We have investigated the viscosity and the plateau modulus of actin solutions with a magnetically driven rotating disk rheometer. For entangled solutions we observed a scaling of the plateau modulus versus concentration with a power of 7͞5. The measured terminal relaxation time increases with a power 3͞2 as a function of polymer length. We interpret the entanglement transition and the scaling of the plateau modulus in terms of the tube model for semiflexible polymers. [S0031-9007(98)07135-X] PACS numbers: 87.15. Da, 61.25.Hq, 83.50.Fc Networks of semiflexible macromolecules are major constituents of biological tissue. There is experimental evidence [1-4] that certain aspects of biologically important macromolecules, such as DNA and actin, are well described by the minimal theoretical model of a semiflexible macromolecule, also known as the wormlike chain model. This model represents the polymer as a smooth inextensible contour with an energy cost for bending and includes ideal flexible chains as a limiting case. The bending modulus of the single molecule can be expected to be constitutive also for the collective mechanical properties of gels and sufficiently concentrated solutions of semiflexible polymers. (Recently, possible contributions from twist have also been discussed [5].) However, very little is known about how semiflexible polymers build up statistical networks and how the macroscopic stresses and strains are mediated to the single molecules in such networks. This is also known as the entanglement problem. In this Letter, we report on experiments performed with a magnetically driven rotating disk rheometer, which elucidate some important aspects of the entanglement problem. The systems under scrutiny are in vitro polymerized actin solutions of various concentrations c and average polymer lengths L. Actin [6] forms large semiflexible polymers with a persistence length ᐉ p of about 17 mm [7,8] (comparable to typical filament lengths in our experiments) and is the most abundant cytoskeletal element in most eucariotic cells. We have analyzed the transition from the dilute to the semidilute phase (the entanglement transition) as a function of polymer length and concentration. The data can be interpreted in terms of a virial expansion for effective "tubes." For entangled solutions we observed a scaling of the plateau modulus G 0 versus actin concentration c. This is compared with various theoretical predictions [9][10][11][12][13][14]. Lastly, we analyzed the dependence of the zero shear rate viscosity on polymer length, which exhibits a much weaker length dependence than one would expect theoretically from work by Odijk [9] and Doi [15].Actin was prepared as previously described [16] and purified in a second step using gel column chromatog-raphy (Sephacryl S-300). Monomeric actin (called G-actin) was kept in G-buffer, consisting of 2 mM Imidazol (pH 7.4), 0.2 mM CaCl 2 , 0.2 mM DTT, 0.5 mM ATP, and 0.005 vol % NaN 3 . Polymerization was initiated by adding 1͞10 of the sample volume of 10-fold concentrated...

We have studied the structural and viscoelastic properties of assembling networks of the extracellular matrix protein type-I collagen by means of phase contrast microscopy and rotating disk rheometry. The initial stage of the assembly is a nucleation process of collagen monomers associating to randomly distributed branched clusters with extensions of several microns. Eventually a sol-gel transition takes place, which is due to the interconnection of these clusters. We analyzed this transition in terms of percolation theory. The viscoelastic parameters (storage modulus G' and loss modulus G") were measured as a function of time for five different frequencies ranging from omega = 0.2 rad/s to 6.9 rad/s. We found that at the gel point both G' and G" obey a scaling law, with the critical exponent Delta = 0.7 and a critical loss angle being independent of frequency as predicted by percolation theory. Gelation of collagen thus represents a second order phase transition.

We recently established an in vitro assay that monitors the fusion between latex-bead phagosomes and endocytic organelles in the presence of J774 macrophage cytosol . Here, we show that different reagents affecting the actin cytoskeleton can either inhibit or stimulate this fusion process. Because the membranes of purified phagosomes can assemble F-actin de novo from pure actin with ATP (Defacque et al., 2000a), we focused here on the ability of membranes to nucleate actin in the presence of J774 cytosolic extracts. For this, we used F-actin sedimentation, pyrene actin assays, and torsional rheometry, a biophysical approach that could provide kinetic information on actin polymerization and gel formation. We make two major conclusions. First, under our standard in vitro conditions (4 mg/ml cytosol and 1 mM ATP), the presence of membranes actively catalyzed the assembly of cytosolic F-actin, which assembled into highly viscoelastic gels. A model is discussed that links these results to how the actin may facilitate fusion. Second, cytosolic actin paradoxically polymerized more under ATP depletion than under high-ATP conditions, even in the absence of membranes; we discuss these data in the context of the well described, large increases in F-actin seen in many cells during ischemia.

We present a systematic comparison of microrheological and macrorheological measurements of the viscoelastic storage and loss moduli, G'(f) and G"(f), respectively, of solutions of the semiflexible biopolymer F-actin. Using magnetic tweezers microrheometry and rotating disk macrorheometry, we show that microscopic values for G'(f) and G"(f) are significantly smaller than macroscopic results over the frequency range f = 0.004-4 Hz, whereas the qualitative shape of the spectra is similar. These findings confirm recent theoretical predictions [A. C. Maggs, Phys. Rev. E 57, 2091 (1998)]. The discrepancy affects not only absolute values of G'(f) and G"(f): although microscopic and macroscopic plateau regime are found in the same frequency range, the two methods yield different values for the entanglement time which determines the high-frequency end of the plateau. By investigating F-actin solutions of different mean filament lengths, we show that microscopic and macroscopic G'(f) and G"(f) converge, if the probe particle used in microrheometry becomes large compared to the length of actin filaments.

The cytoskeletal protein filament F-actin has been treated in a number of recent studies as a model physical system for semiflexible filaments. In this work, we studied the viscoelastic properties of entangled solutions of the filamentous bacteriophage fd as an alternative to F-actin with similar physical parameters. We present both microrheometric and macrorheometric measurements of the viscoelastic storage and loss moduli, G'(f ) and G"(f ), respectively, in a frequency range 0.01