Figure 12.

Model for CBD interaction with TTX-R Na channels. A, CBD is assumed to bind weakly to R (K_R = 5 μm), tightly to F (K_F = 0.60 μm), and more tightly to S (K_S = 0.15 μm). B–D, Channels move among R, F, and S states with voltage-dependent rate constants chosen to approximate voltage-dependent occupancy in the different states with conditioning pulses of various durations. Channels move from R to F with a forward rate constant of 3/(1 + exp(–(V + 8.7)/6.5) and a backward rate constant of 0.12 + 0.9/(1 + exp(V + 23.7/6.5). Channels move from R to S with a forward constant of 0.004/(1 + exp(–(V + 14.3)/9.3)) and a backward constant of 0.004/(1 + exp((V + 64.3)/9.3)). Channels move from F to S with a forward rate constant of 0.005 and a backward rate constant determined by other rate constants to preserve microscopic reversibility. CBD binds to R with an on rate (KonR) of 0.02 ms⁻¹µm⁻¹ and unbinds with off rate (koffR) of 0.1 ms⁻¹. CBD binds to F with an on rate (KonF) of 0.02 ms⁻¹µm⁻¹ and unbinds with off rate (koffF) of 0.012 ms⁻¹. CBD binds to S with an on rate (KonS) of 0.02 ms⁻¹µm⁻¹ and unbinds with an off rate (koffS) of 0.003 ms⁻¹. The rate constants for movements from R-CBD to F-CBD and F-CBD to S-CBD are the same as for movements from R to F and from F to S. To preserve microscopic reversibility, the rate constant for movement from F-CBD to R-CBD is multiplied by a factor of (koffF/koffR) * (konR/konF) relative to that for F to R, and the rate constant for movement from S-CBD to F-CBD is multiplied by a factor of (koffS/koffF) * (konF/konS) relative to that for S to F. For preserving microscopic reversibility in the cycle of unbound and bound R and S states, the rate constant from R-CBD to S-CBD is the rate constant from R to S divided by the square root of (koffS/koffR) * (konR/konS) and the rate constant S-CBD to R-CBD is the rate constant from S to R multiplied by the square root of (koffS/koffR) * (konR/konS). B, Prediction of voltage dependence of fast inactivation (green) and slow inactivation (blue) at equilibrium if each occurred in the absence of the other. C, Left, Prediction of channel fraction in R state (i.e., available channels) after 50 ms conditioning pulses in control (solid black line) and with 5 μm CBD (solid red line). Dashed red line shows channel availability in CBD normalized to 1 at −100 mV. Right, Occupancy of channels in fast and slow inactivated states in control (solid lines) and occupancy of channels in the corresponding CBD-bound states with 5 μm CBD (dashed lines). D, Left, Prediction of channel fraction in R with the indicated protocol for measuring slow inactivation, with 5 s conditioning pulses followed by 10 ms at −100 mV to allow recovery of channels in the fast inactivated state. Right, Occupancy of channels in fast and slow inactivated states in control (solid lines) and occupancy of channels in the corresponding CBD-bound states with 5 μm CBD (dashed lines).