Intra-membrane ligand diffusion and cell shape modulate juxtacrine patterning

A key problem in developmental biology is how pattern and planar polarity are transmitted in epithelial structures. Examples include Drosophila neuronal differentiation, ommatidia formation in the compound eye, and wing hair polarization. A key component for the generation of such patterns is direct cell-cell signalling by transmembrane ligands, called juxtacrine signalling. Previous models for this mode of communication have considered homogeneous distributions in the cell membrane, and the role of polarity has been largely ignored. In this paper we determine the role of inhomogeneous protein and receptor distributions in juxtacrine signalling. We explicitly include individual membrane segments, diffusive transport of proteins and receptors between these segments, and production terms with a combination of local and global responses to ligand binding. Our analysis shows that intra-membrane ligand transport is vital for the generation of long wavelength patterns. Moreover, with no ligand transport, there is no pattern formation for lateral induction, a process in which receptor activation up-regulates ligand production. Biased production of ligand also modulates patterning bifurcations and predicted wavelengths. In addition, biased ligand and receptor trafficking can lead to regular polarity across a lattice, in which each cell has the same orientation-directly analogous to patterns of hairs in the Drosophila wing. We confirm the trends in pattern wavelengths previously observed for patterns with cellular homogeneity-lateral inhibition tends to give short-range patterns, while lateral induction can give patterns with much longer wavelengths. Moreover, the original model can be recovered if intra-membrane bound receptor diffusion is included and rapid equilibriation between the sides is considered. Finally, we consider the role of irregular cell shapes and waves in such networks, including wave propagation past clones of non-signalling cells.     

Mathematical modelling of juxtacrine patterning

Spatial pattern formation is one of the key issues in developmental biology. Some patterns arising in early development have a very small spatial scale and a natural explanation is that they arise by direct cell—cell signalling in epithelia. This necessitates the use of a spatially discrete model, in contrast to the continuum-based approach of the widely studied Turing and mechanochemical models. In this work, we consider the pattern-forming potential of a model for juxtacrine communication, in which signalling molecules anchored in the cell membrane bind to and activate receptors on the surface of immediately neighbouring cells. The key assumption is that ligand and receptor production are both up-regulated by binding. By linear analysis, we show that conditions for pattern formation are dependent on the feedback functions of the model. We investigate the form of the pattern: specifically, we look at how the range of unstable wavenumbers varies with the parameter regime and find an estimate for the wavenumber associated with the fastest growing mode. A previous juxtacrine model for Delta-Notch signalling studied by Collier et al. (1996, J. Theor. Biol. 183, 429–446) only gives rise to patterning with a length scale of one or two cells, consistent with the fine-grained patterns seen in a number of developmental processes. However, there is evidence of longer range patterns in early development of the fruit fly Drosophila. The analysis we carry out predicts that patterns longer than one or two cell lengths are possible with our positive feedback mechanism, and numerical simulations confirm this. Our work shows that juxtacrine signalling provides a novel and robust mechanism for the generation of spatial patterns.     

Effects of Intrinsic and Extrinsic Noise Can Accelerate Juxtacrine Pattern Formation

Epithelial pattern formation is an important phenomenon that, for example, has roles in embryogenesis, development and wound-healing. The ligand Epithelial Growth Factor (EGF) and its receptor EGF-R, constitute a system that forms lateral induction patterns by juxtacrine signalling—binding of membrane-bound ligands to receptors on neighbouring cells. Owen et al. developed a generic ordinary differential equation model of juxtacrine lateral induction that exhibits stable patterning under some conditions. The model predicts relatively slow pattern formation. We examine here the effects of both intrinsic and extrinsic cellular noise arising from the stochastic treatment of this model, and show that this noise could have an accelerating effect on the patterning process.     

How far can a juxtacrine signal travel?

Juxtacrine signalling is the process of cell communication in which ligand and receptors are both anchored in the cell membrane. We develop three mathematical models for this process, involving different mathematical representations of the dynamics of membrane-bound ligand and free and bound receptors, within an epithelial sheet. We consider the dynamics of this system following a localized disturbance, such as would be provided by a source of ligand or by the generation of a free edge via wounding. We study the ability of the juxtacrine mechanism to transmit a signal away from this disturbance, and show analytically that the spatial half-life of the signal can in fact be arbitrarily large. This result is quite general, since we use a generic reaction kinetic scheme; the key assumption is that ligand and receptor production are both upregulated by binding. Moreover, the result applies to all three of our model formulations. We conclude by discussing applications of the result to the particular case of the transforming growth factor alpha binding to epidermal growth factor receptor in epidermal wound healing.     

Spatial Organization of EphA2 at the Cell-Cell Interface Modulates Trans-Endocytosis of EphrinA1

EphA2 is a receptor tyrosine kinase (RTK) that is sensitive to spatial and mechanical aspects of the cell’s microenvironment. Misregulation of EphA2 occurs in many aggressive cancers. Although its juxtacrine signaling geometry (EphA2’s cognate ligand ephrinA1 is expressed on the surface of an apposing cell) provides a mechanism by which the receptor may experience extracellular forces, this also renders the system challenging to decode. By depositing living cells on synthetic supported lipid membranes displaying ephrinA1, we have reconstituted key features of the juxtacrine EphA2-ephrinA1 signaling system while maintaining the ability to perturb the spatial and mechanical properties of the membrane-cell interface with precision. In addition, we developed a trans-endocytosis assay to monitor internalization of ephrinA1 from a supported membrane into the apposing cell using a quantitative three-dimensional fluorescence microscopy assay. Using this experimental platform to mimic a cell-cell junction, we found that the signaling complex is not efficiently internalized when lateral reorganization at the membrane-cell contact sites is physically hindered. This suggests that EphA2-ephrinA1 trans-endocytosis is sensitive to the mechanical properties of a cell’s microenvironment and may have implications in physical aspects of tumor biology.     

Spatial Organization of EphA2 at the Cell-Cell Interface Modulates Trans-Endocytosis of EphrinA1

EphA2 is a receptor tyrosine kinase (RTK) that is sensitive to spatial and mechanical aspects of the cell’s microenvironment. Misregulation of EphA2 occurs in many aggressive cancers. Although its juxtacrine signaling geometry (EphA2’s cognate ligand ephrinA1 is expressed on the surface of an apposing cell) provides a mechanism by which the receptor may experience extracellular forces, this also renders the system challenging to decode. By depositing living cells on synthetic supported lipid membranes displaying ephrinA1, we have reconstituted key features of the juxtacrine EphA2-ephrinA1 signaling system while maintaining the ability to perturb the spatial and mechanical properties of the membrane-cell interface with precision. In addition, we developed a trans-endocytosis assay to monitor internalization of ephrinA1 from a supported membrane into the apposing cell using a quantitative three-dimensional fluorescence microscopy assay. Using this experimental platform to mimic a cell-cell junction, we found that the signaling complex is not efficiently internalized when lateral reorganization at the membrane-cell contact sites is physically hindered. This suggests that EphA2-ephrinA1 trans-endocytosis is sensitive to the mechanical properties of a cell’s microenvironment and may have implications in physical aspects of tumor biology.     

Continuum limits of pattern formation in hexagonal-cell monolayers

Intercellular signalling is key in determining cell fate. In closely packed tissues such as epithelia, juxtacrine signalling is thought to be a mechanism for the generation of fine-grained spatial patterns in cell differentiation commonly observed in early development. Theoretical studies of such signalling processes have shown that negative feedback between receptor activation and ligand production is a robust mechanism for fine-grained pattern generation and that cell shape is an important factor in the resulting pattern type. It has previously been assumed that such patterns can be analysed only with discrete models since significant variation occurs over a lengthscale concomitant with an individual cell; however, considering a generic juxtacrine signalling model in square cells, in O’Dea and King (Math Biosci 231(2):172–185 2011), a systematic method for the derivation of a continuum model capturing such phenomena due to variations in a model parameter associated with signalling feedback strength was presented. Here, we extend this work to derive continuum models of the more complex fine-grained patterning in hexagonal cells, constructing individual models for the generation of patterns from the homogeneous state and for the transition between patterning modes. In addition, by considering patterning behaviour under the influence of simultaneous variation of feedback parameters, we construct a more general continuum representation, capturing the emergence of the patterning bifurcation structure. Comparison with the steady-state and dynamic behaviour of the underlying discrete system is made; in particular, we consider pattern-generating travelling waves and the competition between various stable patterning modes, through which we highlight an important deficiency in the ability of continuum representations to accommodate certain dynamics associated with discrete systems.     

Multiscale analysis of pattern formation via intercellular signalling

Lateral inhibition, a juxtacrine signalling mechanism by which a cell adopting a particular fate inhibits neighbouring cells from doing likewise, has been shown to be a robust mechanism for the formation of fine-grained spatial patterns (in which adjacent cells in developing tissues diverge to achieve contrasting states of differentiation), provided that there is sufficiently strong feedback. The fine-grained nature of these patterns poses problems for analysis via traditional continuum methods since these require that significant variation takes place only over lengthscales much larger than an individual cell and such systems have therefore been investigated primarily using discrete methods. Here, however, we apply a multiscale method to derive systematically a continuum model from the discrete Delta-Notch signalling model of Collier et al. (J.R. Collier, N.A.M. Monk, P.K. Maini, J.H. Lewis, Pattern formation by lateral inhibition with feedback: a mathematical model of Delta-Notch intercellular signalling, J. Theor. Biol., 183, 1996, 429-446) under particular assumptions on the parameters, which we use to analyse the generation of fine-grained patterns. We show that, on the macroscale, the contact-dependent juxtacrine signalling interaction manifests itself as linear diffusion, motivating the use of reaction-diffusion-based models for such cell-signalling systems. We also analyse the travelling-wave behaviour of our system, obtaining good quantitative agreement with the discrete system.     

Discrete models of autocrine cell communication in epithelial layers

Pattern formation in epithelial layers heavily relies on cell communication by secreted ligands. Whereas the experimentally observed signaling patterns can be visualized at single-cell resolution, a biophysical framework for their interpretation is currently lacking. To this end, we develop a family of discrete models of cell communication in epithelial layers. The models are based on the introduction of cell-to-cell coupling coefficients that characterize the spatial range of intercellular signaling by diffusing ligands. We derive the coupling coefficients as functions of geometric, cellular, and molecular parameters of the ligand transport problem. Using these coupling coefficients, we analyze a nonlinear model of positive feedback between ligand release and binding. In particular, we study criteria of existence of the patterns consisting of clusters of a few signaling cells, as well as the onset of signal propagation. We use our model to interpret recent experimental studies of the EGFR/Rhomboid/Spitz module in Drosophila development.     

Oscillations and patterns in spatially discrete models for developmental intercellular signalling

We extend previous models for nearest neighbour ligand-receptor binding to include both lateral induction and inhibition of ligand and receptor production, and different geometries (strings of cells and hexagonal arrays, in addition to square arrays). We demonstrate the possibility of lateral inhibition giving patterns with a characteristic length scale of many cell diameters, when receptor production is included. In contrast, lateral induction combined with inhibition of receptor synthesis cannot give rise to a patterning instability under any circumstances. Interesting new dynamics include the analytical prediction and consequent numerical observation of spatiotemporal oscillations, this depends crucially on the production terms and on the relationship between the decay rates of ligand and free receptor. Our approach allows for a detailed comparison with the model for Delta-Notch interactions of Collier et al. [4], and we find that a formal reduction may be made only when the ligand receptor binding kinetics are very slow. Without such very slow receptor kinetics, spatial pattern formation via lateral inhibition in hexagonal cellular arrays requires significant activation of receptor production, a feature that is not apparent from previous analyses.Send offprint requests to:Markus R. Owen     

Juxtacrine Signaling Is Inherently Noisy

Juxtacrine signaling is an important class of signaling systems that plays a crucial role in various developmental processes ranging from coordination of differentiation between neighboring cells to guiding axon growth during neurogenesis. Such signaling systems rely on the interaction between receptors on one cell and trans-membrane ligands on the membrane of a neighboring cell. Like other signaling systems, the ability of signal-receiving cells to accurately determine the concentration of ligands, is affected by stochastic diffusion processes. However, it is not clear how restriction of ligand movement to the two-dimensional (2D) cell membrane in juxtacrine signaling affects the accuracy of ligand sensing. In this study, we use a statistical mechanics approach, to show that long integration times, from around one second to several hours, are required to reach high-sensing accuracy (better than 10%). Surprisingly, the accuracy of sensing cannot be significantly improved, neither by increasing the number of receptors above three to five receptors per contact area, nor by increasing the contact area between cells. We show that these results impose stringent constraints on the dynamics of processes relying on juxtacrine signaling systems, such as axon guidance mediated by Ephrins and developmental patterns mediated by the Notch pathway.     

Mutual inactivation of Notch receptors and ligands facilitates developmental patterning

Developmental patterning requires juxtacrine signaling in order to tightly coordinate the fates of neighboring cells. Recent work has shown that Notch and Delta, the canonical metazoan juxtacrine signaling receptor and ligand, mutually inactivate each other in the same cell. This cis-interaction generates mutually exclusive sending and receiving states in individual cells. It generally remains unclear, however, how this mutual inactivation and the resulting switching behavior can impact developmental patterning circuits. Here we address this question using mathematical modeling in the context of two canonical pattern formation processes: boundary formation and lateral inhibition. For boundary formation, in a model motivated by Drosophila wing vein patterning, we find that mutual inactivation allows sharp boundary formation across a broader range of parameters than models lacking mutual inactivation. This model with mutual inactivation also exhibits robustness to correlated gene expression perturbations. For lateral inhibition, we find that mutual inactivation speeds up patterning dynamics, relieves the need for cooperative regulatory interactions, and expands the range of parameter values that permit pattern formation, compared to canonical models. Furthermore, mutual inactivation enables a simple lateral inhibition circuit architecture which requires only a single downstream regulatory step. Both model systems show how mutual inactivation can facilitate robust fine-grained patterning processes that would be difficult to implement without it, by encoding a difference-promoting feedback within the signaling system itself. Together, these results provide a framework for analysis of more complex Notch-dependent developmental systems.     

Juxtacrine activation of epidermal growth factor (EGF) receptor by membrane-anchored heparin-binding EGF-like growth factor protects epithelial cells from anoikis while maintaining an epithelial phenotype

Loss of cell-matrix adhesion is often associated with acute epithelial injury, suggesting that "anoikis" may be an important contributor to cell death. Resistance against anoikis is a key characteristic of transformed cells. When nontransformed epithelia are injured, activation of the epidermal growth factor (EGF) receptor (EGFR) by paracrine/autocrine release of soluble ligands can induce a prosurvival program, but there is generally evidence for concomitant dedifferentiation. The EGFR ligand, heparin-binding EGF-like growth factor (HB-EGF), is synthesized as a membrane-anchored precursor that can activate the EGFR via juxtacrine signaling or can be released and act as a soluble growth factor. In Madin-Darby canine kidney cells, expression of membrane-anchored HB-EGF increases cell-cell and cell-matrix adhesion. Therefore, these studies were designed to test the effects of juxtacrine HB-EGF signaling upon cell survival and epithelial integrity when cells are denied proper cell-matrix interactions. Cells expressing a noncleavable mutated form of membrane-anchored HB-EGF demonstrated increased survival from anoikis, formed larger cell aggregates, and maintained epithelial characteristics even following prolonged detachment from the substratum. Physical association between membrane-anchored HB-EGF and EGFR was observed. Signaling studies indicated synergistic effects of EGFR activation and phosphatidylinositol 3-kinase signaling to regulate apoptotic and survival pathways. In contrast, although administration of exogenous EGF partially suppressed anoikis in wild type cells, it also led to an increased expression of mesenchymal markers, suggesting dedifferentiation. Taken together, we propose a novel role for membrane-anchored HB-EGF in the cytoprotection of epithelial cells.     

The membrane protein CD9/DRAP 27 potentiates the juxtacrine growth factor activity of the membrane-anchored heparin-binding EGF-like growth factor

The membrane-anchored heparin-binding EGF-like growth factor precursor (proHB-EGF)/diphtheria toxin receptor (DTR) belongs to a class of transmembrane growth factors and physically associates with CD9/DRAP27 which is also a transmembrane protein. To evaluate the biological activities of proHB-EGF/DTR as a juxtacrine growth factor and the biological significance of its association with CD9/DRAP27, the mitogenic activity of proHB-EGF/DTR was analyzed using stable transfectants of mouse L cells expressing both human proHB-EGF/DTR and monkey CD9/DRAP27, or either one alone. Juxtacrine activity was assayed by measuring the ability of cells in co-culture to stimulate DNA synthesis in an EGF receptor ligand dependent cell line, EP170.7. LH-2 cells expressing human proHB-EGF/DTR stimulated EP170.7 cell growth moderately. However, LCH-1 cells, a stable co-transfectant expressing both human proHB-EGF/DTR and monkey CD9/DRAP27 cDNAs, dramatically unregulated the juxtacrine growth factor activity of proHB-EGF/DTR approximately 25 times over that of LH-2 cells even though both cell types expressed similar levels of proHB-EGF/DTR on the cell surface. Anti-CD9/DRAP27 antibodies which were not able to neutralize the mitogenic activity of soluble HB-EGF suppressed LCH-1 cell juxtacrine growth activity to the same extent as did anti-HB-EGF neutralizing antibodies and CRM 197, specific inhibitors of human HG-EGF. These findings suggest that optimal expression of the juxtacrine growth activity of proHB-EGF/DTR requires co-expression of CD9/DRAP27. These studies also indicate that growth factor potentiation effects which have been observed previously for soluble growth factors also occurs at the level of cell surface associated growth factors.     

Competition in Notch Signaling with Cis Enriches Cell Fate Decisions

Notch signaling is involved in cell fate choices during the embryonic development of Metazoa. Commonly, Notch signaling arises from the binding of the Notch receptor to its ligands in adjacent cells driving cell-to-cell communication. Yet, cell-autonomous control of Notch signaling through both ligand-dependent and ligand-independent mechanisms is known to occur as well. Examples include Notch signaling arising in the absence of ligand binding, and cis-inhibition of Notch signaling by titration of the Notch receptor upon binding to its ligands within a single cell. Increasing experimental evidences support that the binding of the Notch receptor with its ligands within a cell (cis-interactions) can also trigger a cell-autonomous Notch signal (cis-signaling), whose potential effects on cell fate decisions and patterning remain poorly understood. To address this question, herein we mathematically and computationally investigate the cell states arising from the combination of cis-signaling with additional Notch signaling sources, which are either cell-autonomous or involve cell-to-cell communication. Our study shows that cis-signaling can switch from driving cis-activation to effectively perform cis-inhibition and identifies under which conditions this switch occurs. This switch relies on the competition between Notch signaling sources, which share the same receptor but differ in their signaling efficiency. We propose that the role of cis-interactions and their signaling on fine-grained patterning and cell fate decisions is dependent on whether they drive cis-inhibition or cis-activation, which could be controlled during development. Specifically, cis-inhibition and not cis-activation facilitates patterning and enriches it by modulating the ratio of cells in the high-ligand expression state, by enabling additional periodic patterns like stripes and by allowing localized patterning highly sensitive to the precursor state and cell-autonomous bistability. Our study exemplifies the complexity of regulations when multiple signaling sources share the same receptor and provides the tools for their characterization.     

Two novel patterns of transforming growth factor beta (TGF-beta) binding to cell surface proteins are dependent upon the binding of TGF-beta 1 and indicate a mechanism of positive cooperativity.

Three isoforms of the transforming growth factor beta (TGF-beta) family, TGF-beta 1, TGF-beta 2, and TGF-beta 3, bind specifically and with high affinity to several cell surface components known as type I, type II, and type III proteins. The type I and II proteins may serve as biological receptors, whereas the type III protein does not appear to be associated with TGF-beta-mediated cell responses, and its function remains unknown. Binding data on confluent monolayers of rat skeletal myoblasts of the L6 cell line reveals two novel patterns of TGF-beta 1 binding. Saturation of the type I receptor with native TGF-beta 2 induces a 7-fold increase in binding of radiolabeled TGF-beta 1 at the type II protein. No induction of type II receptor binding was observed on subconfluent cells indicating a density-dependent phenomenon. The data suggest that the type I and type II proteins may interact during ligand binding in a manner which may be indicative of a regulatory role that is activated by the phase of cell growth or differentiation. A second observation is the binding of TGF-beta to a glycoprotein of 180 kDa and referred to here as the "type VI" binding protein. This protein is not related to previously described TGF-beta binding proteins, and its distribution appears universal among cell types. The level of TGF-beta 1 binding to this protein is dependent on the presence of TGF-beta 2. It is not known whether this protein transmits biological information or whether it serves as an accessory protein of a TGF-beta receptor complex.     

The neural cell adhesion molecule NCAM is an alternative signaling receptor for GDNF family ligands

Intercellular communication involves either direct cell-cell contact or release and uptake of diffusible signals, two strategies mediated by distinct and largely nonoverlapping sets of molecules. Here, we show that the neural cell adhesion molecule NCAM can function as a signaling receptor for members of the GDNF ligand family. Association of NCAM with GFRalpha1, a GPI-anchored receptor for GDNF, downregulates NCAM-mediated cell adhesion and promotes high-affinity binding of GDNF to p140(NCAM), resulting in rapid activation of cytoplasmic protein tyrosine kinases Fyn and FAK in cells lacking RET, a known GDNF signaling receptor. GDNF stimulates Schwann cell migration and axonal growth in hippocampal and cortical neurons via binding to NCAM and activation of Fyn, but independently of RET. These results uncover an unexpected intersection between short- and long-range mechanisms of intercellular communication and reveal a pathway for GDNF signaling that does not require the RET receptor.     

Dual role of the actin cytoskeleton in regulating cell adhesion mediated by the integrin lymphocyte function-associated molecule-1.

Intracellular signals are required to activate the leukocyte-specific adhesion receptor lymphocyte function-associated molecule-1 (LFA-1; CD11a/CD18) to bind its ligand, intracellular adhesion molecule-1 (ICAM-1). In this study, we investigated the role of the cytoskeleton in LFA-1 activation and demonstrate that filamentous actin (F-actin) can both enhance and inhibit LFA-1-mediated adhesion, depending on the distribution of LFA-1 on the cell surface. We observed that LFA-1 is already clustered on the cell surface of interleukin-2/phytohemagglutinin-activated lymphocytes. These cells bind strongly ICAM-1 and disruption of the actin cytoskeleton inhibits adhesion. In contrast to interleukin-2/phytohemagglutinin-activated peripheral blood lymphocytes, resting lymphocytes, which display a homogenous cell surface distribution of LFA-1, respond poorly to intracellular signals to bind ICAM-1, unless the actin cytoskeleton is disrupted. On resting peripheral blood lymphocytes, uncoupling of LFA-1 from the actin cytoskeleton induces clustering of LFA-1 and this, along with induction of a high-affinity form of LFA-1, via "inside-out" signaling, results in enhanced binding to ICAM-1, which is dependent on intact intermediate filaments, microtubules, and metabolic energy. We hypothesize that linkage of LFA-1 to cytoskeletal elements prevents movement of LFA-1 over the cell surface, thus inhibiting clustering and strong ligand binding. Release from these cytoskeletal elements allows lateral movement and activation of LFA-1, resulting in ligand binding and "outside-in" signaling, that subsequently stimulates actin polymerization and stabilizes cell adhesion.