Electrical properties of cell membrane I
(Diffusion & Equilibrium Potential)
DR QAZI IMTIAZ RASOOL
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.
BASICS FACTS
Molecular Gradients
outside
(in mM)
Na+
K+
142
inside
(in mM)
14
4
140
Mg2+
1-2
0.5
Ca2+
1-2
10-4
H+
HCO3Cl-
(pH 7.4)
28
110
(pH 7.2)
10
5-15
SO42-
1
2
PO3-
4
75
protein
5
40
Lipid Bilayer
CO2
ions
glucose
N2
H2O
urea
O2
halothane
Diffusion
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)
Ion Channels
Characteristics:
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.
in
Na+ and
Na+
other ions
out
Ion concentrations
Outside of Cell
K+
Na+
Cl-
Cell Membrane in resting state
K+
Na
+
Cl-
Inside of Cell
A-
Cell Membrane is Semi-Permeable
K+
Na+
Cl-
Outside of Cell
Cell Membrane at rest
K+
Na+
Cl-
Inside of Cell
(K+) can pass
through to equalize
its concentration
Na+ and Cl- cannot
pass through
A- 55 to -100mv
Result - inside is
negative relative to
outside
ELECTRICAL POTENTIAL=CHARGE SEPARATION
In H2O, without a membrane
hydrated Cl is smaller than hydrated Na+ therefore faster:
Hydration Shells
-
+
ClNa+
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
ELECTRONEUTRAL DIFFUSSION
LOW SALT
CONC;
HIGH SALT
CONC;
+
+
-
+
+
-
+
-
+
-
+
-
+
-
-
-
BARRIER SEPARATES THE
TWO SOLUTIONS
ELECTRONEUTRAL DIFFUSSION
HIGH SALT
CONC;
+
+
LOW SALT
CONC;
+
-
+
+
-
-
+
-
+
+
-
-
+
-
BARRIER REMOVED
CHARGE SEPARATION = ELECTRICAL POTENTIAL
Diffusion Potentials(DP)
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.
EQUILIBRIUM POTENTIAL (EP)
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.
2.
Potential for ion movement
Current
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
Electrical potential (EMF)
+
-
-
-
-
-
- - - -- - - -- - -- - - - - - - -
+
When will the
negatively charged
molecules stop
entering the cell?
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.
Calculating equilibrium potential
The Nernst Equation
- at which an ion will be in electrochemical equilibrium.
At this potential: total energy inside = total energy outside
+
RT [ K ]
E 
log
ZF
[K ]
o
Equilibrium potential (mV) , Eion =
Electrical Energy Term: zFV
Chemical Energy Term: RT.ln[Ion]
K
+
i
EK = -90mV
ENa = +60mv
Z is the charge, 1 for Na+ and K+, 2 for Ca2+ and Mg2+, -1 for ClF 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
CAPACITANCE
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
Electrical properties
The membrane potential
difference of -50 to
+120mV
In the resting state, the intracellular space contains more negative ions than the
extracellular space
THE MEMBRANE POTENTIAL
Extracellular
Fluid
K+
Na+
Potassium channel is more open
causing potassium to be faster
+
M
E
M
B
R
A
N
E
Intracellular
Fluid
Sodium channel is less open
causing sodium to be slower
-
MEMRANE POTENTIAL
(ABOUT 90 -120 mv)
Membrane potential
1.
2.
Cell membrane acts as a barrier--ICF from mixing with ECF
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.
Membrane Potential:
Goldman Equation
P [ K ] + P [ Na ] P [Cl ]
RT
V 
log
F
P [ K ] + P [ Na ] P [Cl ]
+
K
+
o
Na
+
m
K
-
o
cl
+
i
Na
o
-
i
cl
i
NOTE:
P’ = permeability
1.
2.
3.
P = permeability
At rest: PK: PNa: PCl = 1.0 : 0.4 : 0.45
Net potential movement for all ions
Known Vm:Can predict direction of movement of any ion
~
EQUIVALENT ELECTRICAL CIRCUIT MODEL
RMP
1.
Em = (EK * gK) + (ENa * gNa) + (ECl * gCl)
gNa + gK + gCl
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
Chord Conductance Equation
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
Vm 
g
g
K
+g
K
Na
+g
E
Cl
K
+
g
g
K
+g
Na
Na
+g
E
Cl
Na
+
g
g
K
+g
Cl
Na
+g
E
Cl
Cl
Passive distribution
Donnan equilibrium
The ratio of positively charged permeable ions equals
the ratio of negatively charged permeable ions
Start
I
Equilibrium
II
K+
Cl-
I
II
[K+] = [K+]
[Cl-] = [Cl-]
DONNAN EQUILIBRIUM
Mathematically expressed:
+
-
[ K ]I [Cl ]II

+
[ K ]II [Cl ]I
•Another way of saying the number of positive charges must
equal the number of negative charges on each side of the
membrane
PASSIVE DISTRIBUTION
BUT, in real cells there are a large number of
negatively charged, impermeable molecules
(proteins, nucleic acids, other ions)
call them A-
1.
2.
Start
I
AK+
Cl-
Equilibrium
II
I
A[K+] > [K+]
[Cl-] < [Cl-]
II
DONNAN POTENTIAL:
Equilibrium
I
-A- --[K+] ----
[Cl-]
+’ve = -’ve
+
+
+
+
+
+
+
+]
[K
+
+
+
+
>
II
[K+]I = [A-]I + [Cl-]I
[K+]II = [Cl-]II
< [Cl-]
+’ve = -’ve
space-charge neutrality
If [A-]I is large, [K+]I must
also be large
A=phosphate anions+
protiens macromolecules
EXAMPLE
1.
The product of Diffusible Ions is the same on the
two sides of a membrane.
Initial
50 K+
50 Pr -
50 K+
50 Cl100 Osmoles
Step 2
33 K
33 Cl66 Osmoles
33 K
33 Cl33 ml
Ions
Move
134 Osmoles
+
Final
100 Osmoles
67 K+
17 Cl50 Pr -
+
Total Volume
100 ml
67 K+
17 Cl50 Pr 67 ml
H2O
moves
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.