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{ l }={ l 1, l 2,..., l N }

# { l }={ l 1, l 2,..., l N }

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## { l }={ l 1, l 2,..., l N }

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1. How large is a Polymer Blob? Freely-Jointed-Chain Modell {l}={l1,l2,...,lN} The average end to end distance: Estimation: Size of a Viral dsDNA with ca 50kbp ? with l≈3Å => approx. 70nm With p≈50nm => ca 1,5 µm ! Random Walk

2. The simple model of a random walk resulted • for the end to end distance oft the polymer blob: • Problem: The polymer cannot occupy the same space. Thus the average quadratic end to end distance should be bigger. Energy Density: The average end to end distance is used as measure for the radius of the polymers. The excluded Volume • 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 BPM §1.4.2

3. In contrast to the FJC Model • 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: (von FJC Model) BPM §1.4.2

4. Java-Simulation Self-avoiding Random Walk http://polymer.bu.edu/java/java/saw/sawapplet.html

5. s s  A measure for the stiffness of a polymer is the persistence length Lp, which measures at which length s=Lp the orientation and s are not correlated any more. oBdA The Worm-Like-Chain Model for semiflexible Polymers A measure for the correlation of the orientation is the following average value: =0 BPM §1.4.2

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

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

8. Connection between FJC und WLC-Modell s Both models yield the same average end to end distance when the chain of FJC coincides with twice the persistence length l=2Lp Comparison with FJC BPM §1.4.2

9. Force Extension Curves: Comparison of Models Freely Jointed Chain (FJC) Worm-like Chain Model (WLC) With Stretch Modulus K0 of Monomer (e.g. stretching of DNA) For negligiblefluctuations

10. Force Extension Curve of dsDNA