Viscoelastic Properties of Microtubule Networks
Entry by Sandeep Koshy, AP 225, Fall 2010
Title: Viscoelastic Properties of Microtubule Networks
Authors: Yi-Chia Lin, Gijsje H. Koenderink, Frederick C. MacKintosh, and David A. Weitz
This work by Lin et. al. studies the linear and nonlinear viscoelastic properties of naturally entangled microtubule solutions as well as artificially cross-linked networks of microtubules. It was found that the microtubules demonstrated a concentration dependent elastic modulus and yield stress. Creep testing revealed that cross-linked networks fully recovered after prolonged stress application, while entangled networks failed to fully recover. The widely used Doi-Edwards model was applied to the rheological data and was to poorly fit the experimental measurements. A simple model to account for interaction forces which may be present between crossing microtubule filaments was applied and found to be reasonably consistent with the data. This work contributes insight into understanding the mechanical characteristics of microtubules which compose a large part of the cytoskeleton in all eukaryotic cells.
Soft Matter Keywords: polymer, rheology, intermolecular interactions, viscoelastic
Tubulin monomers from bovine brain were allowed to polymerize by dissolving in BRB buffer. Cross-linking was induced by treating networks with succinimidyl ester-biotin and then adding NeutrAvidin which forms irreversible bonds with biotin.
Network structure characterization
Networks were covalently labeled with succinimidyl ester-Alexa 488 for visualization and the mesh and pore size were determined by direct observation using confocal microscopy. Pore size was measured in another manner by using particle tracking. Colloidal polystyrene beads of various sizes were mixed in the tubulin prepolymer and their motion was tracked in order to determine their mean square displacement after network formation. These measurements were then correlated with the pore size.
Tubulin monomers were polymerized between the plates of a rheometer. The linear viscoeleastic moduli at various concentrations was measured by applying a sinusoidal stress and measuring the resulting strain. Creep tests involved the application of a constant stress for 100 s and the resultant strain was measured during network recovery.
Fig 1. Confocal images of microtubules. Top: Unassembled microtubules. Bottom: A) Entangled and B) cross-linked microtubule networks.
The microtubule rods formed from tubulin monomers were found to be polydisperse. The networks formed after polymerization were found to be homogeneous with no liquid crystalline structure formation with both entangled and cross-linked networks. Confocal imaging gave mean pore diameter measurements of 1 um for solutions and 1.5 um for cross-linked networks. Particle tracking gave 1.2 um for solutions while cross-linked networks were found to have a mean pore diameter of 1.7 um.
Figure 2. Viscoelastic measurements. Left) Elastic (G’) and viscous (G’’) moduli of entangled (open symbols) and cross-linked (solid symbols) networks for tubulin concentrations of 1 mg/ml (squares) and 5 mg/ml (circles). Middle) Elastic modulus at a fixed tubulin concentration 1 mg/ml at various ratios (Rn) of crosslinker. Right) The plateau modulus (Go) as a function of molar ratio of biotin labeled tubulin (Rb).
Small amplitude oscillatory stress measurements were performed on networks created in situ between rheometer plates. The elastic modulus was greater than the viscous modulous at all conditions. The elastic modulus was seen to increase with an increase in the amount of crosslinker used. A power law scaling of Go was observed with Rb.
Figure 3. Creep testing.
Creep testing showed a power law increase with time in the resultant strain with time (Fig 3, inset). Upon removal of the constant stress, the cross-linked networks recovered fully but the entangled networks demonstrated a residual strain of approximately 0.012.
Figure 4. Comparison of data to the Doi-Edwards model.
The moduli observed with the entangled networks was compared with a common model used for rigid, noninteracting rod systems of uniform length. This model fit the data extremely poorly, with the observed microtubules being 10 times stiffer than they were predicted to be. The authors did not consider the fact that the rods used in their work may not have been of uniform length as indicated by their previous confocal imaging. The authors suggest that intermolecular interactions exist within rods that cause this deviation from the predicted behavior without explicitly stating the interaction force. It is possible that van der Waals forces, hydrogen bonding and ionic interactions were present in this protein network. The authors also state that denatured tubulin or the presence of microtubule-associated proteins may have caused these deviations.
Figure 5. Simple model of crosslinking within entangled networks.
The authors created a simple model where an interaction energy was assumed to exist between crossed fibers. The model assumed that upon application of shear stress, these weak crosslinking interactions could be broken (Fig. 5-A). Their model fit the experimental data to a reasonable extent.