The viscoelastic moduli of actin/filamin solutions: a micro-rheologic study.

The viscoelastic properties of protein solutions were measured in a frequency-dependent manner after polymerization. Fig. l a -d show the storage modulus (G') , loss modulus (G"), viscosity (q) and phase shift (9) of actin solutions and actin solutions cross-linked with filamin at various concentrations recorded between 2x1 O-3Hz and 2Hz. Results of these measurements indicate that polymerized actin and polymerized actin crosslinked with filamin at a molar ratio of 1000 : 1 gave identical curves and values for (G'), (G") and (q). However, decreasing the molar ratio of actin : filamin to 500-100 : 1 results in a significant change in all parameters. The plateau moduli for (G.), (G") and (q) are increased by a factor of 2-2.5 at actin to filamin ratios of 500-100 : 1. Another important aspect is demonstrated by the nonphase shift (9) between 2xlO-3Hz and 2xlO-*Hz (at so-called minimum retaxation times) of actin when cross-linked with filamin at molar ratios of 500-100 : 1. This is indicative of permanent, stable cross-linking. Though only a few measurements of the elastic moduli of cross-linked actin solutions have been carried out, some interesting information can be presented: a) The increase in viscosity up to fivefold at actin to filamin molar ratios of 100 : 1 show that the distance between actin filaments becomes substantially smaller; and as these cannot reach their equilibrium configuration form gels of densely packed filaments. The increase of the elastic portion by a factor of two at high degrees of cross-linking suggests negligible phase separation and actin filament interconnection with filamin. b) For fixed networks of long polymers e.g. actin filaments, the elastic constant has been proposed to be linearly related to the number of cross-links per unit volume which is inversely proportional to the number of monomers between cross-links [6]. The mesh size density determined by quasielastic light scattering is -0.5pm for actin concentration I0.5mg/ml [7]. At an actin to cross-linker ratio of 100 : 1 the average calculated contour length between two binding sites (LEI 00x2.7nm) is approx 0.27pm. This result supports the assumption made in (a) that filamin forms tighter actin filament networks. Future work will, therefore, include temperaturedependent measurements of the storage modulus (G') to provide data on entropy elasticity of filamin cross-linked actin networks. This work was supported by the Deutsche Forschungsgesellschaft. We thank Ms H. Kirpal for protein preparations. 1. Pollard, T.D.. & Cooper, J. (1986) Ann. Rev.