Molecular and Brownian dynamics study of ion selectivity and conductivity in the potassium channel

Modulation of Asymmetric Flux in Heterotypic Gap Junctions by Pore Shape, Particle Size and Charge

Gap junction channels play a vital role in intercellular communication by connecting cytoplasm of adjoined cells through arrays of channel-pores formed at the common membrane junction. Their structure and properties vary depending on the connexin isoform(s) involved in forming the full gap junction channel. Lack of information on the molecular structure of gap junction channels has limited the development of computational tools for single channel studies. Currently, we rely on cumbersome experimental techniques that have limited capabilities. We have earlier reported a simplified Brownian dynamics gap junction pore model and demonstrated that variations in pore shape at the single channel level can explain some of the differences in permeability of heterotypic channels observed in in vitro experiments. Based on this computational model, we designed simulations to study the influence of pore shape, particle size and charge in homotypic and heterotypic pores. We simulated dye diffusion under whole cell voltage clamping. Our simulation studies with pore shape variations revealed a pore shape with maximal flux asymmetry in a heterotypic pore. We identified pore shape profiles that match the in silico flux asymmetry results to the in vitro results of homotypic and heterotypic gap junction formed out of Cx43 and Cx45. Our simulation results indicate that the channel's pore-shape established flux asymmetry and that flux asymmetry is primarily regulated by the sizes of the conical and/or cylindrical mouths at each end of the pore. Within the set range of particle size and charge, flux asymmetry was found to be independent of particle size and directly proportional to charge magnitude. While particle charge was vital to creating flux asymmetry, charge magnitude only scaled the observed flux asymmetry. Our studies identified the key factors that help predict asymmetry. Finally, we suggest the role of such flux asymmetry in creating concentration imbalances of messenger molecules in cardiomyocytes. We also assess the potency of fibroblasts in aggravating such imbalances through Cx43-Cx45 heterotypic channels in fibrotic heart tissue.

Computational simulations of asymmetric fluxes of large molecules through gap junction channel pores

Gap junction channels are formed out of connexin isoforms, which enable molecule and ion selective diffusion amongst neighboring cells. HeLa cells expressing distinct connexins (Cx) allow the formation of heterotypic channels, where we observed a molecular charge-independent preferential flux of large fluorescent molecules in the Cx45 to Cx43 direction. We hypothesize that the pore's shape is a significant factor along-side charge and transjunctional voltages for this asymmetric flux. To test this hypothesis, we developed a 3D computational model simulating Brownian diffusion of large molecules in a gap junction channel pore. The basic pore contour was derived from x-ray crystallographic structures of Cx43 and Cx26 and approximated using basic geometric shapes. Lucifer yellow dye molecules and cesium counter-ions were modeled as spheres using their respective Stokes radii. Our simulation results from simple diffusion and constant concentration gradient experiments showed that only charged particles yield asymmetric fluxes in heterotypic pores. While increasing the inner mouth size resulted in a near-quadratic rise in flux, the rise was asymptotic for outer mouth radii increase. Probability maps and average force per particle per pore section explain the asymmetric flux with variation in pore shape. Furthermore, the simulation results are in agreement with our in vitro experimental results with HeLa cells in Cx43-Cx45 heterotypic configurations. The presence of asymmetric fluxes can help us to understand effects of the molecular structure of the pore and predict potential differences in vivo.

Conductance simulation of the purinergic P2X2, P2X4, and P2X7 ionic channels using a combined Brownian dynamics and molecular dynamics approach

This paper investigates the application of an original combined approach of molecular and Brownian dynamic methods with quantum chemistry calculations for modeling the process of conductance of ion channels using purinergic P2X family receptors P2X2, P2X4, and P2X7 as a case study. A simplified model of the ionic channel in the lipid bilayer has been developed. A high level of conductance (30 pS) of P2X2 ionic channel together with the key role of Asp349 in forming the selectivity filter of P2X2 has been shown by using this approach. Calculated P2X2 permeability to monovalent cations Li(+), Na(+), and K(+) conforms to the free diffusion coefficient of these ions, which shows the low selectivity of P2X2 ionic channel.

Dynamics may significantly influence the estimation of interatomic distances in biomolecular X-ray structures

Atomic positions obtained by X-ray crystallography are time and space averages over many molecules in the crystal. Importantly, interatomic distances, calculated between such average positions and frequently used in structural and mechanistic analyses, can be substantially different from the more appropriate time-average and ensemble-average interatomic distances. Using crystallographic B-factors, one can deduce corrections, which have so far been applied exclusively to small molecules, to obtain correct average distances as a function of the type of atomic motion. Here, using 4774 high-quality protein X-ray structures, we study the significance of such corrections for different types of atomic motion. Importantly, we show that for distances shorter than 5 Å, corrections greater than 0.5 Å may apply, especially for noncorrelated or anticorrelated motion. For example, 14% of the studied structures have at least one pair of atoms with a correction of ≥ 0.5 Å in the case of noncorrelated motion. Using molecular dynamics simulations of villin headpiece, ubiquitin, and SH3 domain unit cells, we demonstrate that the majority of average interatomic distances in these proteins agree with noncorrelated corrections, suggesting that such deviations may be truly relevant. Importantly, we demonstrate that the corrections do not significantly affect stereochemistry and the overall quality of final refined X-ray structures, but can provide marked improvements in starting unrefined models obtained from low-resolution X-ray data. Finally, we illustrate the potential mechanistic and biological significance of the calculated corrections for KcsA ion channel and show that they provide indirect evidence that motions in its selectivity filter are highly correlated.

Ion conductance vs. pore gating and selectivity in KcsA channel: Modeling achievements and perspectives

KcsA potassium channel belongs to a wide family of allosteric proteins that switch between closed and open states conformations in response to a stimulus, and act as a regulator of cation activity in living cells. The gating mechanism and cation selectivity of such channels have been extensively studied in the literature, with a revival emphasis these latter years, due to the publication of the crystallized structure of KcsA. Despite the increasing number of research and review papers on these topics, quantitative interpretation of these processes at the atomic scale is far from achieved. On the basis of available experimental and theoretical data, and by including our recent results, we review the progresses in this field of activity and discuss the weaknesses that should be corrected. In this spirit, we partition the channel into the filter, cavity, extra and intracellular media, in order to analyze separately the specificity of each region. Special emphasis is brought to the study of an open state for the channel and to the different properties generated by the opening. The influence of water as a structural and dynamical component of the channel properties in closed and open states, as well as in the sequential motions of the cations, is analyzed using molecular dynamics simulations and ab initio calculations. The polarization and charge transfer effects on the ions' dynamics and kinetics are discussed in terms of partial charge models.

Exploring the origin of the ion selectivity of the KcsA potassium channel

The availability of structural information about biological ion channels provides an opportunity to gain a detailed understanding of the control of ion selectivity by biological systems. However, accomplishing this task by computer simulation approaches is very challenging. First, although the activation barriers for ion transport can be evaluated by microscopic simulations, it is hard to obtain accurate results by such approaches. Second, the selectivity is related to the actual ion current and not directly to the individual activation barriers. Thus, it is essential to simulate the ion currents and this cannot be accomplished at present by microscopic MD approaches. In order to address this challenge, we developed and refined an approach capable of evaluating ion current while still reflecting the realistic features of the given channel. Our method involves generation of semimacroscopic free energy surfaces for the channel/ions system and Brownian dynamics (BD) simulations of the corresponding ion current. In contrast to most alternative macroscopic models, our approach is able to reproduce the difference between the free energy surfaces of different ions and thus to address the selectivity problem. Our method is used in a study of the selectivity of the KcsA channel toward the K+ and Na+ ions. The BD simulations with the calculated free energy profiles produce an appreciable selectivity. To the best of our knowledge, this is the first time that the trend in the selectivity in the ion current is produced by a computer simulation approach. Nevertheless, the calculated selectivity is still smaller than its experimental estimate. Recognizing that the calculated profiles are not perfect, we examine how changes in these profiles can account for the observed selectivity. It is found that the origin of the selectivity is more complex than generally assumed. The observed selectivity can be reproduced by increasing the barrier at the exit and the entrance of the selectivity filter, but the necessary changes in the barrier approach the limit of the error in the PDLD/S-LRA calculations. Other options that can increase the selectivity are also considered, including the difference between the Na+...Na+ and K+...K+ interaction. However, this interesting effect does not appear to lead to a major difference in selectivity since the Na+ ions at the limit of strong interaction tend to move in a less concerted way than the K+ ions. Changes in the relative binding energies at the different binding sites are also not so effective in changing the selectivity. Finally, it is pointed out that using the calculated profiles as a starting point and forcing the model to satisfy different experimentally based constraints, should eventually provide more detailed understanding of the different complex factors involved in ion selectivity of biological channels.

The role of the dielectric barrier in narrow biological channels: a novel composite approach to modeling single-channel currents

A composite continuum theory for calculating ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential-of-Mean-Force-Poisson-Nernst-Planck theory (PMFPNP), to compute ion currents. As in standard PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, information about the dynamic relaxation of the protein and the surrounding medium is incorporated into the model of ion permeation by including the free energy of inserting a single ion into the channel, i.e., the potential of mean force along the permeation pathway. In this way the dynamic flexibility of the channel environment is approximately accounted for. The PMF profile of the ion along the Gramicidin A channel is obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations when an ion resides at a particular location in the channel with a continuum electrostatics calculation of the free energy. The diffusion coefficient of a potassium ion within the channel is also calculated using the MD trajectory. Therefore, except for a reasonable choice of dielectric constants, no direct fitting parameters enter into this model. The results of our study reveal that the channel response to the permeating ion produces significant electrostatic stabilization of the ion inside the channel. The dielectric self-energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passes through it. Also, the model accounts for the experimentally observed saturation of ion current with increase of the electrolyte concentration, in contrast to the predictions of standard PNP theory.

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.

A model of the glycine receptor deduced from Brownian dynamics studies

We have developed a three-dimensional model of the alpha1 homomeric glycine receptor by using Brownian dynamics simulations to account for its observed physiological properties. The model channel contains a large external vestibule and a shallow internal vestibule, connected by a narrow, cylindrical selectivity filter. Three rings of charged residues from the pore-lining M2 domain are modeled as point charges in the protein. Our simulations reproduce many of the key features of the channel, such as the current-voltage profiles, permeability ratios, and ion selectivity. When we replace the ring of alanine residues lining the selectivity filter with glutamates, the mutant model channel becomes permeable to cations, as observed experimentally. In this mutation, anions act as chaperones for sodium ions in the extracellular vestibule, and together they penetrate deep inside the channel against a steep energy barrier encountered by unaccompanied ions. Two subsequent amino acid mutations increase the cation permeability, enabling monovalent cations to permeate through the channel unaided and divalent cations to permeate when chaperoned by anions. These results illustrate the key structural features and underlying mechanism for charge selectivity in the glycine receptor.

A model of calcium channels

We propose a model of calcium channels that can explain most of their observed properties, including the anomalous mole fraction effect and mutation of the glutamate residues. The structure grossly resembles that of the KcsA potassium channel except for the presence of an extracellular vestibule and a shorter selectivity filter containing four glutamate residues. Using this model in electrostatic calculations and Brownian dynamics simulations, we study mechanisms of ion permeation and selectivity in the channel. Potential energy profiles calculated for multiple ions in the channel provide explanations of ion permeation, the block of Na(+) currents by Ca(2+) ions, and many other observed properties. Brownian dynamics simulations provide quantitative predictions for the channel currents which reproduce available experimental data.

Molecular dynamics estimates of ion diffusion in model hydrophobic and KcsA potassium channels

Molecular dynamics simulations are carried out to obtain estimates of diffusion coefficients of biologically important Na+, K+, Ca2+ and Cl- ions in hydrophobic cylindrical channels with varying radii and large reservoirs. Calculations for the cylindrical channels are compared to those for the KcsA potassium channel, for which the protein structure has recently been determined from X-ray diffraction experiments. Our results show that ion diffusion is maintained at reasonably high levels even within narrow channels, and does not support the very small diffusion coefficients used in some continuum models in order to fit experimental data. The present estimates of ion diffusion coefficients are useful in the calculation of channel conductance using the Poisson-Nernst-Planck theory, or Brownian dynamics.