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1 Electrical Signaling in the Nervous System is The Bulk Solution - PDF document

Sep 26, 2022 •358 likes •457 views

Equivalent Circuit Model of the Neuron Generator Potentials, Synaptic Potentials and Action Potentials All Can Be Described by the Equivalent Circuit Model of the Membrane The Nerve (or Muscle) Cell can be Represented by a Collection of

  1. Equivalent Circuit Model of the Neuron Generator Potentials, �Synaptic Potentials and Action Potentials All Can Be Described by the Equivalent Circuit Model of the Membrane The �Nerve (or Muscle) Cell can be Represented by a Collection of Batteries, Resistors and Capacitors PNS, Fig 2-11 Equivalent Circuit of the Membrane and Ions Cannot Diffuse Across the Hydrophobic Barrier of the Lipid Bilayer 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 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. Electrical Signaling in the Nervous System is The Bulk Solution Remains Electroneutral Caused by the Opening or Closing of Ion Channels + - - + - - - - + + + - - + - + - - - + + + - - - - + - - + The Resultant Flow of Charge into the Cell Drives the Membrane Potential Away From its Resting Value PNS, Fig 7-1 Each K + Channel Acts as a Conductor Ion Channel Selectivity and Ionic Concentration (Resistance) Gradient Result in an Electromotive Force PNS, Fig 7-5 PNS, Fig 7-3 An Ion Channel Acts Both as a Conductor and as a Battery All the K + Channels Can be Lumped into One Equivalent Structure RT [K + ] o E K = • ln zF [K + ] i PNS, Fig 7-6 PNS, Fig 7-7 2

  3. An Ionic Battery Contributes to V M in Proportion to the When g K is Very High, g K •E K Predominates Membrane Conductance for That Ion 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 ) • ln V m = zF (P K {K + } i + P Na {Na + } i + P Cl {Cl - } o ) 3

  4. Ions Leak Across the Membrane at At Resting Potential The Cell is in a Resting Potential Steady-State Out In PNS, Fig 7-10 Passive Properties Affect Synaptic Integration 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 Experimental Set-up for Equivalent Circuit for Injecting Current into Cell Injecting Current into a Neuron PNS, Fig 8-2 PNS, Fig 7-2 4

  5. If the Cell Had Only Resistive Properties If the Cell Had Only Resistive Properties ∆ V m = I x R in PNS, Fig 8-2 If the Cell Had Only Capacitive Properties If the Cell Had Only Capacitive Properties ∆ V m = ∆ Q/C PNS, Fig 8-2 The Vm Across C is Always Equal to Because of Membrane Capacitance, Vm Across the R Voltage Always Lags Current Flow Out ∆ V m = IxR in ∆ V m = ∆ Q/C τ = R in x C in τ In PNS, Fig 8-2 PNS, Fig 8-3 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 8-5 Receptor Potentials and �Synaptic Potentials Synaptic Integration Convey Signals over Short Distances Action Potentials Convey Signals over Long Distances PNS, Fig 2-11 PNS, Fig 12-13 The Action Potential Equivalent Circuit of the Membrane and Passive Electrical Properties 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 – 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 PNS, Fig 2-10 6

  7. Sequential Opening of Na + and K + Channels A Positive Feedback Cycle Generates the Generate the Action Potential Rising Phase of the Action Potential Rising Phase of Falling Phase of Rest Action Potential Action Potential Open Na + Channels Na + Channels Close; Voltage-Gated Na + Channels K + Channels Open Open Channels Closed Na + + + + - - + + - - Inward I Na Depolarization K + - - + - - + + - - + - - + - - - - + + - - + + + + + + + + + - - - - - - + + + + - - - + - + + + + - - + + + - - + - - + + + + + + - + + - - - - - - - - - + + + - - + - - + + + + + The Voltage Clamp Generates a Depolarizing Step by Voltage Clamp Circuit Injecting Positive Charge into the Axon Command Voltage Clamp: 1) Steps 2) Clamps PNS, Fig 9-2 PNS, Fig 9-2 Opening of Na + Channels Gives Rise to Na + Electronically Generated Current Counterbalances the Na + Membrane Current Influx That Tends to Cause V m to Deviate from Its Commanded Value Command Command g = I/V PNS, Fig 9-2 PNS, Fig 9-2 7

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

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