the outer membrane (cis and trans sites) induces distinct structural alterations of Tom40. To a large extent, these changes are mediated by interaction with the mitochondrial targeting sequence. We propose that such targeting sequence-induced adaptations are a critical feature of translocases in order to facilitate the movement of preproteins across cellular membranes.     

Beyond non-integer Hill coefficients: A novel approach to analyzing binding data,applied to Na+-driven transporters

Prokaryotic and eukaryotic Na⁺-driven transporters couple the movement of one or more Na⁺ ions down their electrochemical gradient to the active transport of a variety of solutes. When more than one Na⁺ is involved, Na⁺-binding data are usually analyzed using the Hill equation with a non-integer exponent n. The results of this analysis are an overall K_d-like constant equal to the concentration of ligand that produces half saturation and n, a measure of cooperativity. This information is usually insufficient to provide the basis for mechanistic models. In the case of transport using two Na⁺ ions, an n < 2 indicates that molecules with only one of the two sites occupied are present at low saturation. Here, we propose a new way of analyzing Na⁺-binding data for the case of two Na⁺ ions that, by taking into account binding to individual sites, provides far more information than can be obtained by using the Hill equation with a non-integer coefficient: it yields pairs of possible values for the Na⁺ affinities of the individual sites that can only vary within narrowly bounded ranges. To illustrate the advantages of the method, we present experimental scintillation proximity assay (SPA) data on binding of Na⁺ to the Na⁺/I⁻ symporter (NIS). SPA is a method widely used to study the binding of Na⁺ to Na⁺-driven transporters. NIS is the key plasma membrane protein that mediates active I⁻ transport in the thyroid gland, the first step in the biosynthesis of the thyroid hormones, of which iodine is an essential constituent. NIS activity is electrogenic, with a 2:1 Na⁺/I⁻ transport stoichiometry. The formalism proposed here is general and can be used to analyze data on other proteins with two binding sites for the same substrate.     

Fast kinetic studies on the allosteric interactions between acetylcholine receptor and local anesthetic binding sites.

Preincubation of receptor-rich membrane fragments from Torpedo marmorata with tertiary amine local anesthetics and several toxins such as histrionicotoxin, crotoxin and cerulotoxin, modifies the amplitude and time course of the relaxation processes monitored upon rapid mixing of the membrane fragments with the fluorescent agonist, Dns-C6-Cho. In particular, the amplitude of the rapid relaxation process, which is proportional to the fraction of acetylcholine receptor sites in a high-affinity state, increases; accordingly, the rate constant of the 'slow' and 'intermediate' relaxation processes also increases up to ten times (except with histrionicotoxin) whereas in a higher range of local anesthetic concentrations the rate constant of the 'rapid' relaxation process decreases. The data are accounted for by a two-state model of the acetylcholine regulator, assuming distinct binding sites for cholinergic agonists and local anesthetics and allosteric interactions between these two classes of sites; local anesthetics stabilize the regulator in a high-affinity state for agonists even in the absence of agonist, and modify the rate constants for th interconversions between the low-affinity and high-affinity states. The model accounts for the 'slow' fluorescence increase monitored upon addition of local anesthetics to a suspension of receptor-rich membranes supplemented with trace amounts of Dns-C6-Cho. The effect of local anesthetics on the apparent rate constant of the 'rapid' relaxation process can be accounted for on the basis of an additional low-affinity binding of local anesthetics to the acetylcholine receptor site. Finally the increase of the apparent rate constant of the 'intermediate' relaxation process can be simply accounted for by assuming the existence of a third state, corresponding to the 'active' state, to which local anesthetics bind and block ionic transport.     

An Iris-Like Mechanism of Pore Dilation in the CorA Magnesium Transport System

Magnesium translocation across cell membranes is essential for numerous physiological processes. Three recently reported crystal structures of the CorA magnesium transport system revealed a surprising architecture, with a bundle of giant α-helices forming a 60-Å-long pore that extends beyond the membrane before widening into a funnel-shaped cytosolic domain. The presence of divalent cations in putative intracellular regulation sites suggests that these structures correspond to the closed conformation of CorA. To examine the nature of the conduction pathway, we performed 110-ns molecular-dynamics simulations of two of these structures in a lipid bilayer with and without regulatory ions. The results show that a 15-Å-long hydrophobic constriction straddling the membrane-cytosol interface constitutes a steric bottleneck whose location coincides with an electrostatic barrier opposing cation translocation. In one of the simulations, structural relaxation after the removal of regulatory ions led to concerted changes in the tilt of the pore helices, resulting in iris-like dilation and spontaneous hydration of the hydrophobic neck. This simple and robust mechanism is consistent with the regulation of pore opening by intracellular magnesium concentration, and explains the unusual architecture of CorA.     

Interfacial barriers to gas transport: probing solid-gas interfaces at the atomistic level

ABSTRACT

An understanding of interfacial barriers underpinning fluid transport in nanoporous membranes is critical for the design of efficient next generation membranes, to harness their potential for industrial scale separations. Such barriers include the contribution of external and internal interfacial barriers, and strongly depend on smoothness of the pore surface, pore size, shape, tortuosity, structural defects such as pore blockage and thermodynamic state of the fluid. We review recent progress in the transport of a fluid through nanoporous membrane materials such as zeolites and carbon nanotubes, which hold promise for industrial significance, but their application is subject to strong interfacial barriers. The contribution of interfacial barriers to the overall transport in these membrane materials is found to be particularly significant when the pore surface is uniform as well as at low temperatures and pressures. Further, such barriers that arise from internal defects such as grain boundaries are found to be remarkable and detrimental to separation kinetics. The internal interfacial barriers are found to be significant, and are enhanced when a dense medium such as a polymer is present at the interface, suggesting that interfacial barriers can play a key role in mixed matrix membranes and is an important area requiring further attention.     

A physical model for the simultaneous membrane transport and metabolism of drugs.

A simple model for the simultaneous passive membrane transport and bioconversion of a drug, which may be a weak electrolyte or a neutral molecule, is mathematically described. It includes an aqueous diffusion layer and an operational aqueous pore pathway. The applicability of the model is shown for the in situ rat intestinal transport of prostaglandin F_2a.     

An Energy-Barrier Model for the Permeation of Monovalent and Divalent Cations Through the Maxi Cation Channel in the Plasma Membrane of Rye Roots

The depolarization-activated, high-conductance ``maxi' cation channel in the plasma membrane of rye (Secale cereale L.) roots is permeable to a wide variety of monovalent and divalent cations. The permeation of K⁺, Na⁺, Ca²⁺ and Ba²⁺ through the pore could be simulated using a model composed of three energy barriers and two ion binding sites (a 3B2S model), which assumed single-file permeation and the possibility of double cation occupancy. The model had an asymmetrical free energy profile. Differences in permeation between cations were attributed primarily to differences in their free energy profiles in the regions of the pore adjacent to the extracellular solution. In particular, the height of the central free energy peak differed between cations, and cations differed in their affinities for ion binding sites. Significant ion repulsion occurred within the pore, and the mouths of the pore had considerable surface charge. The model adequately described the diverse current vs. voltage (I/V) relationships obtained over a wide variety of experimental conditions. It described the phenomena of non-Michaelian unitary conductance vs. activity relationships for K⁺, Na⁺ and Ca²⁺, differences in selectivity sequences obtained from measurements of conductance and permeability ratios, changes in relative cation permeabilities with solution composition, and the complex effects of Ba²⁺ and Ca²⁺ on K⁺ currents through the channel. The model enabled the prediction of unitary currents and ion fluxes through the maxi cation channel under physiological conditions. It could be used, in combination with data on the kinetics of the channel, as input to electrocoupling models allowing the relationships between membrane voltage, Ca²⁺ influx and Ca²⁺ signaling to be studied theoretically. Received: 29 April 1998/Revised: 20 November 1998     

Polyol permeability of the human red cell. Interpretation of glucose transport in terms of a pore

The kinetic equations describing transport through a pore that has a binding site and that undergoes a conformational change are identical to those of a carrier model. Therefore, in order to distinguish between the two models it is necessary to test specific predictions based on detailed mechanistic models. A pore model is described in which the substrate (glucose) is able to reach the single binding site only from the outside when the pore is in conformation I and only from the inside when it is conformation II. On the basis of this model it is predicted that solutes which do not have any specific affinity for the binding site should still have a finite permeability via the glucose transport system if they are the same size or smaller than glucose. This permeability should be proportional to the volume of distribution of the solute in the pore and should therefore decrease with increasing molecular size. A geometric pore volume can be estimated from this size dependence. In order to test these predictions, the glucose-dependent permeability of a series of 4-carbon (erythritol), 5-carbon (d-arabitol, l-arabitol and xylitol) and 6-carbon (d-mannitol, d-sorbitol and $\text{myo-}\text{inositol}$) polyols was measured. The permeability of all the polyols is decreased by the presence of glucose and the $\text{K}{}_{\mathrm{<mtext>I</mtext>}}$ of this “inhibitable” component is similar to that of d-sorbose, suggesting that this component is associated with the glucose transport system. Since these observations could be explained entirely in terms of a specific affinity for a carrier binding site, they do not exclude a carrier mechanism. However, as predicted for the pore model, this “inhibitable” permeability decreased with increasing molecular size and the calculated geometric pore volume was of a size that would be expected for a cell membrane pore.     

The Kinetics of Osmotic Transport through Pores of Molecular Dimensions

This paper presents a theoretical analysis of the kinetics of osmotic transport across a semipermeable membrane. There is a thermodynamic connection between the rate of flow under a hydrostatic pressure difference and the rate of flow due to a difference in solute concentration on the two sides. One might therefore attempt to calculate the osmotic transport coefficient by applying Poiseuille's equation to the flow produced by a difference in hydrostatic pressure. Such a procedure is, however, inappropriate if the pores in the membrane are too small to allow molecules to “overtake.” It then becomes necessary to perform a statistical calculation of the transport coefficient, and such a calculation is described in this paper. The resulting expression for the number of solvent molecules passing through a pore per second is J = m D₁ δn₁/l² where m is the number of solvent molecules in the pore, l is the length of the pore, D₁ is the self-diffusion coefficient of the solute, and δn₁ the difference in solvent mole fraction on the two sides of the membrane. This equation is used for estimating the number of pores per unit area of the squid axon membrane; the result is 6 × 10⁹ pores/cm².     

Human platelet alpha 2-adrenergic receptors: labeling with 3H-yohimbine, a selective antagonist ligand

³H-Yohimbine, a potent and selective pharmacological antagonist of α₂-adrenergic receptors, labeled human platelet membrane α₂-receptors with high affinity. Binding was rapid and reversible at 25°C. Both saturation and kinetic experiments indicated a single order of binding sites, with an equilibrium K_D value of 1.0–1.5 nM. Low Mg²⁺ concentrations increased the K_D for ³H-yohimbine without altering the B_max. The ³H-yohimbine site exhibited α₂-receptor specificity: (?)-norepinephrine and (?)-isoproterenol were 4.8 and 330 times less potent than (?)-epinephrine; (?)-catecholamines were 17–35 times more potent than corresponding (+)-catecholamines; the selective α₁-antagonist prazosin was 340 times less potent than yohimbine. Catecholamine agonists exhibited shallow curves in inhibiting ³H-yohimbine binding, with pseudo-Hill coefficients (n_H) of less than 1.0, whereas the n_H of antagonists was 1.0. No specific binding of ³H-prazosin to platelet membranes was observed, indicating the absence of α₁-receptors. ³H-Yohimbine labeled fewer platelet sites than did ³H-dihydroergocryptine under identical conditions (80 vs 130 receptors/ cell), and may be a more specific and useful antagonist probe of platelet α₂-receptors than ³H-dihydroergocryptine.     

Free energy and kinetics of cAMP permeation through connexin26 via applied voltage and milestoning

The connexin family is a diverse group of highly regulated wide-pore channels permeable to biological signaling molecules. Despite the critical roles of connexins in mediating selective molecular signaling in health and disease, the basis of molecular permeation through these pores remains unclear. Here, we report the thermodynamics and kinetics of binding and transport of a second messenger, adenosine-3′,5′-cyclophosphate (cAMP), through a connexin26 hemichannel (Cx26). First, inward and outward fluxes of cAMP molecules solvated in KCl solution were obtained from 4 μs of ± 200 mV simulations. These fluxes data yielded a single-channel permeability of cAMP and cAMP/K⁺ permeability ratio consistent with experimentally measured values. The results from voltage simulations were then compared with the potential of mean force (PMF) and the mean first passage times (MFPTs) of a single cAMP without voltage, obtained from a total of 16.5 μs of Voronoi-tessellated Markovian milestoning simulations. Both the voltage simulations and the milestoning simulations revealed two cAMP-binding sites, for which the binding constants K_D and dissociation rates k_off were computed from PMF and MFPTs. The protein dipole inside the pore produces an asymmetric PMF, reflected in unequal cAMP MFPTs in each direction once within the pore. The free energy profiles under opposite voltages were derived from the milestoning PMF and revealed the interplay between voltage and channel polarity on the total free energy. In addition, we show how these factors influence the cAMP dipole vector during permeation, and how cAMP affects the local and nonlocal pore diameter in a position-dependent manner.     

Interactions of hydrogen molecules with complexes of lithium cation and aromatic nitrogen-containing heterocyclic anions

Highly stable salt functional groups consisting of lithium cation and aromatic anions (C _n H _n N_5?n ?Li) are studied for hydrogen storage using ab initio calculations, force field development, and grand canonical Monte Carlo simulations. Second-order Møller–Plesset perturbation theory with the resolution of identity approximation calculations are calibrated at the CCSD(T)/complete basis set (CBS) level of theory. The calibrations on different types of binding sites are different, but can be used to correct the van der Waals interactions systematically. The anion and salt functional groups provide multiple binding sites. With increased number of nitrogen atoms in the aromatic anion, the number of binding sites increases but the average binding energy decreases. Among the functional groups considered, CHN₄-Li exhibits the largest number of binding sites (14) and a weak average binding energy of 5.7 kJ mol^–1 with CCSD(T)/CBS correction. The calculated adsorption isotherms demonstrate that the introduction of the functional group significantly enhances hydrogen uptake despite relatively weak average binding energy. Therefore, it is concluded that searching for functional groups with the larger number of binding sites is another key factor for enhancing the hydrogen storage capacity, given that other conditions such as free volume and surface area are fixed.     

Structure and function of the nuclear pore complex: new perspectives.

The double membrane of the nuclear envelope is a formidable barrier separating the nucleus and cytoplasm of eukaryotic cells. However, movement of specific macromolecules across the nuclear envelope is critical for embryonic development, cell growth and differentiation. Transfer of molecules between the nucleus and cytoplasm occurs through the aqueous channel formed by the nuclear pore complex (NPC)

1 Abbreviations: NPC, nuclear pore complex; GlcNac, N-acetylglucosamine; WGA, wheat germ agglutinin

. Although small molecules may simply diffuse across the NPC, transport of large proteins and RNA requires specific transport signals and is energy dependent. A family of pore glycoproteins modified by O-linked N-acetylglucosamine moieties are essential for transport through the NPC. Recent evidence suggests that the regulation of nuclear transport may also involve the inteaction of RNA and nuclear proteins with specific binding proteins that recognize these transport signals. Are these nuclear pore glycoproteins and signal binding proteins the ‘gatekeepers’ that control access to the genetic material? Recent evidence obtained from a combination of biochemical and genetic approaches suggests – perhaps.     

Ion Selectivity of the KcsA Channel: A Perspective from Multi-Ion Free Energy Landscapes

Potassium (K⁺) channels are specialized membrane proteins that are able to facilitate and regulate the conduction of K⁺ through cell membranes. Comprising five specific cation binding sites (S₀-S₄) formed by the backbone carbonyl groups of conserved residues common to all K⁺ channels, the narrow selectivity filter allows fast conduction of K⁺ while being highly selective for K⁺ over Na⁺. To extend our knowledge of the microscopic mechanism underlying selectivity in K⁺ channels, we characterize the free energy landscapes governing the entry and translocation of a Na⁺ or a K⁺ from the extracellular side into the selectivity filter of KcsA. The entry process of an extracellular ion is examined in the presence of two additional K⁺ in the pore, and the three-ion potential of mean force is computed using extensive all-atom umbrella sampling molecular dynamics simulations. A comparison of the potentials of mean force yields a number of important results. First, the free energy minima corresponding to configurations with extracellular K⁺ or Na⁺ in binding site S₀ or S₁ are similar in depth, suggesting that the thermodynamic selectivity governed by the free energy minima for those two binding sites is insignificant. Second, the free energy barriers between stable multi-ion configurations are generally higher for Na⁺ than for K⁺, implying that the kinetics of ion conduction is slower when a Na⁺ enters the pore. Third, the region corresponding to binding site S₂ near the center of the narrow pore emerges as the most selective for K⁺ over Na⁺. In particular, while there is a stable minimum for K⁺ in site S₂, Na⁺ faces a steep free energy increase with no local free energy well in this region. Lastly, analysis shows that selectivity is not correlated with the overall coordination number of the ion entering the pore, but is predominantly affected by changes in the type of coordinating ligands (carbonyls versus water molecules). These results further highlight the importance of the central region near binding site S₂ in the selectivity filter of K⁺ channels.