Ionic Equilibria & Membrane Potential

Csilla Egri KIN 306 Spring 2012

Not everyone has to look so haggard doing science…

Outline

Membrane potential Nernst and GHK equations Electrophysiology

Methods Current measurements

Voltage-gated ion channels Na channel K channel

Channelopathies

2

Membrane potential - Review3

Figure 7-1 Kandel

electrochemical membrane potential (Vm) exists due to:

a) differences in ion concentrations on opposite sides of the membrane

b) selective permeability of membrane to various charged ions

Neuronal resting Vm

≈ -60 to -70mVWhat molecule(s) are responsible for the excess intracellular negative

charge?

Selective permeability4

Figure 6-9 B&B

Cell permeability to any one ion changes with opening/closing of ion channels

Direction of movement of one ion dictated by the electrochemical driving force:

(Vm - Eion)Membrane potential

Nernst potential

Driving force

Nernst Potential5

3 equivalent definitions: Predicts Vm if membrane were permeable to only ion ‘x’ The membrane potential at which there is no driving

force (no net influx/efflux) for ion ‘x’ = equilibrium potential

The membrane potential above which the direction of flux of ion ‘x’ reverses = reversal potential

RT/F = 60 mV at 310 K (37° C)

in

outX X

X

zF

RTE

][

][ln=

(Vm - Eion)Membrane potential

Nernst potential

Driving force

Goldman-Hodgkin-Katz equation

6

Predicts actual resting membrane potential (Vm)

Accounts for membrane permeability (conductance) to all major ions

oCliNaiK

iCloNaoKm ClPNaGKG

ClGNaGKG

zF

RTv

][][][

][][][ln −++

−++

++++=

Due to non-voltage gated K+ “leak” channels, at rest: GK>>GNa>GCl

Therefore resting Vm approaches that of the most permeant ion (EK)

Typical ionic concentration gradients

7

Ion Extracellular (mM)

Intracellular (mM)

Enernst

(mV at 37ºC)

Na+ 145 12 +67K+ 4.5 155 -95Ca2+ 1 10-4 +123Cl- 116 4.2 -89

What would happen to Vm if extracellular [K+] increased (hyperkalemia)?

What if extracellular [K+] decreased (hypokalemia)?

Maintenance of ionic concentration gradients

8

Na/K pump: uses energy from ATP to transport 3Na+ out for every 2K+ in Electrogenic pump (creates a net movement of positive

charge out of the cell movement of charged ions = current)

Na/Ca exchanger: Uses electrochemical energy of Na+ to drive efflux of Ca2+

(3Na+ in for one Ca2+ out) Electrogenic

Cation-chloride cotransporters: Use electrochemical gradients of cations to transport

chloride into or out of cell (depends on type of transporter) Electroneutral Mainly present in inhibitory neurons

Total membrane current (Im)9

Total membrane current (Im) is the sum of two components:

Im = Ii + Ic

Ionic current (Ii) movement of ions across the membrane through

channels

Ii = Gion x (Vm - Eion)

Ionic current

Capacitativecurrent

Ionic conductanc

e

Membrane potential

Nernst potential

Driving force

Membrane capacitance (Cm)10

Figure 6-9 B&B

Membrane capacitance (Cm) determines the ability to separate charges of opposite sign

The charge (Q) stored by a capacitor is the product of capacitance and voltage

d

ACm

κ=

mmVCQ =

Capacitative current (IC)11

capacitive current (Ic) equal to the rate of change in charge

separation

does not require movement of ions across the cell membrane, just change in Vm

Always occurs when the membrane experiences a change in voltage. Always

has an exponential decay Does not tell us anything about ion channel

function Can be used to indicate relative size of the

cell

tVCtQI mmc // ∆=∆=

Fig 6-12 B&B

Ic

Ic

d

ACm

κ= mmVCQ =

Electrophysiology – current clamp

12

Electrodes inserted in the cell membrane record the difference in membrane potential between the inside and outside of the cell

Current clamp injects current and observes resulting voltage changes

Fig 6-12 B&B

Electrophysiology – voltage clamp

13

Fig 6-13 B&B

voltage clamp holds membrane voltage constant and observes resulting current changes

Two common methods: Two-electrode voltage clamp for

large cells (squid giant axon, xenopus laevis oocytes) Electrodes actually impale cell

Patch clamp for smaller cells (mammalian cells, cultured neurons) Glass pipette filled with electrolyte

solution makes contact with cell membrane

Ic

IcIi

Electrophysiology – voltage clamp

14

Two-electrode voltage clamp

Patch clamp

Fig 6-13,14 B&B

Ionic Current Measurements15

Figure 6-13 B&B

Typical ionic current trace in response to a depolarizing stimulus when a cell membrane contains voltage gated Na+ channels

Ii Ii

Voltage Gated Na+ Channel (NaV) Structure

Figure 7-12 B&B

Inactivation gate

Inactivation gate

4 homologous domains (D1-D4) each with 6 transmembrane spanning segments (S1-S6)

Tertiary protein structure folds to form central aqueous pore (the α subunit, pore lined by S5-S6)

Accessory β subunits modulate channel gating and trafficking to the membrane

9 isoforms (NaV1.1-1.9) localized to different tissues

16

Voltage Gated Na+ Channel (NaV) Structure

Figure 7-12 B&B

Inactivation gate

Inactivation gate

17

voltage sensors – positively charged S4 segments. Move across electric field (membrane) in response to changes in Vm. Movement of all four S4s leads to channel activation.

activation gate - in center of channel pore normally closed at resting membrane potential

inactivation gate – intracellular linker between D3 and D4 normally open at resting membrane potential occludes channel pore (closes) shortly after activation time and voltage dependent

Voltage Gated Na+ Channel (NaV)Function

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Determines the rising phase of the action potential

Probability of activation gate opening increases with increasing membrane depolarization. at apprx -55mV, enough NaV channels open to

initiate all-or-none action potential inactivation gate closes about 1-2 ms later NaV channels cannot be reactivated (opened)

until inactivation gate re-opens (near resting Vm)

Voltage Gated Na+ Channel (NaV)Structure related to function

19

Mem

bran

e po

tent

ial (

mV)

Ioni

c cu

rrent

(nA)

Time (ms)0 15-70

+10

0

-2

1 2

3 4 51

2

3

45

Voltage gated K+ Channels (Kv)Structure

20

Figure 7-12 B&B

4 α subunits each with 6 transmembrane segments (S1-S6) Tertiary protein results from assembly of the 4 α subunits creating a central

aqueous pore lined by S5-S6 One accessory β subunit modulates channel function 40 isoforms with different gating and current generating properties localized

to different tissues

Voltage gated K+ Channels (Kv)Function

21

Have two important divisions, Kv channels that mediate either:

Delayed outward rectifying currents Activation has a sigmoidal, delayed lag phase Responsible for the downward phase of the action

potential Transient A-type outward rectifying

currents Activate and inactivate over a short time scale Important in determining interval between action

potentialsBoth pass only outward current B&B pg. 197

Voltage gated K+ Channels (Kv)Function

22

Gao B , Ziskind-Conhaim L J Neurophysiol 1998;80:3047-3061

Control: current trace depicting all types of Kv currents in a mouse motorneuronIK: non-inactivating delayed rectifier K currentIA: transient A-type K current

Voltage dependence of activation

23

Figure 7-7B&B

Na+ K+

When P0=0.5 half the channels are

open, half are closed. The Vm that

this occurs at is called the V1/2 of

activation

Macroscopic current-voltage relationships

24

Where on this figure is the equilibrium potential for K+ and Na+?

Why is the I-V relationship for Na+ biphasic?

Figure 7-6 B&B

Ii = Gion x (Vm - Eion)

Channelopathies25

Amino acid mutations in ion channels leading to improper protein function and disease

Schematic of NaV1.4 and associated disease causing mutationsFigure 7-15 B&B

Paramyotonia congenita (PMC)26

PMC patients have no symptoms at warm temperatures, but are subject to cold induced myotonia (muscle stiffness). With intensive cooling, the myotonia can give way to periodic paralysis of the muscles.

Caused by mutations to NaV1.4, predominant in skeletal muscle, that impair inactivation of the channel Mild impairment to inactivation: results in small depolarizing

current, bringing the membrane slightly closer to threshold and increasing cellular excitability myotonia or stiffness

Severe impairments to inactivation: can significantly depolarize membrane (from -90mV to -40mV) placing unmutated channels in the inactivated state membrane is refractory muscle weakness or paralysis

Both genotype and phenotype are heterogeneousWhy cold exacerbates PMC symptoms is yet to be determined.

WebCT readings: Paramyotonia Congenita

Objectives

After this lecture you should be able to: Describe what gives rise to the membrane potential and how

ionic concentration gradients are maintained Describe the ways in which electrical properties of

membranes can be measured and distinguish between current clamp and voltage clamp

Define the components of total membrane current List the key features of voltage gated sodium and potassium

channels, including structure, voltage-dependence of activation and current-voltage relationships

Explain the causes of PMC and distinguish between the molecular causes of myotonia and weakness or paralysis

27

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1. Would you use voltage or current clamp to observe action potentials in neurons in response to excitatory neurotransmitters?

2. At a membrane potential of -30mV, would there be more Na+ or K+ current?

3. If a person with PMC had elevated serum K+ levels, would this increase or decrease the likelihood of experiencing an episode of myotonia?

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