Passive transport across the lipid bilayer

Lungs

Diffusion of gasses

Rate factors: membrane, temperature, distance, & size

Transmembrane diffusion: passive & down a concentration gradient

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.

membrane out in

Con

cent

ratio

n

x l

Cout

Cin Cm1

Cm2

xCDJx ∂

∂−=

Fick’s 1st law

lCCD

tm

sJ mmx

211 −−=

∂

∂=

Fick’slawforpassivetransportofneutralpar4clesthroughthemembrane:

Diffusion coefficient profiles for selected solutes in a DPPC bilayer at 323 oK.

in

m

out

m

CC

CCK 21 ==

membrane out in

Con

cent

ratio

n

x l

Cout

Cin Cm1

Cm2

K =Cm

Cw

= exp µwo −µm

o

RT"

#$

%

&'

Cm – concentration just inside the hydrophobic core of the bilayer, Cw – concentration in the aqueous solution.

The chemical potential in the water phase (µw) = the chemical potential in the membrane (µm):

mommw

oww CRTCRT lnln +==+= µµµµ

The concentration at the surface of the membrane (Cm) ⎟⎟

⎠

⎞⎜⎜⎝

⎛ −=

RTCC

om

ow

wmµµexp

The membrane:water partition coefficient (Kp)

membrane out in

Con

cent

ratio

n

x l

Cout

Cin Cm1

Cm2

Flux, and therefore the rate of transfer across the membrane are proportional to the partitioning coefficient.

Partitioning coefficient is a quantitative measure of the how lipophilic is the compound.

Higher partitioning coefficient indicates better solubility and faster transport across the membrane

Fick’s law for passive transport of neutral particles through the membrane:

( )oi

om

ow CCRTd

DJ −⎟⎟⎠

⎞⎜⎜⎝

⎛ −−=

µµexp

The permeability coefficient

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎠

⎞⎜⎝

⎛=RTd

DPom

ow µµexp

dDKP P=

Permeability coefficients are a combined property of the solute

and the membrane system.

xCDJx ∂

∂−=

J = −DdK Ci −Co( )

P in membranes is strongly correlated with K for nonpolar solvent

Physicochemical and RBC

distributional properties for

water, urea and thiourea

Molecule diffusion across the aqueous layers

adjacent to either surface of the membrane.

Unstirred Layers

1 µm to 500 µm thickness.

  For water soluble compounds – diffusion across the unstirred layers will have relatively less effect.

  It is most prominent for relatively nonpolar compounds – the diffusion across the membrane itself will be relatively fast.

  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 ( )momim CCPJ −=§  The flow through the unstirred layers

( )miii

i CCdDJ −=( )omo

oo CCdDJ −=

Therefore momi CCPJ

−= miii CCDJd

−= omoo CCDJd

−=

After summing: oioi CCDd

Dd

PJ −=⎟

⎠

⎞⎜⎝

⎛ ++1

The effect of unstirred layers is to decrease the permeability so the apparent permeability coefficient (Papp) is smaller than P:

Dd

Dd

PPoi

app

++=11

At steady-state JJJJ oim ===