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Published equation contexts

CmdVdt=−gˉNam3h(V−ENa)−gˉKn4(V−EK)−gL(V−EL)+IextC_m \frac{dV}{dt} = -\bar{g}_{Na} m^3 h (V - E_{Na}) - \bar{g}_K n^4 (V - E_K) - g_L (V - E_L) + I_{ext}

Why this formula appears here

The model’s core equation describes membrane current as the sum of capacitive, sodium, potassium, and leak components: CmdVdt=−gˉNam3h(V−ENa)−gˉKn4(V−EK)−gL(V−EL)+IextC_m \frac{dV}{dt} = -\bar{g}_{Na} m^3 h (V - E_{Na}) - \bar{g}_K n^4 (V - E_K) - g_L (V - E_L) + I_{ext}. where m , h , and n are voltage- and time-dependent gating variables each obeying their own first-order kinetics. This is worth stating in full because it is the paradigm the rest of the field either extends or reacts against: a biophysical mechanism, expressed as a dynamical system, fit to directly measured current, with no free parameter standing in for an unmeasured process. It is why the model is still taught unmodified, and why its two authors and John Eccles shared the 1963 Nobel Prize in Physiology or Medicine. It is also, strictly, a model of one…

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tt

Symbol t

t occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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gˉNa\bar{g}_{Na}

Symbol barg_Na

bargNg_Na is one of the signed contributions combined to compute the quantity on the left.

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gˉK\bar{g}_K

Symbol barg_K

bargKg_K is one of the signed contributions combined to compute the quantity on the left.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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CmdVdt=−gˉNam3h(V−ENa)−gˉKn4(V−EK)−gL(V−EL)+IextC_m \frac{dV}{dt} = -\bar{g}_{Na} m^3 h (V - E_{Na}) - \bar{g}_K n^4 (V - E_K) - g_L (V - E_L) + I_{ext}

Equation 1 · Neuroscience

From Origins to Frontier: A History of Systems and Computational Neuroscience

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The model’s core equation describes membrane current as the sum of capacitive, sodium, potassium, and leak components: CmdVdt=−gˉNam3h(V−ENa)−gˉKn4(V−EK)−gL(V−EL)+IextC_m \frac{dV}{dt} = -\bar{g}_{Na} m^3 h (V - E_{Na}) - \bar{g}_K n^4 (V - E_K) - g_L (V - E_L) + I_{ext}. where m , h , and n are voltage- and time-dependent gating variables each obeying their own first-order kinetics. This is worth stating in full because it is the paradigm the rest of the field either extends or reacts against: a biophysical mechanism, expressed as a dynamical system, fit to directly measured current, with no free parameter standing in for an unmeasured process. It is why the model is still taught unmodified, and why its two authors and John Eccles shared the 1963 Nobel Prize in Physiology or Medicine. It is also, strictly, a model of one…

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