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Transcript
Hodgin & Huxley • The problem: Explain action potentials • The preparation: loligo giant axons • What was known: – Time dependent conductance: Curtis & Cole – Multiple batteries in play • Likely players Na+, K+ : Hodgkin & Katz • A new method: Voltage Clamp Action Potentials “Overshoot” Hodgkin & Huxley, 1939 Nature 144:473-96 Loligo forbesi Parallel conductance model How to study the process of action potential generation Voltage Clamp • 3 electrodes used: – Vo – Vi – Ii (injected current, measured with I-mon) • Advantages – Space clamp – axial wires used – – Can effectively eliminate Ic – V is fixed – Used to isolate time dependent changes in I Voltage clamp currents in loligoModern convention: Original presentation: - Vm relative to rest -referenced to inside of cell -amplitude & polarity appropriate for necessary charging of membrane Isolation of the “outward current” gK(t) • Sigmoid onset • Noninactivating • Exponential offset Model of gK gK gk n4 n nc no n dn n (1 n) n n dt With dn / dt 0, i.e. at steady state, n n n n If n no when t 0 : n n (n no ) exp( t / n ) where n 1 /( n n ) obtain n to give best fit to I K obtain n from g K /g K max Then n n / n , and n (1 n ) / n Equilibrium n(V), noo • Similar to a Boltzmann distribution Rate constants for gate n • Derived from onset or offset of gK upon DV n n / n , n (1 n ) / n gK fitted to HH equation • Reasonable fit to onset, offset & steady state Isolate iNa by algebraic subtraction • Appears Ohmic • Sigmoidal onset • Increase in gNa is reversible • g(V) is independent of i sign Current flow through pNa is Ohmic • Open channel I/V curve • Instantaneous conductance gNa kinetics • Both activation and inactivation speed up with depolarization Model of gNa h m m (m mo ) exp( t / m ) h m h h (h ho ) exp( t / h ) hc h o mc mo m obtain h and m to give best fit to I Na g Na g Na m h 3 obtain h (V ) from prepulse data at rest mo 0 and with strong depolariza tion h 1 g Na g [1 exp( t / m )] exp( t / h ) ' Na where g ' Na 3 g Na m h 3 o obtain m from 3 ' g Na Then h h / h , and h (1 h ) / h Then m m / m , and m (1 m ) / m hoo • Determined with prepulse experiments Rate constants for gate h • Derived from onset or offset of gNa upon DV Rate constants for gate m • Derived from onset or offset of gNa upon DV Summary of equilibrium states and time constants for HH gates HH model equations I Cm dV g K n4 (V VK ) g Na m3h(V VNa ) gl (V Vl ) dt dh h (1 h) h h dt dm m (1 m) m m dt dn n (1 n) n n dt - All s and s are dependent on voltage but not time - Calculate I from sum of leak, Na, K - Can calculate dV/dt, and approximate V1 =V(t+Dt) HH fit to expermentally determined gNa Voltage clamp currents are reproduced by simulations …as are action potentials Evolution of channel gates during action potential Modern view of voltage gated ion channels Markov model of states & transitions • Allosteric model of Taddese & Bean – Only 2 voltage dependent rates Allosteric model results • Reproduces transient & sustained current Generality of model • Many ion channels described in different neuronal systems • Each has unique – – – – Equilibrium V activation range Equilibrium V inactivation range Kinetics of activation and inactivation Reversal potential • These contribute to modification of spike firing in different V and f domains