The document discusses ionic equilibria and membrane potential, including the Nernst and Goldman-Hodgkin-Katz equations. It describes voltage-gated sodium and potassium channels, their structure and function, and how they contribute to the generation and repolarization of action potentials. The document also discusses channelopathies like paramyotonia congenita, a sodium channel mutation that causes muscle stiffness and weakness in response to cold temperatures due to impaired channel inactivation.

1. Ionic Equilibria & Membrane
Potential
Csilla Egri KIN 306 Spring 2012
Not everyone has to look so haggard doing science…

2. Outline
 Membrane potential
 Nernst and GHK equations
 Electrophysiology
 Methods
 Current measurements
 Voltage-gated ion channels
 Na channel
 K channel
 Channelopathies
2

3. Membrane potential - Review
3
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 -70mV
What molecule(s) are responsible
for the excess intracellular negative
charge?

4. Selective permeability
4
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

5. Nernst Potential
5
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
out
X
X
X
zF
RT
E
][
][
ln=
(Vm - Eion)
Membrane
potential
Nernst
potential
Driving
force

6. Goldman-Hodgkin-Katz
equation6
 Predicts actual resting membrane potential
(Vm)
 Accounts for membrane permeability
(conductance) to all major ions
oCliNaiK
iCloNaoK
m
ClPNaGKG
ClGNaGKG
zF
RT
v
][][][
][][][
ln −++
−++
++
++
=
Due to non-voltage gated K+ “leak” channels, at
rest: GK>>GNa>GCl
Therefore resting Vm approaches that of the
most permeant ion (E )

7. Typical ionic concentration
gradients7
Ion Extracellu
lar (mM)
Intracellu
lar (mM)
Enernst
(mV at
37ºC)
Na+
145 12 +67
K+
4.5 155 -95
Ca2+
1 10-4
+123
Cl-
116 4.2 -89
What would happen to Vm if extracellular [K+] increased
(hyperkalemia)?
What if extracellular [K+] decreased (hypokalemia)?

8. Maintenance of ionic concentration
gradients8
 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

9. 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
Capacitative
current
Ionic
conductanc
e
Membrane
potential
Nernst
potential
Driving
force

10. 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
A
Cm
κ
=
mmVCQ =

11. 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
A
Cm
κ
= mmVCQ =

12. Electrophysiology – current
clamp12
 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

13. Electrophysiology – voltage
clamp13
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

14. Electrophysiology – voltage
clamp14
 Two-electrode voltage
clamp
 Patch clamp
Fig 6-13,14 B&B

15. Ionic Current Measurements
15
Figure 6-13 B&B
Typical ionic current trace in
response to a depolarizing
stimulus when a cell membrane
contains voltage gated Na+
Ii Ii

16. 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

17. 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

18. Voltage Gated Na+
Channel (NaV)
Function18
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)

19. Voltage Gated Na+
Channel (NaV)
Structure related to function19
Membrane
potential(mV)Ioniccurrent(nA)
Time (ms)
0 15
-70
+10
0
-2
1 2
3 4 5
1
2
3
4
5

20. Voltage gated K+
Channels (Kv)
Structure20
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

21. Voltage gated K+
Channels (Kv)
Function21
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
potentials
Both pass only outward current B&B pg. 197

22. Voltage gated K+
Channels (Kv)
Function22
Gao B , Ziskind-Conhaim L J Neurophysiol 1998;80:3047-3061
Control: current trace depicting all types of Kv currents in a mouse
motorneuron
IK: non-inactivating delayed rectifier K current
IA: transient A-type K current

23. Voltage dependence of
activation23
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

24. Macroscopic current-voltage
relationships24
 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)

25. Channelopathies
25
 Amino acid mutations in ion channels leading to improper protein
function and disease
Schematic of NaV1.4 and associated disease causing mutations
Figure 7-15 B&B

26. 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 heterogeneous
Why cold exacerbates PMC symptoms is yet to be determined.
WebCT readings: Paramyotonia Congenita

27. 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

28. 28
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?
Test your knowledge