Asymmetric Interplay Between K+ and Blocker and Atomistic Parameters From Physiological Experiments Quantify K+ Channel Blocker Release

Abstract

Modulating the activity of ion channels by blockers yields information on both the mode of drug action and on the biophysics of ion transport. Here we investigate the interplay between ions in the selectivity filter (SF) of K⁺ channels and the release kinetics of the blocker tetrapropylammonium in the model channel Kcv_NTS. A quantitative expression calculates blocker release rate constants directly from voltage-dependent ion occupation probabilities in the SF. The latter are obtained by a kinetic model of single-channel currents recorded in the absence of the blocker. The resulting model contains only two adjustable parameters of ion-blocker interaction and holds for both symmetric and asymmetric ionic conditions. This data-derived model is corroborated by 3D reference interaction site model (3D RISM) calculations on several model systems, which show that the K⁺ occupation probability is unaffected by the blocker, a direct consequence of the strength of the ion-carbonyl attraction in the SF, independent of the specific protein background. Hence, Kcv_NTS channel blocker release kinetics can be reduced to a small number of system-specific parameters. The pore-independent asymmetric interplay between K⁺ and blocker ions potentially allows for generalizing these results to similar potassium channels.

Keywords: 3D RISM; blocker kinetics; carbonyl-ion interaction; extended beta distributions; ion binding; selectivity filter; viral potassium channels.

FIGURE 1

Block of single-channel currents in Kcv_NTS in DPhPC membranes by cytosolic TPrA. (A,B) Representative time series measured in symmetrical 100 mM KCl at different membrane voltages between +160 mV and −160 mV (A) without TPrA and (B) with 0.1 mM TPrA. (C) Time series measured in different concentrations of TPrA at +120 and −120 mV. The scale bar refers to all three panels in this figure. C marks the closed state. The data for ±120 mV without TPrA are displayed in both (A,C). (D) Alignment of the pore loop of two viral K⁺ channels (Kcv_NTS, Rauh et al., 2017b), the one used in this study, and Kcv_PBCV–1 (Tayefeh et al., 2009), a bacterial K⁺ channel (KcsA, UniProtKB/Swiss-Prot: P0A334.1) and three eukaryotic potassium channels (Shaker, GenBank: CAA29917.1, hERG, GenBank: BAA37096.1, and human Kv1.5, NCBI Reference Sequence: NP_002225.2). Sequence conservation (^∗identity, : conservative,. semi-conservative) was calculated with the Clustal Omega Webapp. The selectivity filter sequence is underlined, the pore helix is shaded in gray. (E) Schematic illustration of the blocking process, the binding site is only accessible from the cytosolic pore entrance.

FIGURE 2

Kinetics of the TPrA block. (A) Kinetic Markov model used for the fits of the amplitude histograms (Supplementary Figure S1). The states O (open) and F, M, S (three closed states of different dwell times) are those used previously in the 4-state model of gating in the unblocked Kcv_NTS (Rauh et al., 2017a, 2018). The blocked state B is introduced by the blocker TPrA. (B) Voltage dependence of the rate constant $k_{\text{BO}}=k_{\text{off}}^{\text{O}}$ measured at cytosolic TPrA concentrations of 0.05 mM ●, 0.1 mM , 0.5 mM , 1 mM , and 5 mM ο. (C) Voltage dependence of $k_{\text{OB}}=k_{\text{on}}^{\text{O}}[\text{TPrA}]$ measured at the same concentrations as k_BO, (D) Voltage dependence of $k_{\text{on}}^{\text{O}}$ as determined by dividing k_OB by the concentration of TPrA in mol. Data points are the geometric mean of 3 to 4 individual channels, error bars represent the geometric standard deviation. Some data points around 0 mV are missing because of insufficient signal-to-noise ratio.

FIGURE 3

Relating the voltage dependence of the rate constant of blocker release in the open state ($k_{\text{off}}^{\text{O}}$) to the ion distribution at S4 adjacent to the binding site of the blocker. (A) 5-state model of ion hopping (Roux, 2005) with the rate constants k_ij (i, j = 1 to 5) obtained from the previous analysis (Rauh et al., 2018). Numerical values for the rate constants are given in Supplementary Table S1 (B,C). The probabilities P_m (m = 1 to 5) of the occurrence of the states 1 to 5 in the model of Roux (2005) calculated from Eqs. S4 to S9 for the case (B) that the channel is open and not blocked (redrawn from the original data of Rauh et al., 2018) and (C) that the channel is blocked (k₁₂ = k₂₁ = k₃₂ = 0). P(S4) is the probability that there is an ion in binding site S4 (purple in panel A) close to the binding site of the blocker. According to panel (A), P(S4) = P₃ + P₄ + P₅. The inset shows the probabilities for the open and blocked channel at 0 mV, as taken from panels (B,C). (D) Comparison of the measured $k_{\text{off}}^{\text{O}}$ with the values predicted by Eq. 4 based on P(S4). Black line: Fit of the experimentally determined $k_{\text{off}}^{\text{O}}$ (black circles, pooled from all TPrA concentrations) with 100 mM symmetric KCl. Parameters a and b were free fit parameter in Eq. 3. Orange line: Prediction of Eq. 3 for 100 mM cytosolic and 500 mM external KCl. Parameters a and b were taken from the symmetric fit. Orange circles: experimentally determined $k_{\text{off}}^{\text{O}}$ (with 5 mM TPrA). Data points show mean and standard deviation, shaded areas depict 99% confidence intervals.

FIGURE 4

(A,B) K⁺ ion concentration profiles and (C,D) cumulative equilibrium constants as function of channel length coordinate z starting from the origin as shown in the inset in (A) from finite concentration (1 M, uv, solid lines) and infinite dilution (single hydrated ion, uu, dashed lines) 3D RISM calculations of KcsA (pdb code 2HVK) with (red) and without (purple) TBA placed in the cavity. (E,F) cumulative results for four reduced models with and without TBA comprising isolated carbonyl cages for KcsA (2HVK, Yohannan et al., 2007, crystalized with TBA and 1K4C (Zhou et al., 2001) crystalized without TBA), KirBac3.1 (3ZRS, Bavro et al., 2012) and the computationally determined filter model of Kcv_PBCV–1 (Tayefeh et al., 2009; Hoffgaard et al., 2015). (A,C,E) from calculations with original force field, (B,D,F) with down-scaled filter carbonyl charges leading to halved local dipole moments. The inset in panel (A) represents the full 2HVK system in cartoon representation. The inset in panel (F) shows a superposition of all reduced filter carbonyl groups in the same color code as the curves.