HOD DEPARTMENT OF PHYSIOLOGY GOVT; MEDICAL COLLEGE SRINAGAR KASHMIR INDIA

1. Electrical properties of cell membrane I
(Diffusion & Equilibrium Potential)
DR QAZI IMTIAZ RASOOL

2. OBJECTIVES
1. Define diffusion potential of an ion and simply
conclude how to calculate it
2. Discuss the concept of charge separation.
3. Explain the methods of calculation of equilibrium
potential when the membrane is permeable to
several ions.
4. Define Donnan equilibrium and discuss its
consequences
5. Apply this knowledge to a practical instance.

3. BASICS FACTS
Molecular Gradients
Na+
K+
Mg2+
Ca2+
H+
HCO3
-
Cl-
SO4
2-
PO3
-
protein
inside
(in mM)
14
140
0.5
10-4
(pH 7.2)
10
5-15
2
75
40
outside
(in mM)
142
4
1-2
1-2
(pH 7.4)
28
110
1
4
5

4. ions glucose
H2O
urea
Lipid Bilayer
CO2
O2
N2
halothane

5. 1. lipid-soluble molecules move readily across the membrane
(rate depends on lipid solubility)
2. H2O soluble molecules cross via channels or pores
(a) (b)
Diffusion

6. 1. Ungated
Determined by size, shape, distribution of charge, et
2.Gated voltage (e.g. voltage-dependent Na+ channels)
chemically (e.g. nicotinic ACh receptor channels.
Characteristics:
Na+
in
out
Na+ and other ions
Ion Channels

7. Ion concentrations
Cell Membrane in resting state
K+
Na+ Cl-K+
A-
Outside of Cell
Inside of Cell
Na+ Cl-

8. Cell Membrane is Semi-Permeable
Cell Membrane at rest
Na+ Cl-
K+
Na+ Cl-K+ A-
Outside of Cell
Inside of Cell
(K+) can pass
through to equalize
its concentration
Na+ and Cl- cannot
pass through
Result - inside is
negative relative to
outside
- 55 to -100mv

10. ELECTRICAL POTENTIAL=CHARGE SEPARATION
- +
Hydration Shells
In H2O, without a membrane
hydrated Cl
- is smaller than hydrated Na+ therefore faster:
Cl-
Na+

11. Basic Concepts
Forces that determine ionic movement
Volt;- A charge difference between 2 points
in space
1. Electrostatic forces
1. Opposite charges attract
2. Identical charges repel
2. Concentration forces
1. Diffusion – movement of ions through semipermeable
membrane
2. Osmosis – movement of water from region of high
concentration to low

12. ELECTRONEUTRAL DIFFUSSION
HIGH SALT
CONC;
LOW SALT
CONC;
+
-
BARRIER SEPARATES THE
TWO SOLUTIONS
+
-
+
-
+
-
+
-+
-
+
-
+
-

13. ELECTRONEUTRAL DIFFUSSION
HIGH SALT
CONC;
LOW SALT
CONC;
+
-
BARRIER REMOVED
+
-
+
-
+
-
+
-+
-
+
-
+
-
+ -
CHARGE SEPARATION = ELECTRICAL POTENTIAL

14. is the potential difference generated across a membrane when a charged
solute (an ion) diffuses down its concentration gradient.
( caused by diffusion of ions.)
can be generated only if the membrane is permeable to that ion.
FEATURES;-1. if not permeable to the ion, no DP will be generated no matter
how large a conc; gradient is present.
2. magnitude/Unit =, measured in mV,
3. depends on the size of the concentration gradient, where the concentration
gradient is the driving force.
4. Sign of the DP depends on the charge of the diffusing ion.
5. DP are created by the movement of only a few ions, and they do not cause
changes in the concentration of ions in bulk solution.
Diffusion Potentials(DP)

15. EP(electrochemical equilibrium), is the DIFFUSION POTENTIAL that
exactly balances or opposes the tendency for diffusion down the
concentration difference. At the chemical and electrical driving
forces acting on an ion are equal and opposite,
FEATURES;-
1.Membrane is polarized
2.More –ve particles in than out
3. Bioelectric Potential i.e,battery
1. Potential for ion movement
2. Current
EQUILIBRIUM POTENTIAL (EP)

16. At Electrochemical Equilibrium:
4.Concentration gradient for
the ion is exactly balanced
by the electrical gradient
5.No net flux of the ion
6.No requirement for any
sort of energy-driven pump
to maintain the concentration
gradient

17. -
Electrical potential (EMF)
The Nernst potential (equilibrium potential) is the theoretical
intracellular electrical potential that would be equal in magnitude but
opposite in direction to the concentration force.
-
-
-
- -
-
-
-
- -
-
- -
-
-
-
-
-
-
-
-
-
-
-
- -
-
-
-
-
-
-
-
-
-
+
-
-
--
-
-
-
-
- -
-
-
-
-
-
- -
+ When will the
negatively charged
molecules stop
entering the cell?
-

18. Calculating equilibrium potential
The Nernst Equation
- at which an ion will be in electrochemical equilibrium.
At this potential: total energy inside = total energy outside
Electrical Energy Term: zFV
Chemical Energy Term: RT.ln[Ion]
Z is the charge, 1 for Na+ and K+, 2 for Ca2+ and Mg2+, -1 for Cl-
F is Faraday’s Constant = 9.648 x 104 Coulombs / mole
R is the Universal gas constant = 8.315 Joules / °Kelvin * mole
T is the absolute temperature in °Kelvin
Equilibrium potential (mV) , Eion =
EK = -90mV
ENa = +60mv
i
o
K
K
K
ZF
RT
E
][
][
log +
+


19. 1. Cell membranes form an insulating barrier that acts
like a parallel plate capacitor (1 μF /cm2)
2. Only a small number of ions must cross the membrane to
create a significant voltage difference
3. Bulk neutrality of internal and external solution
4. Cells need channels to regulate their volume
5. Permeable ions move toward electrochemical equilibrium
6. Eion =calculated as NERST POTENTIAL
7. Electrochemical equilibrium does not depend on permeability,
only on the concentration gradient
CAPACITANCE

20. Electrical properties
The membrane potential
In the resting state, the intracellular space contains more negative ions than the
extracellular space
difference of -50 to
+120mV

21. THE MEMBRANE POTENTIAL
M
E
M
B
R
A
N
E
Extracellular
Fluid Intracellular
Fluid
Na+
K+
Sodium channel is less open
causing sodium to be slower
Potassium channel is more open
causing potassium to be faster
+ - MEMRANE POTENTIAL
(ABOUT 90 -120 mv)

23. Membrane potential
1. Cell membrane acts as a barrier--ICF from mixing with ECF
2. 2 solutions have different concentrations of their ions. Furthermore, this difference in
concentrations leads to a difference in charge of the solutions..
3. Therefore,+ve ions will tend to gravitate towards -ve solution. Likewise, -ve ions will
tend to gravitate towards +ve solution.
4. Then the difference between the inside voltage and outside voltage is determined
membrane potential.
When a membrane is permeable to several different ions, DP
developed depends on:
1.Polarity of the electrical charge of ions.
2. Permeability of the membrane (P) to each ion.
3. Concentration of each ion in two compartments separated by
the membrane.
MP is calculated by Goldman-Hodgkin-Katz equation.

24. icliNaiK
ocloNaoK
m
ClPNaPKP
ClPNaPKP
F
RT
V
][][][
][][][
log -++
-++
+
+

Membrane Potential:
Goldman Equation
1. P = permeability
At rest: PK: PNa: PCl = 1.0 : 0.4 : 0.45
2. Net potential movement for all ions
3. Known Vm:Can predict direction of movement of any ion
~
NOTE:
P’ = permeability

25. EQUIVALENT ELECTRICAL CIRCUIT MODEL
1. With unequal distribution of ions and differential resting conductances to those
ions,
2. We can use the Nernst equation and Ohm’s law in an equivalent circuit model
to predict a stable resting membrane potential of -75 mV, as is seen in many
cells
NB, this is a steady state and not an equilibrium, since K+ and Na+ are not at their
equilibrium potentials; there is a continuous flux of those ions at the RMP
RMP Em = (EK * gK) + (ENa * gNa) + (ECl * gCl)
gNa + gK + gCl

26. Chord Conductance Equation
Cl
E
Cl
g
Na
g
K
g
Cl
g
Na
E
Cl
g
Na
g
K
g
Na
g
K
E
Cl
g
Na
g
K
g
K
g
Vm
++
+
++
+
++

1. Vm = EK+ +ENa+ + ECl-....
Vm = membrane potential, not equal to Eion;
2. Weighted avg of equilibrium potentials of all ions to which membrane is
permeable
3. Esp. K+, Na+, Cl-; changes in ECF K+ alters RMP in all cells

27. Passive distribution
Donnan equilibrium
The ratio of positively charged permeable ions equals
the ratio of negatively charged permeable ions
III
K+
Cl-
III
[K+] = [K+]
[Cl-] = [Cl-]
Start Equilibrium

28. DONNAN EQUILIBRIUM
Mathematically expressed:
•Another way of saying the number of positive charges must
equal the number of negative charges on each side of the
membrane
[ ] [ ]
[ ] [ ]
I II
II I
K Cl
K Cl
+ -
+ -


29. PASSIVE DISTRIBUTION
1. BUT, in real cells there are a large number of
negatively charged, impermeable molecules
(proteins, nucleic acids, other ions)
2. call them A-
III
K+
Cl-
Start
A- III
[K+] > [K+]
[Cl-] < [Cl-]
Equilibrium
A-

30. DONNAN POTENTIAL:
III
[K+] > [K+]
[Cl-] < [Cl-]
Equilibrium
A- [K+]I = [A-]I + [Cl-]I
[K+]II = [Cl-]II
If [A-]I is large, [K+]I must
also be large
A=phosphate anions+
protiens macromolecules
+’ve = -’ve+’ve = -’ve
space-charge neutrality
-----------
+++++++++++

31. EXAMPLE
1. The product of Diffusible Ions is the same on the
two sides of a membrane.
33 K+
33 Cl-
67 K+
50 Pr -
17 Cl-Step 2
66 Osmoles 134 Osmoles
50 K+ 50 K+
50 Cl-
50 Pr -
Initial
100 Osmoles 100 Osmoles
Final
33 ml 67 ml
33 K+
33 Cl-
67 K+
50 Pr -
17 Cl-
Total Volume
100 ml
Ions
Move
H2O
moves

32. Human Potentials
1. Strong potentials in muscles--EMG, ECG (electromyogram
and electrocardiogram).
2. Weaker potentials from brain--EEGs.
3. Evoked potentials allow study of changes.
4. Computer averaging allows study of deep brain potentials:
Event-related potentials in sensory systems and cognition.