Competitive coordination of the dual roles of the Hedgehog co-receptor in homophilic adhesion and signal reception

Hedgehog (Hh) signaling patterns embryonic tissues and contributes to homeostasis in adults. In Drosophila, Hh transport and signaling are thought to occur along a specialized class of actin-rich filopodia, termed cytonemes. Here, we report that Interference hedgehog (Ihog) not only forms a Hh receptor complex with Patched to mediate intracellular signaling, but Ihog also engages in trans-homophilic binding leading to cytoneme stabilization in a manner independent of its role as the Hh receptor. Both functions of Ihog (trans-homophilic binding for cytoneme stabilization and Hh binding for ligand sensing) involve a heparin-binding site on the first fibronectin repeat of the extracellular domain. Thus, the Ihog-Ihog interaction and the Hh-Ihog interaction cannot occur simultaneously for a single Ihog molecule. By combining experimental data and mathematical modeling, we determined that Hh-Ihog heterophilic interaction dominates and Hh can disrupt and displace Ihog molecules involved in trans-homophilic binding. Consequently, we proposed that the weaker Ihog-Ihog trans interaction promotes and stabilizes direct membrane contacts along cytonemes and that, as the cytoneme encounters secreted Hh ligands, the ligands trigger release of Ihog from trans Ihog-Ihog complex enabling transport or internalization of the Hh ligand-Ihog-Patched -receptor complex. Thus, the seemingly incompatible functions of Ihog in homophilic adhesion and ligand binding cooperate to assist Hh transport and reception along the cytonemes.


INTRODUCTION
Hedgehog (Hh) signaling plays essential roles in patterning of multicellular embryos and maintaining adult organ homeostasis. Aberration in the precise temporal-spatial regulation and transduction of the Hh signaling pathway is involved in some birth defects (Muenke and Beachy 2000) and various proliferative disorders, such as the growth of malignant tumors (Varjosalo and Taipale 2008).
Hh protein precursor undergoes autoprocessing and lipid modification that generates the mature Hh ligand as an amino-terminal signaling peptide (HhN) dually modified by palmitoyl and cholesteryl adducts (Mann and Beachy 2004). Intracellular signaling is triggered by binding of the dually lipidated Hh ligand to the receptor. The Drosophila Hh receptor regulates the component, Smoothened, and limits the range of signaling by sequestering Hh ligand. The Hh receptor is comprised of Patched (Ptc) and a member of the Ihog family, which in Drosophila is one of the functionally interchangeable proteins encoded by interference Hedgehog (ihog) or brother of ihog (boi) (Lum et al. 2003;McLellan et al. 2006;Yao et al. 2006;Camp et al. 2010;Chou et al. 2010;Hartman et al. 2010;Yan et al. 2010;Zheng et al. 2010).
The Ihog family proteins are type I single-span transmembrane proteins with immunoglobulin (Ig) and fibronectin type III (FNIII) domains, resembling typical cell adhesion molecules in the Ig-CAM (Ig cell adhesion molecule) superfamily. Previous biochemical and structural studies showed that the first FNIII domain (Fn1) in the extracellular portion of Ihog is involved in binding to the Hh ligand (McLellan et al. 2006;Yao et al. 2006), whereas the second FNIII domain (Fn2) of Ihog interacts with Ptc. Both Fn1 and Fn2 domains are required for Hh signal reception through the formation of a high-affinity multimolecular complex of Ihog, Ptc, and Hh ). Ihog proteins not only play an essential role in Hh signal transduction but also mediate cell-cell interactions in a homophilic, calcium-independent manner Hsia et al. 2017;Wu et al. 2019). The region that mediates the trans Ihog-Ihog interaction overlaps with the region that mediates the interaction with Hh on the Ihog Fn1 domain and includes a region where the negatively charged glycan heparin binds (McLellan et al., 2006;Wu et al., 2019). Heparin is required for not only Hh-Ihog interactions but also Ihog-Ihog homophilic trans interactions in vitro (McLellan et al. 2006;Zhang et al. 2007;Wu et al. 2019).
The presence of dual functions as an adhesion protein and as a signaling protein is not unique to Ihog proteins. Other members of the Ig-CAM family, such as the netrin receptor DCC, the Slit receptor Robo, and neural cell adhesion molecule (N-CAM), have dual roles. These proteins act as molecular "glue" that holds cells together and as molecular sensors to mediate cellular responses, such as motility, proliferation, and survival (Juliano 2002;Orian-Rousseau and Ponta 2008). However, ligand binding and cell adhesion are often structurally separated and involve different extracellular domains (Frei et al. 1992;Martin-Bermudo and Brown 1999;Sjostrand et al. 2007). In contrast, the Ihog protein couples these distinct functions within the same region. The physiological consequences of coupling two distinct functions into the same region of the Ihog protein are unknown.
In the Drosophila wing imaginal discs, Hh is secreted in the posterior (P) compartment and spreads toward the anterior (A) compartment (Basler and Struhl 1994;Capdevila et al. 1994;Tabata and Kornberg 1994). Hh signaling does not occur in P compartment cells because they do not express critical components of the Hh pathway, such as the major transcriptional effector Ci (Eaton and Kornberg 1990). In contrast, A compartment cells can receive and respond to Hh but are unable to produce Hh. In A compartment cells located close to the source of Hh ligand production at the A/P boundary, Hh signaling triggers pathway activity and, consequently, an increase in the transcription of target genes (Ingham et al. 1991;Basler and Struhl 1994;Capdevila et al. 1994;Tabata and Kornberg 1994;Chen and Struhl 1996). A model of Hh secretion and transport from the basal surface of the Drosophila wing imaginal discs epithelia involves movement of Hh along cytonemes (Gradilla et al. 2014;Chen et al. 2017;Gonzalez-Mendez et al. 2017), which are dynamic thin cellular protrusions specialized for the intercellular exchange of signaling proteins (Ramirez-Weber and Kornberg 1999;Roy et al. 2011;Gradilla and Guerrero 2013;Kornberg 2014). Intriguingly, when Ihog is co-expressed with the cytoskeletal and membrane markers of these structures, these thin cellular protrusions are much easier to be detected microscopically (Callejo et al. 2011;Bilioni et al. 2013;Bischoff et al. 2013;Gonzalez-Mendez et al. 2017), which suggests that Ihog has roles in generating or stabilizing cytonemes. Moreover, overexpressed Ihog is used as a cytoneme marker to visualize these structures (Portela et al. 2019;Gonzalez-Mendez et al. 2020). Yet whether and how Ihog promotes cytoneme growth or stabilization and how cytonemes contribute to Hh transport and signal reception remain poorly understood.
Here, we report that cytoneme-localized Ihog proteins engage in trans-homophilic binding leading to cytoneme stabilization in a manner independent of the receptor role of Ihog in transducing the Hh signal. The Ihog-Ihog trans-homophilic binding site overlaps with the Ihog-Hh binding interface and requires the heparin binding site, suggesting direct competition between the dual roles of Ihog proteins. By combining experimental data and mathematical modeling, we determined Hh binding to Ihog dominates and can disrupt pre-established Ihog-Ihog trans-homophilic interactions, resulting in Hh-Ihog complexes. Our results indicated that the weaker Ihog-Ihog trans interactions promote and stabilize membrane contacts along the cytonemes and the disruption of some of these interactions by the stronger Hh-Ihog interaction could contribute to cytoneme-mediated transport of Hh or internalization of the ligand-receptor complex. Thus, we proposed that the apparently incompatible functions of Ihog in homophilic adhesion and ligand binding cooperate to assist Hh transport and reception along cytonemes.

Ihog stabilizes cytonemes in a manner independent of Hh receptor function
The Hh receptor component Ihog localizes to cytonemes in the Drosophila wing imaginal discs and abdominal histoblasts. Increasing Ihog abundance makes cytonemes in the histoblasts less dynamic and enables easier microscopic detection of these structures in the wing disc (Callejo et al. 2011;Bilioni et al. 2013;Bischoff et al. 2013;Gonzalez-Mendez et al. 2017). However, it is not clear how ectopic Ihog proteins influence the behavior and morphology of cytonemes. To explore the mechanism by which Ihog proteins affect cytonemes, we transiently expressed Ihog or the actin-binding domain of moesin fused to green fluorescent protein (GFP) (GMA-GFP) in the Hh-receiving cells in the A compartment using a ptc-GAL4 driver in combination with tub-GAL80 ts . Cytonemes projecting from the ptc-GAL4 expressing cells were examined in the 3 rd instar larvae wing discs 24 hours after shifting to 29°C by staining with antibodies recognizing GFP or Ihog (Fig. 1A). Unlike the short, mostly uniform cytonemes visualized by staining for GMA-GFP, the cytonemes with ectopic expression of Ihog were longer with periodic dense structures (Fig. 1B, C). These dense structures are proposed to represent stable links between Hh-sending and Hh-receiving cytonemes (Gonzalez-Mendez et al. 2017).
Several other Hh pathway components, including the Hh ligands, Ptc, and the Drosophila glypicans Division abnormally delayed (Dally) and Dally-like (Dlp), localize to cytonemes (Ayers et al. 2010;Chen et al. 2017;Gonzalez-Mendez et al. 2017). To determine if these effects of Ihog were unique to Ihog, we ectopically expressed each of these components individually using the ptc-GAL4 driver in the wing imaginal disc cells. For these experiments, we included UAS-Myr-RFP, which encodes a myristoylated form of red fluorescent protein, to mark the cell membrane and enable visualization of the cytonemes. Of the tested Hh components, only expression of Ihog lead to formation of the dense structures or increased cytoneme length (Supplementary Fig. 1, Fig. 1A -C). We defined the increased cytoneme length and presence of dense structures as "cytoneme stabilization." Previous biochemical and structural studies showed that the Ihog Fn1 domain is involved in binding to the Hh ligand via a heparin-binding surface (McLellan et al. 2006;, whereas the Fn2 of Ihog interacts with Ptc. Both Fn1 and Fn2 domains are required for formation of a high-affinity multimolecular complex of Ihog with Ptc and Hh during Hh signal reception . We performed a structure-function analysis by expressing Ihog variants lacking either the first FNIII domain (Fn1) (IhogΔFn1) or the second Fn2 (IhogΔFn2) or with mutations in the heparin-binding surface (Ihog xHep ) and quantified the cytoneme-stabilizing effects. These studies revealed that both the increased frequency of dense structures and length of the cytonemes required Fn1 and an intact heparin-binding surface ( Fig. 1A -C).
Ptc not only encodes a component of the Hh receptor but is also a transcriptional target of Hh signaling. The highest expression of Ptc is in a stripe of A cells immediately adjacent to the A/P compartment boundary, whereas much lower ptc expression occurs in the A compartment away from the boundary and no expression occurs in the cells of the P compartment. We generated randomly distributed Ihog-overexpressing cells throughout the A and P compartments in the wing imaginal discs. We observed stabilized cytonemes emanating from with Ihog-expressing clones located not only at the Ptc high A/P compartment boundary but also within the Ptc low A compartment and Ptc neg P compartment ( Fig. 2A, upper row). Thus, the cytoneme-stabilizing effect of Ihog was independent of Ptc, consistent with the ability of Ihog lacking the Fn2 domain to perform this function. Moreover, the expression of Ptc-binding deficient IhogΔFn2 in the A/P boundary cells resulted in stable cytonemes projecting both posteriorly towards the Hh-secreting P cells and anteriorly away from the Hh source (Fig. 2B).
These observations indicated that Ihog stabilizes cytonemes through a mechanism different from that used for the formation of Ihog-Ptc receptor complex, which exhibits high-affinity binding to Hh ligands.
In the wing imaginal discs, Hh is secreted from the P compartment and there is little to no Hh that diffuses several cell diameters into the A compartment (Zecca et al. 1995;Mullor et al. 1997;Strigini and Cohen 1997). Ihog interacts with Hh both in the context of the Ihog-Ptc complex and independently from Ptc (McLellan et al. 2006;Yan et al. 2010;Zheng et al. 2010).
We reasoned that, if Ihog Fn1-mediated binding to Hh contributes to the cytoneme-stabilizing effect, cytonemes projecting from the Ihog-expressing wing disc cells in the A or P compartment should display different properties. Consistent with Ihog interacting with Hh, Hh staining colocalized with Ihog-expressing cytonemes either projecting from clones located within the P compartment or from boundary clones projecting posteriorly toward the Hh source ( Fig. 2A, lower row). No or very little Hh staining was detected with Ihog-expressing cytonemes from clones within the A compartment or with Ihog-expressing cytonemes from clones at the A/P boundary and extending into the A compartment. Despite the absence or limited amount of Hh ligands, Ihog expression stabilized all the cytonemes projecting within or toward the A compartment. These results indicated that Ihog Fn1-mediated binding to Hh ligands did not account for the stable cytonemes visualized by ectopic Ihog expression in the wing imaginal disc cells.
Quantification of cytoneme length and the number of dense structures per cytoneme for Ihog-expressing clones in the A compartment, P compartment, and at the boundary showed that cytoneme stabilization by Ihog was independent of position within the wing disc and thus the abundance of Ptc or Hh ligands (Fig. 2C,D). We also quantified cytoneme-stabilizing properties for IhogΔFn2 in flip-out clones located close to the A/P compartment boundary, which also showed no difference between cytonemes projecting posteriorly towards the Hh-secreting P cells and those projecting anteriorly away from the Hh source (Fig. 2E, F). Collectively, our results indicated that neither the presence of Ptc nor Hh is necessary for Ihog-mediated cytoneme stabilization. This function of Ihog was separate from its function in the Hh receptor.

Ihog facilitates cytoneme stabilization through homophilic trans binding supported by glypicans
Previously, we showed that the Ihog Fn1 domain not only plays an essential role in Hh signal transduction but also mediates cell-cell interactions in a homophilic manner (Hsia et al. 2017;Wu et al. 2019). Because our data indicated that Ihog stabilized cytonemes through the Fn1 domain in a manner independent of Hh receptor function (Fig. 1, 2), we hypothesized that Ihog Fn1-mediated homophilic trans interactions were responsible for cytoneme stabilization.
The region that we identified as mediating the trans Ihog-Ihog interaction overlaps with the Heparin used in previous in vitro assays is an intracellular glycosaminoglycan (GAG) that is not present on the cell surface or along the cytonemes. Thus, heparin is unlikely to mediate Ihog-Ihog trans interactions in vivo. Heparan sulfate, which is an extracellular GAG structurally related to heparin and ubiquitously located on the cell surface or in the surrounding extracellular matrix, was subsequently found to supply the function of heparin and mediate Ihog-Hh interaction in vitro (Zhang et al. 2007). Heparan sulfate is also covalently attached to proteins forming heparan sulfate proteoglycans (HSPGs), thus, heparan sulfate or HSPGs may serve as the physiological correlate of heparin to mediate Ihog-Ihog homophilic trans binding and Ihog-Hh binding. Dally and Dlp are two Drosophila glycosylphosphatidylinositol (GPI)anchored HSPGs, which can be membrane-tethered or released from cells upon cleavage (Bernfield et al. 1999). Dally and Dlp are known to be involved in modulating the transport and reception of the Hh signal (Lum et al. 2003;Lin 2004;Tabata and Takei 2004;Eugster et al. 2007;Ayers et al. 2010;Yan et al. 2010;Bilioni et al. 2013). Ihog-expressing cytonemes rarely however, Dally abundance is highest along the D/V boundary (Fujise et al. 2001;Fujise et al. 2003;Han et al. 2005). In agreement with these different distributions, both Dally and Dlp were enriched along the cytonemes and at the apical and lateral cell contacts of Ihog-expressing cells away from the D/V boundary, whereas the Ihog-expressing cells flanking the D/V boundary were positive for Dally with little or no detectable Dlp (Fig. 3B, blue outline; Supplementary Fig.   2). Similar to the Ihog-mediated homophilic binding, Ihog-induced Dlp accumulation occurred in the absence of the Ihog Fn2 domain (Fig. 3A). In contrast, neither ectopic expression of IhogΔFn1 nor Ihog xHep , both of which lack homophilic binding capability, resulted in the accumulation of Dlp (Fig. 3A). Taken together, these results indicated that Ihog Fn1-mediated homophilic trans interactions, assisted by the heparan sulfate chains of Dally or Dlp in the wing imaginal discs, contribute to cytoneme stabilization.

Homophilic Ihog trans interactions promote direct cytoneme-cytoneme contact formation
We previously found that ectopic expression of Ihog in the non-adherent Drosophila S2 Collectively, the observations in S2 cells suggested that filopodia-localized Ihog proteins engaged in homophilic trans binding evidenced by the contact initiation among non-adjacent Ihog-expressing S2 cells.
To explore if such events occurred in vivo, we generated Ihog-expressing clones in the wing imaginal discs and found that cytonemes projecting from closely positioned clones appeared to come into contact (Figs. 4A; arrows). Unlike cultured S2 cells, the wing imaginal disc epithelial cells tightly adhere to their immediate neighbors and maintained stable cellneighbor relationships (Garcia-Bellido et al. 1973;Gibson et al. 2006). Cytoneme-cytoneme interaction is unlikely to lead to move the cell body, thus a reduction in the distance between non-adjacent Ihog-expressing clones could not be used as the functional readout of Ihog-Ihog trans-interaction along the cytonemes. Therefore, we examined whether direct membrane contacts were established along Ihog-localized cytonemes.
Membrane contacts are typically separated by less than 100 nm of extracellular space, which is below the resolution of conventional light microscopy. To examine whether membrane contacts were established along Ihog-stabilized cytonemes, we combined the CoinFLP-LexGAD/GAL4 system and the GFP Reconstitution Across Synaptic Partners (GRASP) system (Feinberg et al. 2008;Gordon and Scott 2009;Bosch et al. 2015). CoinFLP-LexGAD/GAL4 allows generation of tissues composed of clones that express either GAL4 or LexGAD, thus enabling the study of interactions between different groups of genetically manipulated cells (Bosch et al. 2015). In the GRASP system, two complementary parts of a 'split GFP' (spGFP1-10 and spGFP11) are fused to the extracellular domains of mouse CD4, one under UAS control and the other under LexAop control. Whereas individually the membrane-tethered spGFP fragments are not fluorescent, reconstitution of GFP generates fluorescence at the boundary of immediately adjacent clones that express the complementary spGFP fragments (Bosch et al. 2015). We expressed RFP-tagged Ihog together with CD4-spGFP1-10 and HA-tagged IhogΔFn2 with CD4-spGFP11. With this system, we monitored cells for the presence of either Ihog or IhogΔFn2 using an antibody recognizing Ihog and cells positive for only IhogΔFn2 using an antibody against the HA tag.
As expected from the CoinFLP system, clones expressing Ihog-RFP plus CD4-spGFP1-10 and those expressing IhogΔFn2-HA plus CD4-spGFP11 were randomly distributed in the wing imaginal discs. When these two types of clones were located immediately adjacent to each other, GRASP fluorescence was detected both at the apical lateral contacts and along the basal

Modeling predicts that homophilic Ihog trans interactions increase cytoneme length and bundling
We developed a stochastic model to investigate the influence of the homophilic transinteraction strength on the dynamics of cytonemes. In the model, cytonemes were represented as filamentous structures with variable numbers of discrete segments. We considered the elongation, shrinkage, translocation, and interaction events of cytonemes around the cell surface: An elongation or shrinkage event was represented by the addition or removal of one segment to or from an existing cytoneme; a translocation event was represented as the movement of a cytoneme along the cell surface; and interaction events of two cytonemes in contact were represented by pairwise interactions between segments.
We set the elongation probability of the "# cytoneme to exponentially decay with its length: where %&'()*"+'( / is the base elongation probability at the cell surface, is the decay coefficient, and + is the number of segments in the "# cytoneme (that is the length that the cytoneme extended from the cell surface). This decay relationship represents the increasing difficulty in transporting materials to the tip of the cytoneme as elongation occurs and increasing difficulty in the occurrence of elongation as the membrane tension increases, thereby resisting elongation.
The shrinkage rate at the tip of the "# cytoneme is modeled as To enhance simulation efficiency, we employed the quasi-equilibrium approximation (Goutsias 2005) to simulate the pairwise interactions between segments on neighboring cytonemes. First, we computed the probability of establishing a homophilic trans interaction between a pair of neighboring cytoneme segments: Based on +("%.*B"+'( , we randomly assigned a binary state variable, ; +,K (0 for not interacting, 1 for interacting), to the "# pair of neighboring segments in the "# and "# cytonemes for each simulation step. Thus, the total homophilic interactions of the "# cytoneme is calculated as The cytonemes can also translocate along the cell periphery. We simulated the system with no ( ++ = 0) homophilic trans interactions (Fig. 5A, left) and with homophilic trans interactions of moderate strength ( ++ = 15) ( Fig. 5A, right). Without any homophilic trans interactions, the simulations resulted in much fewer numbers of segments (shorter cytoneme length). For ++ = 15, the simulations predicted more variability in the length of cytonemes than was predicted at ++ = 0. By capturing 1001 snapshots from the random simulations for ++ = 0 and 15, we found that the simulations produced cytoneme lengths that were significantly longer at ++ = 15 (Fig. 5B). Additionally, the number of established pairwise interactions between cytonemes greatly increased at ++ = 15 (Fig. 5C). Thus, the simulations indicated that cytoneme length correlated with the number of cytoneme-cytoneme interaction events (Fig. 5D, Pearson r = 0.7939). By varying the strength of homophilic trans interactions, we also found that average cytoneme length increased with stronger cytoneme-cytoneme interactions (Fig. 5E).
In the snapshots of the simulations, we observed extensive pairwise interactions among adjacent cytonemes only when we set ++ > 0 (Figs. 5A, arrows). We defined this phenomenon as "cytoneme bundling" and quantified this phenomenon with a cytoneme bundling index (see Methods). The cytoneme bundling index increased as the strength of the homophilic trans interactions among cytonemes increased (Fig. 5F). Furthermore, with increasing cytonemecytoneme homophilic trans-interaction strength ++ , we observed a decreased proportion of singular cytonemes and an increased proportion of cytonemes within the cytoneme bundles ( Supplementary Fig. 6). These results predicted that cytonemes of Ihog-overexpressing cells would form extensive contacts and appear as bundles. By regular confocal microscopy, we observed an increase in dense contact sites, but we did not detect clear evidence of cytoneme bundles in the Ihog-overexpressing wing disc. This is likely because the diameter of cytonemes [100-200 nm (Mattila and Lappalainen 2008;Kornberg 2014)] is much less than the resolution limit (~250 nm laterally) of confocal microscopy. We used Airyscan technology, which has a lateral resolution of 120 nm (Huff 2015)., to test the prediction of Ihog-induced bundling of cytonemes in the wing disc. We imaged Ihog-expressing cytonemes in wing discs cells colabeled with membrane marker glycosyl-phosphatidyl-inositol-YFP (Greco et al. 2001 Also consistent with the model predictions, we found that knockdown of ihog in the absence of its close paralog-encoding gene boi resulted in cytonemes with significantly reduced length compared with the length of cytonemes in boi mutant animals retaining normal expression of Ihog ( Supplementary Fig. 8). Thus, the in vivo observations supported the predictions from the computational modeling that the augmented cytoneme-cytoneme interactions mediated by ectopic Ihog lead to elongated and bundled cytonemes.

Heterophilic Ihog-Hh binding dominates over homophilic Ihog trans interaction
A single Ihog protein can participate in either an Ihog-Ihog trans interaction or an Ihog-Hh interaction; therefore, a single Ihog protein can mediate either its cytoneme-stabilizing function or its ligand-binding function, but not both simultaneously. The dissociation constant for the nonlipid-modified recombinant HhN and the extracellular portion of Ihog containing the Fn1 and  Fig. 10). Using these cells, we assessed the relative strengths of Ihog-mediated ligand binding and homophilic trans interactions.
A heterogeneous aggregation of cells exhibits distinct morphological patterns when the relative strengths of the heterotypic and homotypic cell-cell adhesions differ. For example, a checkerboard-like pattern can occur when heterotypic cell-cell adhesions dominate (Honda et al. 1986). Therefore, we hypothesized that the morphological patterns produced by the aggregated Hh-and Ihog-expressing cells reflect the relative affinity of Ihog-Hh (heterotypic) and Ihog-Ihog (homotypic) interactions. To test this hypothesis, we prepared S2 cells expressing Hh or HhN and cells expressing Ihog, along with either GFP or monomeric Cherry (mCherry), mixed the cells, and assessed the pattern of the aggregated clusters (Fig. 6). We found that Hh-expressing cells remained dispersed when cultured by themselves (Fig. 6A, mCherry+Hh, GFP+Hh) and aggregated when mixed with Ihog-expressing cells (Fig. 6A, mCherry+Ihog, GFP+Hh). In contrast, HhN-expressing cells remained dispersed when cultured by themselves (Fig. 6A, mCherry+HhN, GFP+HhN).
When HhN-expressing cells were cocultured with Ihog-expressing cells, only the Ihogexpressing cells clustered (Fig. 6A, mCherry+Ihog, GFP+HhN). We compared the patterns of the cells in the clusters containing only Ihog-expressing cells and those containing both Ihogexpressing cells and Hh-expressing cells. We observed a checkerboard-like pattern with evenly distributed red and green cells in aggregates formed by cells expressing Hh with GFP and cells expressing Ihog with mCherry (Fig. 6B). Most center cells within the cell aggregates had 4 or 5 neighbors (Fig. 6C). Furthermore, among those neighbors, cells expressing the same transfected proteins and thus of the same color ("like" cell) were rare (Fig. 6B, D). In contrast, aggregates of Ihog-expressing cells labeled with either GFP or mCherry exhibited a honeycomb pattern (Fig. 6B): Most center cells had 5 or 6 neighbors (Fig. 6C), and ~50% were "like" cells ( Fig. 6B, D). For each aggregation assay, we confirmed by immunoblotting that transfected cells from the same experiment used for the aggregation assays expressed comparable amounts of Ihog and Hh proteins ( Supplementary Fig. 11). Therefore, the different cellular patterns formed by cells expressing Hh and cells expressing Ihog versus those formed by differentially labeled Ihog-expressing cells suggested that the heterophilic interaction between Ihog and Hh is stronger than the homophilic trans interaction between Ihog proteins on an opposing cell surface.

Ihog-Hh and homophilic Ihog trans interaction
Directly determining the affinities of the homophilic and heterophilic interactions is difficult because the affinities depend on the conformation of the Ihog dimers (trans-interacting or cis-interacting) and the membrane association of Hh. Thus, we took a computational approach to estimate the relative affinities of these two Ihog interactions. Motivated by the observations that cells expressing Hh and Ihog produced a different pattern from the cells expressing Ihog, we estimated the difference in strength between the heterophilic Ihog-Hh and homophilic Ihog-Ihog trans interactions by modeling these interactions using a vertex-based in silico assay (Bi et al. 2015;Park et al. 2016). We explicitly included heterogeneous cell composition in our model in the following manner: The cells were approximated by polygons that can freely change their locations and shapes. Consequently, two interacting cells were represented by two polygons sharing a common edge. This interaction leads to an energy reduction, the magnitude of which depends on various properties including the strength of the cell-cell adhesive interactions. From the cell shapes and configurations of neighboring cells, mechanical energy (ei) was calculated for each cell according to (Farhadifar et al. 2007) as:

K∈(%+)#P'.+() B%&&:
(1) The first term is the areal elasticity, which is represented by (the elastic coefficient), + (the area of the th cell), and / (the preferred cell area). The second term is the contractile energy, which is represented by (the contractile coefficient) and + (the perimeter of the th cell). The third term is the net adhesive energy between the th cell and its neighbors, where \ 7 \ ] is the line density of the adhesive energy between cell types + and K , and +K is the length of the common edge between the two cells. We have ``, `a , and aa , depending on the types of surface proteins expressed by the cells: both expressing Ihog, II, or one expressing Ihog and one expressing Hh, IH. Here, aa = 0, because we did not observe cells both expressing Hh in contact with each other in the aggregation assays.
We used the Monte Carlo method (Metropolis 1953) to simultaneously simulate 100 cells within a 2-dimensional space. Gaps between cells were simulated as empty polygons that do not contribute to the mechanical energy of the system. With this system, the aggregation or segregation of cells is governed by ∑ + . As a control, we simulated 100 Ihog-expressing cells with half labeled red and half labeled green, which produced a honeycomb morphological pattern (Fig. 7A), within which a given center cell had 5.8 ± 0.6 neighbors, and 2.4 ± 0.9 of them had the same color label as the center cell (Fig. 7C, I~I bars).
We simulated 50 Ihog-expressing cells and 50 Hh-expressing cells (Fig. 7B). When we altered the ratio of the heterotypic and the homotypic interaction strength (``, `a values), the morphology of the mixed system changed. From these values and the patterns, we obtained the average number and type of neighbor cells for any given center cell. We found that when `a is 30 times larger than ``, the mixed system exhibited the checkerboard-like morphological pattern (Fig. 6B), within which each center cell had 4.1 ± 0.7 neighbors, and only 0.3 ± 0.5 of them were "like" cells ( Fig. 7C, I~H bars).
This simulation study of the effect of the parameter ``: `a predicted that the number and type of neighbor cells are sensitive to the `a :`` ratio. A honeycomb-to-checkerboard transition occurred when `a :`` is between 20 and 30 (Fig. 7D, E). Therefore, the neighbor statistics from the experimental aggregation assay and the computational modeling suggested To test this, we performed both computational model simulations and experiments with S2 cells.
With `a :``=30 in the computational model, we observed the development of the checkerboard pattern as the simulation reached steady state (Fig. 7F).
In the S2 cell experiment, we mixed differentially labeled Hh-expressing cells with preformed aggregates of Ihog-expressing cells (Fig. 7G). Within 30 minutes after cell mixing, Hh-expressing cells were found on the surface of the pre-existing aggregates of Ihogexpressing cells, which we interpreted as Hh binding to Ihog proteins that were not engaged in homophilic adhesion. Over time, Hh-expressing cells were found inside the Ihog-expressing cell aggregates, such that, by 12 hours after mixing, all cell aggregates contained similar numbers of Hh-expressing cells and Ihog-expressing cells arranged in a checkerboard-like pattern (Fig.   7G). This pattern is consistent with cell rearrangements caused by differential adhesion with the Hh-Ihog interaction exhibiting a higher affinity than the Ihog-Ihog homophilic trans interaction.
Moreover, the observed cellular rearrangement indicated the Hh ligand disrupts trans Ihog-Ihog binding by competing for the Ihog Fn1 domain. Taken together, these results suggested Hh binding to Ihog is dominant over Ihog-Ihog homophilic interactions and effectively competes for Ihog even in the context of pre-established Ihog-Ihog trans-homophilic interactions.

DISCUSSION
We investigated the functional roles of the Hh receptor Ihog by determining a mechanism by which the Ihog proteins stabilizes cytonemes in the Drosophila wing imaginal disc. We found a dual role for cytoneme-localized Ihog proteins in Hh signal transduction and in interactions. Our model is also consistent with the reported affinity of Hh for the Ihog-Ptc receptor complex, which is higher than the affinity of Hh for the co-receptor Ihog alone . Indeed, the presence of Ptc in the Hh-receiving cytoneme is critical to Hh reception in the responding cells (Chen et al. 2017). Thus, we propose that the integration of the functions of Ihog -promotion of cytoneme-cytoneme contacts, Hh delivery, and Hh signal receptiondepends on the differential affinity (Ihog-Ihog < Ihog-Hh < Ptc-Ihog-Hh) and the competitive binding between Ihog for itself (in trans) and Hh (Fig. 8).
The trans-homophilic Ihog-Ihog interaction is not only critical for cytoneme stabilization but also for A/P compartment boundary maintenance in the Drosophila wing discs (Hsia et al. 2017). Notably, both Hh release and cytoneme formation occurs at the basal side of the wing disc epithelium (Callejo et al. 2011;Bilioni et al. 2013;Bischoff et al. 2013;Gradilla et al. 2014;Chen et al. 2017;Gonzalez-Mendez et al. 2017), making weaker Ihog-Ihog trans interactions accessible for replacement by stronger Ihog-Hh interactions along the cytonemes, where Ihog also functions as the receptor for Hh transport and reception (Fig. 8). In contrast, farther from the source of secreted Hh, heterophilic Ihog-Hh interactions would be infrequent along the lateral side of epithelia, where the trans Ihog-Ihog interactions play essential roles in modulating A/P cell segregation and lineage restriction (Hsia et al. 2017). In addition, direct membrane contacts are much more extensive along the lateral sides of epithelia compared with that formed along cytonemes (Fig. 5), favoring persistent Ihog-Ihog trans interactions that create an additional barrier for direct competition from the basally released Hh ligands. Thus, in agreement with the functional needs and the availability of Hh ligands, Ihog-Ihog homophilic trans interactions along the cytonemes are dynamic and readily switchable, whereas those at the lateral cell-cell junctions are more stable and less likely to be disrupted (Fig. 8).
Beside the wing imaginal disc epithelia, cytoneme-mediated Hh reception and transport has been described in other Drosophila tissues, such as the abdominal and the female germline stem cell niche (Rojas-Rios et al. 2012;Bischoff et al. 2013;Gonzalez-Mendez et al. 2017). The involvement of cytonemes in Hh signaling has been extended from insect to vertebrates by studies of the limb bud of chick embryo and cultured mouse embryonic fibroblasts (Sanders et al. 2013;Hall et al. 2020

Cell culture and transfection
Drosophila S2  To assess cell aggregation, low-magnification fields of similar cell density were randomly taken from each cell aggregation experiment, and the cell clusters were scored if they contained three or more cells. The aggregation effect was quantified as the ratio of certain transfected cells within clusters to total transfected cells (both clustered and non-clustered). Each bar shows the mean ± SD from 20-30 different images. Unpaired two-tailed t test was used for statistical analysis. Statistical analysis was performed using GraphPad Prism software.

Cell immunostaining and imaging
48 hours after transfection, dissociated S2 cells were allowed to settle and adhere for 60 min on a glass coverslip. Cells were then washed twice with PBS, fixed in 4% formaldehyde (Electron Microscopy Sciences) in PBS, blocked and permeabilized by 1.5% normal goat serum (NGS) & 0.1% Triton X-100 in PBS, incubated with primary antibody in PBS containing 1.5% NGS and 0.1% Triton X-100 for 1 hr at room temperature, washed 3 times with 0.1% Triton X-100/PBS, incubated with secondary antibody (with or without Phalloidin) and washed with 0.1% Triton X-100/PBS. The stained cells were mounted using the Vectashield anti-fade mounting medium (H-1000) and imaged with a Zeiss spinning disc confocal microscope.

Computational model of cytonemes
We simulated the cytonemes using a in silico stochastic assay. The cell surface is simplified as a linear base line with length (shown as the black solid lines in the bottom of Fig. 5A). In the initial step, we randomly picked 30% × locations along the base line as the initial locations for the cytonemes. The initial cytoneme lengths are all 0.
In each simulation step, the binary interaction variable ; +K was randomly assigned for each pair of neighboring segments according to Eq. 3. From ; +K , the number of tip interactions for each cytoneme ( + ) and the total homophilic trans interaction for the "# cytoneme For each choice of ++ , we allow the cytoneme system to evolve for more than 5,000,000 steps. Data were collected after 1,000,000 simulation steps when the cytoneme system reached steady state. In our showed results, we set = 100, %&'()*"+'( / = 5, :#.+(*)% / = 0.5 and = 0.2. We tested different parameters and the general conclusions remained the same.
The cytoneme bundles were identified as a collection of parallel cytonemes located close together and forming more than 3 pairwise contacts between two cytonemes. The cytoneme bundling index is calculated by multiplying the minimum cytoneme length by the cytoneme number within each bundle.

Computational modeling of cell rearrangement
We modeled the Ihog-Ihog and Ihog-Hh interactions using a vertex-based in silico assay (Bi et al. 2015;Park et al. 2016). Based on mechanical free energy calculated according to Eq. 5, we used the Metropolis Monte Carlo method to perform the simulations. Simulations were performed within a × 2-D square space with a periodic boundary condition along the x-and y-axes. The initial conditions were sets of randomly generated morphologies: We first assigned cellular points and 5 × environmental points randomly distributed in the 2-D space, then used the Voronoi tessellation function in MatLab to partition the space into 6 × polygons based on these points, representing the cells and the empty space surrounding them.
We implemented Metropolis Monte Carlo simulations by moving the 6 × points according to the mechanical energy: In each tentative move, a random point is selected and a random displacement is assigned to it; the moved point causes re-partitioning of the 2-D monolayer using the Voronoi tessellation function, which results in a change in the monolayer's mechanical energy, ƒ ; a random number ∈ [0, 1] is picked and the tentative move will be accepted if and only if ≤ mint1, exp(− ƒ / } )u.
We allowed the monolayer to randomly evolve for more than 650,000 steps. To ensure simulation efficiency, we adjusted the maximum allowed displacement to maintain the overall accept rate to be around 25~40%. Data were collected after 200,000 simulation steps when the monolayer's morphology had reached steady state.
In our simulations, is set to 20, and both the Hh-expressing S2 cells and the Ihogexpressing S2 cells are set with a unit area / = 1. For simplicity, we assumed that areal elastic coefficient = 500 and the contractile coefficient = 6 are the same for different types of cells.
To account for the differential cell-cell adhesion, aa was set to 0 (Hh-expressing cells do not aggregate), ``= 0.25 for interaction between Ihog-expressing cells, we modulated the ratio `a :`` to set `a for our parameter study.

Imaginal discs immunostaining and imaging
Wing discs from 3 rd instar larvae were dissected, fixed in 4% formaldehyde (Electron Microscopy Sciences) in PBS, blocked and permeabilized by 5% normal goat serum (NGS) & 0.3% Triton X-100 in PBS, incubated with primary antibody in PBS containing 5% NGS and 0.3% Triton X-100 overnight at 4°C, washed 3 times with 0.3% Triton X-100/PBS, incubated with secondary antibody, and washed with 0.3% Triton X-100/PBS. The stained discs were mounted and imaged with a ZEISS spinning disc confocal microscope or a ZEISS LSM 880 with Airyscan. Average cytoneme length was determined using ImageJ and plotted using GraphPad Prism software.

MBP-HhN purification
The

Statistical analysis
All data in column graphs are shown as mean values with SD and plotted using GraphPad Prism software. Statistical analyses were performed with unpaired two-tailed t-test, one-way ANOVA followed by Dunnett's, Sidak's or Tukey's multiple comparisons test, or two-sided Fisher's exact test was used for statistical analysis as described in the figure legends. The sample sizes were set based on the variability of each assay and are listed in the Figure   legends. Independent experiments were performed as indicated to guarantee reproducibility of findings. Differences were considered statistically significant when P < 0.01. and P (cytonemes projecting posteriorly towards the source of Hh). Each bar shows the mean ± SD (n = 30). One-way ANOVA followed by Tukey's multiple comparison test (C, D) or the twotailed unpaired t-test (E, F) was used for statistical analysis. ns, not significant. were plotted against "" ranging from 0 to 50. Each bar shows the mean ± SD, n = 1001. The two-tailed unpaired t-test (B, C) or one-way ANOVA followed by Sidak's multiple comparison test (E, F) was used for statistical analysis. ***P < 0.001, ****P < 0.0001. (G) Wing discs from 3 rd instar larvae carrying ptc-GAL4, tub-GAL80 ts and UAS-GPI-YFP; UAS-Ihog-RFP were immunostained for YFP (GPI, green) and Ihog (Ihog, red), followed by imaging with Airyscan.