Monte Carlo simulations of ionic channel selectivity

Monte Carlo simulations have been developed to study the selectivityof ionic channels in biological membranes. The channel is consideredto be in either of two possible states: (i) densely packed withions, the ions moving in single file in one direction, or alternatively,(ii) sparsely packed, where holes could appear at any particulartime thereby allowing bidirectional movement of ions. The twomodels enable us to envisage a quantitative flux of permeableions in the presence of smaller sized ions, taking into considerationtheir concentrations in the bulk solutions, the ion-channelinteractions and probability with which they fill up the channel.The programs are written in FORTRAN-77 (MS-FORTRAN) for an IBM-compatiblepersonal computer. From the simulation results we observe anenzymatic function of the channel and also note that the smallersized ions tend to block the movement of permeable ions. Thesimulations represent a technique for visualization of the factorsthat decide ionic permeability and help in manipulating theireffects with ease and speed which would otherwise involve intricateexperimental setups. Received on September 7, 1990; accepted on January 14, 1991     

Ion-water and ion-polypeptide correlations in a gramicidin-like channel. A molecular dynamics study.

This work describes a molecular dynamics study of ion-water and ion-polypeptide correlation in a model gramicidin-like channel (the polyglycine analogue) based upon interaction between polarizable, multipolar groups. The model suggests that the vicinity of the dimer junction and of the ethanolamine tail are regions of unusual flexibility. Cs+ binds weakly in the mouth of the channel: there it coordinates five water molecules and the #11CO group with which it interacts strongly and is ideally aligned. In the channel interior it is generally pentacoordinate; at the dimer junction, because of increased channel flexibility, it again becomes essentially hexacoordinate. The ion is also strongly coupled to the #13 CO but not to either #9 or #15, consistent with 13C NMR data. Water in the channel interior is strikingly different from bulk water; it has a much lower mean dipole moment. This correlates with our observation (which differs from that of previous studies) that water-water angular correlations do not persist within the channel, a result independent of ion occupancy or ionic polarity. In agreement with streaming potential measurements, there are seven single file water molecules associated with Cs+ permeation; one of these is always in direct contact with bulk water. At the mouth of an ion-free channel, there is a pattern of dipole moment alteration among the polar groups. Due to differential interaction with water, exo-carbonyls have unusually large dipole moments whereas those of the endo-carbonyls are low. The computed potential of mean force for CS+ translocation is qualitatively reasonable. However, it only exhibits a weakly articulated binding site and it does not quantitatively account for channel energetics. Correction for membrane polarization reduces, but does not eliminate, these problems.     

Modeling permeation energetics in the KcsA potassium channel

The thermodynamics of cation permeation through the KcsA K(+) channel selectivity filter is studied from the perspective of a physically transparent semimicroscopic model using Monte Carlo free energy integration. The computational approach chosen permits dissection of the separate contributions to ionic stabilization arising from different parts of the channel (selectivity filter carbonyls, single-file water, cavity water, reaction field of bulk water, inner helices, ionizable residues). All features play important roles; their relative significance varies with the ion's position in the filter. The cavity appears to act as an electrostatic buffer, shielding filter ions from structural changes in the inner pore. The model exhibits K(+) vs. Na(+) selectivity, and roughly isoenergetic profiles for K(+) and Rb(+), and discriminates against Cs(+), all in agreement with experimental data. It also indicates that Ba(2+) and Na(+) compete effectively with permeant ions at a site near the boundary between the filter and the cavity, in the vicinity of the barium blocker site.     

Current and selectivity in a model sodium channel under physiological conditions: Dynamic Monte Carlo simulations

A reduced model of a sodium channel is analyzed using Dynamic Monte Carlo simulations. These include the first simulations of ionic current under approximately physiological ionic conditions through a model sodium channel and an analysis of how mutations of the sodium channel's DEKA selectivity filter motif transform the channel from being Na(+) selective to being Ca(2+) selective. Even though the model of the pore, amino acids, and permeant ions is simplified, the model reproduces the fundamental properties of a sodium channel (e.g., 10 to 1 Na(+) over K(+) selectivity, Ca(2+) exclusion, and Ca(2+) selectivity after several point mutations). In this model pore, ions move through the pore one at a time by simple diffusion and Na(+) versus K(+) selectivity is due to both the larger K(+) not fitting well into the selectivity filter that contains amino acid terminal groups and K(+) moving more slowly (compared to Na(+)) when it is in the selectivity filter.     

Molecular origin of the cation selectivity in OmpF porin: single channel conductances vs. free energy calculation

Ion current through single outer membrane protein F (OmpF) trimers was recorded and compared to molecular dynamics simulation. Unidirectional insertion was revealed from the asymmetry in channel conductance. Single trimer conductance showed particularly high values at low symmetrical salt solution. The conductance values of various alkali metal ion solutions were proportional to the monovalent cation mobility values in the bulk phase, LiCl相似文献   

Brownian dynamics study of a multiply-occupied cation channel: application to understanding permeation in potassium channels.

The behavior of a multiply-occupied cation-selective channel has been computed by Brownian dynamics. The length, cross-section, ion-ion repulsion force, and ionic mobility within the channel are all estimated from data and physical reasoning. The only free parameter is a partition energy at the mouth of the channel, defining the free energy of an ion in the channel compared to the bath. It is presumed that this partition energy is associated with the energetics of exchanging a bulk hydration environment for a channel hydration environment. Varying the partition energy alone, keeping all other parameters fixed, gives approximately the full range of magnitudes of single channel conductances seen experimentally for K channels. Setting the partition energy at -11 kT makes the computed channel look similar to a squid axon K channel with respect to magnitude of conductance, shape of the I-V curve, non-unity of Ussing flux ratio exponents, decrease of current and increase of conductance with extracellular ion accumulation, and saturation at high ion concentration in the bathing solution. The model includes no preferred binding sites (local free energy minima) for ions in the channel. Therefore it follows that none of the above-mentioned properties of K channels are strong evidence for the existence of such sites. The model does not show supersaturation of current at very high bathing concentrations nor any pronounced voltage-dependence of the Ussing flux ratio exponent, suggesting that these features would require additional details not included in the model presented herein.     

Monte Carlo simulation of the water in a channel with charges.

A Monte Carlo simulation of water in a channel with charges suggests the existence of water in immobile, high density, essentially glasslike form near the charges. The channel model has a conical section with an opening through which water molecules can pass, at the narrow end of the cone, and a cylindrical section at the other end. When the charges are placed near the narrow section of the model, the "glass" effectively blocks the channel; with the charges removed, the channel opens. The effect can be determined from the rate of passage of the water molecules through the pore, from the average orientation of the water molecule, and from distortion of the distribution of molecules. In the simulations carried out to date, no external ions have been considered. In addition to the energy, the Helmholtz free energy has been calculated.     

Water and ion permeation in bAQP1 and GlpF channels: a kinetic Monte Carlo study

The kinetic Monte Carlo reaction-path-following technique is applied to determine the lowest-energy water pathway and the coordinating amino acids in bAQP1 and GlpF channels, both treated as rigid. In bAQP1, water molecules pass through the pore between the asparagine-proline-alanine (NPA) and selectivity filter (SF) sites one at a time. The water chain is interrupted at the SF where one water forms three stable hydrogen bonds with protein atoms. In this SF, water's conformation depends on the protonation locus of H182. In GlpF, two water molecules bond simultaneously to the NPA asparagines and pass through the SF in zigzag fashion. No water single-file forms in rigid GlpF. To accommodate a single file of waters requires narrowing the GlpF pore. Our results reveal that in both proteins a proposed bipolar water arrangement is thermally disrupted in the NPA region, especially in the cytoplasmic part of the pore. The equilibrium hydrogen-bonded chain is occasionally interrupted in the hydrophobic zones adjacent to the NPA motifs. The permeation of alkali cations through bAQP1 and GlpF is barred due to a large free-energy barrier in the NPA region as well as a large energy barrier blocking entry from the cytoplasm. Permeation of halides is prevented due to two large energy barriers in the cytoplasmic and periplasmic pores as well as a large free-energy barrier barring entry from the periplasm. Our results, based on modeling charge permeation, support an electrostatic rather than orientational basis for proton exclusion. Binding within the aquaporin pore cannot compensate sufficiently for dehydration of the protonic charge; there is also an electrostatic barrier in the NPA region blocking proton transport. The highly ordered single file of waters, which is drastically interrupted at the SF of bAQP1, may also contribute to proton block.     

Dynamics and energetics of water permeation through the aquaporin channel

Structural properties of water inside bovine aquaporin-1 are investigated by molecular simulation. The calculations, which are based on the recently determined X-ray structure at 2.2 A resolution (Sui et al., Nature 2001;414:872-878), are carried out on one monomeric subunit immersed in a water-n-octane-water bilayer. Molecular dynamics (MD) simulations suggest that His182, a fully conserved residue in the channel pore, is protonated in the delta position. Furthermore, they reveal a highly ordered water structure in the channel, induced by the electrostatic properties of the protein. Multiple-steering MD simulations are used to calculate the free-energy of water diffusion. To the best of our knowledge, this represents the first free-energy calculation based on the new, high-resolution structure of the pore. The calculated barrier is 2.5 kcal/mol, and it is associated to water permeation through the Asn-Pro-Ala (NPA) region of the pore, where water molecules are only hydrogen-bonded with themselves. These findings are fully consistent with those based on the previous MD studies on the human protein (de Groot and Grubmüller, Science 2001;294:2353-2357).     

Control of cation permeation through the nicotinic receptor channel

We used molecular dynamics (MD) simulations to explore the transport of single cations through the channel of the muscle nicotinic acetylcholine receptor (nAChR). Four MD simulations of 16 ns were performed at physiological and hyperpolarized membrane potentials, with and without restraints of the structure, but all without bound agonist. With the structure unrestrained and a potential of −100 mV, one cation traversed the channel during a transient period of channel hydration; at −200 mV, the channel was continuously hydrated and two cations traversed the channel. With the structure restrained, however, cations did not traverse the channel at either membrane potential, even though the channel was continuously hydrated. The overall results show that cation selective transport through the nAChR channel is governed by electrostatic interactions to achieve charge selectivity, but ion translocation relies on channel hydration, facilitated by a trans-membrane field, coupled with dynamic fluctuations of the channel structure.     

The selectivity filter of the cation channel TRPM4

Transient receptor potential channel melastatin subfamily (TRPM) 4 and its close homologue, TRPM5, are the only two members of the large transient receptor potential superfamily of cation channels that are impermeable to Ca(2+). In this study, we located the TRPM4 selectivity filter and investigated possible structural elements that render it Ca(2+)-impermeable. Based on homology with known cation channel pores, we identified an acidic stretch of six amino acids in the loop between transmembrane helices TM5 and TM6 ((981)EDMDVA(986)) as a potential selectivity filter. Substitution of this six-amino acid stretch with the selectivity filter of TRPV6 (TIIDGP) resulted in a functional channel that combined the gating hallmarks of TRPM4 (activation by Ca(2+), voltage dependence) with TRPV6-like sensitivity to block by extracellular Ca(2+) and Mg(2+) as well as Ca(2+) permeation. Neutralization of Glu(981) resulted in a channel with normal permeability properties but a strongly reduced sensitivity to block by intracellular spermine. Neutralization of Asp(982) yielded a functional channel that exhibited extremely fast desensitization (tau < 5 s), possibly indicating destabilization of the pore. Neutralization of Asp(984) resulted in a non-functional channel with a dominant negative phenotype when coexpressed with wild type TRPM4. Combined neutralization of all three acidic residues resulted in a functional channel whose voltage dependence was shifted toward very positive potentials. Substitution of Gln(977) by a glutamate, the corresponding residue in divalent cation-permeable TRPM channels, altered the monovalent cation permeability sequence and resulted in a pore with moderate Ca(2+) permeability. Our findings delineate the selectivity filter of TRPM channels and provide the first insight into the molecular basis of monovalent cation selectivity.     

Molecular determinants of permeation through the cation channel TRPV4

We have studied the molecular determinants of ion permeation through the TRPV4 channel (VRL-2, TRP12, VR-OAC, and OTRPC4). TRPV4 is characterized by both inward and outward rectification, voltage-dependent block by Ruthenium Red, a moderate selectivity for divalent versus monovalent cations, and an Eisenman IV permeability sequence. We identify two aspartate residues, Asp(672) and Asp(682), as important determinants of the Ca(2+) sensitivity of the TRPV4 pore. Neutralization of either aspartate to alanine caused a moderate reduction of the relative permeability for divalent cations and of the degree of outward rectification. Neutralizing both aspartates simultaneously caused a much stronger reduction of Ca(2+) permeability and channel rectification and additionally altered the permeability order for monovalent cations toward Eisenman sequence II or I. Moreover, neutralizing Asp(682) but not Asp(672) strongly reduces the affinity of the channel for Ruthenium Red. Mutations to Met(680), which is located at the center of a putative selectivity filter, strongly reduced whole cell current amplitude and impaired Ca(2+) permeation. In contrast, neutralizing the only positively charged residue in the putative pore region, Lys(675), had no obvious effects on the properties of the TRPV4 channel pore. Our findings delineate the pore region of TRPV4 and give a first insight into the possible architecture of its permeation pathway.     

Molecular determinants of permeation through the cation channel TRPM6

TRPM6 and its closest relative TRPM7 are members of the Transient Receptor Potential Melastatin (TRPM) subfamily of cation channels and are known to be Mg2+ permeable. By aligning the sequence of the putative TRPM6 pore with the pore sequences of the other subfamily members, we located in the loop between the fifth and the sixth transmembrane domain, a stretch of amino acids residues, 1028GEIDVC1033, as the potential selectivity filter. Two negatively charged residues, E1024 (conserved in TRPM6, TRPM7, TRPM1 and TRPM3) and D1031 (conserved along the entire TRPM subfamily), were identified as important determinants of cation permeation through TRPM6, because neutralization of both residues into an alanine resulted in non-functional channels. Neutralization of E1029 (conserved in TRPM6, TRPM7, TRPM4 and TRPM5) resulted in channels with increased conductance for Ba2+ and Zn2+, decreased ruthenium red sensitivity and larger pore diameter compared to wild-type TRPM6. Changing the residue I1030 into methionine, resulted in channels with lower conductance for Ni2+, decreased sensitivity to ruthenium red block and reduced pore diameter. Thus, these data demonstrate that amino acid residues E1024, I1030 and D1031 are important for channel function and that subtle amino acid variation in the pore region accounts for TRPM6 permeation properties.     

Mechanisms of cation permeation in cardiac sodium channel: description by dynamic pore model.

The selective permeability to monovalent metal cations, as well as the relationship between cation permeation and gating kinetics, was investigated for native tetrodotoxin-insensitive Na-channels in guinea pig ventricular myocytes using the whole-cell patch clamp technique. By the measurement of inward unidirectional currents and biionic reversal potentials, we demonstrate that the cardiac Na-channel is substantially permeable to all of the group Ia and IIIa cations tested, with the selectivity sequence Na(+) >/= Li(+) > Tl(+) > K(+) > Rb(+) > Cs(+). Current kinetics was little affected by the permeant cation species and concentrations tested (相似文献   

A Monte Carlo study of the dynamics of G-protein activation.

To link quantitatively the cell surface binding of ligand to receptor with the production of cellular responses, it may be necessary to explore early events in signal transduction such as G-protein activation. Two different model frameworks relating receptor/ligand binding to G-protein activation are examined. In the first framework, a simple ordinary differential equation model is used to describe receptor/ligand binding and G-protein activation. In the second framework, the events leading to G-protein activation are simulated using a dynamic Monte Carlo model. In both models, reactions between ligand-bound receptors and G-proteins are assumed to be diffusion-limited. The Monte Carlo model predicts two regimes of G-protein activation, depending upon whether the lifetime of a receptor/ligand complex is long or short compared with the time needed for diffusional encounters of complexes and G-proteins. When the lifetime of a complex is relatively short compared with the diffusion time, the movement of ligand among free receptors by binding and unbinding ("switching") significantly enhances G-protein activation. Receptor antagonists dramatically reduce G-protein activation and, thus, signal transduction in this case, and significant clustering of active G-proteins near receptor/ligand complexes results. The simple ordinary differential equation model poorly predicts G-protein activation for this situation. In the alternative case, when diffusion is relatively fast, ligand movement among receptors is less important and the simple ordinary differential equation model and Monte Carlo model results are similar. In this case, there is little clustering of active G-proteins near receptor/ligand complexes. Results also indicate that as the GTPase activity of the alpha-subunit decreases, the steady-state level of alpha-GTP increases, although temporal sensitivity is compromised.     

Lateral diffusion and aggregation. A Monte Carlo study.

Aggregation in a lipid bilayer is modeled as cluster-cluster aggregation on a square lattice. In the model, clusters carry out a random walk on the lattice, with a diffusion coefficient inversely proportional to mass. On contact, they adhere with a prescribed probability, rigidly and irreversibly. Monte Carlo calculations show that, as expected, rotational diffusion of the aggregating species is highly sensitive to the initial stages of aggregation. Lateral diffusion of an inert tracer obstructed by the aggregate is a sensitive probe of the later stages of aggregation. Cluster-cluster aggregates are much more effective barriers to lateral diffusion of an inert tracer than the same area fraction of random point obstacles is, but random point obstacles are more effective barriers than the same area fraction of compact obstacles. The effectiveness of aggregates as obstacles is discussed in terms of particle-particle correlation functions and fractal dimensions. Results are applicable to aggregation of membrane proteins, and at least qualitatively to aggregation of gel-phase lipid during lateral phase separation.     

Anomalous diffusion due to binding: a Monte Carlo study.

In classical diffusion, the mean-square displacement increases linearly with time. But in the presence of obstacles or binding sites, anomalous diffusion may occur, in which the mean-square displacement is proportional to a nonintegral power of time for some or all times. Anomalous diffusion is discussed for various models of binding, including an obstruction/binding model in which immobile membrane proteins are represented by obstacles that bind diffusing particles in nearest-neighbor sites. The classification of binding models is considered, including the distinction between valley and mountain models and the distinction between singular and nonsingular distributions of binding energies. Anomalous diffusion is sensitive to the initial conditions of the measurement. In valley models, diffusion is anomalous if the diffusing particles start at random positions but normal if the particles start at thermal equilibrium positions. Thermal equilibration leads to normal diffusion, or to diffusion as normal as the obstacles allow.     

A Monte Carlo study of the self-assembly of bacteriorhodopsin

Bacteriorhodopsin (BR) and specific lipid molecules self-assemble into a quasi two-dimensional lattice structure known as the purple membrane (PM). In the PM, BR molecules exist in a trimeric form with lipid molecules present in the space enclosed by each trimeric unit and in the inter-trimer space. These trimeric units, which have a roughly circular cross-section, are arranged in hexagonal patterns with long-ranged crystalline order. In this work, we investigate the self-assembly of BR in the PM via Monte Carlo simulations of a two-dimensional model of the membrane and proteins. The protein molecules are modeled as 120 degrees sectors of a circle and the lipid molecules enter into the model through effective protein-protein interactions. The sectors cannot overlap with each other, and in addition to this excluded volume interaction there are site-site attractive interactions between specific points of the proteins to mimic interactions between helices on the proteins and lipid-induced interactions. At low values of the attractive well depth, the proteins are found in the monomeric form at all concentrations. At moderate and high values of the attractive well depth, trimers are formed as the concentration increases, and with a further increase in concentration the trimers organize into a hexagonal lattice. The interactions between the proteins and those induced by the intra-trimer lipids play an equally important role in the formation of trimers and the lattice. The lipids in the inter-trimer space cause the trimers to orient in a specific direction in the hexagonal crystal lattice.     

Anion, cation, and zwitterion selectivity of phospholemman channel molecules.

Phospholemman (PLM), a 72-amino acid membrane protein with a single transmembrane domain, forms taurine-selective ion channels in lipid bilayers. Because taurine forms zwitterions, a taurine-selective channel might have binding sites for both anions and cations. Here we show that PLM channels indeed allow fluxes of both cations and anions, making instantaneous and voltage-dependent transitions among conformations with drastically different ion selectivity characteristics. This surprising and novel ion channel behavior offers a molecular explanation for selective taurine flux across cell membranes and may explain why molecules in the phospholemman family can induce cation- or anion-selective conductances when expressed in Xenopus oocytes.     

Modeling of ion permeation in calcium and sodium channel selectivity filters

Structure-function studies have shown that it is possible to convert a sodium channel to a calcium-selective channel by a single amino acid substitution in the selectivity filter locus. Ion permeation through the "model selectivity filter" was modeled with a reduced set of functional groups representative of the constituent amino acid side chains. Force-field minimizations were conducted to obtain the energy profile of the cations as they get desolvated and bind to the "model selectivity filter." The calculations suggest that the ion selectivity in the calcium channel is due to preferential binding, whereas in the sodium channel it is due to exclusion. Energetics of displacement of a bound cation from the calcium "model selectivity filter" by another cation suggest that "multi-ion mechanism" reduces the activation barrier for ion permeation. Thus, the simple model captures qualitatively most of the conduction characteristics of sodium and calcium channels. However, the computed barriers for permeation are fairly large, suggesting that ion interaction with additional residues along the transport path may be essential to effect desolvation.