Nascent adhesions differentially regulate lamellipodium velocity and persistence

Cell migration is essential to physiological and pathological biology. Migration is driven by the motion of a leading edge, in which actin polymerization pushes against the edge and adhesions transmit traction to the substrate while membrane tension increases. How the actin and adhesions synergistically control edge protrusion remains elusive. We addressed this question by developing a computational model in which the Brownian ratchet mechanism governs actin filament polymerization against the membrane and the molecular clutch mechanism governs adhesion to the substrate (BR-MC model). Our model predicted that actin polymerization is the most significant driver of protrusion, as actin had a greater effect on protrusion than adhesion assembly. Increasing the lifetime of nascent adhesions also enhanced velocity, but decreased the protrusion’s motional persistence, because filaments maintained against the cell edge ceased polymerizing as membrane tension increased. We confirmed the model predictions with measurement of adhesion lifetime and edge motion in migrating cells. Adhesions with longer lifetime were associated with faster protrusion velocity and shorter persistence. Experimentally increasing adhesion lifetime increased velocity but decreased persistence. We propose a mechanism for actin polymerization-driven, adhesion-dependent protrusion in which balanced nascent adhesion assembly and lifetime generates protrusions with the power and persistence to drive migration.


Introduction
ARP2/3 activation [43], and a constant rate of adhesion unbinding (k off = 0.1 s -1 ) that matches the 134 unloaded lifetime of integrin-ligand bonds [44][45][46]. We found that individual membrane 135 segments exhibited initial velocity peaks of 30 -40 nm/s and slower velocities as the protrusion 136 progressed ( Figure 2B). Within the corresponding segments of the lamellipodium, actin 137 retrograde flow increased as the protrusion progressed ( Figure 2C (11.7 -21.7 nm/s [24,33]). The differences in time at which maximum edge velocity and 150 maximum retrograde flow were reached are in quantitative agreement with the observed timing 151 of lamellipodia actin retrograde in areas lacking significant traction force [24,32,33,40]. 152 We also validated the effects of membrane tension on the force relationships. consistent with experimental data that shows high retrograde flow from the high rate of actin 165 polymerization against the tense membrane, but slow protrusion velocity due to the high tension 166 [20,31,32,52]. 167 168 Actin polymerization and adhesion assembly and disassembly control lamellipodium 169 velocity 170 In order to decipher the contributions of actin filament polymerization and adhesion 171 dynamics to membrane velocity, we systematically varied the rates of actin branching, adhesion 172 assembly, and adhesion disassembly (k branch , k on , and k off ). For simplicity, we averaged the 173 velocity of the 101 membrane segments, including the fixed edges of the modeling domain, 174 which resulted in lower velocities than reported in Figure 2. We found that increasing k branch 175 four-fold (from 0.2 to 0.8 s -1 ), with fixed adhesion assembly and disassembly rates (k on = k off, = 176 0.1 s -1 ), resulted in a 30% increase in protrusion velocity (from 16.6 nm/s to 21.5 nm/s, Figure  177 3A). Increasing adhesion assembly rate k on five-fold (from 0.1 to 0.5 s -1 ), with fixed k branch = 0.5 178 s -1 and adhesion k off = 0.3 s -1 , resulted in a 10% increase in protrusion velocity (from 17.8 nm/s to 19.6 nm/s, Figure 3B). Increasing the disassembly rate of adhesions five-fold decreased 180 protrusion velocity 10% (from 19.8 nm/s to 18.4 nm/s, Figure 3C). Together, these results 181 indicate that actin assembly is the main driver of edge velocity and that actin's control can be 182 augmented by adhesion formation and lifetime. We tested how actin filament polymerization 183 and adhesion dynamics together govern membrane motion by systematically varying k branch and 184 k off . Membrane velocity increased with k branch and decreased with k off ( Figure 3D). We also 185 tested how adhesion formation and lifetime control protrusion velocity by simultaneously 186 varying k on and k off and found that protrusion velocity peaks with the highest adhesion assembly 187 rate and lowest adhesion disassembly rate ( Figure 3E). This indicates that protrusion velocity 188 depends on both adhesion assembly and maintenance. We found that the traction force 189 transmitted by adhesions also peaked with the highest adhesion assembly rate and lowest 190 adhesion disassembly rate, suggesting that adhesion traction force promotes edge protrusion 191 ( Figure 3F). 192

193
The lifetime of nascent adhesions regulates the velocity of the membrane 194 Adhesion traction determines the lifetime () of adhesions, which is the inverse of 195 unbinding rate (= 1/k off ). To test the role of adhesion lifetime in protrusion, we incorporated a 196 force-dependent molecular clutch mechanism into the computational model. The molecular 197 clutch bases the probability of adhesion-actin bond breakage on tension and thus creates a 198 variable rate of adhesion inactivation (k off ). We tested three different force-lifetime relations for 199 the adhesions, varying for maximum lifetime, ( Figure 4A). The breaking point for the 200 actin-adhesion bond, or force corresponding to , was set at 30 pN [48][49][50]. The peaks in 201 lifetime were either 3 s, 7.5 s, or 12 s, typical behavior of integrin unbinding from fibronectin 202 under load [48]. We used these force-lifetime relationships to control the probability of 203 adhesion-actin bond breakage during simulations with variable actin polymerization rate. We 204 found that membrane velocity increased proportionally with both k branch and ( Figure 4B). 205 Increasing actin assembly 4-fold resulted in a 17% increase in edge velocity (from 13.3 to 15.6 206 nm/s, using = 3 s), while increasing adhesion lifetime 4-fold resulted in about a 6% 207 increase in velocity (from 15.6 to 16.5 nm/s, using k branch = 0.8 s -1 ). This result matched our 208 findings on actin and adhesion-mediated control of edge motion in the absence of the molecular 209 clutch ( Figure 3D).   We evaluated the contribution of actin assembly and adhesion lifetime to pushing force 226 on the membrane and the retrograde flow that results from membrane counterforce. We found 227 that force on the membrane increased with both k branch and , as peak force on the membrane 228 occurred at the highest k branch and ( Figure 4C). Actin assembly was the main driver. With 229 = 3 s, a four-fold increase in k branch (from 0.2 -0.4 s -1 ) increased pushing force 21% (from 230 0.38 to 0.46 pN). With k branch = 0.2 s -1 , four-fold increase in (from 3 -12 s) increased 231 pushing force 11% (from 0.38 to 0.42 pN). In contrast, actin retrograde flow increased with 232 k branch but decreased with ( Figure 4D)

Integrin activation promotes lamellipodium velocity and decreases its persistence 256
To experimentally test the finding that adhesion lifetime promotes lamellipodia 257 protrusion velocity but limits persistence, we labeled adhesions in COS7 epithelial cells using 258 transient expression of Paxillin-mApple and imaged adhesion and edge dynamics during 5 min 259 of steady-state migration. We segmented the adhesions using focal adhesion analysis software 260 for quantification of the adhesions' lifetime [51] and used morphodynamics software to track the 261 edge motion [52] ( Figure 6A and B). We noted that protrusions exhibited adhesions with 262 heterogeneous lifetimes, in which clusters of short-living adhesions co-resided with a few 263 longer-lifetime adhesions. The range of long lifetimes varied per movie, which appeared to be 264 related with edge protrusion. For example, a cell in which the longest lifetimes are ~4.7 min 265 (orange-colored adhesions in Figure 6A) showed slow, persistent progression of the cell edge 266 ( Figure 6A). On contrary, a cell in which the longest lifetimes are ~10.6 min (yellow-colored 267 adhesions in Figure 6B) showed fast and more fluctuating protrusion behavior ( Figure 6B). 268 Accordingly, we sampled the lifetimes of the top 1 percentile of long-living adhesions per movie 269 and obtained the corresponding protrusion velocities and persistent times of the closest edge 270 segments. Plotting edge velocity and persistence as a function of adhesion lifetime showed that 271 cell protrusions with longer mean adhesion lifetimes were associated with faster protrusion 272 velocity but shortened protrusion persistence ( Figure 6C and D). 273 We also treated COS7 cells with Mn +2 , which increases adhesion lifetime and density 274 [44][45][46]48]. Mn +2 stabilizes nascent adhesions by promoting integrins' structural shift to high-275 affinity conformations for binding to extracellular matrix [10,53,54]. The cells transiently 276 expressed Emerald-Lifeact to label the cell edge. We imaged the cells' steady-state protrusion-277 retraction cycles and quantified protrusion velocity and persistence with morphodynamics 278 software. We found that integrin activation with Mn +2 increased mean protrusion velocity but 279 decreased persistence when compared to untreated cells ( Figure 6E and F). Together, these 280 results support our model that longer adhesion lifetimes are associated with faster protrusion 281 velocity but reduced protrusion persistence. 282 283 Discussion 284 Using our novel particle-based BR-MC model, we discovered that actin polymerization is 285 the main driver of lamellipodium velocity and that the force-dependent clutch mechanism of 286 nascent adhesions differentially controls lamellipodium velocity and persistence. Experiments in 287 migrating epithelial cells substantiated that nascent adhesion lifetime promotes protrusion 288 velocity and limits persistence. Directional migration requires persistent edge motion [1, 2], 289 which is optimal at intermediate extracellular matrix density and nascent adhesion concentration 290 [55]. Our findings suggests that in addition to extracellular matrix density, the strength of the 291 adhesion-actin interaction controls protrusion persistence. 292 Our study clarifies the contributions of lamellipodium actin polymerization and nascent 293 adhesions to overall edge motion. Previous models have indicated both that actin polymerization 294 is sufficient to drive edge protrusion and that adhesion promotes protrusion [28,31,[56][57][58][59]. In 295 the recent model by Garner et al., filament polymerization alone generated stable protrusion [60], 296 which resembles the lamellipodia of fish keratocytes that glide with a static cell shape [61]. Yet, 297 the density of adhesion activation has been shown to promote and be required for protrusion 298 velocity and persistence in protrusion-retraction cycles [28,59]. We showed that increasing 299 actin polymerization most significantly enhances protrusion velocity and that increasing the 300 nascent adhesion lifetime further supports edge velocity through the molecular clutch 301 mechanism. However, we found that increasing nascent adhesion lifetime reduced the edge 302 motional persistence when membrane tension was moderate, as in the initiation phase of 303 membrane motion. In live cells cycling through the phases of protrusion initiation, 304 reinforcement, and retraction, nascent adhesion lifetime associated with and promoted 305 lamellipodium protrusion velocity but limited persistence. This suggests that the nascent-306 adhesion mediated regulation in the beginning of edge protrusion dictates the overall protrusion 307 activity. 308 We propose a mechanism for nascent adhesion lifetime's differential control of edge 309 velocity and persistence: the increase in edge velocity emerges from the traction that the

Model of lamellipodium protrusions based on Brownian Ratchet and Molecular Clutch 363 (BR-MC) 364
We developed a 2D model of lamellipodium protrusion based on combining the 365 Brownian ratchet mechanism for actin filament polymerization against a cell edge [11,22,35,366 37] with the molecular clutch mechanism for adhesions [38,39] capped. Actin filaments polymerize against the edge membrane at assembly rate k pol and 374 branching rate k branch , which generates pushing force that induces outward membrane motion 375 ( Figure 1A). Integrins undergo cycles of activation and deactivation, which correspond to their 376 addition to and removal from the simulation domain. These mechanisms are governed by kinetic 377 rates (Table 1) as elongation of new filaments from existing (mother) filaments in the direction towards the 419 membrane and at an angle relative to the mother filament.
is randomly selected from a 420 normal distribution with a mean of 70 deg and standard deviation of 10 deg. Filaments capping 421 occurs at a rate k cap , which stops filaments polymerization and branching. 422 Actin filament polymerization follows the Brownian ratchet mechanism. In order to 423 account for the effects of membrane tension on actin filaments polymerization, filaments 424 presenting barbed ends within 15 nm from the membrane slow their polymerization rate 425 depending on the force on them. For these filaments, the probability of polymerization is 426 calculated as P polym = C p k polym dt, where the polymerization coefficient, C p , varies between 0 and 427 1: 428 where F M is membrane tension, F B is a confining boundary which ensures a reflective boundary, 429 and = 4.11 pN nm. 430 Actin filament connection to adhesions. When a filamentary unit is within a distance 431 r thresh from integrin, a harmonic interaction potential is established between the filament and 432 integrin, with force: F A = r 0,A k A , where k A is the integrin-filament spring constant, and r 0,A is the 433 distance from the equilibrium, resulting from actin retrograde flow. When an integrin switches 434 its state from active to inactive, the connection with the actin filament is lost and integrin 435 disappears. 436 Filament motion follows Langevin dynamics. The total force on each actin filaments is 437 computed as: = + + + , where F T is a Brownian, stochastic force following the 438 fluctuation dissipation theorem, F A is the force from one or more bound integrins, F M is the force 439 exerted by the membrane, and F B is the boundary force which acts as a repulsive potential 440 preventing the filaments from crossing. When one filament presents one or more branches 441 and/or branches on branches, the interconnected filaments are treated as a rigid structure. 442 Integrin representation and dynamics. Integrins are represented as single point particles 447 existing in two functional states: active or inactive, as they undergo cycles of activation and 448 deactivation at rates k on and k off , respectively. When active, integrins are placed in random 449 positions in the simulation domain and provide anchor points for filaments motion. When inactive, they are removed from the domain. While integrin activation is governed by k on , their 451 de-activation occurs through one of two mechanisms: force-independent or force-dependent 452 unbinding. In the first case, k off has a constant value (Table 1). In the second case, k off depends 453 biphasically on the tension between actin filament and integrin, F A . According to the catch-bond 454 model for integrin unbinding, the unbinding rate is a sum of two exponentials with opposite signs 455 ( Figure 4A and Photometrics Prime 95B camera configured at a 100 MHz readout speed to decrease readout 495 noise with Metamorph. Images were taken every 3 s for 5 min, with sequential images at every 496 time point with the TIRF angle set to optimal TIRF and with the TIRF angle set as vertical for 497 effective widefield imaging. The acquired images had an effective pixel size of 45 nm. Imaging 498 was performed at 37°C, 5% carbon dioxide, and 70% humidity. Laser powers were decreased as 499 much as possible and the exposure time set at 200-400 ms to avoid phototoxicity. 500 501 Adhesion segmentation, detection, and tracking 502 Nascent adhesions were detected and segmented using point source detection as 503 previously described in [51,74]. Briefly, fluorescence images were filtered using the Laplacian 504 of Gaussian filter and then local maxima were detected. Each local maximum was then fitted 505 with an isotropic Gaussian function (standard deviation: 2.1 pixels, i.e. ~180 nm) and outliers 506 were removed using a goodness of fit test (p=0.05). The point sources detected for nascent 507 adhesions were tracked over the entire frames of the time-lapse images using uTrack [75]. 508 Models were run until additional iterations no longer changed the result output. 527 The non-parametric Mann-Whitney U test was used to test for difference in the means for all 528 modeling data and adhesion-edge analyses. Experiment sample size was chosen based on a 529 minimum of three independent biological replicates and hundreds to thousands of 530 adhesions and protrusion events analyzed, respectively, within each replicate. The 531 Kolmogorov-Smirnov test was used to test for difference in the distribution of edge motion 532 upon Mn +2 treatment. Unless otherwise mentioned in each figure caption, * p<0.05, ** p<0.01, 533 *** p<0.001, **** p<0.0001.