Molecular dynamics simulation of cation motion in water-filled gramicidinlike pores.

A model calculation is carried out to study the potential energy profile of a sodium ion with several water molecules inside a simplified model of the gramicidin ion channel. The sodium ion is treated as a Lennard-Jones sphere with a point charge at its center. The Barnes polarizable water model is used to mimic the water molecules. A polarizable and deformable gramicidinlike channel is constructed based on the model obtained by Koeppe and Kimura. Potential minima and saddle points are located and the static energy barriers are computed. The potential minima at the two mouths of the channel exhibit an aqueous solvation structure very different from that at any of the interior minima. These sites are approximately 23.6 and 24.4 A apart for binding of a sodium ion and a cesium ion, respectively. Ionic motion from these exterior sites to the first interior minimum requires substantial rearrangement of the waters of solvation; this rearrangement may be the hydration/dehydration step in ionic permeation through the channel. Based on these results, a mechanism by which the sodium ion moves from the exterior binding site to the interior of the channel is proposed. Our model channel accommodates about eight water molecules and the transport of the ion and water within the channel is found to be single file. Results of less extensive calculations for Cs+ and Li+ ions in a channel with or without water are also reported.     

Possible Allosteric Significance of Water Structures in Proteins

Abstract

In recent theoretical molecular dynamics studies of ion solvation and transport through the model peptide ionophore, gramicidin A, it has been observed that the waters forming a linear single file within the channel have solvation and dynamic properties quite different from those found in bulk water. Strongly correlated motions among the interior single file column of waters persist over 20 Å. A speculation is entertained that related water structures could provide a mechanism for long range enzymatic allosteric effects as an alternative to chemical action at a distance propagated through the protein itself. Two possible specific mechanisms are discussed, hydraulic and “proton wire”. As a further control mechanism, the possibility is considered of modulating the allosteric effect though protein motion to open or close the channel thus producing a “valve” in the hydraulic line or a “switch” in the proton wire.     

Possible allosteric significance of water structures in proteins

In recent theoretical molecular dynamics studies of ion solvation and transport through the model peptide ionophore, gramicidin A, it has been observed that the waters forming a linear single file within the channel have solvation and dynamic properties quite different from those found in bulk water. Strongly correlated motions among the interior single file column of waters persist over 20 A. A speculation is entertained that related water structures could provide a mechanism for long range enzymatic allosteric effects as an alternative to chemical action at a distance propagated through the protein itself. Two possible specific mechanisms are discussed, hydraulic and "proton wire". As a further control mechanism, the possibility is considered of modulating the allosteric effect though protein motion to open or close the channel thus producing a "valve" in the hydraulic line or a "switch" in the proton wire.     

Water and polypeptide conformations in the gramicidin channel. A molecular dynamics study.

Theoretical studies of ion channels address several important questions. The mechanism of ion transport, the role of water structure, the fluctuations of the protein channel itself, and the influence of structural changes are accessible from these studies. In this paper, we have carried out a 70-ps molecular dynamics simulation on a model structure of gramicidin A with channel waters. The backbone of the protein has been analyzed with respect to the orientation of the carbonyl and the amide groups. The results are in conformity with the experimental NMR data. The structure of water and the hydrogen bonding network are also investigated. It is found that the water molecules inside the channel act as a collective chain; whereas the conformation in which all the waters are oriented with the dipoles pointing along the axis of the channel is a preferred one, others are also accessed during the dynamics simulation. A collective coordinate involving the channel waters and some of the hydrogen bonding peptide partners is required to describe the transition of waters from one configuration to the other.     

Structure and dynamics of hydronium in the ion channel gramicidin A.

The effects of the hydronium ion, H(3)0+, on the structure of the ion channel gramicidin A and the hydrogen-bonded network of waters within the channel were studied to help elucidate a possible mechanism for proton transport through the channel. Several classical molecular dynamics studies were carried out with the hydronium in either the center of a gramicidin monomer or in the dimer junction. Structural reorganization of the channel backbone was observed for different hydronium positions, which were most apparent when the hydronium was within the monomer. In both cases the average O-O distance between the hydronium ion and its nearest neighbor water molecule was found to be approximately 2.55 A, indicating a rather strong hydrogen bond. Importantly, a subsequent break in the hydrogen-bonded network between the nearest neighbor and the next-nearest neighbor(approximately 2.7 -3.0 A) was repeatedly observed. Moreover, the carbonyl groups of gramicidin A were found to interact with the charge on the hydronium ion, helping in its stabilization. These facts may have significant implications for the proton hopping mechanism. The presence of the hydronium ion in the channel also inhibits to some degree the reorientational motions of the channel water molecules.     

Solvent effects in ionic transport through transmembrane protein channels

Ion transport through a gramicidin A like channel in the presence of solvent molecules with van der Waals parameters of water has been studied by means of the molecular dynamics simulation technique. It was found that the presence of solvent molecules in the channel has a tendency to equalize the effective masses of the ions through "association" thus giving the experimentally found ion selectivity to the gramicidin A channel.     

Time-correlation analysis of simulated water motion in flexible and rigid gramicidin channels.

Molecular dynamics simulations have been done on a system consisting of the polypeptide membrane channel former gramicidin, plus water molecules in the channel and caps of waters at the two ends of the channel. In the absence of explicit simulation of the surrounding membrane, the helical form of the channel was maintained by artificial restraints on the peptide motion. The characteristic time constant of the artificial restraint was varied to assess the effect of the restraints on the channel structure and water motions. Time-correlation analysis was done on the motions of individual channel waters and on the motions of the center of mass of the channel waters. It is found that individual water molecules confined in the channel execute higher frequency motions than bulk water, for all degrees of channel peptide restraint. The center-of-mass motion of the chain of channel waters (which is the motion that is critical for transmembrane transport, due to the mandatory single filing of water in the channel) does not exhibit these higher frequency motions. The mobility of the water chain is dramatically reduced by holding the channel rigid. Thus permeation through the channel is not like flow through a rigid pipe; rather permeation is facilitated by peptide motion. For the looser restraints we used, the mobility of the water chain was not very much affected by the degree of restraint. Depending on which set of experiments is considered, the computed mobility of our water chain in the flexible channel is four to twenty times too high to account for the experimentally measured resistance of the gramicidin channel to water flow. From this result it appears likely that the peptide motions of an actual gramicidin channel embedded in a lipid membrane may be more restrained than in our flexible channel model, and that these restraints may be a significant modulator of channel permeability. For the completely rigid channel model the "trapping" of the water molecules in preferred positions throughout the molecular dynamics run precludes a reasonable assessment of mobility, but it seems to be quite low.     

Structure and dynamics of one-dimensional ionic solutions in biological transmembrane channels.

The structure and dynamics of solvated alkali metal cations in transmembrane channels are treated using the molecular dynamics simulation technique. The simulations are based on a modified Fischer-Brickmann model (Fischer, W., and J. Brickmann, 1983, Biophys. Chem., 18:323-337) for gramicidin A-type channels. The trajectories of all particles in the channel as well as two-dimensional pair correlation functions are analyzed. It is found from the analysis of the stationary simulation state that one-dimensional solvation complexes are formed and that the number of water molecules in the channel varies for different alkali metal cations.     

Sodium in gramicidin: an example of a permion.

The reaction path and free energy profile of Na+ were computed in the interior of the channel protein gramicidin, with the program MOIL. Gramicidin was represented in atomic detail, but surrounding water and lipid molecules were not included. Thus, only short range interactions were investigated. The permeation path of the ion was an irregular spiral, far from a straight line. Permeation cannot be described by motions of a single Na+ ion. The minimal energy path includes significant motion of water and channel atoms as well as motion of the permeating ion. We think of permeation as motion of a permion, a quasi-particle that includes the many body character of the permeation process, comparable with quasi-particles like holes, phonons, and electrons of solid-state physics. Na+ is accompanied by a plug of water molecules, and motions of water, Na+, and the atoms of gramicidin are highly correlated. The permion moves like a linear polymer made of waters and ion linked and moving coherently along a zigzag line, following the reptation mechanism of polymer transport. The effective mass, free energy, and memory kernel (of the integral describing time-dependent friction) of short range interactions were calculated. The effective mass of the permion (properly normalized) is much less than Na+. Friction varies substantially along the path. The free energy profile has two deep minima and several maxima. In certain regions, the dominant motions along the reaction path are those of the channel protein, not the permeating ion: there, ion waits while the other atoms move. At these waiting sites, the permion's motion along the reaction path is a displacement of the atoms of gramicidin that prepare the way for the Na+ ion.     

Stochastic theory of ion movement in channels with single-ion occupancy. Application to sodium permeation of gramicidin channels.

The electrodiffusion equations were solved for the one-ion channel both by the analytical method due to Levitt and also by Brownian dynamic simulations. For both types of calculations equilibration of ion distribution between the bath and the ends of the channel was assumed. Potential profiles were found that give good fits to published data on Na+ permeation of gramicidin channels. The data were best fit by profiles that have no relative energy maximum at the mouth of the channel. This finding suggests that alignment of waters or channel charged groups inside the channel in response to an ion's approach may provide an energetically favorable situation for entry sufficient to overcome the energy required for removing bulk waters of hydration. An alternative possibility is that the barrier to ion entry is situated outside the region restricted to single-ion occupancy. Replacement of valine with more polar amino acids at the No. 1 location was found to correspond to a deepening of the potential minima near the channel mouths, an increase in height of the central barrier to ion translocation across the channel, and possibly a reduction in the mobility of the ion-water complex in the channel. The Levitt theory was extended to calculate passage times for ions to cross the channel and the blocking effects of ions that entered the channel but didn't cross. These quantities were also calculated by the Brownian dynamics method.     

Semi-Markov models for brownian dynamics permeation in biological ion channels

Constructing accurate computational models that explain how ions permeate through a biological ion channel is an important problem in biophysics and drug design. Brownian dynamics simulations are large-scale interacting particle computer simulations for modeling ion channel permeation but can be computationally prohibitive. In this paper, we show the somewhat surprising result that a small-dimensional semi-Markov model can generate events (such as conduction events and dwell times at binding sites in the protein) that are statistically indistinguishable from brownian dynamics computer simulation. This approach enables the use of extrapolation techniques to predict channel conduction when performing the actual brownian dynamics simulation that is computationally intractable. Numerical studies on the simulation of gramicidin A ion channels are presented.     

Valence selectivity of the gramicidin channel: a molecular dynamics free energy perturbation study.

The valence selectivity of the gramicidin channel is examined using computer simulations based on atomic models. The channel interior is modeled using a gramicidin-like periodic poly (L,D)-alanine beta-helix. Free energy perturbation calculations are performed to obtain the relative affinity of K+ and Cl- for the channel. It is observed that the interior of the gramicidin channel provides an energetically favorable interaction site for a cation but not for an anion. Relative to solvation in bulk water, the carbonyl CO oxygens can provide a favorable interaction to stabilize K+, whereas the amide NH hydrogens are much less effective in stabilizing Cl-. The results of the calculations demonstrate that, as a consequence of the structural asymmetry of the backbone charge distribution, a K+ cation can partition spontaneously from bulk water to the interior of the gramicidin channel, whereas a Cl- anion cannot.     

Ion transport in a model gramicidin channel. Structure and thermodynamics.

The potential of mean force for Na+ and K+ ions as a function of position in the interior of a periodic poly(L,D)-alanine model for the gramicidin beta-helix is calculated with a detailed atomic model and realistic interactions. The calculated free energy barriers are 4.5 kcal/mol for Na+ and 1.0 kcal/mol for K+. A decomposition of the free energy demonstrates that the water molecules make a significant contribution to the free energy of activation. There is an increase in entropy at the transition state associated with greater fluctuations. Analysis reveals that the free energy profile of ions in the periodic channel is controlled not by the large interaction energy involving the ion but rather by the weaker water-water, water-peptide and peptide-peptide hydrogen bond interactions. The interior of the channel retains much of the solvation properties of a liquid in its interactions with the cations. Of particular importance is the flexibility of the helix, which permits it to respond to the presence of an ion in a fluidlike manner. The distortion of the helix is local (limited to a few carbonyls) because the structure is too flexible to transmit a perturbation to large distances. The plasticity of the structure (i.e., the property to deform without generating a large energy stress) appears to be an essential factor in the transport of ions, suggesting that a rigid helix model would be inappropriate.     

Molecular dynamics simulations of the gramicidin A-dimyristoylphosphatidylcholine system with an ion in the channel pore region

To investigate the process of ion permeation in an ion channel systematically, we performed molecular dynamics (MD) simulations on a gramicidin A (GA)-phospholipid model system with an ion in the channel pore region. Each of the three types of ions (Ca2+, Na+ Cl-) was placed at five different positions along the channel axis by replacing a water molecule. MD simulations were performed on each system at constant pressure and constant temperature. The MD trajectories showed that the Ca2+ and Na+ ions could stably fluctuate in the pore region, but the Cl- ion was pushed out because of the unfavorable interaction with the channel. This result is consistent with experimental data. It was also found that the conformation of the GA channel underwent a significant change due to the presence of the ion, and the two ends of the GA monomer were more flexible than its middle region. In particular, the dramatic change of local pore radius near the ion indicated this kind of deformation. The strong interaction between the ion and carbonyl oxygen atoms of GA was the major contributor to this change. Furthermore, it was found that the ethanolamine group of the GA molecule was the most flexible group in the GA channel and often observed to block the entrance of GA. These results imply that the deformation of channel structure plays a very important factor in ion permeation, and the ethanolamine group may play a key role in regulating ion entry into the pore. In conclusion, our results indicate that the ion has a dominant influence on the structure of the GA channel and that the flexibility of the ion channel is a crucial factor in the ion permeation process.     

Influence of protein flexibility on the electrostatic energy landscape in gramicidin A

We describe an electrostatic model of the gramicidin A channel that allows protein atoms to move in response to the presence of a permeating ion. To do this, molecular dynamics simulations are carried out with a permeating ion at various positions within the channel. Then an ensemble of atomic coordinates taken from the simulations are used to construct energy profiles using macroscopic electrostatic calculations. The energy profiles constructed are compared to experimentally-determined conductance data by inserting them into Brownian dynamics simulations. We find that the energy landscape seen by a permeating ion changes significantly when we allow the protein atoms to move rather than using a rigid protein structure. However, the model developed cannot satisfactorily reproduce all of the experimental data. Thus, even when protein atoms are allowed to move, the dielectric model used in our electrostatic calculations breaks down when modeling the gramicidin channel.     

Ab initio molecular dynamics study of proton transfer in a polyglycine analog of the ion channel gramicidin A.

Proton transfer in biological systems is thought to often proceed through hydrogen-bonded chains of water molecules. The ion channel, gramicidin A (gA), houses within its helical structure just such a chain. Using the density functional theory based ab initio molecular dynamics Car-Parrinello method, the structure and dynamics of proton diffusion through a polyglycine analog of the gA ion channel has been investigated. In the channel, a proton, which is initially present as hydronium (H3O+), rapidly forms a strong hydrogen bond with a nearest neighbor water, yielding a transient H5O2+ complex. As in bulk water, strong hydrogen bonding of this complex to a second neighbor solvation shell is required for proton transfer to occur. Within gA, this second neighbor shell included not only a channel water molecule but also a carbonyl of the channel backbone. The present calculations suggest a transport mechanism in which a priori carbonyl solvation is a requirement for proton transfer.     

Molecular dynamics simulation accurately predicts the experimentally-observed distributions of the (C, N, O) protein atoms around water molecules and sodium ions

A molecular dynamics simulation of the operator binding domain of the lambda repressor protein has been carried out. The protein was embedded in explicit waters, Na(+) and CL(-) ions. The Amber 4.1 computer package and the Cornell et al. Force field were used for energy-minimization and molecular dynamics simulation. We find that the atoms distributions in the environment of waters and Na(+) ions are in excellent agreement with those derived from the analysis of water molecules in crystal structures and ion-binding proteins. We also find that, on the whole, both distributions are similar to each other.     

Simulation of voltage-driven hydrated cation transport through narrow transmembrane channels.

Molecular dynamics studies for the voltage-driven transport of the alkali metal ions lithium, sodium, and potassium through gramicidin A-type channels filled with water molecules are presented. The number of water molecules in the channel is obtained from a previous study (Skerra, A., and J. Brickmann, 1987, Biophys. J., 51:969-976). It is shown that the selectivity of the intrachannel ion diffusion through our model pore conforms to the experimentally observed selectivity of the gramicidin A channel. It is demonstrated that the number of water molecules in the channel plays a key role for the selectivity.     

Extended dipolar chain model for ion channels: electrostriction effects and the translocational energy barrier.

We reinvestigate the dipolar chain model for an ion channel. Our goal is to account for the influence that ion-induced electrostriction of channel water has on the translocational energy barriers experienced by different ions in the channel. For this purpose, we refine our former model by relaxing the positional constraint on the ion and the water dipoles and by including Lennard-Jones contributions in addition to the electrostatic interactions. The positions of the ion and the waters are established by minimization of the free energy. As before, interaction with the external medium is described via the image forces. Application to alkali cations show that the short range interactions modulate the free energy profiles leading to a selectivity sequence for translocation. We study the influence of some structural parameters on this sequence and compare our theoretical predictions with observed results for gramicidin.