Measurement of the persistence length of polymerized actin using fluorescence microscopy

Ott, Albrecht; Magnasco, Marcelo O.; Simon, Jean‐Marc; Libchaber, Albert

doi:10.1103/physreve.48.r1642

Cited by 317 publications

(328 citation statements)

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“…Variants of this technique have been used to measure the bending stiffness of biopolymers such as actin and microtubules (15)(16)(17)(18). Here, we exploit the intrinsic near-infrared fluorescence of semiconducting SWCNTs to image individual nanotubes moving freely in aqueous surfactant suspension as they undergo Brownian motion in a quasi-two-dimensional sample chamber (19,20).…”

mentioning

confidence: 99%

Diameter-dependent bending dynamics of single-walled carbon nanotubes in liquids

Fakhri¹,

Tsyboulski

Cognet

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

136

132

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By relating nanotechnology to soft condensed matter, understanding the mechanics and dynamics of single-walled carbon nanotubes (SWCNTs) in fluids is crucial for both fundamental and applied science. Here, we study the Brownian bending dynamics of individual chirality-assigned SWCNTs in water by fluorescence microscopy. The bending stiffness scales as the cube of the nanotube diameter and the shape relaxation times agree with the semiflexible chain model. This suggests that SWCNTs may be the archetypal semiflexible filaments, highly suited to act as nanoprobes in complex fluids or biological systems.actin ͉ microrheology ͉ semiflexible filaments and polymers ͉ stochastic dynamics ͉ nanomechanics

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mentioning

confidence: 99%

Diameter-dependent bending dynamics of single-walled carbon nanotubes in liquids

Fakhri¹,

Tsyboulski

Cognet

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

136

132

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“…Filamentous or F-actin, the most abundant of these cytoskeletal proteins, forms by the polymerization of actin monomers in the presence of K 1 or Mg 21 , resulting in a semiflexible polymer that can be many microns long. Its persistence length, l p , has been measured to be about 10 20 mm [2][3][4], about 3 orders of magnitude larger than the filament diameter, d…”

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confidence: 99%

Scaling of the Microrheology of Semidilute F-Actin Solutions

1999

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The viscoelasticity of actin networks is probed over an extended range of frequencies using microrheology techniques, where the thermal motion of small beads in the network is measured using diffusing-wave spectroscopy. Despite large sample-to-sample variations, the data exhibit an unexpected scaling behavior and can all be collapsed onto a single master curve, indicative of a surprising universality in the elastic properties. The scaled data provide a precise measure of the average behavior of the actin networks and indicate that at high frequencies v, the shear modulus, increases as v 3͞4 . [ S0031-9007(99) PACS numbers: 87.19.Tt, 61.25.Hq, 83.10.Nn, 83.50.Fc Eukaryotic cells owe their mechanical strength mainly to the cytoskeleton, an intricate network of filamentous proteins such as tubulin, vimentin, spectrin, and actin [1]. Filamentous or F-actin, the most abundant of these cytoskeletal proteins, forms by the polymerization of actin monomers in the presence of K 1 or Mg 21 , resulting in a semiflexible polymer that can be many microns long. Its persistence length, l p , has been measured to be about 10 20 mm [2-4], about 3 orders of magnitude larger than the filament diameter, d7 nm [5]. Because of this large aspect ratio, actin filaments form semidilute solutions at extremely low volume fractions w ϳ ͑d͞l p ͒ 2 , with an elastic modulus orders of magnitude larger than that of flexible polymers at the same volume fraction. A theoretical understanding of this elasticity is still controversial; very different results are predicted using effective medium models [6], models based on mechanical networks [7,8], networks of semiflexible molecules with effectively permanent cross-links [9], and models which consider the unique properties of networks, at different concentrations, of semiflexible polymers [6,[10][11][12][13]. Experimental measures of the modulus also suffer from wide variations, with reported values of the frequency dependent elastic modulus, G 0 ͑v͒, varying by as much as 2 orders of magnitude for apparently identical samples [14]. While the origin of this variation is not fully resolved, it is likely a combined effect caused by the variation in the filament length distribution and by the presence of small quantities of proteins which can act as chemical cross-links, leading to dramatic, but random, changes in the modulus. A definitive test of the proposed theoretical models requires a highly purified sample with carefully controlled filament length distribution [15]. However, it is perhaps even more crucial to develop a better understanding of the behavior of the actin networks more typically produced, both to better comprehend their properties and to determine the origin of the variability.One feature of the elastic response of actin networks that should transcend the difficulty in obtaining reproducible shear moduli is the behavior at high frequencies.When the wavelength of elastic excitation is shorter than the average spacing between entanglements, the modulus should be sensitive only to p...

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“…Fluorescence microscopy as in [15] could be another possible method. It is to be remembered of course that real polymers are well-modeled by the WLC model provided we can neglect monomer-monomer interactions (steric, electrolytic etc.).…”

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confidence: 99%

Triple Minima in the Free Energy of Semiflexible Polymers

Dhar

Chaudhuri

2002

Phys. Rev. Lett.

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We study the free energy of the worm-like-chain model, in the constant-extension ensemble, as a function of the stiffness λ for finite chains of length L. We find that the polymer properties obtained in this ensemble are qualitatively different from those obtained using constant-force ensembles. In particular we find that as we change the stiffness parameter, t = L/λ, the polymer makes a transition from the flexible to the rigid phase and there is an intermediate regime of parameter values where the free energy has three minima and both phases are stable. This leads to interesting features in the force-extension curves.PACS numbers: 87.15.-v, 05.20.-y, 36.20.-r, 05.40.-a The simplest model for describing semiflexible polymers without self-avoidance is the so called Worm-LikeChain (WLC) model [1][2][3]. In this model the polymer is modeled as a continuous curve that can be specified by a d−dimensional (d > 1) vectorx(s), s being the distance, measured along the length of the curve, from one fixed end. The energy of the WLC model is just the energy due to curvature and is given bywhereû(s) = ∂x/∂s is the tangent vector and satisfieŝ u 2 = 1. The parameter κ specifies the stiffness of the chain and is related to the persistence length λ defined through û(s).û(s ′ ) = e −|s−s ′ |/λ . It can be shown thatThe thermodynamic properties of such a chain can be obtained from the free energy which can be either the Helmholtz's (F ) free energy or the Gibb's (G) energy. In the former case one considers a polymer whose ends are kept at a fixed distance r [one end fixed at the origin and the other end atr = (0, ...0, r)] by an average force f = ∂F (r, L)/∂r, while in the latter case one fixes the force and the average extension is given by r = −∂G(f, L)/∂f . It can be shown that in the thermodynamic limit L → ∞ the two ensembles are equivalent and related by the usual Legendre transform G = F −f r. For a system with finite L/λ, the equivalence of the two ensembles is not guaranteed, especially when fluctuations become large. We note that real polymers come with a wide range of values of the parameter t = L/λ [e.g. λ ≈ 0.1µm for DNA while λ ≈ 1µm for Actin and their lengths can be varied] and fluctuations in r (or f ) can be very large. Then the choice of the ensemble depends on the experimental conditions. Experiments on stretching polymers are usually performed by fixing one end of the polymer and attaching the other end to a bead which is then pulled by various means (magnetic, optical, mechanical, etc.). In such experiments one can either fix the force on the bead and measure the average polymer extension, or, one could constrain the bead's position and look at the average force on the polymer. In the former case, the Gibb's free energy is relevant while it is the Helmholtz in the second case. This point has been carefully analyzed by Kreuzer and Payne in the context of atomic force microscope experiments [4]. Theoretically, the constant-force ensemble is easier to treat, and infact an exact numerical solution has been o...

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Measurement of the persistence length of polymerized actin using fluorescence microscopy

Cited by 317 publications

References 13 publications

Diameter-dependent bending dynamics of single-walled carbon nanotubes in liquids

Diameter-dependent bending dynamics of single-walled carbon nanotubes in liquids

Scaling of the Microrheology of Semidilute F-Actin Solutions

Triple Minima in the Free Energy of Semiflexible Polymers

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