Transcript Document

Lecture 17
Introduction into Electrophysiology
Approaches to the Nernst eqn
What is driving force for an ion moving across the
membrane?
The Goldman eqn
Components of excitable membranes and their role
in spike generation
(Reading: chapters 11 and 23)
Equilibrium (reversal) potential
#2
#1
K+
Cl#3
K+
Cl-
K+
Cl-
equilibrium
+ +
+
K
K
- +
Cl- - + Cl-
At 37oC:
let K+ cross
cin
e
cout
Cl-

z
kT
(Boltzmann)
(Nernst)
RT cin
ln
zF cout
61.5
cin

log
(mV)
z
cout
  
Erev
K+
The distribution of charged particles in two wells
separated by an electric potential difference 
G
cin
 e kT
cout

G  ze
ze 
cin
 e kT
cout

Boltzmann
Work of transfer of a charge across a  gap
or per mole:
 cin
zF   RT ln
 cout
energy
differences:
zF 
cin
 e RT
cout

electric
chemical




Why logarithmic?
nRT
P
V
PV  nRT
1
dG  PdV  nRT dV
V
V2
V2

G   PdV  nRT
V1

V1
normalizing to the volume
c2 V1

c1 V2
dV
1
dV  nRT ln V2  ln V1 
V
 V2 
 V1 
 nRT ln   nRT ln 
 V1 
 V2 
c = n/V
 c2 
 RT ln 
 c1 
What is driving force?
E (mV)
K+
Cl-
K+
Cl-
K+
ClI K  g K ( E  EK )
I
K+
Cl-
I
driving
force
V
EK = 0
V
EK < 0
But there are several types of ions inside and
outside the cell, and each of them has its own
reversal potential. Hmmm.
How do they contribute to the effective membrane
potential that is measured by a micro-electrode?
The exact value of Em is given by Goldman eqn.
_
K+
Na+
Cl-
R1
K+
Na+
Cl-
R2
_
+
pK [K ]in  pNa [ Na ]in  pCl [Cl ]out
RT

ln
F
pK [K  ]out  pNa [ Na  ]out  pCl [Cl  ]in

Emem
+


Goldman eqn describes not an equilibrium, but a steady-state, thus
pumps are required to maintain it.
Bi-ionic system is described by Goldman eqn
in its short form:
K+
pK
K+
pNa
Na+
Na+

Emem  61.5  log
[K ]in 
[K  ]out 
p Na
pK
p Na
pK
[ Na  ]in
[ Na  ]out
(mV)
Em = -70 mV
Erev
[K+]in = 150 mM
[K+]out = 5 mM
-90 mV
[Na+]in = 15
[Na+]out = 150
+60
[Cl-]in = 9
[Cl-]out = 125
-70
[Ca2+]in = 10-4
[Ca2+]out = 2
+129
Conventions:
Membrane potential is
always measured
“INSIDE” vs. “OUTSIDE”
depolarization
Erest= -70 mV
hyperpolarization
Action Potentials
from B. Hille, Ion Channels of Excitable Membranes
in
Na+
pK
+40 mV
time
K+
pNa
spike
K+
ENa=+60 mV
out
Na+
Erest=-70 mV
EK = -90 mV

Emem  61.5  log
[K ]in 
[K  ]out 
p Na
pK
p Na
pK

[ Na ]in
[ Na  ]out
(mV)
8-12
The peak of K+ current coincides with the falling phase of the action potential
What is necessary for spike generation?
3. Fast V-gated Na+ channels
Na+
4. Delayed V-gated K+ channels
K+
2K+
3Na+
1. Na/K pump
K+
2. Leakage K+ channel
K+
Na+
+30
-70
K+
Na+
Rf
Patch-clamp circuit
stimulus
voltage-gated channels
Em
+10
threshold = -50
-70
pore domain
Fast Na+ channel
C
voltage
sensor
4 subunits form a channel
O
refractory period
I
Delayed K+ channel
Number of closed states n = 3-7
C1
C2
Cn
O
I
Passage through several nonconductive states provides the
delay for activation
Ensemble response is the sum of
multiple small stochastic currents
of single channels
from B. Hille, Ion Channels of Excitable Membranes
Structure of V-gated channel with the inactivation gate
The voltage sensors are not shown
Inactivation of a K+ channel mutant without the inactivation gate
can be rescued with a synthetic peptide