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Microrheometry of Semiflexible Actin Networks Through Enforced Single-Filament Reptation: Frictional Coupling and Heterogeneities in Entangled Networks

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Microrheometry of Semiflexible Actin Networks Through Enforced Single-Filament Reptation: Frictional Coupling and Heterogeneities in Entangled Networks Microrheometry of semiflexible actin networks through enforced single-filament reptation: Frictional coupling and heterogeneities in entangled networks M. A. Dichtl† and E. Sackmann Lehrstuhl fu¨r Biophysik E22, Technische Universita¨t Mu¨ nchen, James-Franck-Strasse, D-85747 Garching, Germany Edited by Harden M. McConnell, Stanford University, Stanford, CA, and approved December 27, 2001 (received for review August 16, 2001) Magnetic tweezers are applied to study the enforced motion of filaments embedded in networks may be visualized and analyzed single actin filaments in entangled actin networks to gain insight by fluorescence microscopy (16) or by labeling with colloidal into friction-mediated entanglement in semiflexible macromolec- probes (17). In previous work, the latter possibility was used to ular networks. Magnetic beads are coupled to one chain end of test relate macroscopic viscoelastic impedance spectra to thermally filaments, which are pulled by 5 to 20 pN force pulses through driven single-filament motion. entangled solutions of nonlabeled actin, the test filaments thus The frequency-dependent viscoelastic impedance G*(␻) ϭ acting as linear force probes of the network. The transient filament GЈ(␻) ϩ iGЉ(␻) exhibits three distinct frequency regimes (18): at ␯ ϭ ␻͞ ␲ Ͼ ͞␶ ␶ Ͼ Ϫ2 ␶ motion is analyzed by microfluorescence, and the deflection- high frequencies, 2 1 e [ e 10 sec; note that e versus-time curves of the beads are evaluated in terms of a is the relaxation time of the bending mode of a chain segment of ⌳ mechanical equivalent circuit to determine viscoelastic parameters, length equal to the entanglement length e (6)], the shear elastic which are then interpreted in terms of viscoelastic moduli of the modulus GЈ(␻)Љ and the loss modulus GЉ(␻) increase with network. We demonstrate that the frictional coefficient character- frequency according to a power law GЈ(␻), GЉ(␻)ϰ␻0.75, which izing the hydrodynamic coupling of the filaments to the surround- has been shown to be determined by the entropic tension of the ing network is much higher than predicted by the tube model, single filaments (6, 8, 9, 11). The power law was verified suggesting that friction-mediated interfilament coupling plays an microscopically by analysis of the local motion of single filaments important role in the entanglement of non-cross-linked actin net- by using the colloidal probe technique (17). At medium fre- ͞␶ Ͻ ␯ Ͻ ͞␶ works. Furthermore, the local tube width along the filament quencies (1 d 1 e), a rubber-like plateau arises, and this contour (measured in terms of the root-mean-square displacement regime is determined by the affine shear deformation of the ␯ Ͻ ͞␶ characterizing the lateral Brownian motion of the test filament) network (11, 12). For 1 d, the entangled network becomes reveals strong fluctuations that can lead to transient local pinching fluid-like and the viscoelastic moduli decay to zero, whereas at ␯Ӎ ͞␶ ␶ Љ ␻ of filaments. 1 d ( d, terminal relaxation time), the loss modulus G ( ) exhibits a maximum. etworks of filamentous actin (F-actin) are of great interest Viscoelastic impedance spectra of the entangled actin network Nfrom the point of view of both cell biology and polymer were calculated on the basis of the classical tube model (11, 12, physics and have thus been the subject of intense experimental 19, 20). Excellent agreement between the theoretical predictions and the spectra measured by torsional rheometry was found for and theoretical studies. On the one hand, actin is a major ␯ Ͼ ͞␶ the high-frequency regime ( 1 e), whereas at the low- structural component of the intracellular scaffold (the cytoskel- CHEMISTRY frequency end of the plateau and within the terminal regime, the eton) and plays a key role in various cellular processes, such as theory underestimates the measured viscoelastic moduli. Thus, cell locomotion (1, 2), the transport processes within cells (3), or the measured friction coefficient is higher by a factor of 10 than the control of cell adhesion on surfaces (4). To fulfill this the theoretical prediction (see refs. 11 and 21), strongly suggest- multiplicity of tasks, nature uses a large number of helper ing that the tube model underestimates the frictional coupling proteins. These include severing proteins by which the length of between the filament and the environment. The failure of the actin filaments can be manipulated, monomer-sequestering pro- simple tube model also became evident by recent studies with the teins that allow the control of the polymer concentration, and colloidal probe technique showing that the tube diameter varies finally a manifold of cross-linker proteins enabling the genera- drastically (17). tion of randomly organized gels or arrangements of bundles To gain more detailed insight into the dynamic coupling acting as cell-stabilizing fibers or cables for intracellular trans- between single filaments and the surrounding chains, we applied port (5). the recently developed magnetic tweezer technique to study the On the other hand, F-actin is a prototype of a semiflexible enforced reptation of single test filaments. Magnetic beads (with polymer. Highly versatile models of entangled and cross-linked diameters smaller than mesh size) were attached to the end of networks of semiflexible macromolecules can be designed by phalloidin-stabilized and fluorescent-labeled actin filaments, controlling the structure through the manifold of manipulating which were embedded in entangled actin networks. These test proteins to study the distinct physical properties of this particular filaments were pulled through the network in a step-wise manner class of polymer networks. Such semiflexible polymer networks by application of sequences of force pulses on the magnetic exhibit outstanding viscoelastic features, which are determined by a subtle interplay of entropic and enthalpic contributions to the elastic free energy of the individual filament (6–12). This paper was submitted directly (Track II) to the PNAS office. One distinct advantage of actin as model polymer is the large Abbreviations: F-actin, filamentous actin; G-actin, monomeric actin. ␮ contour length (typically in the 10- m range) (13) and persis- † Ӎ ␮ To whom reprint requests should be addressed. E-mail: [email protected]. tence length (Lp 17 m) (10, 14, 15) enabling the design of The publication costs of this article were defrayed in part by page charge payment. This networks with mesh sizes in the optical wavelength regime. article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Therefore, the conformational dynamics and motion of single §1734 solely to indicate this fact. www.pnas.org͞cgi͞doi͞10.1073͞pnas.052432499 PNAS ͉ May 14, 2002 ͉ vol. 99 ͉ no. 10 ͉ 6533–6538 Downloaded by guest on September 25, 2021 tweezer. The motion of the bead and the attached filament was analyzed by dynamic image processing. The filament motion induced by a force pulse consists of three regimes: first, a fast deflection with constant velocity associated with a deformation of the network; second, a slowing-down regime followed by flow of the filament with respect to the network; and third, partial relaxation associated with a backflow of the filament after switching off the force. The enforced filament motion is analyzed in terms of a mechanical equivalent circuit. The viscoelastic moduli obtained compare reasonably well with results of frequency-dependent measurements by torsional macrorheometry or magnetic bead microrheology. Distinct differences suggest, however, that the microviscoelastic moduli depend on the shape of the force probe and its interaction with the environment. A remarkable finding is that the frictional coupling between single filaments and the surrounding network is much stronger than predicted by the simple tube model of entangled macro- molecular networks. The heterogeneity of the entangled network was studied by pulling test filaments through the meshwork by sequences of force pulses. Very pronounced fluctuations of the effective tube diameter are observed that may even lead to the transient trapping of filaments in local narrows of the reptation tube, confirming previous findings that the tube diameter exhibits local narrows (17, 22). Materials and Methods The Magnetic Tweezers Setup. The experiments were performed with a previously described magnetic force microscope (23). This so-called magnetic tweezers setup allows application of se- Fig. 1. Typical response of test filaments to an applied external force. (a) quences of constant force pulses onto magnetic beads. It consists Image of a test filament embedded in an unlabeled actin network recorded by of a central measuring unit composed of a sample holder and one fluorescence microscopy. The magnetic bead was coupled to the fluorescent- magnetic coil (1,200 turns of 0.7-mm copper wire with an iron labeled filament at the right end. The superimposed arrow indicates the direction of the magnetic force F(t). (b) Two typical trajectories of the colloidal core exhibiting a sharp edge). This device is mounted on an beads attached to different test filaments are shown at high magnification AXIOVERT 10 microscope (Zeiss, Oberkochen, Germany). (Insets). Moreover, the filament contour before the application of the force The coil current is produced by a homemade voltage-controlled pulse is presented to show the overall length and curvature of the test current supply that transforms the voltage signal of a function filament. Note that the beads move not only along
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