Download Lect3

Announcements:
•
Last lecture
1. Organization of the nervous system
2. Introduction to the neuron
•
Today – electrical potential
1.
2.
3.
4.
Generating membrane potential
Nernst equation
Goldman equation
Maintaining ionic distributions
Neural Signaling
A Simple Circuit
Within
neurons
electrical
Between
neurons
chemical &
electrical
Bioelectric Potentials
• Neurons have an electrical potential
(voltage) across the cell membrane
• The inside of the cell is more negative
than the outside
– called the Resting Membrane Potential
Measuring Membrane Potential
amplifier
microelectrode
Reference
electrode
Resting potential
0 mV
cell
-80 mV
Bathing solution
time
Electrophysiology techniques
Silver / Silver chloride
wire electrode
Amplifier
output
Reference electrode
3M KCl solution
Glass micropipette
Very tiny hole (<<0.1m)
Resting Membrane Potential
• How is it generated?
1. differential distribution of ions inside
and outside the cell
2. Selective Permeability of the
membrane to some ions
• How does unequal concentration of ions
give rise to membrane potential ?
Equal concentrations of ions
voltmeter
0 volts
Artificial ion selective
membrane (only K+, not Cl-)
I
Cl-
II
K+
Cl-
K+
0.01 M
KCL
0.01 M
KCL
Cl-
K+
K+
Cl-
No net movement
Unequal concentrations of ions
-
volts
+
Ion selective membrane
(only K+, not Cl-)
I
Cl-
II
K+
Cl-
K+
0.1 M
KCL
0.01 M
KCL
Cl-
K+
K+
+
K
-
Cl
K+
ClCl-
K+ concentration
gradient
K+
Initial
K+ ClCl-
K+
ClK+
New Equilibrium
Cl-
K+
K+
Cl-
Cl-
Cl-
K+
Cl-
Cl-
K+
K+
CHEMICAL
Cl-
K+
Cl-
Cl-
K+
ClCl-
+K+
+
+ K+
+
+
K
+
+
K
+
Cl-
Cl-
Cl-
Cl-
CHEMICAL
ELECTRICAL
Unequal concentrations of ions
• Initial diffusion of K+ down concentration
gradient from I to II
• This causes + charge to accumulate in II
because + and - charges are separated
– Remember that Cl- can’t cross the
membrane !
• Therefore II becomes positive relative to I
Equilibrium Potential
•
As II becomes +, movement of K+ is repelled
•
Every K+ near the membrane has two
opposing forces acting on it:
1. Chemical gradient
2. Electrical gradient
•
These two forces exactly balance each
other
•
Called the electrochemical equilibrium
•
•
•
The electrical potential that develops is called
the equilibrium potential for the ion.
Electrical potential at which there is no
net movement of the ion
Note:
1. only a very small number of ions actually contribute
to the electrical potential
2. the overall concentrations of K and Cl in solution do
not change.
• To calculate the equilibrium potential of any ion
(eg. K, Na, Ca,) at any concentration
– we use the Nernst Equation:
Nernst Equation
Gas Constant
Temp (K)
Ion Concentration I
RT [ X ]I
Ex 
ln
zF [ X ]II
Equilibrium Potential
of X ion (eg. K+) in Volts
Valence of
ion (-1, +1, +2)
Ion Concentration II
Faraday constant
Nernst Equation
• At 18C, for a monovalent ion, and converting to
log10 ,the equation simplifies to:
X
0.058
[X
]I  I

0.058
EXEx z log
log[ X ]II
z
 X  II
• By convention electrical potential inside of cells
is expressed relative to the outside of the cell
0.058
[ X ]outside
Ex 
log
z
[ X ]inside
Example: K+
in
out
EK 
0.1 M
KCL
X I
0.058
log
z
 X  II
0.02 M
KCL
0.058
[ X ]out
EK 
log
z
[ X ]in
0.02
EK  0.058log
0.1
= -0.040 Volts
= - 40 mV
• Therefore,
– initial movement of K+ down concentration
gradient
– When electrical potential of -40 mV develops,
there will be no net movement of K+
– Thus K+ is in electrochemical equilibrium
What if there is more than
one permeable ion?
in
0.1 M KCl
0.02 M NaCl
out
K+
Na+
0.01 M KCl
0.2 M NaCl
Na+
K+
K+
Na+
K+
Na+
Na+
K+
Permeable to K+ and Na+, but not Cl-
Na+
K+
• To calculate the overall potential of
multiple ions
• use the Goldman Equation
• Considers the permeability of ions and
their concentrations
Goldman equation
Voltage
PK[ K ]outside  PNa[ Na]outside  PCl[Cl ]inside
Vm  0.058log
PK[ K ]inside  PNa[ Na]inside  PCl[Cl ]outside
Permeability
Ion concentration
Because Cl is negative
Goldman equation
•
Example, typical mammalian cell:
1. Assume permeability for Na is 1/100 of permeability
for K, and permeability of Cl is 0
2. Assume [K]in= 140, [K]out=5
[Na]in =10, [Na]out=120
1[5]  0.01[120]  0
Vm  0.058log
1[140]  0.01[10]  0
Vm  78mV
Goldman equation
• The resting membrane potential of most
cells is predicted by the Goldman equation
Summary & Key Concepts
1. Unequal distributions of an ion across a
selective membrane
•
causes an electrochemical potential called
the equilibrium potential
2. Two opposing forces act on ions at the
membrane
1. A chemical force down the concentration
gradient
2. An opposing electrical force
Summary & Key Concepts
3. The equilibrium potential for an ion is
described by the Nernst equation
4. Cell membranes are permeable to more
than one ion
5. the membrane electrical potential is
described by the Goldman equation
So What???
• Everything the nervous system and
muscles do depends on the resting
membrane potential
Sample question
•
If two concentrations of KCl solution
across a membrane give an equilibrium
potential for K+ of -60 mV, what will the
equilibrium potential be if the
concentrations on each side are
reversed
A.
B.
C.
D.
-120 mV
0
+60 mV
-30 mV