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

Electrostatic potential 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 dyn/cm

Schematics for measuring surface potentials in lipid monolayers

what’s wrong?

Differential Scanning Calorimeter (DSC): Phase transition for DPPC (Dipalmitoyl phosphatidylcholine) For DOPC (oleyl)…-18°C For DPPC (palmytoyl)…+41°C  S =  H/T m

Mixtures of phospholipids Two phases

Increases short-range order Broadens phase transition Sizes are wrong?

Biochim Biophys Acta Dec 30;1746(3): DOPC/DPPC POPC…palmitoyl, oleyl Phospholipid/ganglioside Lateral Phase Separation

Diffusion is a result of random motion which simply maximizes entropy Einstein treatment: c1c1 c2c2 ll but C distance negative slope therefore: but (Fick’s law) (one dimension)

y x z 1D 2D 3D l

Diffusion = random walk time X, distance Diffusion equation Fick’s law fluxgradient rate

Variance Normal distribution Random walk in one dimension D = diffusion coefficient t = time p1x() p2x() p3x() x, cm t = 1 s t = 10 s t = 100 s D = cm 2 /s root-mean-square (standard) deviation x = deviation from the origin Replace: where

x,  area inside 1  = 0.68 If we step 1 sigma (  ) away from the origin, what do we see? concentration observer

x = x 1, x 2, x 3 t = t 1, t 2, t 3 t, s x, cm  = cm  = cm  = cm t 1 = 1 s t 2 = 10 s t 3 = 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 t = 1 s t = 10 s t = 100 s x = cm x = cm x = D = cm 2 /s

Diffusion across exchange epithelium Einstein eqn: - mean square distance (cm 2 ) D – diffusion coefficient (cm 2 /s) t – time interval (s) “random walk”