Biopolymers and their networks
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Basic physics of biopolymers and their networks

Biopolymers 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). 

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 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.


CP Broedersz, M Depken, NY Yao, MR Pollak, DA Weitz, FC MacKintosh
Cross-link governed dynamics of biopolymer networks
Physical Review Letters, 105: 238101 (2010).

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.

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).
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.

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 all-atom 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 cross-linked and bundled actin networks

, (2004). 304: 1301-1305.

Gardel, ML, Shin, JH, MacKintosh, FC, Mahadevan, L, Matsudaira, PA, Weitz, DA: 
Scaling of F-actin network rheology to probe single filament elasticity and dynamics

Physical Review Letters
, (2004). 93: 188102.

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 cross-linked cytoskeletal and semiflexible polymer networks, 

Physical Review E
68, 061907 (2003). (PDF)


Microrheology of biopolymers

GH Koenderink, M Atakhorrami, FC MacKintosh, and CF Schmidt, 
High-frequency 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, 
Short-time 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, 
High-frequency microrheology of wormlike micelles
Physical Review E
, (2005). 72: 011504 (PDF)

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