LECTURE 3: ION CHANNELS & THE RESTING MEMBRANE POTENTIAL

REQUIRED READING: Kandel text, Chapters 7, pgs 105-139

- - - - - - - - - - - - - - - - - - - - - - - - - -

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Vm = Vin - Vout

In resting neuron:

Vm ~ - 60 to - 75 mV

Membrane potential is a BATTERY providing power to drive currentswhen the cell is activated

This lecture discusses how membrane potential is establishedand maintained

- - - - - - - - - - - - - - - - - - - - - - - - - -

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + +

MEASURING THE RESTING MEMBRANE POTENTIAL:MICROPIPET FILLED WITH HIGH SALT

For this method, recording pipet has a very fine tip and is filled with a high salt solution (e.g. 3M KCl), so that pipet has very low resistance.In this way, the voltage measured by amplifier accurately reflects the voltage across the cell membrane.

(method not useful in very small cells due to pipet salt poisoning of cells)

Vpipet Vm (actual)

Rm (actual)Rpipet

Vm (measured) = Vm (actual) + Vpipet

when Rpipet <<< Rm (actual)

VVmm (measured)(measured) = V = Vmm (actual)(actual)

MEASURING THE RESTING MEMBRANE POTENTIAL:PATCH PIPET IN “WHOLE-CELL” CONFIGURATION

Patch pipet filled with cytoplasm-like solution is touched to cell membrane; with negative pressure, the pipet makes a very tight

“cell-attached” or “on-cell” seal onto membrane (leak resistance > 10 G)

Applying gentle suction can break the membrane inside the pipet, making pipet fluidcontiguous with the cytoplasm. This is the “whole-cell” configuration.

When break is made into cell, the pipet can record the membrane potential

TWO TYPES OF PROTEIN COMPLEXES CONTRIBUTE TO ESTABLISHING THE RESTING MEMBRANE POTENTIAL

ION PUMP -- drives a specific ion or group of ions from one side of the plasma membrane to the other side

Pumps drive ions ONE-WAY and use energy from ATP hydrolysisto make the process energetically favorable

ION CHANNEL -- protein complex containing a small pore which allows a specific ion or group of ions to pass

Flow of ions through channels is PASSIVE and is driven by theprevailing chemical and electrical gradients

A channel is an ion-specific resistor with a certain conductance ( g )

For most channels, the conductance is the same for ions flowing IN or OUT

Other channels allow ions to pass with greater conductance in one direction;these are called RECTIFYING CHANNELS

e.g., a channel with greater conductance of inward current is calledan inwardly rectifying channel

Na/K ATPase PUMP

Na+

22

33

ATP ADP + Pi

insideinside

outsideoutside

K+Na+/K+ ATPase USES ENERGY FROM ATP HYDROLYSIS TO PUMP

SODIUM IONS OUT OF CELL &POTASSIUM IONS INTO CELLAT A 3 Na+ : 2 K+ RATIOAT A 3 Na+ : 2 K+ RATIO

CONSEQUENCES OF PUMP ACTIVITY

[ K+ ]in >> [ K+ ]out

[ Na+ ]in << [ Na+ ]out

Net positive charge pumped outof cell causes a matching amount

of permeable chloride anions to moveout passively through channels

[ Cl- ]in << [ Cl- ]out

IONS CHANNELS

insideinside

outsideoutside

K+

Na+POTASSIUMCHANNEL

(non-gated, “leak”)

Some types of ion channels are “gated”, meaning the ion-selective pore can be either open or shut (not in-between)Such channels can be gated by ligands, phosphorylation, or voltage

Other types of ion channels are open all the timeThese channels referred to as “leak” channels

POTASSIUM CHANNELS FAVOR A NEGATIVE MEMBRANE POTENTIAL

Potassium channels are the most abundant leak channels in neurons.

Because the Na/K pump makes [K+]in >> [K+]out , potassium ions move

outwards through channels due to the chemical driving potential, EK .

(EK can be thought of as a potassium “battery”)

Net outward ion flow continues until opposed by a membrane

potential, Vm , of equal force built up in the membrane capacitor.

When Vm = 0, large K+ effluxAT EQUILIBRIUM

When Vm = EK, zero net K+ flux

inin

outout

K+

K+ Na+

Na+

Cl-

Cl- A-

inin

outout

K+

K+ Na+

Na+

Cl-

Cl- A-

+ + + +

- - - -

+ - + -

+ - + -

CIRCUIT REPRESENTATION OF POTASSIUM CONDUCTANCE,POTASSIUM BATTERY, AND MEMBRANE CAPACITANCE

When Vm = 0, large K+ efflux When Vm = EK, zero net K+ flux

inin

outout

K+

K+Na+

Na+

Cl-

Cl- A-

inin

outout

K+

K+Na+

Na+

Cl-

Cl- A-

+ + + +

- - - -

+ - + -

+ - + -

+

-

IK

CM

EK

gK

+

-

IK = 0

CM

EK

gK + + + _ _ _VM = 0 VM = EK

What is the strength of the potassium battery EK ???

THE NERNST EQUATION

The cytoplasmic and extracellular concentrations of an iondetermine the chemical driving force for that ion and

the equilibrium membrane potential if this is the ONLY ionthat is permeable through the membrane

EK+ = 58 mV

1log 5

130

Nernst EquationNernst Equation

Where EX is the chemical potential and z is the charge of ion X

[K+]in = 130 mM [K+]out = 5 mM z = +1

EX = 58 mV

z log [X]out

[X]in

= - 82 mV

For potassium:

inin

outout

K+

K+Na+

Na+

Cl-

Cl- A-

+ + + +

- - - -inin

outout

K+

K+Na+

Na+

Cl-

Cl- A-

+ - + -

+ - + -

When Vm = 0, large K+ efflux

IK = 2 pA

When Vm = EK, zero net K+ flux

IK = 0 pA

Vm

IK

EK = - 82 mV

slope = K = 25 pS IK = 2 pA

VOLTAGE-CURRENT RELATION OF THE POTASSIUM BATTERY

inin

outout

+

-EK = - 82 mV

K = 25 pS

I K =

2

pA

inin

outout

+

-EK = - 82 mV

K = 25 pS

I K =

0

Conductivity of single K channelK = 25 pS

Total K conductivity (gK )

gK = K X NK

where NK is # K channels

IK = gK x ( Vm - EK )

Vm = EK + IK RK

gK and Cm DETERMINE HOW FAST Vm CHANGES TO EK

inin

outout

K+

K+Na+

Na+

Cl-

Cl- A-

+ - + -

+ - + -

Vm (mV)

t

- 82

0

~ Cm / gK

channels open

The greater the value of gK , the greater the potassium current ( IK ) and

the faster the transition to the potassium Nernst potential ( EK)

The greater the value of Cm , the longer the potassium current ( IK ) and

the slower the transition to the potassium Nernst potential ( EK)

RESTING POTENTIAL SET BY RELATIVE PERMEABILITIES

OF K+, Na+, & Cl- IONS

EK = - 82.1 mV 1.0

ENa = + 84.8 mV 0.05

ECl = - 63.6 mV 0.2

Nernst Potential Relative Permeability (P)

Resting membrane potential reflects the relative permeabilitiesof each ion and the Nernst potential of each ion

When the resting membrane potential is achieved, there isongoing influx of sodium and a matching efflux of potassium.

Na/K ATPase is continually needed to keep the ion gradientsfrom running down over time

gK EK + gNa ENa + gCl ECl gK + gNa + gCl

Vm =PK EK + PNa ENa + PCl ECl

PK + PNa + PCl

=~

THE GOLDMAN EQUATION

PK EK + PNa ENa + PCl ECl

PK + PNa + PClVm =

from before

Nernst equatiion EX = 58 mV

z log [X]out

[X]in

Goldman equation Vm = 58 mV log10

PK[K+]o + PNa[Na+]o + PCl[Cl-]i PK[K+]i + PNa[Na+]i + PCl[Cl-]o

( )The greater an ion’s concentration and permeability, the more

it contributes to the resting membrane potentialWhen one ion is by far the most permeable, Goldman eq. reduces to Nernst eq.

RELATIVE PERMEABILITY & THE RESTING POTENTIAL

PK EK + PNa ENa + PCl ECl

PK + PNa + PClVm =

[K+]o

[K+]i

PK

= 5 mM

= 130 mM

= 145 mM

= 5 mM = 8 mM

[Na+]o

[Na+]i

PNa

[Cl-]o = 100 mM

[Cl-]i

PCl= 0.2= 0.05= 1

EK= - 82.1 mV ENa

= 84.8 mV ECl= - 63.6 mV

VVmm = - 72.4 mV = - 72.4 mV

GRAPHIC AND CIRCUIT REPRESENTATIONS OF ION FLOWSACROSS THE MEMBRANE AT THE RESTING POTENTIAL

inin

outout

K+

K+

+ + +

- - -

Cl-

Cl-K+

K+

K+

K+ Na+

Na+

+ + ++ + ++ + +

- - - - - -- - - - - -- - -

+ + + + + +Vm = - 72.4 mV

EEKK = - 82.1 mV = - 82.1 mV EENaNa = + 84.8 mV = + 84.8 mV

IIK K + + IINaNa + + IIClCl = = 00

AT STEADY STATE:

inin

outout

+

-EK = - 82.1 mV

gK = 2 nS

I K =

1

9.4

p

A

RK = 0.5 G

inin

outout

-+ENa = + 84.8 mV

gNa = 0.1 nS

I Na =

-

15

.7

pA

RNa = 10 G

EEKK + I + IKKRRKK = Vm = EENaNa + I + INaNaRRNaNa = EEClCl + I + IClClRRClCl-82.1 mV + (19.4 pA)(0.5 G-82.1 mV + (19.4 pA)(0.5 G)) = -72.4 mV = +84.8 mV + (-15.7 pA)(10 G+84.8 mV + (-15.7 pA)(10 G)) = -63.6 mV + (-3.5 pA)(2.5 G-63.6 mV + (-3.5 pA)(2.5 G))

Vm =inin

outout

-72.4 mV

+++

-- -

outout

-+

ECl = - 63.6 mV

gCl = 0.4 nS

I Cl =

-3

.5 p

A

RCl = 2.5 G

INCREASING SODIUM PERMEABILITY UNDERLIES SODIUM INFLUXAND MEMBRANE DEPOLARIZATION DURING ACTION POTENTIAL

During action potential, the number of open sodium channels increases dramatically

EK = - 82 mV 1.0 1.0

ENa = + 85 mV 0.05 5.05.0

ECl = - 64 mV 0.2 0.2

Nernst Potential Prest Paction-

potential

GOLDMAN EQUATION-PREDICTED Vm

Rest During Action Potential

- 70 mV ++ 36 mV 36 mV

When sodium channels open, sodium ions flow in rapidly because of the negative membrane potential and the strong inward sodium battery

Inward sodium current depolarizes membrane and moves it towards the positive potential predicted by Goldman’s equation

(this positive potential is never fully achieved due to additional channel dynamics)

Next Lecture: MEASURING MEMBRANE CONDUCTANCE AND CAPACITANCE &VOLTAGE-CLAMP RECORDING

REQUIRED READING: Kandel text, Chapters 8, 9 (beginning), pgs 140-153