Energetics of discrete selectivity bands and mutation-induced transitions in the calcium-sodium ion channels family

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Energetics of discrete selectivity bands and mutation-induced transitions in the calcium-sodium ion channels family

I. Kaufman, D. G. Luchinsky, R. Tindjong, P. V. E. McClintock, and R. S. Eisenberg

Phys. Rev. E 88, 052712 – Published 19 November 2013

Abstract

We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model of a biological ion channel as functions of the fixed charge $Q_{f}$ at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 ( $Q_{f} = 1 e$ ), M1 (3 $e$ ), M2 (5 $e$ ), with a set of sodium conduction bands L0 (0.5 $e$ ), L1 (1.5 $e$ ), thereby obtaining a completed pattern of conduction and selectivity bands vs $Q_{f}$ for the sodium-calcium channels family. An increase of $Q_{f}$ leads to an increase of calcium selectivity: L0 (sodium-selective, nonblocking channel) $\to$ M0 (nonselective channel) $\to$ L1 (sodium-selective channel with divalent block) $\to$ M1 (calcium-selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is putatively identified with the eukaryotic sodium channel The scheme created is able to account for the experimentally observed mutation-induced transformations between nonselective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrierless conduction. The pattern of periodic conduction bands is explained on the basis of sequential neutralization taking account of self-energy, as $Q_{f} (z, i) = z e (1 / 2 + i)$ , where $i$ is the order of the band and $z$ is the valence of the ion. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca $^{2 +} /$ Na $^{+}$ valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.

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Received 8 May 2013

DOI:https://doi.org/10.1103/PhysRevE.88.052712

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

I. Kaufman¹, D. G. Luchinsky^1,2, R. Tindjong¹, P. V. E. McClintock^1,*, and R. S. Eisenberg³

¹Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
²Mission Critical Technologies Inc., 2041 Rosecrans Ave. Suite 225 El Segundo, California 90245, USA
³Department of Molecular Biophysics and Physiology, Rush Medical College, 1750 West Harrison, Chicago, Illinois 60612, USA

^*p.v.e.mcclintock@lancaster.ac.uk

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Vol. 88, Iss. 5 — November 2013

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Figure 1
Computational domain for a generic model of the calcium ion channel (reworked from Ref. [44]). Its selectivity filter is treated as an axisymmetric, water-filled, cylindrical hole of radius $R = 3$ Å and length $L = 12 - 16$ Å through the protein hub in the cellular membrane. The $x$ axis is coincident with the channel axis and $x = 0$ in the middle of the channel. There is a centrally placed, uniformly charged, rigid ring of negative charge $Q_{f} = 0 - 6.5 e$ embedded in the wall at $R_{Q} = R$ . The left-hand bath, modeling the extracellular space, contains nonzero concentrations of Ca $^{2 +}$ or Na $^{+}$ ions. These are injected on the axis at the Smoluchowski diffusion rate at a distance $R_{a} = R$ outside the left-hand entrance. The domain length $L_{d} = 100$ Å, the domain radius $R_{d} = 100$ Å, the grid size $h = 0.5$ Å, and a potential difference of 0–75 mV is applied between the left and right domain boundaries.Reuse & Permissions
Figure 2
Polarization effects in the generic model of ion channel. (a) Electrostatic potential map $U (x, r)$ for zero membrane potential and centered monovalent cation inside the selectivity filter, whose spatial limits are indicated y the white lines. Color bar is in units of $k_{B} T / e$ , contour step is 1 in the same units. The equipotential lines are almost equally spaced and almost perpendicular to the $x$ axis, illustrating the quasi-1D behavior of the electrostatic field. (b) Electrostatic amplification of the electrostatic field inside the channel: the potential $U$ of a monovalent ion within the channel (blue, full curve) significantly exceeds the corresponding potential in bulk water (red, dashed) $U_{0}$ due to induced polarization charge that appears at the water-protein interface. (c) The axial self-energy potential $U_{s}$ accounts for the dielectric contribution to the hydration barrier. (d) the radial self-energy $U_{r}$ provides a stable point in the center of the channel cross section, at $r = 0$ .Reuse & Permissions
Figure 3
BD simulations showing calcium conduction and occupancy bands of the generic ion channel model (partly reworked from Ref. [44]). (a) Plots of the calcium ionic current $J$ as a function of the fixed charge $Q_{f}$ at the selectivity filter for pure calcium bath of different concentration [Ca] (20, 40 and 80 mM as indicated) show distinct, clearly resolved, conduction bands M0, M1, and M2 for which there are respectively zero, one, or two calcium ions trapped saturately at the selectivity filter. (b) The peaks in conduction correspond to transitions of occupancy $P$ between these saturated levels.Reuse & Permissions
Figure 4
BD simulations showing sodium conduction and occupancy bands of the generic ion channel model. (a) Plots of the sodium ionic current $J$ as a function of the fixed charge $Q_{f}$ at the selectivity filter for a pure sodium bath of different concentration [Na] (20, 40 and 80 mM as indicated) show broadened conduction bands L0, L1, and L2 for which there are respectively zero, one, or two calcium ions trapped saturately at the selectivity filter. (b) The broad conduction peaks still correspond to transitions of occupancy $P$ between these saturated levels.Reuse & Permissions
Figure 5
BD simulations showing conduction and selectivity of the generic ion channel model in mixed and pure baths (partly reworked from Ref. [44]). Note the logarithmic ordinate scale. (a) The calcium current $J_{C a}$ as a function of the fixed charge $Q_{f}$ at the selectivity filter in the mixed bath (blue point down triangles) shows significant attenuation for bands M1 and M2 as compared with the pure bath (red point-up triangles). (b) The sodium current $J_{N a}$ as a function of $Q_{f}$ in the mixed bath (blue point-down triangles) exhibits progressive blockage by calcium as compared to the pure bath (red point-up triangles). (c) A plot of the selectivity ratio $S = J_{C a} / J_{N a}$ for the mixed bath shows growth of selectivity for $Q_{f}$ above L0 and strong peaks corresponding to the M1 and M2 calcium bands.Reuse & Permissions
Figure 6
Band L0. BD simulations showing conduction and occupancy in a mixed salt bath with Na $^{+}$ (blue, point-down, triangles) and Ca $^{2 +}$ (red, point-up, triangles); the lines are guides to the eye. (a) Sodium and calcium currents $J$ and (b) occupancies $P$ vs the Ca $^{2 +}$ concentration $[Ca]$ for $[Na] = 30$ mM. L0 shows moderate sodium conductivity without the divalent block corresponding to AMFE. (c) Mutual occupancy profiles for Na $^{+}$ (blue peaked curve) and Ca $^{2 +}$ ions (red monotonic curve) show that the Ca $^{2 +}$ ion cannot enter the channel.Reuse & Permissions
Figure 7
The nonselective band M0. BD simulations showing conduction and occupancy in a mixed salt bath with Na $^{+}$ (blue, point-down, triangles) and Ca $^{2 +}$ (red, point-up, triangles); the lines are guides to the eye. (a) Sodium and calcium currents $J$ and (b) occupancies $P$ vs Ca $^{2 +}$ concentration $[Ca]$ for $[Na] = 30$ mM. M0 shows nonselective currents both in pure and mixed baths. (c) Mutual occupancy profiles for Na $^{+}$ and Ca $^{2 +}$ ions show an absence of any blockade of Na $^{+}$ ions by the Ca $^{2 +}$ ions, and a time-shared occupancy mode.Reuse & Permissions
Figure 8
The sodium-selective band L1. BD simulations showing conduction and occupancy in a mixed salt bath with Na $^{+}$ (blue, point-down, triangles) and Ca $^{2 +}$ (red, point-up, triangles); the lines are guides to the eye. (a) Sodium and calcium currents $J$ and (b) occupancies $P$ vs Ca $^{2 +}$ concentration $[Ca]$ for $[Na] = 30$ mM. L1 shows strong blockade without AMFE at $P_{C a} = 1$ with a threshold of ${[Ca]}_{50} \approx 1$ mM. (c) Mutual occupancy profiles for Na $^{+}$ and Ca $^{2 +}$ ions show substitution and blockade of Na $^{+}$ ions by the first Ca $^{2 +}$ ion, which by itself completely occupies the channel.Reuse & Permissions
Figure 9
BD simulations showing AMFE in a mixed salt bath for the M1 calcium channel (reworked from [44]) with Na $^{+}$ (blue, point-down, triangles) and Ca $^{2 +}$ (red, point-up, triangles); the lines are guides to the eye. (a) Sodium and calcium currents $J$ and (b) occupancies $P$ vs the Ca $^{2 +}$ concentration $[Ca]$ for $[Na] = 30$ mM. M1 shows strong blockade and AMFE at $P_{C a} = 1$ , with a threshold of ${[Ca]}_{50} \approx 30 μ$ M. (c) Mutual occupancy profiles for Na $^{+}$ and Ca $^{2 +}$ show blockade of Na $^{+}$ ions by one Ca $^{2 +}$ ion.Reuse & Permissions
Figure 10
AMFE in a mixed salt bath for the M2 channel (reworked from Ref. [44]) with Na $^{+}$ (blue, point-down, triangles) and Ca $^{2 +}$ (red, point-up, triangles); the lines are guides to the eye. (a) Sodium and calcium currents $J$ and (b) occupancies $P$ vs the Ca $^{2 +}$ concentration ${[Ca]}_{50}$ for $[Na] = 30$ mM. M2 shows strong blockade and AMFE at $P_{C a} = 1$ with a threshold of ${[Ca]}_{50} \approx 150 μ$ M. (c) Mutual occupancy profiles for Na $^{+}$ and Ca $^{2 +}$ ions show blockade of Na $^{+}$ ions by a pair of Ca $^{2 +}$ ions.Reuse & Permissions
Figure 11
The mutation-induced increase of divalent (calcium or barium) over monovalent (sodium) selectivity $S_{C a} = J_{C a} / J_{N a}$ , $S_{B a} = J_{B a} / J_{N a}$ : the BD simulations are compared with experiment. The generic model predicts fast growth of $S_{C a}$ from 0.01 for L0 to 100 for M1 (blue circles). The simulation results are in reasonable agreement with the experimental results for $S_{B a}$ in Ca $_{v}$ to sodium-selective mutants (green triangles, where $Q_{f}$ is scaled by M1) [13].Reuse & Permissions
Figure 12
The appearance of a barrierless path for the channel M0. (a) The electrostatic potential energy profile along the channel's $x$ axis is plotted vs the fixed charge $Q_{f}$ . The energy differences across the profile are minimal at a particular value of $Q_{f} = Q_{opt}$ . (b) This optimal profile for permeation (red) appears as the result of a balance between repulsion by the dielectric boundary force (blue) and attraction to the fixed charge (green, dashed).Reuse & Permissions
Figure 13
Energetics and Brownian dynamics of the single-ion permeation in the sodium L0 and calcium M0 bands. (a) The L0 band potential energy vs the fixed charge $Q_{f}$ . The energy difference along the profile shows a clear minimum at $Q_{opt} = 0.45 e$ . (b) The peak in the sodium current $J$ vs $Q_{f}$ calculated from electrostatics (blue curve) lies relatively close to the BD-simulated L0 peak (green point-up triangles, detrended). (c) The M0 potential energy vs the fixed charge $Q_{f}$ . The energy difference along the profile show a sharp minimum at $Q_{opt} = 0.87 e$ . (d) The peak in the calcium current $J$ vs $Q_{f}$ calculated from electrostatics (blue curve) lies close to the BD-simulated M0 peak. (green point-up triangles).Reuse & Permissions
Figure 14
Energetics and Brownian dynamics for double-ion permeation of the sodium L1 and calcium M1 bands. (a) The L1 band potential energy vs the fixed charge $Q_{f}$ . The energy difference along the profile shows a wide minimum at $Q_{opt} = 1.5 e$ . (b) The peak in the sodium current $J$ vs $Q_{f}$ calculated from electrostatics is shifted down compared to the very weak BD-simulated conductance peak L1 (green point-down triangles). (c) The M1 calcium band potential energy vs fixed charge $Q_{f}$ . The energy difference along the profile show a deep minimum at $Q_{opt} = 3 e$ . (d) The peak in the calcium current $J$ vs $Q_{f}$ calculated from electrostatics (blue curve) lies close to the BD-simulated M1 peak in selectivity (green point-down triangles).Reuse & Permissions
Figure 15
(a) Double-ion Na $^{+}$ -Na $^{+}$ potential energy surface (PES) for the model channel with $Q_{f} =$ L1 $(1.5 e)$ , shown as a contour plot. The contour separation is 1 $k_{B} T$ , and the color bar labels are in units of $k_{B} T$ . The diagonal ridge in the upper-left corner represents the electrostatic barrier along the main diagonal of the map $x_{1} = x_{2}$ . The map area related to the selectivity filter is limited by the white lines. The optimal trajectory S (red dashed line) traverses two orthogonal valleys in the direction shown by the arrows and represents a knock-on event. The first ion initially captured at the center of the selectivity filter is pushed and substituted for by the second ion arriving at the channel mouth. (b) The potential energy $E$ profile along S represents almost barrierless permeation. (c), (d) show the same quantities for the heterogeneous Ca $^{2 +}$ -Na $^{+}$ double ion: the binding site is initially occupied by a Ca $^{2 +}$ ion that should be pushed by a Na $^{+}$ ion. The optimal trajectory $S$ navigates via two valleys separated by a saddle, which creates an intermediate potential barrier ( $Δ E \approx 8 k_{B} T$ ), corresponding to divalent blockade of Na $^{+}$ .Reuse & Permissions
Figure 16
(a) Double-ion Ca $^{2 +}$ -Ca $^{2 +}$ potential energy surface (PES) for the model channel with $Q_{f} =$ M1 $(3.0 e)$ , shown as a contour plot. The contour separation is 2 $k_{B} T$ , and the color bar labels are in units of $k_{B} T$ . The diagonal ridge in the upper left corner represents the electrostatic barrier along the main diagonal of the map $x_{1} = x_{2}$ . The map area related to the selectivity filter is limited by the white lines. The optimal trajectory $S$ (red dashed line) traverses two deep ( $\approx 60 k_{B} T$ ) orthogonal valleys in the direction shown by the arrows, and represents a knock-on event. The first ion initially captured at the center of the selectivity filter is pushed out and substituted for by the second ion arriving at the channel mouth. (b) The potential energy $E$ profile along $S$ demonstrates almost barrierless permeation ( $Δ E < 2 k B T$ ). (c), (d) show the same quantities for the heterogeneous Ca $^{2 +}$ -Na $^{+}$ double-ion: the binding site is initially occupied by a Ca $^{2 +}$ ion that should be pushed by a Na $^{+}$ ion. The optimal trajectory $S$ navigates via a deep valley ended by high potential barrier ( $Δ E \approx 20 k_{B} T$ ), corresponding to deep divalent blockade of the Na $^{+}$ current.Reuse & Permissions
Figure 17
BD simulations showing the pattern of conduction bands and valence selectivity for Na $^{+}$ , Ca $^{2 +}$ , and La $^{3 +}$ ions. (a) The conduction bands for Na $^{+}$ are overlapped and smooth [replotted for easier comparison from Fig. 4a]. (b) Ca $^{2 +}$ conduction exhibits clearly resolved peaks M0, M1, M2 (c) La $^{3 +}$ conduction exhibits the clearly resolved peaks T0 and T1.Reuse & Permissions

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