Molecular dynamics study of the KcsA potassium channel

Probing Ion Configurations in the KcsA Selectivity Filter with Single-Isotope Labels and 2D IR Spectroscopy

The potassium ion (K+) configurations of the selectivity filter of the KcsA ion channel protein are investigated with two-dimensional infrared (2D IR) spectroscopy of amide I vibrations. Single 13C-18O isotope labels are used, for the first time, to selectively probe the S1/S2 or S2/S3 binding sites in the selectivity filter. These binding sites have the largest differences in ion occupancy in two competing K+ transport mechanisms: soft-knock and hard-knock. According to the former, water molecules alternate between K+ ions in the selectivity filter while the latter assumes that K+ ions occupy the adjacent sites. Molecular dynamics simulations and computational spectroscopy are employed to interpret experimental 2D IR spectra. We find that in the closed conductive state of the KcsA channel, K+ ions do not occupy adjacent binding sites. The experimental data is consistent with simulated 2D IR spectra of soft-knock ion configurations. In contrast, the simulated spectra for the hard-knock ion configurations do not reproduce the experimental results. 2D IR spectra of the hard-knock mechanism have lower frequencies, homogeneous 2D lineshapes, and multiple peaks. In contrast, ion configurations of the soft-knock model produce 2D IR spectra with a single peak at a higher frequency and inhomogeneous lineshape. We conclude that under equilibrium conditions, in the absence of transmembrane voltage, both water and K+ ions occupy the selectivity filter of the KcsA channel in the closed conductive state. The ion configuration is central to the mechanism of ion transport through potassium channels.

Computational study of ion permeation through claudin-4 paracellular channels

Claudins (Cldns) form a large family of protein homologs that are essential for the assembly of paracellular tight junctions (TJs), where they form channels or barriers with tissue-specific selectivity for permeants. In contrast to several family members whose physiological role has been identified, the function of claudin 4 (Cldn4) remains elusive, despite experimental evidence suggesting that it can form anion-selective TJ channels in the renal epithelium. Computational approaches have recently been employed to elucidate the molecular basis of Cldns' function, and hence could help in clarifying the role of Cldn4. In this work, we use structural modeling and all-atom molecular dynamics simulations to transfer two previously introduced structural models of Cldn-based paracellular complexes to Cldn4 to reproduce a paracellular anion channel. Free energy calculations for ionic transport through the pores allow us to establish the thermodynamic properties driving the ion-selectivity of the structures. While one model shows a cavity permeable to chloride and repulsive to cations, the other forms barrier to the passage of all the major physiological ions. Furthermore, our results confirm the charge selectivity role of the residue Lys65 in the first extracellular loop of the protein, rationalizing Cldn4 control of paracellular permeability.

A bottom-up approach to the ion recognition mechanism of K+ channels from laser spectroscopy of hydrated partial peptide-alkali metal ion complexes

K⁺ channels allow selective permeation of K⁺, but not physiologically abundant Na⁺, at almost diffusion limit rates. The conduction mechanism of K⁺ channels is still controversial, with experimental and computation studies supporting two distinct conduction mechanisms: either with or without water inside the channel. Here, we employ a bottom-up approach on hydrated alkali metal complexes of a model peptide of K⁺ channels, Ac-Tyr-NHMe, to characterize metal-peptide, metal-water, and water-peptide interactions that govern the selectivity of K⁺ channels at a molecular level. Both the extension to the series of alkali metal ions and to temperature-dependent studies (approaching physiological values) have revealed the clear difference between permeable and non-permeable ions in the spectral features of the ion complexes. Furthermore, the impact of hydration is discussed in relation to the K⁺ channels by comparisons of the non-hydrated and hydrated complexes.

What have molecular simulations contributed to understanding of Gram-negative bacterial cell envelopes?

Bacterial cell envelopes are compositionally complex and crowded and while highly dynamic in some areas, their molecular motion is very limited, to the point of being almost static in others. Therefore, it is no real surprise that studying them at high resolution across a range of temporal and spatial scales requires a number of different techniques. Details at atomistic to molecular scales for up to tens of microseconds are now within range for molecular dynamics simulations. Here we review how such simulations have contributed to our current understanding of the cell envelopes of Gram-negative bacteria.

P-Loop Channels: Experimental Structures, and Physics-Based and Neural Networks-Based Models

The superfamily of P-loop channels includes potassium, sodium, and calcium channels, as well as TRP channels and ionotropic glutamate receptors. A rapidly increasing number of crystal and cryo-EM structures have revealed conserved and variable elements of the channel structures. Intriguing differences are seen in transmembrane helices of channels, which may include π-helical bulges. The bulges reorient residues in the helices and thus strongly affect their intersegment contacts and patterns of ligand-sensing residues. Comparison of the experimental structures suggests that some π-bulges are dynamic: they may appear and disappear upon channel gating and ligand binding. The AlphaFold2 models represent a recent breakthrough in the computational prediction of protein structures. We compared some crystal and cryo-EM structures of P-loop channels with respective AlphaFold2 models. Folding of the regions, which are resolved experimentally, is generally similar to that predicted in the AlphaFold2 models. The models also reproduce some subtle but significant differences between various P-loop channels. However, patterns of π-bulges do not necessarily coincide in the experimental and AlphaFold2 structures. Given the importance of dynamic π-bulges, further studies involving experimental and theoretical approaches are necessary to understand the cause of the discrepancy.

Double Ion Trap Laser Spectroscopy of Alkali Metal Ion Complexes with a Partial Peptide of the Selectivity Filter in K+ Channels─Temperature Effect and Barrier for Conformational Conversions

Potassium ion channels selectively permeate K⁺, as well as Rb⁺ and Cs⁺ to some degree, while excluding Na⁺ and Li⁺. Conformations of alkali metal complexes of Ac-Tyr-NHMe, a model peptide of the selectivity filter in a K⁺ channel, were previously found to correlate with the permeability of alkali metal ions to a K⁺ channel by cold ion trap infrared spectroscopy. With an additional temperature-controlled ion trap, we examined the conformations of the alkali metal complexes, allowing the ions to collide with a He buffer gas at different temperatures, prior to spectroscopic investigation. The conformational distribution of the K⁺-peptide complex shows the most significant variation with temperature, which suggests that this complex has more flexibility when complexed with K⁺ and suggests lower barrier heights than other metal-peptide complexes. The variability of the conformational distribution with temperature for the ions follows the same order of ion permeability of a K⁺ channel. This work demonstrates that the additional temperature-controlled ion trap is a powerful tool to explore the conformational landscape of flexible molecular systems.

Cooperative and synchronized rotation in motorized porous frameworks: impact on local and global transport properties of confined fluids

Simulations reveal the influence of rotating molecular motors and the importance of orientation and directionality for altering the transport properties of fluids. This has outlined that motors with specific rotation can generate directed diffusion.

Modulation of Function, Structure and Clustering of K+ Channels by Lipids: Lessons Learnt from KcsA

KcsA, a prokaryote tetrameric potassium channel, was the first ion channel ever to be structurally solved at high resolution. This, along with the ease of its expression and purification, made KcsA an experimental system of choice to study structure–function relationships in ion channels. In fact, much of our current understanding on how the different channel families operate arises from earlier KcsA information. Being an integral membrane protein, KcsA is also an excellent model to study how lipid–protein and protein–protein interactions within membranes, modulate its activity and structure. In regard to the later, a variety of equilibrium and non-equilibrium methods have been used in a truly multidisciplinary effort to study the effects of lipids on the KcsA channel. Remarkably, both experimental and “in silico” data point to the relevance of specific lipid binding to two key arginine residues. These residues are at non-annular lipid binding sites on the protein and act as a common element to trigger many of the lipid effects on this channel. Thus, processes as different as the inactivation of channel currents or the assembly of clusters from individual KcsA channels, depend upon such lipid binding.

Molecular Dynamics and Neutron Scattering Studies of Potassium Chloride in Aqueous Solution

Neutron diffraction with isotopic substitution (NDIS) experiments were done on both natural abundance potassium and isotopically labeled ⁴¹KCl heavy water solutions to characterize the solvent structuring around the potassium ion in water. Preliminary measurements suggested that the literature value for the coherent neutron scattering length (2.69 fm) for ⁴¹K was significantly in error. This value was remeasured using a neutron powder diffractometer and found to be 2.40 fm. This revision increases significantly the contrast between the natural abundance K and ⁴¹K by about 30% (from 1.0 to 1.3 fm). The experimentally determined structure factor of the potassium ion was then compared to that calculated from molecular dynamics (MD) simulations. Previous neutron scattering measurements of potassium gave a solvation number of 5.5 (see below). In this study, the NDIS and MD results are in good agreement and allowed us to derive a coordination number of 6.1 for water molecules and 0.8 for chloride ions around each K⁺ ion in 4 molal aqueous KCl solution.

Excitation energy transport with noise and disorder in a model of the selectivity filter of an ion channel

A selectivity filter is a gate in ion channels that is responsible for the selection and fast conduction of particular ions across the membrane (with high throughput rates of 10⁸ ions s^-1 and a high 1:10⁴ discrimination rate between ions). It is made of four strands as the backbone, and each strand is composed of sequences of five amino acids connected by peptide units H-N-C=O in which the main molecules in the backbone that interact with ions in the filter are carbonyl (C=O) groups that mimic the transient interactions of ion with binding sites during ion conduction. It has been suggested that quantum coherence and possible emergence of resonances in the backbone carbonyl groups may play a role in mediating ion conduction and selectivity in the filter. Here, we investigate the influence of noise and disorder on the efficiency of excitation energy transfer (EET) in a linear harmonic chain of N  =  5 sites with dipole-dipole couplings as a simple model for one P-loop strand of the selectivity filter backbone in biological ion channels. We include noise and disorder inherent in real biological systems by including spatial disorder in the chain, and random noise within a weak coupling quantum master equation approach. Our results show that disorder in the backbone considerably reduces EET, but the addition of noise helps to recover high EET for a wide range of system parameters. Our analysis may help for better understanding of the coordination of ions in the filter as well as the fast and efficient functioning of the selectivity filters in ion channels.

Exopolysaccharides from Marine and Marine Extremophilic Bacteria: Structures, Properties, Ecological Roles and Applications

The marine environment is the largest aquatic ecosystem on Earth and it harbours microorganisms responsible for more than 50% of total biomass of prokaryotes in the world. All these microorganisms produce extracellular polymers that constitute a substantial part of the dissolved organic carbon, often in the form of exopolysaccharides (EPS). In addition, the production of these polymers is often correlated to the establishment of the biofilm growth mode, during which they are important matrix components. Their functions include adhesion and colonization of surfaces, protection of the bacterial cells and support for biochemical interactions between the bacteria and the surrounding environment. The aim of this review is to present a summary of the status of the research about the structures of exopolysaccharides from marine bacteria, including capsular, medium released and biofilm embedded polysaccharides. Moreover, ecological roles of these polymers, especially for those isolated from extreme ecological niches (deep-sea hydrothermal vents, polar regions, hypersaline ponds, etc.), are reported. Finally, relationships between the structure and the function of the exopolysaccharides are discussed.

A Kepler Workflow Tool for Reproducible AMBER GPU Molecular Dynamics

With the drive toward high throughput molecular dynamics (MD) simulations involving ever-greater numbers of simulation replicates run for longer, biologically relevant timescales (microseconds), the need for improved computational methods that facilitate fully automated MD workflows gains more importance. Here we report the development of an automated workflow tool to perform AMBER GPU MD simulations. Our workflow tool capitalizes on the capabilities of the Kepler platform to deliver a flexible, intuitive, and user-friendly environment and the AMBER GPU code for a robust and high-performance simulation engine. Additionally, the workflow tool reduces user input time by automating repetitive processes and facilitates access to GPU clusters, whose high-performance processing power makes simulations of large numerical scale possible. The presented workflow tool facilitates the management and deployment of large sets of MD simulations on heterogeneous computing resources. The workflow tool also performs systematic analysis on the simulation outputs and enhances simulation reproducibility, execution scalability, and MD method development including benchmarking and validation.

Transmembrane dynamics of the Thr-5 phosphorylated sarcolipin pentameric channel

Sarcolipin (SLN), an important membrane protein expressed in the sarcoplasmic reticulum (SR), regulates muscle contractions in cardiac and skeletal muscle. The phosphorylation at amino acid Thr5 of the SLN protein modulates the amount of Ca(2+) that passes through the SR. Using molecular dynamics simulation, we evaluated the phosphorylation at Thr5 of pentameric SLN (phospho-SLN) channel's energy barrier and pore characteristics by calculating the potential of mean force (PMF) along the channel pore and determining the diffusion coefficient. The results indicate that pentameric phospho-SLN promotes penetration of monovalent and divalent ions through the channel. The analysis of PMF, pore radius and diffusion coefficient indicates that Leu21 is the hydrophobic gate of the pentameric SLN channel. In the channel, water molecules near the Leu21 pore demonstrated a clear hydrated-dehydrated transition; however, the mutation of Leu21 to an Alanine (L21A) destroyed the hydrated-dehydrated transitions. These water-dynamic behaviors and PMF confirm that Leu21 is the key residue that regulates the ion permeability of the pentameric SLN channel. These results provide the structural-basis insights and molecular-dynamic information that are needed to understand the regulatory mechanisms of ion permeability in the pentameric SLN channel.

Equilibrium fluctuation relations for voltage coupling in membrane proteins

A general theoretical framework is developed to account for the effects of an external potential on the energetics of membrane proteins. The framework is based on the free energy relation between two (forward/backward) probability densities, which was recently generalized to non-equilibrium processes, culminating in the work-fluctuation theorem. Starting from the probability densities of the conformational states along the "voltage coupling" reaction coordinate, we investigate several interconnected free energy relations between these two conformational states, considering voltage activation of ion channels. The free energy difference between the two conformational states at zero (depolarization) membrane potential (i.e., known as the chemical component of free energy change in ion channels) is shown to be equivalent to the free energy difference between the two "equilibrium" (resting and activated) conformational states along the one-dimensional voltage couplin reaction coordinate. Furthermore, the requirement that the application of linear response approximation to the free energy functionals of voltage coupling should satisfy the general free energy relations, yields a novel closed-form expression for the gating charge in terms of other basic properties of ion channels. This connection is familiar in statistical mechanics, known as the equilibrium fluctuation-response relation. The theory is illustrated by considering the coupling of a unit charge to the external voltage in the two sites near the surface of membrane, representing the activated and resting states. This is done using a coarse-graining (CG) model of membrane proteins, which includes the membrane, the electrolytes and the electrodes. The CG model yields Marcus-type voltage dependent free energy parabolas for the response of the electrostatic environment (electrolytes etc.) to the transition from the initial to the final configuratinal states, leading to equilibrium free energy difference and free energy barrier that follow the trend of the equilibrium fluctuation relation and the Marcus theory of electron transfer. These energetics also allow for a direct estimation of the voltage dependence of channel activation (Q-V curve), offering a quantitative rationale for a correlation between the voltage dependence parabolas and the Q-V curve, upon site-directed mutagenesis or drug binding. Taken together, by introducing the voltage coupling as the energy gap reaction coordinate, our framework brings new perspectives to the thermodynamic models of voltage activation in voltage-sensitive membrane proteins, offering an a framework for a better understating of the structure-function correlations of voltage gating in ion channels as well as electrogenic phenomena in ion pumps and transporters. Significantly, this formulation also provides a powerful bridge between the CG model of voltage coupling and the conventional macroscopic treatments.

Unraveling the mechanism of selective ion transport in hydrophobic subnanometer channels

Recently reported synthetic organic nanopore (SONP) can mimic a key feature of natural ion channels, i.e., selective ion transport. However, the physical mechanism underlying the K(+)/Na(+) selectivity for the SONPs is dramatically different from that of natural ion channels. To achieve a better understanding of the selective ion transport in hydrophobic subnanometer channels in general and SONPs in particular, we perform a series of ab initio molecular dynamics simulations to investigate the diffusivity of aqua Na(+) and K(+) ions in two prototype hydrophobic nanochannels: (i) an SONP with radius of 3.2 Å, and (ii) single-walled carbon nanotubes (CNTs) with radii of 3-5 Å (these radii are comparable to those of the biological potassium K(+) channels). We find that the hydration shell of aqua Na(+) ion is smaller than that of aqua K(+) ion but notably more structured and less yielding. The aqua ions do not lower the diffusivity of water molecules in CNTs, but in SONP the diffusivity of aqua ions (Na(+) in particular) is strongly suppressed due to the rugged inner surface. Moreover, the aqua Na(+) ion requires higher formation energy than aqua K(+) ion in the hydrophobic nanochannels. As such, we find that the ion (K(+) vs. Na(+)) selectivity of the (8, 8) CNT is ∼20× higher than that of SONP. Hence, the (8, 8) CNT is likely the most efficient artificial K(+) channel due in part to its special interior environment in which Na(+) can be fully solvated, whereas K(+) cannot. This work provides deeper insights into the physical chemistry behind selective ion transport in nanochannels.

Noise assisted excitation energy transfer in a linear model of a selectivity filter backbone strand

In this paper, we investigate the effect of noise and disorder on the efficiency of excitation energy transfer (EET) in a N = 5 sites linear chain with 'static' dipole-dipole couplings. In fact, here, the disordered chain is a toy model for one strand of the selectivity filter backbone in ion channels. It has recently been discussed that the presence of quantum coherence in the selectivity filter is possible and can play a role in mediating ion-conduction and ion-selectivity in the selectivity filter. The question is 'how a quantum coherence can be effective in such structures while the environment of the channel is dephasing (i.e. noisy)?' Basically, we expect that the presence of the noise should have a destructive effect in the quantum transport. In fact, we show that such expectation is valid for ordered chains. However, our results indicate that introducing the dephasing in the disordered chains leads to the weakening of the localization effects, arising from the multiple back-scatterings due to the randomness, and then increases the efficiency of quantum energy transfer. Thus, the presence of noise is crucial for the enhancement of EET efficiency in disordered chains. We also show that the contribution of both classical and quantum mechanical effects are required to improve the speed of energy transfer along the chain. Our analysis may help for better understanding of fast and efficient functioning of the selectivity filters in ion channels.

Visualizing KcsA conformational changes upon ion binding by infrared spectroscopy and atomistic modeling

The effect of ion binding in the selectivity filter of the potassium channel KcsA is investigated by combining amide I Fourier-transform infrared spectroscopy with structure-based spectral modeling. Experimental difference IR spectra between K(+)-bound KcsA and Na(+)-bound KcsA are in good qualitative agreement with spectra modeled from structural ensembles generated from molecular dynamics simulations. The molecular origins of the vibrational modes contributing to differences in these spectra are determined not only from structural differences in the selectivity filter but also from the pore helices surrounding this region. Furthermore, the coordination of K(+) or Na(+) to carbonyls in the selectivity filter effectively decouples the vibrations of those carbonyls from the rest of the protein, creating local probes of the electrostatic environment. The results suggest that it is necessary to include the influence of the surrounding helices in discussing selectivity and transport in KcsA and, on a more general level, that IR spectroscopy offers a nonperturbative route to studying the structure and dynamics of ion channels.

Systematic Parameterization of Monovalent Ions Employing the Nonbonded Model

Monovalent ions play fundamental roles in many biological processes in organisms. Modeling these ions in molecular simulations continues to be a challenging problem. The 12-6 Lennard-Jones (LJ) nonbonded model is widely used to model monovalent ions in classical molecular dynamics simulations. A lot of parameterization efforts have been reported for these ions with a number of experimental end points. However, some reported parameter sets do not have a good balance between the two Lennard-Jones parameters (the van der Waals (VDW) radius and potential well depth), which affects their transferability. In the present work, via the use of a noble gas curve we fitted in former work (J. Chem. Theory Comput. 2013, 9, 2733), we reoptimized the 12-6 LJ parameters for 15 monovalent ions (11 positive and 4 negative ions) for three extensively used water models (TIP3P, SPC/E, and TIP4P(EW)). Since the 12-6 LJ nonbonded model performs poorly in some instances for these ions, we have also parameterized the 12-6-4 LJ-type nonbonded model (J. Chem. Theory Comput. 2014, 10, 289) using the same three water models. The three derived parameter sets focused on reproducing the hydration free energies (the HFE set) and the ion-oxygen distance (the IOD set) using the 12-6 LJ nonbonded model and the 12-6-4 LJ-type nonbonded model (the 12-6-4 set) overall give improved results. In particular, the final parameter sets showed better agreement with quantum mechanically calculated VDW radii and improved transferability to ion-pair solutions when compared to previous parameter sets.

Permeation redux: thermodynamics and kinetics of ion movement through potassium channels

The fundamental biophysics underlying the selective movement of ions through ion channels was launched by George Eisenman in the 1960s, using glass electrodes. This minireview examines the insights from these early studies and the explosive progress made since then.

Modeling ion channels: past, present, and future

Ion channels are membrane-bound enzymes whose catalytic sites are ion-conducting pores that open and close (gate) in response to specific environmental stimuli. Ion channels are important contributors to cell signaling and homeostasis. Our current understanding of gating is the product of 60 plus years of voltage-clamp recording augmented by intervention in the form of environmental, chemical, and mutational perturbations. The need for good phenomenological models of gating has evolved in parallel with the sophistication of experimental technique. The goal of modeling is to develop realistic schemes that not only describe data, but also accurately reflect mechanisms of action. This review covers three areas that have contributed to the understanding of ion channels: traditional Eyring kinetic theory, molecular dynamics analysis, and statistical thermodynamics. Although the primary emphasis is on voltage-dependent channels, the methods discussed here are easily generalized to other stimuli and could be applied to any ion channel and indeed any macromolecule.

Pore dynamics and conductance of RyR1 transmembrane domain

Ryanodine receptors (RyR) are calcium release channels, playing a major role in the regulation of muscular contraction. Mutations in skeletal muscle RyR (RyR1) are associated with congenital diseases such as malignant hyperthermia and central core disease (CCD). The absence of high-resolution structures of RyR1 has limited our understanding of channel function and disease mechanisms at the molecular level. Previously, we have reported a hypothetical structure of the RyR1 pore-forming region, obtained by homology modeling and supported by mutational scans, electrophysiological measurements, and cryo-electron microscopy. Here, we utilize the expanded model encompassing six transmembrane helices to calculate the RyR1 pore region conductance, to analyze its structural stability, and to hypothesize the mechanism of the Ile4897 CCD-associated mutation. The calculated conductance of the wild-type RyR1 suggests that the proposed pore structure can sustain ion currents measured in single-channel experiments. We observe a stable pore structure on timescales of 0.2 μs, with multiple cations occupying the selectivity filter and cytosolic vestibule, but not the inner chamber. We further suggest that stability of the selectivity filter critically depends on the interactions between the I4897 residue and several hydrophobic residues of the neighboring subunit. Loss of these interactions in the case of polar substitution I4897T results in destabilization of the selectivity filter, a possible cause of the CCD-specific reduced Ca(2+) conductance.

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.

Physics of ion channels

We review the basic physics involved in transport of ions across membrane channels in cells. Electrochemical forces that control the diffusion of ions are discussed both from microscopic and macroscopic perspectives. A case is made for use of Brownian dynamics as the minimal phenomenological model that provides a bridge between experiments and more fundamental theoretical approaches. Application of Brownian and molecular dynamics methods to channels with known molecular structures is discussed.

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.

Molecular dynamics simulations of membrane proteins

Membrane proteins control the traffic across cell membranes and thereby play an essential role in cell function from transport of various solutes to immune response via molecular recognition. Because it is very difficult to determine the structures of membrane proteins experimentally, computational methods have been increasingly used to study their structure and function. Here we focus on two classes of membrane proteins-ion channels and transporters-which are responsible for the generation of action potentials in nerves, muscles, and other excitable cells. We describe how computational methods have been used to construct models for these proteins and to study the transport mechanism. The main computational tool is the molecular dynamics (MD) simulation, which can be used for everything from refinement of protein structures to free energy calculations of transport processes. We illustrate with specific examples from gramicidin and potassium channels and aspartate transporters how the function of these membrane proteins can be investigated using MD simulations.

Comparison of three-dimensional poisson solution methods for particle-based simulation and inhomogeneous dielectrics

Particle-based simulation represents a powerful approach to modeling physical systems in electronics, molecular biology, and chemical physics. Accounting for the interactions occurring among charged particles requires an accurate and efficient solution of Poisson's equation. For a system of discrete charges with inhomogeneous dielectrics, i.e., a system with discontinuities in the permittivity, the boundary element method (BEM) is frequently adopted. It provides the solution of Poisson's equation, accounting for polarization effects due to the discontinuity in the permittivity by computing the induced charges at the dielectric boundaries. In this framework, the total electrostatic potential is then found by superimposing the elemental contributions from both source and induced charges. In this paper, we present a comparison between two BEMs to solve a boundary-integral formulation of Poisson's equation, with emphasis on the BEMs' suitability for particle-based simulations in terms of solution accuracy and computation speed. The two approaches are the collocation and qualocation methods. Collocation is implemented following the induced-charge computation method of D. Boda et al. [J. Chem. Phys. 125, 034901 (2006)]. The qualocation method is described by J. Tausch et al. [IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 20, 1398 (2001)]. These approaches are studied using both flat and curved surface elements to discretize the dielectric boundary, using two challenging test cases: a dielectric sphere embedded in a different dielectric medium and a toy model of an ion channel. Earlier comparisons of the two BEM approaches did not address curved surface elements or semiatomistic models of ion channels. Our results support the earlier findings that for flat-element calculations, qualocation is always significantly more accurate than collocation. On the other hand, when the dielectric boundary is discretized with curved surface elements, the two methods are essentially equivalent; i.e., they have comparable accuracies for the same number of elements. We find that ions in water--charges embedded in a high-dielectric medium--are harder to compute accurately than charges in a low-dielectric medium.

Ion solvation and structural stability in a sodium channel investigated by molecular dynamics calculations

The stability and ion binding properties of the homo-tetrameric pore domain of a prokaryotic, voltage-gated sodium channel are studied by extensive all-atom molecular dynamics simulations, with the channel protein being embedded in a fully hydrated lipid bilayer. It is found that Na(+) ion presents in a mostly hydrated state inside the wide pore of the selectivity filter of the sodium channel, in sharp contrast to the nearly fully dehydrated state for K(+) ions in potassium channels. Our results also indicate that Na(+) ions make contact with only one or two out of the four polypeptide chains forming the selectivity filter, and surprisingly, the selectivity filter exhibits robust stability for various initial ion configurations even in the absence of ions. These findings are quite different from those in potassium channels. Furthermore, an electric field above 0.5V/nm is suggested to be able to induce Na(+) permeation through the selectivity filter.

Molecular dynamics simulations of the TrkH membrane protein

TrkH is a transmembrane protein that mediates uptake of K(+) through the cell membrane. Despite the recent determination of its crystallographic structure, the nature of the permeation mechanism is still unknown, that is, whether K(+) ions move across TrkH by active transport or passive diffusion. Here, molecular dynamics simulations and the umbrella sampling technique have been employed to shed light on this question. The existence of binding site S3 and two alternative binding sites have been characterized. Analysis of the coordination number renders values that are almost constant, with a full contribution from the carbonyls of the protein only at S3. This observation contrasts with observations of K(+) channels, where the contribution of the protein to the coordination number is roughly constant in all four binding sites. An intramembrane loop is found immediately after the selectivity filter at the intracellular side of the protein, which obstructs the permeation pathway, and this is reflected in the magnitude of the energy barriers.

Simulating electrostatic energies in proteins: perspectives and some recent studies of pKas, redox, and other crucial functional properties

Electrostatic energies provide what is arguably the most effective tool for structure-function correlation of biological molecules. Here, we provide an overview of the current state-of-the-art simulations of electrostatic energies in macromolecules, emphasizing the microscopic perspective but also relating it to macroscopic approaches. We comment on the convergence issue and other problems of the microscopic models and the ways of keeping the microscopic physics while moving to semi-macroscopic directions. We discuss the nature of the protein dielectric "constants" reiterating our long-standing point that the dielectric "constants" in semi-macroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering different functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding, and protein stability. We emphasize the microscopic overcharging approach for studying pK(a) 's of internal groups in proteins and give a demonstration of power of this approach. We also emphasize recent advances in coarse grained models with a physically based electrostatic treatment and provide some examples including further directions in treating voltage activated ion channels.

First-passage-time analysis of atomic-resolution simulations of the ionic transport in a bacterial porin

We have studied the dynamics of chloride and potassium ions in the interior of the Outer membrane porin F (OmpF) under the influence of an external electric field. From the results of extensive all-atom molecular dynamics (MD) simulations of the system, we computed several first-passage-time (FPT) quantities to characterize the dynamics of the ions in the interior of the channel. Such FPT quantities obtained from MD simulations demonstrate that it is not possible to describe the dynamics of chloride and potassium ions inside the whole channel with a single constant diffusion coefficient. However, we showed that a valid, statistically rigorous description in terms of a constant diffusion coefficient D and an effective deterministic force F(eff) can be obtained after appropriate subdivision of the channel in different regions suggested by the x-ray structure. These results have important implications for popular simplified descriptions of channels based on the one-dimensional Poisson-Nernst-Planck equations. Also, the effect of entropic barriers on the diffusion of the ions is identified and briefly discussed.

Insights on the permeability of wide protein channels: measurement and interpretation of ion selectivity

Ion channels are hollow proteins that have evolved to exhibit discrimination between charged solutes. This property, known as ion selectivity is critical for several biological functions. By using the bacterial porin OmpF as a model system of wide protein channels, we demonstrate that significant insights can be gained when selectivity measurements are combined with electrodiffusion continuum models and simulations based on the atomic structure. A correct interpretation of the mechanisms ruling the many sources of channel discrimination is a first, indispensable step for the understanding of the controlled movement of ions into or out of cells characteristic of many physiological processes. We conclude that the scattered information gathered from several independent approaches should be appropriately merged to provide a unified and coherent picture of the channel selectivity.

Multiple Scales in the Simulation of Ion Channels and Proteins

Computation of living processes creates great promise for the everyday life of mankind and great challenges for physical scientists. Simulations molecular dynamics have great appeal to biologists as a natural extension of structural biology. Once a biologist sees a structure, she/he wants to see it move. Molecular biology has shown that a small number of atoms, sometimes even one messenger ion, like Ca(2+), can control biological function on the scale of cells, organs, tissues, and organisms. Enormously concentrated ions-at number densities of ~20 M-in protein channels and enzymes are responsible for many of the characteristics of living systems, just as highly concentrated ions near electrodes are responsible for many of the characteristics of electrochemical systems. Here we confront the reality of the scale differences of ions. We show that the scale differences needed to simulate all the atoms of biological cells are 10(7) in linear dimension, 10(21) in three dimensions, 10(9) in resolution, 10(11) in time, and 10(13) in particle number (to deal with concentrations of Ca(2+)). These scales must be dealt with simultaneously if the simulation is to deal with most biological functions. Biological function extends across all of them, all at once in most cases. We suggest a computational approach using explicit multiscale analysis instead of implicit simulation of all scales. The approach is based on an energy variational principle EnVarA introduced by Chun Liu to deal with complex fluids. Variational methods deal automatically with multiple interacting components and scales. When an additional component is added to the system, the resulting Euler Lagrange field equations change form automatically-by algebra alone-without additional unknown parameters. Multifaceted interactions are solutions of the resulting equations. We suggest that ionic solutions should be viewed as complex fluids with simple components. Highly concentrated solutions-dominated by interactions of components-are easily computed by EnVarA. Successful computation of ions concentrated in special places may be a significant step to understanding the defining characteristics of biological and electrochemical systems. Indeed, computing ions near proteins and nucleic acids may prove as important to molecular biology and chemical technology as computing holes and electrons has been to our semiconductor and digital technology.

APBSmem: a graphical interface for electrostatic calculations at the membrane

Electrostatic forces are one of the primary determinants of molecular interactions. They help guide the folding of proteins, increase the binding of one protein to another and facilitate protein-DNA and protein-ligand binding. A popular method for computing the electrostatic properties of biological systems is to numerically solve the Poisson-Boltzmann (PB) equation, and there are several easy-to-use software packages available that solve the PB equation for soluble proteins. Here we present a freely available program, called APBSmem, for carrying out these calculations in the presence of a membrane. The Adaptive Poisson-Boltzmann Solver (APBS) is used as a back-end for solving the PB equation, and a Java-based graphical user interface (GUI) coordinates a set of routines that introduce the influence of the membrane, determine its placement relative to the protein, and set the membrane potential. The software Jmol is embedded in the GUI to visualize the protein inserted in the membrane before the calculation and the electrostatic potential after completing the computation. We expect that the ease with which the GUI allows one to carry out these calculations will make this software a useful resource for experimenters and computational researchers alike. Three examples of membrane protein electrostatic calculations are carried out to illustrate how to use APBSmem and to highlight the different quantities of interest that can be calculated.

Mechanism of potassium-channel selectivity revealed by Na(+) and Li(+) binding sites within the KcsA pore

Potassium channels allow K(+) ions to diffuse through their pores while preventing smaller Na(+) ions from permeating. Discrimination between these similar, abundant ions enables these proteins to control electrical and chemical activity in all organisms. Selection occurs at the narrow selectivity filter containing structurally identified K(+) binding sites. Selectivity is thought to arise because smaller ions such as Na(+) do not bind to these K(+) sites in a thermodynamically favorable way. Using the model K(+) channel KcsA, we examined how intracellular Na(+) and Li(+) interact with the pore and the permeant ions using electrophysiology, molecular dynamics simulations and X-ray crystallography. Our results suggest that these small cations have a separate binding site within the K(+) selectivity filter. We propose that selective permeation from the intracellular side primarily results from a large energy barrier blocking filter entry for Na(+) and Li(+) in the presence of K(+), not from a difference of binding affinity between ions.

Protein dynamics detected in a membrane-embedded potassium channel using two-dimensional solid-state NMR spectroscopy

We report longitudinal (15)N relaxation rates derived from two-dimensional ((15)N, (13)C) chemical shift correlation experiments obtained under magic angle spinning for the potassium channel KcsA-Kv1.3 reconstituted in multilamellar vesicles. Thus, we demonstrate that solid-state NMR can be used to probe residue-specific backbone dynamics in a membrane-embedded protein. Enhanced backbone mobility was detected for two glycine residues within the selectivity filter that are highly conserved in potassium channels and that are of core relevance to the filter structure and ion selectivity.

Model development for the viral Kcv potassium channel

A computational model for the open state of the short viral Kcv potassium channel was created and tested based on homology modeling and extensive molecular-dynamics simulation in a membrane environment. Particular attention was paid to the structure of the highly flexible N-terminal region and to the protonation state of membrane-exposed lysine residues. Data from various experimental sources, NMR spectroscopy, and electrophysiology, as well as results from three-dimensional reference interaction site model integral equation theory were taken into account to select the most reasonable model among possible variants. The final model exhibits spontaneous ion transitions across the complete pore, with and without application of an external field. The nonequilibrium transport events could be induced reproducibly without abnormally large driving potential and without the need to place ions artificially at certain key positions along the transition path. The transport mechanism through the filter region corresponds to the classic view of single-file motion, which in our case is coupled to frequent exchange of ions between the innermost filter position and the cavity.

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.