Counterion-Induced Abnormal Slowdown of F-Actin Diffusion across the Isotropic-to-Nematic Phase Transition

Jun He, Jorge Viamontes, and Jay X. Tang

Phys. Rev. Lett. 99, 068103 – Published 9 August 2007

Abstract

We report an abnormal slowdown of the longitudinal diffusion of $F$ -actin across the isotropic-to-nematic phase transition region. To probe the underlying physics of this counterintuitive discovery, we compared the diffusion of F-actin, microtubules and fd virus in F-actin solutions across the transition region and found the F-actin diffusion markedly different from the other two filament types. Also, the viscous drag probed by F-actin was found to increase sharply with $[{Mg}^{2 +}]$ in the nematic but not in the isotropic state. Based on the experimental results, we propose that the abnormal slowdown is caused by the weak electrostatic attraction between actin filaments in the nematic phase, in which neighboring filaments in parallel associate with each other transiently as they collide due to thermal fluctuations.

Received 30 March 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.068103

Authors & Affiliations

Jun He, Jorge Viamontes, and Jay X. Tang^*

Department of Physics, Brown University, Rhode Island 02912, USA

^*Jay_Tang@Brown.edu

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Vol. 99, Iss. 6 — 10 August 2007

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Images

Figure 1
(a) Overlay of the center threads of a single actin filament from a series of time-lapsed images. The white thread shows the initial position of the filament, with the later configurations added as black threads. This filament shows primarily a 1-D diffusion, as if being confined within a virtual tube. (b) A typical plot of the longitudinal diffusion coefficient of individual filaments vs. filament length ( $⊙$ ). This solution has a concentration of $5.14 mg / ml$ and an average filament length $\bar{l} = 2.7 μ m$ . The dotted curve is the fit to Eq. (1) to obtain $η_{m}$ . In this case, we find $η$ to be 2.69 cP. The inset shows the longitudinal MSD of two representative filaments. The fit to $(Δ X)^{2} = 2 D t$ gives the diffusion coefficients for $1.9 μ m$ (▵) and $6.9 μ m$ (▪) filaments, $0.72$ and $0.30 μ m^{2} / \sec $ , respectively.Reuse & Permissions
Figure 2
(a) Microscopic viscosity $η_{m}$ as a function of actin concentration across the $I − N$ phase transition region is shown for three $\bar{l}$ values of 2.7, 4, and $7 μ m$ . All three series of samples show a marked increase of $η_{m}$ in the transition region. (b) The specific retardance (S.R.) is plotted against actin concentration across the same region. The increase of the order parameter (proportional to the specific retardance) is shown to be concurrent with the rise of $η_{m}$ in the transition region.Reuse & Permissions
Figure 3
The comparison of $η_{m}$ of F-actin (▪), microtubules (★) and fd virus (◊) in F-actin solutions with 50 mM KCl and 2 mM ${MgCl}_{2}$ across $I − N$ phase transition. Also, the data of fd diffusion in fd solution, converted from Ref. 23, is presented as a comparison ( $⊙$ ). In addition, $η_{m}$ of F-actin in F-actin solutions with 50 mM $K C l$ but no ${MgCl}_{2}$ is also shown (▴). The concentrations are normalized with respect to the phase transition concentration. The normalized concentration of 1 stands for $2 mg / ml$ for F-actin and $15.5 mg / ml$ for fd, respectively.Reuse & Permissions
Figure 4
(a) The illustration of weak attraction between actin filaments induced in the $N$ phase by divalent counterions. The “-” symbols represent negative charges on F-actin, and the “++” symbols represent divalent counterions. The dark filament is confined in a virtual tube defined by its surrounding filaments. The divalent counterions temporarily associate parts of the filaments. (b) $η_{m}$ of F-actin in the $N$ phase ( $4 mg / ml$ ) is plotted against $[{Mg}^{2 +}]$ (▪). The data in the $I$ phase ( $1 mg / ml$ ) is also shown (▵). The fit to our model is given in the dashed line.Reuse & Permissions

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