1. Chapter 5: Membrane Potentials and Action Potentials
Slides by Thomas H. Adair, PhD

2. Molecular Gradients inside outside 14 142 140 4 0.5 1-2 Na+ 10-4 K+
(in mM) 14
140
0.5
10-4
(pH 7.2) 10
5-15 2 75 40
outside
(in mM)
142 4
1-2
(pH 7.4) 28
110 1 5
Na+ K+
Mg2+
Ca2+ H+
HCO3-
Cl-
SO42-
PO3-
protein

3. K+ Na+ Active Transport inside outside Na+ K+ 3 Na+ 2 K+
ATP K+
3 Na+
2 K+
ADP
Remember: sodium is pumped out of the cell, potassium is pumped in...

4. Simple Diffusion
inside
outside K+
Na+

5. - charge difference across the membrane -
Membrane Potential (Vm):
- charge difference across the membrane -
inside
outside
…how can passive diffusion of potassium and sodium lead to development of negative membrane potential? K+ K+
Na+
Na+

6. K+ Simplest Case Scenario: inside outside
If a membrane were permeable to only K+ then… K+ K+
K+ would diffuse down its concentration gradient until the electrical potential across the membrane countered diffusion.

7. K+ Simplest Case Scenario: inside outside
If a membrane were permeable to only K+ then… K+ K+
The electrical potential that counters net diffusion of K+ is called the K+ equilibrium potential (EK).

8. The Potassium Nernst Potential
…also called the equilibrium potential
EK = log Ki Ko
Example: If Ko = 5 mM and Ki = 140 mM
EK = -61 log(140/4)
EK = -61 log(35)
EK = -94 mV
So, if the membrane were permeable only to K+, Vm would be -94 mV

9. Na+ Simplest Case Scenario: inside outside
If a membrane were permeable to only Na+ then…
Na+
Na+ would diffuse down its concentration gradient until potential across the membrane countered diffusion.
Na+
The electrical potential that counters net diffusion of Na+ is called the Na+ equilibrium potential (ENa).

10. So, if the membrane were permeable only to Na+, Vm would be +61 mV
The Sodium Nernst Potential
Nai
Nao
EK = log
Example: If Nao = 142 mM and Nai = 14 mM
EK = -61 log(14/142)
EK = -61 log(0.1)
EK = +61 mV
So, if the membrane were permeable only to Na+, Vm would be +61 mV

11. Resting Membrane Potential
Vm -90 to -70
EK -94
ENa +61
0 mV
Vm for warm blooded animals in skeletal muscle and nerve is between -55 and -100 mV. Vm is between -55 and -30 for smooth muscle fibers. Most textbooks give a value of -70 mV for nerve and skm.
Why is Vm so close to EK?
Ans. The membrane is far more permeable to K than Na..

12. . . The Goldman-Hodgkin-Katz Equation p V ] [ ' log = 61 p V ] [ ' log
(also called the Goldman Field Equation)
Calculates Vm when more than one ion is involved. o Cl i Na K m p V ] [ '
log . - + = 61 i Cl o Na K m p V ] [ '
log . - + =
-61 or
Cl ions are distributed across the membrane in accordance with their equilibrium potential – when Vm changes, Cl ions redistribute themselves in accordance to the new Vm, i.e., Eq Cl = Vm. Cell membranes of muscles have Cl permeability equal to or greater than that of K.
NOTE:
P’ = permeability

13. The Goldman-Hodgkin-Katz Equation
Take home message…
The resting membrane potential is closest to the equilibrium potential for the ion with the highest permeability!

14. Resting Membrane Potential Summary
Figure 5-5; Guyton & Hall 40 40

15. Resting and action potentials
Recall that cells:
contain high a K+ concentration
have membranes that are essentially permeable to K+ at rest
Membrane electrical potential difference (membrane potential) is generated by diffusion of K+ ions and charge separation
measured in mV (=1/1000th of 1V)
typically resting membrane potentials in neurons are -70 to 90 mV – +
0 mV
-80 mV +
Voltmeter + – –

16. Properties of action potentials
threshold
-70
+60 mV
Stimulus
Action potentials:
are all-or-none events
threshold voltage (usually 15 mV positive to resting potential)
are initiated by depolarization
action potentials can be induced in nerve and muscle by extrinsic (percutaneous) stimulation
have constant amplitude
APs do not summate - information is coded by frequency not amplitude.
Fiber diameter (mm)
Velocity (m/s) 3 6 9
Myelinated
(cat) 12 75 15 50 25
have constant conduction velocity
True for given fiber. Fibers with large diameter conduct faster than small fibers. As a general rule:
non-myelinated
(squid)
800
400
myelinated fiber diameter (in mm) x 4.5 = velocity in m/s.
Square root of unmyelinated fiber diameter = velocity in m/s

17. The AP - membrane permeability
1 ms
+61
(mV)
-90
ENa EK
downstroke
During the upstroke of an action potential:
Na permeability increases
due to opening of Na+ channels
memb. potential approaches ENa
upstroke
resting potential
During the downstroke of an action potential:
Na permeability decreases
due to inactivation of Na+ channels
Membrane
hyperpolarized
K permeability increases
due to opening of K+ channels
mem. potential approaches EK
Number of open channels
Na+ channels
K+ channels
After hyperpolarization of membrane following an action potential:
not always seen!
There is increased K+ conductance
due to delayed closure of K+ channels
Copyright © 2006 by Elsevier, Inc.

18. Ion channels Ion channels - structure Ion channel - properties
proteins that span the membrane
have water filled channel that runs through protein
Ion channel - properties
Have conducting states and non-conducting states
transition between states = ‘gating’
open
inactivation
inactivated
closed
depolarization
repolarization
channels ‘gate’ in response to:
changes in membrane potential (usually depolarization)
voltage-gated channels. Action potential propagation relies on voltage-gated channels
occupation of receptor
ligand-gated or receptor operated channels (ROCs). These initiate action potentials
mechanical forces
mechanosensitive channels - important for hearing.

19. Propagation:
Opening of Na+ channels generates local current circuit that depolarizes adjacent membrane, opening more Na+ channels…
Rest
Stimulated
(local depolarization)
Propagation
(current spread)

20. Signal Transmission: Myelination
Schwann cells surround the nerve axon forming a myelin sheath
Sphingomyelin decreases membrane capacitance and ion flow 5,000-fold
Sheath is interrupted every 1-3 mm : node of Ranvier
Figure 5-16; Guyton & Hall

21. Saltatory Conduction AP’s only occur at the nodes (Na
channels concentrated here!)
increased velocity
energy conservation
Figure 5-17; Guyton & Hall

22. - non-myelinated vs myelinated -
Conduction velocity
- non-myelinated vs myelinated -
non-myelinated
myelinated

23. Multiple Sclerosis
Patients have a difficult time describing their symptoms. Patients may present with paresthesias of a hand that resolves, followed in a couple of months by weakness in a leg or visual disturbances. Patients frequently do not bring these complaints to their doctors because they resolve. Eventually, the resolution of the neurologic deficits is incomplete or their occurrence is too frequent, and the diagnostic dilemma begins.
- MS is an immune-mediated inflammatory demyelinating disease of the CNS -
- About 1 person per 1000 in US is thought to have the disease - The female-to-male ratio is 2:1 - whites of northern European descent have the highest incidence
Copyright © 2006 by Elsevier, Inc.