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Nat Cell Biol. Author manuscript; available in PMC Jun 1, 2009.
Published in final edited form as:
PMCID: PMC2597050
NIHMSID: NIHMS70873

Fluctuations of intracellular forces during cell protrusion

Abstract

We propose a model to infer from live cell images of actin filament (F-actin) flow intracellular force variations during protrusion-retraction cycles of epithelial cells in a wound healing response. To establish mechanistic relations between force development and cytoskeleton dynamics, force fluctuations were correlated with fluctuations in F-actin turnover, flow, and F-actin-vinculin coupling. Our analyses suggest that force transmission at focal adhesions (FA) requires binding of vinculin to F-actin and integrin (indirectly), which is modulated at the vinculin-integrin but not the vinculin-F-actin interface. Force transmission at FAs is co-localized in space and synchronized in time with transient increases of the boundary force at the cell edge. Surprisingly, the maxima in adhesion and boundary forces lag maximal edge advancement by ~40 s. Maximal F-actin assembly is observed ~20 s after maximal edge advancement. Based on these findings, we propose that protrusion events are limited by membrane tension and that the characteristic duration of a protrusion cycle is determined by the efficiency in reinforcing F-actin assembly and adhesion formation as tension increases.

Introduction

Cell protrusion requires the precise integration of polymerization of actin filaments (F-actin) at the leading edge1-3, coupling of F-actin to the extracellular matrix (ECM)4-6, and contraction7, 8. While each of these force-generating processes has been characterized in great molecular detail, their coordination in space and time and their relationships to F-actin network dynamics are poorly understood. To study these aspects, intracellular forces must be mapped at the spatial and temporal scales of protrusion dynamics9.

Methods to probe forces with subcellular resolution have employed traction force microscopy (TFM)5, 10-12, optical traps13, 14, or atomic force microscopy15, 16. However, these measurements capture only the extracellular portion of cell-generated forces. They neither reveal the location of cell contraction nor the force balance between contraction and edge propulsion. In addition, they are mechanically invasive and offer limited insights of spatial force relationships, precluding undistorted analyses of force regulation.

Here, we propose to map with single-micron resolution force fluctuations during protrusion and retraction cycles of epithelial cells based on a mechanical model that relates variations in F-actin network flow tracked by fluorescent speckle microscopy (FSM) to variations in intracellular force levels. We found that adhesion force transients were inversely correlated with the motion coupling of F-actin and vinculin speckles4. This indicates that cell adhesion is regulated at the vinculin-integrin but not the F-actin-vinculin interface. Spatiotemporal correlation of force fluctuations with F-actin assembly, flow and cell edge movements established an inverse relationship between edge advancement and boundary force, suggesting that membrane tension limits cell protrusion in a dynamic cycle whose time scale is determined by putative feedback between tension increase and F-actin assembly.

Results

Principles of force prediction and model assumptions

Forces in lamellipodium and lamella of epithelial cells were inferred from the F-actin network flow field u(x, t) measured by quantitative FSM17, 18 (Fig. 1a). Spatiotemporal gradients in direction and/or magnitude of the flow vectors indicate local deformations of the F-actin network (Fig. 1b) associated with intracellular forces (Supplementary Note 1). Our goal was to predict the distribution of boundary forces FI at the leading edge, [partial differential]ΩLE, and contraction and adhesion forces FII+III inside the cellular region, Ω, that would optimally explain the measured network deformation. The concept of force reconstruction can be understood by analogy of a Hookean spring under tension (Fig. 1c). The force F required to extend a spring is proportional to the extension u relative to the relaxation length L, i.e. the external force is balanced by spring-internal stresses. The ratio ε=u/L is referred to as the strain. Knowing the spring constant k and the strain, the force is F=k·ε.

Figure 1
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 ([partial differential]Ω ...

While with a spring the material properties are well-defined and constant, they are difficult to calibrate for an F-actin network and they continuously change as the cell migrates. To date, no method exists to probe the material properties of F-actin in living cells at the spatial and temporal scale of FSM data. To overcome this information gap, we relied our analysis on four central assumptions: i) At the length scale of live cell light microscopy (~0.5 - 1μm) F-actin networks are locally isotropic and continuous; ii) At the time scale of FSM movies (1-10 sec/frame) the response of F-actin networks to force changes is predominantly linear elastic19 (Supplementary Note 2); iii) At any time point the F-actin network is in a resting quasi-steady state; and iv) The mechanical coupling of the lamellipodium and lamella actin networks20, 21 is sufficiently rigid to approximate the actin cytoskeleton at the leading edge as a single material entity (Supplementary Note 3).

There are two main sources of material anisotropy in F-actin networks: filament branching and filament bundling. Branching occurs an order of magnitude below the length scales observed by light microscopy. As indicated by our results below, filament bundles are often large enough to be resolved explicitly as force-bearing and/or force generating structures between isotropic regions. Thus, the simplification of an isotropic network mostly neglects small alignments of actin filaments which do not affect force predictions on a length scale of ~1μm.

In view of the mainly elastic behavior of F-actin over δt = 1 - 10 s, we describe the flow changes between consecutive frames of FSM movies as the transiently elastic response of the network to force application. Over ΔT ~ 100 s, the network exhibits a plastic response as filaments disassemble and reassemble22, 23. Stresses produced by shorter-term force transient are continually relaxed. The characteristics of such a material model are illustrated in Figure 1d. Thus, force fluctuations can be predicted by analysis of the spatial and temporal variation of F-actin flow assuming quasi-steady state material properties.

Inference of force transients

F-actin flow fields were recorded with multi-fluorophore speckles, allowing the measurement of F-actin flow gradients over sub-micron distances17. Using the continuum mechanical model and numerical force inference discussed in Supplementary Notes 4 and 5 we predicted maps of intracellular force transients (Fig. 2a). These maps indicate on a relative scale force variations between different cellular locations and between time-points. Inference of absolute force levels would require measurements of the elastic properties of lamellipodial and lamellar F-actin structures. No method exists to accomplish this at the length scale of flow gradients. Nevertheless, relative force levels were sufficient to examine the modulation of contraction, adhesion and boundary forces during protrusion and retraction events.

Figure 2
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 ...

Boundary forces (Fig. 2a, region I) reflect the pressure the growing F-actin network experiences at the cell edge. A region of forward directed force vectors (Fig. 2a, region II) indicates the resistance F-actin retrograde flow experiences near the cell edge. A region of opposing retrograde and anterograde force vectors localizes ~10 μm behind the cell edge (Fig. 2a, regions III and IV). Retrograde flow in region III is accompanied by forces parallel to the flow direction. Slower anterograde flow in region IV is accompanied by forces of almost similar magnitude. Conversely, fast flow speeds between regions II and III (Fig. 2b) are accompanied by low force levels. These observations illustrate ‘flow-speed’ and ‘force-strength’ are not directly related. Strong forces occur in regions with high strain, which is independent of the flow speed.

The force reconstruction algorithm distinguishes between boundary forces FI and domain forces FII+III. To infer the contribution of adhesion and contraction to the domain force transients, we defined the cone rule (Figure 2c, d; Supplementary Note 6) assuming that in adhesion-dominated regions forces are anti-parallel to network flow while force and flow vectors are approximately parallel in contraction-dominated regions. Accordingly, in Figure 2e the lamellipodium at the cell edge is an adhesion-dominant region whereas contraction-dominant regions distribute throughout the lamella. Figure 2e-I highlights a mixed-force region where adhesion forces are gradually overcome by contraction forces as the flow field is deflected into centers of high contractile activity. Further evaluation of the proposed model and numerical approach to force reconstruction was performed on simulated force fields with simulated measurement noise (Supplementary Note 7). We also tested the colocalization of contraction forces with myosin-II motors (Supplementary Note 8, Fig. S4 and Video 1) and of adhesion forces with eGFP-vinculin (Fig 3a), following previous reports of correlations between vinculin density with traction force5, 24. Overall, these analyses established the possibility to predict from F-actin flow adhesion, contraction, and boundary force transients that mediate morphological changes during protrusion and retraction.

Figure 3
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 ...

Strong adhesion forces require simultaneous linking of vinculin to F-actin and integrins

Predicted high adhesion forces co-localized with high eGFP-vinculin intensity only in regions where the cell edge was in a protruding state (Fig 3a). High eGFP-vinculin signals could also be observed in the absence of adhesion forces (asterisks Fig. 3b, upper panel). Kymograph analyses showed local cell edge retraction and sliding of the FA site in these regions (Top and Bottom). In contrast, the adhesion site in the Middle region is stationary over ~15 minutes and the cell edge advances by ~7 μm between minute 6 and 9 (Video 2). Previous analyses of the relative motion between F-actin and vinculin suggested that the motion coupling of spectrally distinct actin and vinculin speckles, assessed by the Direction Coupling Score (DCS) and the Velocity Magnitude Coupling Score (VMCS)4, increased concurrently with the sliding of the FA site (green and blue curves in Fig. 3b, lower-right panel, T and B). In contrast, DCS and VMCS values fluctuated at a medium level when cells protruded (Fig. 3b, lower-right panel, M). Based on this data it was proposed that in protruding regions vinculin would bind transiently and directly or indirectly to both F-actin and integrins, while in retracting regions the link to the integrins would be selectively released. Thus, vinculin would be a key component of a regulatable slippage clutch that transmits forces from the F-actin network to the ECM.

To test this hypothesis, further mechanical evidence was needed to show that changes in the motion coupling between vinculin and F-actin would alter force transmission. By combining intracellular force reconstruction and multispectral speckle analysis we found that the predicted adhesion force increased when the motion of vinculin speckles was partially coupled to the F-actin flow, and vanished when the motion of vinculin and F-actin speckles was fully coupled (compare time courses of VMCS/DCS with time courses of adhesion force in Fig. 3b-lower right panel and Fig. 3c). Importantly, the only information used to predict these adhesion force changes was the temporal variation of F-actin flow gradients. Thus, force predictions and motion coupling of F-actin and vinculin speckles are truly independent variables reporting the dynamic state of adhesions.

Coupling of predicted adhesion and boundary forces

Efficient cell protrusion requires a balance of propulsive forces at the leading edge and adhesion forces behind the protruding sector. To investigate the coordination of propulsive and adhesive forces, we performed a spatiotemporal correlation analysis of boundary and adhesion force transients along the leading edge. Predicted force magnitudes were averaged in probing windows that moved with the cell edge (Fig. 4a; Video 3) and were copied column-by-column into a color-coded matrix (blue - weak forces; red - strong forces) referred to as activity maps (Fig. 4b). Activity maps of adhesion and boundary forces show similar spatiotemporal organizations. Both forces drop in bottom and top sectors at 4 min and 10 min, respectively (arrows). These events coincide with the onset of FA sliding (arrows in Fig. 3b).

Figure 4
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 ...

To quantify the coupling of predicted boundary and adhesion force transients, we computed their cross-correlation both as a function of temporal and spatial shifts. The resulting cross-correlation score map indicates whether and by how much the two forces are co-modulated (Fig. 4c). The position of the maximal correlation score determines the time lag between adhesion and boundary force transients (horizontal displacement of the peak from 0) and the spatial shifts between force transients along the cell leading edge (vertical displacement of the peak from 0). A sharp peak at zero shifts was obtained: when the boundary force is high, the adhesion force is high, and vice versa. This finding suggests that adhesions adjacent to the leading edge balance propulsive forces while network contraction contributes much less to the adhesion forces in this region.

Timing of force modulation relative to morphological and cytoskeletal dynamic events

Next, we applied spatiotemporal cross-correlation analysis to identify the timing between predicted boundary/adhesion forces, velocities of cell edge movement9; and rates of F-actin assembly/disassembly23. For each of these parameters an activity map was constructed, in this example using 24 probing windows (Fig. 5a). The cell exhibits a burst of forward motion in a ~5 μm-wide sector of the leading edge, while remaining stationary or undergoing slow retraction in other sectors (Video 4). The analyses confirmed that boundary and adhesion forces are co-localized and synchronized (Fig. 5a-left, b-III/IV and c-i). Visual inspection of time-lapse sequences of adhesion/boundary force maps and maps of F-actin assembly/disassembly suggested that the forward movement of the cell edge was accompanied by transient increases in force and F-actin assembly (Fig. 5a-right). Cross-correlation analysis revealed that the increase in boundary/adhesion force lags the increase in F-actin assembly by ~20 sec (Fig. 5a-right, b-III/IV/V and c-ii, Video 4). Variations in assembly/disassembly rates lag behind the corresponding variations in protrusion/retraction velocities also by 20 sec (Fig. 5b-I/V and c-iii). Thus, boundary force increases should be delayed by 40 sec relative to the corresponding protrusion event, as confirmed by cross-correlation (Fig. 5b-I/IV and c-iv).

Figure 5
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. ...

Together, these analyses established the following sequence of events during cell protrusion (Fig. 5d). Upon initial activation of F-actin assembly, the leading edge advances rapidly against low plasma-membrane tension (low boundary force). Hence, work produced by F-actin polymerization is mostly converted cell edge advancement and the protrusion velocity is significantly higher than retrograde flow (Fig. 5b-I/II). 20 sec after maximal protrusion F-actin assembly reaches the maximum rate. During this period boundary and adhesion forces begin to rise indicating a tension increase in the expanding plasma-membrane. Boundary and adhesion force maxima are reached 20 sec later. At this time-point edge advancement is largely stalled and substantial work by F-actin polymerization is converted into retrograde flow. Hence, fastest retrograde flow rates were reached concurrently with the peak in boundary force (Fig. 5c-v). The internal consistency among these events provides additional validation of the force predictions that corroborate with independent measurements of cell edge movement and F-actin turnover.

Discussion

Morphogenic cell functions require precise spatiotemporal coordination of intracellular forces, often in concert with local cytoskeleton reorganization. We implemented a method to infer intracellular force fields from the transiently elastic response of the F-actin network observed by actin speckle flows. Inference of absolute force distributions would require knowledge of network elasticity and prestress. Several approaches have been proposed to probe these parameters in living cells25-28; however, none of them match the resolution of FSM or capture the properties of thin protruding lamella and lamellipodia, which are of interest here.

Without a precise profile of network material properties, it is still possible to estimate force transients on a relative scale. Variations of the elastic modulus up to one order of magnitude have no qualitative effect on force predictions in lamella and lamellipodia (Supplementary Note 8). This robustness originates in the different length scales of network deformation and material property changes. Network deformations vary over less than a micron, material properties in lamellipodium and lamella vary over 5-10 microns. Thus, the flow gradients resolved by speckles (distances of ~500 nm) are dominated by force transients. While the method is limited to the specific space- and time-scales captured by FSM its particular strength is that forces are probed passively and without mechanical influence on the cell. Hence, force fluctuations can be tracked during rapid processes such as cell edge protrusion.

We exploited these capabilities to analyze how force transmission from the cytoskeleton to the ECM relates to vinculin-F-actin interactions within focal adhesions as observed by motion coupling of vinculin and actin speckles4. Vinculin molecules may undergo transitions between four binding states (Fig. 3d, panel I): a) direct binding to F-actin only; b) indirect binding to integrin only (e.g. via talin29); c) simultaneous binding to F-actin and integrin; and d) binding to neither. State d) does not contribute to speckle images30. State c) is likely short-lived compared to states a) and b), but critical for transmitting intracellular forces to the ECM4. Partial coupling of vinculin to actin speckle motion, as observed in stationary FAs behind protruding edges, could be associated with both scenarios I (clutch engaged) and II (clutch disengaged). Similarly, full coupling, as observed in sliding FAs during edge retraction, could be associated with both scenarios III (clutch disengaged) and IV (clutch weakly engaged). Thus, the coupling of speckle motion is not representative of the state of force transmission.

By relating speckle motion coupling to force generation in individual FAs we excluded scenarios II and IV. Predicted adhesion forces were high when the motion of vinculin speckles is only partially coupled to F-actin speckle flow. Tight coupling of vinculin and actin speckle flows results in almost complete loss of force (asterisks in Fig. 3b-lower-right panel and Fig. 3c-Bottom sector), suggesting that vinculin is the core of a molecular clutch that modulates force transmission from the contractile cytoskeleton to the ECM.

We then scrutinized relationships between predicted adhesion force and boundary force during protrusion events. At the time scales of our analyses the two forces are tightly co-modulated. First, this means that contraction contributes little to the force balance at the leading edge, confirming previous conclusions from F-actin flow data alone20. Second, this means that between cell boundary and adhesion sites forces are transmitted instantaneously. Importantly, this prediction is not by construction of the mathematical model. Adhesion and boundary force predictions are numerically independent if network deformations at FAs and at the boundary are resolved separately (see Eq. S4 - S6). Network deformations were calculated between neighboring speckles, i.e. over 0.5-1μm, significantly less than the 2-3μm between cell boundary and adhesion sites (Supplementary Note 7). The instantaneous coupling of adhesion and boundary forces confirmed that over a few seconds lamellipodium and lamella are mechanically well-integrated and predominantly elastic (Supplementary Note 3).

Adhesion and boundary forces gradually increase during a protrusion event while the rate of edge advancement decreases. Edge advancement is stalled at the time point of maximum boundary force (~40 s after fastest edge advancement; Fig. 5d). This suggests that the rate of cell protrusion is limited by increasing tension in the plasma-membrane, a result that has been difficult to obtain by direct measurements of boundary forces16. Consistent with this interpretation, maximal F-actin retrograde flow coincides with the boundary force maximum (Fig. 5c-v, Fig. 5d), suggesting that upon reaching a tension level precluding further expansion of the plasma-membrane, the work by F-actin assembly is converted into retrograde flow. The onset of a new protrusion cycle requires relaxation of tension, for instance by lipid flow within31 or vesicular transport to the plasma-membrane32, 33.

Multiplication of the sum of edge motion and F-actin flow velocities (Fig. 5b-I/II) with the predicted boundary force (Fig. 5b-IV) yields the instantaneous power output of the protrusion machinery (Fig. 5b-VI). Given the time-shifts between edge movement and boundary force, maximal power output is expected to fall between the peaks of protrusion velocity and force. Indeed, the cross-correlation score between edge velocity and power peaks at -20 s (Fig. 5c-vi; Fig. 5d). Power output is energy production per time unit. The energy required to advance the cell edge is presumably harnessed from the binding energy of monomers newly incorporated into the network34. Accordingly, the power output, but not the protrusion velocity, is expected to rise concurrently with the rate of F-actin polymerization. To test this hypothesis, we used FSM to generate activity maps of F-actin assembly and disassembly (Fig. 5b-V). Cross-correlation between these activities and edge velocity confirmed that the peak in F-actin assembly is delayed by 20 s to the peak in protrusion velocity (Fig. 5c-iii). Consistently, the correlation score between power output and F-actin assembly is maximal at 0 s (Fig. 5c-vii).

In summary, contrary to a model where protrusion rates are directly related to actin assembly rates1, relatively low assembly rates at the onset of a protrusion cycle are sufficient to rapidly push forward the plasma-membrane. The rate of polymerization increases as the plasma-membrane expands, possibly mediated by tension-feedback. 20 s after peak protrusion, tension reaches a threshold level beyond which the efficiencies of feedback and/or F-actin assembly begin to decay. 40 s after peak protrusion, the resistance of the plasma-membrane is too high to allow further advancement. The interval from feedback activation at low tension to feedback inhibition under high tension sets the time scale of a cell protrusion cycle. The molecular details of feedbacks between membrane tension and F-actin assembly remain elusive. Possible mechanisms include curvature-dependent transport and/or scaffolding of signaling molecules within the plasma-membrane35, 36. Unraveling these connections will critically depend upon in situ measurements of the timing between forces, feedback signals, and cytoskeleton dynamics. The presented force reconstruction will provide an unprecedented source of high-resolution data to achieve this goal.

Methods

Cell culture and microinjection

Ptk1 cells were cultured in Ham’s F-12 medium (GIBCO), supplemented with 10% FBS, 100 U/ml penicillin, 0.1 mg/ml streptomycin, 1 mM sodium pyruvate, and 2 mM of L-glutamine. The cells were incubated at 37°C/5% CO2. Cells were plated on acid-washed glass coverslips for 20 - 24 hours before experiments. To reduce the effects of photobleaching, 1.0U of oxyrase (Oxyrase Inc.) were added to 1 ml of culture medium. Cells were microinjected with X-Rhodamine-conjugated actin using an Eppendorf Transjector 5246 (Eppendorf Inc.) into the cell cytoplasm at 0.5 mg/ml, as described in37. Plasmid DNA encoding eGFP-vinculin was nucleoinjected as described in4. Full length myosin regulatory light chain (MRLC) cDNA with EcoRI and BamHI restriction sites was cloned into a pHAT2 vector containing a histidine tag followed by an enhanced GFP (eGFP) sequence (obtained from Torsten Wittmann, UCSF). eGFP-MRLC was expressed in BL21(DE3) E. coli and purified on a Talon metal affinity resin (Clontech Laboratories, Inc.) according to the manufacturer’s instructions. eGFP-RLC was co-microinjected with X-Rhodamine-conjugated actin at 1.0 and 0.5 mg/ml, respectively.

Microscopy

Time-lapse image sequences were acquired by spinning disk confocal microscopy utilizing a 100X/1.4 NA Plan Apo phase objective lens from Nikon. Images were acquired at 10 second intervals, with illumination at the 568 nm (X-Rhodamine) and 488 nm (eGFP) provided by a 2.5W KrAr laser (Coherent). Images were captured using a CoolSNAP-HQ2 camera from Photometrics.

Image Analysis

FSM time-lapse sequences were analyzed by custom-written software to obtain velocities of F-actin flow18, assembly/disassembly rate of F-actin network30 and velocities of cell edge movement9.

Force Reconstruction

The prediction of intracellular forces from F-actin network flows relied on a continuum-mechanical model that related forces inside the cell and at the cell boundary to network flows (Supplementary Note 4). Based on these equations, the problem was inverted, i.e. forces were derived from the measured flow fields (Supplementary Note 5). The solution of the inverse problem was determined by identifying the force field among many candidate fields that would produce a flow field most similar to the measured flow field. This approach optimized the spatial filtering of measurement noise, which would otherwise yield nonsensical force spikes. The predicted intracellular forces were further decomposed into adhesion-dominant and contraction-dominant forces, using the cone rule (Fig. 2c) to distinguish the specific local relationships between force direction and network flow associated with adhesion and contraction forces (Supplementary Note 6).

Supplementary Material

Acknowledgment

We gratefully acknowledge funding from NIH R01 GM71868 and the Cell Migration Consortium, Grant No U54 GM064346 from NIGMS.

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