Mechanisms of permeation and selectivity in calcium channels

Structural biology of voltage-gated calcium channels

Voltage-gated calcium (Cav) channels mediate Ca2+ influx in response to membrane depolarization, playing critical roles in diverse physiological processes. Dysfunction or aberrant regulation of Cav channels can lead to life-threatening consequences. Cav-targeting drugs have been clinically used to treat cardiovascular and neuronal disorders for several decades. This review aims to provide an account of recent developments in the structural dissection of Cav channels. High-resolution structures have significantly advanced our understanding of the working and disease mechanisms of Cav channels, shed light on the molecular basis for their modulation, and elucidated the modes of actions (MOAs) of representative drugs and toxins. The progress in structural studies of Cav channels lays the foundation for future drug discovery efforts targeting Cav channelopathies.

Bio-Inspired Subnanofluidics: Advanced Fabrication and Functionalization

Biological ion channels can realize high-speed and high-selective ion transport through the protein filter with the sub-1-nanometer channel. Inspired by biological ion channels, various kinds of artificial subnanopores, subnanochannels, and subnanoslits with improved ion selectivity and permeability are recently developed for efficient separation, energy conversion, and biosensing. This review article discusses the advanced fabrication and functionalization methods for constructing subnanofluidic pores, channels, tubes, and slits, which have shown great potential for various applications. Novel fabrication methods for producing subnanofluidics, including top-down techniques such as electron beam etching, ion irradiation, and electrochemical etching, as well as bottom-up approaches starting from advanced microporous frameworks, microporous polymers, lipid bilayer embedded subnanochannels, and stacked 2D materials are well summarized. Meanwhile, the functionalization methods of subnanochannels are discussed based on the introduction of functional groups, which are classified into direct synthesis, covalent bond modifications, and functional molecule fillings. These methods have enabled the construction of subnanochannels with precise control of structure, size, and functionality. The current progress, challenges, and future directions in the field of subnanofluidic are also discussed.

Highly Selective Lithium Transport through Crown Ether Pillared Angstrom Channels

Biological ion channels use the synergistic effects of various strategies to realize highly selective ion sieving. For example, potassium channels use functional groups and angstrom-sized pores to discriminate rival ions and enrich target ions. Inspired by this, we constructed a layered crystal pillared by crown ether that incorporates these strategies to realize high Li+ selectivity. The pillared channels and crown ether have an angstrom-scale size. The crown ether specifically allows the low-barrier transport of Li+ . The channels attract and enrich Li+ ions by up to orders of magnitude. As a result, our material sieves Li+ out of various common ions such as Na+ , K+ , Ca2+ , Mg2+ and Al3+ . Moreover, by spontaneously enriching Li+ ions, it realizes an effective Li+ /Na+ selectivity of 1422 in artificial seawater where the Li+ concentration is merely 25 μM. We expect this work to spark technologies for the extraction of lithium and other dilute metal ions.

Experimental and Theoretical Brownian Dynamics Analysis of Ion Transport During Cellular Electroporation of E. coli Bacteria

Escherichia coli bacterium is a rod-shaped organism composed of a complex double membrane structure. Knowledge of electric field driven ion transport through both membranes and the evolution of their induced permeabilization has important applications in biomedical engineering, delivery of genes and antibacterial agents. However, few studies have been conducted on Gram-negative bacteria in this regard considering the contribution of all ion types. To address this gap in knowledge, we have developed a deterministic and stochastic Brownian dynamics model to simulate in 3D space the motion of ions through pores formed in the plasma membranes of E. coli cells during electroporation. The diffusion coefficient, mobility, and translation time of Ca2+, Mg2+, Na+, K+, and Cl- ions within the pore region are estimated from the numerical model. Calculations of pore's conductance have been validated with experiments conducted at Gustave Roussy. From the simulations, it was found that the main driving force of ionic uptake during the pulse is the one due to the externally applied electric field. The results from this work provide a better understanding of ion transport during electroporation, aiding in the design of electrical pulses for maximizing ion throughput, primarily for application in cancer treatment.

Light-Augmented Multi-ion Interaction in MXene Membrane for Simultaneous Water Treatment and Osmotic Power Generation

The mixing of wastewater and natural water releases abundant osmotic energy. Harvesting this energy could significantly reduce the energy and economic cost of water treatment, leading to sustainable wastewater treatment technology. Yet, such energy harvesting is highly challenging because it requires a material that is highly permeable to nontoxic ions while rejecting toxic ions in wastewater to reach high power density and prevent environmental pollution. In this work, we demonstrate that a light-augmented biomimetic multi-ion interaction in an MXene membrane can simultaneously realize high permeability of Na+ ions for enhanced osmotic power generation and high selectivity to heavy metal ions up to a ratio of 2050 for wastewater treatment. The Na+ permeability is enhanced by the photothermal effect of the MXene membrane. The transport of heavy metal ions, however, is suppressed because, under angstrom-confinement, heavy metal ions are strongly electrostatically repelled by the increased number of permeating Na+ ions. As a result, the membrane can stably generate osmotic power from simulated industrial wastewater, and the power density can be enhanced by 4 times under light illumination of approximate 1 sun intensity. This work highlights the importance of multi-ion interaction for the transport properties of ionic materials, which remains rarely investigated and poorly understood in previous studies.

Calcium binding and permeation in TRPV channels: Insights from molecular dynamics simulations

Some calcium channels selectively permeate Ca2+, despite the high concentration of monovalent ions in the surrounding environment, which is essential for many physiological processes. Without atomistic and dynamical ion permeation details, the underlying mechanism of Ca2+ selectivity has long been an intensively studied, yet controversial, topic. This study takes advantage of the homologous Ca2+-selective TRPV6 and non-selective TRPV1 and utilizes the recently solved open-state structures and a newly developed multisite calcium model to investigate the ion binding and permeation features in TRPV channels by molecular dynamics simulations. Our results revealed that the open-state TRPV6 and TRPV1 show distinct ion binding patterns in the selectivity filter, which lead to different ion permeation features. Two Ca2+ ions simultaneously bind to the selectivity filter of TRPV6 compared with only one Ca2+ in the case of TRPV1. Multiple Ca2+ binding at the selectivity filter of TRPV6 permeated in a concerted manner, which could efficiently block the permeation of Na+. Cations of various valences differentiate between the binding sites at the entrance of the selectivity filter in TRPV6. Ca2+ preferentially binds to the central site with a higher probability of permeation, repelling Na+ to a peripheral site. Therefore, we believe that ion binding competition at the selectivity filter of calcium channels, including the binding strength and number of binding sites, determines Ca2+ selectivity under physiological conditions.

A cooperative knock-on mechanism underpins Ca2+-selective cation permeation in TRPV channels

The selective exchange of ions across cellular membranes is a vital biological process. Ca2+-mediated signaling is implicated in a broad array of physiological processes in cells, while elevated intracellular concentrations of Ca2+ are cytotoxic. Due to the significance of this cation, strict Ca2+ concentration gradients are maintained across the plasma and organelle membranes. Therefore, Ca2+ signaling relies on permeation through selective ion channels that control the flux of Ca2+ ions. A key family of Ca2+-permeable membrane channels is the polymodal signal-detecting transient receptor potential (TRP) ion channels. TRP channels are activated by a wide variety of cues including temperature, small molecules, transmembrane voltage, and mechanical stimuli. While most members of this family permeate a broad range of cations non-selectively, TRPV5 and TRPV6 are unique due to their strong Ca2+ selectivity. Here, we address the question of how some members of the TRPV subfamily show a high degree of Ca2+ selectivity while others conduct a wider spectrum of cations. We present results from all-atom molecular dynamics simulations of ion permeation through two Ca2+-selective and two non-selective TRPV channels. Using a new method to quantify permeation cooperativity based on mutual information, we show that Ca2+-selective TRPV channel permeation occurs by a three-binding site knock-on mechanism, whereas a two-binding site knock-on mechanism is observed in non-selective TRPV channels. Each of the ion binding sites involved displayed greater affinity for Ca2+ over Na+. As such, our results suggest that coupling to an extra binding site in the Ca2+-selective TRPV channels underpins their increased selectivity for Ca2+ over Na+ ions. Furthermore, analysis of all available TRPV channel structures shows that the selectivity filter entrance region is wider for the non-selective TRPV channels, slightly destabilizing ion binding at this site, which is likely to underlie mechanistic decoupling.

Probing ion binding in the selectivity filter of the Cav1.1 channel with molecular dynamics

Cav1.1 is the voltage-gated calcium channel essential for the contraction of skeletal muscles upon membrane potential changes. Structural determination of the Cav1.1 channel opens the avenue toward understanding of the structure-function relationship of voltage-gated calcium channels. Here, we show that there exist two Ca2+-binding sites, termed S1 and S2, within the selectivity filter of Cav1.1 through extensive molecular dynamics simulations on various initial ion arrangement configurations. The formation of both binding sites is associated with the four Glu residues (Glu292/614/1014/1323) that constitute the so-called EEEE locus. At the S1 site near the extracellular side, the Ca2+ ion is coordinated with the negatively charged carboxylic groups of these Glu residues and of the Asp615 residue either in a direct way or via an intermediate water molecule. At the S2 site, Ca2+ binding shows two distinct states: an upper state involving two out of the four Glu residues in the EEEE locus and a lower state involving only one Glu residue. In addition, there exist two recruitment sites for Ca2+ above the entrance of the filter. These findings promote the understanding of mechanism for ion permeation and selectivity in calcium channels.

Structures of the R-type human Cav2.3 channel reveal conformational crosstalk of the intracellular segments

The R-type voltage-gated Ca²⁺ (Ca_v) channels Ca_v2.3, widely expressed in neuronal and neuroendocrine cells, represent potential drug targets for pain, seizures, epilepsy, and Parkinson's disease. Despite their physiological importance, there have lacked selective small-molecule inhibitors targeting these channels. High-resolution structures may aid rational drug design. Here, we report the cryo-EM structure of human Ca_v2.3 in complex with α2δ-1 and β3 subunits at an overall resolution of 3.1 Å. The structure is nearly identical to that of Ca_v2.2, with VSD_II in the down state and the other three VSDs up. A phosphatidylinositol 4,5-bisphosphate (PIP2) molecule binds to the interface of VSD_II and the tightly closed pore domain. We also determined the cryo-EM structure of a Ca_v2.3 mutant in which a Ca_v2-unique cytosolic helix in repeat II (designated the CH2_II helix) is deleted. This mutant, named ΔCH2, still reserves a down VSD_II, but PIP2 is invisible and the juxtamembrane region on the cytosolic side is barely discernible. Our structural and electrophysiological characterizations of the wild type and ΔCH2 Ca_v2.3 show that the CH2_II helix stabilizes the inactivated conformation of the channel by tightening the cytosolic juxtamembrane segments, while CH2_II helix is not necessary for locking the down state of VSD_II.

Angstrom-scale ion channels towards single-ion selectivity

Artificial ion channels with ion permeability and selectivity comparable to their biological counterparts are highly desired for efficient separation, biosensing, and energy conversion technologies. In the past two decades, both nanoscale and sub-nanoscale ion channels have been successfully fabricated to mimic biological ion channels. Although nanoscale ion channels have achieved intelligent gating and rectification properties, they cannot realize high ion selectivity, especially single-ion selectivity. Artificial angstrom-sized ion channels with narrow pore sizes <1 nm and well-defined pore structures mimicking biological channels have accomplished high ion conductivity and single-ion selectivity. This review comprehensively summarizes the research progress in the rational design and synthesis of artificial subnanometer-sized ion channels with zero-dimensional to three-dimensional pore structures. Then we discuss cation/anion, mono-/di-valent cation, mono-/di-valent anion, and single-ion selectivities of the synthetic ion channels and highlight their potential applications in high-efficiency ion separation, energy conversion, and biological therapeutics. The gaps of single-ion selectivity between artificial and natural channels and the connections between ion selectivity and permeability of synthetic ion channels are covered. Finally, the challenges that need to be addressed in this research field and the perspective of angstrom-scale ion channels are discussed.

Theoretical investigation on the effect of terahertz wave on Ca2+ transport in the calcium channel

The question of whether terahertz (THz) waves can interact with ions in channels of nerve cells and cause a further reaction has attracted much attention. To answer this question, we investigate the spontaneous radiation generated by Ca²⁺ moving in calcium channels and the effect of THz radiation on the transport of Ca²⁺ by solving the mathematical physical model through Brownian dynamics (BD) simulations. It is obtained that the moving Ca²⁺ in a calcium channel can generate electromagnetic radiation, the corresponding spectrum of which is concentrated in the THz range. Meanwhile, both the ion number in the channel and the background temperature are proved to have significant effects on the spontaneous emission spectra. The studies also show that external THz radiation can accelerate Ca²⁺ transport through the ion channel. These results are expected to provide a theoretical basis for the future treatment of THz waves in the neurological field.

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.

Terahertz Wave Enhances Permeability of the Voltage-Gated Calcium Channel

A deficiency of Ca²⁺ fluxes arising from dysfunctional voltage-gated calcium channels has been associated with a list of calcium channelopathies such as epilepsy, hypokalemic periodic paralysis, episodic ataxia, etc. Apart from analyzing the pathogenic channel mutations, understanding how the channel regulates the ion conduction would be instructive to the treatment as well. In the present work, in relating the free energetics of Ca²⁺ transport to the calcium channel, we demonstrate the importance of bridging Ca²⁺ hydration waters, which form hydrogen bonds with channel -COO^- and -C═O groups and enable a long-distance effect on the Ca²⁺ permeation. By firing a terahertz wave which resonates with the stretching mode of either the -COO^- or the -C═O group, we obtain significantly enhanced selectivity and conductance of Ca²⁺. The Ca²⁺ free energy negatively grows nearly 5-fold. The direct evidence is the reinforced hydrogen bonds. In addition, thanks to forced vibrations, -COO^- contributes to raised permeation as well even under a field in resonance with -C═O, and vice versa. Since the resonant terahertz field could manipulate the conduction of calcium channels, it has potential applications in therapeutic intervention such as rectifying a Ca²⁺ deficiency in degraded calcium channels, inducing apoptosis of tumor cells with overloaded calcium etc.

Application of a Statistical and Linear Response Theory to Multi-Ion Na+ Conduction in NaChBac

Biological ion channels are fundamental to maintaining life. In this manuscript we apply our recently developed statistical and linear response theory to investigate Na+ conduction through the prokaryotic Na+ channel NaChBac. This work is extended theoretically by the derivation of ionic conductivity and current in an electrochemical gradient, thus enabling us to compare to a range of whole-cell data sets performed on this channel. Furthermore, we also compare the magnitudes of the currents and populations at each binding site to previously published single-channel recordings and molecular dynamics simulations respectively. In doing so, we find excellent agreement between theory and data, with predicted energy barriers at each of the four binding sites of ∼4,2.9,3.6, and 4kT.

Dynamics of ionic flows via Poisson-Nernst-Planck systems with local hard-sphere potentials: Competition between cations

We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flows through a membrane channel with three ion species, two positively charged with the same valence and one negatively charged. Bikerman's local hard-sphere potential is included in the model to account for ion sizes. The problem is treated as a boundary value problem of a singularly perturbed differential system. Under the framework of a geometric singular perturbation theory, together with specific structures of this concrete model, the existence and uniqueness of solutions to the boundary value problem for small ion sizes is established. Furthermore, treating the ion sizes as small parameters, we derive an approximation of individual fluxes, from which one can further study the qualitative properties of ionic flows and extract concrete information directly related to biological measurements. Of particular interest is the competition between two cations due to the nonlinear interplay between finite ion sizes, diffusion coefficients and boundary conditions, which is closely related to selectivity phenomena of open ion channels with given protein structures. Furthermore, we are able to characterize the distinct effects of the nonlinear interplays between these physical parameters. Numerical simulations are performed to identify some critical potentials which play critical roles in examining properties of ionic flows in our analysis.

Ionic Coulomb blockade and the determinants of selectivity in the NaChBac bacterial sodium channel

Mutation-induced transformations of conductivity and selectivity in NaChBac bacterial channels are studied experimentally and interpreted within the framework of ionic Coulomb blockade (ICB), while also taking account of resonant quantised dehydration (QD) and site protonation. Site-directed mutagenesis and whole-cell patch-clamp experiments are used to investigate how the fixed charge Q_f at the selectivity filter (SF) affects both valence selectivity and same-charge selectivity. The new ICB/QD model predicts that increasing ∣Q_f∣ should lead to a shift in selectivity sequences toward larger ion sizes, in agreement with the present experiments and with earlier work. Comparison of the model with experimental data leads to the introduction of an effective charge Q_f^∗ at the SF, which was found to differ between Aspartate and Glutamate charged rings, and also to depend on position within the SF. It is suggested that protonation of the residues within the restricted space of the SF is important in significantly reducing the effective charge of the EEEE ring. Values of Q_f^∗ derived from experiments on divalent blockade agree well with expectations based on the ICB/QD model and have led to the first demonstration of ICB oscillations in Ca²⁺ conduction as a function of the fixed charge. Preliminary studies of the dependence of Ca²⁺ conduction on pH are qualitatively consistent with the predictions of the model.

Proposed Dynamics of CDB3 Activation in Human Erythrocytes by Nifedipine Studied with Scanning Flow Cytometry

Nifedipine is calcium channels and pumps blocker widely used in medicine. However, mechanisms of nifedipine action in blood are not clear. In particular, the influence of nifedipine on erythrocytes is far from completely understood. In this work, applying scanning flow cytometry, we observed experimentally for the first time the dynamics behind a significant increase of HCO₃ ^- /Cl^- transmembrane exchange rate of CDB3 (main anion exchanger, AE1, Band 3, SLC4A1) of human erythrocytes in the presence of nifedipine in blood. It was found that the rate of CDB3 activation is not limited by the rate of nifedipine binding and/or Ca²⁺ transport. In order to explain the experimental data, we suggested a kinetic model assuming that the rate of CDB3 activation is limited by the dynamics of the balance between two intracellular processes (1) the activation of CDB3 limited by its interaction with intracellular Ca²⁺ , and (2) the spontaneous deactivation of CDB3. Thus the use of scanning flow cytometry allowed to clarify quantitatively the molecular kinetic mechanism of nifedipine action on human erythrocytes. In particular, the efficiency (~30) and rates of activation (~0.3 min^-1 ) and deactivation (~10^-3 min^-1 ) of CDB3 in human erythrocytes was evaluated for two donors. © 2019 International Society for Advancement of Cytometry.

Ion Permeation Mechanism in Epithelial Calcium Channel TRVP6

Calcium is the most abundant metal in the human body that plays vital roles as a cellular electrolyte as well as the smallest and most frequently used signaling molecule. Calcium uptake in epithelial tissues is mediated by tetrameric calcium-selective transient receptor potential (TRP) channels TRPV6 that are implicated in a variety of human diseases, including numerous forms of cancer. We used TRPV6 crystal structures as templates for molecular dynamics simulations to identify ion binding sites and to study the permeation mechanism of calcium and other ions through TRPV6 channels. We found that at low Ca²⁺ concentrations, a single calcium ion binds at the selectivity filter narrow constriction formed by aspartates D541 and allows Na⁺ permeation. In the presence of ions, no water binds to or crosses the pore constriction. At high Ca²⁺ concentrations, calcium permeates the pore according to the knock-off mechanism that includes formation of a short-lived transition state with three calcium ions bound near D541. For Ba²⁺, the transition state lives longer and the knock-off permeation occurs slower. Gd³⁺ binds at D541 tightly, blocks the channel and prevents Na⁺ from permeating the pore. Our results provide structural foundations for understanding permeation and block in tetrameric calcium-selective ion channels.

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.

Electrosorption at functional interfaces: from molecular-level interactions to electrochemical cell design

This perspective discusses the fundamental processes behind electrosorption at charged interfaces, and highlights advances in electrode design for sustainable technologies in water purification and ion-selective separations.

Modeling ion permeation through a bacterial voltage-gated calcium channel CaVAb using molecular dynamics simulations

Ca²⁺ion binds tightly to the center of the selectivity filter of voltage-gated calcium channels.

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.

Understanding Sodium Channel Function and Modulation Using Atomistic Simulations of Bacterial Channel Structures

Sodium channels are chief proteins involved in electrical signaling in the nervous system, enabling critical functions like heartbeat and brain activity. New high-resolution X-ray structures for bacterial sodium channels have created an opportunity to see how these proteins operate at the molecular level. An important challenge to overcome is establishing relationships between the structures and functions of mammalian and bacterial channels. Bacterial sodium channels are known to exhibit the main structural features of their mammalian counterparts, as well as several key functional characteristics, including selective ion conduction, voltage-dependent gating, pore-based inactivation and modulation by local anesthetic, antiarrhythmic and antiepileptic drugs. Simulations have begun to shed light on each of these features in the past few years. Despite deviations in selectivity signatures for bacterial and mammalian channels, simulations have uncovered the nature of the multiion conduction mechanism associated with Na(+) binding to a high-field strength site established by charged glutamate side chains. Simulations demonstrated a surprising level of flexibility of the protein, showing that these side chains are active participants in the permeation process. They have also uncovered changes in protein structure, leading to asymmetrical collapses of the activation gate that have been proposed to correspond to inactivated structures. These observations offer the potential to examine the mechanisms of state-dependent drug activity, focusing on pore-blocking and pore-based slow inactivation in bacterial channels, without the complexities of inactivation on multiple timescales seen in eukaryotic channels. Simulations have provided molecular views of the interactions of drugs, consistent with sites predicted in mammalian channels, as well as a wealth of other sites as potential new drug targets. In this chapter, we survey the new insights into sodium channel function that have emerged from studies of simpler bacterial channels, which provide an excellent learning platform, and promising avenues for mechanistic discovery and pharmacological development.

Effects of electromagnetic field exposure on conduction and concentration of voltage gated calcium channels: A Brownian dynamics study

A three-dimensional Brownian Dynamics (BD) in combination with electrostatic calculations is employed to specifically study the effects of radiation of high frequency electromagnetic fields on the conduction and concentration profile of calcium ions inside the voltage-gated calcium channels. The electrostatic calculations are performed using COMSOL Multiphysics by considering dielectric interfaces effectively. The simulations are performed for different frequencies and intensities. The simulation results show the variations of conductance, average number of ions and the concentration profiles of ions inside the channels in response to high frequency radiation. The ionic current inside the channel increases in response to high frequency electromagnetic field radiation, and the concentration profiles show that the residency of ions in the channel decreases accordingly.

Enjoy the Trip: Calcium in Mitochondria Back and Forth

In the last 5 years, most of the molecules that control mitochondrial Ca(2+) homeostasis have been finally identified. Mitochondrial Ca(2+) uptake is mediated by the Mitochondrial Calcium Uniporter (MCU) complex, a macromolecular structure that guarantees Ca(2+) accumulation inside mitochondrial matrix upon increases in cytosolic Ca(2+). Conversely, Ca(2+) release is under the control of the Na(+)/Ca(2+) exchanger, encoded by the NCLX gene, and of a H(+)/Ca(2+) antiporter, whose identity is still debated. The low affinity of the MCU complex, coupled to the activity of the efflux systems, protects cells from continuous futile cycles of Ca(2+) across the inner mitochondrial membrane and consequent massive energy dissipation. In this review, we discuss the basic principles that govern mitochondrial Ca(2+) homeostasis and the methods used to investigate the dynamics of Ca(2+) concentration within the organelles. We discuss the functional and structural role of the different molecules involved in mitochondrial Ca(2+) handling and their pathophysiological role.

Selecting ions by size in a calcium channel: the ryanodine receptor case study

Many calcium channels can distinguish between ions of the same charge but different size. For example, when cations are in direct competition with each other, the ryanodine receptor (RyR) calcium channel preferentially conducts smaller cations such as Li(+) and Na(+) over larger ones such as K(+) and Cs(+). Here, we analyze the physical basis for this preference using a previously established model of RyR permeation and selectivity. Like other calcium channels, RyR has four aspartate residues in its GGGIGDE selectivity filter. These aspartates have their terminal carboxyl group in the pore lumen, which take up much of the available space for permeating ions. We find that small ions are preferred by RyR because they can fit into this crowded environment more easily.

Ion conduction and conformational flexibility of a bacterial voltage-gated sodium channel

Voltage-gated Na(+) channels play an essential role in electrical signaling in the nervous system and are key pharmacological targets for a range of disorders. The recent solution of X-ray structures for the bacterial channel NavAb has provided an opportunity to study functional mechanisms at the atomic level. This channel's selectivity filter exhibits an EEEE ring sequence, characteristic of mammalian Ca(2+), not Na(+), channels. This raises the fundamentally important question: just what makes a Na(+) channel conduct Na(+) ions? Here we explore ion permeation on multimicrosecond timescales using the purpose-built Anton supercomputer. We isolate the likely protonation states of the EEEE ring and observe a striking flexibility of the filter that demonstrates the necessity for extended simulations to study conduction in this channel. We construct free energy maps to reveal complex multi-ion conduction via knock-on and "pass-by" mechanisms, involving concerted ion and glutamate side chain movements. Simulations in mixed ionic solutions reveal relative energetics for Na(+), K(+), and Ca(2+) within the pore that are consistent with the modest selectivity seen experimentally. We have observed conformational changes in the pore domain leading to asymmetrical collapses of the activation gate, similar to proposed inactivated structures of NavAb, with helix bending involving conserved residues that are critical for slow inactivation. These structural changes are shown to regulate access to fenestrations suggested to be pathways for lipophilic drugs and provide deeper insight into the molecular mechanisms connecting drug activity and slow inactivation.

Energetics of discrete selectivity bands and mutation-induced transitions in the calcium-sodium ion channels family

We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model of a biological ion channel as functions of the fixed charge Q(f) at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 (Q(f)=1e), M1 (3e), M2 (5e), with a set of sodium conduction bands L0 (0.5e), L1 (1.5e), thereby obtaining a completed pattern of conduction and selectivity bands vs Q(f) for the sodium-calcium channels family. An increase of Q(f) leads to an increase of calcium selectivity: L0 (sodium-selective, nonblocking channel) → M0 (nonselective channel) → L1 (sodium-selective channel with divalent block) → M1 (calcium-selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is putatively identified with the eukaryotic sodium channel The scheme created is able to account for the experimentally observed mutation-induced transformations between nonselective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrierless conduction. The pattern of periodic conduction bands is explained on the basis of sequential neutralization taking account of self-energy, as Q(f)(z,i)=ze(1/2+i), where i is the order of the band and z is the valence of the ion. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca(2+)/Na(+) valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.

The mitochondrial calcium uniporter is a multimer that can include a dominant-negative pore-forming subunit

Mitochondrial calcium uniporter (MCU) channel is responsible for Ruthenium Red-sensitive mitochondrial calcium uptake. Here, we demonstrate MCU oligomerization by immunoprecipitation and Förster resonance energy transfer (FRET) and characterize a novel protein (MCUb) with two predicted transmembrane domains, 50% sequence similarity and a different expression profile from MCU. Based on computational modelling, MCUb includes critical amino-acid substitutions in the pore region and indeed MCUb does not form a calcium-permeable channel in planar lipid bilayers. In HeLa cells, MCUb is inserted into the oligomer and exerts a dominant-negative effect, reducing the [Ca(2+)]mt increases evoked by agonist stimulation. Accordingly, in vitro co-expression of MCUb with MCU drastically reduces the probability of observing channel activity in planar lipid bilayer experiments. These data unveil the structural complexity of MCU and demonstrate a novel regulatory mechanism, based on the inclusion of dominant-negative subunits in a multimeric channel, that underlies the fine control of the physiologically and pathologically relevant process of mitochondrial calcium homeostasis.

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.

Na(+)/Ca(2+) selectivity in the bacterial voltage-gated sodium channel NavAb

The recent publication of a number of high resolution bacterial voltage-gated sodium channel structures has opened the door for the mechanisms employed by these channels to distinguish between ions to be elucidated. The way these channels select between Na⁺ and K⁺ has been investigated in computational studies, but the selectivity for Na⁺ over Ca²⁺ has not yet been studied in this way. Here we use molecular dynamics simulations to calculate the energetics of Na⁺ and Ca²⁺ transport through the channel. Single ion profiles show that Ca²⁺ experiences a large barrier midway through the selectivity filter that is not seen by Na⁺. This barrier is caused by the need for Ca²⁺ to partly dehydrate to pass through this region and the lack of compensating interactions with the protein. Multi-ion profiles show that ions can pass each other in the channel, which is why the presence of Ca²⁺ does not block Na⁺ conduction despite binding more strongly in the pore.

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.

Extension of Brownian dynamics for studying blockers of ion channels

We present new Brownian dynamics techniques for studying blockers of ion channels. By treating the channel as a fixed body, simulating the blocker molecules using rigid bodies, and using an implicit water force field with explicit ions, we are able to carry out fast simulations that can be used to investigate the dynamics of block and unblock, deduce binding modes, and calculate binding affinities. We test our program using the NavAb bacterial sodium channel, whose structure was recently solved (Payandeh et al. Nature, 2011, 475, 353-358) in conjunction with the μ-conotoxin PIIIA blocker. We derive an ohmic current-voltage relationship for channel permeation, calculate potentials of mean force for blocker unbinding, and deduce multiple binding modes for the blocker. Our results are shown to be compatible with other computational and experimental results. Finally, we discuss future improvements such as the inclusion of flexible side chains. After these improvements are carried out, we anticipate our program will be an extremely useful new tool that could be used to help develop new drugs to treat a range of ion-channel related diseases.

Competition among Ca2+, Mg2+, and Na+ for model ion channel selectivity filters: determinants of ion selectivity

Because voltage-gated ion channels play critical biological roles, understanding how they can discriminate the native metal ion from rival cations in the milieu is of great interest. Although Ca(2+), Mg(2+), and Na(+) are present in comparable concentrations outside the cell, the factors governing the competition among these cations for the selectivity filter of voltage-gated Ca(2+) ion channel remain unclear. Using density functional theory combined with continuum dielectric methods, we evaluate the effect of (1) the number, chemical type, and charge of the ligands lining the pore, (2) the pore's rigidity, size, symmetry, and solvent accessibility, and (3) the Ca(2+) hydration number outside the selectivity filter on the competition among Ca(2+), Mg(2+), and Na(+) in model selectivity filters. The calculations show how the outcome of this competition depends on the interplay between electronic and solvation effects. Selectivity for monovalent Na(+) over divalent Ca(2+)/Mg(2+) is achieved when solvation effects outweigh electrostatic effects; thus filters comprising a few weak charge-donating groups such as Ser/Thr side chains, where electrostatic effects are relatively weak and are easily overcome by solvation effects, are Na(+)-selective. In contrast, selectivity for divalent Ca(2+)/Mg(2+) over monovalent Na(+) is achieved when metal-ligand electrostatic effects outweigh solvation effects. The key differences in selectivity between Mg(2+) and Ca(2+) lie in the pore size, oligomericity, and solvent accessibility. The results, which are consistent with available experimental data, reveal how the structure and composition of the ion channel selectivity pore had adapted to the specific physicochemical properties of the native metal ion to enhance the competitiveness of the native metal toward rival cations.

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.

Permeation properties of the hair cell mechanotransducer channel provide insight into its molecular structure

Mechanoelectric transducer (MET) channels, located near stereocilia tips, are opened by deflecting the hair bundle of sensory hair cells. Defects in this process result in deafness. Despite this critical function, the molecular identity of MET channels remains a mystery. Inherent channel properties, particularly those associated with permeation, provide the backbone for the molecular identification of ion channels. Here, a novel channel rectification mechanism is identified, resulting in a reduced pore size at positive potentials. The apparent difference in pore dimensions results from Ca(2+) binding within the pore, occluding permeation. Driving force for permeation at hyperpolarized potentials is increased because Ca(2+) can more easily be removed from binding within the pore due to the presence of an electronegative external vestibule that dehydrates and concentrates permeating ions. Alterations in Ca(2+) binding may underlie tonotopic and Ca(2+)-dependent variations in channel conductance. This Ca(2+)-dependent rectification provides targets for identifying the molecular components of the MET channel.

Mechanism of ion permeation and selectivity in a voltage gated sodium channel

The rapid and selective transport of Na(+) through sodium channels is essential for initiating action potentials within excitable cells. However, an understanding of how these channels discriminate between different ion types and how ions permeate the pore has remained elusive. Using the recently published crystal structure of a prokaryotic sodium channel from Arcobacter butzleri, we are able to determine the steps involved in ion transport and to pinpoint the location and likely mechanism used to discriminate between Na(+) and K(+). Na(+) conduction is shown to involve the loosely coupled "knock-on" movement of two solvated ions. Selectivity arises due to the inability of K(+) to fit between a plane of glutamate residues with the preferred solvation geometry that involves water molecules bridging between the ion and carboxylate groups. These mechanisms are different to those described for K(+) channels, highlighting the importance of developing a separate mechanistic understanding of Na(+) and Ca(2+) channels.