# Balance between Apical Membrane Growth and Luminal Matrix Resistance Determines Epithelial Tubule Shape

Bo Dong, Edouard Hannezo, Shigeo Hayashi

► To cite this version:

Bo Dong, Edouard Hannezo, Shigeo Hayashi. Balance between Apical Membrane Growth and Luminal Matrix Resistance Determines Epithelial Tubule Shape. Cell Reports, 2014, 7 (4), pp.941-950. 10.1016/j CELREP. 2014.03.066. hal-01311650

HAL Id: hal-01311650

https://hal.sorbonne-universite.fr/hal-01311650

Submitted on 4 May 2016

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Balance between Apical Membrane Growth and Luminal Matrix Resistance Determines Epithelial Tubule Shape

Bo Dong,<sup>1,*</sup> Edouard Hannezo,<sup>2</sup> and Shigeo Hayashi<sup>1,3,*</sup>

## SUMMARY

The morphological stability of biological tubes is crucial for the efficient circulation of fluids and gases. Failure of this stability causes irregularly shaped tubes found in multiple pathological conditions. Here, we report that *Drosophila* mutants of the ESCRT III component Shrub/Vps32 exhibit a strikingly elongated sinusoidal tube phenotype. This is caused by excessive apical membrane synthesis accompanied by the ectopic accumulation and over-activation of Crumbs in swollen endosomes. Furthermore, we demonstrate that the apical extracellular matrix (aECM) of the tracheal tube is a viscoelastic material coupled with the apical membrane. We present a simple mechanical model in which aECM elasticity, apical membrane growth, and their interaction are three vital parameters determining the stability of biological tubes. Our findings demonstrate a mechanical role for the extracellular matrix and suggest that the interaction of the apical membrane and an elastic aECM determines the final morphology of biological tubes independent of cell shape.

## INTRODUCTION

Biological tubules are shaped into networks of distinct patterns to function in fluid and gas transportation for metabolism and homeostasis (Baer et al., 2009). In vascular tubulogenesis, flow mechanics transduced to cells determine tube morphology (Hahn and Schwartz, 2009). In the *Drosophila* tracheal system, tube length, width, and integrity are regulated by apical extracellular matrix (aECM) (Jaźwińska et al., 2003; Luschnig et al., 2006; Wang et al., 2006), Crumbs (Crb)-dependent apical membrane growth (Laprise et al., 2010), and cell/cell junctions (Beitel and Krasnow, 2000). Mutations of aECM and septate junction (SJ) components cause tube overelongation, indicating that they restrict axial elongation (Luschnig et al., 2006; Nelson et al.,

2010; Wang et al., 2006). Recently, tyrosine kinase Src42A has been identified as a factor required for axial elongation (Förster and Luschnig, 2012; Nelson et al., 2012). Although some molecular mechanisms for epithelial tube size control have been uncovered, how the apical membrane and extracellular matrix (ECM) interact to affect tube geometry is still poorly understood.

ESCRT (endosomal sorting complex required for transport) III is cytoplasmic machinery required for membrane deformation, internalization, and scission (Wollert et al., 2009). The shrub gene in *Drosophila* encodes Vps32 (homologous to mammalian CHMP4 and yeast Snf7), a subunit of ESCRT III, which regulates endocytotic sorting of membrane-associated proteins leading to lysosomal degradation (Hori et al., 2011). Shrub is essential for dendritic morphogenesis (Sweeney et al., 2006) and organogenesis in *Drosophila* embryos (Vaccari et al., 2009).

In this study, we report that *Drosophila* mutants of the ESCRT III component Shrub/Vps32 exhibit a strikingly elongated and sinusoidal tube phenotype. Excessive apical membrane accumulation in this mutant was accompanied by ectopic accumulation of Crb in endosomes. We provide evidence that the aECM component is an elastic material coupled to the apical membrane and that this coupling is required for tube length regulation. We developed a physical model in which stability of a tube is determined by aECM elasticity, apical-membrane growth, and their association. Our findings suggest that the interaction of the apical membrane and elastic aECM determines the stability of biological tubes.

## RESULTS AND DISCUSSION

### Shrub Restricts Apical Membrane Overexpansion

In a search for mutants affecting ESCRT function, we found that shrub (ESCRT III component) affected tube length. The dorsal trunk (DT) of the tracheal tube in shrub<sup>2</sup> mutants was abnormally long and wavy, with a pitch of approximately one turn per segment, whereas control DTs were straight (Figures 1A and 1F). Similar phenotypes were observed in embryos with a P element (P[EPgy2]shrb<sup>EY05194</sup>) insertion (Figure 1B) and another allele of shrub mutant Vps32<sup>G5</sup> (Figure 1C). Overexpression of Shrub-GFP, which acts as a dominant-negative form (Sweeney

<figure><img src="image_2.png" /></figure>

<footnote n="1"><sup>1</sup>Laboratory for Morphogenetic Signaling, RIKEN Center for Developmental Biology, 2-2-3 Minatojima-minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japan</footnote>

<footnote n="2"><sup>2</sup>Physicochimie Curie (Institut Curie/CNRS-UMR168/UPMC), Institut Curie, Centre de Recherche, 26 rue d'Ulm, 75248 Paris Cedex 05, France</footnote>

<footnote n="3"><sup>3</sup>Department of Biology, Kobe University Graduate School of Science, 1-1 Rokkodai-cho, Nada-ku, Kobe, Hyogo 657-8051, Japan</footnote>

<footnote>*Correspondence: dong@cdb.riken.jp (B.D.), shayashi@cdb.riken.jp (S.H.)
http://dx.doi.org/10.1016/j.celrep.2014.03.066</footnote>

<footnote>This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).</footnote>
<figure><img src="image_3.png" /><figcaption>Figure 1. Apical Membrane Overgrowth Contributes to the Abnormally Elongated and Wavy Tracheal Tube in *shrub* Mutant Embryos</figcaption></figure>

(A) Stage 14 and 16 control (*shrub*⁴/+) and *shrub*⁴ homozygous mutant embryos were stained with a fluorescent CBP to show the tube lumen of the DT.

(B) Stage 16 embryo with a P element (*P*(*EPgy2*|*shrub*EY05194) insertion in 73 nucleotides upstream of the *shrub*-coding region.

(C) Stage 16 homozygous *Vps32*G5 mutant embryos were stained with CBP to show the overelongated DT.

(D) Stage 16 Shrub-GFP-expressing embryos (Shrub-GFP driven by *btl*-GAL4, a tracheal driver) were stained with CBP.

(E) Overexpression of Serp-GFP in stage 16 WT and *shrub*⁴ mutant embryos.

(F) Quantification of DT length in control, *shrub*⁴, Shrub-GFP-expressing, and *Vps32*G5 embryos at the indicated developmental stages. Significant difference is shown in the DT length between the *shrub*⁴, *Vps32*G5 mutant, or Shrub-GFP-expressing embryos and the control embryos by Student's t test (\*\*p < 0.01).

(G) Stage 16 control and *shrub*⁴ homozygous embryos immunostained for laminin A to label the basement membrane, Uif for the apical membrane, and CBP for the lumen.

(H) 3×TagRFP driven by *btl*-GAL4 expressing in *shrub*⁴ mutant embryos.

(legend continued on next page)
et al., 2006) in the tracheal system, phenocopied the *shrub* mutant phenotype (Figures 1D and 1F). On the other hand, the *shrub*⁴ tube diameter was comparable to that of control embryos, and the apical surface was smooth (Figure 2A). These results strongly indicate that Shrub activity is essential for restricting the tube length.

To identify which part of the membrane compartment contributes to tube elongation, the apical and basement membranes were labeled with anti-Uninflatable (Uif) and anti-laminin A antibodies, respectively. In optical sections of the control trachea, the two labels appeared as parallel lines separated by cytoplasm of a uniform width (Figure 1G). In contrast, the DT of *shrub*⁴ mutants showed an increased amount of apical membrane, with irregularly shaped cytoplasm. However, the basement membrane of the *shrub*⁴ mutants expanded only slightly (Figure 1G), leading to a disproportionately elongated and wavy apical membrane and a relatively straight basement membrane (Figure 1G). Analysis of apical and basal cell outline labeled by cytoplasmic TagRFP revealed the same conclusion (Figure 1H). We furthermore analyzed the apical area of individual cells and found that apical surfaces of DT cells in *shrub*⁴ mutants were 38% larger than in controls (Figures 1I and 1J). We investigated the possible contribution of aberrant cytoskeletal organization in the *shrub* mutants, but the subcortical actin organization was normal (Figure S1A). Given that ESCRT components are tumor suppressors, whose absence might lead to cell proliferation (Vaccari et al., 2009), we also counted the number of DT cells in the sixth tracheal metamere but found no significant difference between the control and *shrub* mutants (Figures S1B and S1C). Taken together, our results suggest that the *shrub* mutation promotes the preferential overgrowth of the DT apical membrane.

## Shrub Negatively Regulates Crb Activity

To identify the downstream process controlled by *shrub*, we examined the localization of Crb, which encodes an apical membrane determinant (Tepass et al., 1990; Wodarz et al., 1995). In the *shrub*⁴ mutants, Crb showed normal apical marginal localization in the tracheal system at an early stage (stage 14) (blue arrowheads in Figure S2A), and ectopic accumulation was found in both trachea and epidermis (yellow arrowheads in Figures S2A and S2B). At the late stage, Crb was lost from the apical membrane (blue arrowheads in Figure 2A) and formed prominent cytoplasmic aggregates (yellow arrowheads in Figure 2A), and the total Crb expression level detected by western blotting was markedly increased (Figure 2B). These results suggest that the loss of Shrub caused defective Crb turnover, leading to accumulation at an ectopic location where misregulated Crb activity stimulates apical membrane overgrowth. To verify this idea, we tested the epistatic relationship between *shrub* and *crb*. The introduction of one copy of the loss-of-function *crb* allele indeed suppressed the DT length phenotype of the *shrub*⁴ mutants (Figure 2D).

Why does the *shrub* mutation cause Crb-dependent apical membrane overgrowth while reducing Crb's apical localization (Figure 2A)? It was previously suggested that the membrane-bound intracellular domain of Crb fails to localize to the apical membrane (Pellikka et al., 2002), but it is sufficient for directing apical membrane growth when it is expressed in *crb* mutants (Klebes and Knust, 2000; Wodarz et al., 1995). To examine whether the accumulated Crb in endosome signals for apical membrane growth in the *shrub* mutant, we overexpressed the membrane-bound cytoplasmic domain of Crb (Myc-Crb<sub>intra</sub>) (Klebes and Knust, 2000) in wild-type (WT) embryos and found that it indeed caused apical membrane overgrowth and showed convoluted tracheal tube (Figure S2C).

In *shrub*⁴ mutant, apical area of tracheal cells was increased toward anterior-posterior (AP) axis orientation (Figure 1I and 1J), but not along the circumferential surface (Figure 2A), suggesting that a mechanism that directs overaccumulated apical membrane toward AP axis must be present. Src42A was previously shown to promote growth of apical membrane in DT cells and orient it into AP direction (Förster and Luschnig, 2012; Nelson et al., 2012). In order to ask if there is an epistatic relationship between shrub and Src42A, we combined *shrub*⁴ and *Src42A*<sup>26-1</sup> (Takahashi et al., 2005) mutations and found that in the double mutants, phenotypes of each single mutant canceled each other, and tracheal tube length was normal as WT (Figure S2D), suggesting that either Src42A acts downstream of Shrub or they act in different signaling pathways on tube length regulation. In any case, Src42A remains active in *shrub* mutants and is responsible for the phenotype of axial overelongation.

## Additional Defects in the *shrub* Mutants

It was reported that overactivation of Crb is responsible for the tube overelongation phenotype of SJ gene *Coracle* (*cora*) (Laprise et al., 2010). In order to study if SJ is affected in *shrub* mutants, we examined the localization of *Cora* and *Kune-kune* (Nelson et al., 2010). Although those markers maintained cell junctional localization, minor (*Cora*) and strong (*Kune-kune*) cytoplasmic mislocalization was observed (Figure S2E). In addition, *Kune-kune* appeared in punctate cytoplasmic structures (Figure S2E). A dextran dye-injection experiment demonstrated that epithelial barrier function was defective in *shrub* mutants (Figure S2E). We also studied the localization of another key determinant of the apical membrane, atypical protein kinase C (aPKC), and found that neither its apical localization (Figure 2C) nor its expression level (Figure 2B) was altered in the *shrub*⁴ mutants. We further examined expression of the two chitin deacetylases, Serpentine (Serp) and Vermiform (Verm), and found that luminal localization of Verm was normal, and Serp was slightly reduced (Figure S3D). Because *cora* mutation caused mislocalization of both Serp and Verm, the *shrub* phenotype represents partial loss of SJ function. Taken together, Shrub has multiple downstream targets, including apical and SJ proteins, and secreted chitin deacetylase. Among them, the defects in Crb,

(I) Stage 16 control and *shrub*⁴ mutant embryos were stained with DE-cadherin to show the apical surface of DT cells.

(J) Quantification of the apical surface area ratio between *shrub*⁴ mutant and the control embryos. Significant increase is shown of apical surface area in the *shrub*⁴ mutant compared with that in control by Student's t test (**p** < 0.01).

Scale bars represent 50 µm (A–E and H, top) and 10 µm (G, I, and H, bottom).
<figure><img src="image_4.png" /><figcaption>**Figure 2. Localization of Apical Membrane Proteins in shrub⁴ Mutants**</figcaption></figure>

(A) Control and *shrub*⁴ mutant embryos immunostained for apical membrane proteins Crb and Uif. Yellow arrowheads show the colocalized Crb and Uif accumulated in the cytoplasm. Blue arrowheads indicate the nearly complete loss of Crb from the apical membrane, where a significant level of Uif remained.

(B) Western blotting of whole-cell lysates from 24 WT and *shrub*⁴ mutant embryos probed with anti-Crb and anti-aPKC.

(C) Stage 16 embryos immunostained for aPKC and Uif.

(D) Stage 16 *shrub*⁴ mutant and *shrub*⁴ crb²/+ embryos were stained with CBP.

(E) Schematic representation of Shrub's control of apical membrane biogenesis through the regulation of Crb activity via intracellular trafficking pathways and/or Sj. In WT (left), the Crb activity is maintained by a balance between Rab11- and retromer-mediated recycling and degradation pathways. The loss of Shrub (right) causes Crb to accumulate in swollen endosomes, and the Crb activity is upregulated, which induces apical membrane biogenesis, resulting in apical membrane overgrowth. The loss of Shrub also caused defect of epithelial barrier function, which might also contribute to the Crb overactivity and the overgrowth of apical membrane in *shrub* mutants.

Scale bars represent 10 µm (A and C) and 50 µm (D).
Serp, and SJ protein localization can account for the observed phenotype. Genetic suppression of *shrub* phenotype by reduction of *crb* gene dosage argues that Crb is the major target of Shrub-dependent regulation of apical membrane growth.

Next, we investigated the identity of the structure containing the cytoplasmic Crb and Uif aggregates in the *shrub* mutants. The aggregates colocalized with the *Drosophila* ESCRT 0 component hepatocyte growth factor-regulated tyrosine kinase substrate (Lloyd et al., 2002) (Figure S2F) and the late-endosome marker Rab7 (Figure S2G), but not with the recycling endosome marker Rab11 (Figure S2H). The ESCRT complexes mediate the internal budding of the endosomal membrane for the sorting of proteins for lysosomal degradation, and some endocytosed Crb is recycled to the cell surface by pathways dependent on Rab11 (Roeth et al., 2009), Exo84 (Blankenship et al., 2007), or retromer (Pocha et al., 2011; Zhou et al., 2011). Our observations indicate that Crb activity is additionally downregulated by an ESCRT III-dependent late-endosomal sorting process that balances the processes of biogenesis and degradation flux. In *shrub* mutants, Crb accumulated at the endosomal membrane budding site and signaled its downstream pathway to activate apical membrane overgrowth from this ectopic location (Figure 2E). It should be noted that defect of SJ caused by loss of Shrub might also contribute to Crb overactivation (Figure 2E).

## Physical Parameters Defining Tube Stability

Our findings indicate that the excess apical membrane growth in the *shrub* mutants coupled with the Src42A-dependent axial polarization mechanism (Förster and Luschnig, 2012; Nelson et al., 2012) caused the overelongation of the DT. The periodicity of the wavy tube implied that its shape might follow a physical rule. On a timescale of hours, developing animal tissues are well described by the theory of growing elastic media (Li et al., 2012; Savin et al., 2011). In the *Drosophila* tracheal system, because the basement membrane in the *shrub* mutants only exhibits a very weak deformation compared to the apical membrane, the sinusoidal tube phenotype must result from mechanical properties of the apical membrane and the aECM, which together shape the tube. We therefore made three key predictions for the physical model of this process: first, the axial increase in apical membrane and membrane cortex synthesis provides an expansion force; second, aECM has an elastic component capable of balancing the expansion force; and third, the apical membrane and elastic luminal core are mechanically coupled, which determines the final length of the tube. The first prediction appears to be met by the results described above along with a previous observation that apical membrane growth is the major contributor of tube elongation (Laprise et al., 2010). Our model concerns the late stage of tracheal morphogenesis when Src42A-dependent axial elongation predominates over diameter expansion. In this stage, apical membrane expansion mainly drives the tube elongation. To test the remaining predictions, we studied the physical properties of the luminal matrix and its interaction with the apical membrane.

## Characterization of Luminal Matrix

To examine the physical properties of the aECM of the tracheal tube, we performed fluorescence recovery after photobleaching

(FRAP) experiments, using GFP-"tagged" luminal proteins. A major component of the luminal matrix is chitin, a polymer of N-acetylglucosamine that uniformly fills the tracheal lumen (Figure 1). A proteinaceous matrix also contributes to the lumen. One of the known components is Dumpy (Dp), a giant zona pellucida (ZP) domain matrix protein required for epithelial integrity (predicted maximum size 2443.4 kDa; Wilkin et al., 2000). The loss of Dp or another ZP domain protein, Piopio (Pio), causes the tracheal tube to twist and break (Bökel et al., 2005; Jażwińska et al., 2003), indicating that ZP proteins are involved in the mechanical stability of the tube and the maintenance of the tube integrity (Jażwińska et al., 2003; Wilkin et al., 2000).

We first investigated the localization of endogenous Dp, using a GFP "trapped" strain (http://www.flyprot.org), and found that Dp localized to the tracheal lumen (Figure 3A). The pattern of Dp-GFP distribution was different from that of chitin, with a denser layer forming a "shell" (blue arrowheads in Figures 3A' and 3A''), and a central core (yellow arrowhead in Figures 3A' and 3A''). This is identical to the pattern of Pio (Jażwińska et al., 2003). Remarkably, our results showed that even 68 min after photobleaching the Dp-GFP, none of the fluorescence had recovered, so that the exchange and/or diffusion of Dp-GFP is negligible on the timescale of the morphogenetic event (Figure 3B; Movie S1). From the theory of entangled biopolymer networks, this indicates that the aECM is in the rubber plateau (Frey et al., 1998) and can be described as an elastic material.

This absence of recovery allowed us to study whether the ECM elongated in concert with the epithelial tube, by measuring the elongation rate of the Dp labeling in the core matrix. The length of the photobleached region (bleached length [BL]) and the distance between cellular landmarks (the dorsal and ventral branch, designated tubule length [TL]) were measured separately (Figure 3B). During the 68 min experiment, both TL and BL elongated in parallel by approximately 30% (Figures 3B and 3C; Movie S1). These findings show that the Dp matrix is stretched by a force applied from the cells (Figure 3D) and must therefore be connected to the epithelium. The idea that the Dp matrix behaves elastically on the timescales agrees with the previously reported role of Dp as an elasticity molecule, which modulates mechanical tension within cuticle and wing (Wilkin et al., 2000).

To better characterize the properties of the ECM, we next performed the FRAP experiment using ANF-GFP (37.8 kDa) as a marker of an inert secreted protein (Rao et al., 2001). Its luminal fluorescence recovered rapidly (half-maximal recovery time of 17 s), accompanied by a reduction of fluorescence in the adjacent region (yellow arrowheads in Figure 3E; Movie S2), before reaching a plateau below the initial fluorescence level. This result is consistent with the presence of an immobile fluorescent fraction and indicates that the aECM is composed of a Dp gel and a solvent whose effective viscosity can be estimated. Fitting the fluorescence recovery curve with a model of simple diffusion for the mobile fraction (Figure 3G) yielded a diffusion constant of 13 µm²/s for ANF-GFP. For a globular protein of this size (Stokes radius, ~3 nm) to diffuse with this diffusion constant, the fluid would be approximately ten times the viscosity of water, which is in the range of the diffusion characteristics of GFP in cellular compartments (Dayel et al., 1999). The decrease in GFP fluorescence in a distant region of the same DT (orange
<figure><img src="image_5.png" /><figcaption>**Figure 3. Viscoelastic Properties of the Luminal Matrix**</figcaption></figure>

(A) Dp-GFP is present in the lumen and does not colocalize with the apical membrane protein Crb (A'). It concentrated in a central matrix core (yellow arrowheads in A' and A'') and in the peripheral region (blue arrowheads in A' and A'').

(B) FRAP experiment using Dp-GFP in DT. The white lines with double arrowheads indicate the BL and cellular landmarks (tube length) between two branchpoints (TL).

(C) Quantification of the BL and TL elongation in the FRAP experimental embryos in (B).

(D) Schematic representation of the stretching of Dp matrix core by tube growth.

(E) FRAP experiments using ANF-GFP.

(F) Quantification of the relative fluorescence intensity in the FRAP experiment in (E). Note that emerald GFP in the orange and green boxed regions was excited by the 405 laser at the time of photobleaching (asterisks).

(legend continued on next page)
<figure><img src="image_6.png" /><figcaption>**Figure 4. Anchorage of Apical Membrane to aECM**</figcaption></figure>

(A–H) WT (A) and homozygous of *Pio*<sup>2R-16</sup> (B), *dp*<sup>olvR</sup> (C), *Eogt*<sup>34.2</sup> (D), *shrub*<sup>4</sup> (E), *Pio*<sup>2R-16</sup> *shrub*<sup>4</sup> (F), *dp*<sup>olvR</sup> *shrub*<sup>4</sup> (G), and *Eogt*<sup>34.2</sup> *shrub*<sup>4</sup> (H) mutant embryos were stained with CBP to show the DT of trachea. Scale bar represents 50 µm.

(I) Theoretical model for tube instability. Tracheal tube elongation in the AP axis (Z) is driven by an expansion force F caused by the synthesis of the apical membrane (blue lines), which is anchored to the elastic aECM (red line). The lumen also harbors diffusible molecules (light blue dots) in the viscous solvent.

(J) Sinusoidal deformation of the apical surface, under an increase in force F and normal matrix rigidity.

square) was slower than in the adjacent region (Figures 3E and 3F), suggesting that the diffusion of ANF-GFP is restricted.

Serp-CBD (chitin-binding domain)-GFP (33.2 kDa) also showed typical FRAP recovery characteristics (Figures 3H and 3I; Movie S3; Förster et al., 2010), with a half-maximal recovery time of 27 s and diffusion constant of 7.5 µm²/s (Figure 3J). The curves are well fitted by this single constant, without an immobile fraction (Figure 3G). The slower diffusion rate of Serp-CBD-GFP compared to ANF-GFP implies that binding with chitin fibers restricts its diffusion. Taken together, the FRAP experiments indicate that the aECM is a complex viscoelastic gel stretched by the epithelial tube, as hypothesized by the physical model, with smaller molecules diffusing in a viscous solvent.

## Mechanical Coupling of Apical Membrane and Core Matrix

To address the third prediction of the model, we examined how the elastic luminal core matrix is mechanically coupled to the

expansion force of the apical membrane. We first examined the tracheal tube phenotype in the reduction of elastic matrix (*dp*<sup>olvR</sup> and *Pio*<sup>2R-16</sup> mutants) and found that dorsal and ventral branches lost their connections with DT (Jazwińska et al., 2003), and DT of *dp*<sup>olvR</sup> mutants showed overelongated phenotypes (Figures 4A–4C and S4A). In *dp*<sup>olvR</sup> *shrub*<sup>4</sup> and *Pio*<sup>2R-16</sup> *shrub*<sup>4</sup> double mutants, DT showed excess elongation (Figures 4E–4G and S4A), indicating that elastic matrix is essential for integrity of the tubular network and provides a mechanical tension balancing the AP elongation force to specify the correct tube length. Recently, endoplasmic reticulum-resident O-linked-N-acetylglucosamine transferase (EOGT) had been identified to mediate Dp-dependent interaction between epithelial cell and ECM (Sakaidani et al., 2011). We therefore examined tube phenotype in loss-of-function *Eogt*<sup>34.2</sup> mutant and found that DT showed overgrowth phenotype (Figures 4D and S4A). Combination of *Eogt*<sup>34.2</sup> and *shrub*<sup>4</sup> presented additional DT elongation (Figures 4D and 4H). These data support the idea that the

(G) Numerical integrations of protein diffusion based on the estimated diffusion constant of ANF-GFP and Serp-CBD-GFP.

(H) FRAP experiments with Serp-CBD-GFP.

(I) Quantification of the relative fluorescent intensity in the FRAP experiment in (H).

(J) Comparison of the relative fluorescent intensity in the FRAP experiment between ANF-GFP and Serp-CBD-GFP. Scale bars represent 10 µm.
coupling of apical membrane and Dp matrix core is essential for tube length regulation.

## Physical Model of Sinusoidal Tube Shape

We model a tracheal tube of length (L) taking into account two components: a hard Dp/chitin core with rigidity ($E_c$) and radius ($r_0$), and a soft surrounding tube composed of a monolayer of cells, with rigidity ($E_t$). At least in the initial phase of the instability, the basal membrane stays fixed (Figure 4I), so we neglect its deformation, although our findings hold by assuming a very stiff but deformable substrate around the tracheal tube.

We assume that the major force of tube elongation is the axial expansion of the apical membrane and cortex cytoskeleton driven by Crb and Src42A. This expansion force ($\gamma$) has components that should be summed: apical membrane synthesis $\gamma_s$, which is a tube-intrinsic force; and the adhesion of the membrane to the Dp/chitin core $\gamma_a$, which is proportional to the concentration of links between the aECM and the apical membrane, and is oriented toward the axial direction due to the polarizing function of Src42A (Förster and Luschnig, 2012; Nelson et al., 2012). An adhesion force of $10^{-3}$ N/m, typical of cell substrate tension, is sufficient to elongate significantly an ECM core with an elastic modulus of $10^3$ Pa, typical of biological tissues (Engler et al., 2006). Starting from a nonstretched elastic core of length ($L_0$), a tube with a free end elongates to the final length ($L_f$) at which expansion force is balanced by the adhesive and elastic forces, coming mainly from the stretching of the Dp/chitin core:

$$L_f = L_0 \left( 1 + 2 \frac{\gamma}{E_c r_0} \right).$$

However, if the two ends of the tube are constrained (at the late stage of tube elongation), the only way for the apical surface to grow when the basal area is held constant is through a buckling instability (Hannezo et al., 2012), i.e., a sinusoidal shape, described by the function $w(z) = A \cos(qz)$ (Figure 4J), analogous to the observation of microtubule buckling in an elastic gel (Brangwynne et al., 2006). Based on this model of tube instability (Hannezo et al., 2012), we thus predict the tube to buckle into a sinusoidal shape when $\gamma$ exceeds the critical expansion force $\gamma_c = \sqrt{E_c E_t}$ with a predicted wavelength of

$$\lambda_0 \approx 2\pi r_0 \left(\frac{E_c}{E_t}\right)^{1/4}.$$

This wavelength reflects a compromise between the energetic cost of deforming the cell tube and the energetic cost of deforming the elastic matrix. It is worth noting that the locations of dorsal- and ventral-branching points sometimes, but not always, correspond to the curved regions of the sinusoidal tube (Figures 1C, 1D, and 1G). However, overelongated tubes with two turns per segment (Figures 1E and 4G) bend at the location independent of branchpoint position. Therefore, the sinusoidal shape of mutant DTs reflects their intrinsic physical properties consistent with our physical model, with some contribution from branchpoints.

## Test and Predictions of the Model

One of the assumptions behind the model is that apical membrane and core matrix can vary independently and that their relative

values determine the final tube shape. In the shrub mutant, abundant chitin accumulated in the shrub mutant trachea (Figure 1A), with a slightly altered fibrous-like pattern (Figure S3A). A FRAP experiment in shrub mutants demonstrated that the diffusion characteristics of Serp-CBD-GFP were identical to those in control embryos (Figures S3B and S3C). The Pio distribution was also normal in the shrub mutants (Figure S3D). Because the Pio distribution depends on Dp (Jaźwińska et al., 2003), this result implies that Dp's function remained intact. All of the above observations collectively indicate that the influence of shrub mutation on the luminal matrix properties is small, if present at all. So, in the model, the shrub mutant would only increase $\gamma$ with a normal $E_c$. The shrub mutant DT showed approximately one turn per segment ($\lambda_0 = 29 \pm 5$ µm; n = 10), which would indicate that $E_c$ is much greater than $E_t$ ($E_c = 12 \pm 8$ E_t) from the equation above. This value supports the dominant role of the elastic core matrix in restricting tube elongation (Figure 3D).

In the case of chitin deacetylase mutants, the modulus of the core $E_c$ is expected to be reduced (Luschnig et al., 2006; Wang et al., 2006), and our model predicts that buckling can occur for normal $\gamma$ but at a smaller wavelength. We confirm the prediction by measuring the average wavelength for serp$^{RB}$ mutant ($\lambda_0 = 19 \pm 6$ µm; n = 12), which would yield a 3-fold decrease in matrix modulus ($E_c = 3$ E_t).

Then, we additionally test the model by simultaneously increasing $\gamma$ and decreasing $E_c$, which is expected to further decrease the wavelength of oscillation. The overexpression of Serp in WT trachea was previously shown to cause overelongation of the DT (Figure 1E) (wavelength is $21 \pm 5$ µm; n = 8) (Figure S4B). We found that overexpressing Serp in the shrub$^4$ background caused further elongation of the DT, with an even shorter wavelength ($14 \pm 4$ µm; n = 8) of about two turns per segment (Figure 1E), again confirming the model predictions. Double mutants of shrub$^4$ pio$^{2R-16}$ (Figure 4F) and shrub$^4$ dp$^{olvR}$ (Figure 4G) also gave rise to additional tube elongation and shorter wavelengths compared with mutants of shrub$^4$. Thus, our model provides a framework for understanding how matrix elasticity and apical membrane growth contribute to the buckling behavior of the tubule.

Here, we demonstrated that apical membrane biogenesis is negatively controlled by ESCRT III, which directs its specific target protein Crb to endosomes for degradation. The retrograde sorting of the endocytosed luminal component Serp also occurs in multivesicular bodies/late endosomes (Dong et al., 2013). Thus, two branches of the endosomal sorting pathway, regulated by ESCRT and the retromer, respectively, regulate the two key processes of tracheal morphogenesis by controlling the trafficking of specific cargo molecules for apical membrane growth and luminal matrix modification. This study demonstrated that the mechanical coupling of the apical membrane and luminal core matrix determines the tracheal tube morphology. We show the pertinence of our model by verifying several nontrivial predictions on the wavelength of the elongated pattern. The morphogenesis of other organ systems might now be studied in light of the involvement of diverse endosomal trafficking pathways and the physical model presented here.
# EXPERIMENTAL PROCEDURES

## Fly Strains and Genetics

shrub⁴/CyO and UAS-Shrub-GFP were kind gifts from Fenbiao Gao; Vps32⁹⁵ was from David Bilder; UAS-Myc-Crb<sub>intra</sub> was from Elisabeth Knust's lab; UAS-Serp-CBD-GFP and UAS-Serp-GFP were gifts from Stefan Luschnig; ANF-GFP was a gift from Christos Samakovlis; Src42A²⁶⁻¹/CyO was from Kaoru Saigo; UAS-3×TagRFP was made by Housei Wada; pioc²R⁻¹⁶/CyO and pioc²R⁻¹⁶, dpoc²R⁰/SM5 were from Markus Affolter; Eogt³⁴.²/CyO was from Tetsuya Okajima; dpoc²R⁰/SM5, GFP-trapped Dp (http://www.flyprot.org), and crb¹¹A²² were from the Drosophila Genetic Resource Center in Kyoto; and P element-inserted P[EPgy2]shrbEY⁰⁵I⁹⁴ strain was from the Bloomington Stock Center. da-GAL4 and btl-GAL4 were used to drive the expression of UAS transgenes in the embryos.

## Immunofluorescence

The primary antibodies used in this study were mouse anti-Crb (Cq4,1:40, 1:100 for western blotting; Developmental Studies Hybridoma Bank [DSHB]); guinea pig anti-Iif (1:500; a gift from Robert E. Ward; Zhang and Ward, 2009); rabbit anti-aPKC (SC-216) (1:500, and 1:2,000 for western blotting; Santa Cruz Biotechnology); rabbit anti-Rab11 (1:8,000) and rabbit anti-Rab7 (1:3,000), kind gifts from Tsubasa Tanaka and Akira Nakamura (Tanaka and Nakamura, 2008); guinea pig anti-Hrs (1:3,000; a gift from Hugo Bellen); mouse anti-laminin A (1:500; a gift from Y. Takagi); phalloidin (1:100; Sigma-Aldrich); rabbit anti-Serp (1:300) and anti-Verm (1:300) (gifts from Stefan Luschnig); mAb 2A12 antigen (1:2; DSHB); rabbit anti-Pio (1:100; a gift from Markus Affolter); rabbit anti-Kune-kune (1:1,000; a gift from Mikio Furuse); rat anti-DE-cadherin (DCAD 2) (1:20; DSHB); mouse anti-Cora (1:200; DSHB); anti-α-tubulin (DM1A) (1:8,000 for western blotting; Sigma-Aldrich); and chitin-binding probe (CBP) (1:200). Additional CBP was prepared from a bacterial expression construct according to the protocol provided by Yinhua Zhang (New England Biolabs).

# SUPPLEMENTAL INFORMATION

Supplemental Information includes Supplemental Experimental Procedures, four figures, and three movies and can be found with this article online at http://dx.doi.org/10.1016/j.celrep.2014.03.066.

# ACKNOWLEDGMENTS

We thank F. Gao, R.E. Ward, S. Luschnig, T. Okajima, M. Affolter, D. Bilder, E. Knust, T. Tanaka, A. Nakamura, C. Samakovlis, K. Saigo, M. Furuse, the Bloomington Stock Center, Drosophila Genetic Resource Center in Kyoto, Japan, and the Developmental Studies Hybridoma Bank for generously providing antibodies and fly stocks; H. Wada for UAS-3×TagRFP fly and dye injection; Y.H. Zhang for plasmid and protocol for CBP preparation; and J. Prost and J.F. Joanny for their support for the project and discussion. We also thank T. Shibata, Y. Morishita, T. Kondo, and G. Sheng for critically reading the manuscript. This work was supported by a Grant-in-Aid for Scientific Research on Innovative Areas from MEXT Japan to S.H. and the RIKEN Foreign Postdoctoral Researcher Program to B.D.

Received: August 8, 2013

Revised: March 13, 2014

Accepted: March 26, 2014

Published: May 1, 2014

# REFERENCES

Baer, M.M., Chanut-Delalande, H., and Affolter, M. (2009). Cellular and molecular mechanisms underlying the formation of biological tubes. Curr. Top. Dev. Biol. 89, 137–162.

Beitel, G.J., and Krasnow, M.A. (2000). Genetic control of epithelial tube size in the *Drosophila* tracheal system. Development 127, 3271–3282.

Blankenship, J.T., Fuller, M.T., and Zallen, J.A. (2007). The *Drosophila* homolog of the Exo84 exocyst subunit promotes apical epithelial identity. J. Cell Sci. 120, 3099–3110.

Bökel, C., Prokop, A., and Brown, N.H. (2005). Papillote and Piopio: *Drosophila* ZP-domain proteins required for cell adhesion to the apical extracellular matrix and microtubule organization. J. Cell Sci. 118, 633–642.

Brangwynne, C.P., MacKintosh, F.C., Kumar, S., Geisse, N.A., Talbot, J., Mahadevan, L., Parker, K.K., Ingber, D.E., and Weitz, D.A. (2006). Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement. J. Cell Biol. 173, 733–741.

Dayel, M.J., Hom, E.F., and Verkman, A.S. (1999). Diffusion of green fluorescent protein in the aqueous-phase lumen of endoplasmic reticulum. Biophys. J. 76, 2843–2851.

Dong, B., Kakihara, K., Otani, T., Wada, H., and Hayashi, S. (2013). Rab9 and retromer regulate retrograde trafficking of luminal protein required for epithelial tube length control. Nat Commun 4, 1358.

Engler, A.J., Sen, S., Sweeney, H.L., and Discher, D.E. (2006). Matrix elasticity directs stem cell lineage specification. Cell 126, 677–689.

Förster, D., and Luschnig, S. (2012). Src42A-dependent polarized cell shape changes mediate epithelial tube elongation in *Drosophila*. Nat. Cell Biol. 14, 526–534.

Förster, D., Armbruster, K., and Luschnig, S. (2010). Sec24-dependent secretion drives cell-autonomous expansion of tracheal tubes in *Drosophila*. Curr. Biol. 20, 62–68.

Frey, E., Kroy, W., and Wilhelm, J. (1998). Viscoelasticity of biopolymer networks and statistical mechanics of semiflexible polymers. Adv. Struct. Biol. 5, 135–168.

Hahn, C., and Schwartz, M.A. (2009). Mechanotransduction in vascular physiology and atherogenesis. Nat. Rev. Mol. Cell Biol. 10, 53–62.

Hannezo, E., Prost, J., and Joanny, J.F. (2012). Mechanical instabilities of biological tubes. Phys. Rev. Lett. 109, 018101.

Hori, K., Sen, A., Kirchhausen, T., and Artavanis-Tsakonas, S. (2011). Synergy between the ESCRT-III complex and Deltex defines a ligand-independent Notch signal. J. Cell Biol. 195, 1005–1015.

Jažwińska, A., Ribeiro, C., and Affolter, M. (2003). Epithelial tube morphogenesis during *Drosophila* tracheal development requires Piopio, a luminal ZP protein. Nat. Cell Biol. 5, 895–901.

Klebes, A., and Knust, E. (2000). A conserved motif in Crumbs is required for E-cadherin localisation and zonula adherens formation in *Drosophila*. Curr. Biol. 10, 76–85.

Laprise, P., Paul, S.M., Boulanger, J., Robbins, R.M., Beitel, G.J., and Tepass, U. (2010). Epithelial polarity proteins regulate *Drosophila* tracheal tube size in parallel to the luminal matrix pathway. Curr. Biol. 20, 55–61.

Li, B., Cao, Y.-P., Feng, X.-Q., and Gao, H. (2012). Mechanics of morphological instabilities and surface wrinkling in soft materials: a review. Soft Matter 8, 5728–5745.

Lloyd, T.E., Atkinson, R., Wu, M.N., Zhou, Y., Pennetta, G., and Bellen, H.J. (2002). Hrs regulates endosome membrane invagination and tyrosine kinase receptor signaling in *Drosophila*. Cell 108, 261–269.

Luschnig, S., Bätz, T., Armbruster, K., and Krasnow, M.A. (2006). serpentine and vermiform encode matrix proteins with chitin binding and deacetylation domains that limit tracheal tube length in *Drosophila*. Curr. Biol. 16, 186–194.

Nelson, K.S., Furuse, M., and Beitel, G.J. (2010). The *Drosophila* Claudin Kune-kune is required for septate junction organization and tracheal tube size control. Genetics 185, 831–839.

Nelson, K.S., Khan, Z., Molnár, I., Mihály, J., Kaschube, M., and Beitel, G.J. (2012). *Drosophila* Src regulates anisotropic apical surface growth to control epithelial tube size. Nat. Cell Biol. 14, 518–525.

Pellikka, M., Tanentzapf, G., Pinto, M., Smith, C., McGlade, C.J., Ready, D.F., and Tepass, U. (2002). Crumbs, the *Drosophila* homologue of human CRB1/RP12, is essential for photoreceptor morphogenesis. Nature 416, 143–149.
Pocha, S.M., Wassmer, T., Niehage, C., Hoflack, B., and Knust, E. (2011). Retromer controls epithelial cell polarity by trafficking the apical determinant Crumbs. Curr. Biol. **21**, 1111–1117.

Rao, S., Lang, C., Levitan, E.S., and Deitcher, D.L. (2001). Visualization of neuropeptide expression, transport, and exocytosis in *Drosophila melanogaster*. *J. Neurobiol.* **49**, 159–172.

Roeth, J.F., Sawyer, J.K., Wilner, D.A., and Peifer, M. (2009). Rab11 helps maintain apical crumbs and adherens junctions in the *Drosophila* embryonic ectoderm. PLoS ONE **4**, e7634.

Sakaidani, Y., Nomura, T., Matsuura, A., Ito, M., Suzuki, E., Murakami, K., Nadano, D., Matsuda, T., Furukawa, K., and Okajima, T. (2011). O-linked-N-acetylglucosamine on extracellular protein domains mediates epithelial cell-matrix interactions. Nat Commun **2**, 583.

Savin, T., Kurpios, N.A., Shyer, A.E., Florescu, P., Liang, H., Mahadevan, L., and Tabin, C.J. (2011). On the growth and form of the gut. Nature **476**, 57–62.

Sweeney, N.T., Brenman, J.E., Jan, Y.N., and Gao, F.B. (2006). The coiled-coil protein shrub controls neuronal morphogenesis in *Drosophila*. Curr. Biol. **16**, 1006–1011.

Takahashi, M., Takahashi, F., Ui-Tei, K., Kojima, T., and Saigo, K. (2005). Requirements of genetic interactions between Src42A, armadillo and shotgun, a gene encoding E-cadherin, for normal development in *Drosophila*. Development **132**, 2547–2559.

Tanaka, T., and Nakamura, A. (2008). The endocytic pathway acts downstream of Oskar in *Drosophila* germ plasm assembly. Development **135**, 1107–1117.

Tepass, U., Theres, C., and Knust, E. (1990). crumbs encodes an EGF-like protein expressed on apical membranes of *Drosophila* epithelial cells and required for organization of epithelia. Cell **61**, 787–799.

Vaccari, T., Rusten, T.E., Menut, L., Nezis, I.P., Brech, A., Stenmark, H., and Bilder, D. (2009). Comparative analysis of ESCRT-I, ESCRT-II and ESCRT-III function in *Drosophila* by efficient isolation of ESCRT mutants. J. Cell Sci. **122**, 2413–2423.

Wang, S., Jayaram, S.A., Hemphälä, J., Senti, K.A., Tsarouhas, V., Jin, H., and Samakovlis, C. (2006). Septate-junction-dependent luminal deposition of chitin deacetylases restricts tube elongation in the *Drosophila* trachea. Curr. Biol. **16**, 180–185.

Wilkin, M.B., Becker, M.N., Mulvey, D., Phan, I., Chao, A., Cooper, K., Chung, H.J., Campbell, I.D., Baron, M., and MacIntyre, R. (2000). *Drosophila* dumpy is a gigantic extracellular protein required to maintain tension at epidermal-cuticle attachment sites. Curr. Biol. **10**, 559–567.

Wodarz, A., Hinz, U., Engelbert, M., and Knust, E. (1995). Expression of crumbs confers apical character on plasma membrane domains of ectodermal epithelia of *Drosophila*. Cell **82**, 67–76.

Wollert, T., Wunder, C., Lippincott-Schwartz, J., and Hurley, J.H. (2009). Membrane scission by the ESCRT-III complex. Nature **458**, 172–177.

Zhang, L., and Ward, R.E., 4th. (2009). uninflatable encodes a novel ectodermal apical surface protein required for tracheal inflation in *Drosophila*. Dev. Biol. **336**, 201–212.

Zhou, B., Wu, Y., and Lin, X. (2011). Retromer regulates apical-basal polarity through recycling Crumbs. Dev. Biol. **360**, 87–95.