A structure-based model that describes activation and inactivation of a sodium channel

While the Hodgkin-Huxley formalism successfully describes sodium channel gating, the molecular origin of its nonlinear voltage dependence remains unclear. We developed a structure-based model of Na_v1.4 representing the four voltage-sensing domains, the isoleucine-phenylalanine-methionine (IFM) motif and the S6 gate as interacting binary variables, with activation parameters constrained by domain-specific fluorescence measurements. The fitted model reveals strongly heterogeneous voltage sensors whose interactions produce cooperative activation, suppressing channel opening at subthreshold voltages. Using timescale separation, we coarse-grain the 64-microstate system to obtain the Hodgkin-Huxley-like factorization P_o = m × h, where $m$ represents cooperative activation and $h$ represents availability. The reduced theory shows that the voltage dependence of $h_{\infty }\left(V\right)$ is inherited from the domain-IV voltage sensor. Because domain IV activates at more hyperpolarized voltages than the collective activation of domains I-III required for opening, availability declines before the channel reaches its main activation range. Coupling of domain IV to IFM engagement and S6 gate closure further controls the magnitude of this shift. Thus, the model identifies the molecular origin of the separation between activation and availability curves. KEY POINTS: Sodium channels are proteins in nerve and muscle cells that open briefly to trigger electrical signals, then close. The 1952 Hodgkin-Huxley model captures this behaviour by treating the channel's four voltage sensors as independent. However, experiments show the sensors are not independent: moving one changes how the others respond to voltage. We built a structure-based mathematical model of the muscle sodium channel in which all four sensors and the inactivation gate interact and fitted it to measurements of each sensor's movement. The model reproduces classic channel behaviour but shows it arises from strong cooperation between sensors and explains why the channel stops being able to open at more negative voltages than those that open it - an effect traced to a single sensor. This voltage gap helps set the range over which muscle sodium channels carry current. Analogous shifts in related sodium-channel isoforms also underlie inherited heart-rhythm disorders, linking structure to disease.