A Theoretical Model for Calculating Voltage Sensitivity of Ion Channels and the Application on Kv1.2 Potassium Channel

Abstract

Voltage sensing confers conversion of a change in membrane potential to signaling activities underlying the physiological processes. For an ion channel, voltage sensitivity is usually experimentally measured by fitting electrophysiological data to Boltzmann distributions. In our study, a two-state model of the ion channel and equilibrium statistical mechanics principle were used to test the hypothesis of empirically calculating the overall voltage sensitivity of an ion channel on the basis of its closed and open conformations, and determine the contribution of individual residues to the voltage sensing. We examined the theoretical paradigm by performing experimental measurements with Kv1.2 channel and a series of mutants. The correlation between the calculated values and the experimental values is at respective level, R² = 0.73. Our report therefore provides in silico prediction of key conformations and has identified additional residues critical for voltage sensing.

Introduction

Voltage-gated ion channels are the principal protein machinery that senses changes in transmembrane potential. Through voltage-sensitive conformation changes, these channel proteins switch on and off the ion conduction pore. Most voltage-gated ion channels have a voltage-sensing domain (VSD). Shaker-type potassium channels are tetrameric proteins, with each subunit consisting of six transmembrane segments (S1–S6) flanked by cytoplasmic amino and carboxyl terminal domains. The transmembrane segments S1–S4 form the VSD, where S4 contains four to eight positively charged residues (1–5). Depolarization causes movement of S4 segments, which leads to the transfer of an electric charge across the membrane (6–10). This small transient capacitive current, measurable experimentally, is commonly referred to as “gating charge”.

Gating charge was first postulated by Hodgkin and Huxley in the 1950s (11–14) and was experimentally measured by Armstrong and Bezanilla in the 1970s (15). A change in voltage (V) in the membrane potential would shift the relative free energy of the closed and open conformations (16). Accordingly, the probability (P_O) that a channel will be open can be computed by the following equation (17),

$$P_O=\frac{1}{1+e^{\beta \left(\Delta G_c+\Delta G_e\right)}},$$ (1)

where β = 1/k_BT (k_B is the Boltzmann constant, T is absolute temperature), ΔG_c is the free energy change between the open and closed states of an ion channel when the membrane potential V = 0, and ΔG_c is voltage-independent. ΔG_e is the electric potential energy required to open the channel. ΔG_e determines the strength of voltage sensing and is proportional to the membrane voltage. Therefore, the parameters of ΔG_c and ΔG_e permit a quantitative description of the voltage-sensing and gating of ion channels.

Calculation of ΔG_c has been a challenge because both the intrinsic energy of a protein and the interaction energy between the protein and environments are hard to quantify. Inclusion of the solvation barrier energies of S4 and the electrostatic energy between S4 charges and neighboring countercharges, the energy calculation in the studies of Lecar et al. (18) and Grabe et al. (19) gave evidences of some transition states during the gating process. This strategy has also given an estimate of the work done by an external field to move S4 charges, a key determinant for calculating ΔG_e (18). In addition, three distinct theoretical routes, named W-, Q-, and G-route, have been formulated to calculate the gating charge, which is directly associated with ΔG_e (20,21). These efforts have provided a foundation to calculate ΔG_e if the conformations of two voltage-triggered states are available. It is conceivable that the calculated ΔG_e at different voltages would provide a quantitative description of voltage sensitivity for an interested ion channel.

In this study, we tested what to our knowledge is a new theoretical framework to predict voltage sensitivity by obtaining ΔG_e through calculation using closed and open conformations available for Kv1.2 channels. The correlation between calculation-based prediction and experimental results validated the predictability in voltage-sensitivity for a series of S4 mutants. Application of this method has identified additional residues within the VSD that are critical for voltage-sensitivity.

Materials and Methods

Structural models

Long et al. (22) have constructed the structural models of closed and open Kv1.2 based on its crystal structure using the Rosetta-Membrane method (23). We used these models as starting structures to produce the conformational ensembles of closed and open states of Kv1.2 channel. To simulate the conformational changes under the electrophysiological environment, we applied depolarized and hyperpolarized potentials, respectively, to the closed and open states of each channel during MD simulations. A key point for the MD simulations is to assign an electronic potential gradient to the transmembrane. It has been reported that transmembrane voltage could be induced by imposing a net charge imbalance across the membrane (24–28). As shown in Fig. 1 and Fig. S1 in the Supporting Material, we placed two lipid bilayers in a unit cell that induce two independent salt-water baths, an inner bath with 127 K⁺ and 129 Cl⁻ ions and an outer bath containing 129 K⁺ and 127 Cl⁻ ions. The inner and outer salt-water baths contain two negative and positive net charges, respectively, which results in a ∼167 mV potential gradient across each lipid bilayer (see Fig. S1 A). For the upper lipid bilayer, the outside salt-water bath shows higher voltage than the inside salt-water bath. For the lower bilayer, the outside salt-water bath shows lower voltage than the inside one. The closed and open structures of Kv1.2 or one of its mutants are then positioned into the upper and lower lipid bilayers, respectively (Fig. 1 B). The starting models of the closed and open states of each Kv1.2 mutant were constructed by mutating the structural models of Pathak et al. (23). To reduce the size of the simulation systems, only the coordinates of residues 150–420 were adopted in the simulations. After adding water molecules, the simulation systems contain ∼374,000 atoms.

Figure 1.

Structural models for the theory framework development and molecular dynamics simulations. (A) Schematic diagram showing the conformational energy change (ΔG_c) and electric energy change (ΔG_e) of a Kv1.2 channel under the application of voltage. The closed and open Kv1.2 structures built using the Rosetta-Membrane method (23) are shown in green ribbon, except the S6 segments are shown in red cartoon view to indicate the closed and open pores. (B) Structural models for molecular dynamics simulations. The closed and open structures of Kv1.2 or its mutants are, respectively, put into environments with depolarized and hyperpolarized potentials induced by using charge imbalance method.

MD simulations

MD simulations were carried out by using GROMACS 4.5 (29) under the NPT and periodic boundary conditions. The pressure was kept constant by using the Berendsen (30) method. Systems were coupled to temperature baths using the v-rescale method (31). The simulation protocol and parameters were similar to the previous simulations (32); Berger force field (33–36) was applied to the lipids and OPLS-AA force field (37) was assigned to channels, water molecules and ions. Two force fields were coupled by applying the half-ε double-pairlist method (32). SETTLE algorithm (38) was used to constrain the bond of water molecules and LINCS (39) was used to constrain all other bond lengths. The time step is 2 fs and electrostatic interactions were calculated with the particle-mesh Ewald algorithm (40). Cutoffs of 12 Å were used for both the particle-mesh Ewald and van der Waals interactions.

Results and Discussion

Theoretical formulation for predicting voltage sensitivity

We assume that a voltage-gated ion channel (e.g., Kv1.2) has two predominant states, i.e., the channel only adopts two conformations during gating, from the closed to the open state for depolarization and from the open to the closed state for hyperpolarization (Fig. 1 A).

To derive the formula for calculating ΔG_e, which is directly associated with voltage sensitivity as mentioned above, we treat a channel molecule as a group of charged particles (atoms) moving in a electric field $\left(\overrightarrow{E}\right)$ produced by the externally applied voltage (V). The electric field around membrane proteins has been suggested to be nonuniform (19,41–43). To simplify the calculation model, the electric field is assumed to be constant in this study, hence ΔG_e can be calculated by

$$\Delta G_e=\sum _{i=1}^N{q}_i\delta {\overrightarrow{r}}_i\overrightarrow{E},$$ (2)

where N is the total number of atoms, q_i is the atomic charge of the i^th atom, and $\delta {\overrightarrow{r}}_i$ is the displacement of atom i in the electric field (21). Because the ion channel is perpendicularly embedded in the membrane, and the voltage is also perpendicularly applied to the membrane, therefore

$$\delta {\overrightarrow{r}}_i\overrightarrow{E}=\left(\delta x_i\overrightarrow{i}+\delta y_i\overrightarrow{j}+\delta z_i\overrightarrow{k}\right)\left(-E\overrightarrow{k}\right)=-\delta z_{i}E,$$ (3)

where, assuming that the z axis directs from inside to outside, the electric field is applied from the outside of the membrane, and E = V/d, where d is the thickness of the membrane. Then, Eq. 2 can be rewritten as (18)

$$\Delta G_e=-\frac{V}{d}\sum _{i=1}^N{q}_i{\delta }_{zi},$$ (4)

and Q_s defined as

$$Q_s=\frac{1}{d}\sum _{i=1}^N{q}_i\delta z_i.$$ (5)

If we assume that the applied electric field does not affect the thermodynamics of the channel, ΔG_c is a constant at a specified temperature (e.g., T = 300 K). Thus,

$$e^{\beta \Delta G_c}=\frac{1}{K_O},$$ (6)

where K_O is the equilibrium constant for the conformational change of the ion channel from the closed to the open state when the transmembrane voltage is zero (44). Substituting Eqs. 5 and 6 to 1, we obtained Eq. 7, a relationship between open channel probability and voltage,

$$P_O=\frac{K_O}{K_O+e^{-\beta Q_{s}V}}.$$ (7)

Defining

$$k_s=\beta \frac{1}{d}\sum _{i=1}^N{q}_i\delta z_i=\beta Q_s,$$ (8)

then Eq. 7 could be written as

$$P_O=\frac{K_O}{K_O+e^{-k_{s}V}},$$ (9)

where K_O is the derivative of ΔG_c and k_s is the derivative of the ΔG_e. To obtain a quantitative description of the voltage-sensing and gating of ion channels, K_O and k_s could be used to replace ΔG_c and ΔG_e. Accordingly, the P_O-V curve is sigmoidal, representing the full functional dependence of P_O on voltage (V). The steepness of the P_O-V curve can be deduced by calculating the partial derivative of P_O with respect to V, and it can be estimated that the steepness reaches its maximum value k_s/4 when e^−k_sV = K_O. At this point, 50% of the channels are open and the corresponding voltage V_1/2 = 1/k_s ln K_O. Generally, V_1/2 and k_s are used to describe the sigmoid function. V_1/2 is the function of ΔG_c and ΔG_e. The value k_s, which is only related to ΔG_e, reflects the strength of voltage sensing. Experimentally, the G/V curve is usually the basis for fitting the electrophysiological data to the Boltzmann distribution to obtain the values of V_1/2 and k_s (the reciprocal of slope value). Therefore, this permitted us to compare the theoretically calculated k_s values with the experimental 1/slope values.

The advantage of our approach for predicting voltage sensitivity is that the sensitivity (k_s) is the summation of the contribution of each atom (Eqs. 5 and 8). Therefore, we can calculate the Q_s value of each atom, residue or even a segment or domain (Q^r_s),

$$Q_s^r=\frac{1}{d}\sum _{j=1}^M{q}_j\delta z_j,$$ (10)

where q_i and δz_i have the same meanings as in Eqs. 4 and 5, and q_j and δz_j are, respectively, the atomic charge and displacement of its z axis coordinate of atom j in the part to be estimated. Moreover, because both the atomic charge and z axis coordinate can be either positive or negative, Q^r_s can be positive or negative. Thus, Eq. 10 can be used to predict the sites for voltage sensing.

Model of Kv1.2 for predicting voltage sensitivity

First, we applied our theory in calculating the sensitivity of Kv1.2 channel. Equation 8 indicates that, to predict the voltage sensitivity of an ion channel (k_s), it needs to know the electric charge and displacement in the membrane of each atom of the channel. This means that detailed structural information at atomic resolution for both the closed and open states of the channel is needed. The recent x-ray crystal structure of the mammalian Kv1.2 channel appears to represent the open state (22); the x-ray crystal structure that represents the closed state of the ion channel has not been reported. However, structural models of the closed state have been reported, based on the Kv1.2 crystal structure and their voltage-clamp fluorometry measurement by using the Rosetta-Membrane method and MD simulations (23,45). The accuracy of these models has been tested by evaluating experimental results and subsequent application for calculation of gating charge (21). Therefore, these models offer a promising starting point for this study.

To acquire values of k_s and Q^r_s, it is necessary to calculate the displacement of each atom between two conformations. To reduce the calculation error, we used an average strategy to calculate the atomic displacement, which was also employed by Khalili-Araghi et al. (21) for calculating gating charge. We obtained a group of samples for the closed state conformations and another group of samples for the open state conformations. Then we aligned the two groups of samples into the same coordination frame. From this, we were able to calculate the average z coordinates over a range of conformation samples, 〈z_i^O〉 and 〈z_i^C〉, for the closed and open states, respectively. Here, O represents open state, C designates closed state, and 〈…〉 represents the average value of the inside parameter. Thus, the displacement of atom i, δz_i, can be obtained (δz_i = 〈z_i^O〉 − 〈z_i^C〉).

We used MD simulations to obtain the conformation samples. To mimic the electrophysiological conditions, we embedded the open conformation of Kv1.2 into a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipid bilayer applied by a depolarized potential, and the closed conformation into a POPC lipid bilayer enforced by a hyperpolarized potential (Fig. 1 B). The absolute values of both the depolarized and hyperpolarized potentials are all set to ∼167 mV (see Fig. S1). We then merged the two structural systems (Kv1.2 structure + lipid bilayer) of closed and open states into one structural model for MD simulations (Fig. 1 B). Together, 20 (10 pairs of closed state and open state for each channel) MD simulations were performed on the Kv1.2 channel, including wild-type Kv1.2 and nine functional mutants (see Fig. S1 B). The timescale for each simulation is 200 ns. The mutation sites are shown in Fig. 2 A.

Figure 2.

Structural model of voltage-sensing domain of WT Kv1.2 and calculated results of residue contributions to voltage sensitivity. (A) Side view of the locations for the residues that were mutated in this study. For clarity, only S1–S6 segments in one subunit are shown. (B) Movements of residues R294, R297, R300, R303, K306, and K322 from the closed (green) to the open state (red) in the WT channel. (Spheres) Residues. (Black) Open and (blue) closed conformations, respectively. (C) Calculated Q^r_s value of each residue in the WT channel.

Proof of concept with wild-type Kv1.2 and mutants

Structural models used in our calculation do not take into consideration glycosylation or other posttranslational modifications. To correlate the experimental measurement with that of structural prediction more effectively, we selected a Kv1.2 form lacking the glycosylation site (N207Q) (46). This quasi-wild-type channel (referred to as “WT” hereafter) is fully functional as previously reported and is therefore used as a basis for comparison with other mutants.

As shown in Fig. 2 B, the MD simulations indicate that most of the positively charged residues in S4 of the WT undergo large displacements from the closed state to the open state, suggesting that these residues may make a larger contribution to voltage sensing. By using Eq. 10, we calculated the Q^r_s value of each residue for the WT to quantify their contributions to voltage sensitivity. As shown in Fig. 2 C, the positively charged residues in S4 that have been reported to be critical for voltage sensing (1–6,10,47–51) indeed show large positive Q^r_s values and provide the major part of the Q_s values of the whole channel. Consistency between our theoretical prediction and available experimental data reinforces the reliability of our theoretical framework for prediction of voltage sensing.

Furthermore, for these important charges, we designed four new mutations by substituting the four arginines in S4 with glutamine (Table 1). The experimental results indicated that when R300 or R303 were neutralized, the channel was nonfunctional. R294Q and R297Q mutants were functional. The predicted k_s values of these two mutants are 0.156 and 0.158 mV⁻¹, respectively (Table 1), indicating that the voltage sensitivities of these two mutants are weaker than that of the WT channel (k_s = 0.202 mV⁻¹). The mutagenesis and electrophysiological assays verified that the voltage sensitivities of R294Q and R297Q mutants are indeed weaker than those of WT (Table 1, Fig. 3 A and see Fig. S2).

Table 1.

Voltage sensitivities of Kv1.2 channel and its mutants

Channel	ks∗	1/slope†
WT	0.202	0.0722
R294Q	0.156	0.0597
R297Q	0.158	0.0675
R300Q	No function	No function
R303Q	No function	No function
K306Q	0.195	0.0713
K322A	0.213	0.0810
K322L	No function	No function
F180Y	0.161	0.0618
F180W	No function	No function
E183A	0.205	0.0780
E183D	No function	No function
E236A	0.214	0.0909
E236D	0.204	0.0734
E236L	0.173	0.0581

^∗Theoretically calculated k_s values, mV⁻¹.

^†1/slope values representing the channel's voltage sensitivity were derived from the G-V curves obtained by electrophysiological measurements, mV⁻¹.

Figure 3.

Experimental data versus calculated voltage sensitivities of WT Kv1.2 and its mutants. (A) The G-V curves of WT Kv1.2 versus R294Q, R297Q, K306Q, K322A, and E236D mutants. (B) The G-V curves of WT Kv1.2 versus F180Y, E183A, E236L, and E236A mutants. (C) Correlation between the calculated k_s values and experimental 1/slope values. (Red dot) WT channel.

The function for the first four positive charges in the S4 segment (e.g., R294, R297, R300, and R303 for Kv1.2 channel) is clear in that they contribute positively to the voltage sensing and gating charge (1–6,10,47–51). The function of the fifth positive charge in S4 (e.g., K306 for Kv1.2) is ambiguous, however. By studying Shaker K⁺ channel by charge neutralization, Seoh et al. (5) concluded that the fifth positive charge makes a smaller contribution to voltage sensing. We also mutated the corresponding K306 to glutamine. Both our calculated and experimental results indicate that the K306Q mutation slightly decreased the voltage sensitivity of the channel (Table 1 and Fig. 3 A). This result is in agreement with the conclusion of Seoh et al. (5) that the fifth positively charged residue plays a less important role in voltage sensing.

It has been reported that some acidic and aromatic residues in S2 and S3 segments appear to affect the gating charge for the Shaker K⁺ channel (5,52–56). With this information, we designed several mutants for E183 and F180 to obtain channels with different voltage sensitivity. Our theoretical method was then applied to these mutants to test whether it could calculate the changes in voltage sensitivity and the effects of these mutations on the voltage sensitivity. We obtained two functional mutants, E183A and F180Y. Theoretical prediction suggests that, in comparison with the WT channel, E183A mutant would be slightly more sensitive to voltage changes, whereas the F180Y mutation would dramatically decrease the channel's voltage sensitivity as the calculated k_s values indicated (Table 1). This theoretical prediction was then verified by electrophysiological experiments. The 1/slope value of E183A was 0.0780 mV⁻¹, which is slightly higher than that of WT (0.0722 mV⁻¹). The 1/slope value of F180Y is 0.0618 mV⁻¹, smaller than that of WT (Table 1 and Fig. 3 B).

Encouraged by the above results, we tried to make predictions for the new residues relevant to voltage sensing of Kv1.2. From the residue contribution of sensitivity predicted by our method, we observed that K322 in WT contributes negatively to the whole voltage sensing, Q^r_s = −0.09 (Fig. 2 C and see Table S1 in the Supporting Material). This residue is located at the C-terminal of the S4-S5 linker and it has not been studied for its role in voltage sensing. Thus, we designed a mutant to neutralize this positive charge by substituting this residue with alanine, K322A. Our calculation indicated that the k_s value of the K322A mutant channel (0.213 mV⁻¹) would be larger than that of the WT channel (0.202 mV⁻¹) (Table 1). Electrophysiological experiments verified that the K322A was more sensitive than WT with 1/slope values of 0.081 mV⁻¹ vs. 0.072 mV⁻¹.

MD simulations on the WT channel indicate that E236, another acidic residue in S2, is essential for stabilizing the channel structure (see Fig. S3). In the closed state, this negatively charged residue forms three hydrogen bonds to R240, N256, and R300, respectively, and in the open state, it forms hydrogen bonds to the side chains of R309 and K306 (see Fig. S3). Therefore, E236 might be important in voltage sensing. We designed three mutations, E236A, E236L, and E236D for testing. Theoretically calculated k_s values predict that mutating glutamate to alanine or leucine changes the voltage sensitivity in opposite directions, whereas mutation to aspartate would not significantly affect the voltage sensitivity (Table 1). Indeed, the 1/slope values of E236A, E236L, and E236D are 0.909, 0.581, and 0.734 mV⁻¹, respectively.

The above results indicate that the methodology could predict the voltage sensitivity of the channels and the effects of mutations on voltage sensing by theoretically calculating the k_s values. As indicated, the experimental 1/slope values support the theoretical predictions. To examine the correlation between the calculated k_s values and experimental 1/slope values, Fig. 3 C summarizes the correlation between the calculated sensitivities and that derived from the G-V curves with R² = 0.73.

Roles of positively charged residues in S4

For K⁺ and Na⁺ channels, the S4 segments containing four to eight positively charged residues (normally Arg or Lys residues) contribute most of the charge movements (1–6,10,47–51). In this context, several mechanisms for voltage sensing have been proposed. Our theoretical calculation may provide additional data addressing atomic details for residue movements associated with voltage sensing.

Through MD simulations, we obtained the average conformations for both the closed and open states of the Kv1.2 channel. Fig. 2 B shows movements of the residues located in S4. During depolarization, all five positively charged sensors (R294, R297, R300, R303, and K306) move outwards by various degrees, from 5.4 to 16.6 Å (Fig. 2 B), which is in agreement with previous results (57,58). As expected from the residue movement, both theoretical calculation and electrophysiological assay indicated that the movements of the first two positively charged residues contributed positively to the voltage sensing for the whole channel (Table 1). As we did not obtain the functional mutants for the third (R300) or the fourth (R303) positively charged residues at S4, a definitive conclusion for these two residues of Kv1.2 remains unavailable. But from the research results of other K⁺ channels, these two residues are also important to the sensitivity of the channel voltage (1–6,10,47–51). Therefore, the literature reports support our calculation results.

The fifth positively charged residue (K306) is a special situation. Theoretical calculation on the WT channel indicates that K306 should contribute positively to the channel sensitivity because its Q^r_s value is as large as 0.17 (Fig. 2 C and see Table S1). Intuitively, the mutation K306Q should decrease the sensitivity of the channel. Nevertheless, both our calculation and experimental results on this mutant indicate that the voltage sensitivity of K306Q is almost the same as that of the WT channel (Table 1 and Fig. 3 A). Thus, as shown in Fig. 4, we calculated the contribution of the residue to the voltage sensitivity and analyzed the structural features for the K306Q mutant channel. Although the neutralization of K306 substituted by glutamine cancels the positive contribution of this residue to the voltage sensitivity, this mutation rearranges the structures of both closed and open states of the channel, causing larger outward movements for R294, R300, R303, and R309 (Fig. 4 B). This structural rearrangement compensates for the contribution loss due to the K306Q mutation (Fig. 4 A). Admittedly, one could argue about the validity of modeling and its predicted conformational changes; it is, however, of considerable value that MD formulates a testable mechanism on which experiments may be designed.

Figure 4.

Voltage sensitivity correlates with conformational changes for the K306Q mutant. (A) The calculated Q^r_s value of each residue in the K306Q mutant. (B) Comparison of the positions of the sensing residues in the WT channel with those in the K306Q mutant within the lipid bilayer. (Green) Closed WT; (cyan) open WT; (magenta) closed K306Q; and (yellow) open K306Q. Several important charged residues are displayed as sticks.

Biological implications for the function of K322 and E236

By calculating the voltage sensitivity of the whole channel (k_s) and the contribution of each residue to the voltage sensitivity (Q^r_s), we identified two important residues for voltage sensing, K322 and E236, implying the biological importance of the two residues.

S4-S5 linker mediates coupling between voltage sensing and channel activation (59–61). The S4-S5 linker of Kv1.2 also contains two positively charged residues: K312 and K322. The positive charge of position 322 is conserved within several K⁺ channels, including Kv4.3, Kv5.1, Kv9.1, Kv10.1, Kv2.1, and Kv6.1 (62) (see Fig. S4). The role of this residue in channel gating remains unknown, however. One reason might be that mutation of this position for most K⁺ channels produced nonfunctional channels. For example, for the small conductance calcium-activated potassium channel, mutation of the lysine in the S4-S5 linker to either alanine or methionine precluded trafficking of the channel to the membrane (63). The functional Kv1.2 mutant K322A in this study enabled us to reveal a potential role of this residue in voltage sensing initially predicted by calculation of Q^r_s. Indeed, the detailed mechanism underlying this finding is still unknown. One cannot rule it may also have a role in coupling VSD and pore conformation. This should be a topic for further investigation.

Recently, Choveau et al. (61) studied the function of the S4-S5 linker of KCNQ1 channel in voltage sensing and suggested a mechanistic model in which the S4-S5 linker acts as a voltage-dependent ligand bound to its receptor S6 segment in the resting state, and this interaction locks the channel in a closed state (59–61). Our study supports this conclusion with respect to structure and energy. MD simulation of WT indicated that, during depolarization, K322 moved inward (Fig. 2 B), thereby resulting in a negative contribution to the voltage sensitivity (Fig. 2 C). From Eq. 4 one can see that the voltage sensitivity of a channel is associated with the electrical potential energy required to open the channel. The inward movement of K322 produces an unfavorable contribution to the electrical energy for opening the channel, suggesting that K322 and its interactions are more stable in the closed/resting state during the depolarization process. As shown in Fig. 2 C, the contribution of other residues to the voltage sensing is negligible, suggesting that K322 may play an important role in voltage sensing and gating for the Kv1.2 channel. Indeed, neutralizing this residue by alanine substitution increases voltage sensitivity (Fig. 3 A and Table 1).

Structurally, K322 is located at the C-terminal of S4-S5 linker, making tight contact with S5 and S6 segments, helping to form the channel pore (Fig. 2 A). Examination of the MD simulation trajectories of the closed states of the WT and K322A channels reveals that the root-mean square deviation (RMSD) of the S4-S5 linker of the K322A channel is larger than that of the WT channel (Fig. 5 A), and the short α-helix consisting of S4-S5 linker in the K322A channel is unfolded to a certain extent (Fig. 5 B), indicating that the K322 may play a role in stabilizing the structure of the S4-S5 linker. The pore of the open state of the mutant channel has a wider opening than that of the WT channel, as indicated by the calculated profiles of the pore diameter and pore structural superposition of the open state of K322A channel with that of WT (Fig. 5, C and D).

Figure 5.

Large-scale structural rearrangement movements of Kv1.2 channel induced by K322A mutation. (A) RMSDs of the backbone atoms of the S4-S5 linkers in the closed WT (black) and K322A mutant (red). (B) The short α-helixes consisting of S4-S5 linkers in the K322A (magenta) channel are unfolded in larger scales in comparison with those of WT channel (green). (C) The radius profiles along the channel pore. The shadow indicates the gate region. The radius of the closed WT (green) and K322A (magenta) are similar in the gate region; however, the open K322A (yellow) channel is more open than the open WT channel (cyan). (D) Inside view of the superposition of the S6 segments of the open WT (cyan) and K322A mutant (yellow).

E236 is another residue that might be involved in voltage sensing. Liu et al. (64) also found that D466 of the HERG channel, the counterpart of E236 in Kv1.2 (see Fig. S4), may contribute to voltage sensing during the activation process. The E236D mutation did not change the voltage sensitivity of Kv1.2 channel. In contrast, the mutation E236A increases the voltage sensitivity and mutation E236L decreases the voltage sensitivity (Fig. 3 B and Table 1). For more detailed understanding of this result, we calculated the sensitivity contribution of each residue in the E236A and E236L mutants (Figs. 6 and 7, and see Table S1) and found that E279, an acidic residue located at the loop between S2 and S3 segments, contributes negatively to the voltage sensing in the E236L mutant (Fig. 7 A). A detailed analysis of the MD trajectories and structural snapshots reveals that the position of E279 in the closed E236L mutant is lower than that in the open E236L mutant (Fig. 7 B). In contrast, E279 stays at the same level in open and closed states of WT channels (Fig. 7 B). In contrast to E236L, increase of voltage-sensing mutant E236A was not clearly related to another residue (Fig. 6). Therefore, mutation E236A might increase the voltage sensing through weak effects of multiple interactions.

Figure 6.

Voltage sensitivity correlates with conformational changes for the E236A channel. (A) Calculated Q^r_s value of each residue in E236A mutant. (B) Locations of some important residues in the closed WT (green), open WT (cyan), closed E236A (magenta), and open E236A (yellow) mutants showing the displacements from the closed state to open state in the two channels. Several charged residues are displayed as sticks.

Figure 7.

Voltage sensitivity correlates with conformational changes for the E236L channel. (A) Calculated Q^r_s value of each residue in E236L mutant. (B) Locations of some important residues in the closed WT (green), open WT (cyan), closed E236L (magenta), and open E236L (yellow) mutants showing the displacements from the closed state to open state in the two channels. Several charged residues are displayed as sticks.

Conclusion

Voltage sensing is important for voltage-gated ion channels because it helps establishing the membrane potential in cells (65). The concept of voltage sensing is usually related to a phenomenological parameter—i.e., the gating charge (17,44,66,67). In experimental measurements, however, the 1/slope value derived from fitting Boltzmann distributions is commonly used to describe the voltage sensitivity. In our study, a two-state model of ion channel and equilibrium statistical mechanics principle were employed to develop the methodology for calculating the voltage sensitivity (k_s) using the coordinates of the channel's structures. The value k_s represents the essence of the experimental 1/slope value.

One should note that the reliability of our method is associated with the accuracy of the structures of the open and closed states of Kv1.2 channel, in particular associated with the applicability of the structural model of the closed state, because there is no crystal structure for this state and a structural model proposed by Pathak et al. (23) used in our study as starting point might not be fully accurate (21,68). To reduce the unreliability from the structural models, we performed 200-ns MD simulations on the structures of both the open and closed states, and used the average coordinates to calculate the voltage sensitivities (k_s values). Additionally, to gain more confidence on the reliability of our method, we designed and analyzed nine functional mutants by both simulation and experimental measurement. Similar MD simulations were performed on these functional mutants (closed state versus open state for each mutant) and the corresponding k_s values were calculated (Table 1). In parallel, the whole-cell voltage-clamp recordings for these mutants were carried out, and the activation curves were obtained by fitting the Boltzmann sigmoidal equation (Fig. 3), from which the voltage sensitivities represented by 1/slope values were obtained experimentally. The correlation between the calculated sensitivities and those derived from the G-V curves is significant (Fig. 3 C), arguing for validity of the theoretical methodology.