Actin Bundling: Initiation Mechanisms and Kinetics

Bundling of rapidly polymerizing actin filaments underlies the dynamics of filopodial protrusions that play an important role in cell migration and cell-cell interaction. Recently, the formation of actin bundles has been reconstituted in vitro, and two scenarios of bundle initiation, involving binding of two filament tips and, alternatively, linking of the tip of one filament to the side of the other, have been discussed. A first theoretical analysis is presented indicating that the two mechanisms can be distinguished experimentally. While both of them result counterintuitively in comparable numbers of bundles, these numbers scale differently with the average bundle length. We propose an experiment for determining which of the two mechanisms is involved in the in vitro bundle formation.

Figure 1

(a) Starlike structure of actin bundles reconstituted in vitro (adapted from 7). (b) Snapshot of the aster after depletion of monomers in a typical Monte Carlo realization based on Eq. (1). The parameters mimic experimental conditions in 7: $Y_0=4.5\times {10}^6$, $({\tau }_p{)}^{-1}=75{\mathrm{s}}^{-1}$, $({\tau }_n{)}^{-1}=5\times {10}^{-6}{\mathrm{s}}^{-1}$, and ${\alpha }_c\delta /h={10}^{-2}$ (the aster thickness $h$ is on the order of several $\delta$). Heavy lines are actin bundles; light lines depict free filaments. (c) Diagram of processes affecting dynamics of filaments and bundles: (A) nucleation of a linear filament, (B) initiation of a bundle (shown for the tip-side mechanism), and (C) incorporation of an unbundled filament into an existing bundle.

Figure 2

The tip-tip mechanism: the number of bundles for varying ${\tau }_p$ and ${\tau }_n$. (a) Mean-field estimates (3) vs numerical solution of Eq. (1) based on ${10}^2$ to ${10}^3$ realizations, for varying ${\tau }_n/{\tau }_p$. (b) Mean-field solution in the absence of filament absorption (solid line) and results of spatial simulations with absorption taken into account (dots with error bars); ${\alpha }_c\delta /h=0.03$, $p=5$; error bars correspond to a standard deviation based on 50–120 realizations. Inset: The average number of filaments per bundle $Nb$ vs ${\tau }_n/{\tau }_p$.

Figure 3

The tip-side mechanism: numerical solution of Eq. (1) and mean-field estimates. (a) Number of all tip-side collisions $N_{\mathrm{coll}}$ (solid line) and fraction of collisions $P_{\alpha <{\alpha }_c}$ that occurred at a sufficiently small angle $\alpha <{\alpha }_c=0.2$ (histogram), integrated over the first 30 s in one Monte Carlo realization and shown as functions of distance from the aster center. (b) Mean-field solution (4) in the absence of filament absorption (solid line) and results of spatial simulations with absorption taken into account (dots with error bars); ${\alpha }_c\delta /h=0.03$, $p=5$; error bars correspond to a standard deviation based on 50–120 realizations. Inset: The average number of filaments per bundle $Nb$ vs ${\tau }_n/{\tau }_p$.

Figure 4

$B_{\infty }-L_{\infty }$ diagram for the tip-tip and tip-side mechanisms in the log-log representation. Experimental data are expected to result in a band of points. While the width of the band depends on variations in ${\alpha }_c\delta /h$, reflecting varying abundance and activity of fascin, elasticity of filaments, thickness of the aster, etc., the slope of the band $\beta$, predicted to have different values for the two mechanisms of bundle initiation, can be used for distinguishing between them. Results of spatial stochastic simulations from Figs. 2b, 3b (open circles) are fitted by straight lines with the slopes $\beta \approx 1.6$ for the tip-side mechanism and $\beta \approx 2.8$ for the tip-tip mechanism. [The corresponding bands are shown for realistically possible ranges of ${\alpha }_c\delta /h$: (0.0005, 0.007) and (0.003, 0.05), for the tip-side and tip-tip initiation, respectively.]