hodgkin huxley Flashcards
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What does the Hodgkin-Huxley model describe?
It models how action potentials are generated in neurons through the interplay of voltage-dependent sodium and potassium channels and a leak current, using differential equations.
What is the main current equation in the Hodgkin-Huxley model?
I = Cm dV/dt + gK n^4 (V - VK) + gNa m^3 h (V - VNa) + gL (V - VL)
What does I represent in the Hodgkin-Huxley equation?
The total membrane current (stimulus + ionic) flowing across the neuron membrane.
What is Cm dV/dt?
The capacitive current — the change in membrane voltage over time, scaled by membrane capacitance Cm.
What is gK n^4 (V - VK)?
The potassium current. gK: Maximal K⁺ conductance; n^4: Probability all 4 K⁺ gates are open; (V - VK): Driving force for potassium.
What is gNa m^3 h (V - VNa)?
The sodium current. gNa: Maximal Na⁺ conductance; m^3: 3 activation gates open; h: inactivation gate open; (V - VNa): Driving force for sodium.
What is gL (V - VL)?
The leak current — passive ion flow through non-voltage-gated channels. gL: Leak conductance; VL: Leak reversal potential.
What is a reversal potential?
The membrane potential at which there is no net flow of a given ion across the membrane.
What are typical reversal potentials in neurons?
VNa: ~ +50 mV; VK: ~ –90 mV; VL: ~ –65 mV
What is conductance (g) in this model?
A measure of how easily ions pass through a channel. It is voltage- and time-dependent and measured in Siemens (S).
How does the gating variable n evolve over time?
dn/dt = αn(V)(1 - n) - βn(V)n; n: Probability a potassium gate is open.
How do the gating variables m and h evolve?
dm/dt = αm(V)(1 - m) - βm(V)m; dh/dt = αh(V)(1 - h) - βh(V)h; m: Na⁺ activation gate; h: Na⁺ inactivation gate.
What do α and β represent in gating equations?
Voltage-dependent rate constants for opening (α) and closing (β) of gates.
What is the biological significance of n^4, m^3h?
They represent the probability that all subunits of a channel are in the right state for ions to pass.
What maintains the ion gradients across the membrane?
The sodium-potassium pump (Na⁺/K⁺ ATPase), which actively transports Na⁺ out and K⁺ in.
What does the equation I = Cm dVm/dt + gK n^4 (Vm - VK) + gNa m^3 h (Vm - VNa) + gL (Vm - VL) represent?
It is the total membrane current equation in the Hodgkin-Huxley model, summing capacitive and ionic currents through potassium, sodium, and leak channels.
What does dn/dt = αn(Vm)(1 - n) - βn(Vm)n describe?
The time evolution of the potassium activation gating variable n, based on voltage-dependent rates of opening (αn) and closing (βn).
What does dm/dt = αm(Vm)(1 - m) - βm(Vm)m describe?
The time evolution of the sodium activation gating variable m, controlled by voltage-dependent opening (αm) and closing (βm) rates.
What does dh/dt = αh(Vm)(1 - h) - βh(Vm)h describe?
The time evolution of the sodium inactivation gating variable h, with αh and βh as voltage-dependent rate constants.
What is αn(Vm) and how is it calculated?
αn(Vm) = (0.01(10 - V)) / (exp((10 - V)/10) - 1), which is the voltage-dependent rate of opening for potassium activation gates.
What is βn(Vm) and how is it calculated?
βn(Vm) = 0.125 * exp(-V/80), the voltage-dependent rate of closing for potassium gates.
What is αm(Vm) and how is it calculated?
αm(Vm) = (0.1(25 - V)) / (exp((25 - V)/10) - 1), the voltage-dependent rate of opening for sodium activation gates.
