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Basic physics of biopolymers and their networksBiopolymers such as DNA and filamentous proteins provide a rich class of so-called semiflexible polymers. These are much more rigid than most synthetic polymers, in some cases by many orders of magnitude, while they still exhibit significant thermal fluctuations. The elastic and dynamic properties of networks and solutions of these semiflexible polymers have been of particular interest in our group. Specifically, in contrast with flexible polymers, the shear modulus of crosslinked networks have a strong dependence on the density of crosslinks, and also show surprising nonlinear strain stiffening. We have also recently shown theoretically that semiflexible networks generally exhibit two distinct mechanical responses to external loads: one in which the strain tends to be uniform (affine), and one in which it tends to vary significantly within the network (non-affine).
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Our recent work:PA
Janmey, ME McCormick, S Rammensee, J Leight, P Georges, and FC MacKintosh, |
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CP Broedersz, M Depken, NY Yao, MR Pollak, DA Weitz, FC MacKintosh Abstract: Recent experiments show that networks of stiff biopolymers cross-linked by transient linker proteins exhibit complex stress relaxation, enabling network flow at long times. We present a model for the dynamics controlled by cross-links in such networks. We show that a single microscopic time scale for cross-linker unbinding leads to a broad spectrum of macroscopic relaxation times and a shear modulus G~omega^1/2 for low frequencies omega. This model quantitatively describes the measured rheology of actin networks crosslinked withalpha-actinin-4 over more than four decades in frequency. |
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YC Lin, NY Yao, C Broedersz, H Herrmann, FC MacKintosh, DA Weitz D Sept and FC MacKintosh C Storm, J
Pastore, FC MacKintosh, TC Lubensky and PA Janmey DA
Head, AJ Levine, and FC MacKintosh. Gardel, ML, Shin,
JH, MacKintosh, FC, Mahadevan,
L, Matsudaira, P, Weitz, DA: Gardel, ML, Shin,
JH, MacKintosh, FC, Mahadevan,
L, Matsudaira, PA, Weitz, DA: Head,
DA, Levine, AJ, and MacKintosh, FC: Head,
DA, Levine, AJ, and MacKintosh, FC: |
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Microrheology of biopolymersGH
Koenderink, M Atakhorrami, FC MacKintosh, and CF Schmidt, M
Atakhorrami, JI Kwiecińska, KM Addas, GH Koenderink, JX Tang, AJ Levine, FC
MacKintosh, and CF Schmidt, TB
Liverpool and FC MacKintosh, M
Atakhorrami, GH Koenderink, CF Schmidt, and FC MacKintosh, M
Buchanan, M Atakhorrami, JF Palierne, FC MacKintosh, and CF Schmidt, |
This site was last updated 03/17/07
When subject to stress or external loads, most materials resist deformation. Any
stable material, for instance, resists compression—even liquids. Solids also
resist simple shear deformations that conserve volume. Under shear, however,
most materials also have a tendency to expand in the direction perpendicular to
the applied shear stress, a response that is known as positive normal stress.
For example, wet sand tends to dilate when sheared, and therefore dries around
our feet when we walk on the beach. In the case of simple solids, elastic rods
or wires tend to elongate when subject to torsion. Here, we show that networks
of semiflexible biopolymers such as those that make up both the cytoskeleton of
cells and the extracellular matrix exhibit the opposite tendency: when sheared
between two plates, they tend to pull the plates together. We show that these
negative normal stresses can be as large as the shear stress and that this
property is directly related to the nonlinear strainstiffening behaviour of
biopolymer gels.
The thermal motion of stiff filaments in a crowded environment is highly constrained and anisotropic; it underlies the behavior of such disparate systems as polymer materials, nanocomposites, and the cell cytoskeleton. Despite decades of theoretical study, the fundamental dynamics of such systems remains a mystery. Using near-infrared video microscopy, we studied the thermal diffusion of individual single-walled carbon nanotubes (SWNTs) confined in porous agarose networks. We found that even a small bending flexibility of SWNTs strongly enhances their motion: The rotational diffusion constant is proportional to the filament-bending compliance and is independent of the network pore size. The interplay between crowding and thermal bending implies that the notion of a filament’s stiffness depends on its confinement. Moreover, the mobility of SWNTs and other inclusions can be controlled by tailoring their stiffness.
Abstract: Cytoskeletal microtubules have been proposed to influence cell
shape and mechanics based on their ability to resist large-scale compressive
forces exerted by the surrounding contractile cytoskeleton. Consistent with
this, cytoplasmic microtubules are often highly curved and appear buckled
because of compressive loads. However, the results of in vitro studies suggest
that microtubules should buckle at much larger length scales, withstanding only
exceedingly small compressive forces. This discrepancy calls into question the
structural role of microtubules, and highlights our lack of quantitative
knowledge of the magnitude of the forces they experience and can withstand in
living cells. We show that intracellular microtubules do bear large-scale
compressive loads from a variety of physiological forces, but their buckling
wavelength is reduced significantly because of mechanical coupling to the
surrounding elastic cytoskeleton. We quantitatively explain this behavior, and
show that this coupling dramatically increases the compressive forces that
microtubules can sustain, suggesting they can make a more significant structural
contribution to the mechanical behavior of the cell than previously thought
possible.