A second S4 movement opens hyperpolarization-activated HCN channels.

Rhythmic activity in pacemaker cells, as in the sino-atrial node in the heart, depends on the activation of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels. As in depolarization-activated K+ channels, the fourth transmembrane segment S4 functions as the voltage sensor in hyperpolarization-activated HCN channels. But how the inward movement of S4 in HCN channels at hyperpolarized voltages couples to channel opening is not understood. Using voltage clamp fluorometry, we found here that S4 in HCN channels moves in two steps in response to hyperpolarizations and that the second S4 step correlates with gate opening. We found a mutation in sea urchin HCN channels that separate the two S4 steps in voltage dependence. The E356A mutation in S4 shifts the main S4 movement to positive voltages, but channel opening remains at negative voltages. In addition, E356A reveals a second S4 movement at negative voltages that correlates with gate opening. Cysteine accessibility and molecular models suggest that the second S4 movement opens up an intracellular crevice between S4 and S5 that would allow radial movement of the intracellular ends of S5 and S6 to open HCN channels.

Selectivity filter modalities and rapid inactivation of the hERG1 channel.

The human ether-á-go-go-related gene (hERG1) channel conducts small outward K+ currents that are critical for cardiomyocyte membrane repolarization. The gain-of-function mutation N629D at the outer mouth of the selectivity filter (SF) disrupts inactivation and K+-selective transport in hERG1, leading to arrhythmogenic phenotypes associated with long-QT syndrome. Here, we combined computational electrophysiology with Markov state model analysis to investigate how SF-level gating modalities control selective cation transport in wild-type (WT) and mutant (N629D) hERG1 variants. Starting from the recently reported cryogenic electron microscopy (cryo-EM) open-state channel structure, multiple microseconds-long molecular-dynamics (MD) trajectories were generated using different cation configurations at the filter, voltages, electrolyte concentrations, and force-field parameters. Most of the K+ permeation events observed in hERG1-WT simulations occurred at microsecond timescales, influenced by the spontaneous dehydration/rehydration dynamics at the filter. The SF region displayed conductive, constricted, occluded, and dilated states, in qualitative agreement with the well-documented flickering conductance of hERG1. In line with mutagenesis studies, these gating modalities resulted from dynamic interaction networks involving residues from the SF, outer-mouth vestibule, P-helices, and S5-P segments. We found that N629D mutation significantly stabilizes the SF in a state that is permeable to both K+ and Na+, which is reminiscent of the SF in the nonselective bacterial NaK channel. Increasing the external K+ concentration induced "WT-like" SF dynamics in N629D, in qualitative agreement with the recovery of flickering currents in experiments. Overall, our findings provide an understanding of the molecular mechanisms controlling selective transport in K+ channels with a nonconventional SF sequence.

The voltage-sensing domain of a hERG1 mutant is a cation-selective channel.

A cationic leak current known as an "omega current" may arise from mutations of the first charged residue in the S4 of the voltage sensor domains of sodium and potassium voltage-gated channels. The voltage-sensing domains (VSDs) in these mutated channels act as pores allowing nonspecific passage of cations, such as Li+, K+, Cs+, and guanidinium. Interestingly, no omega currents have been previously detected in the nonswapped voltage-gated potassium channels such as the human-ether-a-go-go-related (hERG1), hyperpolarization-activated cyclic nucleotide-gated, and ether-a-go-go channels. In this work, we discovered a novel omega current by mutating the first charged residue of the S4 of the hERG1, K525 to serine. To characterize this omega current, we used various probes, including the hERG1 pore domain blocker, dofetilide, to show that the omega current does not require cation flux via the canonical pore domain. In addition, the omega flux does not cross the conventional selectivity filter. We also show that the mutated channel (K525S hERG1) conducts guanidinium. These data are indicative of the formation of an omega current channel within the VSD. Using molecular dynamics simulations with replica-exchange umbrella sampling simulations of the wild-type hERG1 and the K525S hERG1, we explored the molecular underpinnings governing the cation flow in the VSD of the mutant. We also show that the wild-type hERG1 may form water crevices supported by the biophysical surface accessibility data. Overall, our multidisciplinary study demonstrates that the VSD of hERG1 may act as a cation-selective channel wherein a mutation of the first charged residue in the S4 generates an omega current. Our simulation uncovers the atomistic underpinning of this mechanism.

Identification of multiple substrate binding sites in SLC4 transporters in the outward-facing conformation: Insights into the transport mechanism.

Solute carrier family 4 (SLC4) transporters mediate the transmembrane transport of HCO3-, CO32-, and Cl- necessary for pH regulation, transepithelial H+/base transport, and ion homeostasis. Substrate transport with varying stoichiometry and specificity is achieved through an exchange mechanism and/or through coupling of the uptake of anionic substrates to typically co-transported Na+. Recently solved outward-facing structures of two SLC4 members (human anion exchanger 1 [hAE1] and human electrogenic sodium bicarbonate cotransporter 1 [hNBCe1]) with different transport modes (Cl-/HCO3- exchange versus Na+-CO32- symport) revealed highly conserved three-dimensional organization of their transmembrane domains. However, the exact location of the ion binding sites and their protein-ion coordination motifs are still unclear. In the present work, we combined site identification by ligand competitive saturation mapping and extensive molecular dynamics sampling with functional mutagenesis studies which led to the identification of two substrate binding sites (entry and central) in the outward-facing states of hAE1 and hNBCe1. Mutation of residues in the identified binding sites led to impaired transport in both proteins. We also showed that R730 in hAE1 is crucial for anion binding in both entry and central sites, whereas in hNBCe1, a Na+ acts as an anchor for CO32- binding to the central site. Additionally, protonation of the central acidic residues (E681 in hAE1 and D754 in hNBCe1) alters the ion dynamics in the permeation cavity and may contribute to the transport mode differences in SLC4 proteins. These results provide a basis for understanding the functional differences between hAE1 and hNBCe1 and may facilitate potential drug development for diseases such as proximal and distal renal tubular acidosis.

The Single Residue K12 Governs the Exceptional Voltage Sensitivity of Mitochondrial Voltage-Dependent Anion Channel Gating.

The voltage-dependent anion channel (VDAC) is a ß-barrel channel of the mitochondrial outer membrane (MOM) that passively transports ions, metabolites, polypeptides, and single-stranded DNA. VDAC responds to a transmembrane potential by "gating," i.e. transitioning to one of a variety of low-conducting states of unknown structure. The gated state results in nearly complete suppression of multivalent mitochondrial metabolite (such as ATP and ADP) transport, while enhancing calcium transport. Voltage gating is a universal property of ß-barrel channels, but VDAC gating is anomalously sensitive to transmembrane potential. Here, we show that a single residue in the pore interior, K12, is responsible for most of VDAC's voltage sensitivity. Using the analysis of over 40 µs of atomistic molecular dynamics (MD) simulations, we explore correlations between motions of charged residues inside the VDAC pore and geometric deformations of the ß-barrel. Residue K12 is bistable; its motions between two widely separated positions along the pore axis enhance the fluctuations of the ß-barrel and augment the likelihood of gating. Single channel electrophysiology of various K12 mutants reveals a dramatic reduction of the voltage-induced gating transitions. The crystal structure of the K12E mutant at a resolution of 2.6 Å indicates a similar architecture of the K12E mutant to the wild type; however, 60 µs of atomistic MD simulations using the K12E mutant show restricted motion of residue 12, due to enhanced connectivity with neighboring residues, and diminished amplitude of barrel motions. We conclude that ß-barrel fluctuations, governed particularly by residue K12, drive VDAC gating transitions.

Emerging Diversity in Lipid-Protein Interactions.

Membrane lipids interact with proteins in a variety of ways, ranging from providing a stable membrane environment for proteins to being embedded in to detailed roles in complicated and well-regulated protein functions. Experimental and computational advances are converging in a rapidly expanding research area of lipid-protein interactions. Experimentally, the database of high-resolution membrane protein structures is growing, as are capabilities to identify the complex lipid composition of different membranes, to probe the challenging time and length scales of lipid-protein interactions, and to link lipid-protein interactions to protein function in a variety of proteins. Computationally, more accurate membrane models and more powerful computers now enable a detailed look at lipid-protein interactions and increasing overlap with experimental observations for validation and joint interpretation of simulation and experiment. Here we review papers that use computational approaches to study detailed lipid-protein interactions, together with brief experimental and physiological contexts, aiming at comprehensive coverage of simulation papers in the last five years. Overall, a complex picture of lipid-protein interactions emerges, through a range of mechanisms including modulation of the physical properties of the lipid environment, detailed chemical interactions between lipids and proteins, and key functional roles of very specific lipids binding to well-defined binding sites on proteins. Computationally, despite important limitations, molecular dynamics simulations with current computer power and theoretical models are now in an excellent position to answer detailed questions about lipid-protein interactions.

VDAC Gating Thermodynamics, but Not Gating Kinetics, Are Virtually Temperature Independent.

The voltage-dependent anion channel (VDAC) is the most abundant protein in the mitochondrial outer membrane and an archetypical ß-barrel channel. Here, we study the effects of temperature on VDAC channels reconstituted in planar lipid membranes at the single- and multichannel levels within the 20°C to 40°C range. The temperature dependence of conductance measured on a single channel in 1 M KCl shows an increase characterized by a 10°C temperature coefficient Q10 = 1.22 ± 0.02, which exceeds that of the bathing electrolyte solution conductivity, Q10 = 1.17 ± 0.01. The rates of voltage-induced channel transition between the open and closed states measured on multichannel membranes also show statistically significant increases, with temperatures that are consistent with activation energy barriers of ∼10 ± 3 kcal/mol. At the same time, the gating thermodynamics, as characterized by the gating charge and voltage of equipartitioning, does not display any measurable temperature dependence. The two parameters stay within 3.2 ± 0.2 elementary charges and 30 ± 2 mV, respectively. Thus, whereas the channel kinetics, specifically its conductance and rates of gating response to voltage steps, demonstrates a clear increase with temperature, the conformational voltage-dependent equilibria are virtually insensitive to temperature. These results, which may be a general feature of ß-barrel channel gating, suggest either an entropy-driven gating mechanism or a role for enthalpy-entropy compensation.

The Pore-Lipid Interface: Role of Amino-Acid Determinants of Lipophilic Access by Ivabradine to the hERG1 Pore Domain.

Abnormal cardiac electrical activity is a common side effect caused by unintended block of the promiscuous drug target human ether-à-go-go-related gene (hERG1), the pore-forming domain of the delayed rectifier K+ channel in the heart. hERG1 block leads to a prolongation of the QT interval, a phase of the cardiac cycle that underlies myocyte repolarization detectable on the electrocardiogram. Even newly released drugs such as heart-rate lowering agent ivabradine block the rapid delayed rectifier current IKr, prolong action potential duration, and induce potentially lethal arrhythmia known as torsades de pointes. In this study, we describe a critical drug-binding pocket located at the lateral pore surface facing the cellular membrane. Mutations of the conserved M651 residue alter ivabradine-induced block but not by the common hERG1 blocker dofetilide. As revealed by molecular dynamics simulations, binding of ivabradine to a lipophilic pore access site is coupled to a state-dependent reorientation of aromatic residues F557 and F656 in the S5 and S6 helices. We show that the M651 mutation impedes state-dependent dynamics of F557 and F656 aromatic cassettes at the protein-lipid interface, which has a potential to disrupt drug-induced block of the channel. This fundamentally new mechanism coupling the channel dynamics and small-molecule access from the membrane into the hERG1 intracavitary site provides a simple rationale for the well established state-dependence of drug blockade. SIGNIFICANCE STATEMENT: The drug interference with the function of the cardiac hERG channels represents one of the major sources of drug-induced heart disturbances. We found a novel and a critical drug-binding pocket adjacent to a lipid-facing surface of the hERG1 channel, which furthers our molecular understanding of drug-induced QT syndrome.

Current state of theoretical and experimental studies of the voltage-dependent anion channel (VDAC).

Voltage-dependent anion channel (VDAC), the major channel of the mitochondrial outer membrane provides a controlled pathway for respiratory metabolites in and out of the mitochondria. In spite of the wealth of experimental data from structural, biochemical, and biophysical investigations, the exact mechanisms governing selective ion and metabolite transport, especially the role of titratable charged residues and interactions with soluble cytosolic proteins, remain hotly debated in the field. The computational advances hold a promise to provide a much sought-after solution to many of the scientific disputes around solute and ion transport through VDAC and hence, across the mitochondrial outer membrane. In this review, we examine how Molecular Dynamics, Free Energy, and Brownian Dynamics simulations of the large ß-barrel channel, VDAC, advanced our understanding. We will provide a short overview of non-conventional techniques and also discuss examples of how the modeling excursions into VDAC biophysics prospectively aid experimental efforts. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Computational membrane biophysics: From ion channel interactions with drugs to cellular function.

The rapid development of experimental and computational techniques has changed fundamentally our understanding of cellular-membrane transport. The advent of powerful computers and refined force-fields for proteins, ions, and lipids has expanded the applicability of Molecular Dynamics (MD) simulations. A myriad of cellular responses is modulated through the binding of endogenous and exogenous ligands (e.g. neurotransmitters and drugs, respectively) to ion channels. Deciphering the thermodynamics and kinetics of the ligand binding processes to these membrane proteins is at the heart of modern drug development. The ever-increasing computational power has already provided insightful data on the thermodynamics and kinetics of drug-target interactions, free energies of solvation, and partitioning into lipid bilayers for drugs. This review aims to provide a brief summary about modeling approaches to map out crucial binding pathways with intermediate conformations and free-energy surfaces for drug-ion channel binding mechanisms that are responsible for multiple effects on cellular functions. We will discuss post-processing analysis of simulation-generated data, which are then transformed to kinetic models to better understand the molecular underpinning of the experimental observables under the influence of drugs or mutations in ion channels. This review highlights crucial mathematical frameworks and perspectives on bridging different well-established computational techniques to connect the dynamics and timescales from all-atom MD and free energy simulations of ion channels to the physiology of action potentials in cellular models. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

Characterization of the Cation Binding Sites in the NCKX2 Na+/Ca2+-K+ Exchanger.

NCKX1-5 are proteins involved in K+-dependent Na+/Ca2+ exchange in various signal tissues. Here we present a homology model of NCKX2 based on the crystal structure of the NCX_Mj transporter found in Methanoccocus jannaschii. Molecular dynamics simulations were performed on the resultant wild-type NCKX2 model and two mutants (D548N and D575N) loaded with either four Na+ ions or one Ca2+ ion and one K+ ion, in line with the experimentally observed transport stoichiometry. The selectivity of the active site in wild-type NCKX2 for Na+, K+, and Li+ and the electrostatic interactions of the positive Na+ ions in the negatively charged active site of wild-type NCKX2 and the two mutants were evaluated from free energy perturbation calculations. For validation of the homology model, our computational results were compared to available experimental data obtained from numerous prior functional studies. The NCKX2 homology model is in good agreement with the discussed experimental data and provides valuable insights into the structure of the active site, which is lined with acidic and polar residues. The binding of the potassium and calcium ions is accomplished via Asp 575 and 548, respectively. Mutation of these residues to Asn alters the functionality of NCKX2 because of the elimination of the favorable carboxylate-cation interactions. The knowledge obtained from the NCKX2 model can be transferred to other isoforms of the NCKX family: newly discovered pathological mutations in NCKX4 and NCKX5 affect residues that are involved in ion binding and/or transport according to our homology model.

LiCl solvation in N-methyl-acetamide (NMA) as a model for understanding Li(+) binding to an amide plane.

The thermodynamics of ion solvation in non-aqueous solvents remains of great significance for understanding cellular transport and ion homeostasis for the design of novel ion-selective materials and applications in molecular pharmacology. Molecular simulations play pivotal roles in connecting experimental measurements to the microscopic structures of liquids. One of the most useful and versatile mimetic systems for understanding biological ion transport is N-methyl-acetamide (NMA). A plethora of theoretical studies for ion solvation in NMA have appeared recently, but further progress is limited by two factors. One is an apparent lack of experimental data on solubility and thermodynamics of solvation for a broad panel of 1 : 1 salts over an appropriate temperature and concentration range. The second concern is more substantial and has to do with the limitations hardwired in the additive (fixed charge) approximations used for most of the existing force-fields. In this submission, we report on the experimental evaluation of LiCl solvation in NMA over a broad range of concentrations and temperatures and compare the results with those of MD simulations with several additive and one polarizable force-field (Drude). By comparing our simulations and experimental results to density functional theory computations, we discuss the limiting factors in existing potential functions. To evaluate the possible implications of explicit and implicit polarizability treatments on ion permeation across biological channels, we performed potential of mean force (PMF) computations for Li(+) transport through a model narrow ion channel with additive and polarizable force-fields.

Improving the LIE Method for Binding Free Energy Calculations of Protein-Ligand Complexes.

In this work, we introduced an improved linear interaction energy (LIE) method parameterization for computations of protein­ligand binding free energies. The protocol, coined LIE-D, builds on the linear relationship between the empirical coefficient γ in the standard LIE scheme and the D parameter, introduced in our work. The D-parameter encompasses the balance (difference) between electrostatic (polar) and van der Waals (nonpolar) energies in protein­ligand complexes. Leave-one-out cross-validation showed that LIE-D reproduced accurately the absolute binding free energies for our training set of protein­ligand complexes (<|error|> = 0.92 kcal/mol, SDerror = 0.66 kcal/mol, R(2) = 0.90, QLOO(2) = 0.89, and sPRESS(LOO) = 1.28 kcal/mol). We also demonstrated LIE-D robustness by predicting accurately the binding free energies for three different protein­ligand systems outside the training data set, where the electrostatic and van der Waals interaction energies were calculated with different force fields.

Elucidating factors important for monovalent cation selectivity in enzymes: E. coli ß-galactosidase as a model.

Many enzymes require a specific monovalent cation (M(+)), that is either Na(+) or K(+), for optimal activity. While high selectivity M(+) sites in transport proteins have been extensively studied, enzyme M(+) binding sites generally have lower selectivity and are less characterized. Here we study the M(+) binding site of the model enzyme E. coli ß-galactosidase, which is about 10 fold selective for Na(+) over K(+). Combining data from X-ray crystallography and computational models, we find the electrostatic environment predominates in defining the Na(+) selectivity. In this lower selectivity site rather subtle influences on the electrostatic environment become significant, including the induced polarization effects of the M(+) on the coordinating ligands and the effect of second coordination shell residues on the charge distribution of the primary ligands. This work expands the knowledge of ion selectivity in proteins to denote novel mechanisms important for the selectivity of M(+) sites in enzymes.

QM/MM calculations with deMon2k.

The density functional code deMon2k employs a fitted density throughout (Auxiliary Density Functional Theory), which offers a great speed advantage without sacrificing necessary accuracy. Powerful Quantum Mechanical/Molecular Mechanical (QM/MM) approaches are reviewed. Following an overview of the basic features of deMon2k that make it efficient while retaining accuracy, three QM/MM implementations are compared and contrasted. In the first, deMon2k is interfaced with the CHARMM MM code (CHARMM-deMon2k); in the second MM is coded directly within the deMon2k software; and in the third the Chemistry in Ruby (Cuby) wrapper is used to drive the calculations. Cuby is also used in the context of constrained-DFT/MM calculations. Each of these implementations is described briefly; pros and cons are discussed and a few recent applications are described briefly. Applications include solvated ions and biomolecules, polyglutamine peptides important in polyQ neurodegenerative diseases, copper monooxygenases and ultra-rapid electron transfer in cryptochromes.

The molecular mechanism of ion-dependent gating in secondary transporters.

LeuT-like fold Na-dependent secondary active transporters form a large family of integral membrane proteins that transport various substrates against their concentration gradient across lipid membranes, using the free energy stored in the downhill concentration gradient of sodium ions. These transporters play an active role in synaptic transmission, the delivery of key nutrients, and the maintenance of osmotic pressure inside the cell. It is generally believed that binding of an ion and/or a substrate drives the conformational dynamics of the transporter. However, the exact mechanism for converting ion binding into useful work has yet to be established. Using a multi-dimensional path sampling (string-method) followed by all-atom free energy simulations, we established the principal thermodynamic and kinetic components governing the ion-dependent conformational dynamics of a LeuT-like fold transporter, the sodium/benzyl-hydantoin symporter Mhp1, for an entire conformational cycle. We found that inward-facing and outward-facing states of Mhp1 display nearly the same free energies with an ion absent from the Na2 site conserved across the LeuT-like fold transporters. The barrier separating an apo-state from inward-facing or outward-facing states of the transporter is very low, suggesting stochastic gating in the absence of ion/substrate bound. In contrast, the binding of a Na2 ion shifts the free energy stabilizing the outward-facing state and promoting substrate binding. Our results indicate that ion binding to the Na2 site may also play a key role in the intracellular thin gate dynamics modulation by altering its interactions with the transmembrane helix 5 (TM5). The Potential of Mean Force (PMF) computations for a substrate entrance displays two energy minima that correspond to the locations of the main binding site S1 and proposed allosteric S2 binding site. However, it was found that substrate's binds to the site S1 ∼5 kcal/mol more favorable than that to the site S2 for all studied bound combinations of ions and a substrate.

ATP transport through VDAC and the VDAC-tubulin complex probed by equilibrium and nonequilibrium MD simulations.

Voltage-dependent anion channel (VDAC), the major channel of the mitochondrial outer membrane, serves as a principal pathway for ATP, ADP, and other respiratory substrates across this membrane. Using umbrella-sampling simulations, we established the thermodynamic and kinetic components governing ATP transport across the VDAC1 channel. We found that there are several low-affinity binding sites for ATP along the translocation pathway and that the main barrier for ATP transport is located around the center of the channel and is formed predominantly by residues in the N-terminus. The binding affinity of ATP to an open channel was found to be in the millimolar to micromolar range. However, we show that this weak binding increases the ATP translocation probability by about 10-fold compared with the VDAC pore in which attractive interactions were artificially removed. Recently, it was found that free dimeric tubulin induces a highly efficient, reversible blockage of VDAC reconstituted into planar lipid membranes. It was proposed that by blocking VDAC permeability for ATP/ADP and other mitochondrial respiratory substrates tubulin controls mitochondrial respiration. Using the Rosetta protein-protein docking algorithm, we established a tentative structure of the VDAC-tubulin complex. An extensive set of equilibrium and nonequilibrium (under applied electric field) molecular dynamics (MD) simulations was used to establish the conductance of the open and blocked channel. It was found that the presence of the unstructured C-terminal tail of tubulin in the VDAC pore decreases its conductance by more than 40% and switches its selectivity from anionic to cationic. The subsequent 1D potential of mean force (PMF) computations for the VDAC-tubulin complex show that the state renders ATP transport virtually impossible. A number of residues pivotal for tubulin binding to the channel were identified that help to clarify the molecular details of VDAC-tubulin interaction and to provide new insight into the mechanism of the control of mitochondria respiration by VDAC.

Atomistic models of ion and solute transport by the sodium-dependent secondary active transporters.

The recent determination of high-resolution crystal structures of several transporters offers unprecedented insights into the structural mechanisms behind secondary transport. These proteins utilize the facilitated diffusion of the ions down their electrochemical gradients to transport the substrate against its concentration gradient. The structural studies revealed striking similarities in the structural organization of ion and solute binding sites and a well-conserved inverted-repeat topology between proteins from several gene families. In this paper we will overview recent atomistic simulations applied to study the mechanisms of selective binding of ion and substrate in LeuT, Glt, vSGLT and hSERT as well as its consequences for the transporter conformational dynamics. This article is part of a Special Issue entitled: Membrane protein structure and function.

Role of protein matrix rigidity and local polarization effects in the monovalent cation selectivity of crystallographic sites in the Na-coupled aspartate transporter Glt(Ph).

We have studied Li(+)/Na(+)/K(+) selectivity of the bacterial aspartate transporter Glt(Ph) using all-atom molecular dynamics (MD) and free energy simulations (FES) to evaluate the role of different factors that control ion preferences of the binding sites identified in the crystallographic structure. The role of the bound ions in stabilizing the hairpin loop (HP2) by acting as an extracellular gate is discussed. Free energy simulations with classical and polarizable force-fields were used to characterize the role of the protein matrix, the site composition and the induced polarization in the stabilization of native and non-native cations, such as Li(+) and K(+), in the ion-binding sites of the transporter. The role of different factors that control the selectivity of the binding sites was highlighted with a number of reduced models using a scheme recently developed by Yu et al. (Proc. Natl. Acad. Sci. U. S. A., 2010, 107, 20329-20334 and J. Phys. Chem. B, 2009, 113, 8725).

Two mechanisms of ion selectivity in protein binding sites.

A theoretical framework is presented to clarify the molecular determinants of ion selectivity in protein binding sites. The relative free energy of a bound ion is expressed in terms of the main coordinating ligands coupled to an effective potential of mean force representing the influence of the rest of the protein. The latter is separated into two main contributions. The first includes all the forces keeping the ion and the coordinating ligands confined to a microscopic subvolume but does not prevent the ligands from adapting to a smaller or larger ion. The second regroups all the remaining forces that control the precise geometry of the coordinating ligands best adapted to a given ion. The theoretical framework makes it possible to delineate two important limiting cases. In the limit where the geometric forces are dominant (rigid binding site), ion selectivity is controlled by the ion-ligand interactions within the matching cavity size according to the familiar "snug-fit" mechanism of host-guest chemistry. In the limit where the geometric forces are negligible, the ion and ligands behave as a "confined microdroplet" that is free to fluctuate and adapt to ions of different sizes. In this case, ion selectivity is set by the interplay between ion-ligand and ligand-ligand interactions and is controlled by the number and the chemical type of ion-coordinating ligands. The framework is illustrated by considering the ion-selective binding sites in the KcsA channel and the LeuT transporter.