Contractile Units in Disordered Actomyosin Bundles Arise from F-Actin Buckling

Bundles of filaments and motors are central to contractility in cells. The classic example is striated muscle, where actomyosin contractility is mediated by highly organized sarcomeres which act as fundamental contractile units. However, many contractile bundles in vivo and in vitro lack sarcomeric organization. Here we propose a model for how contractility can arise in bundles without sarcomeric organization and validate its predictions with experiments on a reconstituted system. In the model, internal stresses in frustrated arrangements of motors with diverse velocities cause filaments to buckle, leading to overall shortening. We describe the onset of buckling in the presence of stochastic motor head detachment and predict that buckling-induced contraction occurs in an intermediate range of motor densities. We then calculate the size of the “contractile units” associated with this process. Consistent with these results, our reconstituted actomyosin bundles show contraction at relatively high motor density, and we observe buckling at the predicted length scale.

Figure 1

Contraction in actomyosin bundles. (a) Sarcomeric structure as in striated muscle. As motors tend to move toward the filament barbed ends, the sarcomeric structure imposes that each contractile unit (sarcomere) contracts. (b) Bundle devoid of sarcomeric organization or passive cross-linkers, as in our experiments. (c) Motors and polar filaments induce local contraction or extension depending on the geometry of their assembly (filament polarity always dictates the direction of motion [8]). (d) Time-lapse images of a bundle comprised of F-actin and fluorescent myosin thick filaments (inverted contrast) with ${\ell }_0=540\mathrm{nm}$. The initially wavy bundle becomes taut following the addition of 1 mM ATP at $t=0\mathrm{s}$, indicating contraction. Scale bar, $5\mu \mathrm{m}$. (e) Similar experiment with ${\ell }_0=1.5\mu \mathrm{m}$, showing no contraction. Scale bar as in (d). See also movie S1 [18]. (f) Bundle contraction as a function of ${\ell }_0$. Bars indicate standard deviation ($n\ge 25$).

Figure 2

Buckling in nonsarcomeric contractile actomyosin bundles. (a) Time-lapse images of fluorescent actin (inverted contrast) showing F-actin buckling (arrowheads) following the addition of 1 mM ATP at $t=0\mathrm{s}$. Scale bar, $5\mu \mathrm{m}$. See also movie S2 [18]. (b) Relative contraction (filled squares) and number of F-actin buckles (open circles) as a function of time. Data show mean $\pm \mathrm{sd}$ averaged over $n=3$ bundles with ${\ell }_0\simeq 1\mu \mathrm{m}$. (c) The presence of fast (gray) and slow (white) motors generically induce compressive (solid red) and extensile (hatched blue) stresses in filaments. (d) Buckling of the compressed filaments leads to an overall shortening of the bundle.

Figure 3

Stress buildup in bundles with nonidentical motors. (a) In a bundle with motors having nonidentical velocities (shades of gray), filaments of lengths $\approx {\ell }_f$ are subjected to random motor forces at points $\approx {\ell }_0$ apart distributed throughout their length. (b) Prior to contraction, the environment of a filament of interest (red, delimited by dotted lines) can be approximated by a collection of evenly spaced motors (shades of gray).

Figure 4

Model predictions for filament force buildup. (a) Black line: steady-state filament force $f_{\infty }$ as a function of motor spacing ${\ell }_0$ [Eq. (6)]. For ${\ell }_0\ll {\ell }_0^{*}$ and ${\ell }_0\gg {\ell }_0^{*}$, $f_{\infty }\propto {\ell }_0^{-1/2}$ and ${\ell }_0^{-9/2}$, respectively. Colored straight lines: buckling force $F_B\propto {\ell }_0^{-2}$. (b) Typical filament force $(\overline{⟨f^2⟩}{)}^{1/2}$ as a function of time [Eq. (6)]. (c) Contractile unit size ${\ell }_B$ as a function of ${\ell }_0$ as in Eq. (8) (${\ell }_f\simeq 5\mu \mathrm{m}$).