Equivalent Circuit Model of the Neuron

Transcription

1 Generator Potentials, Synaptic Potentials and Action Potentials All Can Be Described by the Equivalent Circuit Model of the Membrane Equivalent Circuit Model of the Neuron PNS, Fig 211 The Nerve (or Muscle) Cell can be Represented by a Collection of Batteries, Resistors and Capacitors Equivalent Circuit of the Membrane and Passive Electrical Properties Ions Cannot Diffuse Across the Hydrophobic Barrier of the Lipid Bilayer 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 VoltageClamp Analysis of the Action Potential The Lipid Bilayer Acts Like a Capacitor Capacitance is Proportional to Membrane Area V m = Q/C V m = Q/C Q must change before V m can change 1

2 The Bulk Solution Remains Electroneutral Electrical Signaling in the Nervous System is Caused by the Opening or Closing of Ion Channels PNS, Fig 71 The Resultant Flow of Charge into the Cell Drives the Membrane Potential Away From its Resting Value Each K Channel Acts as a Conductor (Resistance) Ion Channel Selectivity and Ionic Concentration Gradient Result in an Electromotive Force PNS, Fig 75 PNS, Fig 73 An Ion Channel Acts Both as a Conductor and as a Battery All the K Channels Can be Lumped into One Equivalent Structure PNS, Fig 76 E K = RT [K ] ln o zf [K ] i PNS, Fig 77 2

3 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 g K g K This Equation is Qualitatively Similar to the Goldman Equation The Goldman Equation V m = RT ln (P K {K } o P Na {Na } o P Cl {Cl } i ) V m = ln zf (P K {K } i P Na {Na } i P Cl {Cl } o ) 3

4 Ions Leak Across the Membrane at Resting Potential At Resting Potential The Cell is in a SteadyState Out In PNS, Fig 710 Equivalent Circuit of the Membrane and Passive Electrical Properties Passive Properties Affect Synaptic Integration 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 VoltageClamp Analysis of the Action Potential Experimental Setup for Injecting Current into a Neuron Equivalent Circuit for Injecting Current into Cell PNS, Fig 72 PNS, Fig 82 4

5 If the Cell Had Only Resistive Properties If the Cell Had Only Resistive Properties V m = I x R in PNS, Fig 82 If the Cell Had Only Capacitive Properties If the Cell Had Only Capacitive Properties V m = Q/C PNS, Fig 82 Because of Membrane Capacitance, Voltage Always Lags Current Flow τ = R in x C in The Vm Across C is Always Equal to Vm Across the R V m = IxR in Out V m = Q/C τ PNS, Fig 83 In PNS, Fig 82 5

6 Length Constant λ = r m /r a Spread of Injected Current is Affected by r a and r m V m = I x r m PNS, Fig 85 Synaptic Integration Receptor Potentials and Synaptic Potentials Convey Signals over Short Distances Action Potentials Convey Signals over Long Distances PNS, Fig 1213 PNS, Fig 211 The Action Potential 1) Has a threshold, is allornone, and is conducted without decrement 2) Carries information from one end of the neuron to the other in a pulsecode 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 VoltageClamp Analysis of the Action Potential PNS, Fig 210 6

7 Sequential Opening of Na and K Channels Generate the Action Potential K Rest VoltageGated Channels Closed Na Rising Phase of Action Potential Na Channels Open Falling Phase of Action Potential Na Channels Close; K Channels Open A Positive Feedback Cycle Generates the Rising Phase of the Action Potential Depolarization Open Na Channels Inward I Na Voltage Clamp Circuit The Voltage Clamp Generates a Depolarizing Step by Injecting Positive Charge into the Axon Command Voltage Clamp: 1) Steps 2) Clamps PNS, Fig 92 PNS, Fig 92 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 Command Command g = I/V PNS, Fig 92 PNS, Fig 92 7

8 Where Does the Voltage Clamp Interrupt the Positive Feedback Cycle? The Voltage Clamp Interrupts the Positive Feedback Cycle Here Open Na Channels Open Na Channels Depolarization Inward I Na Depolarization Inward I Na X 8