### Week 2 Membrane Potential and Nernst Equation

```Week 2 Membrane Potential and
Nernst Equation
Key points for resting membrane potential
• Ion concentration across the membrane
• Eion: Equilibrium potential for an ion, and how to use Nernst Equation
to calculate it
• driving force = Vm – Eion
Vm is the membrane potential of the neuron at that time, not always
the resting membrane potential. Eion will change from the value in the
table, depending on the ion concentration across the membrane, and
the temperature.
• Goldman equation: the ion channel permeability and ion
concentrations of all the ions across the membrane decide where the
membrane potential is at that time.
• When the ion concentration and the channel permeability are the
same as indicated in the table, Vm=VRMP, resting membrane potential
• De-polarization and hyper-polarization: the former means the
membrane potential of a neuron becomes more positive, and the
latter means the potential becomes more negative.
Nernst Potential
• Calculates the exact value of the equilibrium potential
for each ion in mV
• Takes into consideration:
– Charge of the ion
– Temperature
– Ratio of the external and internal ion concentrations
Concentration
K+ moving out
Chapter 5 & 6: Ionic
Basis of
Membrane
Potential
Fact:
In face, no net flux.
Explanation:
electrochemical equilibrium
For single ion equilibrium potential, use Nernst Equation
E ion  ( RT / zF ) ln( C out / C in )
or Eion =2.303 RT/zF log(Co/ Cin)
R is the universal gas constant (8,315 mJ/(K Mol)),
T is temperature in degrees Kelvin (K = 273.16+C),
F is Faraday’s constant (96,480 Coulombs/Mol),
z is the valence of the ion (z = 1 for Na+ and K+, z = -1
for Cl-, and z = 2 for Ca2+).
for K+ and Na+: Eion = 62 log (Co/ Ci)
for Cl-: ECl = -62 log (Co/ Ci)
for Ca2+: ECa = 31 log (Co/ Ci)
Extracellular and intracellular ion concentrations
for a “typical” neuron at its resting stage
For example:
EK = 62 log (5/100)
EK = 62 (-1.3)
EK = -80mV
How to calculate E for an ion using given concentrations?
To which direction an ion moves when its channel opens at a given time?
Ions tends to move to the direction that brings the Vm to its own Em
So driving force is the only thing you need to consider at this time!
And only thinking about one ion at a time!
Usually the neurons rest on ~-65mV, the
difference (-15mV) is the driving force for K+
to move out
 try to reach K+ equilibrium potential
Vm > EK (for example, -65mV > -80mV)
K+ more outward, hyper-polarization
Vm = EK
no current/movement, I = 0
Vm < EK (more negative)
K+ move inward, de-polarization
Driving Force = Vm - Eion
To estimat Vm and consider multiple ions, use Goldman
V rest
 58 log
m
62
equation
PN a [ N a ] o  PK [ K ] o  PC l [ C l ]i
PN a [ N a ]i  PK [ K ]i  PC l [ C l ] o
=-68mV
The membrane potential is always driven toward the equilibrium potential of the ion to
which the membrane is most permeable.
That is why we have depolarization during action potential!
- Threshold for massive
amount of voltage gated
Na+ channel to open
- Rising Phase because of
Na+ influx (try to bring
Vm to its own ENa)
- Falling Phase (PNa
decreases, while PK
increases. So K+ become
the dominate one again)
- Undershoot (afterhyperpolarization)
Why K+ channel has the highest P at the resting stage?
T1: voltage-gated Na+ channels open. It
takes about 1ms for them to
inactivate and for voltage-gated K+
channel to open
T2
inactivate
Rising phase
T2, the voltage-gated Na+ channels
inactivate and the voltage-gated K+
channels are opening
Falling Phase
T1
-55mV
T3
Absolute Refractory Period
Na+ channel inactivation
Undershoot (after-hyperpolarization)
T3, The voltage-gated K+ channels close
Relative Refractory Period
Na+ channel de-inactivated, it
becomes possible to have
another AP, just difficult
Characteristics of Action Potentials:
because they are voltage gated channels!!!
1.
2.
3.
4.
5.
6.
Have a threshold for initiation (~ 10 mV depolarization above rest)
All or nothing (below threshold = none, above threshold = all)
Always depolarizing
Constant amplitude (~100 mV)
Constant duration (~2-3 msec)
Have refractory periods
a. absolute (during falling phase)
b. relative (during undershoot a.k.a. afterhyperpolarization)
7. Propagate without decrement
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