1. Introduction to Biophysics Lecture 9 Diffusion through membrane

2. Formation of double helix is highly cooperative process Pitch 3.4 nm
Stabilization:
Stacking interaction between the aromatic bases (dispersion forces).
H-bonds in Watson-Crick base pairs

3. Will it be a solution to diffusion equation? Will normalization hold?

4. One-dimensional diffusion from a point
=0.01 =1 =2 =4
=20
Show that:
Is a solution to diffusion equation
Mass conservation a property which is built into the diffusion equation, and it is wise to check a solution to be sure that this condition is satisfied.
Shows how long it will take a metabolite to diffuse through a cell when it is produced at one location.

5. What about 3D dimensional diffusion from a point?
Because each diffusing particle moves independently in all three dimensions, we can use the multiplication rule for probabilities
r2 = x2+y2+z length squared of the vector r
Implication for distribution of the polymer lengths: distribution of the end-to-end vectors r will be Gaussian.

6. Cell Membrane
Cell

8. Biological Functions of Membrane
Cell membrane is a well organized structure fulfilling a broad spectrum of physiological functions:
Separation from environment. A barrier of diffusion. Controls the ionic composition of the cytoplasm by highly specific transporters (molecular and ion pumps).
Mechanical structure to guaranty cell integrity, shape, movement, endocytose.
As a surface, forms a dynamic matrix for enzymatic reactions. Central in biological communication –membrane receptors. Immunological recognition. Place for energy conversion processes.
Electrically isolating leaflet it contains a mosaic of various passive an active electrical devices, controlling membrane potential.

9. 18-19 Å; 21 Å; 30 Å

10. Effect of shape of phospholipids

11. The permeability of the artificial membrane is diffusive
Pore in the membrane C0
CL=0
Diffusion at steady state
The diffusing substance enters in one place and exits from another at the same
rate. The substance thus diffuses from a source to a sink, with a continuous drop in concentration along the way. There will be a steady flux of material through the system, as the flow into each volume element perfectly balances the flow out. Such a system is said to be in a steady state. (all variables describing the system will be nearly unchanging with time).
Laplace equation

12. x
Pore in the membrane L C0
CL=0
C(x)=C0(1-x/L)
-D =js= DC0/L (or js = Dc/L where c = CL-C0 flux in +x direction)
js = -Psc ,
Ps [cm/s]– permeability, depends on the type of membrane, its thickness and on the diffusion constant of solute molecule.

13. Our model of permeability is possible to check experimentally

14. Refining model of permeability: dissolve and diffuseC1 C2
BC1
membrane
BC2
Ps = BD/L , c = B(C1 – C2)
D- diffusion constant in oil,
B – partition coefficient
The permeability of a pure bilayer membrane is roughly BD times a constant independent of the solute, where B is the partition coefficient of solute and D its diffusion constant in oil.

16. Which membrane will have larger Ps artificial or real cell membrane?

17. Example: relaxation of a concentration jump
Think of a cell as a spherical bag of R=10m, bounded by a membrane that passes alcohol with Ps=20 m/s.
If, initially, the alcohol concentration is cout outside the cell and cin(0) inside, how does the interior concentration is changing with time?

18. Reading: Nelson Chapter 4 (excluding 4.6.3 and 4.6.4)
Glaser 2.5.3
Homework: problems 4.3 and 4.7