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Ionic basis of the resting membrane potential Foundations in Neuroscience I, Oct 3 2017

Ionic basis of the resting membrane potential...Big ideas: Resting membrane potential-Ion transport across the membrane-The electrochemical gradient-Equilibrium potential for Na+,

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Ionic basis of the resting membrane potential

Foundations in Neuroscience I, Oct 3 2017

The next 4 lectures . . .

- The resting membrane potential (today)- The action potential- The neural mechanisms behind them (voltage

gated ion channels)- Neurotransmitter release

Resting potential and action potential: simple view

-

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!

Resting membrane potential

Review: Cell membrane

Credit: Mariana Ruiz Villarreal

Review: Transport across the cell membrane

Review: Transport across the cell membrane

Review: Transport across the cell membrane

Movie?

Electrochemical gradient

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

Resting membrane potential

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.

Pause: Everything cool?

Electrical circuit model for a neuron

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

RC circuits: Capacitors

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

Explain current clamp recordings here

Do movie here?

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 . . .

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

Simulations!

- Start SimCC program (current clamp mode)- File → Open to load file- Start with StepResistance.cc5- Hit Control-Y to run the simulation- Top trace is voltage- Bottom trace is injected current- Parameters menu controls the simulation- Menus on upper right control the display