Exploring the origin of the ion selectivity of the KcsA potassium channel

The availability of structural information about biological ion channels provides an opportunity to gain a detailed understanding of the control of ion selectivity by biological systems. However, accomplishing this task by computer simulation approaches is very challenging. First, although the activation barriers for ion transport can be evaluated by microscopic simulations, it is hard to obtain accurate results by such approaches. Second, the selectivity is related to the actual ion current and not directly to the individual activation barriers. Thus, it is essential to simulate the ion currents and this cannot be accomplished at present by microscopic MD approaches. In order to address this challenge, we developed and refined an approach capable of evaluating ion current while still reflecting the realistic features of the given channel. Our method involves generation of semimacroscopic free energy surfaces for the channel/ions system and Brownian dynamics (BD) simulations of the corresponding ion current. In contrast to most alternative macroscopic models, our approach is able to reproduce the difference between the free energy surfaces of different ions and thus to address the selectivity problem. Our method is used in a study of the selectivity of the KcsA channel toward the K+ and Na+ ions. The BD simulations with the calculated free energy profiles produce an appreciable selectivity. To the best of our knowledge, this is the first time that the trend in the selectivity in the ion current is produced by a computer simulation approach. Nevertheless, the calculated selectivity is still smaller than its experimental estimate. Recognizing that the calculated profiles are not perfect, we examine how changes in these profiles can account for the observed selectivity. It is found that the origin of the selectivity is more complex than generally assumed. The observed selectivity can be reproduced by increasing the barrier at the exit and the entrance of the selectivity filter, but the necessary changes in the barrier approach the limit of the error in the PDLD/S-LRA calculations. Other options that can increase the selectivity are also considered, including the difference between the Na+...Na+ and K+...K+ interaction. However, this interesting effect does not appear to lead to a major difference in selectivity since the Na+ ions at the limit of strong interaction tend to move in a less concerted way than the K+ ions. Changes in the relative binding energies at the different binding sites are also not so effective in changing the selectivity. Finally, it is pointed out that using the calculated profiles as a starting point and forcing the model to satisfy different experimentally based constraints, should eventually provide more detailed understanding of the different complex factors involved in ion selectivity of biological channels.     

Structural differences of matrix metalloproteinases. Homology modeling and energy minimization of enzyme-substrate complexes

Matrix metalloproteinases are extracellular enzymes taking part in the remodeling of extracellular matrix. The structures of the catalytic domain of MMP1, MMP3, MMP7 and MMP8 are known, but structures of enzymes belonging to this family still remain to be determined. A general approach to the homology modeling of matrix metalloproteinases, exemplified by the modeling of MMP2, MMP9, MMP12 and MMP14 is described. The models were refined using an energy minimization procedure developed for matrix metalloproteinases. This procedure includes incorporation of parameters for zinc and calcium ions in the AMBER 4.1 force field, applying a non-bonded approach and a full ion charge representation. Energy minimization of the apoenzymes yielded structures with distorted active sites, while reliable three-dimensional structures of the enzymes containing a substrate in active site were obtained. The structural differences between the eight enzyme-substrate complexes were studied with particular emphasis on the active site, and possible sites for obtaining selectivity among the MMP's are discussed. Differences in the P1' pocket are well-documented and have been extensively exploited in inhibitor design. The present work indicates that selectivity could be further improved by considering the P2 pocket as well.     

Energy distribution and ion selectivity of the bacterial potassium channel

The ion selectivity of the bacterial potassium channel K_CSA is explained upon comparing the energy characteristics of the interaction of cations (Li⁺, Na⁺, K⁺) with atoms of the selectivity filter of the protein pore. Quantum-chemical calculations reveal a deeper potential well for potassium ions, which accounts for preferred K⁺ permeation. It is shown that the conventional methods with AMBER, CHARMM, OPLS force fields in standard parametrization as well as partial re-parametrization give incorrect estimates of ion energy distribution in the channel.     

Microscopic model for selective permeation in ion channels.

Ionic permeation in the selectivity filter of ion channels is analyzed by a microscopic model based on molecular kinetic theory. The energy and flux equations are derived by assuming that: (a) the selectivity filter is formed by a symmetrical array of carbonyl groups; (b) ion movement is near the axis of the channel; (c) a fraction of water molecules is separated from the ion while it moves across the selectivity filter; (d) the applied voltage drops linearly across the selectivity filter; (e) ions move independently. Energy profiles, single channel conductances, and the degree of hydration of K+ in a hypothetical K+ channel are examined by varying the following microscopic parameters: ion radius and mass, channel radius, number of effective water dipoles, and number of carbonyl groups. The i-V curve is linear up to +/- 170 mV. If the positions of energy maxima and minima are fixed, this linear range is reduced to +/- 50 mV. Channel radius and ion-water interactions are found to be two major channel structural determinants for selectivity sequences. Both radius and mass of an ion are important in selectivity mediated by these interactions. The theory predicts a total of 15 possible kinetic selectivity sequences for alkali cations in ion channels with a single selectivity filter.     

Gramicidin channel selectivity. Molecular mechanics calculations for formamidinium, guanidinium, and acetamidinium.

Empirical energy function calculations were used to evaluate the effects of minimization on the structure of a gramicidin A channel and to analyze the energies of interaction between three cations (guanidinium, acetamidinium, formamidinium) and the channel as a function of position along the channel axis. The energy minimized model of the gramicidin channel, which was based on the results of Venkatachalam and Urry (1983), has a constriction at the channel entrance. If the channel is not allowed to relax in the presence of the ions (rigid model), there is a large potential energy barrier for all three cations. The barrier varies with cation size and is due to high van der Waals and ion deformation energies. If the channel is minimized in the presence of the ions, the potential energy barrier to formamidinium entry is almost eliminated, but a residual barrier remains for guanidinium and acetamidinium. The residual barrier is primarily due, not to the expansion of the helix, but, to the disruption of hydrogen bonds between the terminal ethanoloamine and the next turn of the helix which occurs when the carbonyls of the outer turn of the helix librate inward toward the ion as it enters the channel. The residual potential energy barriers could be a possible explanation for the measured selectivity of gramicidin for formamidinium over guanidinium. The results of this full-atomic model address the applicability of the size-exclusion concept for the selectivity of the gramicidin channel.     

Importance of hydration and dynamics on the selectivity of the KcsA and NaK channels

Fundamental concepts governing ion selectivity in narrow pores are reviewed and the microscopic factors responsible for the lack of selectivity of the NaK channel, which is structurally similar to the K+-selective KcsA channel, are elucidated on the basis of all-atom molecular dynamics free energy simulations. The results on NaK are contrasted and compared with previous studies of the KcsA channel. Analysis indicates that differences in hydration of the cation in the pore of NaK is at the origin of the lack of selectivity of NaK.     

Ion-exchange properties of immobilized DNA: influence of the polymer concentration and the solvent nature on the exchange of alkali metals

The method of ion exchange on immobilized DNA, which allows to determine quantitative parameters of ion binding with a high precision, is used for studying of DNA ion selectivity. Insoluble ion exchangers on the DNA basis with the exchange capacity of 0.09 and 0.17 mg-equiv. per 1 g of dry gel are synthesized by means of immobilization of DNA gel in polyacrylamide gel. Constants of ion-exchange equilibrium for the exchanges K+-Na+ and K+-Li+ are determined on these exchangers in water and 50% water-dioxane solution. It is shown that DNA binds selectively only Li+. The selectivity to Li+ increases with the increase of DNA concentration in gel. The specific properties of Li+-DNA in solutions and in the solid state, for example, the impossibility of the B-A transition, are discussed. The selectivity reversal in favor of K+ is observed in water-dioxane solution. The cause of the selectivity reversal and the question of possible participation of cell polyelectrolytes in creation of ion gradients in the living cell are discussed.     

Molecular mechanics simulations of a conformational rearrangement of D-xylose in the active site of D-xylose isomerase.

A proposed reaction mechanism for the enzyme D-xylose isomerase involves the ring opening of the cyclic substrate with a subsequent conformational rearrangement to an extended open-chain form. Restrained energy minimization was used to simulate the rearrangement. In the ring-opening step, the substrate energy function was gradually altered from a cyclic to an open-chain form, with energy minimization after each change. The protein/sugar contact energy did not increase significantly during the process, showing that there was no steric hindrance to ring opening. The conformational rearrangement involves an alteration in the coordination of the substrate to metal ion [1], which was induced by gradually changing restraints on metal/ligand distances. By allowing varying amounts of flexibility in the protein and examining a simplified model system, the interactions of the sugar with metal ion [1] and its immediate ligands were found to be the most important contributors to the energy barrier for the change. Only small changes in the positions of protein atoms were required. The energy barrier to the rearrangement was estimated to be less than the Arrhenius activation energy for the enzymatic reaction. This is in accordance with experimental indications that the isomerization step is rate determining.     

Potassium and sodium ions in a potassium channel studied by molecular dynamics simulations

We have performed simulations of both a single potassium ion and a single sodium ion within the pore of the bacterial potassium channel KcsA. For both ions there is a dehydration energy barrier at the cytoplasmic mouth suggesting that the crystal structure is a closed conformation of the channel. There is a potential energy barrier for a sodium ion in the selectivity filter that is not seen for potassium. Radial distribution functions for both ions with the carbonyl oxygens of the selectivity filter indicate that sodium may interact more tightly with the filter than does potassium. This suggests that the key to the ion selectivity of KcsA is the greater dehydration energy of Na⁺ ions, and helps to explain the block of KcsA by internal Na⁺ ions.     

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 Ca²⁺/Ba²⁺ 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.     

Structural modeling of calcium binding in the selectivity filter of the L-type calcium channel

Calcium channels play crucial physiological roles. In the absence of high-resolution structures of the channels, the mechanism of ion permeation is unknown. Here we used a method proposed in an accompanying paper (Cheng and Zhorov in Eur Biophys J, 2009) to predict possible chelation patterns of calcium ions in a structural model of the L-type calcium channel. We compared three models in which two or three calcium ions interact with the four selectivity filter glutamates and a conserved aspartate adjacent to the glutamate in repeat II. Monte Carlo energy minimizations yielded many complexes with calcium ions bound to at least two selectivity filter carboxylates. In these complexes calcium-carboxylate attractions are counterbalanced by calcium-calcium and carboxylate-carboxylate repulsions. Superposition of the complexes suggests a high degree of mobility of calcium ions and carboxylate groups of the glutamates. We used the predicted complexes to propose a permeation mechanism that involves single-file movement of calcium ions. The key feature of this mechanism is the presence of bridging glutamates that coordinate two calcium ions and enable their transitions between different chelating patterns involving four to six oxygen atoms from the channel protein. The conserved aspartate is proposed to coordinate a calcium ion incoming to the selectivity filter from the extracellular side. Glutamates in repeats III and IV, which are most distant from the repeat II aspartate, are proposed to coordinate the calcium ion that leaves the selectivity filter to the inner pore. Published experimental data and earlier proposed permeation models are discussed in view of our model.     

K(+)/Na(+) selectivity of the KcsA potassium channel from microscopic free energy perturbation calculations

Microscopic molecular dynamics free energy perturbation calculations of the K(+)/Na(+) selectivity in the KcsA potassium channel, based on its experimental three-dimensional structure, are reported. The relative binding free energies for K(+) and Na(+) in the most relevant ion occupancy states of the four-site selectivity filter are calculated. The previously proposed mechanism for ion permeation through the KcsA channel is predicted, in agreement with available experimental data, to have a significant selectivity for K(+) over Na(+). The calculations also show that the individual 'binding site' selectivities are generally not additive and the doubly loaded states of the filter thus display cooperative effects. The only site that is not K(+) selective is that which is located at the entrance to the internal water cavity, suggesting the possibility that internal Na(+) could block outward currents.     

Changes in the epithelial permeability of the large intestine of mice in the process of carcinogenesis

1,2-dimethylhydrazine (DMH), a colon carcinogen, being injected weekly to BALB/c mice, inhibits an active sodium transport, increases the transepithelial passive ion permeation and decreases ion selectivity in the descending colon. A single DMH injection leads to the same alterations, manifested for a month, followed by normalization of all the parameters to the control value. Distinctive, wavy changes in electrophysiological parameters were noted after a single injection of "non-colon" carcinogen 7,12-dimethyl-benz(alpha)antracen. It is supposed that the prolonged drop in active sodium transport, transepithelial resistance and ion selectivity are specific reactions of the colonic epithelium to carcinogenic treatment with DMH.     

Activity coefficients for NaCl-monosaccharide (D-glucose, D-galactose, D-xylose, D-arabinose)-water systems at 298.15 K

Electrochemical cells with a sodium ion selectivity electrode (Na-ISE) versus a chloride ion selectivity electrode (Cl-ISE) as a reference electrode were used to determine the activity coefficients for NaCl-monosaccharide (D-glucose, D-galactose, D-xylose, and D-arabinose) systems in water at 298.15 K. A comparison of the results thus obtained was made with those determined by another electromotive force (emf) method. It is shown that agreement is excellent. The Gibbs free energy parameters of the interactions between these sugars and NaCl in water were evaluated together with the parameter C1(CHOH, exo), indicating the interaction of the exocyclic CHOH group of saccharide molecules and NaCl. The results suggested that the interactions of these monosaccharides with NaCl are controlled mostly by the dominant conformer of their molecules in water.     

Modeling of ion permeation in calcium and sodium channel selectivity filters

Structure-function studies have shown that it is possible to convert a sodium channel to a calcium-selective channel by a single amino acid substitution in the selectivity filter locus. Ion permeation through the "model selectivity filter" was modeled with a reduced set of functional groups representative of the constituent amino acid side chains. Force-field minimizations were conducted to obtain the energy profile of the cations as they get desolvated and bind to the "model selectivity filter." The calculations suggest that the ion selectivity in the calcium channel is due to preferential binding, whereas in the sodium channel it is due to exclusion. Energetics of displacement of a bound cation from the calcium "model selectivity filter" by another cation suggest that "multi-ion mechanism" reduces the activation barrier for ion permeation. Thus, the simple model captures qualitatively most of the conduction characteristics of sodium and calcium channels. However, the computed barriers for permeation are fairly large, suggesting that ion interaction with additional residues along the transport path may be essential to effect desolvation.     

Improved RNA secondary structure prediction by maximizing expected pair accuracy

Free energy minimization has been the most popular method for RNA secondary structure prediction for decades. It is based on a set of empirical free energy change parameters derived from experiments using a nearest-neighbor model. In this study, a program, MaxExpect, that predicts RNA secondary structure by maximizing the expected base-pair accuracy, is reported. This approach was first pioneered in the program CONTRAfold, using pair probabilities predicted with a statistical learning method. Here, a partition function calculation that utilizes the free energy change nearest-neighbor parameters is used to predict base-pair probabilities as well as probabilities of nucleotides being single-stranded. MaxExpect predicts both the optimal structure (having highest expected pair accuracy) and suboptimal structures to serve as alternative hypotheses for the structure. Tested on a large database of different types of RNA, the maximum expected accuracy structures are, on average, of higher accuracy than minimum free energy structures. Accuracy is measured by sensitivity, the percentage of known base pairs correctly predicted, and positive predictive value (PPV), the percentage of predicted pairs that are in the known structure. By favoring double-strandedness or single-strandedness, a higher sensitivity or PPV of prediction can be favored, respectively. Using MaxExpect, the average PPV of optimal structure is improved from 66% to 68% at the same sensitivity level (73%) compared with free energy minimization.     

Transportation behavior of alkali ions through a cell membrane ion channel. A quantum chemical description of a simplified isolated model

Quantum chemical model calculations were carried out for modeling the ion transport through an isolated ion channel of a cell membrane. An isolated part of a natural ion channel was modeled. The model channel was a calixarene derivative, hydrated sodium and potassium ions were the models of the transported ion. The electrostatic potential of the channel and the energy of the channel-ion system were calculated as a function of the alkali ion position. Both attractive and repulsive ion-channel interactions were found. The calculations - namely the dependence of the system energy and the atomic charges of the water molecules with respect to the position of the alkali ion in the channel - revealed the molecular-structural background of the potassium selectivity of this artificial ion channel. It was concluded that the studied ion channel mimics real biological ion channel quite well.     

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.     

Simulation of the effect of an external GHz electric field on the potential energy profile of Ca2+ ions in the selectivity filter of the CaVAb channel

Ca_V channels are transmembrane proteins that mediate and regulate ion fluxes across cell membranes, and they are activated in response to action potentials to allow Ca²⁺ influx. Since ion channels are composed of charge or polar groups, an external alternating electric field may affect the ion‐selective membrane transport and the performance of the channel. In this article, we have investigated the effect of an external GHz electric field on the dynamics of calcium ions in the selectivity filter of the Ca_VAb channel. Molecular dynamics (MD) simulations and the potential of mean force (PMF) calculations were carried out, via the umbrella sampling method, to determine the free energy profile of Ca²⁺ ions in the Ca_VAb channels in presence and absence of an external field. Exposing Ca_VAb channel to 1, 2, 3, 4, and 5 GHz electric fields increases the depth of the potential energy well and this may result in an increase in the affinity and strength of Ca²⁺ ions to binding sites in the selectivity filter the channel. This increase of strength of Ca²⁺ ions binding in the selectivity filter may interrupt the mechanism of Ca²⁺ ion conduction, and leads to a reduction of Ca²⁺ ion permeation through the Ca_VAb channel.