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”