{l}={l 1, l 2,..., l N } The average end to end distance: How large is a Polymer Blob? Estimation: Size of a Viral dsDNA with ca 50kbp ? with l≈3Å => approx. 70nm With p≈50nm => ca 1,5 µm ! Freely-Jointed-Chain Modell Random Walk

Gaub/WS 2006BPM § The excluded Volume The simple model of a random walk resulted for the end to end distance oft the polymer blob: Flory solved the problem with a simple heuristic argument: If two monomers overlap, they repell each other. The Probability that 2 monomers occupy the same space increases with the concentration squared Energy Density: The average end to end distance is used as measure for the radius of the polymers. Problem: The polymer cannot occupy the same space. Thus the average quadratic end to end distance should be bigger.

Gaub/WS 2006BPM § The energy for the excluded volume drives the polymer blob apart. This force has to be balanced by an entropic force which wants to keep the blob together: In contrast to the FJC Model (von FJC Model)

Java-Simulation Self-avoiding Random Walk

Gaub/WS 2006BPM § s   s  A measure for the stiffness of a polymer is the persistence length L p, which measures at which length s=L p the orientation  and  s  are not correlated any more. A measure for the correlation of the orientation is the following average value: oBdA =0 The Worm-Like-Chain Model for semiflexible Polymers

mit    ss R Local Bending Radius Calculation: Energy change of a beam of length  s, if it is bent by the angle 

Äquipartition Theorem in 3-D two angles can fluctuate, each containing the average energy kT/2. in 2-D in 3-D Persistence length Bending is a thermodynamic degree of freedom DNA L p =53 nm Aktin L p = 10 µm Mikrotubuli L p =1 mm

Gaub/WS 2006BPM § Connection between FJC und WLC-Modell s Comparison with FJC Both models yield the same average end to end distance when the chain of FJC coincides with twice the persistence length l=2L p

Force Extension Curves: Comparison of Models Freely Jointed Chain (FJC)Worm-like Chain Model (WLC) With Stretch Modulus K 0 of Monomer (e.g. stretching of DNA) For negligible fluctuations

Force Extension Curve of dsDNA