Ion selectivity in the KcsA potassium channel from the perspective of the ion binding site

The Molecular Mechanism of Ion Selectivity in Nanopores

Ion channels exhibit strong selectivity for specific ions over others under electrochemical potentials, such as KcsA for K+ over Na+. Based on the thermodynamic analysis, this study is focused on exploring the mechanism of ion selectivity in nanopores. It is well known that ions must lose part of their hydration layer to enter the channel. Therefore, the ion selectivity of a channel is due to the rearrangement of water molecules when entering the nanopore, which may be related to the hydrophobic interactions between ions and channels. In our recent works on hydrophobic interactions, with reference to the critical radius of solute (Rc), it was divided into initial and hydrophobic solvation processes. Additionally, the different dissolved behaviors of solutes in water are expected in various processes, such as dispersed and accumulated distributions in water. Correspondingly, as the ion approaches the nanopore, there seems to exist the "repulsive" or "attractive" forces between them. In the initial process ( Collapse

Key Words

• hydrogen bondings
• hydrophobic interactions
• ion selectivity
• nanopore
• water

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Affiliation(s)

Yan-Nan Chen
Yu-Zhen Liu
Qiang Sun Key Laboratory of Orogenic Belts and Crustal Evolution, The School of Earth and Space Sciences, Ministry of Education, Peking University, Beijing 100871, China; (Y.-N.C.); (Y.-Z.L.)

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Computational methods and theory for ion channel research

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

Physics of Selective Conduction and Point Mutation in Biological Ion Channels

We introduce a statistical and linear response theory of selective conduction in biological ion channels with multiple binding sites and possible point mutation. We derive an effective grand-canonical ensemble and generalized Einstein relations for the selectivity filter, assuming strongly coordinated ionic motion, and allowing for ionic Coulomb blockade. The theory agrees well with data from the KcsA K^{+} channel and a mutant. We show that the Eisenman relations for thermodynamic selectivity follow from the condition for fast conduction and find that maximum conduction requires the binding sites to be nearly identical.

Mini-grand canonical ensemble: Chemical potential in the solvation shell

Quantifying the statistics of occupancy of solvent molecules in the vicinity of solutes is central to our understanding of solvation phenomena. Number fluctuations in small solvation shells around solutes cannot be described within the macroscopic grand canonical framework using a single chemical potential that represents the solvent bath. In this communication, we hypothesize that molecular-sized observation volumes such as solvation shells are best described by coupling the solvation shell with a mixture of particle baths each with its own chemical potential. We confirm our hypotheses by studying the enhanced fluctuations in the occupancy statistics of hard sphere solvent particles around a distinguished hard sphere solute particle. Connections with established theories of solvation are also discussed.

Ion-triggered selectivity in bacterial sodium channels

Since the availability of the first crystal structure of a bacterial Na⁺ channel in 2011, understanding selectivity across this family of membrane proteins has been the subject of intense research efforts. Initially, free energy calculations based on molecular dynamics simulations revealed that although sodium ions can easily permeate the channel with their first hydration shell almost intact, the selectivity filter is too narrow for efficient conduction of hydrated potassium ions. This steric view of selectivity was subsequently questioned by microsecond atomic trajectories, which proved that the selectivity filter appears to the permeating ions as a highly degenerate, liquid-like environment. Although this liquid-like environment looks optimal for rapid conduction of Na⁺, it seems incompatible with efficient discrimination between similar ion species, such as Na⁺ and K⁺, through steric effects. Here extensive molecular dynamics simulations, combined with Markov state model analyses, reveal that at positive membrane potentials, potassium ions trigger a conformational change of the selectivity toward a nonconductive metastable state. It is this transition of the selectivity filter, and not steric effects, that prevents the outward flux of K⁺ at positive membrane potentials. This description of selectivity, triggered by the nature of the permeating ions, might have implications on the current understanding of how ion channels, and in particular bacterial Na⁺ channels, operate at the atomic scale.

Intramolecular Interactions Overcome Hydration to Drive the Collapse Transition of Gly15

Simulations and experiments show oligo-glycines, polypeptides lacking any side chains, can collapse in water. We assess the hydration thermodynamics of this collapse by calculating the hydration free energy at each of the end points of the reaction coordinate, here taken as the end-to-end distance (r) in the chain. To examine the role of the various conformations for a given r, we study the conditional distribution, P(R_g|r), of the radius of gyration for a given value of r. The free energy change versus R_g, -k_BT ln P(R_g|r), is found to vary more gently compared to the corresponding variation in the excess hydration free energy. Using this observation within a multistate generalization of the potential distribution theorem, we calculate a tight upper bound for the hydration free energy of the peptide for a given r. On this basis, we find that peptide hydration greatly favors the expanded state of the chain, despite primitive hydrophobic effects favoring chain collapse. The net free energy of collapse is seen to be a delicate balance between opposing intrapeptide and hydration effects, with intrapeptide contributions favoring collapse.

Ion channels and ion selectivity

Specific macromolecular transport systems, ion channels and pumps, provide the pathways to facilitate and control the passage of ions across the lipid membrane. Ion channels provide energetically favourable passage for ions to diffuse rapidly and passively according to their electrochemical potential. Selective ion channels are essential for the excitability of biological membranes: the action potential is a transient phenomenon that reflects the rapid opening and closing of voltage-dependent Na⁺-selective and K⁺-selective channels. One of the most critical functional aspects of K⁺ channels is their ability to remain highly selective for K⁺ over Na⁺ while allowing high-throughput ion conduction at a rate close to the diffusion limit. Permeation through the K⁺ channel selectivity filter is believed to proceed as a 'knockon' mechanism, in which 2-3 K⁺ ions interspersed by water molecules move in a single file. Permeation through the comparatively wider and less selective Na⁺ channels also proceeds via a loosely coupled knockon mechanism, although the ions do not need to be fully dehydrated. While simple structural concepts are often invoked to rationalize the mechanism of ion selectivity, a deeper analysis shows that subtle effects play an important role in these flexible dynamical structures.

Elucidating factors important for monovalent cation selectivity in enzymes: E. coli β-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 β-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.

Importance of Hydrophilic Hydration and Intramolecular Interactions in the Thermodynamics of Helix-Coil Transition and Helix-Helix Assembly in a Deca-Alanine Peptide

For a model deca-alanine peptide the cavity (ideal hydrophobic) contribution to hydration favors the helix state over extended states and the paired helix bundle in the assembly of two helices. The energetic contributions of attractive protein-solvent interactions are separated into quasi-chemical components consisting of a short-range part arising from interactions with solvent in the first hydration shell and the remaining long-range part that is well described by a Gaussian. In the helix-coil transition, short-range attractive protein-solvent interactions outweigh hydrophobic hydration and favor the extended coil states. Analysis of enthalpic effects shows that it is the favorable hydration of the peptide backbone that favors the unfolded state. Protein intramolecular interactions favor the helix state and are decisive in favoring folding. In the pairing of two helices, the cavity contribution outweighs the short-range attractive protein-water interactions. However, long-range, protein-solvent attractive interactions can either enhance or reverse this trend depending on the mutual orientation of the helices. In helix-helix assembly, change in enthalpy arising from change in attractive protein-solvent interactions favors disassembly. In helix pairing as well, favorable protein intramolecular interactions are found to be as important as hydration effects. Overall, hydrophilic protein-solvent interactions and protein intramolecular interactions are found to play a significant role in the thermodynamics of folding and assembly in the system studied.

K(+) and Na(+) conduction in selective and nonselective ion channels via molecular dynamics simulations

Generations of scientists have been captivated by ion channels and how they control the workings of the cell by admitting ions from one side of the cell membrane to the other. Elucidating the molecular determinants of ion conduction and selectivity are two of the most fundamental issues in the field of biophysics. Combined with ongoing progress in structural studies, modeling and simulation have been an integral part of the development of the field. As of this writing, the relentless growth in computational power, the development of new algorithms to tackle the so-called rare events, improved force-field parameters, and the concomitant increasing availability of membrane protein structures, allow simulations to contribute even further, providing more-complete models of ion conduction and selectivity in ion channels. In this report, we give an overview of the recent progress made by simulation studies on the understanding of ion permeation in selective and nonselective ion channels.

Molecular strategies to achieve selective conductance in NaK channel variants

A recent crystallization of several ion channels has provided strong impetus for efforts aimed at understanding the different strategies employed by nature for selective ion transport. In this work, we used two variants of the selectivity filter of NaK channel to explore molecular mechanisms that give rise to K(+)-selectivity. We computed one-dimensional (1D) and two-dimensional (2D) potentials of mean force (PMFs) for ion permeation across the channel. The results indicate that the energies for Na(+) and K(+) permeation across the selectivity filter display significant differences in positions of the binding sites and barriers. One characteristic signature of a K(+)-selective channel is the apparent preservation of the site analogous to that of S2 in KcsA. The S2-bound ion can be almost ideally dehydrated and coordinated by 6 to 8 carbonyls. In a striking contrast, the PMFs controlling transport of ions in a nonselective variant show almost identical profiles for either K(+) or Na(+) and significant involvement of water molecules in ion coordination across the entire selectivity filter. An analysis of differences in 1D PMFs for Na(+) and K(+) suggests that coordination number alone is an insufficient predictor of site selectivity, while chemical composition (ratio of carbonyls and water molecules) correlates well with preference for K(+). Multi-ion effects such as dependence of the barriers and wells for permeant ion on the type of copermeant ion were found to play a significant role in the selectivity signature of the channel as well.

An entropic mechanism of generating selective ion binding in macromolecules

Several mechanisms have been proposed to explain how ion channels and transporters distinguish between similar ions, a process crucial for maintaining proper cell function. Of these, three can be broadly classed as mechanisms involving specific positional constraints on the ion coordinating ligands which arise through: a “rigid cavity”, a ‘strained cavity’ and ‘reduced ligand fluctuations’. Each operates in subtly different ways yet can produce markedly different influences on ion selectivity. Here we expand upon preliminary investigations into the reduced ligand fluctuation mechanism of ion selectivity by simulating how a series of model systems respond to a decrease in ligand thermal fluctuations while simultaneously maintaining optimal ion-ligand binding distances. Simple abstract-ligand models, as well as simple models based upon the ion binding sites in two amino acid transporters, show that limiting ligand fluctuations can create ion selectivity between Li⁺, Na⁺ and K⁺ even when there is no strain associated with the molecular framework accommodating the different ions. Reducing the fluctuations in the position of the coordinating ligands contributes to selectivity toward the smaller of two ions as a consequence of entropic differences.

Differentiating between Na⁺ and K⁺ ions is important for many cellular processes, such as nerve conduction and the regulation of membrane potentials. Different biological molecules utilise different methods to discriminate between ions. In this work, the reduced ligand fluctuation mechanism of ion selectivity is described. This entropy-driven mechanism is due to the limited thermal fluctuations of the atoms in some macromolecular ion binding sites. The elucidation of this mechanism offers a more complete picture of the ways in which the fundamental process of ion selectivity can be achieved.

How does overcoordination create ion selectivity?

Some biological molecules can distinguish between ions of similar nature, which may be achieved by enforcing specific coordination numbers on ions in the binding site. It is suggested that when this number is favourable for one ion type, but too large for another, this creates ion selectivity through the proposed mechanism of 'overcoordination'. Much debate has occurred about the role overcoordination plays, and suggestions made as to how molecules can enforce particular coordination numbers, but there has not been an examination of the microscopic underpinning of ion selectivity by overcoordination. Here we use molecular-dynamics to systematically investigate how the number of ligands affects the ion-ligand and ligand-ligand interaction energies, and thus the thermodynamic ion selectivity, of a combination of model systems: three ions (Li(+)/Na(+)/K(+)) with three different ligands (water/formaldehyde/formamide). We find that the ligand-ligand repulsion controls the changes in geometry of each system with changing ligand number. Ion selectivity by overcoordination is achieved as smaller ions exhibit anomalous geometrical changes with the addition of extra ligands, whilst larger ions do not.

Bennett's acceptance ratio and histogram analysis methods enhanced by umbrella sampling along a reaction coordinate in configurational space

Free energy perturbation, a method for computing the free energy difference between two states, is often combined with non-Boltzmann biased sampling techniques in order to accelerate the convergence of free energy calculations. Here we present a new extension of the Bennett acceptance ratio (BAR) method by combining it with umbrella sampling (US) along a reaction coordinate in configurational space. In this approach, which we call Bennett acceptance ratio with umbrella sampling (BAR-US), the conditional histogram of energy difference (a mapping of the 3N-dimensional configurational space via a reaction coordinate onto 1D energy difference space) is weighted for marginalization with the associated population density along a reaction coordinate computed by US. This procedure produces marginal histograms of energy difference, from forward and backward simulations, with higher overlap in energy difference space, rendering free energy difference estimations using BAR statistically more reliable. In addition to BAR-US, two histogram analysis methods, termed Bennett overlapping histograms with US (BOH-US) and Bennett-Hummer (linear) least square with US (BHLS-US), are employed as consistency and convergence checks for free energy difference estimation by BAR-US. The proposed methods (BAR-US, BOH-US, and BHLS-US) are applied to a 1-dimensional asymmetric model potential, as has been used previously to test free energy calculations from non-equilibrium processes. We then consider the more stringent test of a 1-dimensional strongly (but linearly) shifted harmonic oscillator, which exhibits no overlap between two states when sampled using unbiased Brownian dynamics. We find that the efficiency of the proposed methods is enhanced over the original Bennett's methods (BAR, BOH, and BHLS) through fast uniform sampling of energy difference space via US in configurational space. We apply the proposed methods to the calculation of the electrostatic contribution to the absolute solvation free energy (excess chemical potential) of water. We then address the controversial issue of ion selectivity in the K(+) ion channel, KcsA. We have calculated the relative binding affinity of K(+) over Na(+) within a binding site of the KcsA channel for which different, though adjacent, K(+) and Na(+) configurations exist, ideally suited to these US-enhanced methods. Our studies demonstrate that the significant improvements in free energy calculations obtained using the proposed methods can have serious consequences for elucidating biological mechanisms and for the interpretation of experimental data.

Ion binding sites and their representations by reduced models

The binding of small metal ions to complex macromolecular structures is typically dominated by strong local interactions of the ion with its nearest ligands. Progress in understanding the molecular determinants of ion selectivity can often be achieved by considering simplified reduced models comprised of only the most important ion-coordinating ligands. Although the main ingredients underlying simplified reduced models are intuitively clear, a formal statistical mechanical treatment is nonetheless necessary in order to draw meaningful conclusions about complex macromolecular systems. By construction, reduced models only treat the ion and the nearest coordinating ligands explicitly. The influence of the missing atoms from the protein or the solvent is incorporated indirectly. Quasi-chemical theory offers one example of how to carry out such a separation in the case of ion solvation in bulk liquids, and in several ways, a statistical mechanical formulation of reduced binding site models for macromolecules is expected to follow a similar route. However, there are also important differences when the ion-coordinating moieties are not solvent molecules from a bulk phase but are molecular ligands covalently bonded to a macromolecular structure. Here, a statistical mechanical formulation of reduced binding site models is elaborated to address these issues. The formulation provides a useful framework to construct reduced binding site models, and define the average effect from the surroundings on the ion and the nearest coordinating ligands.

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

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

Transmembrane communication: general principles and lessons from the structure and function of the M2 proton channel, K⁺ channels, and integrin receptors

Signal transduction across biological membranes is central to life. This process generally happens through communication between different domains and hierarchical coupling of information. Here, we review structural and thermodynamic principles behind transmembrane (TM) signal transduction and discuss common themes. Communication between signaling domains can be understood in terms of thermodynamic and kinetic principles, and complex signaling patterns can arise from simple wiring of thermodynamically coupled domains. We relate this to functions of several signal transduction systems: the M2 proton channel from influenza A virus, potassium channels, integrin receptors, and bacterial kinases. We also discuss key features in the structural rearrangements responsible for signal transduction in these systems.

Separating the role of protein restraints and local metal-site interaction chemistry in the thermodynamics of a zinc finger protein

We express the effective Hamiltonian of an ion-binding site in a protein as a combination of the Hamiltonian of the ion-bound site in vacuum and the restraints of the protein on the site. The protein restraints are described by the quadratic elastic network model. The Hamiltonian of the ion-bound site in vacuum is approximated as a generalized Hessian around the minimum energy configuration. The resultant of the two quadratic Hamiltonians is cast into a pure quadratic form. In the canonical ensemble, the quadratic nature of the resultant Hamiltonian allows us to express analytically the excess free energy, enthalpy, and entropy of ion binding to the protein. The analytical expressions allow us to separate the roles of the dynamic restraints imposed by the protein on the binding site and the temperature-independent chemical effects in metal-ligand coordination. For the consensus zinc-finger peptide, relative to the aqueous phase, the calculated free energy of exchanging Zn(2+) with Fe(2+), Co(2+), Ni(2+), and Cd(2+) are in agreement with experiments. The predicted excess enthalpy of ion exchange between Zn(2+) and Co(2+) also agrees with the available experimental estimate. The free energy of applying the protein restraints reveals that relative to Zn(2+), the Co(2+), and Cd(2+)-site clusters are more destabilized by the protein restraints. This leads to an experimentally testable hypothesis that a tetrahedral metal binding site with minimal protein restraints will be less selective for Zn(2+) over Co(2+) and Cd(2+) compared to a zinc finger peptide. No appreciable change is expected for Fe(2+) and Ni(2+). The framework presented here may prove useful in protein engineering to tune metal selectivity.

The role of bulk protein in local models of ion-binding to proteins: comparative study of KcsA, its semisynthetic analog with a locked-in binding site, and valinomycin

In studying ion-selectivity in biomaterials, it is common to study ion-protein interactions within a local neighborhood around the ion. This local system analysis for the S(2) site of KcsA, its semisynthetic analog, and valinomycin yields the free energy change in exchanging K(+) with Na(+) in quantitative agreement with the value obtained by considering ion-interactions with the entire system. But the energetics of ion binding in the local system and in the entire system differ significantly and lead to different conclusions regarding the physical basis of ion selectivity. For configurations sampled from an all-atom simulation, we show that the selectivity free energy can be decomposed into a contribution arising from interactions of the ion with its local neighborhood, ΔW(local), and a term arising from the field imposed on the ion and the binding site by the rest of the medium, ΔW(ϕ). The local contribution ΔW(local) is numerically close to the actual free energy difference because the field contribution is small. The field contribution is small because of cancellation of inversely related ion-medium and site-medium interactions. Our analysis presents a rigorous foundation for the numerical success of the local system analysis and shows that its implications do not always hold for the entire protein.

Mapping the importance of four factors in creating monovalent ion selectivity in biological molecules

The ability of macrocycles, enzymes, ion channels, transporters, and DNA to differentiate among ion types is often crucial to their function. Using molecular dynamics simulations on both detailed systems and simple models, we quantify the importance of several factors which affect the ion selectivity of such molecules, including the number of coordinating ligands, their dipole moment, and their vibrational motion. The information resulting from our model systems is distilled into a series of selectivity maps that can be used to read off the relative free energy associated with binding of different ions, and to provide an estimate of the importance of the various factors. Although our maps cannot capture all elements of real systems, it is remarkable that they produce differential site-binding energies that are in line with experiment and more-detailed simulations for a variety of systems-making them useful for understanding the origins of selective binding and transport. The chemical nature of the coordinating ligands is essential for creating thermodynamic ion selectivity in flexible molecules (such as 18c6), but as the binding site becomes more rigid, the number of ligands (as in ion channels) and the reduction of thermal fluctuations (as in amino-acid transporters) can become important. In the future, our maps could aid in the determination of the local structure from binding energies and assist in the design of novel ion selective molecules.

Multibody effects in ion binding and selectivity

Selective binding of ions to biomolecules plays a vital role in numerous biological processes. To understand the specific role of induced effects in selective ion binding, we use quantum chemical and pairwise-additive force-field simulations to study Na(+) and K(+) binding to various small molecules representative of ion binding functional groups in biomolecules. These studies indicate that electronic polarization significantly contributes to both absolute and relative ion-binding affinities. Furthermore, this contribution depends on both the number and the specific chemistries of the coordinating molecules, thus highlighting the complexity of ion-ligand interactions. Specifically, multibody interactions reduce as well as enhance the dipole moments of the ion-coordinating molecules, thereby affecting observables like coordination number distributions of ions. The differential polarization induced in molecules coordinating these two equivalently charged, but different-sized, ions also depends upon the number of coordinating molecules, showing the importance of multibody effects in distinguishing these ions thermodynamically. Because even small differences in ionic radii (0.4 Å for Na(+) and K(+)) produce differential polarization trends critical to distinguishing ions thermodynamically, it is likely that polarization plays an important role in thermodynamically distinguishing other ions and charged chemical and biological functional groups.

Exploring the ion selectivity properties of a large number of simplified binding site models

The ability to discriminate between different cations efficiently is essential for the proper physiological functioning of many membrane transport proteins. One obvious mechanism of ion selectivity is when a binding site is structurally constrained by the protein architecture and its geometry is precisely adapted to fit an ion of a given size. This mechanism is not effective in the case of flexible protein binding sites that are able to deform structurally or to adapt to a bound ion. In this study, the concept of nontrivial ion selectivity arising in a highly flexible protein binding site conceptually represented as a microdroplet of ligands confined to a small volume is explored. The environment imposed by the spatial confinement is a critical feature of the reduced models. A large number of reduced binding site models (1077) comprising typical ion-coordinating ligands (carbonyl, hydroxyl, carboxylate, water) are constructed and characterized for Na(+)/K(+) and Ca(2+)/Ba(2+) size selectivity using free energy perturbation molecular dynamics simulations. Free energies are highly correlated with the sum of ion-ligand and ligand-ligand mean interactions, but the relative balance of those two contributions is different for K(+)-selective and Na(+)-selective binding sites. The analysis indicates that both the number and the type of ligands are important factors in ion selectivity.

On the utilization of energy minimization to the study of ion selectivity

The major pitfalls in studying ion selectivity in binding site models using energy minimization based methods are examined and discussed. It is shown that the properties derived from energy minimization are strongly configuration-dependent and that the results should be interpreted with caution. It is concluded that computational studies of ion selectivity must include thermal fluctuations and entropic effects.

Ion selectivity from local configurations of ligands in solutions and ion channels

Probabilities of numbers of ligands proximal to an ion lead to simple, general formulae for the free energy of ion selectivity between different media. That free energy does not depend on the definition of an inner shell for ligand-counting, but other quantities of mechanistic interest do. If analysis is restricted to a specific coordination number, then two distinct probabilities are required to obtain the free energy in addition. The normalizations of those distributions produce partition function formulae for the free energy. Quasi-chemical theory introduces concepts of chemical equilibrium, then seeks the probability that is simplest to estimate, that of the most probable coordination number. Quasi-chemical theory establishes the utility of distributions of ligand-number, and sharpens our understanding of quasi-chemical calculations based on electronic structure methods. This development identifies contributions with clear physical interpretations, and shows that evaluation of those contributions can establish a mechanistic understanding of the selectivity in ion channels.

Thermodynamically dominant hydration structures of aqueous ions

The hydration free energy of an ion is separated into a chemical term, arising due to the interaction of the ion with water molecules within the defined coordination sphere (the inner shell), a packing contribution, accounting for forming an ion-free coordination sphere (the observation volume) in the solvent, and a long range correction, accounting for the interaction of the ion with the solvent outside the coordination sphere. The chemical term is recast as a sum over coordination states, with the nth term depending on the probability of observing n water molecules in the observation volume and the free energy of assembling the n water molecules around the ion in the presence of the outer-shell solvent. Each stepwise increment in the coordination number more fully accounts for the chemical contribution, and this molecular aufbau approach is used to interrogate the thermodynamic importance of various hydration structures X[H(2)O](n) of X(aq) (X = Na(+), K(+), F(-)) within a classical molecular mechanics framework. States with n less than (and at best equal to) the most probable coordination state ñ account for all of the chemical term and evince the role of the ion in drawing water molecules into the coordination sphere. For states with n > ñ, the influence of the ion is tempered and changes in coordination states due to density fluctuations in water also appear important. Thus the influence of the ion on the solvent matrix is local, and only a subset of water molecules (n < or = ñ) contributes dominantly to the hydration thermodynamics. The n = 4 state of Na(+) (ñ = 5) and K(+) (ñ = 7) and the n = 6 state of F(-) (ñ = 6) are thermodynamically dominant; adding a water molecule to the dominant state additionally contributes only about 2-3 k(B)T toward the chemical term, but removing a water molecule is very unfavorable.

Hydration number, topological control, and ion selectivity

The topological control hypothesis presented by Bostick and Brooks [Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 9260] has sought to explain binding selectivity in potassium channels based on the premise that a universal measure of ion solvation in different environments is provided by its average coordination structure in bulk water. This leads to the view that ion selectivity is predominantly controlled by the number of ligands coordinating the ion and that the chemical type of those ligands plays a minor role. The significance of the topological control hypothesis and its ability to predict ion selectivity in protein binding sites are examined. It is shown that the framework encounters increasing difficulties when different protein binding sites with similar coordination numbers are considered.