Colloidal gels from proteins and peptides - Physical Gels from Biological and Synthetic Polymers - page 279

However, plots of equilibrium values for G 0 against concentration suggested a c 2 depend-
ence. The fall in modulus with increasing strain was also recorded, and the viscosity
behaviour led these workers to conclude that the actin system was a temporary network,
easily destroyed by external forces. It was not clear, however, whether the temporary
cross-links could be ascribed to entanglement or to non-covalent interactions, or indeed
to residual impurities still present in the samples. Subsequent studies of F actin have led
to similar conclusions, although some workers have concluded that an entanglement
network was involved, and that modulus

- frequency data agreed well with a prediction

for a solution of rigid rods.
The mesh size of the gel also decreased, albeit entirely as expected, as the concen-
tration of actin increased, but some current thinking suggests that the elasticity of the gels
results entirely from the thermal

filaments (Janmey and Weitz, 2004 ).
In other words, because they are so long and thin, they possess inherent thermal

fluctuations of the

uctua-
tions will be reduced, a reduction which costs energy and is entropic (Higgs and Ball,
1989 ; Storm et al., 2005 ), similar to classical rubber elasticity. The magnitude of the
elastic response depends on both actin and cross-link concentration, but gives rise to
strain hardening; but at larger deformations enthalpic effects begin to contribute (Storm
et al., 2005 ). Such a strain hardening effect is also seen in an early theory for rods, in
which there are no cross-links (Doi and Kuzuu, 1980 ).

fluctuations that reduce their end-to-end length. When a strain is applied, these

9.5.3 Tubulin

Microtubules, derived from the globular protein tubulin, are highly organized, hollow,
rod-like assemblies, commonly found in the cytoplasmic material of cells, where they can
be assembled and disassembled by processes involving associated proteins, which in u-

ence the nucleation step which is part of the cooperative assembly process (Berg et al.,
2007a ). Like F actin, the microtubules are part of the

filamentous structural components of
cell cytoplasm, and are involved in several processes including cell mitosis.
The microtubules are large structures, around 50 nm in diameter and with persistence
lengths believed to be as great as 1 mm, and thought to grow from a nucleation ring of
tubulin dimer molecules by addition of further dimers to either surface. The assembly
process has been studied by a variety of techniques including turbidity measurements and
small-angle X-ray scattering.
Lin and co-workers (Lin et al., 2007 ) examined the linear and non-linear viscoelastic
properties of isotropic solutions of puri ed microtubules, as well as networks perma-

nently cross-linked with a speci c reagent. In the linear regime, both solutions and

networks were soft elastic materials with small G 0 and G 00 . For the networks, G 0 was
approximately proportional to c 1.7 , with lower exponents for the solutions, although these
show a concentration-dependent apparent yield stress, which suggests the presence of
effective cross-linking even in these pure microtubule solutions. Such results show that,
like F actin, microtubule assemblies do not generate high-modulus networks on their
own. Consequently, in vivo they must depend on their participation in architectures
involving other components.