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We determine the statistics of the local tube width in F-actin solutions, beyond the usually reported mean value. Our experimental observations are explained by a segment fluid theory based on the binary collision approximation (BCA). In this systematic generalization of the standard mean-field approach effective polymer segments interact via a potential representing the topological constraints. The analytically predicted universal tube width distribution with a stretched tail is in good agreement with the data.
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The phase transition from the isotropic (I) to nematic (N) liquid crystalline suspension of F-actin of average length $3~mu$m or above was studied by local measurements of optical birefringence and protein concentration. Both parameters were detected to be continuous in the transition region, suggesting that the I-N transition is higher than 1st order. This finding is consistent with a recent theory by Lammert, Rokhsar & Toner (PRL, 1993, 70:1650), predicting that the I-N transition may become continuous due to suppression of disclinations. Indeed, few line defects occur in the aligned phase of F-actin. Individual filaments in solutions of a few mg/ml F-actin undergo fast translational diffusion along the filament axis, whereas both lateral and rotational diffusions are suppressed.
The nematic ordering in semiflexible polymers with contour length $L$ exceeding their persistence length $ell_p$ is described by a confinement of the polymers in a cylinder of radius $r_{eff}$ much larger than the radius $r_rho$, expected from the respective concentration of the solution. Large scale Molecular Dynamics simulations combined with Density Functional Theory are used to locate the Isotropic-Nematic ($I-N$)-transition and to validate this cylindrical confinement. Anomalous fluctuations, due to chain deflections from neighboring chains in the nematic phase are proposed. Considering deflections as collective excitations in the nematically ordered phase of semiflexible polymers elucidates the origins of shortcomings in the description of the $I-N$ transition by existing theories.
Anomalous transport and reaction dynamics are considered by providing the theoretical grounds for the possible experimental realization of actin polymerization in comb-like geometry. Two limiting regimes are recovered, depending on the concentration of reagents (magnesium and actin). These are both the failure of the reaction front propagation and a finite speed corresponding to the Fisher-KPP long time asymptotic regime.
We study the motion of oil drops propelled by actin polymerization in cell extracts. Drops deform and acquire a pear-like shape under the action of the elastic stresses exerted by the actin comet. We solve this free boundary problem and calculate the drop shape taking into account the elasticity of the actin gel and the variation of the polymerization velocity with normal stress. The pressure balance on the liquid drop imposes a zero propulsive force if gradients in surface tension or internal pressure are not taken into account. Quantitative parameters of actin polymerization are obtained by fitting theory to experiment.
We show that the exponential length distribution that is typical of actin filaments under physiological conditions dramatically narrows in the presence of (i) crosslinker proteins (ii) polyvalent counterions or (iii) depletion mediated attractions. A simple theoretical model shows that in equilibrium, short-range attractions enhance the tendency of filaments to align parallel to each other, eventually leading to an increase in the average filament length and a decrease in the relative width of the distribution of filament lengths.
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