Wednesday, August 18, 2010

Randomness with a purpose

I am helping teach BIPH3001 Frontiers in Biophysics which is running as a reading course (with a blog) based on Philip Nelson's brilliant text, Biological Physics: Energy, Information, and Life. This week we are looking a chapter 4, Random Walks, Friction, an Diffusion. Here a few highlights. As I have noted previously he has great section headings which often summarise the main point.

4.1.2 Random walks lead to diffusive behavior

4.1.3 The diffusion law is model independent

4.1.4 Friction is quantitatively related to diffusion

Einstein showed that

friction * diffusion constant = kB T

This is the first example of a fluctuation-dissipation relation.

4.2. Excursion: Einstein's role

Einstein saw that the fluctuation-dissipation relation gave a falsifiable quantitative hypothesis. The experiments he proposed and Perrin performed (his actual data is in the Figure above) finally convinced people that atoms really did exist.

4.3.1 The conformation of polymers

The diffusion constant of a polymer scales inversely with the square root of the length (which is proportional to the mass of the polymer)

4.4.1 Diffusion rules the subcellular world

4.6.1 The permeability of artificial membranes is diffusive.

Note how the experimental data below extends over about 6 orders of magnitude!

4.6.2 Diffusion sets a fundamental limit on bacterial metabolism

4.6.3 The Nernst relation sets the scale of membrane potentials

V ~ 60 meV for a concentration difference of an order of magnitude

k_B T ~ 25 meV at room temperature.

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