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Load Adaptation of Lamellipodial Actin Networks
Article
Load Adaptation of Lamellipodial Actin Networks Graphical Abstract
Authors Jan Mueller, Gregory Szep, Maria Nemethova, ..., Kinneret Keren, Robert Hauschild, Michael Sixt
Correspondence [email protected]
In Brief How do mechanical perturbations influence the density and the geometry of actin networks at the leading edge of migrating cells?
Highlights d
Lamellipodial actin density co-fluctuates with the size of the projected area
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Lamellipodial actin density adapts to changes in membrane tension
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Actin branch geometry prescribes adaptations in lamellipodial actin
Mueller et al., 2017, Cell 171, 1–13 September 21, 2017 ª 2017 Elsevier Inc. http://dx.doi.org/10.1016/j.cell.2017.07.051
Please cite this article in press as: Mueller et al., Load Adaptation of Lamellipodial Actin Networks, Cell (2017), http://dx.doi.org/10.1016/ j.cell.2017.07.051
Article Load Adaptation of Lamellipodial Actin Networks Jan Mueller,1 Gregory Szep,1 Maria Nemethova,1 Ingrid de Vries,1 Arnon D. Lieber,2 Christoph Winkler,3,4 Karsten Kruse,5 J. Victor Small,6 Christian Schmeiser,3,4 Kinneret Keren,2,7 Robert Hauschild,1 and Michael Sixt1,8,* 1Institute
of Science and Technology Austria (IST Austria), am Campus 1, 3400 Klosterneuburg, Austria of Physics and Russell Berrie Nanotechnology Institute, Technion, Israel Institute of Technology, Haifa 32000, Israel 3RICAM, Austrian Academy of Sciences, Apostelgasse 23, 1030 Vienna, Austria 4Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria 5NCCR Chemical Biology, Departments of Biochemistry and Theoretical Physics, University of Geneva, 30, quai Ernest-Ansermet, 1211 Geneva, Switzerland 6Institute of Molecular Biotechnology GmbH (IMBA), Dr. Bohr-Gasse 3, 1030 Vienna, Austria 7Network Biology Research Laboratories, Technion, Israel Institute of Technology, Haifa 32000, Israel 8Lead Contact *Correspondence: [email protected] http://dx.doi.org/10.1016/j.cell.2017.07.051 2Department
SUMMARY
Actin filaments polymerizing against membranes power endocytosis, vesicular traffic, and cell motility. In vitro reconstitution studies suggest that the structure and the dynamics of actin networks respond to mechanical forces. We demonstrate that lamellipodial actin of migrating cells responds to mechanical load when membrane tension is modulated. In a steady state, migrating cell filaments assume the canonical dendritic geometry, defined by Arp2/3-generated 70 branch points. Increased tension triggers a dense network with a broadened range of angles, whereas decreased tension causes a shift to a sparse configuration dominated by filaments growing perpendicularly to the plasma membrane. We show that these responses emerge from the geometry of branched actin: when load per filament decreases, elongation speed increases and perpendicular filaments gradually outcompete others because they polymerize the shortest distance to the membrane, where they are protected from capping. This network-intrinsic geometrical adaptation mechanism tunes protrusive force in response to mechanical load.
INTRODUCTION From endocytic processes and vesicle trafficking to cellular locomotion and intracellular pathogen movement, the actomyosin cytoskeleton mediates most of the mechanical responses of eukaryotic cells (Pollard and Cooper, 2009). Actomyosin networks have two principal mechanisms of force generation: (1) polymerization can expand the network by elongating filaments against a load, and (2) myosin motors can contract the network or transport cargo along filaments. Every actin filament is born by a nucleation event. Nucleation is catalyzed by a number of molecular machines, the most prominent being formins and
the Arp2/3 complex. While formins achieve de novo linear nucleation, the Arp2/3 complex binds to an existing filament and branches off a new filament at a 70 angle. Elongation, the addition of new monomers to the growing (barbed) end of the filament, is mainly mediated by formins or by proteins of the VASP family. Both nucleation and elongation are enhanced at the interface to membranes, where growing filaments are shielded from capping proteins, which otherwise terminate filament elongation by sealing the filament’s barbed end (Carlsson, 2010; Pollard, 2007). Arp2/3-dependent actin polymerization is a force-sensitive process. This has been demonstrated in vitro, in minimalist reconstituted systems, whereby increasing the mechanical load on a protruding reconstituted network led to higher network density (Bieling et al., 2016; De´moulin et al., 2014; Parekh et al., 2005). Thus, the network structure was able to adapt to the ambient mechanical conditions and to support force generation and mechanical resilience under varying loads. It has been shown that such adaptation is partially mediated by differential force sensitivities of nucleation, elongation, and capping, leading to enhanced branching under higher loads (Bieling et al., 2016). However, these kinetic effects were only partially able to explain the changes in network density, and it was speculated that the remaining adaptation might be mediated by spatial rearrangements of the network. The mechanochemical response of protruding actin networks has not yet been studied in living cells. However, indirect evidence suggests that the leading edge of a motile cell is able to respond to load. When the lamellipodium, the flat protrusive front of a migrating cell, encounters an elastic obstacle (e.g., the vertical cantilever of an atomic force microscope), it was shown to substantially increase its pushing force, until collapsing when the load became excessive. For a migrating cell encountering a barrier, this means that its front pushes harder until the obstacle is pushed away or the leading edge stalls and the cell either retracts or circumnavigates the barrier (Heinemann et al., 2011; Prass et al., 2006). In fibroblasts or epithelial cells, where lamellipodia typically undergo cycles of protrusion and retraction, it has been suggested that during each protrusive phase the polymerizing actin filaments experience a gradually growing load, because increase Cell 171, 1–13, September 21, 2017 ª 2017 Elsevier Inc. 1
Please cite this article in press as: Mueller et al., Load Adaptation of Lamellipodial Actin Networks, Cell (2017), http://dx.doi.org/10.1016/ j.cell.2017.07.051
in projected cell area is accompanied by increase in membrane tension (the cell stretches out the rather inextensible bag of plasma membrane) (Diz-Mun˜oz et al., 2013; Gauthier et al., 2011; Raucher and Sheetz, 2000; Sens and Plastino, 2015). This growing load on the pushing filaments is accompanied by accelerated incorporation of the actin nucleating Arp2/3 complex, which might, in turn, increase actin network density and boost force generation until the filaments stall and the leading edge retracts (Ji et al., 2008; Lee et al., 2015; Ryan et al., 2012). While these response patterns might result from complex mechanosensitive signaling processes, theoretical considerations put forward the alternative idea that branched actin networks respond to varying polymerization kinetics by changing their geometry (Maly and Borisy, 2001; Schaus et al., 2007; Weichsel and Schwarz, 2010). Such responses would argue that load adaptation is an emergent geometrical property of branched actin. Here, we use the lamellipodium of fish keratocytes to quantitatively examine how protruding actin networks respond to varying forces. We use a combination of quantitative light and electron microscopy to describe geometrical changes of lamellipodial actin upon varying load regimes and employ stochastic modeling to elucidate how the network structure geometrically adapts to counter-forces. RESULTS Temporal Fluctuations in Actin Density Arise at the Leading Edge and Are Correlated with Projected Cell Area and Protrusion Speed To quantitatively explore how lamellipodial actin reacts to changes in load we employed fish keratocytes migrating on planar surfaces (Mogilner and Keren, 2009). We established protocols to derive keratocytes from adult zebrafish, allowing access to stable transgenesis. On serum-coated coverslips, these cells migrate with exceptional speed, persistence, and morphological stability (Keren et al., 2008). We first chose a correlative approach and observed single migrating keratocytes expressing the actin reporter lifeact:GFP (Riedl et al., 2008) with high spatiotemporal resolution (Figure 1A; Movie S1). This allowed us to monitor fluctuations in actin network dynamics and density together with protrusion speed and morphological parameters (Figures 1A–1D, S1A, and S1B). The projected area of a keratocyte typically fluctuated ±5% around a baseline, which was consistent with earlier studies (Keren et al., 2008) (Figure S1A). These limited fluctuations supported the notion that the keratocyte’s plasma membrane does not harbor major membrane reservoirs, which might be mobilized upon mechanical stretch (Lieber et al., 2013). When we measured lifeact:GFP intensity within a 1-mm broad zone behind the leading front, intensity fluctuations were more substantial than area changes and varied ±20% (Figures 1D and S1A). Strikingly, the normalized, temporal fluctuations in projected cell area were tightly correlated with lifeact:GFP intensities as shown by cross-correlation peaks between 0.6–0.7 at time lag zero (Figures 1D, 1E, and S1B). This correlation was also observed in actin:GFP-expressing keratocytes, but not when the plasma membrane was uniformly labeled (Figure S2).
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Correlation analysis of consecutive 1-mm broad lamellipodial regions showed that the time delay between correlation peaks increased with the distance between the measured regions (Figures S1C–S1E). Dividing the respective lag times by the speed of each cell yields distances matching those between adjacent lamellipodial regions (Figure S1F). This analysis showed that, first, as previously demonstrated (Theriot and Mitchison, 1991; Wilson et al., 2010) keratocytes exhibited minimal retrograde flow of actin in relation to the substrate. Second, temporal fluctuations of actin density arise at the leading edge and propagate rearward. We next quantified protrusion speed by optical flow analysis at each pixel along the cell front. Protrusion speed was negatively correlated with both projected cell area and lifeact:GFP intensity with a negative cross-correlation peak between 0.3 and 0.4 at time lag zero (Figures 1B–1E). Lifeact:GFP intensities were equally co-fluctuating with area changes when corrected for the fluctuations in protrusion speed (Figure S1A). Taken together, our quantitative analysis demonstrates that keratocytes migrate slower and produce denser actin networks during intervals when their projected area is larger. Experimental Manipulations of Membrane Tension Reveal a Lamellipodial Response to Altered Load Among several interpretations of these correlative data we considered that a fluctuation in projected cell area might correspond to changes in membrane tension (Raucher and Sheetz, 2000). To dissect the causal relationship between actin network density and membrane tension, we experimentally increased membrane tension by aspirating the trailing edge of migrating keratocytes with a micropipette (Houk et al., 2012) (Figure 2A; Movie S2). As membrane tension equilibrates almost instantaneously over the whole cell, this manipulation allowed us to tune lateral tension at the lamellipodial tip (Diz-Mun˜oz et al., 2013). Experiments were performed by transiently applying four different vacuum levels ranging from 10 to 40 mbar. In all cases, we found that aspiration caused an increase in lifeact:GFP signal concomitant with a moderate decrease in protrusion speed (Figures 2A–2C). Actin density and protrusion speed were dependent on the applied vacuum (Figures 2D and 2E). Following transient aspiration, the band of denser actin network traveled backward (in the cell frame of reference) with the actin flow (Figures 2A and 2C). Under the given parameters the cells kept protruding during aspiration, demonstrating that the increase in tension was below the stall force of the lamellipodium. These results suggested that lamellipodial actin responds to an increase in membrane tension by increasing network density. To experimentally decrease membrane tension we took advantage of the fact that on adhesive substrates cells occasionally form tethered trailing edges, which leads to a stretched morphology (Figure 2F). When these tethers spontaneously detach or when we cut them with a pulsed laser, tension is released and the tether snaps forward. Here, the projected cell area shrunk within a few seconds when the cell went from a stretched to a more compact configuration. Such high recoil velocities indicate the rapid drop in tension, which had previously built up in the stretched cell. To directly test if shrinkage is accompanied by changes in membrane tension, membrane
Please cite this article in press as: Mueller et al., Load Adaptation of Lamellipodial Actin Networks, Cell (2017), http://dx.doi.org/10.1016/ j.cell.2017.07.051
Figure 1. Correlative Analysis of Actin, Projected Cell Area, and Protrusions in Migrating Zebrafish Keratocytes (A) Confocal imaging of lifeact:GFP-expressing keratocyte moving on a glass coverslip. (B) Time frame from (A) showing the 1.09-mm wide area of lifeact:GFP intensity measurements (left), a binary mask used for quantifying the area (middle), and a pseudo-colored Horn-Schunck optical flow analysis image of the leading edge (right). (C) Fluorescence intensity and leading edge velocity maps for the time lapse of the cell shown in (A). (D) Temporal fluctuations of cell area, lifeact:GFP intensity, and protrusion speed averaged across the analyzed region shown in red in (B). (E) Average of temporal cross-correlation functions of 21 migrating keratocytes. Mean and SEM are shown. See also Figures S1 and S2 and Movie S1.
tethers were pulled from the plasma membrane of migrating keratocytes using an optical trap (Lieber et al., 2013) (Figure S3A). While in steady-state migrating cells there was no consistent relation between projected area and tether force, abrupt retraction events were accompanied by area shrinkage concurrent with a drop in tether force and thus membrane tension (Figure S3B). During abrupt retraction, the previously observed correlation between projected cell area and actin intensity at the leading edge manifested in a sudden drop in lamellipodial life-
act:GFP intensity at the moment of area shrinkage (Figures 2F and 2G). The resultant abrupt change in actin density was maintained while it steadily traveled backward (in the cell frame of reference) with the actin flow, further substantiating that altered polymerization originated at the leading edge of the cell (Figures 2F and 2H; Movie S2). Cell shrinkage was also accompanied by a rapid but very transient increase in protrusion speed (Figure 2G). These results suggested that lamellipodial actin responds to a decrease in membrane tension by decreasing network density.
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Figure 2. Cytoskeletal Response to Manipulations of Membrane Tension (A) Lifeact:GFP imaging following micropipette aspiration. (1) Migrating keratocyte before contact with the micromanipulator, (2) aspiration of membrane, and (3) release of vacuum. (B) Temporal fluctuations of lifeact:GFP intensity at the leading edge defined as in Figure 1B, area, and protrusion speed. The area between the dotted lines shows where the cell was aspirated. (C) Kymograph along dashed yellow line in (A). (D) Change in lifeact:GFP signal following aspiration with four different vacuum levels. (E) Change in cell edge protrusion for the same cells as in (D). Mean and SEM are shown for 28 aspiration events in 13 individual cells in (D) and (E).
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As our mechanical manipulations of membrane tension might have caused additional changes in the cells, we chose an independent approach to challenge our hypothesis. Migrating cells were exposed to cycles of altered osmolarity (Diz-Mun˜oz et al., 2013), by supplementing the medium with sucrose versus pure water. Monitoring lifeact:GFP at the leading edge showed that increased osmolarity (water efflux–cell shrinkage) was accompanied by a decrease in lifeact:GFP signal and this was reversed when water was added (water influx–cell swelling) (Figures S3C and S3D). Together, our data show that lamellipodial actin responds to changes in membrane tension by altering its density: density increases following an increase in tension and decreases following a decrease in tension. Quantitative Analysis of Lamellipodial Ultrastructure during Steady-State Migration To gain quantitative insight into lamellipodial architecture at the single filament level we employed three-dimensional (3D) electron microscopy of fixed and negatively stained keratocytes (Vinzenz et al., 2012). This approach allows tracing single filaments in 3D space (Winkler et al., 2012). In keratocyte lamellipodia, filaments are consistently oriented with their barbed ends toward the front (Narita et al., 2012; Sivaramakrishnan and Spudich, 2009; Svitkina et al., 1997), which is in line with the polar forward growth of actin at the leading cell front (Figures S1C– S1F) (Keren, 2011; Lai et al., 2008; Theriot and Mitchison, 1991). In the digitalized tomograms we defined a barbed end as the end of a filament proximal to the leading edge and a pointed end as the one distal to the leading edge. Any barbed end could either represent an actively growing or a capped filament. A pointed end represents (1) a nucleation event generated by Arp2/3 (a branch), (2) a nucleation event generated by an alternative nucleation factor, or (3) a debranched or severed filament (Ydenberg et al., 2013, 2011). Throughout the lamellipodium of steady-state migrating keratocytes we found that the numbers of barbed and pointed ends were balanced (Figures 3A–3D and S4A). Only at the leading front, barbed ends occurred in excess, which is expected due to ongoing polymerization at this site. Next, we analyzed the angles, which the filaments assumed relative to the leading membrane and found that the distribution of their orientations peaked at ±35 (with 0 defined as perpendicular to the leading membrane) (Figure S4B). This configuration predominated in keratocytes as shown by a global order parameter defined as ((Filaments 0 –20 )(Filaments 30 –50 ))/((Filaments 0 –20 )+(Filaments 30 –50 )) as a readout for network orientation (Weichsel and Schwarz, 2010) (Figures 3E and 3F). Together, our tomography data provide a quantitative description of lamellipodial actin as derived from filament configuration. We conclude that in a steady-state migrating keratocyte, nucleation, capping and elongation create an expanding network with
a canonical branch geometry prescribed by the 70 branch structure of the Arp2/3 complex (Svitkina et al., 1997). Network Configuration following Load Increase We next used trailing edge aspiration to interrogate the ultrastructural changes in lamellipodial networks polymerizing against increased load. To this end we employed correlated fluorescence live-cell imaging and electron tomography on lifeact:GFP-expressing keratocytes migrating on electron microscopy grids. After 4 s of 30mbar aspiration, cells were released, fixed and prepared for electron microscopy (Figure 4A; Movie S3). Under the given conditions where density fluctuations arise from the leading edge, the temporal growth-history of lamellipodial actin is spatially encoded in the network: the pre-aspiration zone (proximal to the nucleus) represents steady-state growth, the aspiration zone the increase in load, and the post-aspiration zone at the leading edge the phase at which the load drops again due to the release of the vacuum. In the low-magnification electron micrograph, the transient increase in density during aspiration was clearly visible as a darker zone running parallel to the leading edge (Figure 4A). This was consistent with the lifeact:GFP live cell imaging (Figures 2A– 2C). Electron tomography with automated tracking of actin filaments allowed us to trace the temporal evolution of the load response at the single filament level. The pre-aspiration zone resembled a steady-state lamellipodium with a canonical 70 branched network. Within an 800nm broad aspiration zone (corresponding to a 4-s aspiration time) filament density was markedly increased. At the beginning of the aspiration zone (distal from the leading front, hence earlier in time) a transient drop in the number of barbed ends and a gradual increase in pointed ends created a mismatch between filament birth and death, along with the increase in filament density (Figures 4C and 4D). This increase in filament density was also accompanied by an increase in the 0 –20 and 50 –70 fraction of filament angles, whereas filaments at intermediate angles of 20 –50 increased only moderately (Figures 4E and S4C). At the leading front, filament density decreased to reach values comparable to levels before aspiration (Figure 4D) and filament angles reverted to the canonical branch-pattern (Figures 4E, S4C, and S4D). These data show that an increase in membrane tension causes an increase in network density and a change in geometry, with filaments growing at steeper angles toward the plasma membrane at higher membrane tensions. Network Configuration following Load Decrease We followed the same correlative visualization strategy to analyze the network following a decrease in load. Similar to the laser cutting used in Figures 2F–2H rapid cell shrinkage could also be triggered by mechanically detaching one side of a cell with a micropipette (Figure 5A; Movie S4). This maneuver allowed sufficient experimental control to fix the cell seconds after
(F) Lifeact:GFP signal following fast cell shrinkage. (1) Keratocyte exhibiting stretched morphology, while its trailing edge is tethered to the substrate. (2) The trailing edge is cut with a pulsed laser (yellow arrowhead). (G) Temporal fluctuations of leading edge lifeact:GFP intensity, area, and protrusion speed. The rapid retraction is marked with a dotted line. (H) Kymograph along dashed yellow line in (F). See also Figure S3 and Movie S2.
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Figure 4. Correlated Live Microscopy-Electron Tomography of Ultrastructural Changes in Networks with Increasing Filament Density (A) A migrating keratocyte expressing lifeact:GFP was aspirated at the rear with a micropipette, fixed within z3 s, and prepared for electron microscopy. The cell shifted out of focus because of the manipulating procedure. A transient increase in actin density can be seen in the low-magnification electron micrograph on the right. (B) 5.5-nm tomogram slice of the region marked by a red box in (A). The rear of the cell is toward the left side of the picture, and the cell front is seen on the right. Regions of steady-state density, increased density, and decreased density are marked with black, blue, and red throughout the whole figure. (C) Filament tracks of the lamellipodium shown in (B), with actin filaments shown in green, barbed ends in red, and pointed ends in blue. (D) Filament numbers and densities of barbed and pointed ends in 106-nm-wide spatial bins throughout the lamellipodium shown in (B) and (C). (E) Histogram showing filament angles to the cell edge in 212-nm distance bins. See also Figures S4C and S4D and Movie S3.
shrinkage. Analogous to the increase in actin density following aspiration, the decrease in actin density in the time window of rapid shrinkage was clearly visible as a transition zone in lifeact:GFP signal as well as phalloidin staining (Figure 5A). Both signals showed a sharp decrease indicating the drop in filament density. This was substantiated by low-magnification views of
the same cell after extraction and negative stain, which showed a sharp decrease in electron density, overlapping with the fluorescent imaging (Figures 5A and S6C). Quantification of manually as well as automatically traced filaments together with automated image segmentation showed a drop in filament numbers in the transition zone (Figures 5C, 5D, S5, and S6). As expected,
Figure 3. Electron Tomography of Migrating Wild-Type Keratocytes (A) Overview electron micrograph of migrating keratocyte with acquired tomogram montage marked in red. (B) 5.5-nm slice of a negatively stained tomogram of the actin network behind the leading edge. (C) Automated tracking results of the same region with filaments shown in green, barbed ends in red, and pointed ends in blue. (D) Normalized densities of filaments, barbed ends, and pointed ends in 106-nm-wide bins of four averaged tomogram montages. Graph shows mean and SEM. (E) Scheme showing the filament angle bins used for calculating the global order parameter. (F) Histogram of combined filament length growing at indicated angle toward the cell membrane (black) is shown together with a global order parameter (blue) in 212-nm distance bins defined as ((Filaments 0 –20 )(Filaments 30 –50 ))/((Filaments 0 –20 )+(Filaments 30 –50 )). See also Figures S4A and S4B.
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Figure 5. Correlated Live Microscopy-Electron Tomography of Ultrastructural Changes in Networks with Decreasing Filament Density (A) Migrating keratocyte manipulated with a microneedle to induce a rapid decrease in projected cell area with an accompanying decrease in lifeact:GFP signal, fixed within z3 s, and prepared for electron microscopy. A rapid decrease in the lifeact:GFP signal is preserved in the fixed lifeact:GFP sample and the lowmagnification electron micrograph. (B) 5.5-nm tomogram slice showing the region marked with a red box in (A). The cell edge is seen on the right side, and the region of lower density is distinguishable toward the middle of the micrograph. Region of steady-state network density and decreased density are marked in black and red throughout the whole figure. (C) Filament tracks of the lamellipodium shown in (B), with actin filaments shown in green, barbed ends in red, and pointed ends in blue. (D) Filament numbers and densities of barbed and pointed ends in 106-nm-wide spatial bins throughout the lamellipodium shown in (B) and (C). (E) Histogram showing filament densities growing at the indicated angle from the membrane in 212-nm distance bins. An order parameter (blue) in 212 nm is defined like in Figure 3. See also Figures S5 and S6 and Movie S4.
the pre-transition zone (prior to mechanical manipulation) showed the quantitative signature of the steady-state lamellipodium. The onset of the transition zone was marked by a transient increase of barbed ends, which preceded a drop in pointed ends (Figure 5D). Here, the resultant gap between putative capping and nucleation events explained the concomitant drop in filament density. The transition zone was followed by a leveling of barbed and pointed ends and a continuous recovery of the network toward the cell front. Notably, the transition zone was characterized by radically changed network geometry. When we quantified and parameterized filament angles depending on their position in the network we found that at the onset of cell shrinkage the canon-
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ical ±35 dominated network abruptly changed into a configuration dominated by filaments growing perpendicularly (0 ) to the membrane. Toward the cell front the network again recovered gradually to canonical (Figures 5E and S6D). The change in network geometry was due to selective elimination of filaments: in the transition zone the rate of filament survival strictly depended on filament orientation: filaments at a higher angle were preferentially eliminated, whereas low angle filaments had a higher rate of survival (Figures S5E and S6D). These data show that a decrease in membrane tension causes a decrease in network density and a change in geometry, with more filaments growing perpendicularly to the plasma membrane.
Please cite this article in press as: Mueller et al., Load Adaptation of Lamellipodial Actin Networks, Cell (2017), http://dx.doi.org/10.1016/ j.cell.2017.07.051
A Stochastic 2D Model of Actin-Based Protrusion Recapitulates Light and Electron Microscopy Data To gain a quantitative understanding of the experimental data we built on earlier work by Maly and Borisy (2001) and Weichsel and Schwarz (2010) and developed a stochastic model of lamellipodial network growth. We formulated a two-dimensional (2D) model taking into account filament elongation and Arp2/3-mediated (70 ) nucleation at the leading front. Elongation is terminated by capping whenever filaments detach from the membrane and thereby leave the zone in which they are protected from capping (by elongation factors like VASP or formins). Filaments push the membrane forward according to a force-velocity relation based on thermal fluctuations as described in Dickinson (2009) and Mogilner and Oster (1996, 2003) (for details see STAR Methods and Tables S1 and S2). Here, network geometry dictates that increased protrusion velocity (as caused by decreased load) rapidly decreases filament density in an angle-dependent manner: A filament growing at an angle 4 has to polymerize with ð1=cos4Þ the speed of the advancing membrane in order to keep contact with the membrane. Hence, with increasing protrusion speed filaments growing at higher angles will lag behind the leading edge and therefore detach from the membrane where they are protected from capping (Figures 6A, 6B, S7D, and S7E). Consequently, higher angle filaments will be capped at higher rates and the family of low angle filaments (and their accompanying ±70 side branches) will outcompete the ±35 network. Slowing down the membrane has the opposite effect: More filaments at higher angles are able to catch up with the membrane, leading to a denser network consisting of filaments growing at a broad range of angles. The stochastic simulation is able to reproduce the correlative electron tomography findings of filament orientation and density by using a sharp decrease from 300 pN as force input. 300 pN were taken as a realistic force reported for steady-state migrating fish keratocytes (Lieber et al., 2013). Together, our stochastic simulation faithfully reproduced both kinetics and geometry of network parameters upon externally induced changes in load (Figures 6C, 6D, S7A, and S7B; Tables S1 and S2; Movie S5). Next we wanted to test if the stochastic simulation can produce the co-fluctuations of protrusion speed, actin density and projected area as we observed them in our light microscopy experiments in unperturbed migrating keratocytes (Figure 1). The amount of decrease in tension necessary to obtain the correct response at the filament level in the correlated experiments was used as a scaling factor to relate membrane tension to projected area. The experimental decrease and increase of membrane tension (Figure 2) could be recapitulated by simulating representative protrusion events of 10 s with increasing or decreasing tension (Figure S7C). By using the measured temporal fluctuations in projected cell area (Figure 1D) with the obtained scaling factor as a proxy for tension we could recapitulate the positive correlation of membrane tension and actin density as well as the negative correlations of membrane tension, actin density, and protrusion speed (Figures 7A and 7B). This showed that our filament-level model is able to recapitulate lamellipodial dynamics as we observed them at the cellular scale and using fluorescent markers. Our model predicts that keratocytes migrating on an adhesive substrate in 2D exhibit a
canonically 70 branched network in their lamellipodia the vast majority of the time. This is consistent with the measurements on steady state migrating keratocytes. However, with a low frequency, periods of perpendicular dominated networks (with an order parameter above 0) during phases of high protrusion speed are predicted (Figure 7C). DISCUSSION We demonstrate that the lamellipodial actin network undergoes profound structural changes when filaments pushing against the membrane experience varying load. These changes happen at short time-scales and can be a sheer consequence of the geometrical and kinetic properties of Arp2/3-nucleated branched networks. The key-ingredients of the mechanism we propose are the force-velocity relation determining filament elongation rates, the geometry of protruding networks, and the protection from capping near the membrane. Filaments polymerize faster when growing against decreased loads (here, the load is due to membrane tension). With decreasing load the expanding network reaches a speed, where filaments growing perpendicularly to the membrane gradually ‘‘outrun’’ filaments pushing at steeper angles because these have to travel a longer distance. Hence, these steeper-angle filaments are eliminated, because they lose contact with the membrane, where the polymerizing factors (VASP and formins) protect them from capping proteins. If the perpendicular filaments originate from ‘‘noise’’ in the angular distributions of a purely Arp2/3-nucleated network or if they represent a family nucleated by other factors like formins remains open, as ‘‘non-branch’’ pointed ends in the tomograms might not only represent Arp2/3-independent filaments but could also be Arp2/3 nucleated, but later severed or unbranched. Whereas this proposed mechanism will operate in any Arp2/ 3-nucleated process like endocytosis, phagocytosis, vesicle trafficking, intracellular pathogen transport, dendritic spine formation, etc., its role in cell motility is most intuitive. Unlike in the idealized keratocyte system, cells migrating in physiological environments will almost never experience mechanically isotropic environments. First, a cell usually pushes against an interstitium with inhomogeneous viscoelastic features, and here it has been shown that lamellipodia can increase their force when counter-resistance increases locally (Heinemann et al., 2011; Prass et al., 2006). Second, the adhesiveness of the substrate is often variable (e.g., in any 3D fibrillar environment). As the actin network slides back in areas of the cell, which are less coupled to the substrate, the load experienced by filaments polymerizing against the leading membrane will be reduced. It has been shown that such local inhomogeneities can be compensated by adaptations in polymerization speed, which ‘‘fill up the space’’ resulting from retrograde slippage of the network (Barnhart et al., 2011; Graziano and Weiner, 2014; Renkawitz et al., 2009). Thus, for a cell migrating through a complex 3D environment, the local adaptations we describe serve to keep the cell edge and its actin network coherent. This geometrical adaptation might provide another remarkable feature: wherever two adjacent regions of the network show differential flow speed, the faster network will be less crosslinked to the neighboring, slower, regions, because it is less interconnected by branches. This might
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Figure 6. Stochastic Model Recapitulating Light and Electron Microscopy Results (A) The critical angle at which filaments are not able to keep up with the advancing membrane, 4c , depends on the maximal polymerization rate, set here as 450 nm/s, and the angle of the filament toward the membrane, 4 (black line). A drop in external force leads to a transient increase in protrusion speed leading to a decrease in 4c and a subsequent, angle-dependent decrease in filaments (red line). Force increase causes a decrease in protrusion speed, leading to an increase in 4c and filament density (blue line). (B) Scheme of filaments growing at steady state at intermediate load (middle, gray arrow). Following an increase in load (top, blue arrow) filament density increases and the angle distribution broadens, whereas at a decrease in load (bottom, red arrow) filaments at a higher angle 4i are preferentially capped and density decreases. (C) Visualization of model results with filaments shown in green, barbed ends in red, and pointed ends in blue. Visualization of model results in a regime with force increase (top) and decrease (bottom), D F, at around 900 nm. Subsequent panels are aligned next to the respective force regimes. (D) Filament numbers, barbed, and pointed end density quantified for the three conditions like in Figures 3, 4, and 5. In the unperturbed situation with fixed external force, F, the network assumes a steady state with balanced filament density, branching, and capping. After a decrease in F, capping increases, nucleation decreases, and the network is thinned out, whereas force increase causes a nucleation peak and an increase in filament density. For all graphs, mean and SD for an average of 20 runs are shown. See also Figure S7, Tables S1 and S2, Movie S5, and the STAR Methods.
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Figure 7. The Stochastic Model Recapitulates Cell Migration Parameters of Fish Keratocytes (A) Example of temporal fluctuations in lifeact:GFP intensity, area, and protrusion speed for the cell shown in Figure 1 compared to the migration parameters produced by a simulation run with the projected cell area as scaled tension input. (B) Average of temporal cross-correlation functions of the simulations obtained with the projected cell area of the 21 migrating keratocytes shown in Figure 1. Temporal correlation peaks at time lag zero between lifeact:GFP intensity, projected cell area, and protrusion match the ones observed in vivo. Mean and SEM are shown. (C) Histogram of the order parameters obtained for the 21 steady-state migrating keratocytes. The stochastic model predicts cells migrating with a predominantly negative order parameter, with only occasional switches to positive order parameter values as cells undergo rapid shrinkage and a transient burst in protrusion speed. See also Figure S7.
potentially allow the two networks to slide relative to each other and might explain how lamellipodia or actin cortices can harbor differentially flowing populations of actin as shown previously (Ponti et al., 2004; Vitriol et al., 2015). In our work we used manipulations of membrane tension as a proxy for altered load. For the protruding lamellipodium membrane tension likely plays the same mechanical role as an external load. However, lateral membrane tension cannot act locally as it equilibrates instantaneously across the cell surface (Diz-Mun˜oz et al., 2013; Sens and Plastino, 2015). Based on this potential signaling function it has been proposed that membrane tension acts as a global long-range regulator of cell polarity. Whenever lamellipodial actin stretches the leading membrane it suppresses polymerization at the sides and the trailing edge. Here, polymerization will stall under high membrane tension as it is not boosted by the biochemical enhancers
driving the lamellipodium (Houk et al., 2012). This mechanism to suppress competing protrusions has a pure mechanical component (filaments stall under high load) but is also complemented by a signaling mechanism, where membrane tension triggers mTORC2 signaling, which in turn dampens polymerization (DizMun˜oz et al., 2010). Although this mechanism seems to counteract the geometrical adaptations we describe, it likely acts at much higher force regimes, where filaments ultimately fail to protrude the membrane. We think that the geometrical rules we describe here represent the most basic regulatory framework of Arp2/3-mediated actin polymerization. They are a fundamental feature of the network structure, which demonstrates that mechanosensitivity is inherently built into the architecture of branched networks. Additional layers of regulation by chemoattractant-sensing and mechanosensitive signaling pathways will act on top of this basic
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mechanism and might add modulations e.g., by altering the filament distribution via different nucleators and elongators. STAR+METHODS Detailed methods are provided in the online version of this paper and include the following: d d d d
d
KEY RESOURCES TABLE CONTACT FOR REAGENT AND RESOURCE SHARING EXPERIMENTAL MODEL AND SUBJECT DETAILS B Zebrafish METHOD DETAILS B Keratocyte preparation B mRNA injection B Transfection B Membrane dye B Live cell imaging B Micromanipulators B Osmotic treatment B Tether pulling experiments and force measurements B Image analysis B Electron tomography B Actin filament tracking and analysis B Correlated light and electron microscopy B Stochastic Simulation QUANTIFICATION AND STATISTICAL ANALYSIS
SUPPLEMENTAL INFORMATION Supplemental Information includes seven figures, two tables, and five movies and can be found with this article online at http://dx.doi.org/10.1016/j.cell. 2017.07.051. AUTHOR CONTRIBUTIONS Conceptualization: J.M. and M.S.; Methodology: J.M., G.S., A.D.L., K. Keren, and R.H.; Software: C.W., K. Kruse, and C.S.; Formal Analysis: J.M., G.S., and R.H.; Investigation: J.M., M.N., I.d.V., and A.D.L.; Writing – Original Draft: J.M. and M.S.; Writing – Review & Editing: all authors; Visualization: J.M. and G.S.; Project Administration: M.S.; Funding Acquisition: M.S. ACKNOWLEDGMENTS We thank the scientific support facilities of IST Austria and Biocenter Vienna for technical support and CP Heisenberg for fish lines. This work was supported by the European Research Council (ERC StG 281556), a grant from the Austrian Science Foundation (FWF) (to M.S.), and a grant from Vienna Science and Technology Fund (WWTF) (No. LS13-029 to C.S. and M.S.). Research in the lab of K. Keren was supported by a grant from the United States-Israel Binational Science Foundation (No. 2013275 with Alex Mogilner). Received: January 11, 2017 Revised: May 21, 2017 Accepted: July 31, 2017 Published: August 31, 2017 REFERENCES Barnhart, E.L., Lee, K.C., Keren, K., Mogilner, A., and Theriot, J.A. (2011). An adhesion-dependent switch between mechanisms that determine motile cell shape. PLoS Biol. 9, e1001059.
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Sens, P., and Plastino, J. (2015). Membrane tension and cytoskeleton organization in cell motility. J. Phys. Condens. Matter 27, 273103. Sivaramakrishnan, S., and Spudich, J.A. (2009). Coupled myosin VI motors facilitate unidirectional movement on an F-actin network. J. Cell Biol. 187, 53–60. Small, J.V., Herzog, M., and Anderson, K. (1995). Actin filament organization in the fish keratocyte lamellipodium. J. Cell Biol. 129, 1275–1286. Svitkina, T.M., Verkhovsky, A.B., McQuade, K.M., and Borisy, G.G. (1997). Analysis of the actin-myosin II system in fish epidermal keratocytes: mechanism of cell body translocation. J. Cell Biol. 139, 397–415. Theriot, J.A., and Mitchison, T.J. (1991). Actin microfilament dynamics in locomoting cells. Nature 352, 126–131. Vinzenz, M., Nemethova, M., Schur, F., Mueller, J., Narita, A., Urban, E., Winkler, C., Schmeiser, C., Koestler, S.A., Rottner, K., et al. (2012). Actin branching in the initiation and maintenance of lamellipodia. J. Cell Sci. 125, 2775–2785. Vitriol, E.A., McMillen, L.M., Kapustina, M., Gomez, S.M., Vavylonis, D., and Zheng, J.Q. (2015). Two functionally distinct sources of actin monomers supply the leading edge of lamellipodia. Cell Rep. 11, 433–445. Weichsel, J., and Schwarz, U.S. (2010). Two competing orientation patterns explain experimentally observed anomalies in growing actin networks. Proc. Natl. Acad. Sci. USA 107, 6304–6309. Wilson, C.A., Tsuchida, M.A., Allen, G.M., Barnhart, E.L., Applegate, K.T., Yam, P.T., Ji, L., Keren, K., Danuser, G., and Theriot, J.A. (2010). Myosin II contributes to cell-scale actin network treadmilling through network disassembly. Nature 465, 373–377.
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STAR+METHODS KEY RESOURCES TABLE
REAGENT or RESOURCE
SOURCE
IDENTIFIER
Chemicals, Peptides, and Recombinant Proteins Dulbecco’s Modified Eagle’s Medium
GIBCO
Cat# 10566-016
L-15 Leibovitz medium
Sigma
Cat# L1518
PCR purification kit
Qiagen
Cat# 28106
SP6 mMessage mMachine kit
Invitrogen
Cat# AM1340
Fugene 6
Roche
Cat# 11814443001
Cell Mask Orange
Molecular Probes
Cat# C10045
PLL(20)-g[3.5]-PEG(2)/PEG(3.4)-RGD
Surface Solutions
N/A
PLL-PEG-RGD
Surface Solutions
N/A
Zebrafish line: Tg(actb1:lifeact-GFP)
Gift from Heisenberg Laboratory (IST Austria) Behrndt et al., 2012
N/A
Zebrafish line: wt AB
Gift from Heisenberg Laboratory (IST Austria)
N/A
Zebrafish line: wt TL
Gift from Heisenberg Laboratory (IST Austria)
N/A
pEGFP-actin
Clontech
Cat# 6084-1
zf actin:GFP
This paper
N/A
MATLAB 2015b
The MathWorks
https://ch.mathworks.com/products/matlab
Fiji 1.50d
Schindelin et al., 2012
https://fiji.sc/
Ilastik 1.1.5
The ilastik Team
http://ilastik.org/index.html
SerialEM 3.x
Mastronarde, 2005
http://bio3d.colorado.edu/ftp/SerialEM/
IMOD 4.7
Kremer et al., 1996
http://bio3d.colorado.edu/imod/
Python 2.7
Python Software Foundation
https://www.python.org/download/releases/2.7/
Prism 5.0b
GraphPad
https://www.graphpad.com/scientific-software/ prism/
LabView
National Institutes
http://www.ni.com/en-us/shop.html
NIS - Elements AR 3.2
Nikon Instruments
https://www.nikoninstruments.com/en_EU/ Products/Software/NIS-Elements-AdvancedResearch
Stochastical Simulation – Code repository
Authors of this study
https://github.com/gszep/lamellipodium
200mesh HF15 Gold finder grids
Maxtaform
Cat# G245A
200mesh hexagonal gold grids
Agar Scientific
Cat# AGG2450A
Experimental Models: Organisms/Strains
Recombinant DNA
Software and Algorithms
Other
CONTACT FOR REAGENT AND RESOURCE SHARING Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Michael Sixt ([email protected]). EXPERIMENTAL MODEL AND SUBJECT DETAILS Zebrafish Wild-type zebrafish lines AB and TL and the transgenic line Tg(actb1:lifeact-GFP) (Behrndt et al., 2012) were housed and bred in the IST Austria fish facility. Zebrafish were maintained at 28 C and embryos collected according to standard fish laboratory protocol. Animals were sacrificed for experiments at 6 months to about 1.5 years of age regardless of sex.
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Primary keratocyte cultures for these experiments were prepared from the Central American cichlid Hypsophrys Nicaraguensis as described previously (Lieber et al., 2013). METHOD DETAILS Keratocyte preparation Keratocytes were prepared from adult zebrafish scales (plucked from sacrificed animals) and washed three times with Dulbecco’s Modified Eagle’s Medium (DMEM) (GIBCO). Scales were incubated in START medium (Small et al., 1995) at room temperature for one or two days to allow keratocytes to migrate off in a monolayer. The monolayer was then washed three times in PBS, incubated for 40min with Running Buffer (Small et al., 1995) with 1mM EGTA and the scales removed. The remaining adherent cells were washed three times with PBS, trypsinized for 2min with 0.25% Trypsin-EDTA (GIBCO) at room temperature, resuspended in the same volume of trypsin inhibitor (Sigma) and transferred to a coverslip or electron microscopy grid. After allowing the cells to adhere for 40min the medium was changed to START medium, the cells were incubated for another 40min before live cell imaging or fixation for electron microscopy. mRNA injection To produce synthetic mRNA, zf actin:GFP was linearized by double strand cutting with NotI, purified with a PCR purification kit (Qiagen) and mRNA was synthesized using the SP6 mMessage mMachine Kit (Ambion). 50pg of mRNA were injected in freshly harvested embryos. Zebrafish embryonic keratocytes were prepared from these embryos 1 day post fertilization as described elsewhere (Lou et al., 2015). Transfection The plasmid used for transfection was pEGFP-actin (Clontech). Transfection was performed by mixing 100ml OPTIMEM, 6ml Fugene 6 (Roche) and 1mg plasmid DNA for 30min and adding it to the cells in L-15 Leibovitz medium (Sigma) for 5h. Then the medium was changed to START medium again and the transfected cells were re-plated onto coverslips as described above. Membrane dye As a membrane dye for negative controls CellMask Orange plasma membrane stain (Molecular probes) was used according to the manufacturer’s protocol for live, adherent cell cultures with the following modifications: Keratocytes seeded on glass coverslips were incubated at room temperature for 15min, washed five times with PBS and imaged immediately in START medium. Live cell imaging All live cell imaging was performed at room temperature in START medium. Confocal microscopy was performed with an inverted microscope (Zeiss), equipped with a Spinning disk system (Yokogawa X1, iXon897, Andor), a C-Apochromat 63x/1.2 Water Objective (Zeiss), a motorized stage and 488nm and 561nm lasers. While imaging with this microscope, laser ablations of the trailing edge were performed with a 355nm laser cutter. For widefield imaging an inverted widefield microscope (Nikon), equipped with 60x/1.4 and 100x/1.4 Apochromat Oil Objectives, a motorized stage and a light source with flexible excitation bands (Lumencor) was used. Micropipette aspiration experiments were performed on an upright confocal microscope (SP5, Leica), equipped with HCX 63x/1.4 Apochromat Oil Objective (Leica), a motorized stage and a 488nm laser line. The time interval was 0.2 s-1.0 s. Micromanipulators Micropipettes were produced from 1.0mm diameter glass capillaries as described before (Maıˆtre et al., 2012). For cell manipulations negative pressures from 10mbar to 40mbar were used for aspirating the cell membrane and 0-2mbar of positive pressure to release the cell again. For correlated live and electron microscopy cell membrane was aspirated with 30mbar for about 5 s and extracted and fixed about 3 s after release from the micropipette. The same micromanipulator system was used to induce rapid cell shrinking by carefully detaching part of the cell from the underlying substrate. In this case, the cell was fixed on the grid immediately afterward and prepared for electron microscopy as described below. Osmotic treatment For experiments with changing osmotic pressure, lifeact:GFP expressing keratocytes were subjected to repeated additions of 50ml 0.2M sucrose in START medium and 50ml double distilled water to a starting volume of 300ml START medium. Tether pulling experiments and force measurements Primary keratocyte cultures for these experiments were prepared from the Central American cichlid Hypsophrys Nicaraguensis as described previously (Lieber et al., 2013). One day old cultures were replated and cultured at room temperature in Leibovitz’s L-15 media (GIBCO BRL, Grand Island, NY), supplemented with 14.2 mM HEPES pH 7.4, 10% Fetal Bovine Serum (Invitrogen, Grand Island, NY), and 1% antibiotic-antimycotic (GIBCO BRL). Tether force measurements were carried out as in (Lieber et al., 2013) with a laser tweezers system (PALM microtweezers, Carl Zeiss MicroImaging GmbH, Jena, Germany) using a 63 3 1.2 NA water immersion Cell 171, 1–13.e1–e6, September 21, 2017 e2
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objective and a motorized stage (Ludl Electronic Products, Hawthorne, NY) on an inverted microscope (Axiovert 200M, Zeiss, Jena, Germany). Trapping was done with a 3W 1064nm Nd:YAG laser focused to a diffraction limited spot, and imaging by bright field was done simultaneously. Tether force measurements on cells were done by attaching a Concanavalin A coated bead to the rear part of the cell body and pulling it away by moving the stage. The measured tether force was corrected for the contribution of the dynamic friction due to stage movement, when relevant, as in (Lieber et al., 2013). A membrane tether was held continuously during spontaneous instances of abrupt rear retraction, providing a read out of the changes in the tether force that accompany the large changes in the projected cell area during the retraction event. Membrane tension values T were calculated from the tether force FT using, T = ðFT2 =8p2 BÞ, where B = 0:14pN,mm is the measured bending modulus of the membrane in keratocytes (Lieber et al., 2013). Image analysis Time-lapse images of migrating keratocytes were analyzed in Fiji by first defining the projected cell area by applying a Gaussian blur to the raw image stack and then threshold it to obtain a stack of binary images. The same binary image was used to define a 1.09mm wide region along the leading edge as the lamellipodial region of interest. An optical flow analysis based on the Horn-Schunck method was then used to calculate the optical flow between the binary mask frames. Both the original image stack and the optical flow data were stabilized using a custom-made image-stabilizing MATLAB algorithm. The resulting stabilized stacks were further analyzed by skeletonizing the 1.09mm wide lamellipodium region for each stack slice and plotting both the gray value of the original image and the amount of shift determined by the optical flow analysis along the whole length of the leading edge for every time step. A custom-made MATLAB program was used for this step. The resulting 2D heatmaps of lifeact:GFP, actin:GFP or membrane dye intensity and protrusion were averaged along the length of the leading edge and plotted against time and the whole images were correlated to each other and the projected area. For cross correlation analysis the first derivative of the lifeact:GFP, actin:GFP or membrane dye intensity and protrusion heatmaps as well as the projected cell area were taken and the cross covariance function of MATLAB was used normalized so that the auto-covariance at zero lag equaled 1. For analysis of signal flow within the lamellipodium 1.09mm wide bands were eroded from the leading edge in consecutive steps and the resulting bands were used to quantify the lifeact:GFP intensity in adjacent parts further removed from the leading edge. The resulting heatmaps were correlated to each other using the same procedure as described above and the resulting peaks were multiplied by the speed of the respective cell to obtain the distance lag. The calculated distance was plotted against the known distance between the eroded bands. Electron tomography Cells were grown on 200mesh HF15 Gold finder grids (Maxtaform) and 200mesh hexagonal gold grids (Agar Scientific) coated with 2% Formvar and a 2nm carbon layer and incubated with 0.5mg/ml PLL(20)-g[3.5]-PEG(2)/PEG(3.4)-RGD (Surface Solutions) for 50min. Extraction and fixation was performed using 0.25% glutaraldehyde and 0.5% Triton X-100 in Cytoskeleton Buffer (10mM MES buffer, 150mM NaCl, 5mM EGTA, 5mM glucose, 5mM MgCl2, pH 6.1) for 1min at room temperature. The grids were then transferred to 2% glutaraldehyde in Cytoskeleton buffer for 10min and kept in another dish with 2% glutaraldehyde in Cytoskeleton buffer at 4 C until staining for electron microscopy. For staining, grids were carefully blotted with filter paper from the bottom and immediately stained with 70ml 4% sodium silicotungstate supplemented with BSA-gold fiducials from a gold stock as described before (Vinzenz et al., 2012). Double axis tilt series with typical tilt angles from 65 to +65 and 1 increments following the Saxton scheme were acquired on an FEI Tecnai G20 transmission electron microscope operated at 200kV equipped with a Eagle 4k HS CCD camera (Gatan). The automated acquisition of double axes tilt series was driven by SerialEM 3.x (Mastronarde, 2005). The defocus was set to 5mm for all acquisitions and the primary on-screen magnification was 25,000x. For montage tomograms montages of 2x2 or 3x2 images were acquired for each tilt angle. Back-projection of the tilt series was performed using the IMOD package 4.7 with gold particle fiducials as markers and high-pass filtering of the final reconstruction (Kremer et al., 1996). A typical tomogram comprised 50-70 stacks of 0.92nm and an area of 1.9mm x 1.9mm. The montage tomograms had dimensions of 3.1mm x 3.1mm and 4.0mm x 3.1mm, respectively. Actin filament tracking and analysis Filaments were quantified in three different ways: Manual tracking of the region shown in Figure S6B using 3dmod software. Automated tracking using a MATLAB-based tracking algorithm (Winkler et al., 2012). Computerized segmentation of actin filaments by the pixel classification function of ilastik 1.1 was used to quantify actin filament density in the correlated tomograms (Summarized in Figures S6A–S6C) (Kreshuk et al., 2011). The manually and automatically tracked filaments were further analyzed in the following way. In the tomogram montages the recorded filaments were divided in 106.15nm wide distance bins spanning from the leading edge up to 2.8mm toward the back of the lamellipodium (shown in Figures S4D and S6E). For the single tomograms of actin filament density steps two regions of 300nm each before and after the step were used. In automated tomograms filaments shorter than 55nm were excluded from analysis. Filament numbers indicate the number of individual filaments crossing a plane in the middle of the respective analysis region. Pointed and barbed ends were defined as ends of filaments furthest and closest from the leading edge, which was clearly visible in every
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case, respectively. Filament angles were defined as the angle subtended between a filament and the leading edge in the plane of the flat lamellipodium, with 0 meaning a filament growing perpendicularly toward the leading edge. Angles were weighted by the total length of the filaments growing in that direction. The density in the different angle bins was taken as number of filaments growing at that angle normalized by the size of the angle bin. As a global measure of filament architecture an order parameter was defined as: ðFilaments 10 to + 10 Þ ðFilaments 40 to 20 + Filaments + 20 to + 40 Þ=2 ðFilaments 10 to + 10 Þ + ðFilaments 40 to 20 + Filaments + 20 to + 40 Þ=2 (Weichsel and Schwarz, 2010). Correlated light and electron microscopy For correlated light and electron microscopy 200mesh HF15 Gold Finder grids were coated with 0.5mg/ml PLL-PEG-RGD (Surface Solutions) for 50min. Then keratocytes were allowed to adhere for z1h, imaged directly on the grid with an inverted confocal spinning disk microscope and either aspirated for about 4 s and then released or partly detached from the grid using micromanipulators as described above. Immediately after release from the micropipette or induction of a rapid shrinking event the cells were fixed by taking off the medium and adding the extraction and fixation buffers. To find the correlated cells back, the grids were first completely mapped by using the navigator map function of SerialEM on an FEI Tecnai G20 transmission electron microscope. Once the relevant grid square was found, high magnification montages and tomograms of the transition zones were acquired. Stochastic Simulation Stochastic 2D models of actin-based lamellipodial protrusion have been proposed in the past to show the self-organization of orientation patterns (Maly and Borisy, 2001; Schaus et al., 2007; Weichsel and Schwarz, 2010). These models considered network steady state analysis and simulations with fixed velocity. We build on the published models to include transient responses of leading edge velocity and network organization due to changing external forces exerted on the filaments. This simulation was implemented in python 2.7 and has been made publicly available at https://github.com/gszep/lamellipodium. We formulate a 2D model, where each actin filament is rigid and immobile. The first assumption can be justified by electron tomograms, where mostly straight filaments are observed. Immobility of filaments has to be understood relative to each other, which still permits a coordinated retrograde flow. Thus the state of the network close to the leading edge at time t can be described by the set F ðtÞ with NðtÞ number of growing barbed ends, each having 2D position vectors xðtÞ = ðxðtÞ; yðtÞÞ and constant orientations u. o n (1) F ðtÞ = ðxðtÞ; uÞ1 ; .; ðxðtÞ; uÞNðtÞ u encodes the direction and magnitude ju j = d of elongation with the addition of one actin monomer. The plasma membrane is modeled as a flat edge parallel to the y -axis at position pðtÞ along the x -axis. With all filaments only pushing from one side, the resultant protrusion velocity vðtÞ is positive in the x -direction. Periodic boundary conditions are imposed in the interval 0%yðtÞ < L along the y -axis. We shall describe elongation, branching, and capping events at a barbed end at position x – dropping time variable for convenience – at time t as Poisson processes with rates lðx; tÞ; bðx; tÞ and kðx; tÞ respectively. This means that in a sufficiently small time step from t to t + Dt, the filament will experience one of these events given by rate uðx; tÞ with probability uðx; tÞ Dt. We introduce a useful notation nðx; t j uÞ which is a Boolean variable that tells us whether an event with rate uðx; tÞ happened or not at a barbed end at position x and time t. Elongation happens in the strip of width w behind the leading edge position pðtÞ with the rate l0 and zero otherwise. This assumption is motivated by the observation that most growth happens at the leading edge. l0 pðtÞ w < xðtÞ < pðtÞ lðx; tÞ = (2) 0 elsewhere An elongation event for a particular barbed end means xðt + DtÞ = xðtÞ + u. There are NðtÞ barbed ends, meaning we have to check events at each one of them. Branching occurs at the leading edge with a rate that depends on the linear density of nucleation factors aðtÞ such as Arp2/3 at the leading edge (Weichsel and Schwarz, 2010). Let a0 be the rate of activation that leads to branching. a0 aðtÞ pðtÞ w < xðtÞ < pðtÞ bðx; tÞ = 0 elsewhere Consider the finite availability of nucleation factors and activation being the rate-limiting step in branching new filaments. Let DðtÞ be the linear density of barbed ends along the leading edge, which increases with branching rate a0 aðtÞ and decreases with possibly time dependent capping rate kðtÞ: In addition, we know that there is a finite positive rate of arrival b0 of nucleation factors at the leading edge coming from a reservoir. Finally, nucleation factors are depleted when branching occurs, with a rate a0 DðtÞ depending of barbed end concentration.
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vt DðtÞ = a0 aðtÞDðtÞ kðtÞDðtÞ
vt aðtÞ = b0 a0 aðtÞDðtÞ Assuming that the arrival of nucleation factors at the leading edge is faster than branching or capping events, we can employ the quasi-steady state assumption (Manhart et al., 2015), setting vt aðtÞ = 0. Rearranging for the concentration aðtÞ; we can finally write: 8 > < b0 pðtÞ w < xðtÞ < pðtÞ bðx; tÞ = DðtÞ (3) > : 0 elsewhere Branching add a new filament ðx0 ðt + DtÞ; u0 Þ to the frontier at the position of the barbed end x0 ðt + DtÞ = xðtÞ of the mother filament. The orientation is rotated by a random branching angle q sampled from a distribution. This can be written as a rotation matrix RðqÞ acting on the mother filament orientation u0 = RðqÞu. The branching angle distribution Bðq j m; sÞ is the sum of two Gaussians with respective means at ± m and standard deviations s taken from electron microscopy data. The daughter filament is required to be oriented toward the leading edge, meaning that the random choice might have to be repeated, until this requirement is fulfilled. This model neglects that there is a preferred distance between branches, due to the helical structure of actin filaments (Vinzenz et al., 2012). Capping irreversibly removes a barbed end from the frontier. We assume there is a low capping rate k0 within width w behind the leading edge, and a high rate k1 further behind, leading to filaments being immediately capped outside this zone. 8 < k0 pðtÞ w < xðtÞ < pðtÞ xðtÞ < pðtÞ w (4) kðx; tÞ = k1 : 0 elsewhere Actin filaments polymerizing against the plasma membrane exert a force that in turn sets the protrusion velocity. It has to balance the restricting force due to membrane tension. We assume an equal distribution of the total force among the pushing filaments and the absence of retrograde flow as observed in keratocytes migrating on serum-coated glass coverslips. We use a force-velocity relation based on thermal fluctuations of the membrane and/or the filaments, as is appropriate for the Brownian ratchet model (Lee et al., 2001; Mogilner and Oster, 1996) of polymerization, but also for other established models like the tethered ratchet or end-tracking motors (Dickinson, 2009). This leads to the following rule for updating the position of the leading edge from small time steps: pðt + DtÞ = pðtÞ + vðtÞDt
vðtÞ = l0 d e
dFðtÞ kB T DðtÞ
(5)
Here the maximum possible speed is equal to the maximal polymerization speed l0 d of unobstructed filaments. By FðtÞ we denote the membrane force per leading edge length, DðtÞ the linear density of barbed ends and kB T is the thermal energy. The experiments with a rapid decrease of membrane tension and subsequent return to a steady protruding state are approximated by a stepwise decrease DF in force density at time t for a duration Dt, followed by a stepwise increase back to original force density F0 . F0 DF t < t < t + Dt FðtÞ = (6) elsewhere F0 The initial barbed end positions are sampled from a uniform distribution within the polymerization zone. The orientations are sampled from a uniform distribution along a half circle of radius d. The density DðtÞ is updated before each time step and stored for the sampling of branching events and for updating the velocity of the leading edge. Then we iterate through all binding sites in the frontier, checking first for capping events, then branching, and finally elongation. Finally the position of the membrane is updated, along with the elapsed time. The process is repeated until final simulation time T0 . First the simulation is run for the above parameters except we set DF = 0. The initialization is uniform. Beyond a time T0 10s a steady state in both filament density and angular distribution with respect to the membrane is reached. Using the final state of a previous run as an initial state for the next run, we simulate 20 runs each of time T0 = 10s. By recording all the history of barbed end movement during a run, we collect statistics at the end of each run. This way we end up with 20 data points per statistic, of which we return the mean and standard deviation to produce wild-type regime shown in Figures 6B–6D (middle), Figures S7A–7C (middle) and Movie S5 (first part).
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This unperturbed wild-type steady state with orientation peaks at ± 35 is used as an initial condition for every run of the perturbed simulation. Setting DF = ± 270pN mm1 and executing another 20 runs, collecting statistics at the end of each run obtains the results shown in Figures 6B–6D (top and bottom), Figures S7A–7C (top and bottom) and Movie S5 (second and third part). To analyze if our stochastic model would be able to reproduce the correlations shown in Figure 1, we used the measured changes in projected cell area as input. Using the correlated cells shown in Figures 5 and S3 with known decreases in projected cell area and changes in network parameters, we scaled the changes in projected cell area by normalizing to the maximum value, subtracting a constant value and setting the mean to 300pN. The mean force of the first 2 s was used as constant tension for 5 s to let the simulation reach a steady state, before the force changes scaled from the projected area changes were used as input. The fluctuations in projected area from the 21 migrating keratocytes used for Figure 1 were then used as force input and the resulting output parameters averaged and cross-correlated to generate Figure 7. QUANTIFICATION AND STATISTICAL ANALYSIS MATLAB (MathWorks) and Prism (GraphPad) were used for statistical analysis. For live-cell imaging 21 and 7 individual cells were used for analysis of lifeact:GFP and membrane dye fluctuations, respectively. For membrane aspiration experiments 28 aspiration events in 13 individual cells were performed. For tomography experiments 4 wild-type tomography montages were used as well as 7 correlated shrinking events in 3 individual cells and one correlated aspiration event. Statistical parameters for individual experiments can be found within the figure legends. A paired t test was used for changes in median angle at the density step (Figure S5D). Pearson correlation was used for correlation analysis of measured distances from the leading edge to calculated distances (Figure S1F) and for angle to density decrease analysis (Figure S5E). A p value of < 0.05 was considered statistically significant.
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Supplemental Figures
Figure S1. Details of Quantification of Live Cell Imaging Parameters, Related to Figure 1 (A) Temporal fluctuations of lifeact:GFP signal, projected cell area and protrusion speed of the cell shown in Figure 1 are shown normalized from the maximum value to zero. The lifeact:GFP signal multiplied by the instantaneous speed is shown normalized from the maximum to zero as well.
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(B) Temporal crosscorrelation functions of Area – lifeact:GFP intensity, Area-protrusion speed and lifeact:GFP intensity – Protrusion speed for 21 individual cells are shown in black. Averaged cross-correlation functions from a spline fit to the combined single-cell cross-correlation functions are shown in purple (Area – lifeact:GFP intensity), green (Area – Protrusion speed) and yellow (lifeact:GFP intensity – Protrusion speed). (C) Confocal images of a migrating keratocyte expressing lifeact:GFP were analyzed using consecutive 1.09mm wide regions spanning the lamellipodium. (D) Resulting lifeact:GFP intensity maps are plotted against time. (E) Temporal cross correlation functions of region ‘1’ at the very front of the cell to consecutive regions are plotted as a function of time lag. (F) Time lag between peaks of the curves shown in H multiplied by cell velocity and resulting distances are plotted against distance between analyzed regions. Measured mean and s.d. of twelve cells are shown together with a linear regression (Pearson constant = 0.9997, p = 0.0003).
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Figure S2. Live Cell Imaging Controls with a Membrane Marker and actin:GFP, Related to Figure 1 (A) Example images of migrating keratocytes incubated with the membrane dye CellMask. (B and C) Temporal fluctuations of the resulting intensity maps are shown normalized as in Figure 1D (B) and as in Figure S1A (C). Neither an amplification of area fluctuations nor a correlation could be observed. (D) Resulting temporal cross correlation functions for eight individual cells are shown in black and averaged cross correlation in dark blue. The averaged cross correlation as mean with s.e.m. is shown in dark blue on the right. (E) Zebrafish keratocytes transfected with actin:GFP were analyzed in the same way as shown before for lifeact:GFP. (F) Temporal cross correlation analysis area – GFP signal intensity showing peaks at time lag zero for transfected cells expressing actin:GFP and lifeact:GFP. Additionally cells generated from actin:GFP microinjected Zebrafish embryos were analyzed and showed a positive cross correlation coefficient at time lag zero. Plot shows averaged cross correlation and s.e.m. for seven cells for both actin:GFP transfection and mRNA injection.
Figure S3. Membrane Tension Measurement by Tether Pulling and Membrane Tension Manipulation by Changing Osmotic Pressure, Related to Figure 2 (A) A migrating keratocyte was imaged with bright field microscopy and simultaneously a coated bead controlled by a laser tweezer was used to pull a membrane tether. (B) The measured tether force decrease correlated with rapid decreases in projected cell area. (C) A lifeact:GFP expressing keratocyte was imaged by confocal microscopy and subjected to rapid changes in osmotic pressure of the medium by alternating additions of 0.2M sucrose and pure water. (D) lifeact:GFP signal is negatively correlated with the osmolarity of the medium. When the pressure increases upon addition of 0.2M sucrose, lifeact:GFP signal drops, which is reversible upon restoring a lower osmotic pressure by addition of pure water.
Figure S4. Actin Network Parameters for Individual Tomogram Montages of Keratocyte Lamellipodia, Related to Figures 3 and 4 (A) Filament density, barbed and pointed ends for individual cells shown in Figure 3. Data for individual lamellipodia are shown in black together with average. (B) Filament densities growing at the indicated angle from the cell membrane in 212nm distance bins of the steady state lamellipodia shown in Figure 3. Mean and s.e.m. are shown. (C) Filament densities growing at the indicated angle from the cell membrane in 212nm distance bins of the correlated tomogram shown in Figure 4. The densities are shown as in Figure 4 beginning from toward the rear of the cell on the left until the leading edge on the right. (D) 5.5nm slice of a negatively stained electron tomogram montage showing the region marked by a red box in Figure 4A (left) and corresponding automatically tracked filaments shown color-coded according to their angle from the leading edge (right). The spatial bins used for quantification of network parameters in Figures 4 and S4C are also shown on the right.
Figure S5. Changes in Filament Parameters at a Decrease in Filament Density, Related to Figure 5 (A and B) Network structure analysis of seven lamellipodia tomograms in three correlated cells revealed consistent features at the point, where the actin density decreased due to the manipulation by the micropipette. Overview electron micrographs and 5.5nm tomogram slices are shown for all regions. (C) Averages of filament density, barbed and pointed ends and median angle from the cell edge showed the consistent changes at the density step. (D) Median angles of all analyzed regions are plotted for 300nm space bins before and after the decrease in actin filament density (right). (Paired t test, p = 0.0249). (E) Normalized ratio of filaments after density step to filaments before density step is plotted against the filament angle from the cell edge together with a linear regression curve. (Pearson constant, r = 0.936) Mean and s.e.m. are shown on all graphs.
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Figure S6. Quantification of Correlated Live Microscopy-Electron Tomography, Related to Figure 5 (A) A 5.5nm slice of the tomogram montage used for Figure 5 (left) is shown together with automated tracking results (middle and right). (B) Close-up of region containing the drop in filament density and change in actin architecture with filaments shown in green, barbed ends in red and pointed ends in blue. Manually tracked filaments, barbed and pointed ends of a region including the density step are shown. (C) Filament density quantified by manual and automated tracking, ilastik image analysis and the lifeact:GFP signal of the correlated cell shown in Figure 5. (D) Filament densities in 212nm distance bins growing at different angles toward the membrane. The densities are shown as in Figure 5 beginning from toward the rear of the cell on the left until the leading edge on the right. (E) 5.5nm slice of negatively stained electron tomogram montage showing region marked with red box in Figure 5A (left) and corresponding automatically tracked filaments shown color-coded according to their angle from the leading edge (right). Additionally, the spatial bins used for quantification of network parameters in Figures 5 and S6D are displayed on the left. The cell edge is seen on the right side.
Figure S7. Details of Stochastic Simulation, Related to Figures 6 and 7 The graphs in A–C are aligned as in Figure 6. (A) The temporal changes in filaments in three different angle bins are shown. The number of filaments in the indicated angle bins is constant at growth at constant external force. In the force decrease scenario filaments growing at higher angles are capped preferentially and the network thins out. When force increase is used as an input, filaments in all angle bins increase. (B) Histograms of filament density (black) and order parameter as defined in Figure 3 (blue). Without perturbation the network architecture is dominated by ± 35 peaks and the order parameter is consistently negative. Histograms of filament density before (black) and after (red) decrease in F and order parameter (blue) show biased elimination of filaments growing at higher angle. This leads to a change from the ± 35 architecture to one dominated by straight, 0 , filaments and a transiently positive order parameter. Filaments of all angles increase upon increase in force, which is also reflected in a negative order parameter. (C) The migration parameters force (the input parameter), actin density and protrusion speed fluctuate around steady state values during the unperturbed simulation. The force decrease causes an increase in protrusion speed and a decrease in actin density, with the reciprocal situation observed for the force increase. (D) Capping, elongation and branching rates used for the stochastic model. (E) Underlying lamellipodial feedback loop: Force, F, is set as an external parameter and decreases velocity, v, which is in turn increased by increased filament density, D, as suggested by the elastic ratchet model of actin polymerization. Actin branching is modeled as a zeroth order process and therefore actin density decreases branching rate, b. The parts of the feedback loop linking velocity, v, to the filament density, D, shown in this study are marked in red: Velocity, v, increases capping rate, k, in an angle-dependent manner and leads to a decrease in filament density, D. For all graphs mean and s.d. for an average of 20 runs are shown, for details see STAR Methods.
Load Adaptation of Lamellipodial Actin Networks Graphical Abstract
Authors Jan Mueller, Gregory Szep, Maria Nemethova, ..., Kinneret Keren, Robert Hauschild, Michael Sixt
Correspondence [email protected]
In Brief How do mechanical perturbations influence the density and the geometry of actin networks at the leading edge of migrating cells?
Highlights d
Lamellipodial actin density co-fluctuates with the size of the projected area
d
Lamellipodial actin density adapts to changes in membrane tension
d
Actin branch geometry prescribes adaptations in lamellipodial actin
Mueller et al., 2017, Cell 171, 1–13 September 21, 2017 ª 2017 Elsevier Inc. http://dx.doi.org/10.1016/j.cell.2017.07.051
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Article Load Adaptation of Lamellipodial Actin Networks Jan Mueller,1 Gregory Szep,1 Maria Nemethova,1 Ingrid de Vries,1 Arnon D. Lieber,2 Christoph Winkler,3,4 Karsten Kruse,5 J. Victor Small,6 Christian Schmeiser,3,4 Kinneret Keren,2,7 Robert Hauschild,1 and Michael Sixt1,8,* 1Institute
of Science and Technology Austria (IST Austria), am Campus 1, 3400 Klosterneuburg, Austria of Physics and Russell Berrie Nanotechnology Institute, Technion, Israel Institute of Technology, Haifa 32000, Israel 3RICAM, Austrian Academy of Sciences, Apostelgasse 23, 1030 Vienna, Austria 4Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria 5NCCR Chemical Biology, Departments of Biochemistry and Theoretical Physics, University of Geneva, 30, quai Ernest-Ansermet, 1211 Geneva, Switzerland 6Institute of Molecular Biotechnology GmbH (IMBA), Dr. Bohr-Gasse 3, 1030 Vienna, Austria 7Network Biology Research Laboratories, Technion, Israel Institute of Technology, Haifa 32000, Israel 8Lead Contact *Correspondence: [email protected] http://dx.doi.org/10.1016/j.cell.2017.07.051 2Department
SUMMARY
Actin filaments polymerizing against membranes power endocytosis, vesicular traffic, and cell motility. In vitro reconstitution studies suggest that the structure and the dynamics of actin networks respond to mechanical forces. We demonstrate that lamellipodial actin of migrating cells responds to mechanical load when membrane tension is modulated. In a steady state, migrating cell filaments assume the canonical dendritic geometry, defined by Arp2/3-generated 70 branch points. Increased tension triggers a dense network with a broadened range of angles, whereas decreased tension causes a shift to a sparse configuration dominated by filaments growing perpendicularly to the plasma membrane. We show that these responses emerge from the geometry of branched actin: when load per filament decreases, elongation speed increases and perpendicular filaments gradually outcompete others because they polymerize the shortest distance to the membrane, where they are protected from capping. This network-intrinsic geometrical adaptation mechanism tunes protrusive force in response to mechanical load.
INTRODUCTION From endocytic processes and vesicle trafficking to cellular locomotion and intracellular pathogen movement, the actomyosin cytoskeleton mediates most of the mechanical responses of eukaryotic cells (Pollard and Cooper, 2009). Actomyosin networks have two principal mechanisms of force generation: (1) polymerization can expand the network by elongating filaments against a load, and (2) myosin motors can contract the network or transport cargo along filaments. Every actin filament is born by a nucleation event. Nucleation is catalyzed by a number of molecular machines, the most prominent being formins and
the Arp2/3 complex. While formins achieve de novo linear nucleation, the Arp2/3 complex binds to an existing filament and branches off a new filament at a 70 angle. Elongation, the addition of new monomers to the growing (barbed) end of the filament, is mainly mediated by formins or by proteins of the VASP family. Both nucleation and elongation are enhanced at the interface to membranes, where growing filaments are shielded from capping proteins, which otherwise terminate filament elongation by sealing the filament’s barbed end (Carlsson, 2010; Pollard, 2007). Arp2/3-dependent actin polymerization is a force-sensitive process. This has been demonstrated in vitro, in minimalist reconstituted systems, whereby increasing the mechanical load on a protruding reconstituted network led to higher network density (Bieling et al., 2016; De´moulin et al., 2014; Parekh et al., 2005). Thus, the network structure was able to adapt to the ambient mechanical conditions and to support force generation and mechanical resilience under varying loads. It has been shown that such adaptation is partially mediated by differential force sensitivities of nucleation, elongation, and capping, leading to enhanced branching under higher loads (Bieling et al., 2016). However, these kinetic effects were only partially able to explain the changes in network density, and it was speculated that the remaining adaptation might be mediated by spatial rearrangements of the network. The mechanochemical response of protruding actin networks has not yet been studied in living cells. However, indirect evidence suggests that the leading edge of a motile cell is able to respond to load. When the lamellipodium, the flat protrusive front of a migrating cell, encounters an elastic obstacle (e.g., the vertical cantilever of an atomic force microscope), it was shown to substantially increase its pushing force, until collapsing when the load became excessive. For a migrating cell encountering a barrier, this means that its front pushes harder until the obstacle is pushed away or the leading edge stalls and the cell either retracts or circumnavigates the barrier (Heinemann et al., 2011; Prass et al., 2006). In fibroblasts or epithelial cells, where lamellipodia typically undergo cycles of protrusion and retraction, it has been suggested that during each protrusive phase the polymerizing actin filaments experience a gradually growing load, because increase Cell 171, 1–13, September 21, 2017 ª 2017 Elsevier Inc. 1
Please cite this article in press as: Mueller et al., Load Adaptation of Lamellipodial Actin Networks, Cell (2017), http://dx.doi.org/10.1016/ j.cell.2017.07.051
in projected cell area is accompanied by increase in membrane tension (the cell stretches out the rather inextensible bag of plasma membrane) (Diz-Mun˜oz et al., 2013; Gauthier et al., 2011; Raucher and Sheetz, 2000; Sens and Plastino, 2015). This growing load on the pushing filaments is accompanied by accelerated incorporation of the actin nucleating Arp2/3 complex, which might, in turn, increase actin network density and boost force generation until the filaments stall and the leading edge retracts (Ji et al., 2008; Lee et al., 2015; Ryan et al., 2012). While these response patterns might result from complex mechanosensitive signaling processes, theoretical considerations put forward the alternative idea that branched actin networks respond to varying polymerization kinetics by changing their geometry (Maly and Borisy, 2001; Schaus et al., 2007; Weichsel and Schwarz, 2010). Such responses would argue that load adaptation is an emergent geometrical property of branched actin. Here, we use the lamellipodium of fish keratocytes to quantitatively examine how protruding actin networks respond to varying forces. We use a combination of quantitative light and electron microscopy to describe geometrical changes of lamellipodial actin upon varying load regimes and employ stochastic modeling to elucidate how the network structure geometrically adapts to counter-forces. RESULTS Temporal Fluctuations in Actin Density Arise at the Leading Edge and Are Correlated with Projected Cell Area and Protrusion Speed To quantitatively explore how lamellipodial actin reacts to changes in load we employed fish keratocytes migrating on planar surfaces (Mogilner and Keren, 2009). We established protocols to derive keratocytes from adult zebrafish, allowing access to stable transgenesis. On serum-coated coverslips, these cells migrate with exceptional speed, persistence, and morphological stability (Keren et al., 2008). We first chose a correlative approach and observed single migrating keratocytes expressing the actin reporter lifeact:GFP (Riedl et al., 2008) with high spatiotemporal resolution (Figure 1A; Movie S1). This allowed us to monitor fluctuations in actin network dynamics and density together with protrusion speed and morphological parameters (Figures 1A–1D, S1A, and S1B). The projected area of a keratocyte typically fluctuated ±5% around a baseline, which was consistent with earlier studies (Keren et al., 2008) (Figure S1A). These limited fluctuations supported the notion that the keratocyte’s plasma membrane does not harbor major membrane reservoirs, which might be mobilized upon mechanical stretch (Lieber et al., 2013). When we measured lifeact:GFP intensity within a 1-mm broad zone behind the leading front, intensity fluctuations were more substantial than area changes and varied ±20% (Figures 1D and S1A). Strikingly, the normalized, temporal fluctuations in projected cell area were tightly correlated with lifeact:GFP intensities as shown by cross-correlation peaks between 0.6–0.7 at time lag zero (Figures 1D, 1E, and S1B). This correlation was also observed in actin:GFP-expressing keratocytes, but not when the plasma membrane was uniformly labeled (Figure S2).
2 Cell 171, 1–13, September 21, 2017
Correlation analysis of consecutive 1-mm broad lamellipodial regions showed that the time delay between correlation peaks increased with the distance between the measured regions (Figures S1C–S1E). Dividing the respective lag times by the speed of each cell yields distances matching those between adjacent lamellipodial regions (Figure S1F). This analysis showed that, first, as previously demonstrated (Theriot and Mitchison, 1991; Wilson et al., 2010) keratocytes exhibited minimal retrograde flow of actin in relation to the substrate. Second, temporal fluctuations of actin density arise at the leading edge and propagate rearward. We next quantified protrusion speed by optical flow analysis at each pixel along the cell front. Protrusion speed was negatively correlated with both projected cell area and lifeact:GFP intensity with a negative cross-correlation peak between 0.3 and 0.4 at time lag zero (Figures 1B–1E). Lifeact:GFP intensities were equally co-fluctuating with area changes when corrected for the fluctuations in protrusion speed (Figure S1A). Taken together, our quantitative analysis demonstrates that keratocytes migrate slower and produce denser actin networks during intervals when their projected area is larger. Experimental Manipulations of Membrane Tension Reveal a Lamellipodial Response to Altered Load Among several interpretations of these correlative data we considered that a fluctuation in projected cell area might correspond to changes in membrane tension (Raucher and Sheetz, 2000). To dissect the causal relationship between actin network density and membrane tension, we experimentally increased membrane tension by aspirating the trailing edge of migrating keratocytes with a micropipette (Houk et al., 2012) (Figure 2A; Movie S2). As membrane tension equilibrates almost instantaneously over the whole cell, this manipulation allowed us to tune lateral tension at the lamellipodial tip (Diz-Mun˜oz et al., 2013). Experiments were performed by transiently applying four different vacuum levels ranging from 10 to 40 mbar. In all cases, we found that aspiration caused an increase in lifeact:GFP signal concomitant with a moderate decrease in protrusion speed (Figures 2A–2C). Actin density and protrusion speed were dependent on the applied vacuum (Figures 2D and 2E). Following transient aspiration, the band of denser actin network traveled backward (in the cell frame of reference) with the actin flow (Figures 2A and 2C). Under the given parameters the cells kept protruding during aspiration, demonstrating that the increase in tension was below the stall force of the lamellipodium. These results suggested that lamellipodial actin responds to an increase in membrane tension by increasing network density. To experimentally decrease membrane tension we took advantage of the fact that on adhesive substrates cells occasionally form tethered trailing edges, which leads to a stretched morphology (Figure 2F). When these tethers spontaneously detach or when we cut them with a pulsed laser, tension is released and the tether snaps forward. Here, the projected cell area shrunk within a few seconds when the cell went from a stretched to a more compact configuration. Such high recoil velocities indicate the rapid drop in tension, which had previously built up in the stretched cell. To directly test if shrinkage is accompanied by changes in membrane tension, membrane
Please cite this article in press as: Mueller et al., Load Adaptation of Lamellipodial Actin Networks, Cell (2017), http://dx.doi.org/10.1016/ j.cell.2017.07.051
Figure 1. Correlative Analysis of Actin, Projected Cell Area, and Protrusions in Migrating Zebrafish Keratocytes (A) Confocal imaging of lifeact:GFP-expressing keratocyte moving on a glass coverslip. (B) Time frame from (A) showing the 1.09-mm wide area of lifeact:GFP intensity measurements (left), a binary mask used for quantifying the area (middle), and a pseudo-colored Horn-Schunck optical flow analysis image of the leading edge (right). (C) Fluorescence intensity and leading edge velocity maps for the time lapse of the cell shown in (A). (D) Temporal fluctuations of cell area, lifeact:GFP intensity, and protrusion speed averaged across the analyzed region shown in red in (B). (E) Average of temporal cross-correlation functions of 21 migrating keratocytes. Mean and SEM are shown. See also Figures S1 and S2 and Movie S1.
tethers were pulled from the plasma membrane of migrating keratocytes using an optical trap (Lieber et al., 2013) (Figure S3A). While in steady-state migrating cells there was no consistent relation between projected area and tether force, abrupt retraction events were accompanied by area shrinkage concurrent with a drop in tether force and thus membrane tension (Figure S3B). During abrupt retraction, the previously observed correlation between projected cell area and actin intensity at the leading edge manifested in a sudden drop in lamellipodial life-
act:GFP intensity at the moment of area shrinkage (Figures 2F and 2G). The resultant abrupt change in actin density was maintained while it steadily traveled backward (in the cell frame of reference) with the actin flow, further substantiating that altered polymerization originated at the leading edge of the cell (Figures 2F and 2H; Movie S2). Cell shrinkage was also accompanied by a rapid but very transient increase in protrusion speed (Figure 2G). These results suggested that lamellipodial actin responds to a decrease in membrane tension by decreasing network density.
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Figure 2. Cytoskeletal Response to Manipulations of Membrane Tension (A) Lifeact:GFP imaging following micropipette aspiration. (1) Migrating keratocyte before contact with the micromanipulator, (2) aspiration of membrane, and (3) release of vacuum. (B) Temporal fluctuations of lifeact:GFP intensity at the leading edge defined as in Figure 1B, area, and protrusion speed. The area between the dotted lines shows where the cell was aspirated. (C) Kymograph along dashed yellow line in (A). (D) Change in lifeact:GFP signal following aspiration with four different vacuum levels. (E) Change in cell edge protrusion for the same cells as in (D). Mean and SEM are shown for 28 aspiration events in 13 individual cells in (D) and (E).
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As our mechanical manipulations of membrane tension might have caused additional changes in the cells, we chose an independent approach to challenge our hypothesis. Migrating cells were exposed to cycles of altered osmolarity (Diz-Mun˜oz et al., 2013), by supplementing the medium with sucrose versus pure water. Monitoring lifeact:GFP at the leading edge showed that increased osmolarity (water efflux–cell shrinkage) was accompanied by a decrease in lifeact:GFP signal and this was reversed when water was added (water influx–cell swelling) (Figures S3C and S3D). Together, our data show that lamellipodial actin responds to changes in membrane tension by altering its density: density increases following an increase in tension and decreases following a decrease in tension. Quantitative Analysis of Lamellipodial Ultrastructure during Steady-State Migration To gain quantitative insight into lamellipodial architecture at the single filament level we employed three-dimensional (3D) electron microscopy of fixed and negatively stained keratocytes (Vinzenz et al., 2012). This approach allows tracing single filaments in 3D space (Winkler et al., 2012). In keratocyte lamellipodia, filaments are consistently oriented with their barbed ends toward the front (Narita et al., 2012; Sivaramakrishnan and Spudich, 2009; Svitkina et al., 1997), which is in line with the polar forward growth of actin at the leading cell front (Figures S1C– S1F) (Keren, 2011; Lai et al., 2008; Theriot and Mitchison, 1991). In the digitalized tomograms we defined a barbed end as the end of a filament proximal to the leading edge and a pointed end as the one distal to the leading edge. Any barbed end could either represent an actively growing or a capped filament. A pointed end represents (1) a nucleation event generated by Arp2/3 (a branch), (2) a nucleation event generated by an alternative nucleation factor, or (3) a debranched or severed filament (Ydenberg et al., 2013, 2011). Throughout the lamellipodium of steady-state migrating keratocytes we found that the numbers of barbed and pointed ends were balanced (Figures 3A–3D and S4A). Only at the leading front, barbed ends occurred in excess, which is expected due to ongoing polymerization at this site. Next, we analyzed the angles, which the filaments assumed relative to the leading membrane and found that the distribution of their orientations peaked at ±35 (with 0 defined as perpendicular to the leading membrane) (Figure S4B). This configuration predominated in keratocytes as shown by a global order parameter defined as ((Filaments 0 –20 )(Filaments 30 –50 ))/((Filaments 0 –20 )+(Filaments 30 –50 )) as a readout for network orientation (Weichsel and Schwarz, 2010) (Figures 3E and 3F). Together, our tomography data provide a quantitative description of lamellipodial actin as derived from filament configuration. We conclude that in a steady-state migrating keratocyte, nucleation, capping and elongation create an expanding network with
a canonical branch geometry prescribed by the 70 branch structure of the Arp2/3 complex (Svitkina et al., 1997). Network Configuration following Load Increase We next used trailing edge aspiration to interrogate the ultrastructural changes in lamellipodial networks polymerizing against increased load. To this end we employed correlated fluorescence live-cell imaging and electron tomography on lifeact:GFP-expressing keratocytes migrating on electron microscopy grids. After 4 s of 30mbar aspiration, cells were released, fixed and prepared for electron microscopy (Figure 4A; Movie S3). Under the given conditions where density fluctuations arise from the leading edge, the temporal growth-history of lamellipodial actin is spatially encoded in the network: the pre-aspiration zone (proximal to the nucleus) represents steady-state growth, the aspiration zone the increase in load, and the post-aspiration zone at the leading edge the phase at which the load drops again due to the release of the vacuum. In the low-magnification electron micrograph, the transient increase in density during aspiration was clearly visible as a darker zone running parallel to the leading edge (Figure 4A). This was consistent with the lifeact:GFP live cell imaging (Figures 2A– 2C). Electron tomography with automated tracking of actin filaments allowed us to trace the temporal evolution of the load response at the single filament level. The pre-aspiration zone resembled a steady-state lamellipodium with a canonical 70 branched network. Within an 800nm broad aspiration zone (corresponding to a 4-s aspiration time) filament density was markedly increased. At the beginning of the aspiration zone (distal from the leading front, hence earlier in time) a transient drop in the number of barbed ends and a gradual increase in pointed ends created a mismatch between filament birth and death, along with the increase in filament density (Figures 4C and 4D). This increase in filament density was also accompanied by an increase in the 0 –20 and 50 –70 fraction of filament angles, whereas filaments at intermediate angles of 20 –50 increased only moderately (Figures 4E and S4C). At the leading front, filament density decreased to reach values comparable to levels before aspiration (Figure 4D) and filament angles reverted to the canonical branch-pattern (Figures 4E, S4C, and S4D). These data show that an increase in membrane tension causes an increase in network density and a change in geometry, with filaments growing at steeper angles toward the plasma membrane at higher membrane tensions. Network Configuration following Load Decrease We followed the same correlative visualization strategy to analyze the network following a decrease in load. Similar to the laser cutting used in Figures 2F–2H rapid cell shrinkage could also be triggered by mechanically detaching one side of a cell with a micropipette (Figure 5A; Movie S4). This maneuver allowed sufficient experimental control to fix the cell seconds after
(F) Lifeact:GFP signal following fast cell shrinkage. (1) Keratocyte exhibiting stretched morphology, while its trailing edge is tethered to the substrate. (2) The trailing edge is cut with a pulsed laser (yellow arrowhead). (G) Temporal fluctuations of leading edge lifeact:GFP intensity, area, and protrusion speed. The rapid retraction is marked with a dotted line. (H) Kymograph along dashed yellow line in (F). See also Figure S3 and Movie S2.
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Figure 4. Correlated Live Microscopy-Electron Tomography of Ultrastructural Changes in Networks with Increasing Filament Density (A) A migrating keratocyte expressing lifeact:GFP was aspirated at the rear with a micropipette, fixed within z3 s, and prepared for electron microscopy. The cell shifted out of focus because of the manipulating procedure. A transient increase in actin density can be seen in the low-magnification electron micrograph on the right. (B) 5.5-nm tomogram slice of the region marked by a red box in (A). The rear of the cell is toward the left side of the picture, and the cell front is seen on the right. Regions of steady-state density, increased density, and decreased density are marked with black, blue, and red throughout the whole figure. (C) Filament tracks of the lamellipodium shown in (B), with actin filaments shown in green, barbed ends in red, and pointed ends in blue. (D) Filament numbers and densities of barbed and pointed ends in 106-nm-wide spatial bins throughout the lamellipodium shown in (B) and (C). (E) Histogram showing filament angles to the cell edge in 212-nm distance bins. See also Figures S4C and S4D and Movie S3.
shrinkage. Analogous to the increase in actin density following aspiration, the decrease in actin density in the time window of rapid shrinkage was clearly visible as a transition zone in lifeact:GFP signal as well as phalloidin staining (Figure 5A). Both signals showed a sharp decrease indicating the drop in filament density. This was substantiated by low-magnification views of
the same cell after extraction and negative stain, which showed a sharp decrease in electron density, overlapping with the fluorescent imaging (Figures 5A and S6C). Quantification of manually as well as automatically traced filaments together with automated image segmentation showed a drop in filament numbers in the transition zone (Figures 5C, 5D, S5, and S6). As expected,
Figure 3. Electron Tomography of Migrating Wild-Type Keratocytes (A) Overview electron micrograph of migrating keratocyte with acquired tomogram montage marked in red. (B) 5.5-nm slice of a negatively stained tomogram of the actin network behind the leading edge. (C) Automated tracking results of the same region with filaments shown in green, barbed ends in red, and pointed ends in blue. (D) Normalized densities of filaments, barbed ends, and pointed ends in 106-nm-wide bins of four averaged tomogram montages. Graph shows mean and SEM. (E) Scheme showing the filament angle bins used for calculating the global order parameter. (F) Histogram of combined filament length growing at indicated angle toward the cell membrane (black) is shown together with a global order parameter (blue) in 212-nm distance bins defined as ((Filaments 0 –20 )(Filaments 30 –50 ))/((Filaments 0 –20 )+(Filaments 30 –50 )). See also Figures S4A and S4B.
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Figure 5. Correlated Live Microscopy-Electron Tomography of Ultrastructural Changes in Networks with Decreasing Filament Density (A) Migrating keratocyte manipulated with a microneedle to induce a rapid decrease in projected cell area with an accompanying decrease in lifeact:GFP signal, fixed within z3 s, and prepared for electron microscopy. A rapid decrease in the lifeact:GFP signal is preserved in the fixed lifeact:GFP sample and the lowmagnification electron micrograph. (B) 5.5-nm tomogram slice showing the region marked with a red box in (A). The cell edge is seen on the right side, and the region of lower density is distinguishable toward the middle of the micrograph. Region of steady-state network density and decreased density are marked in black and red throughout the whole figure. (C) Filament tracks of the lamellipodium shown in (B), with actin filaments shown in green, barbed ends in red, and pointed ends in blue. (D) Filament numbers and densities of barbed and pointed ends in 106-nm-wide spatial bins throughout the lamellipodium shown in (B) and (C). (E) Histogram showing filament densities growing at the indicated angle from the membrane in 212-nm distance bins. An order parameter (blue) in 212 nm is defined like in Figure 3. See also Figures S5 and S6 and Movie S4.
the pre-transition zone (prior to mechanical manipulation) showed the quantitative signature of the steady-state lamellipodium. The onset of the transition zone was marked by a transient increase of barbed ends, which preceded a drop in pointed ends (Figure 5D). Here, the resultant gap between putative capping and nucleation events explained the concomitant drop in filament density. The transition zone was followed by a leveling of barbed and pointed ends and a continuous recovery of the network toward the cell front. Notably, the transition zone was characterized by radically changed network geometry. When we quantified and parameterized filament angles depending on their position in the network we found that at the onset of cell shrinkage the canon-
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ical ±35 dominated network abruptly changed into a configuration dominated by filaments growing perpendicularly (0 ) to the membrane. Toward the cell front the network again recovered gradually to canonical (Figures 5E and S6D). The change in network geometry was due to selective elimination of filaments: in the transition zone the rate of filament survival strictly depended on filament orientation: filaments at a higher angle were preferentially eliminated, whereas low angle filaments had a higher rate of survival (Figures S5E and S6D). These data show that a decrease in membrane tension causes a decrease in network density and a change in geometry, with more filaments growing perpendicularly to the plasma membrane.
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A Stochastic 2D Model of Actin-Based Protrusion Recapitulates Light and Electron Microscopy Data To gain a quantitative understanding of the experimental data we built on earlier work by Maly and Borisy (2001) and Weichsel and Schwarz (2010) and developed a stochastic model of lamellipodial network growth. We formulated a two-dimensional (2D) model taking into account filament elongation and Arp2/3-mediated (70 ) nucleation at the leading front. Elongation is terminated by capping whenever filaments detach from the membrane and thereby leave the zone in which they are protected from capping (by elongation factors like VASP or formins). Filaments push the membrane forward according to a force-velocity relation based on thermal fluctuations as described in Dickinson (2009) and Mogilner and Oster (1996, 2003) (for details see STAR Methods and Tables S1 and S2). Here, network geometry dictates that increased protrusion velocity (as caused by decreased load) rapidly decreases filament density in an angle-dependent manner: A filament growing at an angle 4 has to polymerize with ð1=cos4Þ the speed of the advancing membrane in order to keep contact with the membrane. Hence, with increasing protrusion speed filaments growing at higher angles will lag behind the leading edge and therefore detach from the membrane where they are protected from capping (Figures 6A, 6B, S7D, and S7E). Consequently, higher angle filaments will be capped at higher rates and the family of low angle filaments (and their accompanying ±70 side branches) will outcompete the ±35 network. Slowing down the membrane has the opposite effect: More filaments at higher angles are able to catch up with the membrane, leading to a denser network consisting of filaments growing at a broad range of angles. The stochastic simulation is able to reproduce the correlative electron tomography findings of filament orientation and density by using a sharp decrease from 300 pN as force input. 300 pN were taken as a realistic force reported for steady-state migrating fish keratocytes (Lieber et al., 2013). Together, our stochastic simulation faithfully reproduced both kinetics and geometry of network parameters upon externally induced changes in load (Figures 6C, 6D, S7A, and S7B; Tables S1 and S2; Movie S5). Next we wanted to test if the stochastic simulation can produce the co-fluctuations of protrusion speed, actin density and projected area as we observed them in our light microscopy experiments in unperturbed migrating keratocytes (Figure 1). The amount of decrease in tension necessary to obtain the correct response at the filament level in the correlated experiments was used as a scaling factor to relate membrane tension to projected area. The experimental decrease and increase of membrane tension (Figure 2) could be recapitulated by simulating representative protrusion events of 10 s with increasing or decreasing tension (Figure S7C). By using the measured temporal fluctuations in projected cell area (Figure 1D) with the obtained scaling factor as a proxy for tension we could recapitulate the positive correlation of membrane tension and actin density as well as the negative correlations of membrane tension, actin density, and protrusion speed (Figures 7A and 7B). This showed that our filament-level model is able to recapitulate lamellipodial dynamics as we observed them at the cellular scale and using fluorescent markers. Our model predicts that keratocytes migrating on an adhesive substrate in 2D exhibit a
canonically 70 branched network in their lamellipodia the vast majority of the time. This is consistent with the measurements on steady state migrating keratocytes. However, with a low frequency, periods of perpendicular dominated networks (with an order parameter above 0) during phases of high protrusion speed are predicted (Figure 7C). DISCUSSION We demonstrate that the lamellipodial actin network undergoes profound structural changes when filaments pushing against the membrane experience varying load. These changes happen at short time-scales and can be a sheer consequence of the geometrical and kinetic properties of Arp2/3-nucleated branched networks. The key-ingredients of the mechanism we propose are the force-velocity relation determining filament elongation rates, the geometry of protruding networks, and the protection from capping near the membrane. Filaments polymerize faster when growing against decreased loads (here, the load is due to membrane tension). With decreasing load the expanding network reaches a speed, where filaments growing perpendicularly to the membrane gradually ‘‘outrun’’ filaments pushing at steeper angles because these have to travel a longer distance. Hence, these steeper-angle filaments are eliminated, because they lose contact with the membrane, where the polymerizing factors (VASP and formins) protect them from capping proteins. If the perpendicular filaments originate from ‘‘noise’’ in the angular distributions of a purely Arp2/3-nucleated network or if they represent a family nucleated by other factors like formins remains open, as ‘‘non-branch’’ pointed ends in the tomograms might not only represent Arp2/3-independent filaments but could also be Arp2/3 nucleated, but later severed or unbranched. Whereas this proposed mechanism will operate in any Arp2/ 3-nucleated process like endocytosis, phagocytosis, vesicle trafficking, intracellular pathogen transport, dendritic spine formation, etc., its role in cell motility is most intuitive. Unlike in the idealized keratocyte system, cells migrating in physiological environments will almost never experience mechanically isotropic environments. First, a cell usually pushes against an interstitium with inhomogeneous viscoelastic features, and here it has been shown that lamellipodia can increase their force when counter-resistance increases locally (Heinemann et al., 2011; Prass et al., 2006). Second, the adhesiveness of the substrate is often variable (e.g., in any 3D fibrillar environment). As the actin network slides back in areas of the cell, which are less coupled to the substrate, the load experienced by filaments polymerizing against the leading membrane will be reduced. It has been shown that such local inhomogeneities can be compensated by adaptations in polymerization speed, which ‘‘fill up the space’’ resulting from retrograde slippage of the network (Barnhart et al., 2011; Graziano and Weiner, 2014; Renkawitz et al., 2009). Thus, for a cell migrating through a complex 3D environment, the local adaptations we describe serve to keep the cell edge and its actin network coherent. This geometrical adaptation might provide another remarkable feature: wherever two adjacent regions of the network show differential flow speed, the faster network will be less crosslinked to the neighboring, slower, regions, because it is less interconnected by branches. This might
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Figure 6. Stochastic Model Recapitulating Light and Electron Microscopy Results (A) The critical angle at which filaments are not able to keep up with the advancing membrane, 4c , depends on the maximal polymerization rate, set here as 450 nm/s, and the angle of the filament toward the membrane, 4 (black line). A drop in external force leads to a transient increase in protrusion speed leading to a decrease in 4c and a subsequent, angle-dependent decrease in filaments (red line). Force increase causes a decrease in protrusion speed, leading to an increase in 4c and filament density (blue line). (B) Scheme of filaments growing at steady state at intermediate load (middle, gray arrow). Following an increase in load (top, blue arrow) filament density increases and the angle distribution broadens, whereas at a decrease in load (bottom, red arrow) filaments at a higher angle 4i are preferentially capped and density decreases. (C) Visualization of model results with filaments shown in green, barbed ends in red, and pointed ends in blue. Visualization of model results in a regime with force increase (top) and decrease (bottom), D F, at around 900 nm. Subsequent panels are aligned next to the respective force regimes. (D) Filament numbers, barbed, and pointed end density quantified for the three conditions like in Figures 3, 4, and 5. In the unperturbed situation with fixed external force, F, the network assumes a steady state with balanced filament density, branching, and capping. After a decrease in F, capping increases, nucleation decreases, and the network is thinned out, whereas force increase causes a nucleation peak and an increase in filament density. For all graphs, mean and SD for an average of 20 runs are shown. See also Figure S7, Tables S1 and S2, Movie S5, and the STAR Methods.
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Figure 7. The Stochastic Model Recapitulates Cell Migration Parameters of Fish Keratocytes (A) Example of temporal fluctuations in lifeact:GFP intensity, area, and protrusion speed for the cell shown in Figure 1 compared to the migration parameters produced by a simulation run with the projected cell area as scaled tension input. (B) Average of temporal cross-correlation functions of the simulations obtained with the projected cell area of the 21 migrating keratocytes shown in Figure 1. Temporal correlation peaks at time lag zero between lifeact:GFP intensity, projected cell area, and protrusion match the ones observed in vivo. Mean and SEM are shown. (C) Histogram of the order parameters obtained for the 21 steady-state migrating keratocytes. The stochastic model predicts cells migrating with a predominantly negative order parameter, with only occasional switches to positive order parameter values as cells undergo rapid shrinkage and a transient burst in protrusion speed. See also Figure S7.
potentially allow the two networks to slide relative to each other and might explain how lamellipodia or actin cortices can harbor differentially flowing populations of actin as shown previously (Ponti et al., 2004; Vitriol et al., 2015). In our work we used manipulations of membrane tension as a proxy for altered load. For the protruding lamellipodium membrane tension likely plays the same mechanical role as an external load. However, lateral membrane tension cannot act locally as it equilibrates instantaneously across the cell surface (Diz-Mun˜oz et al., 2013; Sens and Plastino, 2015). Based on this potential signaling function it has been proposed that membrane tension acts as a global long-range regulator of cell polarity. Whenever lamellipodial actin stretches the leading membrane it suppresses polymerization at the sides and the trailing edge. Here, polymerization will stall under high membrane tension as it is not boosted by the biochemical enhancers
driving the lamellipodium (Houk et al., 2012). This mechanism to suppress competing protrusions has a pure mechanical component (filaments stall under high load) but is also complemented by a signaling mechanism, where membrane tension triggers mTORC2 signaling, which in turn dampens polymerization (DizMun˜oz et al., 2010). Although this mechanism seems to counteract the geometrical adaptations we describe, it likely acts at much higher force regimes, where filaments ultimately fail to protrude the membrane. We think that the geometrical rules we describe here represent the most basic regulatory framework of Arp2/3-mediated actin polymerization. They are a fundamental feature of the network structure, which demonstrates that mechanosensitivity is inherently built into the architecture of branched networks. Additional layers of regulation by chemoattractant-sensing and mechanosensitive signaling pathways will act on top of this basic
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mechanism and might add modulations e.g., by altering the filament distribution via different nucleators and elongators. STAR+METHODS Detailed methods are provided in the online version of this paper and include the following: d d d d
d
KEY RESOURCES TABLE CONTACT FOR REAGENT AND RESOURCE SHARING EXPERIMENTAL MODEL AND SUBJECT DETAILS B Zebrafish METHOD DETAILS B Keratocyte preparation B mRNA injection B Transfection B Membrane dye B Live cell imaging B Micromanipulators B Osmotic treatment B Tether pulling experiments and force measurements B Image analysis B Electron tomography B Actin filament tracking and analysis B Correlated light and electron microscopy B Stochastic Simulation QUANTIFICATION AND STATISTICAL ANALYSIS
SUPPLEMENTAL INFORMATION Supplemental Information includes seven figures, two tables, and five movies and can be found with this article online at http://dx.doi.org/10.1016/j.cell. 2017.07.051. AUTHOR CONTRIBUTIONS Conceptualization: J.M. and M.S.; Methodology: J.M., G.S., A.D.L., K. Keren, and R.H.; Software: C.W., K. Kruse, and C.S.; Formal Analysis: J.M., G.S., and R.H.; Investigation: J.M., M.N., I.d.V., and A.D.L.; Writing – Original Draft: J.M. and M.S.; Writing – Review & Editing: all authors; Visualization: J.M. and G.S.; Project Administration: M.S.; Funding Acquisition: M.S. ACKNOWLEDGMENTS We thank the scientific support facilities of IST Austria and Biocenter Vienna for technical support and CP Heisenberg for fish lines. This work was supported by the European Research Council (ERC StG 281556), a grant from the Austrian Science Foundation (FWF) (to M.S.), and a grant from Vienna Science and Technology Fund (WWTF) (No. LS13-029 to C.S. and M.S.). Research in the lab of K. Keren was supported by a grant from the United States-Israel Binational Science Foundation (No. 2013275 with Alex Mogilner). Received: January 11, 2017 Revised: May 21, 2017 Accepted: July 31, 2017 Published: August 31, 2017 REFERENCES Barnhart, E.L., Lee, K.C., Keren, K., Mogilner, A., and Theriot, J.A. (2011). An adhesion-dependent switch between mechanisms that determine motile cell shape. PLoS Biol. 9, e1001059.
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Please cite this article in press as: Mueller et al., Load Adaptation of Lamellipodial Actin Networks, Cell (2017), http://dx.doi.org/10.1016/ j.cell.2017.07.051
Lou, S.S., Diz-Mun˜oz, A., Weiner, O.D., Fletcher, D.A., and Theriot, J.A. (2015). Myosin light chain kinase regulates cell polarization independently of membrane tension or Rho kinase. J. Cell Biol. 209, 275–288.
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Maıˆtre, J.L., Berthoumieux, H., Krens, S.F.G., Salbreux, G., Ju¨licher, F., Paluch, E., and Heisenberg, C.P. (2012). Adhesion functions in cell sorting by mechanically coupling the cortices of adhering cells. Science 338, 253–256.
Schaus, T.E., Taylor, E.W., and Borisy, G.G. (2007). Self-organization of actin filament orientation in the dendritic-nucleation/array-treadmilling model. Proc. Natl. Acad. Sci. USA 104, 7086–7091.
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Schindelin, J., Arganda-Carreras, I., Frise, E., Kaynig, V., Longair, M., Pietzsch, T., Preibisch, S., Rueden, C., Saalfeld, S., Schmid, B., et al. (2012). Fiji: an open-source platform for biological-image analysis. Nat. Methods. 9, 676–682.
Manhart, A., Oelz, D., Schmeiser, C., and Sfakianakis, N. (2015). An extended filament based lamellipodium model produces various moving cell shapes in the presence of chemotactic signals. J. Theor. Biol. 382, 244–258. Mastronarde, D.N. (2005). Automated electron microscope tomography using robust prediction of specimen movements. J. Struct. Biol. 152, 36–51. Mogilner, A., and Keren, K. (2009). The shape of motile cells. Curr. Biol. 19, R762–R771. Mogilner, A., and Oster, G. (1996). Cell motility driven by actin polymerization. Biophys. J. 71, 3030–3045. Mogilner, A., and Oster, G. (2003). Force generation by actin polymerization II: the elastic ratchet and tethered filaments. Biophys. J. 84, 1591–1605. Narita, A., Mueller, J., Urban, E., Vinzenz, M., Small, J.V., and Mae´da, Y. (2012). Direct determinaftion of actin polarity in the cell. J. Mol. Biol. 419, 359–368. Parekh, S.H., Chaudhuri, O., Theriot, J.A., and Fletcher, D.A. (2005). Loading history determines the velocity of actin-network growth. Nat. Cell Biol. 7, 1219–1223. Pollard, T.D. (2007). Regulation of actin filament assembly by Arp2/3 complex and formins. Annu. Rev. Biophys. Biomol. Struct. 36, 451–477. Pollard, T.D., and Cooper, J.A. (2009). Actin, a central player in cell shape and movement. Science 326, 1208–1212. Ponti, A., Machacek, M., Gupton, S.L., Waterman-Storer, C.M., and Danuser, G. (2004). Two distinct actin networks drive the protrusion of migrating cells. Science 305, 1782–1786. Prass, M., Jacobson, K., Mogilner, A., and Radmacher, M. (2006). Direct measurement of the lamellipodial protrusive force in a migrating cell. J. Cell Biol. 174, 767–772.
Sens, P., and Plastino, J. (2015). Membrane tension and cytoskeleton organization in cell motility. J. Phys. Condens. Matter 27, 273103. Sivaramakrishnan, S., and Spudich, J.A. (2009). Coupled myosin VI motors facilitate unidirectional movement on an F-actin network. J. Cell Biol. 187, 53–60. Small, J.V., Herzog, M., and Anderson, K. (1995). Actin filament organization in the fish keratocyte lamellipodium. J. Cell Biol. 129, 1275–1286. Svitkina, T.M., Verkhovsky, A.B., McQuade, K.M., and Borisy, G.G. (1997). Analysis of the actin-myosin II system in fish epidermal keratocytes: mechanism of cell body translocation. J. Cell Biol. 139, 397–415. Theriot, J.A., and Mitchison, T.J. (1991). Actin microfilament dynamics in locomoting cells. Nature 352, 126–131. Vinzenz, M., Nemethova, M., Schur, F., Mueller, J., Narita, A., Urban, E., Winkler, C., Schmeiser, C., Koestler, S.A., Rottner, K., et al. (2012). Actin branching in the initiation and maintenance of lamellipodia. J. Cell Sci. 125, 2775–2785. Vitriol, E.A., McMillen, L.M., Kapustina, M., Gomez, S.M., Vavylonis, D., and Zheng, J.Q. (2015). Two functionally distinct sources of actin monomers supply the leading edge of lamellipodia. Cell Rep. 11, 433–445. Weichsel, J., and Schwarz, U.S. (2010). Two competing orientation patterns explain experimentally observed anomalies in growing actin networks. Proc. Natl. Acad. Sci. USA 107, 6304–6309. Wilson, C.A., Tsuchida, M.A., Allen, G.M., Barnhart, E.L., Applegate, K.T., Yam, P.T., Ji, L., Keren, K., Danuser, G., and Theriot, J.A. (2010). Myosin II contributes to cell-scale actin network treadmilling through network disassembly. Nature 465, 373–377.
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STAR+METHODS KEY RESOURCES TABLE
REAGENT or RESOURCE
SOURCE
IDENTIFIER
Chemicals, Peptides, and Recombinant Proteins Dulbecco’s Modified Eagle’s Medium
GIBCO
Cat# 10566-016
L-15 Leibovitz medium
Sigma
Cat# L1518
PCR purification kit
Qiagen
Cat# 28106
SP6 mMessage mMachine kit
Invitrogen
Cat# AM1340
Fugene 6
Roche
Cat# 11814443001
Cell Mask Orange
Molecular Probes
Cat# C10045
PLL(20)-g[3.5]-PEG(2)/PEG(3.4)-RGD
Surface Solutions
N/A
PLL-PEG-RGD
Surface Solutions
N/A
Zebrafish line: Tg(actb1:lifeact-GFP)
Gift from Heisenberg Laboratory (IST Austria) Behrndt et al., 2012
N/A
Zebrafish line: wt AB
Gift from Heisenberg Laboratory (IST Austria)
N/A
Zebrafish line: wt TL
Gift from Heisenberg Laboratory (IST Austria)
N/A
pEGFP-actin
Clontech
Cat# 6084-1
zf actin:GFP
This paper
N/A
MATLAB 2015b
The MathWorks
https://ch.mathworks.com/products/matlab
Fiji 1.50d
Schindelin et al., 2012
https://fiji.sc/
Ilastik 1.1.5
The ilastik Team
http://ilastik.org/index.html
SerialEM 3.x
Mastronarde, 2005
http://bio3d.colorado.edu/ftp/SerialEM/
IMOD 4.7
Kremer et al., 1996
http://bio3d.colorado.edu/imod/
Python 2.7
Python Software Foundation
https://www.python.org/download/releases/2.7/
Prism 5.0b
GraphPad
https://www.graphpad.com/scientific-software/ prism/
LabView
National Institutes
http://www.ni.com/en-us/shop.html
NIS - Elements AR 3.2
Nikon Instruments
https://www.nikoninstruments.com/en_EU/ Products/Software/NIS-Elements-AdvancedResearch
Stochastical Simulation – Code repository
Authors of this study
https://github.com/gszep/lamellipodium
200mesh HF15 Gold finder grids
Maxtaform
Cat# G245A
200mesh hexagonal gold grids
Agar Scientific
Cat# AGG2450A
Experimental Models: Organisms/Strains
Recombinant DNA
Software and Algorithms
Other
CONTACT FOR REAGENT AND RESOURCE SHARING Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Michael Sixt ([email protected]). EXPERIMENTAL MODEL AND SUBJECT DETAILS Zebrafish Wild-type zebrafish lines AB and TL and the transgenic line Tg(actb1:lifeact-GFP) (Behrndt et al., 2012) were housed and bred in the IST Austria fish facility. Zebrafish were maintained at 28 C and embryos collected according to standard fish laboratory protocol. Animals were sacrificed for experiments at 6 months to about 1.5 years of age regardless of sex.
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Primary keratocyte cultures for these experiments were prepared from the Central American cichlid Hypsophrys Nicaraguensis as described previously (Lieber et al., 2013). METHOD DETAILS Keratocyte preparation Keratocytes were prepared from adult zebrafish scales (plucked from sacrificed animals) and washed three times with Dulbecco’s Modified Eagle’s Medium (DMEM) (GIBCO). Scales were incubated in START medium (Small et al., 1995) at room temperature for one or two days to allow keratocytes to migrate off in a monolayer. The monolayer was then washed three times in PBS, incubated for 40min with Running Buffer (Small et al., 1995) with 1mM EGTA and the scales removed. The remaining adherent cells were washed three times with PBS, trypsinized for 2min with 0.25% Trypsin-EDTA (GIBCO) at room temperature, resuspended in the same volume of trypsin inhibitor (Sigma) and transferred to a coverslip or electron microscopy grid. After allowing the cells to adhere for 40min the medium was changed to START medium, the cells were incubated for another 40min before live cell imaging or fixation for electron microscopy. mRNA injection To produce synthetic mRNA, zf actin:GFP was linearized by double strand cutting with NotI, purified with a PCR purification kit (Qiagen) and mRNA was synthesized using the SP6 mMessage mMachine Kit (Ambion). 50pg of mRNA were injected in freshly harvested embryos. Zebrafish embryonic keratocytes were prepared from these embryos 1 day post fertilization as described elsewhere (Lou et al., 2015). Transfection The plasmid used for transfection was pEGFP-actin (Clontech). Transfection was performed by mixing 100ml OPTIMEM, 6ml Fugene 6 (Roche) and 1mg plasmid DNA for 30min and adding it to the cells in L-15 Leibovitz medium (Sigma) for 5h. Then the medium was changed to START medium again and the transfected cells were re-plated onto coverslips as described above. Membrane dye As a membrane dye for negative controls CellMask Orange plasma membrane stain (Molecular probes) was used according to the manufacturer’s protocol for live, adherent cell cultures with the following modifications: Keratocytes seeded on glass coverslips were incubated at room temperature for 15min, washed five times with PBS and imaged immediately in START medium. Live cell imaging All live cell imaging was performed at room temperature in START medium. Confocal microscopy was performed with an inverted microscope (Zeiss), equipped with a Spinning disk system (Yokogawa X1, iXon897, Andor), a C-Apochromat 63x/1.2 Water Objective (Zeiss), a motorized stage and 488nm and 561nm lasers. While imaging with this microscope, laser ablations of the trailing edge were performed with a 355nm laser cutter. For widefield imaging an inverted widefield microscope (Nikon), equipped with 60x/1.4 and 100x/1.4 Apochromat Oil Objectives, a motorized stage and a light source with flexible excitation bands (Lumencor) was used. Micropipette aspiration experiments were performed on an upright confocal microscope (SP5, Leica), equipped with HCX 63x/1.4 Apochromat Oil Objective (Leica), a motorized stage and a 488nm laser line. The time interval was 0.2 s-1.0 s. Micromanipulators Micropipettes were produced from 1.0mm diameter glass capillaries as described before (Maıˆtre et al., 2012). For cell manipulations negative pressures from 10mbar to 40mbar were used for aspirating the cell membrane and 0-2mbar of positive pressure to release the cell again. For correlated live and electron microscopy cell membrane was aspirated with 30mbar for about 5 s and extracted and fixed about 3 s after release from the micropipette. The same micromanipulator system was used to induce rapid cell shrinking by carefully detaching part of the cell from the underlying substrate. In this case, the cell was fixed on the grid immediately afterward and prepared for electron microscopy as described below. Osmotic treatment For experiments with changing osmotic pressure, lifeact:GFP expressing keratocytes were subjected to repeated additions of 50ml 0.2M sucrose in START medium and 50ml double distilled water to a starting volume of 300ml START medium. Tether pulling experiments and force measurements Primary keratocyte cultures for these experiments were prepared from the Central American cichlid Hypsophrys Nicaraguensis as described previously (Lieber et al., 2013). One day old cultures were replated and cultured at room temperature in Leibovitz’s L-15 media (GIBCO BRL, Grand Island, NY), supplemented with 14.2 mM HEPES pH 7.4, 10% Fetal Bovine Serum (Invitrogen, Grand Island, NY), and 1% antibiotic-antimycotic (GIBCO BRL). Tether force measurements were carried out as in (Lieber et al., 2013) with a laser tweezers system (PALM microtweezers, Carl Zeiss MicroImaging GmbH, Jena, Germany) using a 63 3 1.2 NA water immersion Cell 171, 1–13.e1–e6, September 21, 2017 e2
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objective and a motorized stage (Ludl Electronic Products, Hawthorne, NY) on an inverted microscope (Axiovert 200M, Zeiss, Jena, Germany). Trapping was done with a 3W 1064nm Nd:YAG laser focused to a diffraction limited spot, and imaging by bright field was done simultaneously. Tether force measurements on cells were done by attaching a Concanavalin A coated bead to the rear part of the cell body and pulling it away by moving the stage. The measured tether force was corrected for the contribution of the dynamic friction due to stage movement, when relevant, as in (Lieber et al., 2013). A membrane tether was held continuously during spontaneous instances of abrupt rear retraction, providing a read out of the changes in the tether force that accompany the large changes in the projected cell area during the retraction event. Membrane tension values T were calculated from the tether force FT using, T = ðFT2 =8p2 BÞ, where B = 0:14pN,mm is the measured bending modulus of the membrane in keratocytes (Lieber et al., 2013). Image analysis Time-lapse images of migrating keratocytes were analyzed in Fiji by first defining the projected cell area by applying a Gaussian blur to the raw image stack and then threshold it to obtain a stack of binary images. The same binary image was used to define a 1.09mm wide region along the leading edge as the lamellipodial region of interest. An optical flow analysis based on the Horn-Schunck method was then used to calculate the optical flow between the binary mask frames. Both the original image stack and the optical flow data were stabilized using a custom-made image-stabilizing MATLAB algorithm. The resulting stabilized stacks were further analyzed by skeletonizing the 1.09mm wide lamellipodium region for each stack slice and plotting both the gray value of the original image and the amount of shift determined by the optical flow analysis along the whole length of the leading edge for every time step. A custom-made MATLAB program was used for this step. The resulting 2D heatmaps of lifeact:GFP, actin:GFP or membrane dye intensity and protrusion were averaged along the length of the leading edge and plotted against time and the whole images were correlated to each other and the projected area. For cross correlation analysis the first derivative of the lifeact:GFP, actin:GFP or membrane dye intensity and protrusion heatmaps as well as the projected cell area were taken and the cross covariance function of MATLAB was used normalized so that the auto-covariance at zero lag equaled 1. For analysis of signal flow within the lamellipodium 1.09mm wide bands were eroded from the leading edge in consecutive steps and the resulting bands were used to quantify the lifeact:GFP intensity in adjacent parts further removed from the leading edge. The resulting heatmaps were correlated to each other using the same procedure as described above and the resulting peaks were multiplied by the speed of the respective cell to obtain the distance lag. The calculated distance was plotted against the known distance between the eroded bands. Electron tomography Cells were grown on 200mesh HF15 Gold finder grids (Maxtaform) and 200mesh hexagonal gold grids (Agar Scientific) coated with 2% Formvar and a 2nm carbon layer and incubated with 0.5mg/ml PLL(20)-g[3.5]-PEG(2)/PEG(3.4)-RGD (Surface Solutions) for 50min. Extraction and fixation was performed using 0.25% glutaraldehyde and 0.5% Triton X-100 in Cytoskeleton Buffer (10mM MES buffer, 150mM NaCl, 5mM EGTA, 5mM glucose, 5mM MgCl2, pH 6.1) for 1min at room temperature. The grids were then transferred to 2% glutaraldehyde in Cytoskeleton buffer for 10min and kept in another dish with 2% glutaraldehyde in Cytoskeleton buffer at 4 C until staining for electron microscopy. For staining, grids were carefully blotted with filter paper from the bottom and immediately stained with 70ml 4% sodium silicotungstate supplemented with BSA-gold fiducials from a gold stock as described before (Vinzenz et al., 2012). Double axis tilt series with typical tilt angles from 65 to +65 and 1 increments following the Saxton scheme were acquired on an FEI Tecnai G20 transmission electron microscope operated at 200kV equipped with a Eagle 4k HS CCD camera (Gatan). The automated acquisition of double axes tilt series was driven by SerialEM 3.x (Mastronarde, 2005). The defocus was set to 5mm for all acquisitions and the primary on-screen magnification was 25,000x. For montage tomograms montages of 2x2 or 3x2 images were acquired for each tilt angle. Back-projection of the tilt series was performed using the IMOD package 4.7 with gold particle fiducials as markers and high-pass filtering of the final reconstruction (Kremer et al., 1996). A typical tomogram comprised 50-70 stacks of 0.92nm and an area of 1.9mm x 1.9mm. The montage tomograms had dimensions of 3.1mm x 3.1mm and 4.0mm x 3.1mm, respectively. Actin filament tracking and analysis Filaments were quantified in three different ways: Manual tracking of the region shown in Figure S6B using 3dmod software. Automated tracking using a MATLAB-based tracking algorithm (Winkler et al., 2012). Computerized segmentation of actin filaments by the pixel classification function of ilastik 1.1 was used to quantify actin filament density in the correlated tomograms (Summarized in Figures S6A–S6C) (Kreshuk et al., 2011). The manually and automatically tracked filaments were further analyzed in the following way. In the tomogram montages the recorded filaments were divided in 106.15nm wide distance bins spanning from the leading edge up to 2.8mm toward the back of the lamellipodium (shown in Figures S4D and S6E). For the single tomograms of actin filament density steps two regions of 300nm each before and after the step were used. In automated tomograms filaments shorter than 55nm were excluded from analysis. Filament numbers indicate the number of individual filaments crossing a plane in the middle of the respective analysis region. Pointed and barbed ends were defined as ends of filaments furthest and closest from the leading edge, which was clearly visible in every
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case, respectively. Filament angles were defined as the angle subtended between a filament and the leading edge in the plane of the flat lamellipodium, with 0 meaning a filament growing perpendicularly toward the leading edge. Angles were weighted by the total length of the filaments growing in that direction. The density in the different angle bins was taken as number of filaments growing at that angle normalized by the size of the angle bin. As a global measure of filament architecture an order parameter was defined as: ðFilaments 10 to + 10 Þ ðFilaments 40 to 20 + Filaments + 20 to + 40 Þ=2 ðFilaments 10 to + 10 Þ + ðFilaments 40 to 20 + Filaments + 20 to + 40 Þ=2 (Weichsel and Schwarz, 2010). Correlated light and electron microscopy For correlated light and electron microscopy 200mesh HF15 Gold Finder grids were coated with 0.5mg/ml PLL-PEG-RGD (Surface Solutions) for 50min. Then keratocytes were allowed to adhere for z1h, imaged directly on the grid with an inverted confocal spinning disk microscope and either aspirated for about 4 s and then released or partly detached from the grid using micromanipulators as described above. Immediately after release from the micropipette or induction of a rapid shrinking event the cells were fixed by taking off the medium and adding the extraction and fixation buffers. To find the correlated cells back, the grids were first completely mapped by using the navigator map function of SerialEM on an FEI Tecnai G20 transmission electron microscope. Once the relevant grid square was found, high magnification montages and tomograms of the transition zones were acquired. Stochastic Simulation Stochastic 2D models of actin-based lamellipodial protrusion have been proposed in the past to show the self-organization of orientation patterns (Maly and Borisy, 2001; Schaus et al., 2007; Weichsel and Schwarz, 2010). These models considered network steady state analysis and simulations with fixed velocity. We build on the published models to include transient responses of leading edge velocity and network organization due to changing external forces exerted on the filaments. This simulation was implemented in python 2.7 and has been made publicly available at https://github.com/gszep/lamellipodium. We formulate a 2D model, where each actin filament is rigid and immobile. The first assumption can be justified by electron tomograms, where mostly straight filaments are observed. Immobility of filaments has to be understood relative to each other, which still permits a coordinated retrograde flow. Thus the state of the network close to the leading edge at time t can be described by the set F ðtÞ with NðtÞ number of growing barbed ends, each having 2D position vectors xðtÞ = ðxðtÞ; yðtÞÞ and constant orientations u. o n (1) F ðtÞ = ðxðtÞ; uÞ1 ; .; ðxðtÞ; uÞNðtÞ u encodes the direction and magnitude ju j = d of elongation with the addition of one actin monomer. The plasma membrane is modeled as a flat edge parallel to the y -axis at position pðtÞ along the x -axis. With all filaments only pushing from one side, the resultant protrusion velocity vðtÞ is positive in the x -direction. Periodic boundary conditions are imposed in the interval 0%yðtÞ < L along the y -axis. We shall describe elongation, branching, and capping events at a barbed end at position x – dropping time variable for convenience – at time t as Poisson processes with rates lðx; tÞ; bðx; tÞ and kðx; tÞ respectively. This means that in a sufficiently small time step from t to t + Dt, the filament will experience one of these events given by rate uðx; tÞ with probability uðx; tÞ Dt. We introduce a useful notation nðx; t j uÞ which is a Boolean variable that tells us whether an event with rate uðx; tÞ happened or not at a barbed end at position x and time t. Elongation happens in the strip of width w behind the leading edge position pðtÞ with the rate l0 and zero otherwise. This assumption is motivated by the observation that most growth happens at the leading edge. l0 pðtÞ w < xðtÞ < pðtÞ lðx; tÞ = (2) 0 elsewhere An elongation event for a particular barbed end means xðt + DtÞ = xðtÞ + u. There are NðtÞ barbed ends, meaning we have to check events at each one of them. Branching occurs at the leading edge with a rate that depends on the linear density of nucleation factors aðtÞ such as Arp2/3 at the leading edge (Weichsel and Schwarz, 2010). Let a0 be the rate of activation that leads to branching. a0 aðtÞ pðtÞ w < xðtÞ < pðtÞ bðx; tÞ = 0 elsewhere Consider the finite availability of nucleation factors and activation being the rate-limiting step in branching new filaments. Let DðtÞ be the linear density of barbed ends along the leading edge, which increases with branching rate a0 aðtÞ and decreases with possibly time dependent capping rate kðtÞ: In addition, we know that there is a finite positive rate of arrival b0 of nucleation factors at the leading edge coming from a reservoir. Finally, nucleation factors are depleted when branching occurs, with a rate a0 DðtÞ depending of barbed end concentration.
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Please cite this article in press as: Mueller et al., Load Adaptation of Lamellipodial Actin Networks, Cell (2017), http://dx.doi.org/10.1016/ j.cell.2017.07.051
vt DðtÞ = a0 aðtÞDðtÞ kðtÞDðtÞ
vt aðtÞ = b0 a0 aðtÞDðtÞ Assuming that the arrival of nucleation factors at the leading edge is faster than branching or capping events, we can employ the quasi-steady state assumption (Manhart et al., 2015), setting vt aðtÞ = 0. Rearranging for the concentration aðtÞ; we can finally write: 8 > < b0 pðtÞ w < xðtÞ < pðtÞ bðx; tÞ = DðtÞ (3) > : 0 elsewhere Branching add a new filament ðx0 ðt + DtÞ; u0 Þ to the frontier at the position of the barbed end x0 ðt + DtÞ = xðtÞ of the mother filament. The orientation is rotated by a random branching angle q sampled from a distribution. This can be written as a rotation matrix RðqÞ acting on the mother filament orientation u0 = RðqÞu. The branching angle distribution Bðq j m; sÞ is the sum of two Gaussians with respective means at ± m and standard deviations s taken from electron microscopy data. The daughter filament is required to be oriented toward the leading edge, meaning that the random choice might have to be repeated, until this requirement is fulfilled. This model neglects that there is a preferred distance between branches, due to the helical structure of actin filaments (Vinzenz et al., 2012). Capping irreversibly removes a barbed end from the frontier. We assume there is a low capping rate k0 within width w behind the leading edge, and a high rate k1 further behind, leading to filaments being immediately capped outside this zone. 8 < k0 pðtÞ w < xðtÞ < pðtÞ xðtÞ < pðtÞ w (4) kðx; tÞ = k1 : 0 elsewhere Actin filaments polymerizing against the plasma membrane exert a force that in turn sets the protrusion velocity. It has to balance the restricting force due to membrane tension. We assume an equal distribution of the total force among the pushing filaments and the absence of retrograde flow as observed in keratocytes migrating on serum-coated glass coverslips. We use a force-velocity relation based on thermal fluctuations of the membrane and/or the filaments, as is appropriate for the Brownian ratchet model (Lee et al., 2001; Mogilner and Oster, 1996) of polymerization, but also for other established models like the tethered ratchet or end-tracking motors (Dickinson, 2009). This leads to the following rule for updating the position of the leading edge from small time steps: pðt + DtÞ = pðtÞ + vðtÞDt
vðtÞ = l0 d e
dFðtÞ kB T DðtÞ
(5)
Here the maximum possible speed is equal to the maximal polymerization speed l0 d of unobstructed filaments. By FðtÞ we denote the membrane force per leading edge length, DðtÞ the linear density of barbed ends and kB T is the thermal energy. The experiments with a rapid decrease of membrane tension and subsequent return to a steady protruding state are approximated by a stepwise decrease DF in force density at time t for a duration Dt, followed by a stepwise increase back to original force density F0 . F0 DF t < t < t + Dt FðtÞ = (6) elsewhere F0 The initial barbed end positions are sampled from a uniform distribution within the polymerization zone. The orientations are sampled from a uniform distribution along a half circle of radius d. The density DðtÞ is updated before each time step and stored for the sampling of branching events and for updating the velocity of the leading edge. Then we iterate through all binding sites in the frontier, checking first for capping events, then branching, and finally elongation. Finally the position of the membrane is updated, along with the elapsed time. The process is repeated until final simulation time T0 . First the simulation is run for the above parameters except we set DF = 0. The initialization is uniform. Beyond a time T0 10s a steady state in both filament density and angular distribution with respect to the membrane is reached. Using the final state of a previous run as an initial state for the next run, we simulate 20 runs each of time T0 = 10s. By recording all the history of barbed end movement during a run, we collect statistics at the end of each run. This way we end up with 20 data points per statistic, of which we return the mean and standard deviation to produce wild-type regime shown in Figures 6B–6D (middle), Figures S7A–7C (middle) and Movie S5 (first part).
e5 Cell 171, 1–13.e1–e6, September 21, 2017
Please cite this article in press as: Mueller et al., Load Adaptation of Lamellipodial Actin Networks, Cell (2017), http://dx.doi.org/10.1016/ j.cell.2017.07.051
This unperturbed wild-type steady state with orientation peaks at ± 35 is used as an initial condition for every run of the perturbed simulation. Setting DF = ± 270pN mm1 and executing another 20 runs, collecting statistics at the end of each run obtains the results shown in Figures 6B–6D (top and bottom), Figures S7A–7C (top and bottom) and Movie S5 (second and third part). To analyze if our stochastic model would be able to reproduce the correlations shown in Figure 1, we used the measured changes in projected cell area as input. Using the correlated cells shown in Figures 5 and S3 with known decreases in projected cell area and changes in network parameters, we scaled the changes in projected cell area by normalizing to the maximum value, subtracting a constant value and setting the mean to 300pN. The mean force of the first 2 s was used as constant tension for 5 s to let the simulation reach a steady state, before the force changes scaled from the projected area changes were used as input. The fluctuations in projected area from the 21 migrating keratocytes used for Figure 1 were then used as force input and the resulting output parameters averaged and cross-correlated to generate Figure 7. QUANTIFICATION AND STATISTICAL ANALYSIS MATLAB (MathWorks) and Prism (GraphPad) were used for statistical analysis. For live-cell imaging 21 and 7 individual cells were used for analysis of lifeact:GFP and membrane dye fluctuations, respectively. For membrane aspiration experiments 28 aspiration events in 13 individual cells were performed. For tomography experiments 4 wild-type tomography montages were used as well as 7 correlated shrinking events in 3 individual cells and one correlated aspiration event. Statistical parameters for individual experiments can be found within the figure legends. A paired t test was used for changes in median angle at the density step (Figure S5D). Pearson correlation was used for correlation analysis of measured distances from the leading edge to calculated distances (Figure S1F) and for angle to density decrease analysis (Figure S5E). A p value of < 0.05 was considered statistically significant.
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Supplemental Figures
Figure S1. Details of Quantification of Live Cell Imaging Parameters, Related to Figure 1 (A) Temporal fluctuations of lifeact:GFP signal, projected cell area and protrusion speed of the cell shown in Figure 1 are shown normalized from the maximum value to zero. The lifeact:GFP signal multiplied by the instantaneous speed is shown normalized from the maximum to zero as well.
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(B) Temporal crosscorrelation functions of Area – lifeact:GFP intensity, Area-protrusion speed and lifeact:GFP intensity – Protrusion speed for 21 individual cells are shown in black. Averaged cross-correlation functions from a spline fit to the combined single-cell cross-correlation functions are shown in purple (Area – lifeact:GFP intensity), green (Area – Protrusion speed) and yellow (lifeact:GFP intensity – Protrusion speed). (C) Confocal images of a migrating keratocyte expressing lifeact:GFP were analyzed using consecutive 1.09mm wide regions spanning the lamellipodium. (D) Resulting lifeact:GFP intensity maps are plotted against time. (E) Temporal cross correlation functions of region ‘1’ at the very front of the cell to consecutive regions are plotted as a function of time lag. (F) Time lag between peaks of the curves shown in H multiplied by cell velocity and resulting distances are plotted against distance between analyzed regions. Measured mean and s.d. of twelve cells are shown together with a linear regression (Pearson constant = 0.9997, p = 0.0003).
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Figure S2. Live Cell Imaging Controls with a Membrane Marker and actin:GFP, Related to Figure 1 (A) Example images of migrating keratocytes incubated with the membrane dye CellMask. (B and C) Temporal fluctuations of the resulting intensity maps are shown normalized as in Figure 1D (B) and as in Figure S1A (C). Neither an amplification of area fluctuations nor a correlation could be observed. (D) Resulting temporal cross correlation functions for eight individual cells are shown in black and averaged cross correlation in dark blue. The averaged cross correlation as mean with s.e.m. is shown in dark blue on the right. (E) Zebrafish keratocytes transfected with actin:GFP were analyzed in the same way as shown before for lifeact:GFP. (F) Temporal cross correlation analysis area – GFP signal intensity showing peaks at time lag zero for transfected cells expressing actin:GFP and lifeact:GFP. Additionally cells generated from actin:GFP microinjected Zebrafish embryos were analyzed and showed a positive cross correlation coefficient at time lag zero. Plot shows averaged cross correlation and s.e.m. for seven cells for both actin:GFP transfection and mRNA injection.
Figure S3. Membrane Tension Measurement by Tether Pulling and Membrane Tension Manipulation by Changing Osmotic Pressure, Related to Figure 2 (A) A migrating keratocyte was imaged with bright field microscopy and simultaneously a coated bead controlled by a laser tweezer was used to pull a membrane tether. (B) The measured tether force decrease correlated with rapid decreases in projected cell area. (C) A lifeact:GFP expressing keratocyte was imaged by confocal microscopy and subjected to rapid changes in osmotic pressure of the medium by alternating additions of 0.2M sucrose and pure water. (D) lifeact:GFP signal is negatively correlated with the osmolarity of the medium. When the pressure increases upon addition of 0.2M sucrose, lifeact:GFP signal drops, which is reversible upon restoring a lower osmotic pressure by addition of pure water.
Figure S4. Actin Network Parameters for Individual Tomogram Montages of Keratocyte Lamellipodia, Related to Figures 3 and 4 (A) Filament density, barbed and pointed ends for individual cells shown in Figure 3. Data for individual lamellipodia are shown in black together with average. (B) Filament densities growing at the indicated angle from the cell membrane in 212nm distance bins of the steady state lamellipodia shown in Figure 3. Mean and s.e.m. are shown. (C) Filament densities growing at the indicated angle from the cell membrane in 212nm distance bins of the correlated tomogram shown in Figure 4. The densities are shown as in Figure 4 beginning from toward the rear of the cell on the left until the leading edge on the right. (D) 5.5nm slice of a negatively stained electron tomogram montage showing the region marked by a red box in Figure 4A (left) and corresponding automatically tracked filaments shown color-coded according to their angle from the leading edge (right). The spatial bins used for quantification of network parameters in Figures 4 and S4C are also shown on the right.
Figure S5. Changes in Filament Parameters at a Decrease in Filament Density, Related to Figure 5 (A and B) Network structure analysis of seven lamellipodia tomograms in three correlated cells revealed consistent features at the point, where the actin density decreased due to the manipulation by the micropipette. Overview electron micrographs and 5.5nm tomogram slices are shown for all regions. (C) Averages of filament density, barbed and pointed ends and median angle from the cell edge showed the consistent changes at the density step. (D) Median angles of all analyzed regions are plotted for 300nm space bins before and after the decrease in actin filament density (right). (Paired t test, p = 0.0249). (E) Normalized ratio of filaments after density step to filaments before density step is plotted against the filament angle from the cell edge together with a linear regression curve. (Pearson constant, r = 0.936) Mean and s.e.m. are shown on all graphs.
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Figure S6. Quantification of Correlated Live Microscopy-Electron Tomography, Related to Figure 5 (A) A 5.5nm slice of the tomogram montage used for Figure 5 (left) is shown together with automated tracking results (middle and right). (B) Close-up of region containing the drop in filament density and change in actin architecture with filaments shown in green, barbed ends in red and pointed ends in blue. Manually tracked filaments, barbed and pointed ends of a region including the density step are shown. (C) Filament density quantified by manual and automated tracking, ilastik image analysis and the lifeact:GFP signal of the correlated cell shown in Figure 5. (D) Filament densities in 212nm distance bins growing at different angles toward the membrane. The densities are shown as in Figure 5 beginning from toward the rear of the cell on the left until the leading edge on the right. (E) 5.5nm slice of negatively stained electron tomogram montage showing region marked with red box in Figure 5A (left) and corresponding automatically tracked filaments shown color-coded according to their angle from the leading edge (right). Additionally, the spatial bins used for quantification of network parameters in Figures 5 and S6D are displayed on the left. The cell edge is seen on the right side.
Figure S7. Details of Stochastic Simulation, Related to Figures 6 and 7 The graphs in A–C are aligned as in Figure 6. (A) The temporal changes in filaments in three different angle bins are shown. The number of filaments in the indicated angle bins is constant at growth at constant external force. In the force decrease scenario filaments growing at higher angles are capped preferentially and the network thins out. When force increase is used as an input, filaments in all angle bins increase. (B) Histograms of filament density (black) and order parameter as defined in Figure 3 (blue). Without perturbation the network architecture is dominated by ± 35 peaks and the order parameter is consistently negative. Histograms of filament density before (black) and after (red) decrease in F and order parameter (blue) show biased elimination of filaments growing at higher angle. This leads to a change from the ± 35 architecture to one dominated by straight, 0 , filaments and a transiently positive order parameter. Filaments of all angles increase upon increase in force, which is also reflected in a negative order parameter. (C) The migration parameters force (the input parameter), actin density and protrusion speed fluctuate around steady state values during the unperturbed simulation. The force decrease causes an increase in protrusion speed and a decrease in actin density, with the reciprocal situation observed for the force increase. (D) Capping, elongation and branching rates used for the stochastic model. (E) Underlying lamellipodial feedback loop: Force, F, is set as an external parameter and decreases velocity, v, which is in turn increased by increased filament density, D, as suggested by the elastic ratchet model of actin polymerization. Actin branching is modeled as a zeroth order process and therefore actin density decreases branching rate, b. The parts of the feedback loop linking velocity, v, to the filament density, D, shown in this study are marked in red: Velocity, v, increases capping rate, k, in an angle-dependent manner and leads to a decrease in filament density, D. For all graphs mean and s.d. for an average of 20 runs are shown, for details see STAR Methods.