Electric fingerprint of voltage sensor domains

Abstract

A dynamic transmembrane voltage field has been suggested as an intrinsic element in voltage sensor (VS) domains. Here, the dynamic field contribution to the VS energetics was analyzed via electrostatic calculations applied to a number of atomistic structures made available recently. We find that the field is largely static along with the molecular motions of the domain, and more importantly, it is minimally modified across VS variants. This finding implies that sensor domains transfer approximately the same amount of gating charges when moving the electrically charged S4 helix between fixed microscopic configurations. Remarkably, the result means that the observed operational diversity of the domain, including the extension, rate, and voltage dependence of the S4 motion, as dictated by the free energy landscape theory, must be rationalized in terms of dominant variations of its chemical free energy.

Keywords: electrostatics; free energy; ion channel; molecular dynamics; voltage sensor.

Fig. 1.

Hypothetical free energy landscapes showing the S4 energetics in distinct VSs. For fixed $\mathit{X}$ and $\mathit{Y}$ microscopic configurations of S4 under voltage $V$, $\Delta \Delta F\left(V\right)=\Delta \Delta F\left(\text{0}\right)+V\Delta \Delta Q$ is the variation of the helix energy upon perturbation (*) of the protein-membrane surroundings, where $\Delta \Delta F\left(\text{0}\right)$ and $\Delta \Delta Q$ are, respectively, perturbation-induced changes of the chemical free energy and the gating charge. In two contrasting scenarios, $\Delta \Delta F\left(V\right)$ may arise from (i) reshaping of the membrane-voltage field $\varphi \left(\mathit{r}\right)$ that accounts for energetic differences via $V\Delta \Delta Q$ and/or (ii) chemical free energy modifications that account for $\Delta \Delta F\left(\text{0}\right)$.

Fig. 2.

Voltage coupling variation $\Delta \varphi =\left[{\varphi }_{{\mathbf{\chi }}_2}\left({\mathbf{\chi }}_2\right)-{\varphi }_{{\mathbf{\chi }}_1}\left({\mathbf{\chi }}_1\right)\right]$ of the charge $q_i$ when displacing $\Delta \mathbf{\chi }$ along a given path $\mathbf{\chi }$ within the sensor domain. By assuming that ${\varphi }_{\mathbf{\chi }}\left(\mathbf{\chi }\right)$ reshapes as the particle moves along $\mathbf{\chi }$, $\Delta \varphi$ can be decomposed into static (a) and dynamic (b) contributions.

Fig. 3.

Dataset of VS structures. (A) General hourglass-like construction of sensor domains. Shown is the gating pore along which the S4 charges travel during activation. A highly conserved phenyl group (white) plugs the most constricted hydrophobic region along the gating pore and disconnects internally and externally open water crevices. (B) Molecular views of the VS structures. Highlighted is the conformation-dependent position of the S4 basic residues (blue sticks) and the salt-bridges/hydrogen-bonds they form with the acidic/polar residues (red/green sticks) of other VS segments (see Table S2 for details). Only segments S1, S2, and S4 are shown for clarity.

Fig. 4.

Voltage-coupling analysis and field reshaping. (A) Voltage coupling $\varphi \left(z\right)$ and (B) water density $\rho \left(z\right)$ profiles along the TM direction $z$ of the gating pore. For clarity, the entire dataset is presented as an average curve (black) with associated error bars (gray shading). Also shown are coupling and density values for the phenyl center (green) and the S4 basic amino acids in their activated (dark blue) and resting (pink) positions. Note that the average coupling profile (black) is fundamentally distinct from that of a bare lipid bilayer (yellow). The steepest part of $\varphi$ at the phenyl center implies the existence of a focused voltage gradient across the domain compared with the lipid bilayer. (C) Field reshaping ${\mu }_{kl}$ between voltage-sensor structures $k$ and $l$. Diagonal values report the ${\mu }_{kl}^{\mathit{X}\mathit{Y}}$ estimates between conformations of a fixed domain isoform, whereas lower and upper triangular regions of the matrix representation present, respectively, the ${\mu }_{kl}^{\mathit{X}{\mathit{X}}^{*}}$ and ${\mu }_{kl}^{\mathit{Y}{\mathit{Y}}^{*}}$ estimates for a fixed conformation over distinct isoforms. In the computation of ${\mu }_{kl}$, each of the profiles ${\varphi }_k\left(z\right)$ and ${\varphi }_l\left(z\right)$ corresponds to an average over four independent domain subunits. Here, the voltage coupling was determined via an all-atom formulation through the electrical distance definition (Figs. S3 and S4). Independent estimates based on continuum electrostatic calculations are presented in Fig. S5.