

Basic physics of biopolymers and their networks
Biopolymers such as DNA and filamentous proteins provide a rich class of
socalled 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 (nonaffine).

Our recent work:
PA
Janmey, ME McCormick, S Rammensee, J Leight, P Georges, and FC MacKintosh,
Negative
normal stress in semiflexible biopolymer gels.
Nature Materials, 6:48
(2007);
E Conti and FC MacKintosh,
Crosslinked networks of stiff polymers exhibit negative normal stress
Physical Review Letters, 102: 088102 (2009).
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.

N Fakhri, FC MacKintosh, B Lounis, L Cognet, Matteo Pasquali
Brownian motion of stiff filaments in a crowded environment
Science, 330: 1804 (2010).
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 nearinfrared video microscopy, we studied the thermal diffusion of individual singlewalled 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 filamentbending 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.

CP Broedersz, M Depken, NY Yao, MR Pollak, DA Weitz, FC MacKintosh
Crosslink governed dynamics of biopolymer networks
Physical Review Letters, 105: 238101 (2010).
Abstract: Recent experiments show that networks of stiff biopolymers crosslinked by transient linker proteins exhibit complex stress relaxation, enabling network flow at long times. We present a model for the dynamics controlled by crosslinks in such networks. We show that a single microscopic time scale for crosslinker 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 withalphaactinin4 over more than four decades in frequency.

CP
Brangwynne, FC MacKintosh, S Kumar, NA Geisse, J Talbot, L Mahadevan, KK Parker,
DE Ingber, and DA Weitz,
Microtubules can bear enhanced compressive loads in
living cells because of lateral reinforcement.
Journal of Cell Biology, 173: 733 (2006). (Link)
Abstract: Cytoskeletal microtubules have been proposed to influence cell
shape and mechanics based on their ability to resist largescale 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 largescale
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.

M Das and FC MacKintosh
Poisson's ratio in composite elastic media with rigid rods
Physical Review Letters, 105: 138102 (2010).
YC Lin, NY Yao, C Broedersz, H Herrmann, FC MacKintosh, DA Weitz
Origins of elasticity in intermediate filament networks
Physical Review Letters, 104: 058101 (2010).
D Sept and FC MacKintosh
Microtubule elasticity: connecting allatom simulations with continuum mechanics
Physical Review Letters, 104: 018101 (2010).
C Storm, J
Pastore, FC MacKintosh, TC Lubensky and PA Janmey
Nonlinear elasticity in biological gels
Nature 435: 191 (2005). (Link)
DA
Head, AJ Levine, and FC MacKintosh.
Mechanical response of semiflexible
networks to localized perturbations.
Physical Review E, (2005). 72:
061914. (PDF)
Gardel, ML, Shin,
JH, MacKintosh, FC, Mahadevan,
L, Matsudaira, P, Weitz, DA:
Elastic Behavior of crosslinked and bundled
actin networks.
Science, (2004). 304: 13011305. (Link)
Gardel, ML, Shin,
JH, MacKintosh, FC, Mahadevan,
L, Matsudaira, PA, Weitz, DA:
Scaling of Factin network rheology to probe
single filament elasticity and dynamics.
Physical Review Letters,
(2004). 93: 188102. (PDF)
Head,
DA, Levine, AJ, and MacKintosh, FC:
Deformation of crosslinked semiflexible
polymer networks.
Physical Review Letters, (2003). 91: 108102. (PDF)
Head,
DA, Levine, AJ, and MacKintosh, FC:
Distinct regimes of elastic response and
deformation modes of crosslinked cytoskeletal and semiflexible polymer
networks,
Physical Review E 68, 061907 (2003). (PDF)

Microrheology of biopolymers
GH
Koenderink, M Atakhorrami, FC MacKintosh, and CF Schmidt,
Highfrequency
Stress relaxation in semiflexible polymer solutions and networks.
Physical
Review Letters, 96: 138307 (2006). (PDF)
M
Atakhorrami, JI Kwiecińska, KM Addas, GH Koenderink, JX Tang, AJ Levine, FC
MacKintosh, and CF Schmidt,
Correlated fluctuations of microparticles in
viscoelastic solutions: quantitative measurement of material properties by
microrheology in the presence of optical traps.
Physical Review E, 73:
061501 (2006).
TB
Liverpool and FC MacKintosh,
Inertial effects in the response of viscous and
viscoelastic fluids.
Physical Review Letters, (2005). 95:
208303. (PDF)
M
Atakhorrami, GH Koenderink, CF Schmidt, and FC MacKintosh,
Shorttime
inertial response of viscoelastic fluids: Observation of vortex propagation.
Physical Review Letters, (2005). 95: 208302. (PDF)
M
Buchanan, M Atakhorrami, JF Palierne, FC MacKintosh, and CF Schmidt,
Highfrequency
microrheology of wormlike micelles.
Physical Review E, (2005). 72: 011504 (PDF) 