Passive
transport across
the lipid bilayer
Diffusion of gasses
Lungs
Transmembrane diffusion:
passive & down a concentration gradient
Rate factors: membrane, temperature, distance, & size
Membrane permeability to nonelectrolytes
Steps (any can be rate limiting)
1) enter the membrane (potential barrier)
2) diffusion through the bilayer core
3) exit the membrane (potential barrier)
Free energy profiles
for selected solutes
in a DPPC bilayer at
323 oK.
Membrane passive transport mechanisms.
(A) Solubility-diffusion model.
(B) Transient pore model.
(C) Head-group gated model.
(D) Lipid flipping-carrier model.
Circles represent lipid head groups and the gray area indicates the hydrophobic
region occupied by lipid acyl chains. The black oval is the solute molecule.
Fick’slawforpassivetransportofneutral
par4clesthroughthemembrane:
Fick’s 1st law
Concentration
out
membrane
∂C
J x = −D
∂x
in
Cout
Cm1
Cm1 − Cm 2
1 ∂m
Jx =
= −D
s ∂t
l
Cin
Cm2
l
x
Diffusion coefficient profiles for selected
solutes in a DPPC bilayer at 323 oK.
The membrane:water partition coefficient (Kp)
The chemical potential in the water phase (µw) = the chemical potential
in the membrane (µm): µ = µ o + RT ln C = µ = µ o + RT ln C
w
w
w
The concentration at the surface of
the membrane (Cm)
Concentration
out
membrane
m
m
m
⎛ µ wo − µ mo ⎞
⎟⎟
Cm = Cw exp⎜⎜
⎝ RT ⎠
in
" µ wo − µ mo %
Cm
K=
= exp $
'
Cw
# RT &
Cout
Cm1
Cin
Cm – concentration just inside the
hydrophobic core of the bilayer,
Cw – concentration in the aqueous
solution.
Cm2
l
x
Cm1 Cm 2
K=
=
Cout Cin
Fick’s law for passive transport of neutral
particles through the membrane:
Concentration
out
membrane
Flux, and therefore the rate of
transfer across the membrane
are proportional to the
partitioning coefficient.
in
Cout
Cm1
Cin
Partitioning coefficient is a
quantitative measure of the
how lipophilic is the
compound.
Cm2
l
x
Higher partitioning coefficient
indicates better solubility and
faster transport across the
membrane
∂C
J x = −D
∂x
o
o
⎛
µw − µm ⎞
D
⎟⎟(Ci − Co )
J = − exp⎜⎜
d
⎝ RT ⎠
o
o
⎛
µw − µm ⎞
⎛ D⎞
⎟⎟
P = ⎜ ⎟ exp⎜⎜
⎝d⎠
⎝ RT ⎠
The permeability coefficient
Permeability coefficients are a
combined property of the solute
and the membrane system.
DK P
P=
d
P in membranes is
strongly correlated with
K for nonpolar solvent
D
J = − K (Ci − Co )
d
Physicochemical
and RBC
distributional
properties for
water, urea and
thiourea
Unstirred Layers
Molecule diffusion across
the aqueous layers
adjacent to either surface
of the membrane.
1 µm to 500 µm thickness.
  It is most prominent for relatively nonpolar compounds – the
diffusion across the membrane itself will be relatively fast.
  For water soluble compounds – diffusion across the unstirred
layers will have relatively less effect.
  P – a membrane permeability
coefficient
  D – an aqueous diffusion
constant.
  di and do – the thicknesses
of unstirred layers.
  Ci and Co – the bulk concentrations of the compound,
  Cmi and Cmo – the concentrations at the surface of the membrane.
§  The flow through the membrane is
J m = P(Cmi − Cmo )
§  The flow through the unstirred layers
D
J o = (Cmo − Co )
do
D
J i = (Ci − Cmi )
di
At steady-state
Therefore
J m = Ji = Jo = J
Jd i
Jd o
J
= Cmi − Cmo
= Ci − Cmi
= Cmo − Co
P
D
D
After summing:
⎛ 1 di do ⎞
J ⎜ + + ⎟ = Ci − C o
⎝P D D⎠
The effect of unstirred layers is to decrease the permeability so
the apparent permeability coefficient (Papp) is smaller than P:
1
1 di d o
= + +
Papp P D D