Conduction properties of KcsA measured using brownian dynamics with flexible carbonyl groups in the selectivity filter

The Optimized Conformation Dynamics of the KcsA Filter as a Probe for Lateral Membrane Effects: A First Principle Based Femto-Sec Resolution MD Study

We provide a high resolution, all-atom, femto-second molecular dynamics (MD) simulation of the passage of K⁺ ions and H₂O molecules through the selectivity filter of the KcsA potassium ion channel, based on first principle physical methods. Our results show that a change in the length of the selectivity filter of as little as 3%, regardless of whether the filter is made longer or shorter, will reduce the K⁺ ion current by around 50%. In addition, further squeezing or stretching by about 9% can effectively stop the current. Our results demonstrate optimized conformational dynamics that associate an increased mobility of parts in the filter linings with a standard configuration, leading to maximized conduction rates that are highly sensitive to geometrical distortions. We discuss this latter aspect in relation to lateral membrane effects on the filter region of ion channels and the 'force from lipids' hypothesis.

Computational methods and theory for ion channel research

Ion channels are fundamental biological devices that act as gates in order to ensure selective ion transport across cellular membranes; their operation constitutes the molecular mechanism through which basic biological functions, such as nerve signal transmission and muscle contraction, are carried out. Here, we review recent results in the field of computational research on ion channels, covering theoretical advances, state-of-the-art simulation approaches, and frontline modeling techniques. We also report on few selected applications of continuum and atomistic methods to characterize the mechanisms of permeation, selectivity, and gating in biological and model channels.

Quantum Mechanical Coherence of K+ Ion Wave Packets Increases Conduction in the KcsA Ion Channel

We simulate the transmission of K+ ions through the KcsA potassium ion channel filter region at physiological temperatures, employing classical molecular dynamics (MD) at the atomic scale together with a quantum mechanical version of MD simulation (QMD), treating single ions as quantum wave packets. We provide a direct comparison between both concepts, embedding the simulations into identical force fields and thermal fluctuations. The quantum simulations permit the estimation of coherence times and wave packet dispersions of a K+ ion over a range of 0.5 nm (a range that covers almost 50% of the filter domains longitudinal extension). We find that this observed extension of particle delocalization changes the mean orientation of the coordinating carbonyl oxygen atoms significantly, transiently suppressing their ‘caging action’ responsible for selective ion coordination. Compared to classical MD simulations, this particular quantum effect allows the K+ ions to ‘escape’ more easily from temporary binding sites provided by the surrounding filter atoms. To further elucidate the role of this observation for ion conduction rates, we compare the temporal pattern of single conduction events between classical MD and quantum QMD simulations at a femto-sec time scale. A finding from both approaches is that ion permeation follows a very irregular time pattern, involving flushes of permeation interrupted by non-conductive time intervals. However, as compared with classical behavior, the QMD simulation shortens non-conductive time by more than a half. As a consequence, and given the same force-fields, the QMD-simulated ion current appears to be considerably stronger as compared with the classical current. To bring this result in line with experimentally observed ion currents and the predictions based on Nernst–Planck theories, the conclusion is that a transient short time quantum behavior of permeating ions can successfully compromise high conduction rates with ion selectivity in the filter of channel proteins.

Simulations of outer membrane channels and their permeability

Channels in the outer membrane of Gram-negative bacteria provide essential pathways for the controlled and unidirectional transport of ions, nutrients and metabolites into the cell. At the same time the outer membrane serves as a physical barrier for the penetration of noxious substances such as antibiotics into the bacteria. Most antibiotics have to pass through these membrane channels to either reach cytoplasmic bound targets or to further cross the hydrophobic inner membrane. Considering the pharmaceutical significance of antibiotics, understanding the functional role and mechanism of these channels is of fundamental importance in developing strategies to design new drugs with enhanced permeation abilities. Due to the biological complexity of membrane channels and experimental limitations, computer simulations have proven to be a powerful tool to investigate the structure, dynamics and interactions of membrane channels. Considerable progress has been made in computer simulations of membrane channels during the last decade. The goal of this review is to provide an overview of the computational techniques and their roles in modeling the transport across outer membrane channels. A special emphasis is put on all-atom molecular dynamics simulations employed to better understand the transport of molecules. Moreover, recent molecular simulations of ion, substrate and antibiotics translocation through membrane pores are briefly summarized. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Multi-ion versus single-ion conduction mechanisms can yield current rectification in biological ion channels

There is clear evidence that the net magnitude of negative charge at the intracellular end of inwardly rectifying potassium channels helps to generate an asymmetry in the magnitude of the current that will pass in each direction. However, a complete understanding of the physical mechanism that links these charges to current rectification has yet to be obtained. Using Brownian dynamics, we compare the conduction mechanism and binding sites in rectifying and non-rectifying channel models. We find that in our models, rectification is a consequence of asymmetry in the hydrophobicity and charge of the pore lining. As a consequence, inward conduction can occur by a multi-ion conduction mechanism. However, outward conduction is restricted, since there are fewer ions at the intracellular entrance and outwardly moving ions must cross the pore on their own. We pose the question as to whether the same mechanism could be at play in inwardly rectifying potassium channels.

Computational methods of studying the binding of toxins from venomous animals to biological ion channels: theory and applications

The discovery of new drugs that selectively block or modulate ion channels has great potential to provide new treatments for a host of conditions. One promising avenue revolves around modifying or mimicking certain naturally occurring ion channel modulator toxins. This strategy appears to offer the prospect of designing drugs that are both potent and specific. The use of computational modeling is crucial to this endeavor, as it has the potential to provide lower cost alternatives for exploring the effects of new compounds on ion channels. In addition, computational modeling can provide structural information and theoretical understanding that is not easily derivable from experimental results. In this review, we look at the theory and computational methods that are applicable to the study of ion channel modulators. The first section provides an introduction to various theoretical concepts, including force-fields and the statistical mechanics of binding. We then look at various computational techniques available to the researcher, including molecular dynamics, brownian dynamics, and molecular docking systems. The latter section of the review explores applications of these techniques, concentrating on pore blocker and gating modifier toxins of potassium and sodium channels. After first discussing the structural features of these channels, and their modes of block, we provide an in-depth review of past computational work that has been carried out. Finally, we discuss prospects for future developments in the field.

Nonselective conduction in a mutated NaK channel with three cation-binding sites

The NaK channel is a cation-selective protein with similar permeability for K(+) and Na(+) ions. Crystallographic structures are available for the wild-type and mutated NaK channels with different numbers of cation-binding sites. We have performed a comparison between the potentials of mean force governing the translocation of K(+) ions and mixtures of one Na(+) and three K(+) ions in a mutated NaK channel with only three cation-binding sites (NaK-CNG). Since NaK-CNG is not selective for K(+) over Na(+), analysis of its multi-ion potential energy surfaces can provide clues about how selectivity originates. Comparison of the potentials of mean force of NaK-CNG and K(+)-selective channels yields observations that strongly suggest that the number of contiguous ion binding sites in a single-file mechanism is the key determinant of the channel's selectivity properties, as already proposed by experimental studies. We conclude that the presence of four binding sites in K(+)-selective channels is essential for highly selective and efficient permeation of K(+) ions, and that a key difference between K(+)-selective and nonselective channels is the absence/presence of a binding site for Na(+) ions at the boundary between S2 and S3 in the context of multi-ion permeation events.

Conductance properties of the inwardly rectifying channel, Kir3.2: molecular and Brownian dynamics study

Using the recently unveiled crystal structure, and molecular and Brownian dynamics simulations, we elucidate several conductance properties of the inwardly rectifying potassium channel, Kir3.2, which is implicated in cardiac and neurological disorders. We show that the pore is closed by a hydrophobic gating mechanism similar to that observed in Kv1.2. Once open, potassium ions move into, but not out of, the cell. The asymmetrical current-voltage relationship arises from the lack of negatively charged residues at the narrow intracellular mouth of the channel. When four phenylalanine residues guarding the intracellular gate are mutated to glutamate residues, the channel no longer shows inward rectification. Inward rectification is restored in the mutant Kir3.2 when it becomes blocked by intracellular Mg(2+). Tertiapin, a polypeptide toxin isolated from the honey bee, is known to block several subtypes of the inwardly rectifying channels with differing affinities. We identify critical residues in the toxin and Kir3.2 for the formation of the stable complex. A lysine residue of tertiapin protrudes into the selectivity filter of Kir3.2, while two other basic residues of the toxin form hydrogen bonds with acidic residues located just outside the channel entrance. The depth of the potential of mean force encountered by tertiapin is -16.1kT, thus indicating that the channel will be half-blocked by 0.4μM of the toxin.

Testing the applicability of Nernst-Planck theory in ion channels: comparisons with Brownian dynamics simulations

The macroscopic Nernst-Planck (NP) theory has often been used for predicting ion channel currents in recent years, but the validity of this theory at the microscopic scale has not been tested. In this study we systematically tested the ability of the NP theory to accurately predict channel currents by combining and comparing the results with those of Brownian dynamics (BD) simulations. To thoroughly test the theory in a range of situations, calculations were made in a series of simplified cylindrical channels with radii ranging from 3 to 15 Å, in a more complex 'catenary' channel, and in a realistic model of the mechanosensitive channel MscS. The extensive tests indicate that the NP equation is applicable in narrow ion channels provided that accurate concentrations and potentials can be input as the currents obtained from the combination of BD and NP match well with those obtained directly from BD simulations, although some discrepancies are seen when the ion concentrations are not radially uniform. This finding opens a door to utilising the results of microscopic simulations in continuum theory, something that is likely to be useful in the investigation of a range of biophysical and nano-scale applications and should stimulate further studies in this direction.

Theory of single-file multiparticle diffusion in narrow pores

Single-file diffusion of multiple strongly interacting particles in a one-dimensional pore is described within a general analytical framework. The theory accounts for nonequilibrium conditions, explicit particle-particle interactions, external potential acting on the particles and the fluctuations of the number of particles due to their exchange with external equilibrium reservoirs. It is shown that the problem can be reduced to a closed hierarchical set of partial differential equations of increasing dimensionality, which can be solved numerically. Our framework allows computing any macroscopic characteristic of multiparticle diffusion in the pore. It is shown that the pore occupancy probabilities and the current are rational functions of external concentrations in the steady state. The theory is tested on a simplified model of the narrow rigid pore inspired by the selectivity filter of biological ion channel. Perspectives and limitations of the theory are discussed.

Computational studies of gramicidin permeation: an entry way sulfonate enhances cation occupancy at entry sites

The impact on the cation-transport free-energy profile of replacing the C-terminal ethanolamine in the gramicidin A channel with a taurine residue is studied using molecular dynamics simulations of gramicidin A (1JNO) embedded in a lipid bilayer (DMPC) with 1 mol/kg NaCl saline solution. The potential of mean force for ion transport is obtained by umbrella sampling. The presence of a negatively charged sulfonate group at the entrance of the gramicidin channel affects the depth and the location of the binding sites, producing a strong attraction for the cations in the bulk. The potential of mean force by the sulfonate acting directly through electrostatics and van der Waals interactions on the test ion is highly modulated by indirect effects (i.e., sulfonate effects on other components of the system that, in turn, affect the ion free-energy profile in the channel). Because the "entry" sites are located symmetrically at both entry and exit of the channel, the deeper free-energy wells should inhibit exit. Given that the channel has increased conductance experimentally, the simulation results suggest that the channel conductance is normally entry limited.

The selectivity of K+ ion channels: testing the hypotheses

How K(+) channels are able to conduct certain cations yet not others remains an important but unresolved question. The recent elucidation of the structure of NaK, an ion channel that conducts both Na(+) and K(+) ions, offers an opportunity to test the various hypotheses that have been put forward to explain the selectivity of K(+) ion channels. We test the snug-fit, field-strength, and over-coordination hypotheses by comparing their predictions to the results of classical molecular dynamics simulations of the K(+) selective channel KcsA and the less selective channel NaK embedded in lipid bilayers. Our results are incompatible with the so-called strong variant of the snug-fit hypothesis but are consistent with the over-coordination hypothesis and neither confirm nor refute the field-strength hypothesis. We also find that the ions and waters in the NaK selectivity filter unexpectedly move to a new conformation in seven K(+) simulations: the two K(+) ions rapidly move from site S4 to S2 and from the cavity to S4. At the same time, the selectivity filter narrows around sites S1 and S2 and the carbonyl oxygen atoms rotate 20 degrees -40 degrees inwards toward the ion. These motions diminish the large structural differences between the crystallographic structures of the selectivity filters of NaK and KcsA and appear to allow the binding of ions to S2 of NaK at physiological temperature.

Conduction of Na+ and K+ through the NaK channel: molecular and Brownian dynamics studies

Conduction of ions through the NaK channel, with M0 helix removed, was studied using both Brownian dynamics and molecular dynamics. Brownian dynamics simulations predict that the truncated NaK has approximately a third of the conductance of the related KcsA K+ channel, is outwardly rectifying, and has a Michaelis-Menten current-concentration relationship. Current magnitude increases when the glutamine residue located near the intracellular gate is replaced with a glutamate residue. The channel is blocked by extracellular Ca2+. Molecular dynamics simulations show that, under the influence of a strong applied potential, both Na+ and K+ move across the selectivity filter, although conduction rates for Na+ ions are somewhat lower. The mechanism of conduction of Na+ differs significantly from that of K+ in that Na+ is preferentially coordinated by single planes of pore-lining carbonyl oxygens, instead of two planes as in the usual K+ binding sites. The water-containing filter pocket resulting from a single change in the selectivity filter sequence (compared to potassium channels) disrupts several of the planes of carbonyl oxygens, and thus reduces the filter's ability to discriminate against sodium.

Is the mobility of the pore walls and water molecules in the selectivity filter of KcsA channel functionally important?

We performed in-depth analysis of the forces which act on the K(+) ions in the selectivity filter of the KcsA channel in order to estimate the relative importance of static and dynamic influence of the filter wall and water molecules on ion permeation and selectivity. The forces were computed using the trajectories of all-atom molecular dynamics simulations. It is shown that the dynamics of the selectivity filter contributes about 3% to the net force acting on the ions and can be neglected in the studies focused on the macroscopic properties of the channel, such as the current. Among the filter atoms, only the pore-forming carbonyl groups can be considered as dynamic in the studies of microscopic events of conduction, while the dynamic effects from all other atoms are negligible. We also show that the dynamics of the water molecules in the filter can not be neglected. The fluctuating forces from the water molecules can be as strong as net forces from the pore walls and can effectively drive the ions through the local energy barriers in the filter.

Estimating the dielectric constant of the channel protein and pore

When modelling biological ion channels using Brownian dynamics (BD) or Poisson-Nernst-Planck theory, the force encountered by permeant ions is calculated by solving Poisson's equation. Two free parameters needed to solve this equation are the dielectric constant of water in the pore and the dielectric constant of the protein forming the channel. Although these values can in theory be deduced by various methods, they do not give a reliable answer when applied to channel-like geometries that contain charged particles. To determine the appropriate values of the dielectric constants, here we solve the inverse problem. Given the structure of the MthK channel, we attempt to determine the values of the protein and pore dielectric constants that minimize the discrepancies between the experimentally-determined current-voltage curve and the curve obtained from BD simulations. Two different methods have been applied to determine these values. First, we use all possible pairs of the pore dielectric constant of water, ranging from 20 to 80 in steps of 10, and the protein dielectric constant of 2-10 in steps of 2, and compare the simulated results with the experimental values. We find that the best agreement is obtained with experiment when a protein dielectric constant of 2 and a pore water dielectric constant of 60 is used. Second, we employ a learning-based stochastic optimization algorithm to pick out the optimum combination of the two dielectric constants. From the algorithm we obtain an optimum value of 2 for the protein dielectric constant and 64 for the pore dielectric constant.