^{1}and Binny J. Cherayil

^{1,a)}

### Abstract

Recent experimental measurements of the distribution P(w) of transverse chain fluctuations w in concentrated solutions of F-actin filaments [B. Wang, J Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett.104, 118301 (Year: 2010)10.1103/PhysRevLett.104.118301; J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchgessner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett.105, 037801 (Year: 2010)]10.1103/PhysRevLett.105.037801 are shown to be well-fit to an expression derived from a model of the conformations of a single harmonically confined weakly bendable rod. The calculation of P(w) is carried out essentially exactly within a path integral approach that was originally applied to the study of one-dimensional randomly growing interfaces. Our results are generally as successful in reproducing experimental trends as earlier approximate results obtained from more elaborate many-chain treatments of the confining tube potential.

I. INTRODUCTION

II. WEAKLY BENDABLE ROD MODEL AND ITS TUBE-WIDTH DISTRIBUTION

III. DISCUSSION

### Key Topics

- Polymers
- 19.0
- Solution polymerization
- 5.0
- Collision theories
- 3.0
- Cumulative distribution functions
- 2.0
- Eigenvalues
- 2.0

## Figures

The dimensionless tube-width distribution, P N (x), as calculated from Eq. (9) , versus the dimensionless tube width, x, where, and , for the following values of the dimensionless deflection length, l d = L d /L: 0.07, 0.09, 0.12, and 0.15. Inset: P N (x) versus x at l d = 0.3, highlighting the asymmetry of the distribution.

The dimensionless tube-width distribution, P N (x), as calculated from Eq. (9) , versus the dimensionless tube width, x, where, and , for the following values of the dimensionless deflection length, l d = L d /L: 0.07, 0.09, 0.12, and 0.15. Inset: P N (x) versus x at l d = 0.3, highlighting the asymmetry of the distribution.

The scaled tube-width distribution ⟨x⟩P N (x), as calculated from Eq. (9) , versus the scaled tube width x/⟨x⟩ (solid black line) at a value of l d (0.09) that has been adjusted for best fit to experimental data points (open symbols) obtained from the inset to Fig. 3 of Ref. 4(a) using the program in Ref. 16 to reconstruct the data. The different symbols correspond to different chain concentrations, these being (in mg/ml): 0.2 (circles), 0.4 (squares), 0.6 (diamonds), 0.8 (triangles), and 1.0 mg/ml (inverted triangles). The dashed blue curve is the fit obtained by Glaser et al. 4(a) from a self-consistent pair collision theory. The dashed red curve is a fit obtained in Ref. 4(a) from an analytical approximation to that theory.

The scaled tube-width distribution ⟨x⟩P N (x), as calculated from Eq. (9) , versus the scaled tube width x/⟨x⟩ (solid black line) at a value of l d (0.09) that has been adjusted for best fit to experimental data points (open symbols) obtained from the inset to Fig. 3 of Ref. 4(a) using the program in Ref. 16 to reconstruct the data. The different symbols correspond to different chain concentrations, these being (in mg/ml): 0.2 (circles), 0.4 (squares), 0.6 (diamonds), 0.8 (triangles), and 1.0 mg/ml (inverted triangles). The dashed blue curve is the fit obtained by Glaser et al. 4(a) from a self-consistent pair collision theory. The dashed red curve is a fit obtained in Ref. 4(a) from an analytical approximation to that theory.

The coefficient of variation versus chain concentration c (in mg/ml) for experiment (open symbols) and theory (horizontal lines). The open symbols correspond to the data on F-actin shown in Fig. 5 of Ref. 4(b) , as reconstructed using the program in Ref. 16 . The solid line is the curve c v = 0.218 obtained by evaluating c v (using Eq. (9) ) at that value of l d (0.09) at which ⟨x⟩P N (x) best fits the experimental data (see Fig. 2 ). The dashed line is the theoretical curve c v = 0.155 as calculated by Glaser and Kroy. 4(b) Inset: c v versus 1/l d , as calculated from Eq. (9) , showing the location of the point c v = 0.218 at l d = 0.09.

The coefficient of variation versus chain concentration c (in mg/ml) for experiment (open symbols) and theory (horizontal lines). The open symbols correspond to the data on F-actin shown in Fig. 5 of Ref. 4(b) , as reconstructed using the program in Ref. 16 . The solid line is the curve c v = 0.218 obtained by evaluating c v (using Eq. (9) ) at that value of l d (0.09) at which ⟨x⟩P N (x) best fits the experimental data (see Fig. 2 ). The dashed line is the theoretical curve c v = 0.155 as calculated by Glaser and Kroy. 4(b) Inset: c v versus 1/l d , as calculated from Eq. (9) , showing the location of the point c v = 0.218 at l d = 0.09.

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