Monod-Wyman-Changeux Analysis of Ligand-Gated Ion Channel Mutants

Abstract

We present a framework for computing the gating properties of ligand-gated ion channel mutants using the Monod-Wyman-Changeux (MWC) model of allostery. We derive simple analytic formulas for key functional properties such as the leakiness, dynamic range, half-maximal effective concentration ([EC₅₀]), and effective Hill coefficient, and explore the full spectrum of phenotypes that are accessible through mutations. Specifically, we consider mutations in the channel pore of nicotinic acetylcholine receptor (nAChR) and the ligand binding domain of a cyclic nucleotide-gated (CNG) ion channel, demonstrating how each mutation can be characterized as only affecting a subset of the biophysical parameters. In addition, we show how the unifying perspective offered by the MWC model allows us, perhaps surprisingly, to collapse the plethora of dose-response data from different classes of ion channels into a universal family of curves.

Figure 1

Schematic of nAChR and CNGA2 ion channels. (A) The heteropentameric nicotinic acetylcholine receptor (nAChR) has two ligand binding sites for acetylcholine outside the cytosol. (B) The homotetrameric cyclic nucleotide-gated (CNGA2) has four ligand binding sites, one on each subunit, for cAMP or cGMP located inside the cytosol. Both ion channels have a higher probability of being closed in the absence of ligand and open when bound to ligand.

Figure 2

Probability that a ligand-gated ion channel is open as given by the MWC model. (A) Microscopic states and Boltzmann weights of the nAChR ion channel (green) binding to acetylcholine (orange). (B) Corresponding states for the CNGA2 ion channel (purple) binding to cGMP (brown). The behavior of these channels is determined by three physical parameters: the affinity between the receptor and ligand in the open (K_O) and closed (K_C) states and the free energy difference ε between the closed and open conformations of the ion channel.

Figure 3

Characterizing nicotinic acetylcholine receptors with n subunits carrying the L251S mutation. (A) Normalized currents of mutant nAChR ion channels at different concentrations of the agonist acetylcholine (ACh). The curves from right to left show a receptor with n = 0 (wild-type), n = 1 (α₂βγ*δ), $n=2({\alpha }_2^{\ast }\beta \gamma \delta )$), n = 3 (α₂β*γ*δ*), and $n=4({\alpha }_2^{\ast }\beta {\gamma }^{\ast }{\delta }^{\ast })$) mutations, where asterisks (*) denote a mutated subunit. Fitting the data (solid lines) to eqs 1 and 2 with m = 2 ligand binding sites determines the three MWC parameters K_O = 0.1 × 10⁻⁹ M, K_C = 60 × 10⁻⁶ M, and βε⁽ⁿ⁾ = [−4.0, −8.5, −14.6, −19.2, −23.7] from left (n = 4) to right (n = 0). With each additional mutation, the dose-response curve shifts to the left by roughly a decade in concentration while the ε parameter increases by roughly 5 k_BT. (B) The probability p_open(c) that the five ion channels are open can be collapsed onto the same curve using the Bohr parameter F_nAChR(c) given by eq 13. A positive Bohr parameter indicates that c is above the [EC₅₀]. See Supporting Information section C for details on the fitting procedure.

Figure 4

Theoretical prediction and experimental measurements for mutant nAChR ion channel characteristics. The open squares mark the βε values of the five dose-response curves from Figure 3A. (A) The leakiness given by eq 5 increases exponentially with each mutation. (B) The dynamic range from eq 6 is nearly uniform for all mutants. (C) The [EC₅₀] decreases exponentially with each mutation. (D) The effective Hill coefficient h is predicted to remain approximately constant. [EC₅₀] and h offer a direct comparison between the best-fit model predictions (□) and the experimental measurements (●) from Figure 3A. While the [EC₅₀] matches well between theory and experiment, the effective Hill coefficient h is significantly noisier.

Figure 5

States and weights for mutant CNGA2 ion channels. CNGA2 mutants with m = 4 subunits were constructed using n mutated (light red) and m – n wild-type subunits (purple). The affinity between the wild-type subunits to ligand in the open and closed states (K_O and K_C) is stronger than the affinity of the mutated subunits ( $K_{\mathrm{O}}^{\ast }$ and $K_{\mathrm{C}}^{\ast }$). The weights shown account for all possible ligand configurations, with the inset explicitly showing all of the closed states for the wild-type (n = 0) ion channel from Figure 2B. The probability that a receptor with n mutated subunits is open is given by its corresponding open state weight divided by the sum of open and closed weights in that same row.

Figure 6

Normalized currents for CNGA2 ion channels with a varying number n of mutant subunits. (A) Dose-response curves for CNGA2 mutants composed of 4 – n wild-type subunits and n mutated subunits with weaker affinity for the ligand cGMP. Once the free energy ε and the ligand dissociation constants of the wild-type subunits (K_O and K_C) and mutated subunits ( $K_{\mathrm{O}}^{\ast }$ and $K_{\mathrm{C}}^{\ast }$) are fixed, each mutant is completely characterized by the number of mutated subunits n in eq 15. Theoretical best-fit curves are shown using the parameters K_O = 1.2 × 10⁻⁶ M, K_C = 20 × 10⁻⁶ M, $K_{\mathrm{O}}^{\ast }=500\times {10}^{-6}\mathrm{M},K_{\mathrm{C}}^{\ast }=140\times {10}^{-3}\mathrm{M}$, and βε = −3.4. (B) Data from all five mutants collapses onto a single master curve when plotted as a function of the Bohr parameter given by eq 13. See Supporting Information section C for details on the fitting.

Figure 7

Individual state probabilities for the wild-type and mutant CNGA2 ion channels. (A) The state probabilities for the wild-type (n = 0) ion channel. The subscripts of the open (O_j) and closed (C_j) states represent the number of ligands bound to the channel. States with partial occupancy, 1 ≤ j ≤ 3, are most likely to occur in a narrow range of ligand concentrations [cGMP] ∈ [10⁻⁷, 10⁻⁵] M, outside of which either the completely empty C₀ or fully occupied O₄ states dominate the system. (B) The state probabilities for the n = 4 channel. Because the mutant subunits have a weaker affinity to ligand ( $K_{\mathrm{O}}^{\ast }>K_{\mathrm{O}}$ and $K_{\mathrm{C}}^{\ast }>K_{\mathrm{C}}$), the state probabilities are all shifted to the right.

Figure 8

Theoretical prediction and experimental measurements for mutant CNGA2 ion channel characteristics. The open squares (□) represent the five mutant ion channels in Figure 6 with n mutated subunits. (A) All ion channels have small leakiness. (B) The dynamic range of all channels is near the maximum possible value of unity, indicating that they rarely open in the absence of ligand and are always open in the presence of saturating ligand concentrations. (C) The [EC₅₀] increases nonuniformly with the number of mutant subunits. Also shown are the measured values (●) interpolated from the data. (D) The effective Hill coefficient has a valley due to the competing influences of the wild-type subunits (which respond at μM ligand concentrations) and the mutant subunits (which respond at mM concentrations). Although the homotetrameric channels (n = 0 and n = 4) both have sharp responses, the combined effect of having both types of subunits (n = 1, 2, and 3) leads to a flatter response.

Figure 9

Predicting the dose-response of a class of mutants using a subset of its members. (A) The MWC parameters of the nAChR mutants can be fixed using only two data sets (solid lines), which together with eq 20 predict the dose-response curves of the remaining mutants (dashed lines). (B) For the CNGA2 channel, the properties of both the wild-type and mutant subunits can also be fit using two data sets, accurately predicting the responses of the remaining three mutants. Supporting Information section D demonstrates the results of using alternative pairs of mutants to fix the thermodynamic parameters in both systems.

Figure 10

Degenerate parameter sets for nAChR and CNGA2 model fitting. Different sets of biophysical parameters can yield the same system response. (A) Data for the nAChR system in Figure 3 is fit by constraining K_O to the value shown on the x-axis. The remaining parameters can compensate for this wide range of K_O values. (B) The CNGA2 system in Figure 6 can similarly be fit by constraining the K_O value, although fit quality decreases markedly outside the narrow range shown. Any set of parameters shown for either system leads to responses with R² > 0.96.