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” 200 Hz time calibration Later Hodgkin and Katz showed that reducing [Na]o reduced the overshoot Hodgkin & Huxley, 1939 Nature 144:473-96

Loligo forbesi

Parallel conductance model

How to study the process of action potential generation 200 Hz time calibration Later Hodgkin and Katz showed that reducing [Na]o reduced the overshoot

Voltage Clamp 3 electrodes used: Advantages 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 loligo Modern 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

Equilibrium n(V), noo Similar to a Boltzmann distribution

Rate constants for gate n Derived from onset or offset of gK upon DV

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

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 - All as and bs 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 Calculated by hand calculator by integrating at very small time steps

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