Monday April 9, 2014.
Nervous system and biological electricity II
1. Pre-lecture quiz
2. A review of resting potential and Nernst equation
3. Goldman equation
4. Action potential
Information flow through neurons
Nucleus
Dendrites Cell body
Axon
Collect
electrical
signals
Passes electrical signals
to dendrites of another
cell or to an effector cell
Integrates incoming signals
and generates outgoing
signal to axon
Neurons form networks for information flow
Animation of resting potential
• https://www.youtube.com/watch?v=YP_P6bY
vEjE
Outside of cell
Increasing [K+]
outside the
neuron
Microelectrode
Equilibrium!
0 mV
K channel
– 65 mV
Increasingly
negative
charge inside
the neuron
Inside of cell
The Nernst equation can be used to calculate the equilibrium potential of
a given ion
æéX ùö
æéX ùö
RT
ë 1û ÷
ë 1û ÷
ç
ç
E = 2.3
log
= 58mV *log
çé X ù÷
çé X ù÷
ZF
èë 2 ûø
èë 2 ûø
Inside cell
Outside cell
[K+]
400 mM
20 mM
[Na+]
50 mM
440 mM
[Cl-]
51 mM
560 mM
at 20° C
Alan Hodgkin
Andrew Huxley
Squid have axons about 1,000 X wider than humans. This
allowed them to do the early experiments that provided critical
insights into how neurons work.
Squid Neuron - Continued
Important Point #1: They measured actual membrane potential (E-membrane) for the
squid axon.
voltage
meter
SW
nerve
1mm
diameter
axon
0.1mm
diameter
Emembrane-measured = -65 mV
Squid Neuron - Continued
Important Point #2: They measured the concentrations of Na+, K+, and Cl- inside the
squid neuron and outside of it.
Emembrane-measured = -65 mV
voltage
meter
SW
nerve
1mm
diameter
axon
0.1mm
diamter
In
Out
[K+]
400 mM
20 mM
[Na+]
50 mM
440 mM
[Cl-]
51 mM
560 mM
Squid Neuron - Continued
Important Point #2: They measured the concentrations of Na+, K+, and Cl- inside the
squid neuron and outside of it.
What is the predicted membrane potential
based on each of these ions?
To answer . . . we simplify the Nernst equation
to the following for Na+ and K+.
E m em brane
 [ out ] 
 58 m V * log 

[
inside
]


In
Out
[K+]
400 mM
20 mM
[Na+]
50 mM
440 mM
[Cl-]
51 mM
560 mM
For Cl-, we alter the ratio due to the negative
charge (valence). The formula is the following . . .
æ [inside] ö
Emembrane = 58mV *log ç
÷
è [outside] ø
Remember: -log (x) = log (1/x)
What's the e-membrane potential based on K+?
E m em brane
A.
B.
C.
D.
E.
 [ out ] 
 58 m V * log 

[
inside
]


-75mV
+75 mV
-173mV
-1.3 mV
+173mV
In
Out
[K+]
400 mM
20 mM
[Na+]
50 mM
440 mM
[Cl-]
51 mM
560 mM
Squid Neuron - Continued
Important Point #2: They measured the concentrations of Na+, K+, and Cl- inside the
squid neuron and outside of it.
In
Out
Predicted E-membrane from Nernst
Emembrane -K+ = -75 mV
[K+]
400 mM
20 mM
[Na+]
50 mM
440 mM
[Cl-]
51 mM
560 mM
E membrane -Na+ = 55 mV
Emembrane- Cl- = -60 mV
Measured E-membrane
Emembrane-measured = -65 mV
Squid Neuron - Solution
Solution: We need a way to consider the effects of all 3 ions on the membrane
potential. Will the sum of these predicted values equal the measured membrane
potential?
In
Out
Predicted E-membrane from Nernst
Emembrane -K+ = -75
[K+]
400 mM
20 mM
[Na+]
50 mM
440 mM
[Cl-]
51 mM
560 mM
E membrane -Na+ = 55
Emembrane- Cl- = -60
Emembrane-sum= -80
Measured E-membrane
Emembrane-measured = -65 mV
Calculating the total resting potential – the Goldman Equation
The Goldman Equation extends the Nernst Equation to consider the relative
permeabilities of the ions (P): Ions with higher P have a larger effect on Emembrane
E m em brane
  PK  [ K  ] o    PN a  [ N a  ] o    PC l  [ C l  ]i  


at 20° C
 58 m V * log



  PK  [ K ]i    PN a  [ N a ]i    PC l  [ C l ] o  


Permeabilities change during an action potential and how this allows
neurons to “fire”.
More key points on equilibrium &
membrane potential
• The equilibrium potential for an ion is the voltage at
which the concentration and electrical gradients acting
on that ion balance out.
• The Nernst equation is a formula that converts energy
stored in a concentration gradient to the energy stored
as an electrical potential. This is calculated
independently for each ion.
• The Goldman equation calculates a membrane
potential by combining the effects of key individual
ions.
The Action Potential Is a Rapid Change
in Membrane Potential
1. Depolarization
phase
2. Repolarization
phase
Threshold potential
Resting potential
3. Hyperpolarization phase
Outside of cell
Increasing [K+]
outside the
neuron
Microelectrode
Equilibrium!
0 mV
K channel
– 65 mV
Increasingly
negative
charge inside
the neuron
Inside of cell
Voltage-gated sodium channels allow
the action potential to occur
• https://www.youtube.com/watch?v=ifD1YG07
fB8
Voltage-gated channels
Two important types:
1.) Na+ voltage gated channels
2.) K+ voltage gated channels
How voltage-gated channels work
At the resting potential, voltagegated Na+ channels are closed.
Conformational changes open
voltage-gated channels when
the membrane is depolarized.
Patch Clamping Allows Researchers to Record from Individual Channels
Currents through isolated channels can be measured during
an action potential.
Inward
current
from Na+
channels
Outward
current
from K+
channels
Resting Potential - Both voltage gated Na+ and K+ channels are
closed.
Initial Depolarization - Some Na+ channels open. If enough Na+
channels open, then the threshold is surpassed and an action
potential is initiated.
Na+ channels open quickly. K+ channels are still closed.
PNa+ > PK+
Na+ channels self-inactivate, K+ channels are open.
PK+ >> PNa+
Emembrane ≈ E K+
PK+ > PK+ at resting state
Resting Potential - Both Na+ and K+ channels are closed.
Action Potentials Propagate because Charge Spreads down the Membrane
PROPAGATION OF ACTION POTENTIAL
Axon
Neuron
1. Na+ enters axon.
2. Charge spreads;
membrane
“downstream”
depolarizes.
Depolarization at
next ion channel
3. Voltage-gated
channel opens in
response to
depolarization.
Action Potentials Propagate Quickly in Myelinated Axons
Action potentials jump down axon.
Action potential jumps
from node to node
Nodes of Ranvier
Schwann cells (glia)
wrap around axon,
forming myelin sheath
Axon
Schwann cell membrane
wrapped around axon
Wider axons have higher conduction velocities.
Myelinated axons have higher conduction velocities.