Extended Data Fig. 1: Geometric interpretation of the force balance in the molecular clutch system.
(a, b) Intersections of the cell traction force curve, Fc(v), and the myosin II force-velocity curve, Fm(v), correspond to the stationary points (S1 and S2) described by Eq. (8). Stability of such points is mainly determined by the slopes of Fc(v) and Fm(v) curves. If dFm/dv > dFc/dv [panel (a)], the corresponding stationary point (S1) is stable. On the other hand, if dFm/dv < dFc/dv [panel (b)], then the stationary point (S2) is unstable. As an example, consider point B in panel (a). An initial deviation of the system from point S1 (for example, due to dissociation of several molecular clutches) will first result in an increase in retrograde actin flow, since myosin II motors must work against a smaller resisting force. However, the system cannot remain in the new state (point B’) for long, since myosin II motors cannot generate enough force to balance the resisting traction force created by replenished molecular clutches (point B”). As a result, retrograde actin flow will slow down, bringing the system to stationary point S1. Similar considerations apply to the other points shown in panels (a, b). Numerical simulations of the molecular clutch system show good agreement with the above physical considerations, see Extended Data Fig. 3. (c) Example of 3D plots of cell traction force (Fc, colored surface) and myosin II-pulling force (Fm, gray surface) as a function of retrograde actin flow (v) and substrate elasticity (E). The black solid curves formed by the intersection of the two surfaces denote stationary points of the system that attract trajectories to their neighborhood (stable branches), whereas the black dashed curve denotes unstable stationary points (unstable branch). The white dot designates the saddle-node bifurcation point where the stable and unstable branches merge together. All cell traction and retrograde actin flow curves shown in Results were obtained by projecting the stable and unstable branches of 3D plots like those displayed in panel (c) onto the vertical and horizontal planes, respectively.
