Dynamics of wormlike coils: amplitudes of normal bending modes

Aragón, Sergio R.

doi:10.1021/ma00011a064

Cited by 8 publications

(8 citation statements)

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“…[49][50][51] The detailed analysis exhibits a strong influence of the rotational motion on the time dependence of the FCS correlation function for a certain range of polymer lengths. Since actin filaments or fd viruses are within that length scale, FCS provides the opportunity to measure their rotational diffusion coefficient.…”

Section: Discussionmentioning

confidence: 95%

“…͑8͔͒ leads to much simpler normal mode amplitude correlation functions than those obtained by Aragón. [49][50][51] In particular, the various modes form an orthogonal set. The reason is the more adequate treatment of the first mode, which is artificially introduced in the weakly bending rod model.…”

Section: ͑24͒mentioning

confidence: 99%

“…3 As will be shown, this leads to simpler and more adequate mode amplitude correlation functions than those following from the original approach. [49][50][51] The article is organized as follows. In the next section the model is described and its equation of motion is solved.…”

Section: Introductionmentioning

confidence: 99%

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Diffusion and segmental dynamics of rodlike molecules by fluorescence correlation spectroscopy

Winkler

2007

The Journal of Chemical Physics

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The dynamics of weakly bending polymers is analyzed on the basis of a Gaussian semiflexible chain model and the fluorescence correlation spectroscopy (FCS) correlation function is determined. Particular attention is paid to the influence of the rotational motion on the decay of the FCS correlation function. An analytical expression for the correlation function is derived, from which the averaged segmental mean square displacement can be determined independent of any specific model for the polymer dynamics. The theoretical analysis exhibits a strong dependence of the correlation function on the rotational motion for semiflexible polymers with typical lengths and persistence lengths of actin filaments or fd viruses. Hence, FCS allows for a measurement of the rotational motion of such semiflexible polymers. The theoretical results agree well with experimental measurements on actin filaments and confirm the importance of large relaxation times.

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Section: Discussionmentioning

confidence: 95%

Section: ͑24͒mentioning

confidence: 99%

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Diffusion and segmental dynamics of rodlike molecules by fluorescence correlation spectroscopy

Winkler

2007

The Journal of Chemical Physics

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“…This rigid constraint of a locally inextensible contour is the source of the difficulty in modeling the dynamics of (intrinsically) semiflexible polymers. It renders awkward any general theory [11,13,14] which tries to represent this property faithfully. On the other hand, models that relax the constraint too much -as e.g., the so-called Harris-Hearst-Beals model [15] and its latest descendants [16][17][18][19] -include artificial stretching modes and find a Gaussian distribution for all spatial distances along the contour; i.e., the essence of semiflexibility has obviously been lost.…”

Section: Introductionmentioning

confidence: 99%

“…However, as was pointed out by many workers in the field (see, e.g., Refs. [14,21]), it is conceptually important to be aware of the local anisotropy of the bending undulations caused by the rigid constraint of constant contour length.…”

Section: Introductionmentioning

confidence: 99%

Dynamic scattering from solutions of semiflexible polymers

Kroy¹,

Frey²

1997

Phys. Rev. E

120

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The dynamic structure factor of semiflexible polymers in solution is derived from the wormlike chain model. Special attention is paid to the rigid constraint of an inextensible contour and to the hydrodynamic interactions. For the cases of dilute and semidilute solutions exact expressions for the initial slope are obtained. When the hydrodynamic interaction is treated on the level of a renormalized friction coefficient, the decay of the structure factor due to the structural relaxation obeys a stretched exponential law in agreement with experiments on actin. We show how the characteristic parameters of the system (the persistence length ℓp, the lateral diameter a of the molecules, and the mesh size ξm of the network) are readily determined by a single scattering experiment with scattering wavelength λ obeying a ≪ λ ≪ ℓp and λ < ξm. We also find an exact explicit expression for the effective (wave-vector-dependent) dynamic exponent z(k) < 3 for semiflexible polymers and thus an enlightening explanation for a longstanding puzzle in polymer physics.

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Hydrodynamic modes of arbitrarily shaped flexible macromolecules: Influence on dynamic light scattering

Goldstein

1993

Biopolymers

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SYNOPSISThe diffusional motions of flexible macromolecules are analyzed with a n increasingly realistic Rouse-Zimm model, i.e., by modeling the molecule as an arbitrary set of spheres connected by nearly harmonic springs. New features include ( 1 ) nearly arbitrary arrangements of spheres, ( 2 ) arbitrary arrangements of translational and torsional springs, ( 3 ) significant anharmonic corrections to the elastic potential surface, and ( 4 ) inclusion of torsional damping and various hydrodynamic cross-coupling effects (including two types of translational-rotational coupling) with no additional fitted parameters. contain no adjustable parameters other than temperature, viscosity, and the radii and positions of the spheres. These hydrodynamic interactions allow accurate calculations of rigid body diffusion as well as flexible motions.Given the positions, radii, and spring constant matrix, one can calculate a full set of three-dimensional diffusional modes. Because one uses an off-diagonal hydrodynamic resistance matrix instead of a diagonal mass matrix, the diffusional modes are different in structure from vacuum normal modes, and give rise to different rms motions in the laboratory frame. These hydrodynamic modes include the effects of vibrational-translational crosscoupling (i.e., motion along a vibrational coordinate may give rise to a translational force, and vice versa).The diffusional modes are used to simulate dynamic light scattering (DLS) . I examine various molecules with different shapes, flexibilities, and with different scattering vectors. Radial and angular motions influence DLS decays differently. These effects are dependent upon the molecular shape (straight, bent, or curved) and type of flexibility (stretching or bending). Furthermore, small cubic corrections to the potential surface can be significant for DLS of certain geometries such as straight rods and semicircles. 0 1993 John Wiley & Sons, Inc. 409 410 GOLDSTEIN Schmitz5 and references therein). This technique has the following advantages: HYDRODYNAMIC MODES OF ARBITRARILY-SHAPED MACROMOLECULES 4 1 1 with the rigid body diffusion constants, to compute dynamic light scattering by evaluating the scattered electric field correlation function GI ( k , t ) [expressed as a plane wave expansion in Eq. ( 3 6 ) ] . This evaluation uses the results of the rigid anisotropic rotor [ Eq. ( 2 7 ) ] in terms of the isotropic rotor [ Eq. (53) 1, and includes rotational-translational coupling perturbatively in averages over rigid body angles [ Eq. ( 37 ) 1 , plus some approximation for vibrational averaging and some approximation for the remaining time-ordered expectation value in Eq. ( 3 7 ) , as discussed in the text. At a large scattering vector, however, it is more efficient to evaluate GI (k, t ) from a small angle (or short time) expansion [ Eq. (66) ] rather than the more general plane wave expansion.Probably the easiest way to implement these simulations is to obtain the programs used to compute the examples in this article. ( A copy of the programs...

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Dynamics of wormlike coils: amplitudes of normal bending modes

Cited by 8 publications

References 12 publications

Diffusion and segmental dynamics of rodlike molecules by fluorescence correlation spectroscopy

Diffusion and segmental dynamics of rodlike molecules by fluorescence correlation spectroscopy

Dynamic scattering from solutions of semiflexible polymers

Hydrodynamic modes of arbitrarily shaped flexible macromolecules: Influence on dynamic light scattering

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