Sodium activation closing rate

Read the equation

This exponential rate decreases as membrane voltage increases in the displayed voltage convention. It multiplies m in the gate’s closing term −β_m m. Together with α_m it determines the voltage-dependent equilibrium gate value and time scale.

Terms & definitions

How it works

Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

    // α_m(V) = 0.1(V+40)/(1-exp(-(V+40)/10))
    float alpha_m(float V_) const {
        float x = V_ + 40.0f;
        if (std::abs(x) < 1e-6f) return 1.0f;  // L'Hôpital limit
        return 0.1f * x / (1.0f - std::exp(-x / 10.0f));
    }

    // β_m(V) = 4*exp(-(V+65)/18)
    float beta_m(float V_) const {
        return 4.0f * std::exp(-(V_ + 65.0f) / 18.0f);
    }

    // α_h(V) = 0.07*exp(-(V+65)/20)
    float alpha_h(float V_) const {
        return 0.07f * std::exp(-(V_ + 65.0f) / 20.0f);
    }

    // β_h(V) = 1/(1+exp(-(V+35)/10))

β_m(V) = 4*exp(-(V+65)/18)

Related builds