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Equation 1 · Part 2 · From Origins to Frontier: A History of Systems and Computational Neuroscience

Symbol d

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}
dd

What this part means

d is part of the quantity the equation computes from the expression on the right.

Its job in the formula

d is part of the quantity the equation computes from the expression on the right.

The passage around this formula

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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Sources cited in the article section

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