Introduction to Biophysics Lecture 9 Diffusion through membrane

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

2 = At Will it be a solution to diffusion equation? Will normalization hold?

One-dimensional diffusion from a point Show that: =0. 01 =1 =2 Is a solution to diffusion equation =4 =20 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.

What about 3 D dimensional diffusion from a point? Because each diffusing particle moves independently in all three dimensions, we can use the multiplication rule for probabilities r 2 = x 2+y 2+z 2 - length squared of the vector r Implication for distribution of the polymer lengths: distribution of the endto-end vectors r will be Gaussian.

Cell Membrane Cell

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.

18 -19 Å; 21 Å; 30 Å

Effect of shape of phospholipids

The permeability of the artificial membrane is diffusive Pore in the membrane C 0 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

0 x Pore in the membrane L C 0 CL=0 C(x)=C 0(1 -x/L) -D =js= DC 0/L (or js = D c/L where c = CL-C 0 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.

Our model of permeability is possible to check experimentally

Refining model of permeability: dissolve and diffuse BC 1 C 2 membrane C 1 BC 2 Ps = BD/L , c = B(C 1 – C 2) 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.

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

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?

Reading: Nelson Chapter 4 (excluding 4. 6. 3 and 4. 6. 4) Glaser 2. 5. 3 Homework: problems 4. 3 and 4. 7