Modeling ion permeation through a bacterial voltage-gated calcium channel Ca_VAb using molecular dynamics simulations

Abstract

Activation of voltage-gated calcium channels by action potentials leads to the influx of Ca²⁺ ions. In this study, the ion permeation characteristics in bacterial voltage-gated calcium (Ca_VAb) channels were investigated using molecular dynamics simulations. Furthermore, the potential of mean force (PMF) calculations was evaluated to determine the free energy profile for the permeation of cations (Ca²⁺ and Na⁺) and anions (Cl⁻) in the Ca_VAb channel. The results showed that both Ca²⁺ and Na⁺ cations experienced a deep energy well, while the Cl⁻ anion experienced a relatively high energy barrier at the center of the selectivity filter (site 2). Consistent with the experimental data, the results obtained from this study demonstrate that sites 2 and 3 displayed the highest and lowest affinities to Ca²⁺, respectively. These findings also indicate that Na⁺ can easily and quickly pass through the Ca_VAb channel in the absence of Ca²⁺, while Cl⁻ ions lack this ability.

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1. Introduction

Ion channels are pores in cell membranes that allow for the passive diffusion of ions. The channels often contain a highly selective transport system for particular ions, permitting individual ions to move due to the concentration gradient.¹

Voltage-gated calcium (Ca_V) channels, in response to action potentials, are activated in a variety of cell types, leading to the influx of calcium (Ca²⁺) ions. These ions act as secondary messengers in electrical signaling, promoting a number of different cellular events.² Ca²⁺ signaling occurs in the entire life-history of an organism. It is widely believed that life begins with a sudden onset of Ca²⁺ during fertilization. This multifunctional system continues to control a wide variety of processes during development and adult life. In addition to fertilization, Ca²⁺ ions play an important role in gene expression, apoptosis, as well as cell proliferation and differentiation.³

A fundamental problem in the analysis of ion conduction through cell membrane channels is to find out how the channels can be highly selective and can simultaneously conduct millions of ions per second. Ca²⁺ ions pass through Ca_V channels at a rate of 10⁶ per second, while Na⁺ conductance is approximately lower by 500-fold.⁴ Because the extracellular Na⁺ concentration is 70-fold higher than that of Ca²⁺, calcium channels need to be highly selective for Ca²⁺ over Na⁺, notwithstanding the fact that these two ions are roughly similar in size, each about 2 Angstroms in diameter. It is proposed that the ion selectivity of the Ca_V channel results from the high-affinity of Ca²⁺ binding to the selectivity filter, which prevents the influx of Na⁺. The rapid flow of the Ca²⁺ flux through the Ca_V channels seems to employ a knock-off mechanism in which the electrostatic repulsions between the Ca²⁺ ions in the selectivity filter overcome the strong binding of a single Ca²⁺ ion. Ionic repulsions between the adjacent Ca²⁺ ions at these sites allow rapid conduction despite the intrinsic high affinity for Ca²⁺ binding.^4,5

Ca_V channels consist of a single ion-selective pore within the central part of four identical subunits. The central pore consists of two transmembrane sections S5 and S6, together with an interposing ‘pore (P)-loop’ from each domain in a four-fold pseudosymmetrical arrangement. Four voltage sensing modules, comprising S1–S4 transmembrane helices, are symmetrically organized around the central pore (Fig. 1a). Ca_V channels, closely related to voltage-gated Na⁺ (Na_V) channels, are known to be members of the voltage-gated ion channel superfamily.^6–8

Fig. 1 (a) Top view of the Ca_VAb channel structure. The structure of the transmembrane domain of a Ca_VAb channel with four subunits represented by different colors. The 1–6, transmembrane segments S1–S6 subunits are highlighted in white. Ca²⁺ binding sites in the selectivity filter of the Ca_VAb channel. The top view of binding site 1 (b), site 2 (c) and site 3 (d) in the selectivity filter. A symmetry-related backbone is shown by the yellow stick representation; the selected residues (D178, D177, L178 and T175) in the selectivity filter, Ca²⁺ ions and water molecules are illustrated in CPK, blue spheres as well as red and white CPK spheres, respectively. The interaction between Ca²⁺ and oxygen atoms is indicated by dashed lines for site 1 (black lines), site 2 (black and green lines) and site 3 (black lines). (e) Side view of the selectivity filter. The backbone and Ca²⁺ ions are shown in a green stick format and yellow spheres, respectively. The interaction between Ca²⁺ and oxygen atoms is indicated by dashed lines for site 1 (black lines), site 2 (red and blue lines) and site 3 (brown lines). For clarity, the subunit closest to the viewer is not shown. Graphics were rendered with VMD.³⁸

An Na_V channel from Arcobacter butzleri (Na_VAb) has four pore motifs (¹⁷⁵TLESWSM¹⁸¹), forming the ion selectivity filter.⁶ To make a Ca_VAb channel, the amino acids E177, S178 and M181 of the selectivity filter in the Na_VAb channel (PDB code: 3RVY) are replaced by aspartic acid (Asp or D) (¹⁷⁵TLDDWSD¹⁸¹). Unlike Na_VAb that does not conduct extracellular Ca²⁺ ions, Ca_VAb mediates the influx of Ca²⁺ ions into the cells in a voltage-dependent fashion. The Ca²⁺ selectivity of Ca_VAb is primarily determined by the side chains of the amino acids in the selectivity filter.⁹

In the selectivity filter of Ca_VAb (¹⁷⁵TLDDWSD¹⁸¹), there are three binding sites from the extracellular side to the intracellular side, including sites 1, 2 and 3 (Fig. 1e).⁹ At site 1, Ca²⁺ is surrounded by carboxyl groups of D178 located at the outer entrance to the selectivity filter. Further into the pore, there are four acidic side chains of D177 in the wall of the selectivity filter, as well as four side chains of L176 below, leading to the creation of site 2. Unlike site 1, the central Ca²⁺-binding site (site 2) is surrounded by four carboxylate oxygen atoms of D177 above and four backbone carbonyl oxygen atoms of L176 below. The third Ca²⁺ binding site (site 3) is located on the intracellular side of the pore, composed of four carbonyl oxygen atoms of L176 (Fig. 1). In Ca_VAb, permeating ions mainly interact with the amino acid side chains and backbone carbonyl groups in the ion selectivity filter through bound hydration water.⁹

Some theoretical models have been proposed to describe the mechanism of ion selectivity and conductance in Ca²⁺ channels.^10–12 Although these models provide helpful insights into how Ca²⁺ channels may obtain high-throughput selectivity profiles, they are incapable of relating the structural parameters of the channel to its functional elements.¹³

The first attempt to determine the relationship between the observed functional properties of the Ca²⁺ channel and its structure, and to calculate the channel conductance, was made using the Poisson–Nernst–Planck (PNP) theory.¹⁴ Following that, the mechanisms of ion transport and selectivity in Ca²⁺ channels were examined using Brownian dynamics simulations. In that study, the channel was modeled as a rigid structure with fixed charges in the walls, assuming that the glutamate residues were considered to be responsible for ion selectivity.¹⁵

The X-ray images of membrane channels obtained from experimental studies provide an extensive amount of information about the channels.¹⁶ The aim of the present study is to investigate the ion permeation characteristics in the voltage-gated calcium channels. There are several methods for free energy calculation, among these algorithms single ion potential of mean force (PMF) calculations using the umbrella sampling (US) method has been widely used in the investigations of ion channel conduction and selectivity.^17–21 In this study, molecular dynamics (MD) simulations and single ion PMF calculations were carried out to determine the free energy profiles for the permeation of cations (Ca²⁺ and Na⁺) and anions (Cl⁻), thus allowing the calculation of the relative free energies of each ion in the bacterial calcium channel Ca_VAb.

The paper is organized as follows. In Section 2 we provide the modeling methods used in this work. In Section 3 we report our results and discussions, and in Section 4 we provide our conclusions.

2. Methods

2.1 Construction of the MD systems

The initial crystal structure of the calcium channel (Ca_VAb) was obtained from the Protein Data Bank (PDB ID:4MVQ).⁹ Only the pore-forming region from residues 129 to 218 was included in the simulations.²² It should be noted that the pore is made up of four chains (A, B, C and D), and each chain of four identical chains, and residues 129 to 218 have been selected as the pore-forming region. The protein was embedded in an equilibrated membrane consisting of 151 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) lipids using the g_membed tool,²³ a part of the Gromacs package.²⁴ Bulk water molecules were substituted by Ca²⁺ and Cl⁻ ions to achieve an ionic concentration of 150 mM. For the simulations involving Na⁺, one Ca²⁺ ion was replaced with Na⁺, and one Cl⁻ ion was removed to neutralize the system. The system was further equilibrated for the free energy simulations.

All simulations were carried out using the Gromacs simulation software v.4.5.5.²⁴ CHARMM-36 force fields^25,26 were utilized for the lipids and protein, and the TIP3P model was used for the water molecules.²⁷ Electrostatic interactions were calculated at each step by using the particle-mesh Ewald method²⁸ with the short-range electrostatic interaction cut off of 1.4 nm. The LINCS algorithm²⁹ was also used to constrain all H-bonds, allowing an integration step-size of 2 fs. In addition, the Lennard-Jones potential was used with a cutoff of 1.4 nm. The Nose–Hoover thermostat was used to keep the simulation temperature constant by separately coupling the protein, lipids and the solvent (water and ions) to a temperature bath at T = 300 K. Furthermore, the pressure was kept constant at 1 bar by using the Parrinello–Rahman barostat algorithm with a coupling constant of 1 ps. After minimization, the systems were equilibrated for 5 ns. The complete system consisted of the protein, 151 POPC, 7089 TIP3P-water molecules, 55 Ca²⁺ and 86 Cl⁻ (for the system consisting of Ca²⁺ and Cl⁻ ions) or 54 Ca²⁺, 85 Cl⁻ and 1 Na⁺ (for the system consisting of Na⁺, Ca²⁺ and Cl⁻ ions), yielding a system with approximately 47 600 atoms, as illustrated in Fig. 2(a).

Fig. 2 (a) Simulation system. A cross section of the simulation system is shown here. The Ca_VAb protein was embedded into a bilayer lipid containing POPC (in licorice representation), and solvated by TIP3P water (in Surf representation). Protein chains, selectivity filter, Ca²⁺ and Cl⁻ are shown in purple, green, red and yellow, respectively. For clarity, only two of the four protein subunits are presented here. (b) Illustration of the reaction coordinates chosen for the umbrella sampling simulations. The analysis of the reaction pathway was undertaken as the principal axis of the protein channel, designed to be the z axis of the simulation box. The red balls indicate the position of the Ca²⁺ ions. Only a tiny fraction of all positions used as the reference position for the biasing potential is shown here. The lipid bilayer, the selectivity filter for ion permeation, water molecules, Ca²⁺, Cl⁻ and protein are indicated by a licorice representation, green, dot representation, red, yellow and Surf representation, respectively. For clarity, the protein subunit closest to the viewer is not shown. The above graphics were rendered with VMD.³⁸

2.2 Umbrella sampling

The umbrella sampling (US) method was applied to determine the potential of mean force (PMF) of ion permeation.³⁰ Umbrella sampling simulations were used to achieve biased position histograms along the ion reaction coordinates. Since ion permeation has an activation barrier beyond 1.5k_BT,³¹ classical MD simulations would not generate sufficient sampling. However, the umbrella sampling technique is a useful method to overcome this problem; the ion movement is restrained to positions along the reaction coordinates by using a biased potential.²¹

The reaction pathway was determined as the principal axis of the protein channel, designed to be the Z axis of the simulation box (Fig. 2b). The entire pathway covering the range of [−8, 20] Å was divided into 0.7 Å intervals adding up to a total of 40 windows. The ion was subsequently placed into the center of each window, removing overlapping water molecules, followed by energy minimization. In all cases, ion positions were determined according to the center-of-mass (COM) of the channel selectivity filter.

The initial structures used in the window sampling were selected from the structures obtained during the last 5 ns of equilibration. During the umbrella simulation, a harmonic potential of 1000 kJ mol⁻¹ nm⁻² was used to restrain the sampled ion around the center of the window. Each umbrella window was simulated for 1.1 ns in the NPT ensemble. For the analysis, the first 100 ps was omitted as equilibration. The free energy profile was calculated using the g_wham tool, a part of the Gromacs software. The statistical error was estimated with 200 bootstrap iterations.³²

3. Results and discussion

3.1 Structural stability

The protein conformational changes were analyzed by using RMSD with respect to its initial crystallographic structure. Based on the initial structure, the backbone conformational changes were measured over time. In all the simulations, the RMSD of the backbone atoms was about 1.5 Å, reflecting the stability of the channel (Fig. 3).

Fig. 3 RMSD of the backbone atoms for the Ca_VAb protein according to its initial structure as a function of simulation time, demonstrating the stability of the structures.

3.2 Potential of mean force of ions

In the present study, to evaluate the channel selectivity towards Ca²⁺, Na⁺ and Cl⁻ ions, the free energy profiles (PMF) of these three ions were obtained using molecular dynamics simulation and the umbrella sampling method.

3.2.1 PMF of Ca²⁺ in the Ca_VAb channel. In Fig. 4, the free energy profiles of the permeation of a single Ca²⁺ ion through the Ca_VAb channel selectivity filter are illustrated. The PMF profile for Ca²⁺ indicates that the ion is attracted from the bulk (on the right side of the figure) into the channel selectivity filter. The free energy is shown as a function of ion distance from the center-of-mass of the selectivity filter.

Fig. 4 (top) PoreWalker³⁹ output for the Ca_VAb channel. Visualization of a pore section from the Ca_VAb channel. Pore-lining atoms and residues are depicted in orange and blue, respectively. The remaining part of the protein is shown in green. Red spheres illustrate pore centers and their diameters are 1/10 of the pore diameter estimated at that position; the selectivity filter is indicated by the black dashed line box. (Middle panel) Side view of the selectivity filter. Residues in the selectivity filter ¹⁷⁵TLDDWSD¹⁸¹ are shown in a green stick format, and the ion binding sites (S1, S2 and S3) along the ion pathway are illustrated by s1–3 in blue spheres. Only two subunits have been shown for clarity. (Bottom panel) The potential of mean force. The PMF for Ca²⁺ (blue), Na⁺ (red) and Cl⁻ (green) calculated via umbrella sampling is shown as a function of the axial position of the ion, zeroed at the center of the selectivity filter. The ion is represented in bulk water on the right side of the graph and in the central cavity of the channel on the left hand side. The statistical error was estimated with 200 bootstrap iterations.

While Ca²⁺ moves from the bulk to the center of the selectivity filter (about Z = 0 nm), the free energy decreases, but then increases until the end of the selectivity filter. In the PMF of Ca²⁺, there is a deep energy well (about 21.5 kcal mol⁻¹ lower than the bulk value) at the center of the selectivity filter. For Ca²⁺ permeation, the lowest global minimum energy is in accordance with a conformation in which a Ca²⁺ ion is placed at site 2 adjacent to the D177 and L176 residues (about Z = 0 nm).

The energy state decreased (5 kcal mol⁻¹ lower than the bulk value) at the point of the Ca²⁺ entry from the bulk into the opening of the selectivity filter (about Z = 1 nm). In this position, the ion is surrounded by four carboxyl oxygen atoms of D181. In fact, the presence of four negatively charged residues of D181, attracting positively charged Ca²⁺ ions, is the reason why the energy decreases. The energy continues to decrease with a relatively sharp gradient (14 kcal mol⁻¹ lower than the bulk value) from the opening of the selectivity filter (Z = 1 nm) to the binding site 1 (Z = 0.6 nm). In this position, Ca²⁺ is surrounded by four carboxyl oxygen atoms of D178 located at a closer distance than the ion, resulting in a further decrease in the free energy (Fig. 1b). From this point (site 1) onwards, there is a continuous decrease in energy, until reaching the lowest minimum energy (21.5 kcal mol⁻¹ lower than the bulk value) at binding site 2 (Z = 0 nm). At this site, the Ca²⁺ ion is surrounded by four carboxyl oxygen atoms of D177, and four carbonyl oxygen atoms of leu176 (L176) (Fig. 1c). In this region, four carboxyl oxygen and four carbonyl oxygen molecules are attractive enough to make a deep energy well and strongly hold the Ca²⁺ ion in the position. The energy increases steeply for the inward movement of the Ca²⁺ ion from site 2 until it reaches site 3. At site 3, the energy is 9.5 kcal mol⁻¹ greater than the global energy minimum. In this position, Ca²⁺ is surrounded by carbonyl oxygen atoms of Thr175 (T175) (Fig. 1d). In fact, an approximately 9.5 kcal mol⁻¹ energy barrier inhibits the Ca²⁺ ion from exiting its global energy minimum (site 2, Z = 0 nm) and reaching site 3 (Z = −0.6 nm).

The results from this study show that the Ca²⁺ cation experiences a deep energy well at the center of the selectivity filter. A deep energy well has also been observed in other ion channels.^17,33 The lowest global minimum energy for Ca²⁺ is found at site 2 and in the vicinity of D177 and L176 residues (about Z = 0 nm). This deep energy well shows that the Ca²⁺ ion has the highest binding affinity towards site 2, revealing that the stabilization region of Ca²⁺ is at site 2 of the Ca_VAb channel. The evidence for this claim comes from the fact that the movement of calcium ions from site 2 (the center of the selectivity filter) to the binding site 3 (the internal end of the selectivity filter, Z = −0.6 nm) will result in an increase in the free energy, as compared to that of the global minimum energy. The Ca²⁺ ion has to overcome an energy barrier of about 9.5 kcal mol⁻¹ to exit from the global minimum energy. The energy differences between Ca²⁺ ions occupying site 2 (global minimum energy) and Ca²⁺ ions occupying sites 1 (about Z = 0.6 nm) and 3 (about Z = −0.6 nm) were found to be 8.5 and 9.5 kcal mol⁻¹, respectively, indicating that the affinity for site 1 of the Ca²⁺ ion is higher than that of site 3. Larger energy differences and, therefore, more affinity for site 1, seem to be due to more negative charges at this site. Also, results show that site 2 (the central site) and site 3 display the highest and lowest affinities to Ca²⁺ ions, respectively, consistent with the experimental data.⁹ It is proposed that three Ca²⁺ binding sites are required for ion permeation, and only site 2 binds to divalent cations with sufficient affinity to potentially block the channel.³⁴ The intermediate affinity of sites 1 and 3 facilitates Ca²⁺ movement into and out of the central high affinity site, which can result in a high ion conductance.⁹ It is also proposed that the Ca_V channel ion selectivity results from the high-affinity Ca²⁺ binding to the selectivity filter that prevents the influx of Na⁺. On the other hand, at low Ca²⁺ concentrations, a single Ca²⁺ ion strongly attaches to this position (site 2), and inhibits the entry of Na⁺. In this study, because there is a single Ca²⁺ ion at the center of the selectivity filter (site 2), it is similar to low Ca²⁺ concentrations and the free energy graph shows blocking of the ion channel. At high Ca²⁺ concentrations, the rapid flow of the Ca²⁺ flux through the Ca_V channels seems to utilize a knock-off mechanism wherein the electrostatic repulsions between the Ca²⁺ ions in the selectivity filter overcome the strong binding of a single Ca²⁺ ion. Ionic repulsions between the adjacent Ca²⁺ ions at these sites allow rapid conduction despite the intrinsic high affinity for Ca²⁺ binding.^4,5 The Ca_VAb selectivity filter is wide (6 Å diameter) and the ionic diameter of Ca²⁺ is about 2.2 Å. So, the distance between ion and carbonyl and carboxyl groups of ion-binding sites is large. For this reason, it is suggested that the Ca²⁺ ions bind to ion-binding sites (S1, S2 and S3) in a hydrated form through bound water molecules (Fig. 1b–d).⁹ The sites equivalent to sites S1 and S3 in the free energy graph (local minimum energy) are lost probably because the selectivity filter is wide and there is a hydrated form of ion in the selectivity filter.

3.2.2 PMF of Na⁺ in the Ca_VAb channel. Like Ca²⁺, the PMF of the Na⁺ ion exhibits a deep energy well at the center of the selectivity filter at site 2 (Z = 0 nm) (Fig. 4). Site 2 is particularly favorable for both Ca²⁺ and Na⁺ ions in the filter of Ca_VAb.

Similar to the Ca²⁺ ion, when the Na⁺ ion moves through the bulk (Z > 1 nm) to the opening of the selectivity filter (Z = 1 nm), four negatively charged residues of D181 at the opening of the selectivity filter attract Na⁺ cations, and then the free energy is reduced, compared to the bulk (1.5 kcal mol⁻¹ lower than the bulk value). While moving to site 1 (Z = 0.6 nm), Na⁺ is surrounded by four carboxyl oxygen atoms of D178 located at a closer distance than the ion, resulting in a further decrease in the free energy (6.5 kcal mol⁻¹ lower than the bulk value). When reaching the center of the selectivity filter (site 2, Z = 0 nm), Na⁺ is surrounded by four carboxyl oxygen atoms of D177 and four carbonyl atoms of L176. The presence of such strong binding interactions leads to the formation of a deep energy well (19 kcal mol⁻¹ lower than the bulk value) in this position. When reaching site 3, the energy (in the vicinity of the T175, Z = −0.6 nm) increases, as compared to the global energy minimum (16.5 kcal mol⁻¹ lower than the bulk value). Like Ca²⁺, the PMF of Na⁺ exhibits a global minimum energy at site 2 (19 kcal mol⁻¹ lower than the bulk value), where it is surrounded by the rings of carboxyl and carbonyl oxygen atoms. The value of the global minimum energy for Na⁺ is 2.5 kcal mol⁻¹ lower than that for Ca²⁺, indicating that Ca²⁺ binds to the filter more tightly than Na⁺ does. Because Ca²⁺ is more electropositive than Na⁺, it binds more tightly to the selectivity filter, and blocks Na⁺ conductance at low Ca²⁺ concentrations, resulting in the preferential permeation of Ca²⁺ at higher Ca²⁺ concentrations.⁹ An approximately 2.5 kcal mol⁻¹ energy barrier prevents the Na⁺ ion from exiting its global energy minimum configuration in the selectivity filter (site 2) and reaching site 3 (in the vicinity of T175, Z = −0.6 nm). To pass through from site 2 to site 3, the Na⁺ ion has to overcome a 2.5 kcal mol⁻¹ energy barrier, while not only does Ca²⁺ have a larger global minimum energy than Na⁺ (2.5 kcal mol⁻¹ deeper) at site 2, but also the energy level of site 3 for Ca²⁺ is 4.5 kcal mol⁻¹ higher than that of Na⁺, resulting in the need for a higher energy (9.5 kcal mol⁻¹) to move through this barrier and reach site 3. For this reason, Na⁺ seems to easily pass through Ca_VAb channels in the absence of Ca²⁺. In line with our results, other studies have consistently demonstrated that Na⁺ can pass through the channel higher than Ca²⁺ in the absence of Ca²⁺ ions.^35–37 At low Ca²⁺concentrations, a single Ca²⁺ ion strongly attaches to this position (site 2), and inhibits the entry of Na⁺. On the other hand, at high Ca²⁺ concentrations, ionic repulsions between the adjacent Ca²⁺ ions at the binding sites allow rapid conductance, despite the intrinsic high affinity for Ca²⁺ binding.^4,5

3.2.3 PMF of Cl⁻ in the Ca_VAb channel. To better understand the valence selectivity mechanism in channels, the PMF profile of Cl⁻ anions (in addition to the Na⁺ and Ca⁺ cations) through Ca_VAb was determined separately. Cl⁻ exhibits a different PMF profile from Na⁺ and Ca²⁺ cations in the Ca_VAb selectivity filter, and experiences a large barrier inside the channel selectivity filter (Fig. 4). This barrier increases by staying close to the center of the selectivity filter (Z = 0 nm).

The PMF of Cl⁻ steadily increases by staying close to the selectivity filter. In contrast to Na⁺ and Ca²⁺ cations, the free energy of Cl⁻ anions continues to increase when the ion passes through the bulk to the center of the selectivity filter (site 2, Z = 0 nm) and then decreases when the ion moves to site 3 (Z = −0.6 nm).

When getting closer to the opening of the selectivity filter, a Cl⁻ anion is surrounded by four negatively charged residues of D181, and repulsive forces between the negatively charged ions and aspartate residues increase (5 kcal mol⁻¹ above the bulk value) the energy barrier. When a Cl⁻ ion moves to site 1 (Z = 0.6 nm) and is surrounded by four negatively charged residues of D178, the energy barrier further increases (6 kcal mol⁻¹ above the bulk value), until it finally reaches its maximum at the end of site 2 (Z = 0 nm) (9 kcal mol⁻¹ higher than the bulk value). In this position, Cl⁻ is surrounded by four carboxyl oxygen atoms of D177 and four carbonyl oxygen atoms of L176. The presence of high negative charges in this area leads to an increase in the energy barrier to its maximum value. When moving to site 3 (Z = −0.6 nm), Cl⁻ ions are located in the vicinity of four carbonyl oxygen atoms of T175. The presence of less negative charges in this position is the reason why the energy barrier decreases. The energy difference between the bulk level energy of Cl⁻ outside the selectivity filter and site 3 is approximately 5 kcal mol⁻¹, but between the bulk level energy of Cl⁻ outside the selectivity filter and site 1 is 6 kcal mol⁻¹. The presence of more negative charges at site 1 can be the reason for this energy difference. To pass through site 2 to site 3, the energy reduction is about 4 kcal mol⁻¹. An increase in the energy barrier when the anion moves to the depth of the channel, and a subsequent decrease in the energy barrier when the anion moves away from the center of the selectivity filter (Z = 0 nm) provide clear reasons why the ion is not located in the favorite position and lacks the ability to pass. However, under normal physiological conditions, a Cl⁻ anion rarely reaches these binding points, because of the presence of the large energy barrier. Local energy peaks are found at the opening of the selectivity filter and site 1. A slight sudden increase, which reaches its maximum height in these positions, is in accordance with the two rings of the negatively charged residues of D181 and D178 at the opening of the selectivity filter and site 1, respectively, providing a repulsive force to the Cl⁻ anion. In comparison with the PMF of Ca²⁺, the highest energy barrier for Cl⁻ occurs at binding site 2, suggesting that negative charges of the D177 residue may play a major role in choosing Ca²⁺ over Cl⁻ in the Ca_VAb channel. The energy barrier for Cl⁻ and different well-depth ranges for Na⁺ and Ca²⁺ ions are directly related to the magnitude of the measured flow rates for each ion (Ca²⁺ > Na⁺ > Cl⁻).⁹

3.3 Interaction energy

In Fig. 5, the average ion–water and ion–protein interaction energies are displayed as a function of the ion position for Ca²⁺ and Na⁺ in the selectivity filter. Ion–water and ion–protein interactions are almost mirror images of each other. It is also found that there is an increase in the strong attractive interaction between the ion and the protein when the ion gets close to the ring of D177 and L176 (Z = 0 nm). As the ion continues to move through the center of the selectivity filter, the ion–protein and ion–water interactions become more and less negative, respectively.

Fig. 5 Interaction energies of the ions with water and protein. (top) The Ca²⁺–protein (blue) and Ca²⁺–water (red) interactions are plotted as a function of the axial position of the ion in the pore. (bottom) The Na⁺–protein (blue) and Na⁺–water (red) interaction is plotted as a function of the axial position of the ion in the pore. The sum of the ion–water and ion–protein interaction energies is shown for both Na⁺ and Ca²⁺ (green) as a function of the axial position of the ion in the pore.

Where there is an energy well for Na⁺ and Ca²⁺ in the PMF (Z = 0 nm), the ion–protein energy interaction of both ions undergoes changes, demonstrating that the attractive ion–protein interaction increases in this region (becoming more negative), and, thereby, the water–ion interaction decreases (becoming less negative). However, the increased attractive ion–protein interaction in this region reflects the high affinity of these two cations for the selectivity filter. In addition, the higher ion–protein interaction energy for Ca²⁺ over Na⁺ in the selectivity filter is due to the stronger interactions of a Ca²⁺ divalent cation with the protein, representing the higher affinity of Ca²⁺ over Na⁺ for the selectivity filter. Because Ca²⁺ both binds more tightly to the filter and exhibits more affinity to the filter than Na⁺, it seems that Na⁺ ions lack the ability to block Ca²⁺ conductance. This is because of the fact that Na⁺ affinity to the channel should be higher than Ca²⁺ affinity to block the channel. As shown in Fig. 5, the sum of the ion–protein and the ion–water interactions is illustrated as single Na⁺ and Ca²⁺ ions passing through the pore. Since both interactions are almost mirror images of each other, their sum yields a relatively straight line. As expected, when the Cl⁻ anion moves through the center of the selectivity filter the ion–protein energy interaction becomes less negative demonstrating that the repulsive ion–protein interaction increases in this region (Fig. S1, ESI†).

4. Conclusions

In the present study, it was demonstrated that Ca²⁺ and Na⁺ cations experience a deep energy well, while Cl⁻ anions experience a relatively high energy barrier at the center of the selectivity filter (site 2) adjacent to the carbonyl oxygen atoms of D177 and carboxyl oxygen atoms of L176. In addition, the results from this study revealed that site 2 (the central site) and site 3 display the highest and lowest affinity to Ca²⁺, respectively. Because Ca²⁺ is more electropositive than Na⁺, the global minimum energy for Ca²⁺ is more than that for Na⁺, showing that Ca²⁺ binds more tightly to the filter. An increase in the energy barrier when the Cl⁻ ions move to the depth of the channel provides a convincing reason as to why the ion is not located in the desired position and lacks the ability to pass.

Financial and competing interest disclosure

The authors report no conflicts of interest in this work. The authors declared no competing financial interest.

Acknowledgements

This work is a part of the PhD thesis of Jamal Adiban in the field of Medical Nanotechnology at the Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Shahid Beheshti University of Medical Sciences (SBMU). The authors would like to thank Dr Pezhman Sasanpour for useful discussions and the Institute for Research in Fundamental Sciences (IPM) for some technical support. H. Rafii-Tabar would like to thank the Iran Elite Foundation (Bonyade Nokhbegan) for a Chair in Nano-neuroscience.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6mb00690f

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