Generator Potentials, Synaptic Potentials and Action Potentials All Can Be Described by the Equivalent Circuit Model of the Membrane

Nomenclature

Equivalent Circuit Model of the Neuron

Equivalent Circuit of the Membrane and
Passive Electrical Properties

	Equivalent Circuit of the Membrane
		What Gives Rise to C, R, and V?
		Model of the Resting Membrane
	Passive Electrical Properties
		Time Constant and Length Constant
		Effects on Synaptic Integration
	Voltage-Clamp Analysis of the Action Potential

Ions Cannot Diffuse Across the Hydrophobic Barrier of the Lipid Bilayer

The Lipid Bilayer Acts Like a Capacitor

Capacitance is Proportional to Membrane Area

The Bulk Solution Remains Electroneutral

Electrical Signaling in the Nervous System is
Caused by the
Opening or Closing of Ion Channels

Each K⁺ Channel Acts as a Conductor (Resistance)

Ion Channel Selectivity and Ionic Concentration Gradient Result in an Electromotive Force

An Ion Channel Acts Both as a
 Conductor and as a Battery

All the K⁺ Channels Can be Lumped into One Equivalent Structure

An Ionic Battery Contributes to V_M in Proportion to the Membrane Conductance for That Ion

When g_K is Very High, g_K•E_K Predominates

The K⁺ Battery Predominates at Resting Potential

The K⁺ Battery Predominates at Resting Potential

This Equation is Qualitatively Similar to the
Goldman Equation

The Goldman Equation

Ions Leak Across the Membrane at
Resting Potential

Slide 21

Equivalent Circuit of the Membrane and
Passive Electrical Properties

	Equivalent Circuit of the Membrane
		What Gives Rise to C, R, and V?
		Model of the Resting Membrane
	Passive Electrical Properties
		Time Constant and Length Constant
		Effects on Synaptic Integration
	Voltage-Clamp Analysis of the Action Potential

Slide 23

Experimental Set-up for
Injecting Current into a Neuron

Equivalent Circuit for Injecting Current into Cell

If the Cell Had Only Resistive Properties

If the Cell Had Only Resistive Properties

If the Cell Had Only Capacitive Properties

If the Cell Had Only Capacitive Properties

Because of Membrane Capacitance,
Voltage Always Lags Current Flow

Equivalent Circuit for Injecting Current into Cell

The Axon or Dendrite Can be Represented by a Collection of Identical Circuit Elements

Spread of Injected Current is Affected by r_a and r_m

Length Constant l = √r_m/r_a

Slide 35

Receptor Potentials and Synaptic Potentials Convey Signals over Short Distances

Action Potentials Convey Signals over Long Distances

1) Has a threshold, is all-or-none, and is conducted without decrement
2) Carries information from one end of the neuron to the other in a pulse-code

Equivalent Circuit of the Membrane and
Passive Electrical Properties

	Equivalent Circuit of the Membrane
		What Gives Rise to C, R, and V?
		Model of the Resting Membrane
	Passive Electrical Properties
		Time Constant and Length Constant
		Effects on Synaptic Integration
	Voltage-Clamp Analysis of the Action Potential

Sequential Opening of Na ⁺ and K⁺ Channels Generate the Action Potential

The Action Potential is Generated by Sequential Activation of Sodium and Potassium Channels

A Positive Feedback Cycle Generates the
Rising Phase of the Action Potential

Voltage Clamp Circuit

The Voltage Clamp Generates a Depolarizing Step by Injecting Positive Charge into the Axon

Opening of Na ⁺ Channels Gives Rise to Na ⁺ Influx That Tends to Cause V_m to
Deviate from Its Commanded Value

Electronically Generated Current Counterbalances the Na ⁺ Membrane Current

Where Does the Voltage Clamp
Interrupt the Positive Feedback Cycle?

The Voltage Clamp Interrupts the
Positive Feedback Cycle Here