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Generator Potentials, Synaptic Potentials and Action Potentials All Can Be Described by the
Equivalent Circuit Model of the Membrane
PNS, Fig 2-11
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The Nerve (or Muscle) Cell can be Represented by aCollection of Batteries, Resistors and Capacitors
Equivalent Circuit Model of the Neuron
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• 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
Equivalent Circuit of the Membrane andPassive Electrical Properties
![Page 4: Generator Potentials, Synaptic Potentials and Action Potentials All Can Be Described by the Equivalent Circuit Model of the Membrane PNS, Fig 2-11](https://reader036.vdocuments.net/reader036/viewer/2022062518/56649e4f5503460f94b46dda/html5/thumbnails/4.jpg)
Ions Cannot Diffuse Across the Hydrophobic Barrier of the Lipid Bilayer
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+ + + +
- - - -
Vm = Q/C
∆Vm = ∆Q/C
The Lipid Bilayer Acts Like a Capacitor
∆Q must change before∆Vm can change
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Capacitance is Proportional to Membrane Area
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The Bulk Solution Remains Electroneutral
PNS, Fig 7-1
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Electrical Signaling in the Nervous System isCaused by the
Opening or Closing of Ion Channels
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The Resultant Flow of Charge into the CellDrives the Membrane Potential Away From its Resting Value
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Each K+ Channel Acts as a Conductor (Resistance)
PNS, Fig 7-5
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Ion Channel Selectivity and Ionic Concentration Gradient Result in an Electromotive Force
PNS, Fig 7-3
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An Ion Channel Acts Both as a Conductor and as a Battery
RT [K+]o
zF [K+]i
•lnEK =
PNS, Fig 7-6
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All the K+ Channels Can be Lumped into One Equivalent Structure
PNS, Fig 7-7
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An Ionic Battery Contributes to VM in Proportion to the
Membrane Conductance for That Ion
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When gK is Very High, gK•EK Predominates
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The K+ Battery Predominates at Resting Potential
gK≈
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The K+ Battery Predominates at Resting Potential
gK≈
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This Equation is Qualitatively Similar to theGoldman Equation
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Vm = RT•ln (PK{K+}o + PNa{Na+}o + PCl{Cl-}i)
zF (PK{K+}i + PNa{Na+}i + PCl{Cl-}o)•lnVm =
The Goldman Equation
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Ions Leak Across the Membrane atResting Potential
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At Resting Potential The Cell is in aSteady-State
In
Out
PNS, Fig 7-10
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• 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
Equivalent Circuit of the Membrane andPassive Electrical Properties
![Page 22: Generator Potentials, Synaptic Potentials and Action Potentials All Can Be Described by the Equivalent Circuit Model of the Membrane PNS, Fig 2-11](https://reader036.vdocuments.net/reader036/viewer/2022062518/56649e4f5503460f94b46dda/html5/thumbnails/22.jpg)
Passive Properties Affect Synaptic Integration
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Experimental Set-up forInjecting Current into a Neuron
PNS, Fig 7-2
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Equivalent Circuit for Injecting Current into Cell
PNS, Fig 8-2
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If the Cell Had Only Resistive Properties
PNS, Fig 8-2
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If the Cell Had Only Resistive Properties
∆Vm = I x Rin
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If the Cell Had Only Capacitive Properties
PNS, Fig 8-2
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If the Cell Had Only Capacitive Properties
∆Vm = ∆Q/C
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Because of Membrane Capacitance,Voltage Always Lags Current Flow
Rin x Cin
PNS, Fig 8-3
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The Vm Across C is Always Equal toVm Across the R
∆Vm = ∆Q/C∆Vm = IxRin
In
Out
PNS, Fig 8-2
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Spread of Injected Current is Affected by ra and rm
∆Vm = I x rm
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Length Constant = √rm/ra
PNS, Fig 8-5
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Synaptic Integration
PNS, Fig 12-13
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Receptor Potentials and Synaptic Potentials Convey Signals over Short Distances
Action Potentials Convey Signals over Long Distances
PNS, Fig 2-11
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1) Has a threshold, is all-or-none, and is conducted without decrement2) Carries information from one end of the neuron to the other in a pulse-code
The Action Potential
PNS, Fig 2-10
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• 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
Equivalent Circuit of the Membrane andPassive Electrical Properties
![Page 37: Generator Potentials, Synaptic Potentials and Action Potentials All Can Be Described by the Equivalent Circuit Model of the Membrane PNS, Fig 2-11](https://reader036.vdocuments.net/reader036/viewer/2022062518/56649e4f5503460f94b46dda/html5/thumbnails/37.jpg)
Sequential Opening of Na + and K+ Channels Generate the Action Potential
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Rising Phase ofAction PotentialRest
Falling Phase ofAction Potential
Na + ChannelsOpen
Na + Channels Close;K+ Channels Open
Voltage-Gated Channels Closed
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A Positive Feedback Cycle Generates theRising Phase of the Action Potential
Depolarization
Open Na+
Channels
Inward INa
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Voltage Clamp Circuit
Voltage Clamp:1) Steps2) Clamps
PNS, Fig 9-2
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The Voltage Clamp Generates a Depolarizing Step by Injecting Positive Charge into the Axon
Command
PNS, Fig 9-2
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Opening of Na + Channels Gives Rise to Na + Influx That Tends to Cause Vm to
Deviate from Its Commanded Value
Command
PNS, Fig 9-2
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Electronically Generated Current Counterbalances the Na + Membrane Current
Command
g = I/V
PNS, Fig 9-2
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Where Does the Voltage ClampInterrupt the Positive Feedback Cycle?
Depolarization
Open Na+
Channels
Inward INa
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The Voltage Clamp Interrupts thePositive Feedback Cycle Here
Depolarization
Open Na+
Channels
Inward INa
X