Tracer Studies on F-Actin Fluctuations

Goff, Loïc Le; Hallatschek, Oskar; Frey, Erwin; Amblard, François

doi:10.1103/physrevlett.89.258101

Cited by 147 publications

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“…PACS numbers: 61.41.+e, 87.15.La, 87.15.He, 98.75.Da In tracing back the viscoelasticity of the cell to properties of its constituents, a detailed understanding of the mechanical response of single cytoskeletal filaments is indispensable. Due to their large bending stiffness, these filaments exhibit highly anisotropic static [1] and dynamic [2,3,4] features, such as the anomalous t 3 /4 -growth of fluctuation amplitudes in the transverse direction [5,6], i.e., perpendicular to the local tangent. The related response to a localized transverse driving force has so far been examined only by neglecting longitudinal degrees of freedom [6,7], although these polymers are virtually inextensible, and transverse and longitudinal contour deformations therefore coupled.…”

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“…16 /7 and t L ≈ 0.2 s/f ⊥ [ pN] for (unstretched) actin filaments of about 20 µm length [4], which implies that the actin response to myosin motors becomes nonlinear on time scales comparable to the duration of a single power stroke [15]. Filaments in actin networks (mesh size ξ ≈ 1 10 L ≈ 0.5 µm) under stresses of about 1 Pa [11] are usually so short that t f ≫ t L ≈ 10 −4 s, but the coupling nonlinearity should be observable in the viscoelastic response [3].…”

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“…(2b, 4,6). To this end, we introduce two-variable scaling forms [13] that remove any parameter dependence:f (s, t) = γf ⊥ ϕ(s/s f , t/t f ), with the crossover scales t f and s f and γ as in Fig.…”

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Coupling of Transverse and Longitudinal Response in Stiff Polymers

Obermayer

Hallatschek

2007

Phys. Rev. Lett.

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The time-dependent transverse response of stiff inextensible polymers is well understood on the linear level, where transverse and longitudinal displacements evolve independently. We show that for times beyond a characteristic time t f , longitudinal friction considerably weakens the response compared to the widely used linear response predictions. The corresponding feedback mechanism is explained by scaling arguments and quantified by a systematic theory. Our scaling laws and exact solutions for the transverse response apply to cytoskeletal filaments as well as DNA under tension. PACS numbers: 61.41.+e, 87.15.La, 87.15.He, 98.75.Da In tracing back the viscoelasticity of the cell to properties of its constituents, a detailed understanding of the mechanical response of single cytoskeletal filaments is indispensable. Due to their large bending stiffness, these filaments exhibit highly anisotropic static [1] and dynamic [2,3,4] features, such as the anomalous t 3 /4 -growth of fluctuation amplitudes in the transverse direction [5,6], i.e., perpendicular to the local tangent. The related response to a localized transverse driving force has so far been examined only by neglecting longitudinal degrees of freedom [6,7], although these polymers are virtually inextensible, and transverse and longitudinal contour deformations therefore coupled. In this Letter we show that longitudinal motion strongly affects the transverse response even for weakly-bending filaments and leads to relevant nonlinearities beyond a characteristic time t f .The physical key factors controlling the transverse response may be understood from Fig. 1, which shows a weakly-bending polymer (bending undulations are exaggerated for visualization) shortly after a transverse driving force f ⊥ has been applied in the bulk. In response to this force, the contour develops a bulge. Due to the backbone inextensibility, this bulge can continue growing only by pulling in contour length from the filament's tails. This effectively reduces the thermal roughness of the contour [8,9,10], at a rate substantially limited by longitudinal solvent friction. The resulting coupling to the longitudinal response tends to slow down the bulge growth. In order to describe this feedback mechanism, we start with a scaling analysis and treat the simpler athermal case first. To connect to the biologically important situations of prestressed actin networks [11] and prestretched DNA [12], we then extend a recent theory of tension dynamics [13] to calculate the nonlinear response for unstretched and prestretched initial conditions. Consider the overdamped dynamics of an initially straight stiff rod of total length L. Suddenly applying a transverse pulling force f ⊥ , for simplicity in the center of the rod, leads to the growth of a bulge deformation. The generated friction in the transverse and longitudinal direction needs to be balanced by corresponding driving forces. Viscous solvent friction is modeled via anisotropic friction coefficients (per length) ζ ⊥ and ζ = ζζ ⊥ with ζ ≈ ...

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Coupling of Transverse and Longitudinal Response in Stiff Polymers

Obermayer

Hallatschek

2007

Phys. Rev. Lett.

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“…A vital role for these and other cellular functions is played by the cytoskeleton, the structural framework of the cell composed of a network of protein filaments. A major component is filamentous actin (F-Actin), whose physical properties are by now well characterized [1]. The length distribution, spatial arrangement and connectivity of these filaments is controlled by a great variety of regulatory proteins.…”

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Internal Motility in Stiffening Actin-Myosin Networks

et al. 2004

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We present a study on filamentous actin solutions containing heavy meromyosin subfragments of myosin II motor molecules. We focus on the viscoelastic phase behavior and internal dynamics of such networks during ATP depletion. Upon simultaneously using micro-rheology and fluorescence microscopy as complementary experimental tools, we find a sol-gel transition accompanied by a sudden onset of directed filament motion. We interpret the sol-gel transition in terms of myosin II enzymology, and suggest a "zipping" mechanism to explain the filament motion in the vicinity of the sol-gel transition.PACS numbers: 87.16. Ka, 87.15.La, 87.15.Nn, 87.16.Nn Eucaryotic cells show an amazing versatility in their mechanical properties. Not only can they sustain stresses ranging from some tenths to hundreds of Pascals, but they can equally well perform such complex processes as cytokinesis and cell locomotion. A vital role for these and other cellular functions is played by the cytoskeleton, the structural framework of the cell composed of a network of protein filaments. A major component is filamentous actin (F-Actin), whose physical properties are by now well characterized [1]. The length distribution, spatial arrangement and connectivity of these filaments is controlled by a great variety of regulatory proteins.An important family of these regulatory proteins are cross-linkers, which can be further classified as passive or active. The function of passive cross-linkers, e.g. α-actinin, is mainly determined by their molecular structure and the on-off kinetics of their binding sites to actin. Upon changing the association-dissociation equilibrium and hence the degree of cross-linking by varying the temperature the network can be driven from a sol into a gel state [2]. Depending on both the concentration and the affinity of these cross-linkers for F-actin there is a tendency to either form random networks or bundles [3]. Motor proteins of the myosin family can also act as active cross-linkers. When both of its functional head groups are bound to two different filaments they can use the energy of adenosine-triphosphate (ATP) hydrolysis to exert relative forces and motion between them. However, such an event is very unlikely under physiological conditions and ATP saturation, because then myosin II spends only a short fraction of its chemomechanical cycle attached to the filament (duty ratio: r 0.02 [4]). Active relative transport yet becomes possible due to the concerted action of several motors if in vitro myosin II proteins assemble into multimeric minifilaments [5].In this letter we study actin networks containing the heavy meromyosin (HMM) subfragment lacking the light meromyosin domain responsible for myosin II assembly. Our focus is on the viscoelastic phase behavior and internal dynamics of such networks during ATP depletion. We use an experimental setup combining microrheology with fluorescent microscopy of labeled filaments. This allows us to identify a sol-gel transition accompanied by a sudden onset of directed filament...

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“…In the study of bulk rheology of polymer solutions, the dynamics of the flow of start-up or sudden cessation have been discussed theoretically (Prabhakar et al , 2005;Hua & Schieber , 1995) and experimentally (Smith & Chu, 1998;Goff et al , 2002;Goshen et al , 2005). Hua & Schieber (1995) studied the finitely extensible nonlinear elastic (FENE) dumbbell model with internal viscosity (IV).…”

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Effect of internal viscosity on Brownian dynamics of DNA molecules in shear flow

Yang¹,

Melnik²

2007

Computational Biology and Chemistry

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The results of Brownian dynamics simulations of a single DNA molecule in shear flow are presented taking into account the effect of internal viscosity. The dissipative mechanism of internal viscosity is proved necessary in the research of DNA dynamics. A stochastic model is derived on the basis of the balance equation for forces acting on the chain. The Euler method is applied to the solution of the model. The extensions of DNA molecules for different Weissenberg numbers are analyzed. Comparison with the experimental results available in the literature is carried out to estimate the contribution of the effect of internal viscosity.

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Tracer Studies on F-Actin Fluctuations

Cited by 147 publications

References 21 publications

Coupling of Transverse and Longitudinal Response in Stiff Polymers

Coupling of Transverse and Longitudinal Response in Stiff Polymers

Internal Motility in Stiffening Actin-Myosin Networks

Effect of internal viscosity on Brownian dynamics of DNA molecules in shear flow

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