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date: 23 May 2019

Ion Channel Permeation and Selectivity

Abstract and Keywords

Many biological processes essential for life rely on the transport of specific ions at specific times across cell membranes. Such exquisite control of ionic currents, which is regulated by protein ion channels, is fundamental for the proper functioning of the cells. It is not surprising, therefore, that the mechanism of ion permeation and selectivity in ion channels has been extensively investigated by means of experimental and theoretical approaches. These studies have provided great mechanistic insight but have also raised new questions that are still unresolved. This chapter first summarizes the main techniques that have provided significant knowledge about ion permeation and selectivity. It then discusses the physical mechanisms leading to ion permeation and the explanations that have been proposed for ion selectivity in voltage-gated potassium, sodium, and calcium channels.

Keywords: voltage-gated ion channels, ion permeation, ion selectivity, electrophysiology, molecular dynamics

Introduction

The movement of ions across cell membranes through ion channels underlies a wide range of biological processes such as the transmission of nerve impulses, stimulation of muscle contraction, and regulation of cell volume and blood pressure, to name just a few. Structural alterations of ion channels and subsequent malfunctions may cause several channelopathies (Bagal et al., 2013), including epilepsy, long QT syndrome, deafness, and cerebellar ataxia, among others. While the process of ion transport sounds conceptually simple, it requires the coordinated and rapid movement of specific ions across cell membranes at precise times in response to different stimuli through a very intricate mechanism. The elucidation of the steps involved in this complex mechanism, in which ion channels play a fundamental role, is still an area of intense, ongoing research.

The gating (opening and closing) of ion channels to allow the passage of ions can be induced as a response to chemical stimuli, temperature changes, voltage changes, ligand binding, or mechanical forces. Voltage-gated ion channels are responsible for the generation and propagation of action potentials in neurons and other excitable cells (Catterall, 2012). Under depolarizing conditions (increasing transmembrane potential), voltage-gated sodium (Nav) channels open and transport Na+ ions from the extracellular media to the cytosol, causing further depolarization of the membrane. Then, Nav channels are inactivated, and voltage-gated potassium (Kv) channels open and allow the outward transport of K+ ions to reach electrochemical equilibrium with the extracellular medium. This repolarizes (decreases the potential of) the membrane and restores the negative resting potential of the cell. Voltage-gated calcium (Cav) channels are also able to modify the membrane potential by transporting Ca2+ ions from outside to inside the cell. Moreover, this ion transport is also involved in cell signaling processes such as gene transcription (Clapham, 2007).

The delicate process of ion transport requires an exquisite control over the inward and outward permeation of the different ions, whose mechanistic aspects are not yet fully understood. For example, in order to fulfil their role, Kv channels have to prevent the passage of other ions, such as Na+, that would dissipate the electric gradient. Indeed, Kv channels typically let 100–1000 K+ ions pass for every Na+. In addition, Kv channels have to be able to rapidly return the cell to its resting state after an electrical signal and, thus, transport many millions of K+ ions across the membrane every second. Reconciling how a channel can be exquisitely selective yet let ions pass at such large rates is an unresolved intellectual challenge that has fascinated scientists ever since these channels were proposed more than 60 years ago.

This chapter aims to explain what we know about the passage of ions through channels (permeation) and the mechanisms by which channels distinguish between different ion species (selectivity), based on experimental and theoretical research. We will briefly describe the most common experimental and theoretical approaches used to investigate the transport of ions through ion channels. We then turn our attention to the selection and permeation of ions and the mechanisms by which different channels achieve this, focusing on Kv, Nav, and Cav channels, in which exquisite selection is achieved among very similar ions.

Approaches to Studying Permeation and Selectivity

The knowledge gained on ion permeation and selectivity in the last two decades has considerably increased thanks to the use of advanced experimental and theoretical methodologies, especially electrophysiological measurements, structural analysis and dynamics simulations. These techniques enable the inspection of fundamental aspects of the mechanisms of ion transport through ion channels at macroscopic and microscopic levels of resolution and, in many cases, in a time-resolved picture.

Experimental Approaches

The measurement of currents passing through ion channels remains one of the key tools to understanding the steps involved in permeation and the mechanisms of selectivity, as the rate of permeation through an ion channel can be directly measured through single-channel patch-clamp recordings. The permeability of a channel to different ions can be determined by measuring the current with just one permeant ion type present at a time. The permeability ratio is often defined as the current of one ion type measured in this way compared to the current of another. This, however, should be differentiated from a measure of the selectivity of an ion channel that is performed with multiple ion species present. Selectivity measurements usually proceed under “bi-ionic” conditions, with a different permeant species present on each side of the membrane that compete with each other to pass through the channels. With no applied potential, a nonselective channel will pass zero current. But a selective channel will show a net current carried by the more selected species. The degree of selectivity is then typically determined from the reversal potential of the current–voltage relationship (LeMasurier, Heginbotham, & Miller, 2001), which is defined as the potential at which there is no net flow of a particular ion type.

Because the channel protein has to be attractive to permeating ions to enable rapid transport, it is not uncommon for more than one ion to enter a channel at any one time, something that can also be probed by studying ionic currents. If ions move independently though the pore, then, the ratio of efflux to influx is directly related to the activities of the ion type on each side and the membrane potential (Ussing, 1949). But if ions must interact to permeate the pore, this relationship must be modified to include the so-called flux ratio exponent, with a value greater than one indicating non-independent motion (Hodgkin & Keynes, 1955). While an exponent greater than one yields a clear indication of a multi-ion pore, the exact value can vary anywhere between one and the number of ion binding sites in the pore (Heckmann, 1972; Hille & Schwarz, 1978), and saturation of currents at high concentrations can alter the conclusions (Vora, Corry, & Chung, 2008).

Electrophysiological measurements on mutant ion channels have also provided great mechanistic insight into ion permeation (Naylor et al., 2016; Yue, Navarro, Ren, Ramos, & Clapham, 2002). The alteration of ion conductivity and/or selectivity induced by mutation of a particular residue highlights the relevance of the mutated residue in the transport mechanism. In addition to electrophysiological experiments on both wild-type or mutant channels, the determination of atomic resolution structures of ion channels using X-ray crystallography or cryo-electron microscopy has also contributed to advance our knowledge in ion transport. In the last 20 years, atomic-resolution structures have been published for a number of ion channels (Bagnéris et al., 2013; Brohawn, del Marmol, & MacKinnon, 2012; Doyle et al., 1998; Jiang et al., 2003; Lenaeus et al., 2017; Long, Campbell, & Mackinnon, 2005; Long, Tao, Campbell, & MacKinnon, 2007; McCusker et al., 2012; Morais-Cabral, Zhou, & MacKinnon, 2001; Payandeh, Gamal El-Din, Scheuer, Zheng, & Catterall, 2012; Shaya et al., 2014; Shen et al., 2017; Sula et al., 2017; Tang et al., 2014; Wu et al., 2016; Wu et al., 2015; Yan et al., 2017; Zhang et al., 2012; Zhou, Morais-Cabral, Kaufman, & MacKinnon, 2001), which yielded valuable mechanistic information. For example, the electron-density maps provided by these structural methods enabled researchers to hypothesize the number of ion binding sites and their location in the selectivity filter. The mechanistic information gained from electrophysiological experiments and X-ray and cryo-electron microscopy structures for Na+, K+, and Ca+2 channels will be discussed in more detail later.

Theoretical Approaches

The microscopic events that take place as ions pass through a channel—e.g., conformational changes in the protein, solvation/desolvation of ions along the journey, or formation/breaking of ion/protein interactions—are almost impossible to directly interrogate with experimental approaches. However, they can be witnessed in advanced dynamic simulations (Chung & Corry, 2005; Corry, 2017; Maffeo, Bhattacharya, Yoo, Wells, & Aksimentiev, 2012; Oakes, Furini, & Domene, 2016), provided that they are carefully validated against experimental data.

The dynamic simulation of ionic permeation events across ion channels requires very long simulation times because ionic permeation usually occurs in the nanosecond to microsecond time scale, or even longer. A drastic but very efficient approach that can be employed to alleviate the computational cost of the simulation is to represent the structure of the entire system, or part of it, by a structureless continuum dielectric material, as represented in Figure 1A and 1B. This approach is employed in the Poisson-Nernst-Planck (PNP) simulations, in which no atoms are represented explicitly, and in Brownian dynamics (BD) simulations, in which only select atoms (usually the ions) are included explicitly. The theory and the limitations behind these approximations have been extensively discussed (Chung & Corry, 2005; Corry, Kuyucak, & Chung, 2000; Levitt, 1999; Maffeo et al., 2012). An issue with the fully-continuum approach is that the average ion concentration in the pore often cannot adequately represent the forces felt on individual ions as they pass through the narrow pores (Corry et al., 2000). The BD method, while avoiding this issue, also involves many simplifications, including the use of a static protein structure and approximations to account for ion solvation. Both methods allow for the currents through channels to be efficiently determined and have provided important clues about the mechanisms of ion permeation and selectivity, although it remains challenging in these methods to discriminate between very similar ions such as Na+ and K+.

A more realistic description of the mechanism of ion transport through protein channels can be obtained when all the atoms of the system are explicitly accounted for in the model (Figure 1C). This is the case of the all-atom molecular dynamics (MD) methodology, where the motion of each of the atoms is simulated by integrating numerically the Hamilton equations of motion for many short-time intervals (Adcock & McCammon, 2006). The use of MD to simulate ion channels has gained popularity in the last two decades due to the experimentally determined high-resolution ion-channel structures, which can be employed as initial structures in the dynamics, and improvements in computing power that allow simulations to reach the timescale of ion permeation. The integration of the equations of motion requires the computation of the atomic forces at each time step of the simulation. The vast majority of MD simulations of ion channels makes use of classical molecular mechanics (MM) force fields (Corry, 2017; Oakes et al., 2016) to compute the forces due to the very high computational cost of using quantum mechanical (QM) or hybrid QM/MM techniques. The only exceptions to this are full-QM treatments that have been employed to discuss the selectivity of ion channels by drastically simplifying the system to a reduced model of only a few tens of atoms, which tried to mimic the selectivity filter in a static picture (Dudev, Grauffel, & Lim, 2016; Dudev & Lim, 2014).

Even with classical simulations, the modeling of ionic permeation through ion channels is very computationally demanding since it is a very slow process, which may last hundreds of nanoseconds or even microseconds. This means that the simulation of a significant number of events to extract statistically meaningful conclusions would require simulations to reach the millisecond time scale or even more. Consequently, the dynamics are often accelerated by means of several approaches. For example, a large but constant electric field, which helps overcome large potential-energy barriers (Figure 1D), can be applied to generate a net flux of ions (Furini & Domene, 2018; Gumbart, Khalili-Araghi, Sotomayor, & Roux, 2012; Ulmschneider et al., 2013). The net flux of ions generated along the protein pore allows the computation of the conductance and the direct comparison with experiment (Ulmschneider et al., 2013). Alternatively, rather than directly simulating ion conduction, a common method to study permeation is to determine the free energy of the conduction process using techniques such as umbrella sampling (Corry & Thomas, 2012; Li, Sun, Liu, & Gong, 2017; Mahdavi, Kuyucak, & Ye, 2015), from which the steps involved in ion conduction and rates of permeation can be inferred.

Figure 1 Theoretical models usually employed in dynamic simulations of ion permeation through ion channels.

Ion Channel Permeation and SelectivityClick to view larger

A. In Poisson-Nernst-Planck dynamics, the protein, lipid membrane, and water are represented by continuum dielectric materials with specific dielectric constants εi and the ions by a continuous charge distribution. B. In Brownian dynamics, only the ions are represented explicitly. C. All-atom molecular dynamics describe explicitly every atom of the system. The protein, lipids, water, cations, and anions are represented in red, orange, cyan, blue and green, respectively, in panels A, B, and C. D. Representation of a possible potential-energy profile for an ion-permeation pathway through the entire ion channel. The dynamics can be accelerated by applying an electric field, which pushes positive ions to travel in the direction of the field, overcoming the energy barriers.

Potassium Channels

As mentioned in the Introduction, K+ channels have to rapidly transport K+ ions while simultaneously being highly selective for K+ over Na+ in order to rapidly reset the membrane potential and maintain low resting potentials. The examination of unidirectional fluxes of ions through K+ channels led Hodgkin and Keynes to postulate a long, narrow pore holding two to three ions, which conducts in a knock-on mechanism (Hodgkin & Keynes, 1955). However, their data could not rule out the possibility of a vacancy mechanism in which vacancies, not just ions, also diffuse inside the filter. A highly conserved signature TXGYG sequence was found among all K+ selective channels (Heginbotham, Lu, Abramson, & MacKinnon, 1994). This lies in a section of the protein known to interact with a range of toxins, blockers, and permeating ions (MacKinnon & Miller, 1989; MacKinnon & Yellen, 1990). Mutations within this sequence could remove ion selectivity among monovalent ions (Heginbotham et al., 1994), suggesting that this sequence lines a key region of the pore.

Figure 2 Schematic representation of the structure of voltage-gated ion channels.

Ion Channel Permeation and SelectivityClick to view larger

A. Side view of an ion channel composed by a α subunit (red), which is responsible for ion conduction and is present in all the channels, and additional subunits, which regulate the function of the α subunit and are present only in certain classes of channels. The lipid membrane is represented in yellow. B. Top view of the α subunit formed by four domains (DI–DIV), which in turn are composed of six transmembrane helices (TM1–TM6). The TM5 and TM6 helices (light red) form the central pore of the channel along which the ions are transported. These helices are linked by a P-loop that contains the selectivity filter with a signature sequence represented by the letter X. The TM1–TM4 helices form the voltage-sensing domain (VSD) and are located in the external region of the channel. C. Side view of the expanded representation of the four domains, which are covalently bonded in Cav channels and eukaryotic Nav channels such that they are formed from one long protein chain but are non-covalently bonded in Kv channels and prokaryotic Nav channels.

More recently, a large number of atomic resolution structures of different K+ channels have been published (e.g., see Brohawn et al., 2012; Doyle et al., 1998; Jiang et al., 2003; Long et al., 2005; Long et al., 2007; Morais-Cabral et al., 2001; Zhou et al., 2001) showing that common principles underlie ion permeation and selectivity in this diverse class of proteins. Indeed, all eukaryotic and prokaryotic Kv, Nav, and Cav channels share a similar architecture, schematically displayed in Figure 2. The structural region in charge of ion permeation is formed by four domains (DI–DIV) symmetrically arranged around the central pore, which are covalently bonded forming a single peptide chain in Cav channels and eukaryotic Nav channels, but is composed of four separate protein chains in Kv channels and in prokaryotic Nav channels (Grizel, Glukhov, & Sokolova, 2014). In addition to the α subunit, Kv channels also present β and other auxiliary subunits, which regulate the function of the α subunit. Usually, the four domains of the α subunit are identical in Kv channels, although some channels present two or more non-identical domains. Each domain contains six transmembrane helices (TM1–TM6), the first four of which form the voltage-sensing domain, while the pore domain is formed by an outer helix (TM5) and an inner pore lining helix (TM6) joined by a re-entrant P-loop that contains the signature sequence and forms a narrow selectivity filter. Analysis of the crystal structures suggested four ion binding sites within the filter, commonly labelled S1–S4, as well as an external site (S0) and a site within the central cavity (S5) (Morais-Cabral et al., 2001), as seen in Figure 3A. In addition, ions would most commonly occupy either sites S1 and S3 or S2 and S4 separated by water molecules, with conduction requiring the entrance of a third ion to generate a knock-on mechanism (Morais-Cabral et al., 2001) in line with the early suggestions of Hodgkin and Keynes (Hodgkin & Keynes, 1955). This was further supported by a range of BD simulations that indirectly examined the most likely conduction to suggest that two ions typically occupy the pore with an intervening water molecule, with the entry of a third ion required to generate knock-on conduction of ions and water (Aqvist & Luzhkov, 2000; Berneche & Roux, 2001, 2003; Chung, Allen, Hoyles, & Kuyucak, 1999; Chung, Allen, & Kuyucak, 2002). Improving computer power has since allowed MD simulations to be run for long enough to witness large numbers of permeation events. These also supported the idea that ions and water would move through the selectivity filter together with the most likely conduction process shown in Figure 3B (Jensen et al., 2010; Jensen et al., 2012; Jensen, Jogini, Eastwood, & Shaw, 2013; Khalili-Araghi, Tajkhorshid, & Schulten, 2006).

However, other simulation studies have suggested different permeation routes that may either coexist with the traditional steps or replace them altogether (Furini & Domene, 2009; Kopfer et al., 2014). In particular, it has been suggested that ions may pass through the selectivity filter in direct contact with each other, without intervening water molecules, as shown in Figure 3C. In this mechanism, three to four ions populate the selectivity filter simultaneously. While it seems unusual for ions to completely dehydrate and be found so close to one another and for vacancies to appear in the filter, the attraction between the carbonyl oxygen atoms and the ions is suggested to be able to stabilize this configuration. Furthermore, the large electrostatic interactions between the ions mean that thermal fluctuations in ion positions maximize the conduction rate. It is suggested that this so-called direct Coulomb knock-on mechanism yields much more rapid conduction than does the traditional alternating-site model (Kopfer et al., 2014).

Figure 3 Permeation mechanism of K+ ions through a K+ channel.

Ion Channel Permeation and SelectivityClick to view larger

A. Structure of the pore of the KcsA channel with half of the pore removed for clarity. Zoom-in view of the selectivity filter with the TVGYG sequence and six binding sites. The hydrogen atoms are not shown. B. Traditional knock-on mechanism in which alternating K+ ions and water molecules permeate through the selectivity filter. C. Direct Coulomb knock-on mechanism in which only K+ ions and vacancies are able to travel along the selectivity filter. The black arrow in B and C indicates the direction of ion motion (efflux transport). C, N, and O atoms are displayed in cyan, blue, and red, respectively. K+ ions inside the filter are shown in different shades of blue, and the O and H atoms of water in different shades of red and in gray, respectively.

The new model does, however, conflict with a large amount of experimental data. Flux-ratios suggest only two to three ions in the pore (Hodgkin & Keynes, 1955). The X-ray structures posit alternating ions and water (Doyle et al., 1998; Morais-Cabral et al., 2001), a point most clearly seen in anomalous scattering data in which K+ was replaced by Tl+. But it is worth noting that the occupancies seen in these structures cannot be completely accounted for by simple alternating occupancy; for example, the occupancies in S1 and S3 are not exactly equal, nor are those in S2 and S4 (Furini & Domene, 2009; Zhou & MacKinnon, 2004; Zhou & MacKinnon, 2003). A recent re-refinement of the Tl+ scattering data was found to be consistent with close contacts between permeating ions (Kopfer et al., 2014). However, water has been found to pass through K+ channels in the absence of K+ (Hoomann, Jahnke, Horner, Keller, & Pohl, 2013), and streaming potentials suggest at least that one water molecule passes for each K+ ion (Alcayaga, Cecchi, Alvarez, & Latorre, 1989; Ando, Kuno, Shimizu, Muramatsu, & Oiki, 2005; Iwamoto & Oiki, 2011), which is suggestive of alternating occupancy of ions and water in the pore. Recent ultrafast time-resolved infrared spectroscopy experiments were able to detect specific multi-ion configurations in the pore and also showed water to separate neighboring ions in the channels (Kratochvil et al., 2016). Proponents of the idea of K+ ions in direct contact, however, suggest that the experimental data from the infrared experiments can be interpreted to be consistent with either model, and that the streaming potential measurements are done in osmotic gradients that favor water permeation (Kopec et al., 2018; Kopfer et al., 2014).

Whether ions pass through the selectivity filter separated by water or not is a contentious issue that needs to be resolved. Specifically, one can ask why some simulations commonly see adjacent ions, but others do not. Is this a consequence of different force fields or simulation conditions? Can new experimental data shed unambiguous light on the issue? What is probably clear is that multiple permeation pathways exist, and it is a question of which is more common rather than which is correct.

In order to set the negative resting potential of cells and rapidly reset the resting potential after depolarization, K+ channels have to be extraordinarily selective, with about 100-fold preference for K+ over Na+. Tests with other monovalent ions show a selectivity sequence in competitions experiments of Tl+ > K+ > Rb+ > NH4+ » Cs+, Na+, Li+ (Blatz & Magleby, 1984; Block & Jones, 1996; Hagiwara & Takahashi, 1974; Heginbotham & MacKinnon, 1993; Hille, 1973; LeMasurier et al., 2001; Park, 1994; Reuter & Stevens, 1980; Yellen, 1984). Ba2+, which is a similar size to K+, can enter K+ channels and block K+ currents (Armstrong & Taylor, 1980; Neyton & Miller, 1988). As the ability of K+ channels to select between K+ and Na+ is the most physiologically important feature, we focus on this here.

The selectivity filter of K+ channels is narrow, so ions must largely dehydrate if they are to enter from bulk. Alkali cations hold their hydrating water very tightly, with smaller ions having a stronger hydration free energy than larger ions. For example, the hydration free energy of Na+ is about –88 kcal/mol, compared to –70 kcal/mol for K+ (Marcus, 1994; Schmid, Miah, & Sapunov, 2000). Thus, the energetic cost (dehydration penalty) of Na+ losing its water and entering a narrow pore is greater than for K+. This helps us understand the reason why a narrow K+ channel selects for the larger K+ over Na+: a narrow pore has an intrinsic preference for K+ over Na+ (provided both can fit inside) (Song & Corry, 2009). However, for ions to rapidly move into the pore, the free energy penalty for dehydration has to be compensated for by a favorable attraction to the protein. Thus, the net selectivity of the pore relates to the balance between the repulsive (dehydration) and attractive (ion–protein) interaction for each ion.

Several possible explanations for K+ vs. Na+ selectivity were deduced from electrophysiological and electrochemical experiments prior to the publication of atomic-resolution structures. In his study of glass electrodes, Eisenman argued that ligands of differing field strength could selectively bind differently sized ions, and that this might be applicable to biological systems (Eisenman, 1962). That K+ over Na+ selection could be achieved simply by tuning the charge on the ligands (protein) was further supported by pioneering free-energy calculations from MD simulations that highlighted the key role that the electrostatic attraction between ions and their coordinating ligands plays in determining the selectivity of the cyclic antibiotic valinomycin (Aqvist, Alvarez, & Eisenman, 1992). Although this study noted that steric factors that influence the ability of ligands to pack around the ion (and presumably influence the number of ligands contacting the ion) also contribute to the selectivity of the host molecule, this effect has been given less importance than the field strength of the ligands in many discussions of K+ channels. An alternative was the so-called snug-fit model that pictured a pore that could neatly pack around the larger K+ ion, but could not adequately coordinate the smaller Na+ as required to replace the coordinating water molecules (Bezanilla & Armstrong, 1972).

The publication of the first K+ channel structure was thought to support the concept of the snug-fit model, as the backbone carbonyls were seen to form cavities that beautifully coordinated permeating K+ ions, but would be too large for Na+ (Doyle et al., 1998). However, it has since been shown that the inherent flexibility of the protein makes this explanation for selectivity unlikely. In the absence of K+, for example, the selectivity filter is seen to shrink to a much narrower conformation (Zhou et al., 2001), while even the thermal parameters in the K+-bound structure suggest significant atomic vibrations (Noskov, Berneche, & Roux, 2004). Simulations of the binding sites in the K+ channel filter also showed that the protein could retain selectivity even in toy models of the selectivity filter in which the carbonyl ligands were completely free to move so that there was no rigid cavity present (Noskov et al., 2004; Thomas, Jayatilaka, & Corry, 2007). Numerous alternative proposals have thus been put forward. The dipole moment of the carbonyl ligands could intrinsically yield selectivity, in line with Eisenman’s proposal (Noskov et al., 2004). Angstrom-level constraints on the position of the carbonyl atoms can also restrict the number of ligands coordinating the permeating ions, and the presence of eight ligands around each binding site was shown to play an important role in defining selectivity (Bostick, Arora, & Brooks, 2009; Bostick & Brooks, 2007; Thomas et al., 2007; Thomas, Jayatilaka, & Corry, 2011, 2013; Varma & Rempe, 2007). Another possible explanation relates to the concept of strain energy—even if the protein is flexible enough to deform to accommodate Na+, this may come at an energetic cost for the protein (Yu, Noskov, & Roux, 2010). The snug-fit and liquid-like models of selectivity can therefore be seen as opposite ends of a spectrum. If the binding site is very stiff, then selection arises from a snug-fit mechanism. If the site is completely flexible, then the number and dipole moment of the ligands will dictate selectivity. In between these, a combination of factors, including internal strain on the protein, can act together. Thus, in reality, selectivity probably involves contributions from all these factors.

The mechanisms discussed so far revolve around the thermodynamics of ion binding in the selectivity filter—that is, the relative depth of the energy minima for K+ and Na+ in a binding site. But several more recent studies suggest that selectivity may be related to kinetic effects—the different rates to move into or between sites (Liu & Lockless, 2013; Sauer, Zeng, Canty, Lam, & Jiang, 2013; Thompson et al., 2009). Computational and experimental studies have shown that while the cage sites between the planes of carbonyl oxygens selectively bind K+ as discussed previously, Na+ can bind in the plane of carbonyl oxygens—a position that favors Na+ over K+ (Thompson et al., 2009). Therefore, it is dangerous to examine individual sites on their own when explaining selectivity. The implication of this is that Na+ may be able to bind in the selectivity filter, but it has difficulty moving through the pore because of large barriers faced when moving Na+ in a filter that also holds K+ (Egwolf & Roux, 2010; Nimigean & Allen, 2011; Thompson et al., 2009). Recently, it has been shown using mutations in the non-selective NaK channel selectivity filter that the presence of multiple ion binding sites is essential for selectivity. The NaK channel and the so-called NaK2CNG channel have only three ion binding sites in the selectivity filter and are non-selective for K+ over Na+. The NaK2K mutant, however, recovers the fourth ion binding site and has a strong equilibrium preference for K+, suggesting that the multi-ion nature of ion permeation is essential for selectivity (Derebe et al., 2011; Sauer et al., 2013). To reinforce the kinetic aspects of selectivity, it is seen that at equilibrium, the selectivity filter selectively binds K+ even in the non-selective channels, suggesting that the selectivity of permeation cannot simply be derived from equilibrium properties (Liu & Lockless, 2013; Sauer, Zeng, Raghunathan, & Jiang, 2011). However, recently an alternative thermodynamic interpretation has been provided for this data. If ions move through the filter completely dehydrated instead of being separated by water molecules (as suggested by the model in which ions permeate in direct contact with one another), then the selectivity is enhanced by maximizing the dehydration energy difference of Na+ and K+ (Kopec et al., 2018). Thus, the presence of multiple ion binding sites may simply be required to enforce complete dehydration. This agrees with earlier thermodynamics studies that showed that the presence of a water molecule surrounding one of the binding sites significantly reduces its selectivity (Alam & Jiang, 2009; Fowler, Tai, & Sansom, 2008; Noskov & Roux, 2007; Thomas et al., 2011). While it is fair to say that the principles underlying K+ channel selectivity are understood, a simple, intuitively clear explanation is lacking—perhaps because it is a complex physical process that cannot be explained by a single principle alone.

Sodium Channels

Nav channels are responsible for the transport of Na+ ions in excitable cells from the high-Na+ concentration extracellular region to the low-Na+ concentration cytosol (Hille, 2001). The opening of the channel and subsequent transport of Na+ ions through the protein are induced by the depolarization of the cell membrane. The inward current of ions induces further depolarization, generating an action potential that travels along excitable cells and cell networks (Marban, Yamagishi, & Tomaselli, 1998). The mechanistic knowledge of ion permeation in Nav channels is not so extensive as that in Kv channels, due to the delay in resolving the structure of Nav channels with atomic resolution. Specifically, the first crystalized structure, captured in a closed-pore conformation, was reported only in 2011 (Payandeh, Scheuer, Zheng, & Catterall, 2011) from Arcobacter butzleri (NavAb) with cysteine mutations in the TM6 helices. Since then, a few additional full or pore-only bacterial channel structures have been reported in different gating states (Bagnéris et al., 2013; Lenaeus et al., 2017; McCusker et al., 2012; Payandeh et al., 2012; Shaya et al., 2014; Sula et al., 2017; Zhang et al., 2012). In addition, the structures of eukaryotic Nav channels from American cockroach (designated NavPaS) (Shen et al., 2017), electric eel (EeNav1.4) (Yan et al., 2017), and humans (Nav1.4) (Pan et al., 2018) have been obtained by cryo-electron spectroscopy very recently.

The structure of bacterial Nav channels presents features similar to those of Kv channels. They are composed of a large pore-forming α subunit and smaller auxiliary β subunits (Catterall & Swanson, 2015), as represented in Figure 1. The α subunit, responsible for voltage-gated ion permeation, contains four identical domains (DI–DIV), which are not covalently bonded. As for Kv channels, each domain is formed by six transmembrane segments (TM1–TM6), four of which (TM1–TM4) comprise the voltage sensor domain that regulates the channel gating. The other two segments of each domain (TM5–TM6) compose the pore region of the protein. The entrance of ions into the pore domain is regulated by the selectivity filter located in a long P-loop that connects TM5 and TM6. The most common sequence found in the selectivity filter of bacterial Na+ channels is composed of the TLESWS residues (see Figure 4A). Contrary to prokaryotic Na+ channels, the α subunit of eukaryotic Na+ channels is formed by four different domains that are covalently linked; i.e., the channel is formed by a single peptide chain. However, the most important structural difference affecting ion conduction is found in the selectivity filter. While the strongest binding site in the selectivity filter of bacterial Nav channels is formed by one glutamate (E) from each of the four domains, which compose the so-called EEEE ring, the equivalent binding site is formed by the DEKA ring (aspartate [D], glutamate [E], lysine [K], and alanine [A]) in eukaryotic Nav channels (Favre, Moczydlowski, & Schild, 1996). As explained later, both the EEEE and DEKA motifs play a crucial role in the process of ion conduction and selectivity.

Structural data suggested the existence of three binding sites in the selectivity filter of the NavAb channel (Payandeh et al., 2011) composed of the TLESWS sequence (see Figure 4A): the high-field-strength anionic site (SHFS) formed by the side chains of glutamate residues of the EEEE ring, and two sites located deeper in the filter and formed by the backbone carbonyls of leucine (site SCEN) and threonine (site SIN), respectively. Free-energy profiles computed by umbrella-sampling classical MD simulations (Corry & Thomas, 2012) and metadynamics and voltage-biased MD simulations (Stock, Delemotte, Carnevale, Treptow, & Klein, 2013) corroborated the existence of the three binding sites in NavAb. However, additional umbrella-sampling simulations on the same system found free-energy minima only at the SHFS and SCEN sites (Furini & Domene, 2012), while equilibrium classical MD simulations found significant population of Na+ only at SHFS and SIN, while the SCEN site was mainly occupied by water molecules (Carnevale, Treptow, & Klein, 2011). Voltage-biased MD simulations on the prokaryotic channel of Magnetococcus marinus (NavMs) (Ulmschneider et al., 2013) predicted five binding sites in the selectivity filter, which were termed S0, S1, S2, S3, and S4 in analogy to the binding sites of K+ channels. S1, S3, and S4 corresponded to the already established SHFS, SCEN, and SIN sites for NavAb, respectively, while S0 and S5 were identified as new sites located at the vestibule of the selectivity filter, and slightly below SHFS, respectively. However, these two additional ion sites were not found in an experimental study (Naylor et al., 2016), where only SHFS, SCEN, and SIN were clearly identified as ion binding sites. A fourth peak of density was also found between the SCEN and SIN sites, but it was interpreted as a water binding site (Naylor et al., 2016). Contrary to NavAb and NavMs, whose selectivity filter sequence is TLESWS, only two Na+ binding sites were identified in the selectivity filter TLSSWE of the marine alphaproteobacterium HIMB114 (NavRh) by classical MD simulations (Zhang et al., 2013). Although contradictory results were reported for the same prokaryotic Nav channels, and several channels present different selectivity filter sequences, in general, one can conclude that Na+ channels present a smaller number of ion binding sites in the selectivity filter than K+ channels do.

The mechanism of ion permeation throughout Na+ channels significantly differs from the mechanism in K+ channels due to the different size of the selectivity filter. In particular, the selectivity filter of Nav channels is shorter and wider, a fact that was surprising considering that Na+ ions are smaller than K+ ones and therefore should be able to permeate through narrower filters. That the pore is wide enough to accommodate both K+ and Na+ eliminates the possibility of a snug-fit model to explain Na+ selectivity. Two important differences in the ion conduction mechanism between Nav and Kv channels due to the different pore sizes were highlighted by classical MD simulations on the NavAb channel: (i) Na+ ions were found to be always hydrated to some extent along the permeation pathway, and (ii) Na+ ions can be located next to each other in the selectivity filter, contrary to the single-file configuration of K+ ions in Kv channels (Corry & Thomas, 2012; Furini & Domene, 2012). Another theoretical study on the open-pore NavMs channel found that water flux may not be correlated with ion flux in Nav channels since the average dwell time of water molecules in the channel was found to be two orders of magnitude lower than that of Na+ ions (Ulmschneider et al., 2013). However, this contradicted the results of previous classical MD simulations for the NavAb channel in a closed conformation (Carnevale et al., 2011), which predicted a larger dwell time in the channel for the ions than for the water. However, these apparently contradictory results for two channels that present the same sequence in the selectivity filter (TLESWS) could be a consequence of having different gating states in the investigated channels (an open structure for NavMs and a closed one for NavAb).

An important feature of ion conduction that was evidenced by MD (Boiteux, Vorobyov, & Allen, 2014; Carnevale et al., 2011; Corry & Thomas, 2012; Furini & Domene, 2012; Stock et al., 2013; Ulmschneider et al., 2013) and BD simulations (Vora, Corry, & Chung, 2005; Vora et al., 2008) is that ion transport in Nav occurs through a multi-ion mechanism, in which the selectivity filter is populated by more than one ion at any time. The following multi-ion permeation mechanism, displayed in Figure 4B, through the selectivity filter of NavAb was proposed based on umbrella-sampling MD simulations (Corry & Thomas, 2012): (i) A first ion enters the pore and binds to the SHFS site; (ii) a second ion is attracted close to the position of the first one; (iii) the first ion is able to permeate to the inner positions SCEN and SIN while the second ion moves to SHFS; and (iv) the inner ion can permeate to the central cavity of the channel. Along the whole permeation pathway, Na+ ions move through the channel with their first solvation shell almost complete. The comparison of the free-energy profiles for one-ion and two-ion pathways suggested that the conduction of an ion along the filter is favored by the presence of a second ion. However, the relatively low-energy barriers obtained along the single-ion permeation mechanism suggest that transport of individual ions can also take place. The motion of Na+ ions in the multi-ion mechanism was found to be less correlated than the motion of K+ ions through Kv channels; therefore, the Na+ permeation mechanism through NavAb was termed “loosely coupled knock-on conduction.” A contrary, strong knock-on mechanism, shown in Figure 4C, involving the participation of three ions in the selectivity filter of NavAb, was shown by unbiased classical MD simulations (Boiteux et al., 2014). These simulations also predicted the presence of a three-ion pass-way mechanism, where two ions coexist at the EEEE ring before pushing a third ion into the cavity of the protein. All these different results reported for the same ion channel indicate that it is very likely that multiple permeation pathways are operative in the transport of Na+, and that a simplified picture describing the process is difficult to draw.

Figure 4 Permeation mechanism of Na+ ions through a Na+ channel.

Ion Channel Permeation and SelectivityClick to view larger

A. Structure of the pore of the NavAb channel with half of the pore removed for clarity. Zoom-in view of the selectivity filter with the TLE sequence involved in the three binding sites. The hydrogen atoms and side chain of leucine are not shown. B. Loosely coupled knock-on mechanism in which two solvated Na+ ions permeate through the selectivity filter. C. Strong knock-on mechanism in which three solvated Na+ ions permeate. The black arrow in B and C indicates the direction of ion motion (influx transport). C, N, and O atoms are displayed in cyan, blue, and red, respectively. Na+ ions inside the filter are shown in different shades of blue, and the O and H atoms of water in light red and in gray, respectively.

Two quite relevant steps in Na+ conduction, independent of the permeation mechanism, are the attraction of the Na+ ions from the extracellular media to the SHFS site, composed of the EEEE ring, and the subsequent permeation from SHFS to the inner binding sites. The second process involves overcoming a free-energy barrier, which was found to be ≥2 kcal/mol larger for K+ and Ca2+ than for Na+ (Corry, 2013; Corry & Thomas, 2012; Furini & Domene, 2012), explaining the preference of NavAb for Na+ over K+. At the transition point, the solvated ions are located into the plane formed by the four glutamates and, therefore, the available space is limited. Due to its smaller size, the Na+ ion and its solvating water molecules fit better than the solvated K+ ion into the EEEE plane. As a consequence, the water molecules solvating Na+ can adopt an ideal configuration where the intermolecular interactions are more favorable than in the case of solvated K+ (Corry & Thomas, 2012). Whole-cell patch clamping measurements have also shown that the EEEE ring is crucially involved in ion permeability and selectivity of the NavMs channel (Naylor et al., 2016). When the selectivity filter of the channel was mutated from TLESWS to TLDSWS—i.e., the glutamates of the EEEE ring were replaced by aspartates—no electronic density was found at the SHFS binding site of the crystal structure. This means that the ion binding site disappeared upon mutation. As a consequence, the mutant channel presented a lower current density and selectivity for Na+ than the wild-type channel. The protonation state of the glutamate residues of the EEEE ring is also important for the ion transport mechanism. Umbrella-sampling MD simulations have shown that the side chains of protonated glutamate residues are preferentially oriented towards the protein cavity when compared to unprotonated residues (Furini, Barbini, & Domene, 2014). This induces an increase of the energy barrier for Na+ translocation and therefore reduces ion conduction. Despite the importance of the SHFS site in the transport of Na+, additional mutations at different sites of the selectivity filter also strongly affect permeation and selectivity (Shaya et al., 2011; Yue et al., 2002). This result points towards a complex permeation mechanism in which several regions of the selectivity filter are involved.

The conduction mechanism in eukaryotic Nav channels is much less understood than that in bacterial Nav channels due to the lack of atomistic structures, which precluded the performance of theoretical simulations up to now. Although a clear mechanistic picture has not emerged yet, several factors are believed to contribute to Na+ selectivity, including the coordination number of the ion and its partial solvation/desolvation, the electron-donating ability of the residues of the protein pore, and the rigidity and size of the selectivity filter (Dudev & Lim, 2014). The lysine residue present in the DEKA motif is known to be indispensable in Na+ discrimination. Mutation of the lysine residue in the selectivity filter to another amino acid largely eliminates selectivity for Na+ ions (Favre et al., 1996; Schlief, Schönherr, Imoto, & Heinemann, 1996; Sun, Favre, Schild, & Moczydlowski, 1997), even when the charge of the filter is preserved. Indeed, not only the presence of lysine is relevant for the conduction mechanism, but also its position in the DEKA ring. Swopping the glutamate and lysine residues from the wild-type DEKA motif to DKEA reduced the Na+:K+ permeability ratio by a factor of three (Schlief et al., 1996). This behavior was explained based on quantum-mechanical calculations on simplified models of the DEKA and DKEA motifs (Dudev & Lim, 2014). The interactions between lysine and the other residues in the DEKA ring are stronger than those in the DKEA ring. Therefore, the DEKA configuration makes the pore narrower and more rigid, favoring the permeation of the smaller ion.

Since the selectivity filter of mammalian Nav channels presents certain similarities with the bacterial NavRh channel, a mutant version of the latter has been employed in classical MD simulations to get insight into the conduction mechanisms in eukaryotic channels (Xia, Liu, Li, Yan, & Gong, 2013). Specifically, the first ring of serine residues located at the selectivity filter (TLSSWE) was mutated to DEKA in order to mimic the selectivity filter of mammalian Nav channels. Three ion binding sites were identified along the simulations, suggesting that a multi-ion mechanism seems to also be operative in eukaryotic channels. Recent voltage-biased MD simulations, where the pore of the DEKA-mutated NavRh channel was opened by alignment with the open-conformation of the bacterial NavMs channel, investigated the ion permeation mechanism through the full protein (Li et al., 2017). It was found that the multiple ions that can populate the selectivity filter are able to permeate from the filter to the central cavity of the protein through a knock-on mechanism. It was speculated that the coupled ion motion is induced by the presence of the DEKA motif, since ions permeated independently in a non-coupled manner through the wild-type NavRh channel. The first theoretical study employing a real structure from a eukaryotic channel (NavPaS) was reported only recently (Zhang et al., 2018). Unbiased classical MD simulations showed that Na+ ions permeate below the DEKA ring of the selectivity filter partially hydrated and in an asymmetrical manner, strongly interacting with the negatively charged aspartate and glutamate residues of the DEKA motif. In contrast, K+ ions were not able to permeate below the DEKA ring along 300 ns simulations. Despite the relevant mechanistic details obtained from these simulations, the complete absence of K+ ions, together with the small number of Na+ ions, inside the selectivity filter during the unbiased simulations might indicate that the results are not fully converged. Thus, better sampling could be needed to obtain more reliable conclusions. The availability of the recently crystalized NavPaS (Shen et al., 2017), EeNav1.4 (Yan et al., 2017), and Nav1.4 (Pan et al., 2018) eukaryotic channels will encourage further theoretical studies in the coming years, which will provide significant insight into the mechanism of ion conduction through eukaryotic Nav channels.

Calcium Channels

Cav channels are one of the main ways that electrical signals are turned into responses in cells. They are extremely discriminating in terms of the ions that they let pass, selecting Ca2+ over Na+ at a ratio of over 1000:1 (Hess, Lansman, & Tsien, 1986). This degree of selectivity is all the more remarkable given that Na+ is usually many orders of magnitude more numerous than Ca2+ in physiological conditions. Ca2+ channels must rely on more than just the size of passing ions to discriminate between them, as Na+ and Ca2+ have very similar diameters. Our understanding of ion permeation and selectivity in these channels is that they are intimately linked, as the blocking of one ion species by another has been the prime datum for explaining both properties.

Cav channels can be classified according to the degree of membrane depolarization needed to activate them as high-voltage activated channels and low-voltage activated channels. The former ones are protein complexes composed by a pore-forming α1 subunit in addition to ancillary β, α2δ, and γ subunits (see Figure 1). Low-voltage activated channels lack the ancillary subunits and possess only the pore region (Catterall, Perez-Reyes, Snutch, & Striessnig, 2005; Simms & Zamponi, 2014). As in Na+ and K+ channels, the α1 subunit includes the pore, the voltage sensor, and the gating apparatus of the protein. It comprises four homologous domains composed of six transmembrane fragments (TM1–TM6) covalently linked in a single chain. The selectivity filter is also found in the pore loop between segments TM5 and TM6.

Surprisingly, monovalent ions such as Na+ conduct through these channels at higher rates than divalent ions when no divalent ions are present (Almers, Mccleskey, & Palade, 1984; Fukushima & Hagiwara, 1985; Hess et al., 1986; Kostyuk, Mironov, & Shuba, 1983; Kuo & Hess, 1993b). However, such monovalent currents are blocked when the Ca2+ concentration reaches only 1 μM (Almers et al., 1984; Kostyuk et al., 1983). The ability for some ions to block others provides evidence for the high-affinity binding of ions to the pore—the ions that bind most strongly would block the passage of other ions. Thus, working out which ions block other ions suggests which ions are able to most strongly bind to the pore. A range of experiments suggested that the affinity for the pore follows the following sequence: La3+ > Cd2+ > Co2+ > Ca2+ > Sr2+ > Ba2+ > Li+ > Na+ > K+ > Cs+ (Fenwick, Marty, & Neher, 1982; Hess et al., 1986; Lee & Tsien, 1984; Reuter & Scholz, 1977; Taylor, 1988). However, there are some exceptions to this trend. For example, Na+ ions can attenuate Ca2+ currents in some cases. This can be explained by competition for entry to the pore—i.e., kinetic effects—rather than occupancy of the high-affinity binding site (Corry, Allen, Kuyucak, & Chung, 2001; Polo-Parada & Korn, 1997). Single-channel conductance measurements follow the exact opposite order to that for blocking: La3+ < Cd2+ < Co2+ < Ca2+ < Sr2+ < Ba2+ < Li+ < Na+ < K+ < Cs+ (Hess et al., 1986; Kuo & Hess, 1993a, 1993b). This has been explained by the “sticky pore” hypothesis, in which the ions with the highest affinity pass through the pore more slowly, yielding a lower conductance (Bezanilla & Armstrong, 1972).

A consequence of the sticky pore model is that permeation through Ca2+ channels must be a multi-ion process. If the channel binds ions strongly, then it would be hard to generate pico-ampere currents measured with a single-ion pore (Bezanilla & Armstrong, 1972). Furthermore, a number of other strands of evidence support multi-ion permeation. In many cases when two permeating species are mixed, the current through the pore is smaller than for either ion on its own. This so-called anomalous mole fraction effect is seen clearly in mixtures of Ca2+/Ba2+ and Ca2+/Na+ (Almers et al., 1984; Hess & Tsien, 1984). It is most easily explained if the pore holds multiple ions, as in a single-ion pore the current should always lie between the currents found with each ion type on its own. In a multi-ion pore, unfavorable interactions between the ions can slow permeation (although it is not possible to completely exclude a single-ion pore if it undergoes some kind of conformational alteration during permeation). Blockage experiments also support a multi-ion pore. Ca2+ blocks Na+ currents with an affinity of ~1 μM, but Ca2+ currents saturate with an affinity of 14 mM. This can be explained if the first affinity represents binding of Ca2+ to an empty pore or a pore holding Na+, but the second affinity represents a second Ca2+ binding to a pore already holding one divalent ion.

Site-directed mutagenesis showed that four glutamate residues—one from each P loop of the channel—were responsible for generating the high-affinity Ca2+ binding site. Removing any one of these reduces the affinity for Ca2+ as well as the conductance and specificity for Ca2+ (Ellinor, Yang, Sather, Zhang, & Tsien, 1995; Kim, Morii, Sun, Imoto, & Mori, 1993; Parent & Gopalakrishnan, 1995; Yang, Ellinor, Sather, Zhang, & Tsien, 1993). As there was no evidence for any other high-affinity binding site, this so-called EEEE locus has been presumed to be the sole cause of high-affinity binding and selectivity, as it is the case in bacterial Na+ channels. However, reconciling how multi-ion conduction can occur with only a single high-affinity biding site has been a lasting challenge.

The nature of the permeation process makes more sense in the light of recent structural data on Cav channels. The first of these structures made use of the similarity (and probable evolutionary connection) of Ca2+ channels to Na+ channels, noting that Ca+2 selectivity can be inferred on a Na+ channel and vice versa, with only a few point mutations (Heinemann, Terlau, Stuhmer, Imoto, & Numa, 1992; Yue et al., 2002). Conferring Ca2+ selectivity upon the bacterial Na+ channel NavAb by mutating its selectivity filter from TLESWSM to TLDDWSD (to generate the CavAb channel) showed a selectivity filter with three potential ion binding sites (Tang et al., 2014), as shown in Figure 5 (note that this channel has a DDDD locus rather than EEEE). The site 1 at the entrance of the pore is formed by the carboxyl groups of the ring formed by four aspartate residues. Deeper in the pore, the acidic side chains of another aspartate ring and the carbonyl oxygen atoms of leucine residues form the site 2. Finally, the carbonyls from four threonines form the site 3. It is suggested that Ca2+ ions pass through the pore in a knock-off mechanism (see Figure 5A) in which the pore cycles between a state with one hydrated Ca2+ in the central site and a state with two hydrated ions at the distal sites—similar to the model seen in early BD studies (Corry et al., 2001). This mechanism reconciles the apparently contradictory data that multiple ions are required for rapid permeation, but only a single high-affinity site exits, as only the central site has sufficient affinity to block monovalent currents. A knock-off mechanism was also predicted by classical MD simulations for the TRPV6 channel, but the pore showed a larger ion occupancy cycling between two-ion and three-ion states (Sakipov, Sobolevsky, & Kurnikova, 2018). Thus, it is very likely that several permeation mechanisms simultaneously operate, as in the case of Na+ and K+ channels.

Figure 5 Permeation and selectivity mechanisms of Ca2+ ions through an artificial Ca2+ channel (CavAb).

Ion Channel Permeation and SelectivityClick to view larger

A. Selectivity filter of the CavAb channel with the TLDD sequence involved in the three binding sites. The hydrogen atoms and side chain of leucine are not shown. Ion permeations follow a knock-off mechanism where repulsion between adjacent ions accelerates ion conduction. The black arrow indicates the direction of ion motion (influx transport). C, N, and O atoms are displayed in cyan, blue, and red, respectively. Ca2+ ions inside the filter are shown in different shades of blue, and the O and H atoms of water in light red and in gray, respectively. B. Schematic representation of conduction events inside a Cav channel when different ions are present. Ca+2 and Na+ ions are displayed in blue and green, respectively.

Eukaryotic Ca2+ channels are made from a single protein chain containing four homologous repeats that surround the pore. The structures of Cav1.1 show that this can yield an asymmetrical selectivity filter in which ions bind off-axis (Wu et al., 2016; Wu et al., 2015). While the structure of the selectivity filter is not as well defined in these as for CavAb, it suggests at least two sites at which hydrated Ca2+ can bind. It is not clear if this supports the knock-off mechanism, but as for CavAb, only one of the two sites is likely to yield high-affinity binding. It is important to note that the selectivity filters of CavAb and Cav1.1 are different. For example, it is remarkable that the EEEE locus is missing in CavAb and, therefore, the permeation and selectivity mechanisms between these two channels might significantly differ.

The multi-ion nature of permeation has been modeled using a number of different approaches. Rate-theory models showed that a pore holding two binding sites can utilize repulsion between the ions to generate high throughput as well as specificity (Almers et al., 1984; Armstrong & Neyton, 1991; Hess & Tsien, 1984; Kuo & Hess, 1993b; Yang et al., 1993). But these models have difficulty in defining the physical causes of the binding sites themselves (Corry & Hool, 2007). BD simulations showed how multiple ions can compete to occupy the channel to create rapid transport and selectivity, in a set of studies that closely predicted the inferences from the structural studies (Corry et al., 2001; Corry & Chung, 2006; Corry, Vora, & Chung, 2005). In these, the pore is seen to always hold at least one Ca2+ ion that is attracted with high affinity to the ring of glutamate residues. The resident ion can only be displaced by the entrance of another Ca2+ ion, with the electrostatic repulsion between the two ions being sufficient to overcome the attraction of the first ion to the protein, as is represented in Figure 5B. In contrast, permeation in pure Na+ solution is seen to involve three ions. Selectivity can be simply explained in electrostatic terms, as once Ca2+ occupies the pore it can only be replaced by another Ca2+ ion, as the repulsion from an incoming Na+ is insufficient to eject the resident ion due to the strong attraction of the divalent ion to the negatively charged protein.

An alternative mechanism for generating selectivity was proposed from studies using continuum-based theories that suggested that ions compete to achieve charge neutrality with the protein inside a selectivity filter having limited space (Boda, Busath, Henderson, & Sokolowski, 2000; Nonner, Catacuzzeno, & Eisenberg, 2000). Divalent ions are suggested to easily neutralize the protein while occupying little volume, but not enough Na+ ions can fit into the filter to achieve neutrality. While conceptually appealing and able to explain selection among a range of different ion types (Gillespie, 2008; Gillespie, Xu, Wang, & Meissner, 2005), this model requires specific restraints on the filter volume that do not seem to correspond to the larger filters seen in the structural studies that can hold multiple hydrated ions. The determination of a high-resolution structure of the selectivity filter of a Cav channel may elucidate allow the specific reasons for Ca2+/Na+ selection.

Summary

Voltage-gated ion channels are involved in many relevant biological processes of prokaryotic and eukaryotic cells. Despite their indisputable biological relevance, the mechanisms by which ion channels are able to transport ions in a selective way across cell membranes are not yet completely understood. Electrophysiological measurements and the analysis of crystalized and cryo-electron microscopy structures have provided significant knowledge. However, current experimental techniques are not able to access many microscopic mechanistic details of ion permeation and the origins of selectivity and can be difficult to interpret. For example, it was inferred based on early structural information that K+ selectivity in Kv channels arises through a snug-fit mechanism, which appears incorrect in the light of further structures and dynamics simulations. In recent decades, a vast number of theoretical studies based on dynamics simulations has investigated the mechanism of ion transport through ion channels. Dynamics simulations are able to provide a time-dependent picture and great microscopic mechanistic insight. However, simulations should be interpreted carefully and validated against experimental or higher-level theoretical data, because they can provide erroneous or contradictory results. This can be seen in cases in which simulations conducted by different groups have yielded different results, such as ions spaced by water or in direct contact in Kv channels, presumably due to small differences in the force fields and computational implementation. In addition, the most commonly used theoretical models are not able to properly describe some intermolecular interactions that are likely to play a fundamental role in ion conduction, such as polarization, exchange, and charge-transfer interactions.

We have summarized in this chapter the main mechanistic knowledge gained in the last decades in ion transport through Kv, Nav, and Cav channels. Ion permeation most likely occurs with multiple ions via multiple mechanisms in all these channels. Even in the tightly constrained single-file Kv selectivity filter, two permeation pathways probably coexist in which ions are either separated by water or in direct contact. Since Nav channels present a wider selectivity filter, their mechanisms of permeation are more diverse than for Kv channels. In Nav channels, ions permeate almost fully hydrated, and two ions can be located next to each other inside the filter. Conduction through bacterial Nav channels probably occurs via multiple mechanisms, including single-ion conduction, loosely coupled knock-on of two or three ions, or more strongly coupled motions of multiple ions. The conduction mechanism in eukaryotic Nav channels is less clear than that in bacteria due to there being few computational studies to make use of the recent eukaryotic structures. Cav channels also have a wider filter, although it is not clear if ions can bypass each other. Experimental and theoretical work on Cav channels points towards a multi-ion knock-off mechanism, in which the system cycles between a state with one hydrated Ca2+ bound to the central EEEE binding site and a state with two hydrated ions bound to two distal sites.

How these channels select between different ions is even more difficult to explain. Several reasons behind the selectivity of Kv channels have been suggested, but the common factor in these is that the channels make use of the fact that is easier to dehydrate K+ than Na+ as required to enter a narrow pore. However, how the channel is able to balance the dehydration barrier to allow rapid permeation of K+ but not Na+ is less clear. Thermodynamic explanations suggest preferential attraction to the filter due to the number and dipole moment of the ligands and the flexibility of the protein. Kinetic effects can also play an important role in selectivity since the energy barriers that K+ ions have to overcome when moving between binding sites are smaller than the energy barriers for other ions.

Na+ selectivity in bacterial Nav channels has both a thermodynamic and a kinetic origin. The binding of Na+ ions to the EEEE ring is more favorable than the binding of other ions, and the escape from the EEEE site to a different binding site inside the selectivity filter requires overcoming a smaller energy barrier for Na+ than for other ions. The reasons behind selectivity in eukaryotic Nav channels are also not clear yet, but it is thought that several factors may be crucial, including the ion solvation/desolvation energy, the coordination number of the ion, the existence of charge-transfer processes between the protein and the solvated ions, and the rigidity of the selectivity filter. In addition, conductivity measurements have clearly shown that the lysine residue of the DEKA ring is crucially involved in selectivity. However, its specific role is unknown.

Selectivity in Cav channels seems to be explained by the strong electrostatic interaction between Ca2+ and the selectivity filter. Once a Ca2+ ion is bound to the EEEE ring, only another Ca2+ ion is able to replace it, and the repulsion between the ions favors the permeation process. However, additional theories have emerged. For example, theoretical studies suggest that selectivity arises when ions with a large charge:volume ratio, like divalent ions, are able to neutralize the negative charge of the selectivity filter.

Despite the tremendous progress achieved in the knowledge of ion permeation and selectivity in ion channels, even the most widely studied example, K+ channels, has many unresolved questions. For example, how many ions are involved in a permeation event? What are the steps in permeation? What is the most important factor in deriving selectivity for K+? Theoretical simulations will certainly contribute to answering these questions. However, more accurate models, going beyond fixed-charges force fields, able to properly describe all types of interactions present in the system will be required.

Acknowledgements

We thank the Australian Research Council (Grant FT130100781) and the Australian National University for financial support.

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