Cell Biophysics Basic Cell Biology Membrane Biophysics Summer 2008 Sylabus Biophysics II Cell Biophysics English: RM224, 15:15-18:30 Lecture notes with the according references will be published in the www. Basic Cell Biology Membrane Biophysics Active and Passive Physics of the Cytoskeleton Intracellular Transport Neurophysics Photosynthesis

3. Active and Passive Physics of the Cytoskeleton 3.1 Fundamental Polymer Physics Literatur: M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford Press M. Doi, Introduction to Polymer Physics, Oxford Press

Internal Dynamics , reptation rubber elasticity

Ungedehnt   Gedehnt Plateau Modulus E = 3kB ·T · rK

Plateau Modulus of A Semiflexible Polymer Network Rend to end Actin Filament Point Pinned by Crosslinker F.C. MacKintosh, J. Käs and P.A. Janmey, Elasticity of semiflexible biopolymer networks, Phys. Rev. Lett., 75(24), 4425-4428 (1995)

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G’  cA2–6.7 Entangled Networks from M. Gardel et al., Science 2004: Viscoelasticity of concentrated isotropic solutions of semiflexible polymers. 2. Linear response DC Morse - Macromolecules, 1998 Viscoelasticity of concentrated isotropic solutions of semiflexible polymers. 1. Model and stress DC Morse - Macromolecules, 1998 Other Actin Filaments Tube Actin Filament

Polymer reptation The theory of reptation was introduced more than thirty years ago by de Gennes in order to explain some dynamical properties of polymer melts of high molecular weight. The dynamics of such systems is highly influenced by entanglement effects between the long polymer chains. The basic idea of reptation is that each polymer is constrained to move within a topological tube due to the presence of the confining surrounding polymers (see figure). Within this tube the polymer performs a snake-like motion (from this the name reptation) and advances in the melt through the diffusion of stored length along its own contour. Instead of treating the complicated problem of the motion of all chains, one focuses on the much simpler dynamics of a single test chain in a network of fixed obstacles (see figure below), assuming that this approximation for sufficiently long chains does not affect the main physical properties of the system. For a single reptating chain deGennes' theory predicts that the viscosity and longest relaxation time scale as N3 as function of the polymer length N, while the diffusion constant scales as D ~ N-2.

Reptation in Semiflexible Polymer Networks J.Käs, H.Strey and E.Sackmann, Direct imaging of reptation for semiflexible actin filaments, Nature, 368, 226-229 (1994) Deflection length Direct visualization of a tube around an actin filament in a solution of 0.7 mg/ml F-actin. The picture was obtained by superimposition of 64 traces of the contour taken at time intervals of 0.1 s. The insert above the graph displays a snapshot of the filament, which was confined in the tube. Below the tube the mean tube diameter <a> and the actin concentration of the surrounding F-actin matrix are denoted. The gray line shows a snapshot of the undulating chain within the tube and illustrates the concept of a deflection length.

Homework 10 Estimate the difference in plateau modulus between a flexible polymer network, an entangled semiflexible polymer network, and a crosslinked semiflexible polymer network ?