Entanglement, Elasticity, and Viscous Relaxation of Actin Solutions

Abstract

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...

Stress-Dependent Elasticity of Composite Actin Networks as a Model for Cell Behavior

“…1. At the lowest frequency probed, G 0 slightly dominates the response and is twofold larger than that of a pure F-actin solution [17]. Upon increasing R to 1=1000, G 0 increases an order of magnitude to 1 Pa and becomes less frequency dependent, as shown by the solid triangles in Fig.…”

“…088102-3 F-actin solutions [22] rather than those of rigidly crosslinked F-actin networks [13]. By contrast, the maximum stress the networks can withstand is extremely sensitive to the degree of cross-links, suggesting that the nonlinear behavior is dominated by the properties of the FLNa cross-linkers, rather than by the F-actin filaments.…”

Statistical Mechanics of Semiflexible Bundles of Wormlike Polymer Chains

“…Significant progress has also been made towards the description of the collective properties of WLCs, for example, in the form of entangled solutions. One of the hallmarks of this development is the scaling of the plateau shear modulus with concentration G c 7=5 [7][8][9], which is well established experimentally [10,11].…”

“…Significant progress has also been made towards the description of the collective properties of WLCs, for example, in the form of entangled solutions. One of the hallmarks of this development is the scaling of the plateau shear modulus with concentration G c 7=5 [7][8][9], which is well established experimentally [10,11].Another important emerging class of semiflexible polymers consists of bundles of WLCs [12,13]. Semiflexible polymer bundles consisting of F-actin or microtubules are ubiquitous in biology [14] and have unique mechanical properties that may well be exploited in the design of nanomaterials [13].…”

Scaling of the Microrheology of Semidilute F-Actin Solutions

“…While the origin of this variation is not fully resolved, it is likely a combined effect caused by the variation in the filament length distribution and by the presence of small quantities of proteins which can act as chemical cross-links, leading to dramatic, but random, changes in the modulus. A definitive test of the proposed theoretical models requires a highly purified sample with carefully controlled filament length distribution [15]. However, it is perhaps even more crucial to develop a better understanding of the behavior of the actin networks more typically produced, both to better comprehend their properties and to determine the origin of the variability.…”