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The next 4 lectures . . .
- The resting membrane potential (today)- The action potential- The neural mechanisms behind them (voltage
gated ion channels)- Neurotransmitter release
Big ideas: Resting membrane potential
- Ion transport across the membrane- The electrochemical gradient- Equilibrium potential for Na+, K+ and Cl-- Nernst and GHK equations- Passive membrane properties- Electrical circuit model of the membrane- Simulations!
Electrochemical gradient: reaching equilibrium
Positive ions flow down concentration gradient, from out to in
Cell interior becomes electropositive
Net ion flow stops when there is enough positive charge inside to prevent more positive ions from coming in
Electrical potential at which net ion flow is zero -> Equilibrium potential
Depends on concentration of the ions in and out of the cell
Major ions that determine resting potential: Na+, K+, and Cl-
IonExtracellular conc. (mM)
Intracellular conc. (mM)
K+ 4 120
Na+ 150 15
Cl- 120 5
Na+/K+ pump
Major ions that determine resting potential: Na+, K+, and Cl-
Na+/K+ pump
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Equilibriumpotential
K+ 4 120 < 0
Na+ 150 15 > 0
Cl- 120 5 < 0
Major ions that determine resting potential: Na+, K+, and Cl-
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-
eability
K+ 4 120 high
Na+ 150 15 low
Cl- 120 5 low
Na+/K+ pump
Super key point: The membrane potential is dominated by the ion with the largest permeability
IonExtracel.
conc. (mM)Intracellular conc. (mM)
Membrane perm-
eability
K+ 4 120 high
Na+ 150 15 low
Cl- 120 5 low
Nernst Equation and equilibrium potentials
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high < 0
Na+ 150 15 low > 0
Cl- 120 5 low < 0
Nernst Equation and equilibrium potentials
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high < 0
[K+]out : ion concentration outside the cell[K+]in : ion concentration inside the cell
z: charge of the ion (signed)
T: Temperature in KelvinR: constant (universal gas constant 8.3 Joules/molKF: constant (Faraday constant 9.6 x104 coulombs/mol)
Nernst Equation and equilibrium potentials
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high < 0
[K+]out : ion concentration outside the cell[K+]in : ion concentration inside the cell
z: charge of the ion (signed)
T: Temperature in KelvinR: constant (universal gas constant 8.3 Joules/molKF: constant (Faraday constant 9.6 x104 coulombs/mol)
Nernst Equation and equilibrium potentials
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high < 0
[K+]out : ion concentration outside the cell[K+]in : ion concentration inside the cell
z: charge of the ion (signed)
T: Temperature in KelvinR: constant (universal gas constant 8.3 Joules/molKF: constant (Faraday constant 9.6 x104 coulombs/mol)
Nernst Equation and equilibrium potentials
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high < 0
[K+]out : ion concentration outside the cell[K+]in : ion concentration inside the cell
z: charge of the ion (signed)
T: Temperature in KelvinR: constant (universal gas constant 8.3 Joules/molKF: constant (Faraday constant 9.6 x104 coulombs/mol)
Nernst Equation and equilibrium potentials for: Na+ and Cl-
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high -85
Na+ 150 15 low > 0
Cl- 120 5 low < 0
Equilibrium potentials for K+, Na+, and Cl-
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high -85mV
Na+ 150 15 low 58mV
Cl- 120 5 low -79mV
Equilibrium potentials for K+, Na+, and Cl-
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high -85mV
Na+ 150 15 low 58mV
Cl- 120 5 low -79mV
Bringing it all together: the GHK Equation
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high -85mV
Na+ 150 15 low 58mV
Cl- 120 5 low -79
Goldman-Hodgkin-Katz (GHK) equation for K+, Na+ and Cl-
GHK Example: membrane only permeable to Na+
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 0 -85mV
Na+ 150 15 > 0 58mV
Cl- 120 5 0 -79mV
Goldman-Hodgkin-Katz (GHK) equation for K+, Na+ and Cl-
Vm = ENa = 58mv
Bringing it all together: the GHK Equation
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high -85mV
Na+ 150 15 low 58mV
Cl- 120 5 low -79mV
Goldman-Hodgkin-Katz (GHK) equation for K+, Na+ and Cl-
Vm ≈ EK = -75mV
Driving force and Na+/K+ pumps
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high -85mV
Na+ 150 15 low 58mV
Cl- 120 5 low -79mV
Vm ≈ EK = -75mV
Difference between Vm and Equilibrium potential: “Driving force”
Ek < -75mV → K leaks out of the cellENa > -75mV → Na leaks into the cellECl ≈ -75mV → Little net Cl- flow
Somewhere in here would be good to explain that ion concentrations remain stable, that ionic imbalance is extremely tiny in the molar sense, but that it has big effects on electrical potential.
RC circuits: Resistors
V = IR R = R1 + R21/R =
1/R1 + 1/R2
Serial resistance adds linearlyParallel resistance
adds inverselyOhms law
V = I/g
I = gV1/g = 1/g1 + 1/g2 g = g1 + g2
Serial conductanceadds inversely
Parallel conductanceadds linearly
Electrical circuit model for a neuron
Capacitor: Lipid membrane, charges accumulate on either side
Resistor (conductance): ion-specific channels e.g. K+ leak channels
Battery: Equilibrium potential -- i.e. the electrochemical gradient for each ion that drives ion flow across the membrane.
A neuron circuit modelSame Vm regardless of the “path” through the circuit
Vm
Circuit equivalent ofGHK equation
Passive properties of neurons and axons
Voltage changes slowly over time . . . . . . due to capacitance of cell membrane
Passive properties of neurons and axons“Time constant” for charging membrane
Membrane “time constant”
. . . due to capacitance of cell membrane
RmCm
Higher time constant → slower charging time, slower signal propagation, more temporal integration
Lower time constant → faster charging time, faster signal propagation,less temporal integration
Passive properties of neurons and axons
Voltage decays over distance . . .
. . . due to leaky membrane
currentIm Im Im Im
Cable properties“Length constant” for signal spread
Im Im Im Im
Voltage along axon at distance (x) from current sourceWhere voltage is maximal (V0)
Longer length constant → longer propagation of voltageShorter length constant → shorter propagation of voltage
Cable properties recap
Longer length constant → longer propagation of voltageShorter length constant → shorter propagation of voltage
RmCm
Higher time constant → slower charging time, slower signal propagation, more temporal integration
Lower time constant → faster charging time, faster signal propagation,less temporal integration
Time constant for charging capacitor
Length constant for current spread
Summary: electrochemical gradient
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high -85mV
Na+ 150 15 low 58mV
Cl- 120 5 low -79mV
Summary: Nernst and GHK
IonExtracellular conc. (mM)
Intracellular conc. (mM)
Membrane perm-eability
Equilibriumpotential
K+ 4 120 high -85mV
Na+ 150 15 low 58mV
Cl- 120 5 low -79mV
Summary: RC circuit model of the neuronSame Vm regardless of the “path” through the circuit
Vm
Circuit equivalent ofGHK equation
Summary: passive properties of neurons and axons
Voltage decays over distance . . .
RmCm
Time constant Length constant