Polarization Effects in Water-Mediated Selective Cation Transport across a Narrow Transmembrane Channel

A non-B DNA binding peptidomimetic channel alters cellular functions

DNA binding transcription factors possess the ability to interact with lipid membranes to construct ion-permeable pathways. Herein, we present a thiazole-based DNA binding peptide mimic TBP2, which forms transmembrane ion channels, impacting cellular ion concentration and consequently stabilizing G-quadruplex DNA structures. TBP2 self-assembles into nanostructures, e.g., vesicles and nanofibers and facilitates the transportation of Na+ and K+ across lipid membranes with high conductance (~0.6 nS). Moreover, TBP2 exhibits increased fluorescence when incorporated into the membrane or in cellular nuclei. Monomeric TBP2 can enter the lipid membrane and localize to the nuclei of cancer cells. The coordinated process of time-dependent membrane or nuclear localization of TBP2, combined with elevated intracellular cation levels and direct G-quadruplex (G4) interaction, synergistically promotes formation and stability of G4 structures, triggering cancer cell death. This study introduces a platform to mimic and control intricate biological functions, leading to the discovery of innovative therapeutic approaches.

Efficient Sampling of Cavity Hydration in Proteins with Nonequilibrium Grand Canonical Monte Carlo and Polarizable Force Fields

Prediction of the hydration levels of protein cavities and active sites is important to both mechanistic analysis and ligand design. Due to the unique microscopic environment of these buried water molecules, a polarizable model is expected to be crucial for an accurate treatment of protein internal hydration in simulations. Here we adapt a nonequilibrium candidate Monte Carlo approach for conducting grand canonical Monte Carlo simulations with the Drude polarizable force field. The GPU implementation enables the efficient sampling of internal cavity hydration levels in biomolecular systems. We also develop an enhanced sampling approach referred to as B-walking, which satisfies detailed balance and readily combines with grand canonical integration to efficiently calculate quantitative binding free energies of water to protein cavities. Applications of these developments are illustrated in a solvent box and the polar ligand binding site in trypsin. Our simulation results show that including electronic polarization leads to a modest but clear improvement in the description of water position and occupancy compared to the crystal structure. The B-walking approach enhances the range of water sampling in different chemical potential windows and thus improves the accuracy of water binding free energy calculations.

Insight into the K channel's selectivity from binding of K+, Na+ and water to N-methylacetamide

In potassium channels that conduct K+ selectively over Na+, which sites are occupied by K+ or water and the mechanism of selectivity are unresolved questions. The combination of the energetics and the constraints imposed by the protein structure yield the selective permeation and occupancy. To gain insight into the combination of structure and energetics, we performed density functional theory (DFT) calculations of multiple N-methyl acetamide (NMA) ligands binding to K+ and Na+, relative to hydrated K+ and Na+. NMA is an analogue of the amino acid backbone and provides the carbonyl binding to the ions that occurs in most binding sites of the K+ channel. Unconstrained optimal structures are obtained through geometry optimization calculations of the NMA ligand binding. The complexes formed by 8 NMA binding to the cations have the O atoms positioned in nearly identical locations as the O atoms in the selectivity filter. The transfer free energies between bulk water and K+ or Na+ bound to 8 NMA are almost identical, implying there is no selectivity by a single site. For water optimized with 8 NMA, binding is weak and O atoms are not positioned as in the K+ channel selectivity filter, suggesting that the ions are much more favored than water. Optimal structures of 8 NMA binding with two cations (K+ or Na+) are stable and have lower binding free energy than the optimal structures with just one cation. However, in the Na+ case, the optimal structure deforms and does not match the K+ channel; that is, two bound Na+ are destabilizing. In contrast, the two K+ structure is stabilized and the selectivity free energy favors K+. Overall, this study shows that binding site occupancy and the mechanism for K+ selectivity involves multiple K+ binding in multiple neighboring layers or sites of the K+ channel selectivity filter.

Computational drug development for membrane protein targets

The application of computational biology in drug development for membrane protein targets has experienced a boost from recent developments in deep learning-driven structure prediction, increased speed and resolution of structure elucidation, machine learning structure-based design and the evaluation of big data. Recent protein structure predictions based on machine learning tools have delivered surprisingly reliable results for water-soluble and membrane proteins but have limitations for development of drugs that target membrane proteins. Structural transitions of membrane proteins have a central role during transmembrane signaling and are often influenced by therapeutic compounds. Resolving the structural and functional basis of dynamic transmembrane signaling networks, especially within the native membrane or cellular environment, remains a central challenge for drug development. Tackling this challenge will require an interplay between experimental and computational tools, such as super-resolution optical microscopy for quantification of the molecular interactions of cellular signaling networks and their modulation by potential drugs, cryo-electron microscopy for determination of the structural transitions of proteins in native cell membranes and entire cells, and computational tools for data analysis and prediction of the structure and function of cellular signaling networks, as well as generation of promising drug candidates.

Thermodynamics of Metal-Acetate Interactions

Metal ions play crucial roles in protein- and ligand-mediated interactions. They not only act as catalysts to facilitate biological processes but are also important as protein structural elements. Accurately predicting metal ion interactions in computational studies has always been a challenge, and various methods have been suggested to improve these interactions. One such method is the 12-6-4 Lennard-Jones (LJ)-type nonbonded model. Using this model, it has been possible to successfully reproduce the experimental properties of metal ions in aqueous solution. The model includes induced dipole interactions typically ignored in the standard 12-6 LJ nonbonded model. In this we expand the applicability of this model to metal ion-carboxylate interactions. Using 12-6-4 parameters that reproduce the solvation free energies of the metal ions leads to an overestimation of metal ion-acetate interactions, thus, prompting us to fine-tune the model to specifically handle the latter. We also show that the standard 12-6 LJ model significantly falls short in reproducing the experimental binding free energy between acetate and 11 metal ions (Ni(II), Mg(II), Cu(II), Zn(II), Co(II), Cu(I), Fe(II), Mn(II), Cd(II), Ca(II), and Ag(I)). In this study, we describe optimized C4 parameters for the 12-6-4 LJ nonbonded model to be used with three widely employed water models (Transferable Intermolecular Potential with 3 Points (TIP3P), Simple Point Charge Extended (SPC/E), and Optimal Point Charge (OPC) water models). These parameters can accurately match the experimental binding free energy between 11 metal ions and acetate. These parameters can be applied to the study of metalloproteins and transition metal ion channels and transporters, as acetate serves as a representative of the negatively charged amino acid side chains from aspartate and glutamate.

Electronic Polarizability Tunes the Function of the Human Bestrophin 1 Cl - Channel

Mechanisms of anion permeation within ion channels and nanopores remain poorly understood. Recent cryo-electron microscopy structures of the human bestrophin 1 chloride channel (hBest1) provide an opportunity to evaluate ion interactions predicted by molecular dynamics (MD) simulations against experimental observations. We implement the fully polarizable forcefield AMOEBA in MD simulations of open and partially-open states of the hBest1. The AMOEBA forcefield models multipole moments up to the quadrupole; therefore, it captures induced dipole and anion- π interactions. By including polarization we demonstrate the key role that aromatic residues play in ion permeation and the functional advantages of pore asymmetry within the highly conserved hydrophobic neck of the pore. We establish that these only arise when electronic polarization is included in the molecular models. We also show that Cl - permeation in this region can be achieved through hydrophobic solvation concomitant with partial ion dehydration, which is compensated for by the formation of contacts with the edge of the phenylalanine ring. Furthermore, we demonstrate how polarizable simulations can help determine the identity of ion-like densities within high-resolution cryo-EM structures. Crucially, neglecting polarization in simulation of these systems results in the localization of Cl - at positions that do not correspond with their experimentally resolved location. Overall, our results demonstrate the importance of including electronic polarization in realistic and physically accurate models of biological systems.

Statement of Significance

Ion channels are nanoscale protein pores that enable the selective passage of charged ions across cell membranes. Understanding the underlying mechanisms for selective anion permeation through such pores remains a challenge. To simulate their behavior efficiently in silico , fixed charge models are typically employed. However, this approach is insufficient for the study of anions. Here, we use simulations with explicit treatment of electrostatics to investigate the interactions of chloride ions in the human bestrophin 1 channel. We find that electronic polarization tunes the state of the channel and affects the interactions of chloride ions thereby revealing a mechanism for permeation. Furthermore, these simulations can be used to resolve experimental ambiguity in ion-like densities from cryo-EM structures.

Mechanism of Calcium Permeation in a Glutamate Receptor Ion Channel

The α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs) are neurotransmitter-activated cation channels ubiquitously expressed in vertebrate brains. The regulation of calcium flux through the channel pore by RNA-editing is linked to synaptic plasticity while excessive calcium influx poses a risk for neurodegeneration. Unfortunately, the molecular mechanisms underlying this key process are mostly unknown. Here, we investigated calcium conduction in calcium-permeable AMPAR using Molecular Dynamics (MD) simulations with recently introduced multisite force-field parameters for Ca²⁺. Our calculations are consistent with experiment and explain the distinct calcium permeability in different RNA-edited forms of GluA2. For one of the identified metal binding sites, multiscale Quantum Mechanics/Molecular Mechanics (QM/MM) simulations further validated the results from MD and revealed small but reproducible charge transfer between the metal ion and its first solvation shell. In addition, the ion occupancy derived from MD simulations independently reproduced the Ca²⁺ binding profile in an X-ray structure of an NaK channel mimicking the AMPAR selectivity filter. This integrated study comprising X-ray crystallography, multisite MD, and multiscale QM/MM simulations provides unprecedented insights into Ca²⁺ permeation mechanisms in AMPARs, and paves the way for studying other biological processes in which Ca²⁺ plays a pivotal role.

Ideal Conductor Model: An Analytical Finite-Size Correction for Nonequilibrium Molecular Dynamics Simulations of Ion Transport through Nanoporous Membranes

Modulating ion transport through nanoporous membranes is critical to many important chemical and biological separation processes. The corresponding transport timescales, however, are often too long to capture accurately using conventional molecular dynamics (MD). Recently, path sampling techniques, such as forward-flux sampling (FFS), have emerged as attractive alternatives for efficiently and accurately estimating arbitrarily long ionic passage times. Here, we use non-equilibrium MD and FFS to explore how the kinetics and mechanisms of pressure-driven chloride transport through a nanoporous graphitic membrane are affected by its lateral dimensions. We not only find ionic passage times and free energy barriers to decrease dramatically upon increasing the membrane surface area but also observe an abrupt and discontinuous change in the locus of the transition state. These strong finite size effects arise due to the cumulative effect of the periodic images of the leading ion entering the pore on the distribution of the induced excess charge at the membrane surface in the feed. By assuming that the feed is an ideal conductor, we analytically derive a finite size correction term that can be computed from the information obtained from a single simulation and successfully use it to obtain corrected free energy profiles with no dependence on the system size. We then estimate ionic passage times in the thermodynamic limit by assuming an Eyring-type dependence of rates on barriers with a size-independent prefactor. This approach constitutes a universal framework for removing finite size artifacts in molecular simulations of ion transport through nanoporous membranes and biological channel proteins.

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.

Millisecond molecular dynamics simulations of KRas-dimer formation and interfaces

Ras dimers have been proposed as building blocks for initiating the extracellular signal-regulated kinase (ERK)/mitogen-activated protein kinase (MAPK) cellular signaling pathway. To better examine the structure of possible dimer interfaces, the dynamics of Ras dimerization, and its potential signaling consequences, we performed molecular dynamics simulations totaling 1 ms of sampling, using an all-atom model of two full-length, farnesylated, guanosine triphosphate (GTP)-bound, wild-type KRas4b proteins diffusing on 29%POPS (1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-L-serine)-mixed POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) membranes. Our simulations unveil an ensemble of thermodynamically weak KRas dimers spanning multiple conformations. The most stable conformations, having the largest interface areas, involve helix α2 and a hypervariable region (HVR). Among the dimer conformations, we found that the HVR of each KRas has frequent interactions with various parts of the dimer, thus potentially mediating the dimerization. Some dimer configurations have one KRas G-domain elevated above the lipid bilayer surface by residing on top of the other G-domain, thus likely contributing to the recruitment of cytosolic Raf kinases in the context of a stably formed multi-protein complex. We identified a variant of the α4-α5 KRas-dimer interface that is similar to the interfaces obtained with fluorescence resonance energy transfer (FRET) data of HRas on lipid bilayers. Interestingly, we found two arginine fingers, R68 and R149, that directly interact with the beta-phosphate of the GTP bound in KRas, in a manner similar to what is observed in a crystal structure of GAP-HRas complex, which can facilitate the GTP hydrolysis via the arginine finger of GTPase-activating protein (GAP).

Polarization energies in the fragment molecular orbital method

Using isolated and polarized states of fragments, a method for computing the polarization energies in density functional theory (DFT) and density-functional tight-binding (DFTB) is developed in the framework of the fragment molecular orbital method. For DFTB, the method is extended into the use of periodic boundary conditions (PBC), for which a new component, a periodic self-polarization energy, is derived. The couplings of the polarization to other components in the pair interaction energy analysis (PIEDA) are derived for DFT and DFTB, and compared to Hartree-Fock and second-order Møller-Plesset perturbation theory (MP2). The effect of the self-consistent (DFT) and perturbative (MP2) treatment of the electron correlation on the polarization is discussed. The difference in the polarization in the bulk (PBC) and micro (cluster) solvation is elucidated.

Interactions between Artificial Channel Protein, Water Molecules, and Ions Based on Theoretical Approaches

Contemporary techniques of molecular modeling allow for rational design of several specific classes of artificial proteins. Transmembrane channels are among these classes. A recent successful synthesis of self-assembling, highly symmetrical 12- or 16-helix channels by David Baker’s group prompted us to study interactions between one of these proteins, TMHC6, and low-molecular-weight components of the environment: water molecules and ions. To examine protein stability in a polar environment, molecular dynamics (MD) with classical force fields of the AMBER family was employed. Further characteristics of the chosen interactions were obtained using interaction energy calculations with usage of partially polarizable GFN-FF force field of Spicher and Grimme, symmetry-adapted perturbation theory (SAPT) and atoms in molecules (AIM) approaches for models of residues from the channel entry, crucial for interactions with water molecules and ions. The comparison of the interaction energy values between the gas phase and solvent reaction field gives the quantitative estimation of the strength of the interactions. The energy decomposition via the SAPT method showed that the electrostatics forces play a dominant role in the substructure stabilization. An application of the AIM theory enabled a description of the intermolecular hydrogen bonds and other noncovalent interactions.

Electronic Polarization Is Essential for the Stabilization and Dynamics of Buried Ion Pairs in Staphylococcal Nuclease Mutants

Buried charged residues play important roles in the modulation of protein stabilities and conformational dynamics and make crucial contributions to protein functions. Considering the generally nonpolar nature of protein interior, a key question concerns the contribution of electronic polarization to the stabilization and properties of buried charges. We answer this question by conducting free energy simulations using the latest polarizable CHARMM force field based on Drude oscillators for a series of Staphylococcal nuclease mutants that involve a buried Glu-Lys pair in different titration states and orientations. While a nonpolarizable model suggests that the ionized form of the buried Glu-Lys pair is more than 40 kcal/mol less stable than the charge-neutral form, the two titration states are comparable in stability when electronic polarization is included explicitly, a result better reconcilable with available experimental data. Analysis of free energy components suggests that additional stabilization of the ionized Glu-Lys pair has contributions from both the enhanced salt-bridge strength and stronger interaction between the ion-pair and surrounding protein residues and penetrated water. Despite the stronger direct interaction between Glu and Lys, the ion-pair exhibits considerably larger and faster structural fluctuations when polarization is included, due to compensation of interactions in the cavity. Collectively, observations from this work provide compelling evidence that electronic polarization is essential to the stability, hydration, dynamics, and therefore function of buried charges in proteins. Therefore, our study advocates for the explicit consideration of electronic polarization for mechanistic and engineering studies that implicate buried charged residues, such as enzymes and ion transporters.

Ion permeation, selectivity, and electronic polarization in fluoride channels

Fluoride channels (Flucs) export toxic F^- from the cytoplasm. Crystallography and mutagenesis have identified several conserved residues crucial for fluoride transport, but the permeation mechanism at the molecular level has remained elusive. Herein, we have applied constant-pH molecular dynamics and free-energy-sampling methods to investigate fluoride permeation through a Fluc protein from Escherichia coli. We find that fluoride is facile to permeate in its charged form, i.e., F^-, by traversing through a non-bonded network. The extraordinary F^- selectivity is gained by the hydrogen-bonding capability of the central binding site and the Coulombic filter at the channel entrance. The F^- permeation rate calculated using an electronically polarizable force field is significantly more accurate compared with the experimental value than that calculated using a more standard additive force field, suggesting an essential role for electronic polarization in the F^--Fluc interactions.

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.

Water Nanoconfined in a Hydrophobic Pore: Molecular Dynamics Simulations of Transmembrane Protein 175 and the Influence of Water Models

Water molecules within biological ion channels are in a nanoconfined environment and therefore exhibit behaviors which differ from that of bulk water. Here, we investigate the phenomenon of hydrophobic gating, the process by which a nanopore may spontaneously dewet to form a "vapor lock" if the pore is sufficiently hydrophobic and/or narrow. This occurs without steric occlusion of the pore. Using molecular dynamics simulations with both rigid fixed-charge and polarizable (AMOEBA) force fields, we investigate this wetting/dewetting behavior in the transmembrane protein 175 ion channel. We examine how a range of rigid fixed-charge and polarizable water models affect wetting/dewetting in both the wild-type structure and in mutants chosen to cover a range of nanopore radii and pore-lining hydrophobicities. Crucially, we find that the rigid fixed-charge water models lead to similar wetting/dewetting behaviors, but that the polarizable water model resulted in an increased wettability of the hydrophobic gating region of the pore. This has significant implications for molecular simulations of nanoconfined water, as it implies that polarizability may need to be included if we are to gain detailed mechanistic insights into wetting/dewetting processes. These findings are of importance for the design of functionalized biomimetic nanopores (e.g., sensing or desalination) as well as for furthering our understanding of the mechanistic processes underlying biological ion channel function.

Predicting Ion Channel Conductance via Dissipation-Corrected Targeted Molecular Dynamics and Langevin Equation Simulations

Ion channels are important proteins for physiological information transfer and functional control. To predict the microscopic origins of their voltage-conductance characteristics, here we applied dissipation-corrected targeted molecular dynamics in combination with Langevin equation simulations to potassium diffusion through the gramicidin A channel as a test system. Performing a nonequilibrium principal component analysis on backbone dihedral angles, we find coupled protein-ion dynamics to occur during ion transfer. The dissipation-corrected free energy profiles correspond well to predictions from other biased simulation methods. The incorporation of an external electric field in Langevin simulations enables the prediction of macroscopic observables in the form of I-V characteristics.

Momentum removal to obtain the position-dependent diffusion constant in constrained molecular dynamics simulation

The position-dependent diffusion coefficient along with free energy profile are important parameters needed to study mass transport in heterogeneous systems such as biological and polymer membranes, and molecular dynamics (MD) calculation is a popular tool to obtain them. Among many methodologies, the Marrink-Berendsen (MB) method is often employed to calculate the position-dependent diffusion coefficient, in which the autocorrelation function of the force on a fixed molecule is related to the friction on the molecule. However, the diffusion coefficient is shown to be affected by the period of the removal of the center-of-mass velocity, τ v 0 , which is necessary when performing MD calculations using the Ewald method for Coulombic interaction. We have clarified theoretically in this study how this operation affects the diffusion coefficient calculated by the MB method, and the theoretical predictions are proven by MD calculations. Therefore, we succeeded in providing guidance on how to select an appropriate τ v 0 value in estimating the position-dependent diffusion coefficient by the MB method. This guideline is applicable also to the Woolf-Roux method.

Influence of water models on water movement through AQP1

Water diffusion through membrane proteins is a key aspect of cellular function. Essential processes of cellular metabolism are driven by osmotic pressure, which depends on water channels. Membrane proteins such as aquaporins (AQPs) are responsible for enabling water permeation through the cell membrane. AQPs are highly selective, allowing only water and relatively small polar molecules to cross the membrane. Experimentally, estimation of water flux through membrane proteins is still a challenge, and hence, accurate simulations of water permeation are of particular importance. We present a numerical study of water diffusion through AQP1 comparing three water models: TIP3P, OPC, and TIP4P/2005. Bulk diffusion, diffusion permeability, and osmotic permeability are computed and compared among all models. The results show that there are significant differences between TIP3P (a particularly widespread model for simulations of biological systems) and the more recently developed TIP4P/2005 and OPC models. We demonstrate that OPC and TIP4P/2005 reproduce protein-water interactions and dynamics in very good agreement with experimental data. From this study, we find that the choice of the water model has a significant effect on the computed water dynamics as well as its molecular behavior within a biological nanopore.

Thermodynamics of ion binding and occupancy in potassium channels

Potassium channels modulate various cellular functions through efficient and selective conduction of K⁺ ions. The mechanism of ion conduction in potassium channels has recently emerged as a topic of debate. Crystal structures of potassium channels show four K⁺ ions bound to adjacent binding sites in the selectivity filter, while chemical intuition and molecular modeling suggest that the direct ion contacts are unstable. Molecular dynamics (MD) simulations have been instrumental in the study of conduction and gating mechanisms of ion channels. Based on MD simulations, two hypotheses have been proposed, in which the four-ion configuration is an artifact due to either averaged structures or low temperature in crystallographic experiments. The two hypotheses have been supported or challenged by different experiments. Here, MD simulations with polarizable force fields validated by ab initio calculations were used to investigate the ion binding thermodynamics. Contrary to previous beliefs, the four-ion configuration was predicted to be thermodynamically stable after accounting for the complex electrostatic interactions and dielectric screening. Polarization plays a critical role in the thermodynamic stabilities. As a result, the ion conduction likely operates through a simple single-vacancy and water-free mechanism. The simulations explained crystal structures, ion binding experiments and recent controversial mutagenesis experiments. This work provides a clear view of the mechanism underlying the efficient ion conduction and demonstrates the importance of polarization in ion channel simulations.

Polarization shapes the energy landscape of ion conduction in potassium channels.

Advanced Electrostatic Model for Monovalent Ions Based on Ab Initio Energy Decomposition

Ions play important roles in the structures and functions of biomolecules. In biomolecular simulations, ions either directly interact with biomolecules or provide an ionic environment that influences electrostatic interactions of solutes. The AMOEBA+ water model has demonstrated significant advancement of the classical force field for describing molecular interactions due to its improvements on the functional forms to account for essential physics. This work expands the applicability of the AMOEBA+ model toward alkali metal (Li, Na, K, Rb, and Cs) and halogen (F, Cl, Br, and I) ions. Various quantum chemical data on ion-ion and ion-water interactions, experimental ion hydration free energies, and lattice energies of salt crystals are used in the parametrization. The final parameters are verified with other properties outside of the parametrization data, including lattice energies of additional salt crystals and ionic activity coefficients in solution. The new model captures a wide range of ion properties from the gas phase to solution phase and crystals. More importantly, AMOEBA+ provides energy components that are consistent with ab initio energy decomposition. Thus, we expect AMOEBA+ to be more general, transferable, and valuable for the interpretation of intermolecular forces in efficient classical simulations.

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.