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Introduction to electrophysiology 1.
Dr. Tóth András
Today topics
• Transmembran transport
• Donnan equilibrium
• Resting potential
Level of significance
• “Entry” level (even under 6)
• “Student” level (for most of you)
• “Gourmand” level (only for the pros)
1. Transmembran transport
Major types of transmembran transport
1
dx
dcA
JD
x
cDAJ
dx
dcDAJ
=
∆
∆−=
−=J: net rate (flux) of diffusion
A: area
dc/dx: concentrationgradient
D: diffusion coefficient
(D: cm2/s)
Fick’s first law of diffusion
2
ηπ r
kTD
6=
Diffusion of solutes as a consequence of the random
thermal (Brownian) motion of the particles
Stokes–Einsteinequation
Einstein relation____
(∆x2) = 2 Dt
3
Time required for diffusion as a function of diffusion
distance
4
Fick’s law for membrane
x
DK
x
cDAJ
x
cDAJ
∆=
∆
∆−=
∆
∆−=
β
β
Diffusion across a semipermeable membrane
ββββ: partition coefficient
K: permeability coefficient
5
Osmotic motion across a semipermeable membrane
6
Definition of the osmotic pressure
ΦΦΦΦ: osmotic coefficient
ΦΦΦΦic: osmotically effectiveconcentration - osmolarity
van’t Hoff’s Law
π= iRTm
π= iRTc
π = RTΦic
Φic = ∆Tf /1.86
I.e.: 154 mM NaCl solution
ππππ = 6.42 atm
Φ Φ Φ Φic = 0.286 osmol/L
7
Mechanism of facilitated diffusion
8
Principle of transport of ions across ion channels
9
The principle of function of the Na+/K+–ATPase
10
Secondary active transport processes
11
Transport via proteins shows saturation kinetics
Michaelis-Menten
equation
Vmax: maximal rate of
transport
Km: concentration of
the substrate for
which the rate of
transport is equal
to Vmax/2
12
2. Ionic equilibrium
[ ][ ] ( )BA
B
A
o
EEzFX
XRT
zFECRT
−+=∆
++=
+
+
ln
ln
µ
µµ
Electrochemical potential (difference)
13
Nernst equation
[ ][ ] ( )
( ) [ ][ ]
[ ][ ]B
ABA
B
ABA
BA
B
A
X
X
zF
RTEE
X
XRTEEzF
EEzFX
XRT
mEquilibriu
+
+
+
+
+
+
−=−
=−−
−+=
ln
ln
ln0
[ ][ ] lg60
B
A
X X
XmVE
+
+
−=+
For monovalentcations
Z = 1
14
A B
0.1 M
K+
0.01 M
K+
EA – EB = -60 mV
Examples of uses of the Nernst equation
0.1 M
HCO3-
EA – EB = +100 mV
A B
1 M
HCO3-
Is there equilibrium in any of the two cases?
15
A B
0.1 M
K+
0.01 M
K+
EA – EB = −−−−60 mV
Examples of uses of the Nernst equation
A B
At –60 mV the K+ is in electrochemical equilibrium
across the membran
No electric force !!!
+++++++
–––––––
16
1 M
HCO3-
0.1 M
HCO3-
A B
0.1 M
K+
0.01 M
K+
EA – EB = −−−−60 mV
Examples of uses of the Nernst equation
EA – EB = +100 mV
A B
At –60 mV the K+ is in electrochemical equilibrium
across the membran
No electric force
At the given membran potential the HCO3
- is not in electrochemical equilibrium
Electric force: +40 mV
+++++++
–––––––
––––––––
++++++++
17
1 M
HCO3-
0.1 M
HCO3-
A B
[K+] = 0.1 M
[P-] = 0.1 M
[K+] = 0.1 M
[Cl-] = 0.1 M
A B
[K+] =
[Cl-] =
[P-] = 0.1 M
[K+] =
[Cl-] =
Initial state
Before Donnan equilibrium is established
1. The principle of electroneutrality should be preserved !!!
2. The electrochemical potential should be zero for each diffusible ion !!! (Not for the undiffusible ion !!!)
Equilibrium?
18
A B
[K+] = 0.1 M
[P-] = 0.1 M
[K+] = 0.1 M
[Cl-] = 0.1 M
A B
[K+] = 0.133 M*
[Cl-] = 0.033 M*
[P-] = 0.1 M
[K+] = 0.066 M*
[Cl-] = 0.066 M*
Initial state Equilibrium state* (!?)
Gibbs-Donnan equilibrium has been attained
1. The principle of electroneutrality is, indeed, valid !!!
2. The electrochemical potential is zero for K+ and Cl- !!!
3. * So, is there any problem ???
19
A B
[K+] = 0.1 M
[P-] = 0.1 M
[K+] = 0.1 M
[Cl-] = 0.1 M
A B
[K+] = 0.133 M
[Cl-] = 0.033 M
[P-] = 0.1 M
[K+] = 0.066 M
[Cl-] = 0.066 M
Starting state Equilibrium state
In Gibbs-Donnan equilibrium a transmembrane
hydrostatic pressure gradient is present
(There is no equilibrium between pressures !!!)
∆∆∆∆PH = 2.99 atm !!!
20
3. Resting potential
The „concentration battery”
A B
0.1 M
NaCl
0.01 M
NaCl
If the membrane is permeable for cations, but
unpermeable for anions, cation current is
needed to reach equilibrium !!!
21
The „concentration battery”
A B
+
+
+
+
+
+
+
–
–
–
–
–
–
–
In case of electrochemical equilibrium
EA – EB = - 60 mV
Na+
22
0.1 M
NaCl
0.01 M
NaCl
“Measured” intra- and extracellular ionconcentrations
23
A simplified model of the resting membrane potential in
the human skeletal muscle
mV
P
mV
mV
mV
Na
90E 4)
0Prot 3)
P )2
- - 150 Prot
90- 115 3,6 Cl
100- 3,5 160 K
65 145 12 Na
E (mM) EC (mM) IC 1)
m
100K
-
-
eq
−=
=
⟩⟩
+
++
+
+
-90 mV
Cl- Na+
cc cc
cc
E E
E
K+
24
+++
+++
−−−
−=
−=
≈−=
=∆
=
KKmK
NaNamNa
ClClmCl
gEEI
gEEI
gEEI
Rg
R
UI
)(
)(
0)(
1
Conditions for the “chord conductance” equation
Theoretical estimation for the resting potential 1.
25
+
++
+
+
++
+
++++
++
++
+=
−−=−
=+
Na
NaK
Na
K
NaK
Km
KKmNaNam
KNa
Egg
gE
gg
gE
gEEgEE
II
)()(
0
++
++
+=
NaKm EEE1100
1
1100
100
+6
0
0
-70
-90
Na+
K+
Em
The “chord conductance”equation
gNa+ = 1 gK+ = 100
26
The “constant field” (Goldman-Hodgkin-Katz) equation
opClipNaipK
ipClopNaopKm
ClkNakKk
ClkNakKk
F
RTE
][][][
][][][ln
−++
−++
++
++=
Theoretical estimation for the resting potential 2.
27
Major factors affecting resting potential
C
28
Also in cardiac cells the resting potential is supposed to
be [K+] dependent
29
In cardiac cells the resting potential is, indeed, primarily
[K+] dependent
30
Q:
What are the principal differences between the following iontransporters?
1. Sodium-calcium exchanger
2. Sodium-hidrogen exchanger3. Calcium pump of the sarcolemma
What does equilibrium potential mean for a given ion ???
When is Gibbs-Donnan equilibrium present across a living cell membrane?
In Fig. 14 how much Na+ has to pass the membrane to reach equilibrium?
Which are the primary conditions for establishing and maintaining steady resting potential?
What is the reason, for in one cell type (rbc) the resting potential equals –30 mV, while in an
other (cardiac) cell type it equals –90 mV?
What are the major factors determining the actual value of membrane potential?
