Heterotypic intercellular adhesion tunes efficiency of cell-on-cell migration

15 Cell migration across epithelial barriers occurs in diverse developmental, 16 immunological, and pathological contexts. Here we investigate the contribution of 17 heterotypic adhesion between migrating cells and epithelial “substrate” cells to 18 transepithelial migration. Using an in silico model inspired by the migration of 19 primordial germ cells across the midgut epithelium in the Drosophila embryo, we show 20 that heterotypic adhesion modulates migration efficiency in a non-monotonic manner, 21 revealing the existence of an optimal adhesion regime. Consistent with this prediction, 22 in vivo overexpression of E-cadherin in germ cells accelerated their exit from the midgut 23 relative to controls. Beyond providing experimentally testable predictions, our model 24 integrates and explains previous observations on the role of heterotypic adhesion in 25 cell-on-cell migration, offering a framework for understanding transepithelial migration 26 across biological contexts. 27

28 Germ cell migration, intercellular adhesion, E-cadherin, Cellular Potts model, 29 CompuCell3D, in vivo live imaging 30 31 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 3 of 27

32 Cells frequently carry out their functions at locations distinct from their site of origin, 33 making the individual cellular motility that is required for cell migration a critical 34 aspect of their behavior (1, 2). To achieve motility, cells require persistent and directed 35 membrane activity, which is frequently guided by external chemical cues (3–6). This 36 directed membrane activity is enabled by the dynamic nature of cell membranes, which 37 exhibit continuous turnover of cytoskeletal components (7–9) 38 Cell migration, division, differentiation and death enable the development of 39 multicellular organisms from a single cell (10). Cells in various developmental contexts 40 migrate individually as well as collectively (1, 2, 11). Embryonic development unfolds 41 as a tightly regulated cascade of events, where each step must occur within a specific 42 time window to prevent disruption of subsequent stages (12–15). These temporal 43 constraints also apply to cell migration, making not only the path taken but also the 44 timing of arrival critical to proper development (1, 2, 16, 17). 45 In the developing embryo of the fruit fly Drosophila melanogaster, the primordial 46 germ cells (germ cells) are the first cells to form (18). The germ cells form at the 47 posterior tip of the embryo roughly 2.5 hours after egg laying (18, 19). Around 15 48 minutes after their formation, the embryo undergoes gastrulation, and the cluster of 49 germ cells enters the primordial midgut upon invagination of the surrounding tissue 50 during gastrulation (20). Here, the germ cell cluster eventually disassembles, and the 51 germ cells exit the gut by individually passing through the monolayer of epithelial cells 52 that form the midgut (20, 21). The proteins Wunen and Wunen2, which are expressed in 53 the ventral midgut among other tissues, serve as repellents driving the germ cells to exit 54 the midgut dorsally (22–25). Once outside the midgut, the germ cells continue their 55 migration to join the mesodermal cells that form the somatic gonad primordium (26). 56 The Drosophila adhesion protein E-cadherin is encoded by the shotgun (shg) gene, 57 and is maternally deposited in the early embryo (27, 28). Germ cells require this 58 maternally deposited E-cadherin both to form a cohesive cluster and to tether to the 59 invaginating midgut primordium during gastrulation (29–31). Regulation of germ cell 60 E-cadherin during internalization into the midgut is orchestrated by the Trapped in 61 endoderm (Tre1) protein, a G protein-coupled receptor (30, 31). Tre1 enables the germ 62 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 4 of 27 cell cluster to form a radial configuration of polarized cells that detach from the cluster 63 prior to transepithelial migration (30, 31). In embryos laid by females expressing a loss 64 of function shotgun allele (𝑠ℎ𝑔!"#$"), individual germ cells separate from the cluster 65 prematurely (30). Furthermore, in 38% of 𝑠ℎ𝑔!"#$" mutant embryos, germ cells exhibit a 66 delay in crossing the midgut epithelium (30). The posterior midgut, which is the barrier 67 that the germ cells must breach, is made up of epithelial cells (32, 33). Remodeling of the 68 midgut epithelium endows the epithelial barrier with increased permeability, allowing 69 the germ cells to migrate through it (20, 34). High resolution imaging of the germ cells 70 crossing the midgut epithelium has shown that germ cells maintain contacts with the 71 epithelial cells with no evident intercellular space around them (20). In addition, FGF 72 signaling regulates the distribution of zygotic E-cadherin in the posterior midgut to 73 maintain its epithelial integrity (35). FGF mutants display mislocalized E-cadherin and 74 collapse of the midgut lumen, trapping the germ cells within (35). 75 Germ cells expressing defective E-cadherin (𝑠ℎ𝑔!"#$") show delayed 76 transepithelial migration (30), reminiscent of the delay in border cell migration that 77 occurs when nurse cells either lack or overexpress E-cadherin in the D. melanogaster egg 78 chamber (36). Together, these observations suggest the existence of a non-monotonic 79 relationship between migration efficiency and adhesion between migrating and 80 substrate cells. We set out to understand the role of heterotypic adhesion between the 81 migrating cells and “substrate” cells in transepithelial migration, taking as a case study 82 the role of intercellular adhesion mediated by E-cadherin in enabling the germ cells to 83 transmigrate. Leveraging genetic tools and two-photon microscopy, we live imaged the 84 process of transepithelial migration in vivo. We combined the insights gained from live 85 imaging with previously published observations to formulate an in silico model of the 86 process. This model, formulated in the Cellular Potts Model framework (37–39), 87 provides a novel mechanistic understanding of this transepithelial migration process. 88 Our model reveals the existence of optimal heterotypic adhesion between germ cells 89 and the epithelial cells, which maximizes the efficiency of midgut exit. In addition, our 90 in silico model yields testable, potentially generalizable predictions about the role of E-91 cadherin and intercellular adhesion that may be applicable to other systems of 92 heterotypic cell adhesion and migration. 93 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 5 of 27

94 I. Germ cells exit the midgut individually and maintain E -cadherin 95 expression throughout exit 96 To gain insight into the process of germ cell transepithelial migration, we live imaged 97 the process in vivo [Fig. 1b-b”]. Before migration, the germ cells are contained by the 98 epithelial barrier of the midgut [Fig. 1b], and located at a depth of more than 25𝜇𝑚 from 99 the cortex within the embryo (40). To visualize the germ cells, we used the previously 100 generated fly line nos-LifeAct-tdTomato (41) which specifically labels germ cell 101 membrane and cortex through posteriorly localized maternally deposited protein. The 102 cells in the gut epithelium also show some residual labelling since the gut arises from 103 the invaginating posterior blastoderm. The residual labelling generates contrast and 104 helps us estimate the position of the gut during transepithelial migration. 105 We tracked germ cells throughout transepithelial migration, characterizing their 106 progress at a five minute time resolution [SI Videos 1 - 3], and quantified the distances 107 of germ cells from the center to the edge of the midgut lumen as a function of time [Fig. 108 1 c]. Figure 1d-d’ shows the distance covered relative to their initial position (i.e. t = 0) 109 as a function of time for two different embryos. We found that individual germ cells 110 took 30 minutes on average to go through the midgut epithelial barrier [Fig. 1d-d’; SI 111 Videos 1 - 3]. Our live imaging of the transepithelial migration process did not reveal 112 any cell divisions in the midgut epithelial cells that could have generated spaces in the 113 epithelial barrier that would allow for easier exit of germ cells, in contrast to the 114 mechanism that regulates macrophage infiltration in D. melanogaster (42). 115 We also observed E-cadherin localization on the surface of germ cells during the 116 transepithelial migration by immunostaining for GFP in endogenously GFP-tagged E-117 cadherin embryos [Fig. 1e-e’] , a result consistent with previously published 118 experiments (30) that detected E-cadherin by immunostaining. We quantified the 119 intensity of E-cadherin signal at apical and lateral junctions between midgut epithelial 120 cells, as well as at the epithelial-germ cell junctions [Fig 1e’’]. Our quantification 121 revealed that the E-cadherin concentration at the germ cell-epithelial cell interface is not 122 significantly different from that observed between epithelial cells on the lateral side 123 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 6 of 27 [Fig. 1e’, p = 0.31]. The presence of E-cadherin in germ cells during transepithelial 124 migration, where germ cells physically contact epithelial cells (20), along with the 125 delayed midgut exit previously observed in shg loss of function mutants (30), suggests 126 that the expression of E-cadherin in germ cells is functional rather than incidental. 127 128 II. Time to exit the midgut has a non-monotonic dependence on germ cell 129 E-cadherin level 130 Although inspired by germ cell transepithelial migration, our central question is 131 broader: what role does heterotypic E-cadherin adhesion play in cell migration? To 132 generalize our question beyond germ cell transepithelial migration, we turned to in 133 silico modeling, retaining only essential features of the phenomenon. We developed a 134 two-dimensional model of transepithelial migration, where a single motile cell breaches 135 a ring of epithelial cells under the influence of an external, radial chemoattractant 136 gradient [Fig. 2a]. Our two-dimensional model, formulated as a Cellular Potts Model 137 (37, 38), enabled us to consider the cells as finite sized objects capable of deformations in 138 shape. We primarily explored the potential role of chemoattractant strength (λ%) and 139 the concentration of E-cadherin in the germ cells (𝐶&) in the time taken for the germ cells 140 to exit the epithelial barrier (τ'). We ran our simulations for a maximum of 10,000 141 Monte Carlo steps, and saved the position of the germ cell as a function of time for each 142 independent iteration for a given choice of system parameters. Figure 2a shows a 143 typical snapshot from our CompuCell3D simulation, and Figure 2b-b’’ shows the 144 modeled germ cell at three different stages of the transepithelial migration. In the CPM 145 framework, the temperature parameter (𝑇) controls boundary pixel activity, where 146 higher temperatures increase the likelihood of energy-raising pixel flips. To investigate 147 how membrane fluctuations at interepithelial junctions affect migration, we modulated 148 the temperature governing pixel acceptance rates at these boundaries. This allowed us 149 to study how epithelial remodeling influences transepithelial migration. 150 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 7 of 27 Our simulations [Fig. 2c-c’] revealed that elevated epithelial temperature 151 increased tissue permeability to germ cells, resulting in faster exit times (𝜏') and higher 152 escape probabilities (𝑝'). This is consistent with prior experimental findings where 153 failure in epithelial remodeling of the midgut adversely affected germ cell 154 transepithelial migration (20, 34, 43). 155 The strength of the modeled chemoattractant 𝜆% beyond which germ cells 156 successfully migrated through the barrier was positively correlated with epithelial cell 157 E-cadherin concentration 𝐶( [Fig. 3a–a’’]. We interpret this to mean that higher 𝐶( 158 values, indicating stronger adhesion between the epithelial cells, offered greater 159 resistance to the trans-migrating cell. Regardless of the value of 𝐶(, we observed that 160 the time taken to exit the barrier decreased with increased germ cell E-cadherin 161 concentration only up to a point, beyond which there was a sharp increase in the time 162 taken to breach the epithelial barrier [Fig. 3a–a’’]. This non-monotonic dependence of τ' 163 on 𝐶& suggested that there is an optimal range of heterotypic adhesion between germ 164 cell and the epithelial cell. Within this range, adhesion aids the transepithelial 165 migration, but beyond the range, it hinders germ cell movement. The minima of the 166 curves for different values of λ% in Figure 3a–a’’ coincide, indicating that the optimal 167 adhesion value for transepithelial migration is independent of the chemoattractant 168 strength. Interestingly, the coefficient of variation in the time to exit τ' as a function of 169 𝐶& has a trend that is inverse of the one exhibited by τ' [Fig. 3b]. Specifically, the 170 coefficient of variation is highest when the mean is the lowest, which is not due to 171 standard deviation being independent of 𝐶&. Instead, the standard deviation increases 172 with 𝐶& while the mean decreases with 𝐶& [SI Fig. 1]. 173 To better understand the potential role of heterotypic adhesion in determining 174 the speed of exit, we focused on the trajectories of the migrating cells at different values 175 of 𝐶&. We ran our simulations for a maximum duration of 10,000 Monte Carlo steps (44), 176 and the cells which had not exited by then were considered to have failed to exit. In 177 Figure 3c, the trajectories from ~1000 independent iterations are shown for 𝐶& = 4.89 , 178 𝐶( = 10.0 and λ% = 7000. While there are numerous instances of the migrating cell 179 failing at early stages of the transepithelial migration, we see many instances of germ 180 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 8 of 27 cells stuck to the outer edge of the epithelial barrier and failing to complete midgut exit. 181 We considered all the successful trajectories for 𝐶( = 10 and λ% = 7000 and normalized 182 the time for each trajectory, such that τ = 0 and τ = 1 mark the start and end of the 183 transepithelial migration respectively. The time-normalized mean trajectories are shown 184 in Figure 3d, colored according to their values of 𝐶& . We observed that germ cells with 185 lower E-cadherin concentrations spent much of their time getting to the middle of the 186 epithelial barrier, while the second half of the journey, culminating in complete exit 187 from the midgut, was quite rapid. The fraction of total time spent in getting to the 188 middle dropped with increasing germ cell–epithelial cell adhesion, with speed through 189 the barrier becoming constant for high values of 𝐶& (~7.0). To highlight the difference in 190 the fraction of total travel time spent at different halves of the epithelial barrier, we 191 show the fraction of time spent to cover the second half of the epithelial barrier (referred 192 to as τ)) in Figure 3d’. τ) showed a nonlinear increase with 𝐶& approaching 0.5 at lager 193 values of 𝐶&. The probability of success in exiting the epithelial barrier had an inverse 194 non-linear relation to time to exit τ' regardless of the 𝐶( , 𝐶& and λ%, as evident from the 195 scatter plot in Figure 3e. 196 197 III. Overexpression of E-cadherin in germ cells leads to faster exit through 198 the midgut 199 The results of our model suggested that increasing E-cadherin levels in germ cells 200 would enable them to complete the most time-consuming part of their journey, namely 201 traversing from the middle of the midgut lumen through the luminal epithelial surface, 202 more rapidly, thus resulting in a faster net transepithelial migration time. To test this 203 prediction in vivo, we employed the UAS-GAL4 system (45). Maternally deposited E-204 cadherin serves as the primary source of E-cadherin for all early embryonic cells, 205 including both germ cells and somatic cells (28, 30, 46). Notably, even during 206 transepithelial migration (~3 hours after egg laying), germ cell E-cadherin remains 207 predominantly of maternal origin, making RNAi-mediated knockdown in germ cells 208 impractical without destroying embryonic integrity (28, 30, 46). 209 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 9 of 27 Given these constraints, to assess the effects of E-cadherin overexpression on 210 transepithelial migration, we analyzed germ cell progression in embryos of four 211 different maternal genotypes, collected within 30 minutes from synchronously 212 ovipositing mothers and aged for five hours, as follows: (I) WT: Outcrossed wild-type 213 control, expressing endogenous levels of E-cadherin in all cells [nos-Gal4/+ ]; (II) Pan-214 Ecad-OE-A: with ubiquitous E-cadherin overexpression in all cells [nos>Ecad]; (III) Pan-215 Ecad-OE-B: with ubiquitous GFP-tagged E-cadherin overexpression in all cells 216 [nos>Ecad-GFP]; and (IV) GC-Ecad-OE: with germ cell-targeted overexpression of 217 mClover2-tagged E-cadherin [nos> Ecad-mClover2-nosTCE-pgc 3′UTR]. The position of 218 germ cells relative to the midgut lumen boundary in representative embryos from each 219 group is shown in Figure 4a–a’’’. Quantitative analysis revealed that germ cells in all 220 overexpression lines (II–IV) were located farther from the lumen center compared to 221 controls (I) [Fig. 4b]. Furthermore, both the mean germ cell distance from the lumen 222 center [Fig. 4c] and the fraction of germ cells that had exited the midgut [𝑓'*+, in Fig. 4d] 223 were higher in overexpression groups, with the most pronounced effect in the germ 224 cell-targeted overexpression line (IV). 225 These results suggest that higher levels of E-cadherin in germ cells accelerates 226 transepithelial migration, consistent with our theoretical model. We favor the 227 interpretation that the germ cell E-cadherin expression corresponds to the gray region 228 in Figure 4e. Under this interpretation, loss of function shg mutants like 𝑠ℎ𝑔!"#$" (30) 229 would drive the embryo toward the red region shown in Figure 4e, associated with 230 longer τ', while shg overexpression would drive it towards the green region in Figure 231 4e associated with faster germ cell exit. 232 Our model predicted that elevated epithelial E-cadherin would hinder migration 233 by increasing resistance to germ cell exit. Although our experiments did not test this 234 prediction directly, germ cells in our experiments overexpressing E-cadherin in both 235 somatic and germ cells showed reduced germ cell exit times. This apparent discrepancy 236 can be explained by the hypothesis that wild-type E-cadherin levels in somatic 237 epithelial cells are already near saturation. Under this interpretation, finite adhesion 238 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 10 of 27 junction availability and membrane transport limitations would prevent additional E-239 cadherin from forming new junctions at high concentrations (47–50). Thus, in embryos 240 with E-cadherin overexpression in both germ cells and somatic cells, like the ones we 241 examined herein (Fig. 4, groups II and III), we hypothesize that E-cadherin levels higher 242 than wild type levels would have a stronger effect on germ cells than on epithelial cells, 243 effectively mimicking germ cell-specific overexpression. 244 245

246 Our work sheds light on the potential role of heterotypic E-cadherin adhesion during 247 the transepithelial migration of germ cells through the midgut. The predictions of our in 248 silico model could in principle apply to any heterotypic adhesive migration process, as 249 we incorporated only a few features specific to germ cell transepithelial migration. Our 250

suggest a non-monotonic dependence of migration efficiency on the heterotypic 251 adhesion between the migrating cell and the substrate cells [Fig. 4d]. We posit that 252 traction is essential for cell migration, and that transmembrane proteins like integrins 253 facilitate traction by anchoring cells to the extracellular matrix, thereby enabling 254 forward movement (51). Additionally, cadherin-like molecules mediate homotypic 255 adhesion, allowing cells of the same type to form cohesive tissues such as epithelia (46, 256 52). These molecules also participate in heterotypic adhesion when migrating cells 257 interact with others expressing cadherins (53–55). A notable example is the 258 transendothelial migration of melanoma cells, where heterotypic adhesion is clearly 259 observed (53). More broadly, diapedesis - the process by which cells breach endothelial 260 barriers - relies on heterotypic interactions between transmembrane adhesion proteins 261 (54, 55). The prevalence of heterotypic adhesion during transepithelial migration 262 suggests that our work may have broader implications beyond the specific context of 263 Drosophila primordial germ cell migration. 264 Many conserved features of cell migration are applicable well beyond a specific 265 biological context. In a migrating cell, actin filaments polymerize at the leading edge 266 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 11 of 27 and undergo retrograde flow, functioning much like the rotation of wheels in a car (56–267 58). However, the forward motion of a cell depends on its physical coupling to the 268 substrate, just as the tires of a car grip the road to provide traction (56, 57, 59). This 269 mechanism is described by the molecular clutch model of cell motility (60). Adhesion 270 molecules such as integrins and cadherins allow cells to bind to surfaces or to other 271 cells, engaging the molecular clutch (60, 61). Integrin-mediated traction is typically used 272 when cells migrate over an extracellular matrix, whereas cadherins facilitate cell-on-cell 273 migration, as seen in the case of border cell migration (36, 61), and in the transepithelial 274 migration case that we consider here. 275 Our in silico model predicts that an intermediate adhesion strength between 276 migrating cells and substrate cells optimizes transmigration. Our finding aligns with 277 previous observations on D. melanogaster border cell migration in the egg chamber (36, 278 62). In the case of border cell migration, a cluster of six to eight border cells, enclosing a 279 pair of non-motile polar cells, migrates through a “substrate” formed by nurse cells (62). 280 Of these three cell types, polar cells express the highest levels of E-cadherin, which they 281 use to anchor to motile border cells, which have the second highest E-cadherin levels 282 (36). Meanwhile, border cells form transient junctions with nurse cell E-cadherin (which 283 is at the lowest levels of the three cell types in the system), pulling on nurse cells as they 284 migrate (36). Notably, E-cadherin knockdown in nurse cells impedes migration more 285 severely than knockdown in border cells, whereas E-cadherin overexpression in nurse 286 cells slows migration (36). These observations further support the concept that 287 intermediate heterotypic adhesion is optimal for transmigration, specifically E-cadherin 288 enabling the engagement of a molecular clutch (61). Migration in the absence of 289 sufficient intercellular adhesion resembles climbing a slippery ladder—lacking the 290 traction needed for upward movement. Conversely, excessive adhesion is akin to 291 ascending a ladder coated in glue, where detachment becomes the limiting factor. Thus, 292 an optimal level of "stickiness" is crucial for efficient migration. 293 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 12 of 27

294 Fly stocks and maintenance 295 Fly lines w[1118]; P{w[+mC]=GAL4::VP16-nanos.UTR}CG6325[MVD1] (abbreviated 296 herein as nanos-gal4-VP16; stock #4937), w[1118]; P{w[+mC]=UASp-shg.GFP}5B (#58445), 297 y[1] w[*]; TI{TI}shg[GFP] (#60584), and w[*]; P{w[+mC]=UASp-shg.R}5 (#58494) were 298 obtained from the Bloomington Drosophila Stock Center (Indiana, U.S.A.). Fly lines w; 299 nos-Lifeact-tdTomato-P2A-tdKatushka2-CAAX (Lifeact-tdTomato landing site VK00027; 300 abbreviated herein as nos-LifeAct-tdTomato) and w; UASp-DE-cadherin-mClover2-nosTCE-301 pgc 3′UTR (landing site attP2) (Lin et al., 2022) were a gift from Ruth Lehmann 302 (Whitehead Institute, USA). All flies and crosses were maintained on standard fly 303 medium (0.8% agar, 2.75% yeast, 5.2% cornmeal, 11% dextrose) in an incubator at 25˚C, 304 65% RH and 12H:12H light-dark cycle. 305 306 Fly crosses and embryo staging 307 To generate embryonic over-expression, UASp (over-expression) or Oregon R (wild 308 type control) lines were crossed to nanos-gal4-VP16 and heterozygous F1 virgin females 309 were collected. 40-50 F1 virgin females were then crossed with 8-10 Oregon R males and 310 transferred into an egg collection cage with a 5mm apple juice agar plate as base (63). In 311 the case of nos-LifeAct-tdTomato flies, an approximate 1:1 ratio of homozygous males and 312 females were transferred into an identical cage setup. Egg laying was allowed to 313 proceed in 30-minute windows and embryos were aged for five hours after the 314 midpoint of the egg laying window. After collection, embryos were either fixed 315 (embryonic over-expression) or used for live imaging (nos-LifeAct-tdTomato). 316 317 Live imaging 318 Appropriately staged nos-LifeAct-tdTomato embryos were manually dechorionated with 319 forceps on double-sided scotch tape and attached to a standard 90 mm polystyrene Petri 320 dish using heptane glue. The dish was then filled with sterile distilled water and 321 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 13 of 27 mounted on a Zeiss LSM 980 multi-photon microscope. Using a 20x water immersion 322 objective, the total volume of the embryonic gut was imaged at a two-photon excitation 323 wavelength of 1000nm, every 5 or 10 minutes for the indicated period. 324 325 Fixation and immunostaining 326 Appropriately staged embryos were collected on a mesh, rinsed with Milli-Q water, and 327 dechorionated using 70%(v/v) commercial bleach until most of the embryos had lost 328 the chorion (confirmed visually). Embryos were fixed in a 1:1 mix of heptane and 4% 329 paraformaldehyde in 1X phosphate buffered saline (1X PBS) at room temperature with 330 nutation for 20 minutes. After removing the aqueous layer, an equal volume of 100% 331 methanol was added, and embryos were devitellinized by vigorous manual shaking for 332 2–3 minutes. Fixed embryos were stored in 100% methanol at –20 °C. 333 For staining, embryos were rehydrated in 1X PBS, then washed, permeabilized 334 and blocked twice for 15 minutes in PBTB (1X PBS, 0.2% Triton X-100, 1 mg/mL bovine 335 serum albumin (Sigma-Aldrich, A9418). Embryos were then incubated with primary 336 antibodies diluted in PBTB overnight at 4 °C. The next day, embryos were washed (4 × 337 15 min, PBTB) and incubated overnight at 4 °C with fluorophore-conjugated secondary 338 antibodies and DAPI diluted in PBTB containing 4% normal goat serum (Jackson 339 Immunoresearch, 005-000-121). On the third day, embryos were washed (4 × 15 min in 340 1X PBS) and mounted in Vectashield (Vector laboratories, H1000) for imaging. 341 Primary antibodies used were chicken anti-Vasa (1:800) (Repouliou et al., 2025) 342 and mouse anti-GFP conjugated to AlexaFluor 488 (1:1000; (Invitrogen, A-21311). 343 Secondary antibody used was goat anti-chicken (1:200) conjugated to AlexaFluor 568 344 (Invitrogen, A-11041). DNA was stained with DAPI (Sigma-Aldrich, D9542) at 1:2000 345 dilution of a 10 mg/mL stock. 346 347 In silico model of transepithelial migration 348 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 14 of 27 A cross-sectional slice of the epithelial midgut was modelled as a two-dimensional ring 349 formed by 20 epithelial cells. The epithelial ring is embedded in a radial chemical field 350 representing the spatial concentration of the chemoattractant. The magnitude of the 351 chemical concentration increases linearly with the radius, and the minimum coincides 352 with the center of the epithelial ring. At t=0, the germ cell begins slightly off-center, 353 with its initial angle randomly chosen between 0 and 360 degrees, and then migrates 354 outward toward regions of higher chemoattractant concentration. 355 Our two-dimensional model of the epithelial ring and the germ cells was 356 formulated in the Cellular Potts Model (CPM) framework (37–39). The cells in a CPM 357 are represented as a contiguous collection of pixels. Pairwise interactions between 358 pixels at the cell boundaries have an associated energy cost, 𝐽. Given two pixels 𝑎 and 𝑏, 359 we use the value of 𝐽-,/ to reflect the adhesion energy of the cells to which the two 360 interacting boundary pixels belong. Our model assumes that adhesion energy increases 361 with the number of adherens junctions formed, and that the number of adherens 362 junctions is in turn a function of the E-cadherin concentration. The maximum possible 363 number of junctions between two cells is thus determined by the surface E-cadherin 364 concentration of the cell that has fewer such molecules. As a result of our assumptions, 365 if σ(𝑎), σ(𝑏) are the indices of the cells to which pixels 𝑎 and 𝑏 belong, and 𝐶?σ(𝑎)@ and 366 𝐶?σ( 𝑏)@ are the E-cadherin concentrations of the two cells, then the interaction energy 367 term is 𝐽-,/ = 𝑚𝑖𝑛?𝐶?σ(𝑎)@, 𝐶?σ(𝑏)@ @. In our work, we have assumed that all epithelial 368 cells have E-cadherin concentration equal to 𝐶(, and that all germ cells have E-cadherin 369 concentration equal to 𝐶&. The energy function of the system of pixels is given by the 370 following equation: 371 E  =   − F 𝑚𝑖𝑛?𝐶?σ(𝑎)@, 𝐶?σ(𝑏)@ @  -,/ −   F λ! 0  (𝐴0  −  𝐴1)) −   F λ2 0  (𝐿0  −  𝐿1)) 372 The λ! and λ2 terms determine the magnitude of the energy cost required for a cell area 373 and perimeter to deviate from the steady state values 𝐴1 and 𝐿1 respectively. The 374 system is simulated using the metropolis algorithm (44), where the probability of a pixel 375 flip is related to the change in the magnitude of the energy of the system as a result of 376 that specific pixel flip. Under appropriate energy conditions, pixels at the boundary 377 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 15 of 27 may flip to the cell state of one of their neighbors that has a different cell state. At each 378 iteration of the simulation algorithm, one such potential pixel flip is considered, and the 379 pixel is flipped if the resulting system has lower energy than the current state. If the 380 pixel flip would not reduce the energy of the system, the pixel flips with probability 381 𝑝34+5 = 𝑒𝑥𝑝(−Δ𝐸/𝑇), where Δ𝐸 is the change in energy due to the pixel flip and 𝑇 is the 382 temperature. The temperature term 𝑇 represents the extent of stochasticity (noise) in the 383 pixel dynamics, with higher 𝑇 increasing the probability of pixel flips that increase the 384 energy of the system. Chemotaxis is implemented within the CPM framework by 385 biasing pixel flips that aid cell movement in the direction of the gradient of 386 chemoattractant. In the presence of the attractant whose value at any pixel in 2D space 387 is 𝑀-,/, the change in energy due to a pixel flip, where a pixel at (𝑎, 𝑏) is copying the 388 state of a pixel at (𝑎’, 𝑏’) becomes Δ𝐸6 = Δ𝐸 − λ7 ?𝑀-!,/! − 𝑀-,/ @ (39). This additional term 389 favors the pixel flip when the chemical field value at (𝑎’, 𝑏’) is higher than (𝑎, 𝑏). To 390 prevent the epithelial ring from collapsing and forming a cell aggregate without a 391 lumen, we model the lumen as one large cell with a volume constraint. In addition, we 392 mechanically couple the epithelial cells by connecting the centroids of the adjacent cells 393 with springs using the FocalPointPlasticity plugin of CompuCell3D (64). The key 394 parameters that we explored in our work are 𝐶&, 𝐶( and λ%. The CompuCell3D 395 implementation of our model can be found at 396 https://github.com/boyonpointe/GermCellTransepithelialMigration with commit ID 397 7ce2534. 398 399 400 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 16 of 27

401 We thank members of the Extavour Lab for helpful discussions, and Ruth Lehmann for 402 sharing fly lines. 403 404 Data Availability 405 Scripts for Compucell3D simulations and image analysis are available at 406 https://github.com/boyonpointe/GermCellTransepithelialMigration with commit ID 407 7ce2534. 408 409 Author Contributions 410 CK conceived of the study, designed and performed all computational experiments, 411 performed data analysis and interpretation, and wrote the first draft of the manuscript. 412 SG conceived of the study, designed and performed wet lab experiments, and reviewed 413 and edited the manuscript. CGE obtained funding for the study, supervised its execution, 414 and reviewed and edited the manuscript. 415 416 Funding 417 This study was supported by a postdoctoral fellowship to CK through the NSF-Simons 418 Center for Mathematical and Statistical Analysis of Biology at Harvard (award number 419 DMS-1764269), the Harvard Quantitative Biology Initiative, and by funds from Harvard 420 University and the Howard Hughes Medical Institute (HHMI). CGE is an HHMI 421 Investigator. 422 423 Conflicts of Interest 424 The authors declare no conflicts of interest.425 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 17 of 27 Figure 1: Germ cells exit the midgut individually at comparable speeds. (a-a’’) Schematic of D. melanogaster embryonic germ line development. The primordial germ cells are formed at the posterior tip at stage 5. Following gastrulation, they are contained in the midgut at stage 7, and eventually exit the midgut through transepithelial migration at stage 10. (b-b’’) Three snapshots from live imaging of the TEM process as the germ cells make their way through the midgut. (c) The distribution of the distances of the germ cells from center of the midgut lumen at five different time points are shown. Small numbers under plots indicate sample sizes (number of cells). (d- d’’) Movement of germ cells in time measured with respect to their initial (t = 0) position for two different live imaged embryos. Black circles: positions within lumen; magenta rhomboids: positions within the midgut epithelium; white squares: positions outside the midgut. (e) Higher magnification of the midgut during germ cell transepithelial migration. Magenta: E-cadherin; green: germ cell-specific protein Vasa. (e’) Germ cells express E-cadherin during the transepithelial migration (boxes). (e’’) The relative intensity (au: arbitrary units) of the E-cadherin fluorescent signal at the epithelial cell – germ cell junction (𝐸𝐺), lateral epithelial – epithelial junction (𝐸"#$) and apical epithelial – epithelial junctions (𝐸#%& ). n = 24 junctions for all categories. .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 18 of 27 Figure 2: Greater epithelial junctional remodeling aids germ cell transmigration. (a) Snapshot of Cellular Potts Model simulation of a germ cell (yellow) exiting the two-dimensional epithelial ring (green). Pixels at the boundary of the cells are shown in black. Colored arrows point in the direction of chemoattractant gradient; colors represent the concentration of the chemoattractant. (b-b’’) Snapshots of the germ cell (b) before entering the epithelial barrier, (b’) while inside the barrier and (b’’) just before exiting the barrier. Numbers at top right indicate the time in units of Monte Carlo steps (mcs). (c) Average time taken (τ') for the germ cell to exit the midgut decreases with increase in interepithelial dynamics (T(). (c’) Probability of successfully exiting (𝑝') increases with T(. Trends in c and c’ are independent of the strength of the chemoattractant (λ)). The shaded silver line corresponds to 𝑇( = 10, the value at which al simulations described herein are carried out, unless specified otherwise. Simulation parameters: λ) = 7000, 𝐶( = 10, 𝐶* = 5, 𝑇 = 10. .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 19 of 27 Figure 3: Time to exit the epithelial barrier has a non-monotonic dependence on germ cell E-cadherin concentration. (a-a’’) The time a simulated germ cell takes to exit the 2D midgut epithelial barrier as a function of germ cell E-cadherin concentration (𝐶*). (a), (a’) and (a’’) represent increasing epithelial cell E- cadherin concentrations (𝐶( = 8, 𝐶( = 10, 𝐶( = 12 respectively), offering increasing resistance to the germ cell transepithelial migration. The curves in each of the three panels are colored according to the strength of the chemical field (λ)). Regardless of the value of 𝐶(, for strong enough values of λ) the time to exit shows a minimum that is independent of the λ) value. (b) The coefficient of variation in time to exit as a function of 𝐶* for the case of 𝐶( = 10. (c) Trajectories of germ cells for a typical parameter set obtained from 1000 independent stochastic simulations. Silver: successful TEM; brown: germ cell exit failure; black lines: mean position of the epithelial cells forming the 2D barrier. (d) Mean distance covered by the germ cell within the barrier (𝑙') as a function of time . The time 𝜏 is normalized by the total time of travel, where 0 represents time of entry into the barrier and 1 represents time of exit. When the germ cell E- cadherin concentration is low, the germ cell covers much of the distance in a very short interval of time at the end of the journey. Higher germ cell E-cadherin levels lead to the germ cell migrating at roughly uniform speed throughout the journey. (d’) The time taken to cover the second half of the journey 𝜏+ as a function of germ cell E-cadherin concentration. (e) The relationship between 𝜏',&$ and 𝑝',&$ is shown using data aggregated by simulating the model over various values of λ), 𝐶* and 𝐶(. 𝜏',&$ decreases monotonically with 𝑝',&$, implying that the shorter the time to exit, the higher the chances of exiting. .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 20 of 27 Figure 4: Higher germ cell E-cadherin promotes quicker midgut exit in vivo. (a) (L-R) Representative micrographs showing the extent of transepithelial migration in the four experimental groups. I corresponds to the control, II and III represent lines where E-cadherin is overexpressed in all cells and IV corresponds to embryos where E-cadherin overexpression is targeted to the germ cells. (b) The distribution of distances of germ cells from the center of the lumen for the four experimental groups. Grey and black symbols represent cells inside and outside the gut respectively. The distances of the germ cells from the lumen are largest in the condition with increased germ cell-targeted E-cadherin overexpression (IV). Small numbers under plots indicate sample sizes (number of germ cells). (c) Mean distance of the germ cells from the center of the lumen in each embryo for the four experimental groups. Small numbers under plots indicate sample sizes (number of embryos). (d) Fractions of germ cells per embryo that have exited the midgut by 5.25 hours after egg laying in the four experimental groups. Small numbers under plots indicate sample sizes (number of embryos). (e) We hypothesize that the WT embryos (group I) have 𝐶* in the pink shaded region, and that germ cell-targeted E-cadherin expression pushes the system towards the green shaded region, leading to shortening of 𝜏'. .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 21 of 27 SI Figure 1: The mean and the variance of 𝛕𝒆 exhibit converse trends. The figure shows the mean τ' (top) and standard deviation µ.! (bottom) as a function of germ cell E-cadherin concentration 𝐶* for the case when 𝐶( = 10. The peak in the standard deviation as a function of 𝐶* coincides with the minima in the case of time to exit. The differently colored curves correspond to different strengths of the chemoattractant pull λ) . .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 22 of 27 SI Video Legends SI Video 1: Transepithelial migration of germ cells. Dorsal cross-sectional view of the gut during TEM in a nos-LifeAct-tdTomato embryo. Maximum intensity projection of 15 planes spaced at 2 μm. Scale bar is 20 μm. SI Video 2: Transepithelial migration of germ cells: higher magnification 1. Dorsal cross- sectional view of the gut during TEM in a nos-LifeAct-tdTomato embryo. Maximum intensity projection of 20 planes spaced at 2 μm. Scale bar is 20 μm. SI Video 3: Transepithelial migration of germ cells: higher magnification 2. Lateral cross- sectional view of the gut during TEM in a nos-LifeAct-tdTomato embryo. Maximum intensity projection of 20 planes spaced at 2 μm. Scale bar is 20 μm. SI Video 4: CompuCell3D simulation of a germ cell successfully exiting the midgut. The video shows an instance of a germ cell successfully exiting the epithelial ring in our in silico model simulated in CompuCell3D. The parameter values used here are λ% = 4000, 𝐶& = 5.0, 𝐶( = 10.0. SI Video 5: CompuCell3D simulation of a germ cell failing to exit the midgut. The video shows an instance of a germ cell failing to exit the epithelial ring in our in silico model simulated in CompuCell3D. The parameter values used here are λ% = 4000, 𝐶& = 1.0, 𝐶( = 10.0. .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted August 31, 2025. ; https://doi.org/10.1101/2025.08.29.673192doi: bioRxiv preprint Page 23 of 27

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