Lecture 14
Membranes continued
Diffusion
Membrane transport
From S. Feller
Lipid Bilayers are dynamic
distributions of phosphate and carbonyl groups and lateral pressure profiles
from S. White
Distribution of groups along the z-axis
Ele
ctro
stat
ic p
oten
tial
Electric Double Layer (EDL)
Dipole Potential
surface pressure
= 70 dyne/cm
compressed monolayer
surface pressure of the crowding surfactant balances part of the surface tension, thus the apparent surface tension to the left of the barrier is smaller
Lipids at air-water interface
Irving Langmuir
w- surf = surf
surf
w - surface tension of pure water
surf - surface tension in the
presence of surfactant
surf
surf – surface pressure of the surfactant
dipalmitoyl phosphatidylcholine (DPPC)
monolayer-bilyer equivalence pressure 35-40 dyn/cm
Schematics for measuring surface potentials in lipid monolayers
what’s wrong?
Differential Scanning Calorimeter (DSC): Phase transition for DPPC (Dipalmitoyl phosphatidylcholine)
http://employees.csbsju.edu/hjakubowski/classes/ch331/lipidstruct/oldynamicves.html
For DOPC (oleyl)…-18°C
For DPPC (palmytoyl)…+41°C
S = H/Tm
Mixtures of phospholipids
Two phases
www.mpikg-golm.mpg.de/th/people/jpencer/raftsposter.pdf
•Increases short-range order
•Broadens phase transition
Sizes are wrong?
Biochim Biophys Acta. 2005 Dec 30;1746(3):172-85.
DOPC/DPPC
POPC…palmitoyl, oleyl
http://www.nature.com/emboj/journal/v24/n8/full/7600631a.html
Phospholipid/ganglioside
Lateral Phase Separation
Diffusion is a result of random motion which simply maximizes entropy
Einstein treatment:
c1 c2
l l
butl
CC
dx
dc 12
C
distance
negative slope
therefore: butdx
dcDJ net (Fick’s law)
dx
dc
t
lJnet
2
2
1
tlCJ /2
11 tlCJ /
2
12
tlCCJnet /)(2
121
Dtl 22 Dtl 2 (one dimension)
y
x
z
1D
2D
3D
Dtl 22
Dtl 42
Dtl 62 l
222 yxl
2222 zyxl
Diffusion = random walkti
me
X, distance
2
2
x
cD
t
c
Diffusionequation
x
cDJ
Fick’s law
flux gradient
rate
Dt
x
Dttxp
4exp
4
1),(
2
Dt22 Variance
2
21exp
2
1)(
x
xp
Normal distribution Random walk in one dimension
D = diffusion coefficientt = time 0.06 0.04 0.02 0 0.02 0.04 0.06
0
20
40
60
80
100
p1 x( )
p2 x( )
p3 x( )
x, cm
t = 1 s
t = 10 s
t = 100 s
D = 10-5 cm2/s
Dt2
root-mean-square (standard)deviation
x = deviation from the origin
Dtx 2
Replace:
where
0 1 2 3 40
0.5
x,
1.0
0.607
area inside 1 = 0.68
If we step 1 sigma () away from the origin, what do we see?
conce
ntr
ati
on
observer
Dt
x
Dttp
4exp
4
1)(
2
Dt
x
Dtxp
4exp
4
1)(
2
x = x1, x2, x3t = t1, t2, t3
t, s
0 0.005 0.01 0.015 0.02 0.0250
20
40
60
80
100
x, cm
= 0.0045 cm
= 0.014 cm
= 0.045 cm
Dtx 2t1 = 1 s
t2 = 10 s
t3 = 100 s
An observer sees that the
concentration first increases and then
decreases
1 is a special point where the concentration of the diffusible substance reaches its maximum
0 20 40 60 80 1000
10
20
30
40
50
60
t = 1 s
t = 10 s
t = 100 s
x = 0.0045 cm
x = 0.014 cm
x = 0.045
D = 10-5 cm2/s
Diffusion across exchange epithelium
bas ila r m em brane
10 m vascularendothe lium
B LO O D
IN TE R S TIT IU M
Dtx 22 Einstein eqn:
<x2> - mean square distance (cm2)D – diffusion coefficient (cm2/s)t – time interval (s)
“random walk”
