The Gibbs-Donnan Effect in Biological Systems
THE GIBBS-DONNAN EFFECT
By
Prof. Sudhir Kumar Awasthi
Dept. Of Life Sciences
CSJMU
•
Some
ionic species can pass through
the
barrier
while
others
cannot.
•
Solutions may be
gels
or
colloids
as well as
solutions
of electrolytes,
and
as
such the phase
boundary
between
gels, or
a
gel and
a liquid, can
also
act as a
selective
barrier.
•
Electric
potential arising between
two
such
solutions is called the
Donnan
potential.
•
Effect named after the
American physicist
Josiah
Willard
Gibbs
and
the
British
chemist
Frederick
G.
Donnan.
o
sm
ot
i
c
pressure
an
d
K
+
)
at
t
a
c
h
e
d
to
•
Donnan effect
is
extra
attributable
to cations
(Na
+
dissolved
plasma
proteins.
•
Pre
s
e
n
ce
of
a
cha
r
g
e
d
imp
er
m
ea
nt
i
o
n
(for
example, a
protein)
on
one
side
of
a
membrane
will
result
in an
asymmetric distribution
of
permeant
charged
ions.
s
t
at
e
s
•
Gibbs–Donnan
equation
at
equilibrium
(assuming permeant ions
are
Na
+
and
Cl
-
):
•
[Na
Side 1
]
×
[Cl
Side 1
]
=
[Na
Side 2
]
×
[Cl
Side
2
]
S
t
a
r
t
Side 1: 9 Na, 9
Cl
Side 2: 9 Na, 9
Protein
E
q
u
i
l
i
b
r
i
u
m
Side 1: 6 Na, 6
Cl
Side 2: 12 Na, 3 Cl, 9
Protein
•
Also known
as facilitated transport or passive-
mediated
transport.
•
It is the
spontaneous passage of molecules or ions
across
a biological membrane passing through
specific transmembrane integral proteins
(as
opposed
to
active
transport).
•
May occur
either
across
biological membranes
or
through aqueous
compartments
of
an
organism.
•
Polar
molecules and charged
ions
are dissolved
in
water
but
they
cannot
diffuse
freely
across the
plasma membrane due
to the hydrophobic
nature
of
the fatty acid tails
of phospholipids that
make
up
the
lipid
bilayers.
Facilitated
Diffusion
n
o
n
p
o
l
a
r
•
Only
small
a
s
o
x
ygen
can
diffuse
mol
e
c
u
l
e
s,
such
e
a
s
i
ly
acros
s
the
membr
a
n
e
.
transmembrane
channels.
•
These channels
are
gated
so
they
can
open
and
close, thus
regulating
the flow
of
ions
or
small
polar
molecules.
•
Large
r
m
o
l
e
c
u
l
es
are
transmembrane
carrier
tr
a
n
s
p
o
rt
e
d
by
pr
o
te
i
n
s,
such
as permeases that change their conformation as
the
molecules are carried through,
for
example
glucose
or amino
acids.
•
Non-polar molecules, such as
retinol
or
lipids
are
poorly
soluble
in
water.
•
They
are
transported
c
o
mp
a
r
t
me
n
ts
o
f
c
e
lls
or
th
r
ou
g
h
aq
u
eo
u
s
th
r
o
u
gh
e
x
tr
a
c
e
l
l
u
l
a
r
space by water-soluble carriers as
retinol
binding
protein.
•
Metabolites are not changed because
no
energy
is
required for facilitated
diffusion.
•
Only permease
changes
its
shape
in
order
to
transport
the
metabolites.
•
Form
of
transport through cell membrane
which
modifies its
metabolites
is the
group translocation
transportation.
•
Glucos
e
,
sodium
ions
an
d
chloride
ions
are
s
o
me
examples of molecules and
ions that
must efficiently get
across
the
plasma membrane but
to
which
the
lipid
bilayer
of
the
membrane
is virtually
impermeable.
•
Various
attempts have
been
made
by engineers
to
mimic the process
of
facilitated transport
in
synthetic
(i.e.,
non-biological) membranes
for use
in
industrial-scale gas and
liquid
separations, but
these
have met
with
limited success
to
date, most
often for reasons related to
poor carrier stability
and/or
loss
of carrier from
the
membrane.
Kinetics
of
Diffusion
•
F
i
c
k
'
s
f
i
r
s
t
l
a
w
r
e
l
a
t
e
s
d
i
f
f
u
s
i
v
e
f
l
u
x
t
o
t
h
e
c
o
n
c
e
n
t
r
a
t
i
o
n
u
n
d
e
r
s
t
e
a
d
y
s
t
a
t
e
c
o
n
d
i
t
i
o
n
s
.
•
It
p
o
s
t
u
l
ates
th
a
t
t
he
f
l
ux
goe
s
fr
o
m
r
e
g
i
o
n
s
of
hi
g
h
c
o
n
c
en
t
ra
t
ion
concentration,
with
to
regions
a
ma
g
n
i
t
u
d
e
of
l
o
w
th
a
t
is
proportional
to the
concentration gradient (spatial
derivative).
•
In
one
(spatial) dimension, the law
is:
J
=
- D
∂
ϕ
∂
x
•
Where:
•
J
is the
"diffusion
flux" [(amount
of
substance)
per
unit
area per
unit
time], example .
J
measures the
amount of substance that
will flow
through
a small
area during
a small time
interval.
•
D
i
s
t
h
e
d
i
f
f
u
s
i
o
n
c
o
e
f
f
i
c
i
e
n
t
o
r
d
i
f
f
u
s
i
v
i
t
y
i
n
d
i
m
e
n
s
i
o
n
s
o
f
[
l
e
n
g
t
h
2
t
i
m
e
−
1
]
o
r
m
2
/
s
.
•
Φ
(phi)
(for
ideal mixtures) is the concentration
in
dimensions of
[amount
of
substance
per
unit
volume] or
mol/m
3
•
x
is the position [length]
or
m
•
D
is
proportional
to the squared
velocity of
the
diffusing
particles,
which
depends
on
the
temperature,
viscosity
of
the
fluid and
the
size
of
the particles according to the Stokes-Einstein
relation.
•
In dilute
aqueous
solutions
the diffusion
coefficients
of
most ions are similar
and
have
values that
at
room
temperature are
in the
range
bi
o
lo
g
i
c
a
l
n
o
rm
a
l
ly
of
0.6x10
−9
to
2x10
−9
m
2
/s.
For
mol
e
c
u
l
e
s
the
d
i
ff
u
s
i
on
coef
f
i
c
i
e
nts
range
from
10
−11
to
10
−10
m
2
/s.
•
In two
or
more
dimensions
we
must use , the
del
or
gradient
operator,
which
generalises the first
derivative,
obtaining
J = - D
ϕ
•
The
driving force
for the
one-dimensional diffusion
is the
quantity
-
∂
ϕ
∂
x
wh
i
ch
for
i
d
e
a
l
mixt
u
r
es
is
the
c
o
n
c
en
t
ra
t
ion
gradient.
•
In
chemical
systems
other than ideal
solutions
or
mixtures,
the driving
force
for diffusion of each
species
is
the gradient
of
chemical
potential of this
species.
•
Then Fick's
first
law
(one-dimensional
case) can
be written
as:
J
i
=
Dc
i
∂µ
i
RT
∂
x
where the
index
i
denotes
the ith
species,
c is
the concentration
(mol/m
3
),
R is the
universal
gas constant
(J/(K mol)), T is the
absolute
temperature
(K),
and
μ is the chemical
potential
(J/mol).
•
F
i
c
k
'
s
s
e
c
o
n
d
l
a
w
p
r
e
d
i
c
t
s
h
o
w
d
i
f
f
u
s
i
o
n
c
a
u
s
e
s
t
h
e
c
o
n
c
e
n
t
r
a
t
i
o
n
t
o
c
h
a
n
g
e
w
i
t
h
t
i
m
e
:
(delta)
∂
ϕ
=
D
∂
2
ϕ
∂
t
∂
x
where
•
ϕ
is the concentration in dimensions
of
[(amount
of substance)
length
−3
],
example
mole/m
3
•
t
is time
[s]
•
D
is
the
d
i
ff
u
s
i
o
n
c
o
ef
f
i
c
ient
in
d
i
m
e
n
s
i
o
ns
of
[length
2
time
−1
],
example
m
2
/s
•
x
is the position
[length],
example
m
Electrochemical
gradient
•
A
gradient of electrochemical potential, usually
for
an ion
that can
move
across
a
membrane.
•
Gradient consist of
two
parts:
•
First,
an
electrical component caused
by a charge
difference across
the lipid
membrane.
•
Second,
a
chemical component
caused by a
difference
in the chemical
concentration across
a
membrane.
•
A
combination
of these two
factors determines the
thermodynamically favourable direction
for
an
ion's movement
across
a
membrane.
•
Difference
of electrochemical potentials can be
interpreted as
a type
of potential
energy
available
for work in a
cell.
•
An
electrochemical
gradient is analogous to
the
water
pressure across
a
hydroelectric
dam.
•
Membrane transport proteins such as
the
sodium-potassium
pump within the
membrane
are
equivalent
to
turbines that
convert
the
water's potential energy
to other
forms of
physical
or chemical energy and
the ions that
pass through the
membrane
are
equivalent
to
water
that ends
up
at
the bottom
of
the
dam.
•
Also, energy
can
be
used
to pump water up into
the lake
above
the
dam.
•
In similar
manner, chemical
energy
in
cells
can
be
used
to
create electrochemical
gradients.
•
Einstein
has
shown that the
relation
between
molecular movement and diffusion
in a
liquid
may be
expressed by
the
following equation,
when the
particles
move
independently of
each
other.
D
=
∆
2
/
2
t
…
…
…
…
.
1
‘D’ being
the diffusion coefficient
and
‘∆
2’
the
mean
square of
the deviation in a given
direction
in time
‘t’.
•
Further it is assumed
that
the particles
possess
the
same kinetic
energy as gas
molecules
at
the
same
temperature,
the
following
equation
holds
∆
2
=
2
R
T
.
t
…
…
…
.
.
2
N
C
•
where R is the
universal gas
constant, N
is the
Avagadro
number,
T is the
absolute temperature
and
C is a
constant
which
is
called the
frictional
resistance of
the
molecule.
H
e
n
c
e
,
D
=
R
T
.
1
…
…
…
…
.
3
N
C
3
h
o
l
d
e
q
u
a
l
l
y
goo
d
f
o
r
•
Equations
2
and
d
i
s
s
o
l
v
e
d
m
o
l
e
c
u
l
es
and
particles
of
greater
dimensions.
•
For
spherical
molecules
moving
in
a
medium
of
p
r
o
p
o
r
ti
o
n
a
te
l
y
small
mo
l
e
c
u
l
es
Sto
k
es
has
h
o
l
ds
s
h
own
t
h
a
t
a
hydrodynami
c
e
q
u
at
i
on
namely,
C
=
6
π
Z
r
•
where r is the radius
of
a diffusing
particle and
Z
is the viscocity
of
the diffusion
medium. By
substituting
in (3) we
obtain
for D the
following
relation.
D
=
R
T
.
1
N
6
π
Z
r
•
This is known
as
the Stokes-Einstein equation
and is
valid only
when the
aforesaid conditions
are fulfilled.
Osmo
s
is
•
Net
movement of solvent molecules through
a
partially permeable membrane into
a region of
higher solute concentration,
in
order
to equalize
the solute concentrations
on the two
sides
.
or
•
A physical
process
in which
any
solvent moves,
without input
of energy, across a
semipermeable
membrane (permeable to
the
solvent, but not
the
solute)
separating two solutions
of
different
concentrations
.
•
Net
m
o
v
em
e
nt
of
s
o
l
v
e
n
t
is
fr
o
m
the
l
e
s
s
concentrated (
hypotonic
)
to the more
concentrated (
hypertonic
)
solution, which
tends
to
reduce the
difference
in
concentrations.
•
This
effect can
be
countered by
increasing
the
pressure of the
hypertonic solution,
with respect
to the
hypotonic.
•
Osmotic pressure is defined as
the
pressure
required
to maintain an
equilibrium,
with no
net
movement
of
solvent.
•
Osmotic
pressure
is a
colligative property,
meaning that
the osmotic
pressure depends on
the molar
concentration of
the
solute
but not on
its
identity.
•
Osmosis is essential in
biological
systems,
as
biological membranes
are
semipermeable.
•
In
general, cell membranes
are
impermeable
to
large
and
polar
molecules, such as ions,
proteins, and
polysaccharides, while be
i
ng
pe
r
me
a
ble
to
non-po
l
ar
and/or
hydrophobic molecules
like lipids
as well as
to
small
molecules
like
oxygen,
carbon
dioxide,
nitrogen, nitric oxide,
etc.
•
Permeability depends
on
solubility, charge, or
chemistry, as
well
as
solute
size.
•
Water
molecules
tr
a
v
e
l
t
h
r
o
u
gh
the
p
l
a
sm
a
m
e
mb
r
an
e,
to
n
o
p
l
a
st
me
m
b
r
a
n
e
(
v
a
c
u
o
l
e
)
or
protoplast by
diffusing across the
phospholipid
bilayer
via
aquaporins
(small
transmembrane
proteins
similar to those in
facilitated
diffusion
and in
creating
ion
channels).
•
Osmosis
provides
the
primary
means
by
which
water is
transported
into
and out of
cells.
p
r
e
s
s
u
re
of
a
c
e
ll
is
l
a
r
g
e
l
y
•
The
tu
r
g
o
r
maintained
membrane,
by
osmosis,
across
be
t
w
e
en
t
h
e
c
e
ll
in
t
er
i
or
the
cell
and
i
ts
relatively hypotonic
environment.
REFERENCES
Donnan membrane Principle ; Opportunities for
sustainable engineered processes & materials by
S. Sarkar, A.K. Singh Gupta (2016)
Biochemistry by Lubert Stryer (2015)
Biochemistry by Voet & Voet (2015)
The Gibbs-Donnan Effect, named after physicists Gibbs and Donnan, explains the selective permeability of membranes to ions, leading to the establishment of Donnan potential. This phenomenon affects the distribution of ions and proteins across cell membranes, influencing processes like osmosis and ion transport. Additionally, facilitated diffusion, a passive transport mechanism involving specific transmembrane channels and carrier proteins, enables the movement of polar molecules and ions across lipid bilayers without requiring energy expenditure.
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Presentation Transcript
THE GIBBS-DONNAN EFFECT By Prof. Sudhir Kumar Awasthi Dept. Of Life Sciences CSJMU
Some ionic species can pass through the barrier while others cannot. Solutions may be gels or colloids as well as solutions of electrolytes, and as such the phase boundary between gels, or a gel and a liquid, can also act as a selective barrier. Electric potential arising between two such solutions is called the Donnan potential. Effect named after the American physicist Josiah Willard Gibbs and the British chemist Frederick G. Donnan. Donnan effect is extra attributable to cations (Na+ dissolved plasma proteins. osmotic and K+) attached to pressure
Presence of a charged impermeant ion (for example, a protein) on one side of a membrane will result in an asymmetric permeant charged ions. Gibbs Donnan equation at equilibrium (assuming permeant ions are Na+ and Cl-): [NaSide 1] [ClSide 1] = [NaSide 2] [ClSide 2] distribution of states Start Equilibrium Side 1: 9 Na, 9 Cl Side 2: 9 Na, 9 Protein Side 1: 6 Na, 6 Cl Side 2: 12 Na, 3 Cl, 9 Protein
FacilitatedDiffusion Also known as facilitated transport or passive- mediated transport. It is the spontaneous passage of molecules or ions across a biological membrane passing through specific transmembrane opposed to active transport). May occur either across biological membranes or through aqueous compartments of an organism. Polar molecules and charged ions are dissolved in water but they cannot diffuse freely across the plasma membrane due to the hydrophobic nature of the fatty acid tails of phospholipids that make up the lipid bilayers. integral proteins (as
Only as membrane. All across transmembrane channels. These channels are gated so they can open and close, thus regulating the flow of ions or small polar molecules. Larger molecules transmembrane carrier as permeases that change their conformation as the molecules are carried through, for example glucose or amino acids. small nonpolar can molecules, easily such the oxygen diffuse across polar membranes molecules are transported that by proteins form are transported proteins, by such
Non-polar molecules, such as retinol or lipids are poorly soluble in water. They are transported compartments of cells or space by water-soluble carriers as retinol binding protein. Metabolites are not changed because no energy is required for facilitated diffusion. Only permease changes its shape in order to transport the metabolites. Form of transport through cell membrane which modifies its metabolites is the group translocation transportation. through through extracellular aqueous
Glucose, sodium ions and chloride ions are some examples of molecules and ions that must efficiently get across the plasma membrane but to which the lipid bilayer of the membrane is virtually impermeable. Various attempts have been made by engineers to mimic the process of facilitated transport in synthetic (i.e., non-biological) membranes for use in industrial-scale gas and liquid separations, but these have met with limited success to date, most often for reasons related to poor carrier stability and/or loss of carrier from the membrane.
Kinetics ofDiffusion Fick's first law relates diffusive flux to the concentration under steady state conditions. It postulates that the flux goes from regions of high concentration concentration, with a proportional to the concentration gradient (spatial derivative). In one (spatial) dimension, the law is: J = - D to regions magnitude of that low is x
Where: J is the "diffusion flux" [(amount of substance) per unit area per unit time], measures the amount of substance that will flow through a small area during a small interval. D is the diffusion coefficient or diffusivity in dimensions of [length2time 1] orm2/s. (phi) (for ideal mixtures) is the concentration in dimensions of [amount of substance per unit volume] or mol/m3 x is the position [length] or m example . J time
D is proportional to the squared velocity of the diffusing particles, which temperature, viscosity of the fluid and the size of the particles according to the Stokes-Einstein relation. In dilute aqueous coefficients of most ions are similar and have values that at room temperature are in the range of 0.6x10 9 to 2x10 9 molecules the diffusion coefficients range from 10 11 to 10 10m2/s. depends on the solutions the diffusion m2/s. For biological normally
In two or more dimensions we must use , the del or gradient operator, which generalises the derivative, obtaining J = - D The driving force for the one-dimensional diffusion is the quantity - x which for ideal mixtures is the concentration gradient. In chemical systems other than ideal solutions or mixtures, the driving force for diffusion of each species is the gradient of chemical potential of this species. first
Then Fick's first law (one-dimensional case) can be written as: Ji = Dci i RT x where the index i denotes the ith species, c is the concentration (mol/m3), R is the universal gas constant (J/(K mol)), T is the absolute temperature (K), and is the chemical potential (J/mol).
predicts how diffusion Fick's causes the concentration to change with time: (delta) second law = D 2 t x where is the concentration in dimensions of [(amount of substance) length 3], example mole/m3 t is time [s] D is the diffusion coefficient in dimensions of [length2time 1], example m2/s x is the position [length], example m
Electrochemicalgradient A gradient of electrochemical potential, usually for an ion that can move across a membrane. Gradient consist of two parts: First, an electrical component caused by a charge difference across the lipid membrane. Second, a chemical component caused by a difference in the chemical concentration across a membrane. A combination of these two factors determines the thermodynamically favourable direction for an ion's movement across a membrane.
Difference of electrochemical potentials can be interpreted as a type of potential available for work in a cell. An electrochemical gradient is analogous to the water pressure across a hydroelectric dam. Membrane transport sodium-potassium pump within the membrane are equivalent to turbines that convert the water's potential energy to other forms of physical or chemical energy and the ions that pass through the membrane are equivalent to water that ends up at the bottom of the dam. energy proteins such as the
Also, energy can be used to pump water up into the lake above the dam. In similar manner, chemical energy in cells can be used to create electrochemical gradients. Einstein has shown that the relation between molecular movement and diffusion in a liquid may be expressed by the following equation, when the particles move independently of each other. D = 2/ 2t . 1 D being the diffusion coefficient and 2 the mean square of the deviation in a given direction in time t .
Further it is assumed that the particles possess the same kinetic energy as gas molecules at the same temperature, the following equation holds 2= 2RT . t ..2 N C where R is the universal gas constant, N is the Avagadro number, T is the absolute temperature and C is a constant which is called the frictional resistance of the molecule. Hence, D = RT . 1 . 3 N C
Equations 2 and dissolved molecules and particles of greater dimensions. For spherical molecules moving in a medium of proportionately small molecules Stokes has shown that a hydrodynamic equation namely, C = 6 Zr where r is the radius of a diffusing particle and Z is the viscocity of the diffusion medium. By substituting in (3) we obtain for D the following relation. 3 hold equally good for holds
D = RT . 1 N 6 Zr This is known as the Stokes-Einstein equation and is valid only when the aforesaid conditions are fulfilled.
Osmosis Net movement of solvent molecules through a partially permeable membrane into a region of higher solute concentration, in order to equalize the solute concentrations on the two sides. or A physical process in which any solvent moves, without input of energy, across a semipermeable membrane (permeable to the solvent, but not the solute) separating two solutions of different concentrations.
Net movement of solvent is from the less concentrated (hypotonic) concentrated (hypertonic) solution, which tends to reduce the difference in concentrations. This effect can be countered by increasing the pressure of the hypertonic solution, with respect to the hypotonic. Osmotic pressure is defined as the pressure required to maintain an equilibrium, with no net movement of solvent. Osmotic pressure is meaning that the osmotic pressure depends on the molar concentration of the solute but not on its identity. to the more a colligative property,
Osmosis is essential in biological systems, biological membranes are semipermeable. In general, cell membranes are impermeable to large and polar molecules, such proteins, and polysaccharides, while permeable to hydrophobic molecules like lipids as well as to small molecules like oxygen, carbon nitrogen, nitric oxide, etc. Permeability depends on solubility, charge, or chemistry, as well as solute size. as as ions, being and/or non-polar dioxide,
Water molecules travel through the plasma membrane, tonoplast membrane (vacuole) or protoplast by diffusing across the phospholipid bilayer via aquaporins (small transmembrane proteins similar to those in facilitated diffusion and in creating ion channels). Osmosis provides the primary means by which water is transported into and out of cells. pressure The turgor maintained membrane, between the cell interior relatively hypotonic environment. of a cell is largely the and its by osmosis, across cell
REFERENCES Donnan membrane Principle ; Opportunities for sustainable engineered processes & materials by S. Sarkar, A.K. Singh Gupta (2016) Biochemistry by Lubert Stryer (2015) Biochemistry by Voet & Voet (2015)
