Cytoskeletal Deformation at High Strains and the Role of Cross-Link Unfolding Or Unbinding

Cellular and Molecular Bioengineering, Vol. 2, No. 1, March 2009 (Ó 2009) pp. 28–38 DOI: 10.1007/s12195-009-0048-8 Cytoskeletal Deformation at High Strains and the Role of Cross-link Unfolding or Unbinding 1 3 2 1 1,2 HYUNGSUK LEE, BENJAMIN PELZ, JORGE M. FERRER, TAEYOON KIM, MATTHEW J. LANG, 1,2 and ROGER D. KAMM 1Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; 2Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; and 3Physik-Department E22, Technische Universita¨tMu¨nchen, D-85748 Garching b. Munich, Germany (Received 19 January 2009; accepted 2 February 2009; published online 12 February 2009) Abstract—Actin cytoskeleton has long been a focus of proteins present, have met with limited success. Early attention due to its biological significance and unique experiments found a much higher frequency depen- rheological properties. Although F-actin networks have been dence with values of shear modulus that were orders of extensively studied experimentally and several theoretical models proposed, the detailed molecular interactions magnitude lower than those observed in cells. More between actin binding proteins (ABPs) and actin filaments recently, it has been shown that network prestrain that regulate network behavior remain unclear. Here, using plays a critical role, stiffening the matrix to the point an in vitro assay that allows direct measurements on the bond that moduli become comparable to the in vivo val- between one actin cross-linking protein and two actin ues.11,12 Even then, however, the modulus exhibits a filaments, we demonstrate force-induced unbinding and unfolding of filamin. The critical forces prove to be similar, different frequency dependence, ranging from nearly 70 ± 23 pN for unbinding and 57 ± 19 pN for unfolding, constant value for the storage modulus (G¢) at low suggesting that both are important mechanisms governing frequencies, with a gradual transition to a weak power cytoskeletal rheology. We also obtain the mechanical law at higher frequencies. To complicate the situation response of a cross-linked F-actin network to an optically further, different cross-linking proteins apparently trapped microbead and observe abrupt transitions implying rupture or unfolding of cross-links. These measurements are affect the linear rheological behavior in different ways, interpreted with the aid of a computational simulation of the depending in part on whether the network forms large- experiment to provide greater insight into physical mecha- diameter bundles (stress fibers),23 or organizes the actin nisms. filaments into a more orthogonal network.34 Many of these fascinating characteristics remain unexplained, Keywords—F-actin, Filamin, Single molecule, Network. but have been a source of much recent debate. A similar range of views also exist in the modeling community. Various models have been proposed and each has its own proponents. These can be classified INTRODUCTION into several broad categories, which can be character- ized as the cellular solids model, the tensegrity model, Cytoskeletal rheology has captured the interest of and the biopolymer model. In the tensegrity model,20 many researchers because of its importance in tele- an interaction is proposed between certain elements graphing numerous biological processes, but also due that are in tension and others that are under a com- to the rich variety of observed behavior. At small pressive state. These latter could either be internal amplitude, the complex shear modulus in vivo typically structures such as the microtubules or external teth- exhibits a weak power law, undergoing a transition ering to a substrate or extracellular matrix. Theoretical from primarily elastic behavior at low frequencies to descriptions of tensegrity show that the storage mod- one dominated by viscous effects at high frequency.5,8 ulus depends primarily upon the level of prestrain in Attempts to reproduce these characteristics in the lin- the network and is relatively independent of the ear regime using in vitro systems,32,39,40 typically a properties of the matrix elements themselves. In con- reconstituted actin gel with one or more cross-linking trast, the cellular solids model is based on earlier description of macroscopic fibrous materials,13,14 in Address correspondence to Roger D. Kamm, Department of which the elastic behavior is entirely determined by the Mechanical Engineering, Massachusetts Institute of Technology, bending stiffness of the elastic fibers and the fiber Cambridge, MA 02139, USA. Electronic mail: [email protected] concentration. Neither of these models have been 28 1865-5025/09/0300-0028/0 Ó 2009 Biomedical Engineering Society Cytoskeletal Deformation at High Strains and the Role of Cross-link Unfolding or Unbinding 29 extended to include viscoelastic behavior, so they monitored, providing insights into single molecule provide no information on the unique frequency events in a 3-dimensional network. In the isolated dependence described above. One can also view the single molecule measurement, unfolding is distin- actin network as a semi-dilute solution of polymers, guished from unbinding by the sawtooth pattern with the biopolymer model, with or without cross-links that intervals ~30 nm observed in the force-extension are thermally active. Because of the long persistence curves. Both unfolding and unbinding occur at similar length of actin, the individual filaments of an actin gel levels of force, but unbinding is more frequent than exhibit slight deviations from straight segments be- unfolding. Further analysis of measurements at tween cross-link points, but these slight fluctuations different pulling angles suggests that torsion or shear provide for the network elasticity at low strains. Re- induce rupture at smaller force. Compared with the cent models have incorporated the effects of prestrain, results from single molecule assays, the responses of an and produce predictions that capture some of the F-actin network also show similar transitions in the nonlinear behavior.33 force-extension curves indicating that similar events, Based on these previous experimental studies and both bond rupture and unfolding, can be identified, models, despite many fundamental differences, the holding open the promise of analyzing single molecule prevailing view is that prestrain is a critical factor. In events within a 3-dimensional network. living cells, this can result from a combination of external tethering via an assortment of adhesion receptors and internal contraction due to the activity MATERIALS AND METHODS of myosin motors and other forces that associate with the actin filaments. In this highly prestrained condi- Protein Preparation tion, the cross-links are subjected to relatively high G-actin is prepared by dissolving lyophilized G-ac- loads, likely sufficient to cause them to either unfold or tin from rabbit skeletal muscle (Cytoskeleton Inc., unbind, giving rise to entirely new phenomena such as Denver, CO) in fresh G-buffer [5 mM Tris–HCl, matrix irreversibility and network remodeling under 0.2 mM CaCl2, 0.5 mM DTT, 0.2 mM ATP, pH 8.0] stress. While unfolding and unbinding can both give and incubated on ice for ~2 h. For biotinylated actin rise to a certain degree of hysteresis, the underlying filaments, 20 lLof20lM nonlabeled actin monomer mechanisms and relevant time scales will differ. For is mixed with 5 lLof20lM biotinylated actin example, if a strained cross-link unbinds, the filaments (Cytoskeleton Inc., Denver, CO). Actin polymerization will locally rearrange, and the ‘‘dangling’’ cross-linking is initiated by adding a tenth of the final volume of 109 protein might form a new bond at a different location F-buffer [50 mM Tris–HCl, 500 mM KCl, 2 mM in the network, potentially (but not necessarily) MgCl2, 2 mM CaCl2, 2 mM DTT, 5 mM ATP, 0.01% resulting in a new equilibrium state of a remodeled (w/v) NaN3, pH 7.5]. Recombinant filamin A is puri- network. If this same cross-linker unfolds, when the fied from Sf9 cell lysates29 and recombinant human stress is released, the protein may refold given sufficient gelsolin is produced in Escherichia coli.24 Both were time, and return to the original state. Both the time stored at À80 °C before use. scales for reaching equilibrium and the potential for remodeling differ in these two scenarios, and it there- Microsphere Attachment to an Actin Filament fore becomes an important question as to whether unbinding or unfolding is the dominant behavior in One micrometer diameter, carboxylated polystyrene high stress states, especially given the perceived beads (Polysciences Inc., Warrington, PA) are coated importance of high prestrain or prestress in living cells. with gelsolin as described in Suzuki et al.35 with the Here we explore the question of whether unfolding 400 lg proteins: 5 lL of 10 mg/mL actin, 10 lLof or unbinding is more likely to occur. In order to 5 mg/mL gelsolin, 26 lL of 10 mg/mL bovine serum address this question, we examine recent experiments albumin (BSA), and 40 lL of 1 mg/mL rhodamine- from our own laboratory and those from others, as BSA. The gelsolin-coated beads are stored in a rotator well as new data that extend our previous work. We at 4 °C in the dark. Twenty-five microliters of bead rely primarily upon two methods employing an optical solution is diluted with 25 lL of the buffer solution trap that provide insight into single molecule events. [25 mM imidazole–HCl (pH 7.4), 25 mM KCl, 4 mM One is a single molecule pulling assay in which a single MgCl2, 0.1 mM CaCl2, 0.1 mM ATP, 1 mM DTT, actin filament forms a tether with another actin fila- and 0.04% NaN3] and sonicated for 30 s. The bead ment via one specific cross-linker, and an optical trap is solution is washed four times with 50 lL of the same used to precisely control the applied force. Another buffer by centrifugation at 6000 rpm for 4 min.

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