Generator Potentials, Synaptic Potentials and Action Potentials All Can Be Described by the Equivale

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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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Equivalent Circuit Model of the Neuron
The Nerve (or Muscle) Cell can be Represented by
a Collection of Batteries, Resistors and
Capacitors
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Equivalent Circuit of the Membrane andPassive
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

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Ions Cannot Diffuse Across the Hydrophobic
Barrier of the Lipid Bilayer
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The Lipid Bilayer Acts Like a Capacitor
Vm Q/C

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?Vm ?Q/C
?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 theOpening or Closing of Ion
Channels

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The Resultant Flow of Charge into the Cell Drives
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 Ko
ln
EK
zF Ki
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, gKEK 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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The Goldman Equation
Vm RTln (PKKo PNaNao PClCl-i)
ln
Vm
zF (PKKi PNaNai PClCl-o)

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Ions Leak Across the Membrane atResting Potential
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At Resting Potential The Cell is in
a Steady-State
Out
In
PNS, Fig 7-10
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Equivalent Circuit of the Membrane andPassive
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

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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
t Rin x Cin
t
PNS, Fig 8-3
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The Vm Across C is Always Equal toVm Across the R
Out
?Vm ?Q/C
?Vm IxRin
In
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 l vrm/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 DistancesAction
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 andPassive
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

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Sequential Opening of Na and K Channels
Generate the Action Potential
Rising Phase ofAction Potential
Falling Phase ofAction Potential
Rest
Na Channels Open
Na Channels Close K Channels Open
Voltage-Gated Channels Closed
Na
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A Positive Feedback Cycle Generates theRising
Phase of the Action Potential
Open Na Channels
Inward INa
Depolarization
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Voltage Clamp Circuit
Voltage Clamp 1) Steps 2) 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 toDeviate 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?
Open Na Channels
Inward INa
Depolarization
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The Voltage Clamp Interrupts thePositive
Feedback Cycle Here
Open Na Channels
Inward INa
Depolarization
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