Reversible stress softening of actin networks
Entry by Sandeep Koshy, AP 225, Fall 2010
Title: Reversible stress softening of actin networks.
Authors: Ovijit Chaudhuri, Sapun H. Parekh and Daniel A. Fletcher
In this work, Chaudhuri et al. describe the mechanical behavior of dendritic networks of actin filaments. Actin is a protein found in almost all eukaryotic cells which is involved in cell shape and motion. The authors grow actin network between the tip of an atomic force microscope (AFM) and a glass slide and subject the network to rheological measurements. They find stress-stiffening behavior at low stresses and reversible stress-softening behavior at higher stresses. They propose a model for this behavior which involves reversible buckling of actin within the network. This data is important for studying cell movement in both normal cells and cancer cells.
Soft Matter Keywords: polymers, polymer extension and compression, atomic force microscopy, microrheology
Actin is a ubiquitous protein in most eukaryotic cells which is involved in maintaining cell architecture and motility. The mechanical properties of this protein are important to those that study cell migration.
The resistance to extension and compression in polymer filaments is dependent on the persistence length (average length over which the polymer length changes due to thermal fluctuations) and contour length (fully extended length) of the polymer. Flexible polymers exhibit a contour length much greater than the persistence length and show a resistance to extension and compression due to conformational entropy of the chain. These polymers exhibit stress stiffening near full extension since full extension is entropically unfavorable. In stiff polymers, where the persistence length is much greater than the contour length, bending and compression resistance arises from the straining of molecular bonds from equilibrium. Such polymers buckle under high stresses. Only entropic elasticity (stress stiffening) has been largely observed in actin networks. The authors set out to study the behavior of actin networks over physiological length scales to see if they could demonstrate enthalpic elasticity at higher stress regimes.
Microrheology The authors placed an actin polymerization catalyst (ActA) on the tip of an AFM probe. They lowered the probe into cytosolic extract (the fluid inside cells… contains actin monomers) to catalyze the formation of dendritic actin filaments from the tip of the probe to a nearby glass surface. They subjected the network to a sinusoidal stress and measured the deformation.
Stress dependent elasticity measurements
The bottom glass surface of the AFM set up was moved slowly upward and oscillatory measurements were performed. In this way, the stress was incrementally increased and the change in the elasticity was measured. Once the maximum stress (600 Pa) was reached, the glass surface was moved downward and measurements were again performed to determine the elasticity.
The authors polymerized actin monomers into a dendritic actin filament between an AFM tip and a glass surface (Fig. 1 A-B). They moved the tip using a sinusoidal pattern and measured the force transduced by the network using the cantilever. They noted that the cantilever response (pink trace in Fig. 1 C) is damped relative to the driving signal (blue trance in Fig. 1 C), which indicated the effect of network compression. Using this technique, they were able to measure stress and strain as a function of time for the network (Fig. 1 D).
The elastic (filled triangle Fig 2.) and viscous (open triangle Fig. 2) moduli of the networks were determined at various frequencies. The authors fitted a power law model to the elastic modulus (dotted line Fig 2.) and determined the power to be 0.13. This value is within the range previously reported for whole cells.
Stress dependence of the elastic modulus
The authors then explored the stress dependence of the elastic modulus (Fig. 3). For these experiments, they incrementally increased the stress on the actin network and measured the elasticity. They found that for stresses below 15 Pa, the elasticity was constant, which is consistent with the concept of a linear elastic regime. For values between 15 Pa and 270 Pa (the critical stress) they saw increases of elasticity with stress. This is known as the stress stiffening regime. Above the critical stress, the elasticity decreased with increased stress.
Others had proposed that this behavior was due to the fracturing of actin filaments within the network or the unbinding of crosslinks within the network at high stresses. With these explanations, one would expect permanent modifications in the network that would lead to irreversibility of stress softening in the network. The authors provide evidence which is against these previous theories by showing that the elasticity of the network can be recovered upon removal of the stress. The propose that this is due to reversible buckling of elements within the actin network at high stresses.
Mechanism of stress softening and stiffening in actin networks
The authors propose that stress softening occurs at high stresses in dendritic actin networks due to the presence of elastic buckling (Fig. 4). Upon initial application of a stress, the elasticity of the network increases due to the entropic resistance of the filaments. As the stress is increased, certain filaments within the network begin to buckle at the critical stress. Once these filaments buckle, they become infinitely compliant, reducing the number of load bearing elements in the network. They hypothesize that buckled filaments unbuckle when the force is removed, resulting in an increase in the network elasticity. They provide a simple calculation which allows for this possible mechanism.
This study provides evidence that actin networks may be designed by nature to reversibly withstand high loads and avoid catastrophic failure. The data presented is relevant to those who study cell motility; an important phenomena in normal cellular processes and in cancer cell invasion and metastasis.