A mechanosensing mechanism mediated by IRSp53 controls plasma membrane shape homeostasis at the nanoscale

As cells migrate and experience forces from their surroundings, they constantly undergo mechanical deformations which reshape their plasma membrane (PM). To maintain homeostasis, cells need to detect and restore such changes, not only in terms of overall PM area and tension as previously described, but also in terms of local, nano-scale topography. Here we describe a novel phenomenon, by which cells sense and restore mechanically induced PM nano-scale deformations. We show that cell stretch and subsequent compression reshape the PM in a way that generates local membrane evaginations in the 100 nm scale. These evaginations are recognized by the I-BAR protein IRSp53, which triggers a burst of actin polymerization mediated by Rac1 and Arp2/3. The actin polymerization burst subsequently re-flattens the evagination, completing the mechanochemical feedback loop. Our results demonstrate a new mechanosensing mechanism for PM shape homeostasis, with potential applicability in different physiological scenarios. Teaser Cell stretch cycles generate PM evaginations of ≈100 nm which are sensed by IRSp53, triggering a local event of actin polymerization that flattens and recovers PM shape.


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* authors for correspondence, at aleroux@ibecbarcelona.eu and 27 proca@ibecbarcelona.eu. 28 29 Abstract 30 As cells migrate and experience forces from their surroundings, they constantly 31 undergo mechanical deformations which reshape their plasma membrane (PM). 32 To maintain homeostasis, cells need to detect and restore such changes, not only 33 in terms of overall PM area and tension as previously described, but also in 34 terms of local, nano-scale topography. Here we describe a novel phenomenon, 35 by which cells sense and restore mechanically induced PM nano-scale 36 deformations. We show that cell stretch and subsequent compression reshape the 37 PM in a way that generates local membrane evaginations in the 100 nm scale. 38 These evaginations are recognized by the I-BAR protein IRSp53, which triggers 39 a burst of actin polymerization mediated by Rac1 and Arp2/3. The actin 40 polymerization burst subsequently re-flattens the evagination, completing the 41 mechanochemical feedback loop. Our results demonstrate a new 42 mechanosensing mechanism for PM shape homeostasis, with potential 43 applicability in different physiological scenarios. 44 Teaser 45 Cell stretch cycles generate PM evaginations of ≈100 nm which are sensed by 46 IRSp53, triggering a local event of actin polymerization that flattens and 47 Introduction 50 Cells constantly exchange information with their surroundings, and external 51 inputs are first received by their outermost layer, the plasma membrane (PM). 52 This interface, far from being an inert wall, integrates and transmits incoming 53 stimuli, ultimately impacting cell behaviour. In this context, the traditional view 54 of such stimuli as biochemical messengers has now changed to include the 55 concept that physical perturbations are also of major importance (1-3). By 56 sensing and responding to physical and biochemical stimuli, one of the main 57 functions of the PM is to adapt to the changes in shape that cells experience as 58 they migrate or are mechanically deformed, in a variety of physiological 59 conditions (4-9). To date, research in this area has largely focused on the 60 regulation of PM area and tension, at the level of the whole cell (10-12). For 61 instance, cell stretch or decrease in medium osmolarity have been commonly 62 used to raise PM tension, unfolding membrane reserves (ruffles, caveolae), 63 inhibiting endocytosis and promoting exocytosis (13-17) . Conversely, cell 64 exposure to a hypertonic solution or cell compression have been employed to 65 decrease PM tension, leading to an increase on the activity of different endocytic 66 pathways (18-21). These studies have shown that PM tension homeostasis is 67 maintained by regulating PM area through mechanisms like endocytosis, 68 exocytosis, or the assembly and disassembly of PM structures like ruffles and 69 caveolae. 70 However, changes in cell PM area upon mechanical perturbations are 71 necessarily accompanied by changes in topography at the local scale. This is 72 clearly exemplified by caveolae flattening upon cell stretch (22) or creation of 73 PM folds at the sub-µm scale upon cell compression (20). Curvature also arise 74 when membranes are exposed to either external topographical cues (23, 24) or 75 internal pulling by actin filaments (25)(26)(27). To maintain PM homeostasis, cells 76 should thus be able to not only respond to overall changes in PM tension or area, 77 but also to local changes in PM topography. This requirement is even clearer if 78 one considers recent findings showing that tension does not propagate 79 extensively throughout the whole ensemble of the PM, but dissipates in small 80 areas of less than 5 µm (28). However, if such local PM shape homeostasis 81 mechanisms exist, and how they operate, is still unknown. 82 Here, we studied this problem by using as a model the controlled compression of 83 fibroblasts through the application and release of stretch. We show that upon cell 84 compression, bud-shaped PM deformations of negative curvature (evaginations) 85 on the 100 nm scale are formed and enriched by IRSp53, a negative curvature-86 sensing protein. This creates a local node where specific PM topography is 87 selectively coupled through IRSp53 to activate actin polymerization mediated by 88 Rac1 and Arp2/3. The activation of this cascade flattens the structure, recovering 89 the PM shape to its initial state. Our findings demonstrate a local 90 mechanosensing mechanism that controls PM homeostasis when perturbed 91 through compression. 92

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Results 94 Compression generates dynamic PM evaginations of 100 nm in width. 95 To study how PM topography is regulated, we submitted normal human dermal 96 fibroblasts (NHDF) transfected with an EGFP-membrane marker to a 97 physiologically relevant 5% equibiaxial stretch by using a custom-made stretch 98 system composed by a PDMS stretchable membrane clamped between two 99 metal rings, as previously described in (29) (see methods). Cell response during 100 and after stretch was monitored by live fluorescence imaging. As previously 101 described, when tensile stress was applied cells increased their area by depleting 102 PM reservoirs, such as ruffles (10, 20). After 3 minutes, stretch was released, 103 resulting in a compression stimulus. At this point, excess membrane was stored 104 again in folds, visualized as bright fluorescent spots of ≈ 500 nm ( Fig. 1A and  105 Supp. Video SV01). These spots incorporate approximately 1.5% of PM area 106 (Supp. Fig. 1A), and thus store an important fraction of the area modified by cell 107 stretch.  a cycle of stretch and we imaged their response after  144  stretch release. To visualize actin dynamics, cells were co-transfected with a PM  145  marker together with a plasmid expressing an actin nanobody bound to a GFP  146 fluorophore (ACG). As evaginations were being resorbed, actin was recruited to 147 the same spot ( Fig. 2A  infected either with a control (IRSp53 -/-) or an IRSp53-retroviral vector (IRSp53 -201 /-R ) to restore expression levels of IRSp53 similar to wild type fibroblasts, as 202 previously described (52-54). IRSp53 -/cells also stretched by the same amount 203 as IRSp53 -/-R cells (Supp. Fig. 1F) and did not display significant changes in the 204 number of evaginations generated after compression (Supp. Fig. 1G) or in the 205 area stored by those (Supp. Fig 1H). However, and reinforcing the previous 206 result, they showed a severe impairment in the resorption of the evaginations 207 even 180 s after stretch release. We further re-introduced EGFP-tagged full-208 length (FL) wild type IRSp53 into IRSp53 -/by transient transfection. Next, we tested whether the effect of IRSp53 in PM reshaping was local at 217 evaginations, or a general non-specific cell-level effect due to the ability of 218 IRSp53 to organize different NPFs (55, 56). To this end, we generated PM folds 219 of very different nature and curvature. We transiently exposed cells to hypo-220 osmotic medium, leading to cell swelling. As previously described, re-exposure 221 to iso-osmotic medium generates a water outflow from cells. For cells seeded on 222 non-porous substrate such as PDMS, expelled water becomes trapped between 223 the cell and the substrate, forming the dome-shaped invaginations known as 224 vacuole-like dilations (VLDs). VLDs are much larger than compression-225 generated bud-shaped evaginations (several µm in size), with much lower 226 curvature, and resorb in the order of minutes (20). Confirming the local, 227 evagination-specific effect of IRSp53, VLD resorption was equivalent in 228 IRSp53 -/-R and IRSp53 -/cells (Supp. Fig. 2A, B, C and Supp. Videos SV11 and 229 SV12). IRSp53 has also been related to actin polymerization in lamellipodia (44, 230 57). To discard that flattening of the evaginations was due to potential 231 lamellipodial extension (cell spreading) after compression, we analyzed cell 232 spreading dynamics. After a stretch-release cycle, cells did extend lamellipodia 233 and spread during approximately 1 minute (Suppl. Fig. 2D). However, the time 234 constant of spreading (obtained by fitting an exponential curve to the 235 experimental curve) and the amount of area recovered were not altered by the 236 loss of IRSp53 (Supp. Fig. 2E-G), discarding a role of this process in the 237 resorption of evaginations. 238

Homeostasis recovery after stretch requires integrity of SH3 and IBAR 239
IRSp53 domains 240 So far, we have shown that PM remodeling of compression-generated 241 evaginations is a local event, which depends on IRSp53 to organize a burst of 242 actin polymerization that flattens the PM. Next, we investigated if this could be 243 part of a mechanosensing mechanism. Indeed, the I-BAR domain of IRSp53 244 may recognize the curvature generated at the evaginations and further recruit 245 NPFs to coordinate the polymerization event. However, IRSp53 possesses 246 multiple domains with multiple interactors, as illustrated in Fig. 3A IRSp53, leading to actin polymerization in a myosin-independent and Arp2/3-383 dependent manner. IRSp53 has been described to indirectly promote Arp2/3-384 mediated actin polymerization acting both as an upstream (80)  of an actin cortex retracts and flattens cellular blebs, but this mechanism 404 depends on myosin contractility (72), and hence is not applicable here. In 405 contrast, our results show a novel flattening rather than protruding response. To 406 propose a plausible mechanism, we developed a theoretical model coupling the 407 PM and the actin cortex (see methods). We hypothesized that, rather than out-of-408 plane forces, flattening may be the result of in-plane actin flows around 409 evaginations. We thus approximated the actin cortex as a flat 2D active gel. In 410 this model, the PM is adhered to the underlying cortex from which it can 411 delaminate, and experiences frictional in-plane forces proportional to relative 412 slippage (28). This is coupled to our previous model describing interactions 413 between the PM and curved proteins (83). We coarse-grained the signaling 414 pathway triggered by IRSp53 localization and leading to actin polymerization 415 through a regulator species with normalized areal density , which is produced 416 beyond a threshold in IRSp53 enrichment, degraded, and transported by 417 diffusion, with dynamics on time-scales comparable to those of actin dynamics. 418 The effect of this regulator is to locally favor actin polymerization by the Arp2/3 419 complex, and hence bias the competition between a formin-polymerized 420 contractile network component and a branched extensile component (84, 85). 421 We thus modelled the mechanical effect of local polymerization by locally 422 reducing contractility. 423 Our model predicted that curvature-sensitive IRSp53 molecules became 424 enriched in the evagination within a second after its formation. This led to 425 recruitment of the regulator species , resulting in a tension gradient in the 426 vicinity of the evagination. In turn, this induced a centrifugal cortical flow, 427 which frictionally dragged the membrane outwards until flattening. In the 428 absence of curvature, the IRSp53-enriched domain dissolved, the regulator 429 species recovered its uniform baseline, and the cortex recovered its quiescent 430 steady-state ( Fig. 5M and N). Whereas predicted actin flows occur at a scale 431 well below the diffraction limit and can therefore not be observed 432 experimentally, the predicted relative trends of PM and regulator densities 433 qualitatively match our experimental observations when comparing PM and 434 actin (Fig. 2B) or ezrin (Fig. 2E). We note that in the real system, the proposed 435 mechanism based on in-plane actin flows and cortex-PM friction should 436 compete with the classical mechanism based on out-of-plane forces. This may 437 explain why resorption dynamics in experiments ( Fig. 2B and E) were 438 significantly longer and less abrupt than those predicted by the model (Fig. 5N). 439 Predictions are also consistent with our observation that evagination resorption 440 is impaired when inhibiting Arp2/3 ( Fig. 5D) but not myosin or formin activity 441 ( Fig. 5B and C). Indeed, the mechanism is based on a local gradient in extensile 442 versus contractile behavior around the evagination, so it should depend on 443 Arp2/3 (which acts locally at the evagination) and not on formin or myosin, 444 which would regulate overall contractility levels and not specifically local 445 gradients. Thus, our model suggests a chemo-mechanical signaling system that 446 autonomously restores homeostasis of membrane shape. 447

Discussion 448
Our work shows that stretch-compression cycles generate evaginations on the 449 apical PM of the cells with a size on the 100 nm scale, compatible with the 450 sensing range of IBAR proteins (47, 51). Further, we demonstrate the 451 recognition of this curved templates by the curvature-sensing protein IRSp53. 452 The role of IRSp53 is not due to general cell-scale effects, such as lamellipodial 453 extension (44, 57) or endocytosis. Indeed, cell spreading after the stretch-454 compression cycle was not affected by IRSp53 (Supp. Fig. 2). Regarding 455 endocytosis, IRSp53 has been described to regulate the CLIC-GEEC endocytic 456 pathway (50), which is in turn activated upon cell compression (18). However, 457 the I268N-CRIB and 4KE-IBAR IRSp53 mutants strongly impaired endocytosis 458 (50), but fully rescued evagination resorption (Fig. 3F) prior to the experiment. 531

PDMS membrane fabrication 532
The stretchable PDMS membranes were prepared as described in (20). To 533 produce a patterned support to further obtain patterned-PDMS membranes 534 PMMA dishes were plasma cleaned for 20 min and warmed up to 95ºC for 5 535 min. After cooling down using a nitrogen gun, SU 2010 resin was spinned on 536 top of the dish to create a 10 µm layer and prebaked 2,5 min at 95ºC. Dishes 537 were then placed on a mask aligner and exposed for 7,5 s in presence of the 538 designed acetate mask. After post-baking for 3,5 min at 95ºC, the pattern was 539 revealed for 1 min and subsequently extensively washed with isopropanol and 540 verified under the microscope. Finally, PMMA dishes were silanized by 30 s 541 plasma cleaning activation followed by 1 h silane treatment under vacuum. 542 Standard or patterned membranes were mounted on metal rings of our 543 customized stretch system, cleaned, sterilized, and coated with 10 µg/ml 544 fibronectin (Sigma) overnight at 4°C prior to experiments. Patterns were 545 designed as a grid with letters and numbers to allow for correct orientation. 546

Stretch and osmolarity experiments 547
After overnight fibronectin coating, PDMS membranes were quickly washed 548 and 3000 cells were seeded on top and allowed to spread for 45min to 1h in the 549 incubator. Then, rings were mounted on the stretch device coupled to the 550 microscope stage, vacuum was applied for 3 min to stretch the membrane, and 551 then vacuum was released to come back to the initial shape as described in (20). 552 Calibration of the system was done to adjust the vacuum applied to obtain 5 % 553 stretch of the PDMS surface. Hypo-osmotic shocks were performed by exposing 554 cells during 3 min to CO2 independent medium mixed at 50% with de-ionized 555 water in which the concentrations of Ca +2 and Mg +2 had been corrected. Iso-556 osmotic medium was added after the 3 min incubation period. 557

Scanning electron microscopy experiments 558
Cells were prepared as explained in the previous section. Right after stretch 559 release, the sample was fixed in 2.5 % glutaraldehyde EM grade (Electron 560 Microscopy Sciences 16220) plus 2 % PFA (Electron Microscopy Sciences  561 15710-S) diluted in 0.1 M PB buffer at 37ºC for 1 h. Samples were then washed 562 4x for 10 min in 0.1 M Phosphate Buffer (PB) and imaged with epifluorescence 563 microscopy as described below to acquire fluorescence images of the cell PM. 564 PDMS membranes were then cut into 1x0.5 cm rectangles in which the pattern 565 was centered and placed on top of 12 mm coverslips for further processing. 566 Dehydration was carried out by soaking samples in increasing ethanol 567 concentrations (50, 70, 90, 96 and 100 %). After this, samples were critical point 568 dried and covered with a thin layer of gold to be imaged. 569

Transmission electron microscopy experiments 570
Cells were fixed, washed and PDMS membranes were cut and mounted as for 571 SEM imaging. After this, samples were postfixed with 1% OsO4 and 0.8 % 572 K3Fe(CN)6 for 1 h at 4ºC in the dark. membrane was next peeled off and ultrathin sections were cut and mounted on 581 grids for imaging. 582

APEX labelling for TEM imaging 583
Two days prior to the experiment, cells were co-transfected by electroporation 584 with mKate2-P2A-APEX2-csGBP (Addgene #108875) and EGFP-IRSp53-FL 585 in a 3:1 ratio, using the Neon TM Transfection System (Invitrogene) following the 586 protocol provided by the company. Before seeding, cells were sorted for double 587 positive mKate and GFP fluorescence, excluding very high and very low 588 transfection levels. Cells were subsequently seeded and stretched in the same 589 conditions as explained in the stretch experiments section. Right after stretch 590 release, the sample was fixed in 2.5 % glutaraldehyde EM grade (Electron 591 Microscopy Sciences 16220) diluted in 0.1 M Cacodylate buffer at 37ºC for 10 592 min, followed by incubation on ice for 50 min in presence of the fixative. All 593 subsequent steps were performed on ice. The sample was washed 3 times with 594 cold 0.1 M Cacodylate buffer, and next cut into 1x0.5 cm rectangles containing 595 the fixed cells. Cells were washed for 2 min with a fresh cold 1 mg/ml 3,3'-596 diaminobenzidine (DAB) (tablets, Sigmafast, D4293) solution in 0.

Image acquisition 605
Fluorescence images were acquired with Metamorph software using an upright 606 microscope (Nikon eclipse Ni-U) with a 60x water dipping objective (NIR Apo 607 60X/WD 2.8, Nikon) and an Orca Flash 4.0 camera (Hamamatsu). Fluorophore 608 emission was collected every 3s. Cells were imaged in a relaxed state and then 609 for 3 min at 5% stretch, and for 3 min during the release of stretch. SEM images 610 were taken using the xTm Microscope Control software in a NOVA NanoSEM 611 230 microscope (FEI Company) under the high vacuum mode using ET and TL 612 detectors to acquire high and ultra-high resolution images of the cell surface. 613 TEM Samples were observed in a Jeol 1010 microscope (Gatan, Japan) 614 equipped with a tungsten cathode in the CCiTUB EM and Cryomicroscopy 615 Units. Images were acquired at 80 kv with a CCD Megaview 1kx1k. 616 The numerator of this expression corrects evagination fluorescence so that only 632 the signal coming from the evagination itself and not neighboring PM is 633 quantified. The denominator normalizes by total cell fluorescence, and also 634 accounts for progressive photobleaching. All control curves were normalized to 635 1 (maximal fluorescence after stretch release) and the rest of the data 636 represented in the same graph were normalized to the control. Exceptionally, 637 actin and ezrin curves were normalized to 0.5 (maximal fluorescence after the 638 release of stretch) for visualization purposes. To quantify the degree of 639 resorption of the evaginations, as the experimental data could not always be 640 fitted with single exponential decay curve, we adopted the strategy of comparing 641 the residual fluorescence intensity of the PM marker at the las timepoint of 642 acquisition (t180s), on which statistical analysis can be performed. processed for SEM imaging and the same cells were found by manually 673 following their location on the pattern and visual verification was done to check 674 for correct matching. Fluorescent and SEM images were then aligned by using 675 the BigWrap plugin on Fiji. 676

Statistical analysis 677
In the case of data following a normal distribution, T-test or ANOVA was done 678 depending on whether there were 2 or more datasets to compare. For data not 679 following normal distributions, Mann-Whitney or Kruskal-Wallis test were 680 applied depending on whether there were 2 or more datasets to test. All data are 681 shown as mean ± SEM. Specific P and N values can be found in each one of the 682 graphs shown in the figures. 683

Theoretical Model 684
To understand the physical mechanism leading to the active flattening of 685 membrane evaginations caused by compression of the PM, we focused on a 686 single evagination and described it mathematically under the assumption of 687 axisymmetry. We modelled the membrane as locally inextensible thin sheet with 688 bending rigidity = 20 using the Helfrich model and accounted for the 689 viscous stresses due to membrane shearing with membrane 2D viscosity = 690 3 ⋅ 10 −3 pN s/μm (28, 30, 96). We modelled the cortex as a 2D planar active 691 gel adjacent to the membrane. We thus ignored the out-of-plane protrusive 692 forces caused by localized actin polymerization at evaginations enriched in 693 IRSp53, which in a classical view can lead to further protrusion rather than 694 flattening (55). Instead, we focused on the in-plane effect of localized actin 695 polymerization to explain active flattening. In the actual system, we expect both 696 effects to compete. 697 To model the interaction between the membrane and the cortex, we considered 698 an adhesion potential depending on the distance between the membrane and the 699 cortex enabling decohesion with an adhesion tension of = 1.5 ⋅ 10 −5 N/m 700 (30), (Supp. Fig. 6). We also considered in-plane frictional tractions between the 701 membrane and the cortex proportional to their relative velocity, where is the membrane velocity, is the cortex velocity, and is a friction 703 coefficient, which we took as = 20 nN s/µm 3 (28). 704 We generated evaginations with dimensions comparable to those in (Fig. 1) by 705 laterally compressing an adhered membrane patch of radius 0 as discussed in 706 (30). We considered 0 = 150 nm, consistent with the typical separation 707 between evaginations (Fig. 1C). After formation of the evagination, we applied 708 at the boundary of our computational domain the surface tension required to 709 stabilize the evagination, consistent with the long-time stability of such 710 compression-generated evaginations of the PM when cellular activity is 711 abrogated (20). 712 We then considered the model in (83) to capture the interaction between an 713 ensemble of curved proteins (IRSp53) and a membrane. In this model, proteins 714 are described by their area fraction . We fixed the chemical potential of such 715 proteins at the boundary of our computational domain, corresponding to a 716 relatively low area fraction of proteins, � = 0.05. We set the saturation 717 coverage to max = 0.35 due to crowding by other species but in our 718 calculations, coverage did not come close to this limit. We considered an 719 effective surface area per dimer of 300 nm 2 . In this model, the curvature energy 720 density of the membrane-protein system is given by where H is the 721 mean curvature and 0 is a parameter combining the intrinsic curvature of 722 proteins and their stiffness (83). We took 0 = 3 ⋅ 10 −3 nm -1 , which lead to 723 curvature sensing but no significant protein-induced membrane reshaping. With 724 a protein diffusivity of 0.1 µm 2 /s, we obtained protein enrichments on the 725 evagination of about 3-fold within 0.5 s. 726 To model in a coarse grained manner the signalling pathway triggered by 727 IRSp53 localization and leading to actin polymerization, we considered a 728 regulator species given by a normalized surface density , which was produced 729 with a rate depending on IRSp53 enrichment and given by � � � = 730 of saturates, and ⟨ ⟩ is 0 if < 0 and a otherwise. We considered = 2, 733 = 3 and 1 = 1 s -1 . This regulator was degraded with rate 2 , with 2 = 1 734 s -1 and diffused with an effective diffusivity of = 0.1 ⋅ 10 −3 µm 2 /s, much 735 smaller than that of membrane proteins since the regulator is viewed as an actin-736 binding species. In polar coordinates, the governing equation for the transport of 737 this regulator is thus 738 This equation results in a region enriched with , co-localizing with the 740 evagination, and reaching a maximum value of about 1 within about 10 s, 741 comparable to the typical times of actin dynamics. Not being a detailed 742 description of a specific network, the details of this model for are not 743 essential.
The key points are that the production of is triggered by IRSp53 744 enrichment, and that 1 , 2 and are such that over the time-scales of actin 745 dynamics (significantly slower than those of IRSp53 enrichment) a region of 746 high develops close to the evagination. 747 The effect of this regulator is to locally favour actin polymerization by the 748 Arp2/3 complex. The cortex can be viewed as a composite system of 749 interpenetrating actin networks, one polymerized by formins leading to linear 750 filaments and producing contractile forces through the action of myosins and 751 other crosslinkers, and one polymerized by the Arp2/3 complex, with a branched 752 architecture and producing extensile forces by polymerization (84). Combining 753 these two effects, the net active force generation in the actin cortex is contractile. 754 These two networks compete for actin monomers (85), and hence a local 755 enrichment in the regulator leading to enhanced polymerization of the branched 756 network should bias this competition and locally lower contractility in the 757 vicinity of the evagination. In turn, the resulting contractility gradient should 758 generate an in-plane centrifugal cortical flow, which if large enough, might drag 759 the membrane outwards due to frictional forces and actively flatten the 760 evagination. 761 To model such actin flow, we considered simple active gel model where the 762 cortical velocity υc is obtained by force balance between viscous and active 763 forces in the cortex, and given by 764 where η c is the viscosity of the cortex and ( ) is the active tension, which we 766 assume to be a function of the regulator ψ. We note that we neglect in the 767 equation above the force caused by friction between the membrane and the 768 cortex as they slip past each other. This is justified because the hydrodynamic 769 length for the cortex is in the order of microns and above, and hence in the 770 smaller length-scales considered here viscosity dominates over friction. In our 771 calculations, we took ( ) = 0 (1 − 2 ), so that active tension is 772 approximately halved near the evagination when the normalized regulator 773 density reaches about 1 and is equal to 0 far away from it. As boundary 774 conditions, we considered (0) = 0 consistent with polar symmetry and 775 ∂ ∂ ( ) = 0, so that at = the stress at the gel is 0 . We chose 0 / so that 776 the resulting cortical velocities due to gradients in active tension gradients were 777 of about 0.1 µm/s, comparable to the typical actin velocities due to 778 polymerization in the lamellipodium (97). 779 The formation of the evagination triggered in this model a sequence of chemo-780 mechanical signaling event restoring autonomously homeostasis of membrane 781 shape and of all the signaling network. Indeed, within a few seconds, IRSp53 782 became enriched in the evagination by curvature sensing. Then, over a about 10 783 seconds, the actin regulator progressively built up in the vicinity of the 784 evagination, creating a gradient in active tension σ, which in turn created a 785 centrifugal cortical flow. This flow frictionally dragged the membrane outward 786 ironing out the evagination. In the absence of curvature, the IRSp53 domain 787 rapidly dissolved and according to Eq. (1) dropped to zero everywhere, 788 eventually stopping the cortical flow and thus recovering a homeostatic state 789 with a planar membrane and a quiescent cortex. 790 We note that our model is consistent with the fact that myosin inhibition does 791 not affect the resorption process. Indeed, myosin inhibition should lower the 792 baseline active tension, 0 , but should not change the fact that localized 793 polymerization would locally induce and extensile stress, and hence establish a 794 tension gradient and an actin flow. 795 One important difference between our model and the experiments is that, in our 796 calculations, the evaginations rapidly flattened once the contact angle of the 797 evagination became smaller than 90 degrees, whereas in the experiments, the 798 decay of membrane fluorescence was more gradual over a timescale of 3 799 minutes. We hypothesize that this may be due to the fact that localized actin 800 polymerization may fill the evagination with branched actin network, which 801 should apply an out-of-plane force competing with the flattening force causing 802 the centrifugal flow and whose material needs to be cleared out even when 803 localized polymerization has stopped. Both of these effects should slow down 804 the resorption process.