Prediction of intracellular forces from F-actin network flow in Fig. 1. (a) Predicted force vectors (cyan: boundary forces; red: domain forces). Polygons I - IV highlight regions with different force characteristics (see text). (b) Flow field (yellow vectors) that would be produced by the predicted forces. Vectors are overlaid onto the color-coded speed map of the measured network flow. Insert: Comparison of the calculated (yellow) and measured (green) flow indicating the noise filtering during force reconstruction. (c) Cone rule to separate the contributions from adhesion and contraction to the predicted domain force. (d) Distribution of angles between predicted force vectors and measured flow vectors. (e) Classification of predicted forces following the cone rule. In adhesion-dominant regions the magnitude of the adhesion force component is color-coded. Positions with significant contributions from both adhesion and contraction (mixed zone) are indicated by grey dots. Insets e-I and e-II show regions of mixed adhesion and contraction forces, respectively. Mixed forces are further decomposed into a contraction component (blue) and adhesion component (magenta). Scale bar in a: 10 μm.

Predicted adhesion force transients near the leading edge are synchronized in time and co-localized in space with predicted boundary force transients. (a) Definition of edge-tracking probing windows (see Video 3). Per window and time-point averaged boundary and adhesion force transients are calculated. (b) Construction of activity maps of predicted adhesion (left) and boundary forces (right). For one time-point, predicted force magnitudes are collected in all probing windows along the cell edge and copied into one column of the activity map (see example of probing window #19 mapped into the first column). The procedure is repeated for the entire time-lapse sequence to reveal the spatiotemporal organization of force development. Arrows: concurrent dropping of adhesion and boundary forces at the time-points adhesion begin to slide (cf. Fig. 3b). (c) Cross-correlation of adhesion and boundary force activity maps. Scale bar in a: 10 μm.

Reconstruction of intracellular force transients from F-actin network flow. (a) Flow vectors measured by quantitative Fluorescent Speckle Microscopy (qFSM; Scale bar: 10 μm.). (b) Network flow is driven by forces at the cell boundary (∂Ω_LE) and by domain forces within lamellipodium and lamella (Ω). These forces generate transient deformations of the network, observed as spatial gradients in the displacement of fluorescent speckles over the time interval δt between two consecutive frames (illustrated by the transformation of a rectangle, dashed, into a polygon, solid gray lines. Network flows without spatial gradients indicate force free areas. (c) Force prediction from transient deformations of elastic spring. (d) Model of the F-actin network as a transiently elastic material. Over time scales 1s≤δt≤10 s, cross-linked F-actin networks deform predominantly elastically19. Thus, the material behaves like an ensemble of springs. At longer time scales t₂-t₁’ δt, structures (cyan) break while others (light green) form (plastic behavior). As a result pre-stress in the network is relaxed, which preserves the elastic constant and resting length of the spring ensemble (L₁ » L₂); yet, the relationship between the deformation u and the actual force change from t₁ to t₂ is lost. When the extension is fast compared to the time scale of remodeling, as from t₁ to t₁+δt or from t₂ to t₂+δt force changes can be inferred as F₁=k×u₁/L₁ and F₂=k×u₂/L₂.

Relationship between predicted adhesion forces and F-actin-vinculin interactions during protrusion and retraction. (a) Top-left panel: adhesion force magnitude (color-coded) and boundary force (cyan vectors); Top-right panel: dual-color FSM image of F-actin (red) and vinculin (green) (see Video 2). Bottom-left panel: Zoom of the middle sector M showing F-actin flow (yellow vectors), adhesion forces (red vectors) overlaid to adhesion force magnitude (color-coded). Bottom-right panel: eGFP-vinculin signal. (b) Top row: Adhesion force magnitude (color-coded) and F-actin/vinculin signal in two time-points between which the cell edge in the bottom sector (first) and top sector (second) retracts and the adhesions slide (asterisk). Bottom-left column: Kymograph display of vinculin signal along three profiles indicated in the top panels. Bottom-right column: Time courses of the average adhesion (ADHF; red) and boundary forces (BNDF; cyan) in the Top, Bottom and Middle sectors. Also shown are time courses of the direction-coupling score (DCS, green) and the velocity-magnitude-coupling score (VMCS, blue) of F-actin and vinculin speckle motion4. Arrows: onset of decreasing adhesion and boundary forces, which correlates in time with increased motion coupling of F-actin and vinculin speckles. Asterisks: time-points of minimal adhesion forces (correspond to asterisks in top row). (c) Time montages of the adhesion force (ADHF) and the velocity magnitude coupling score (VMCS) in the middle and bottom sectors. (d) Models of a vinculin-mediated clutch. Scale bars: 5 μm.

Coordination of predicted force transients during cell protrusion with F-actin assembly and edge movement. (a) Left panel: Boundary forces (cyan vectors) and adhesion force magnitudes (color-coded) at the leading edge of a protruding epithelial cell. 24 probing windows (overlaid boxes) were used to construct the activity maps shown in b. Zoom in: Predicted boundary (cyan) and adhesion (red) force vectors, and F-actin flow vectors (yellow) overlaid to the adhesion force magnitude (color-coded) in protruding sector of the cell edge. Right panel: Time montage of rates of F-actin polymerization (red) and depolymerization (green, top row); and of adhesion force magnitude (color-coded) and boundary forces (cyan vectors, bottom row) during a protrusion event. The two time series are shifted by 20 sec to account the delay in predicted adhesion/boundary force transients relative to rate changes in F-actin turnover (see text; see Video 4 for time-resolved force and assembly maps). (b) Activity maps of (I) cell edge movement, (II) velocity of F-actin retrograde flow, (III) predicted adhesion force, (IV) predicted boundary force, (V) rate of F-actin polymerization and depolymerization, and (VI) power (boundary force times the sum of the speeds of cell edge protrusion and retrograde flow). (c) Cross-correlation between activities. Negative time lags indicate that the first activity is delayed relative to the second activity. (d) Event sequence during a protrusion cycle. Scale bar in a: 5 μm.