Simulations using an allosteric 12-state model recapitulate features ΔF obtained with ALEXA-488 and MTS-TAMRA. (A) HCN allosteric model based on the scheme originally proposed by Altomare et al. (2001) and extended to 12 states (Wu et al., 2021) was used to simulate activating current and fluorescence using their labeling convention. This scheme does not take account of hysteresis (mode-shift), which would require a more complex model with concomitantly more parameters (e.g., see Männikkö et al., 2005). Vertical transitions represent the closed-to-open transition of the pore and were assumed electroneutral. Horizontal transitions between states C_0..4 and O_0..4 are voltage-dependent and involve independent movement of S4 helices. If all S4 helices have completed their fast transition, a second concerted movement of S4 helices (transitions C₄-C₄*, O₄-O₄*) is proposed to occur. The forward and backward rates of all voltage-dependent transitions were described using the conventional Eyring transition state formulation given by: $α=α0,je−Vzje/kT$⁠, $β=β0,jeVzje/kT$⁠, respectively, where e, k, and T have their usual meanings and z_j is the apparent valence for the transition. Zero voltage rates α₀,β₀ were defined as $α0,j=kjezjekTV0.5,j$ and $β0,j=kje−zjekTV0.5,j$⁠, where j refers to the fast or slow movement. (B) Simulations of I^act, ΔF in response to voltage step protocol (top). For simulating I^act, we determined a set of model parameters (Table S1) based on a fit to the representative data set of measured activating currents with ALEXA-488 labeling that gave a reasonable match to our data. To simulate the fluorescence in response to voltage steps, we assumed that each of the 12 conformational states can contribute to ∆F_total, i.e., $∆Ftotal=∑i=012δiFXi$⁠, where X_i is the state occupancy and $δiF$ is the apparent fluorescence intensity for state i. We assumed that the independent S4 movements (for either open or closed pore) contribute the same fluorescence change per sensor, $δ1F$⁠, $∆F1=∑i=14iδ1F(Ci+Oi))$⁠, whereas the concerted slow movement contributes a change in fluorescence $∆F2=4(C4*+O4*)δ2F$⁠. To account for the difference in ∆F_total found experimentally for ALEXA-488 and MTS-TAMRA labeling, we assumed the former reported both fast and slow S4 movements, whereas the latter only reported the slow component. We did not take account of the differences in activation kinetics for the two labels. (C) The voltage dependence of normalized conductance (G) and ΔF contributions. ∆F_total would correspond to the fluorescence measured by ALEXA-488, whereas ∆F₂ would correspond to that from MTS-TAMRA labeling. Note that the voltage dependence of normalized G and ∆F₂ match well. The fit parameters reported by a single Boltzmann fit were as follows: for G, V_0.5 = −111.7 ± 0.5 mV, z = 1.26 ± 0.02; for ∆F_total, V_0.5 = −78.9 ± 2.2 mV, z = 0.84 ± 0.06; for ∆F₂, V_0.5 = −117.1 ± 0.06, z = 1.51 ± 0.04 (mean ± SE). (D) Simulations of variable prepulse width protocol with an 8-ms increment (compare with Fig. 3 D). As in B, ∆F_total is proposed to represent the ALEXA-488–labeling case, whereas ∆F₂ would represent the MTS-TAMRA–labeling case.