Goldman–Hodgkin–Katz voltage expression

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This expression combines sodium, potassium, and chloride concentrations weighted by their relative permeabilities. Chloride’s inside and outside positions are reversed because it is an anion. The implementation uses fixed concentrations and permeability settings to produce a membrane-potential estimate, under the model’s constant-field assumptions.

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Original context

// Nernst Equation: E_ion = (RT/zF) * ln([ion]_out/[ion]_in)
// Calculates equilibrium potential for a single ion
inline float nernst(float z, float conc_out, float conc_in) {
    return (RT_F / z) * std::log(conc_out / conc_in) * 1000.0f;  // Convert to mV
}

// Goldman-Hodgkin-Katz Equation
// V_m = (RT/F) * ln((P_Na[Na]_o + P_K[K]_o + P_Cl[Cl]_i) / (P_Na[Na]_i + P_K[K]_i + P_Cl[Cl]_o))
struct GHKEquation {
    float P_Na = 1.0f;   // Na+ permeability (relative)
    float P_K = 20.0f;   // K+ permeability (at rest, ~20x Na+)
    float P_Cl = 5.0f;   // Cl- permeability

    float membrane_potential() const {
        float num = P_Na * NA_OUT + P_K * K_OUT + P_Cl * CL_IN;
        float den = P_Na * NA_IN + P_K * K_IN + P_Cl * CL_OUT;
        return RT_F * std::log(num / den) * 1000.0f;  // mV
    }

V_m = (RT/F) * ln((P_Na[Na]_o + P_K[K]_o + P_Cl[Cl]_i) / (P_Na[Na]_i + P_K[K]_i + P_Cl[Cl]_o))

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