Pattern formation through lateral inhibition mediated by Notch signaling

Multicellular organisms are constituted by different kinds of cells which are arranged in a particular way, forming tissues with specific functions. The organization of these different cells can give rise to regular spatiotemporal patterns. In this Thesis we evaluate from a theoretical perspective the effects of different regulatory elements of the Notch signaling pathway in lateral inhibition patterning. These new elements under study are motivated by recent experimental observations. For studying them, we reformulate a phenomenological model proposed by Collier and colleagues (1996). Our modeling approach is based on coupled ordinary differential equations in hexagonal and irregular bidimensional lattices. We use both deterministic and stochastic approaches. We analyze the pattern formation capabilities of our proposed models by using different analytical tools and integrate numerically our dynamical equations. We focus on four main topics. In the first topic we study how a neurogenic differentiation wavefront in the embryonic vertebrate retina depends on the state of the invaded tissue. Our results show that the properties (pattern formed, shape and velocity) of progressing fronts of lateral inhibition depend crucially on the presence of ligand ahead of the differentiation front. We find similar results in a planar growing wavefront that would mimic morphogenetic furrow progression in embryonic Drosophila eye. Hence, our results point to a mechanism for neurogenic front regulation, and to a potential new design principle. In the second topic, we study the effects of a diffusible ligand in the context of lateral inhibition. We show that the diffusible ligand per se combined with its inhibition by Notch is not able to generate a pattern. Our results indicate that diffusible ligand with the classical lateral inhibition circuit softens and destroys the lateral inhibition pattern. At intermediate diffusion rates, diffusion can help to create perfect patterns. The third topic focuses on the study of receptor-ligand interactions within the same cell, what is called cis-interactions. We study the effect of Notch signal-productive cis-interactions in combination with another signaling source in two different situations: (i) in a multicellular scenario, where the other signaling source would be provided by the trans-interactions, and (ii) in a single-cell scenario in which a basal ligand-independent signaling source would be provided. In both situations, we predict that cis-interactions can drive cis-inhibition - i.e. an effective depletion of the signal production rate - at weak cis-signaling rates when acting together with a stronger signaling source, e.g. trans-interactions or with a ligand-independent signaling source. Our work also shows that cis-inhibition in the single-cell system together with a basal signal production can drive bistability. In the multicellular case, we observe that by increasing the amount of cis-interactions in the cis-inhibition scenario the proportion of high-Delta fated cells in a tissue gradually increases. In the fourth topic we study the case of hair cell differentiation in the embryonic chick inner ear. In this context, Notch pathway operates in two opposite modes with two different ligands: first, lateral induction through Jag1 ligand and afterwards, lateral inhibition through Dl1 ligand. We predict that relative signaling rates (or strengths) by Jag1 and Dl1 when bound to Notch are critical for the transit of operating modes. Also, we predict that in the lateral inhibition stage, competition between Dl1 and Jag1 ligands arise. This competition introduces an extra intercellular mutual inhibitory feedback loop, contributing to lateral inhibition. Overall, this Thesis presents new theoretical results and predictions on pattern formation in the context of lateral inhibition mediated by Notch signaling.Els organismes multicel·lulars estan constituïts per diferents tipus cel·lulars ordenats d’una certa manera, formant teixits amb funcions específiques. L’organització de cèl·lules de tipus diferents pot donar lloc a patrons espacio-temporals Aquesta Tesi es basa en l’estudi de com a partir d’un teixit de cèl·lules equivalents — estat homogeni precursor — s’estableixen patrons ordenats de tipus cel·lulars diferents. En particular, ens hem centrat en l’estudi d’un tipus de patrons que sorgeixen en teixits animals que tenen dos tipus cel·lulars i que presenten un ordre fi en el teixit, i.e. de longitud d’ona de poques cèl·lules. Aquest tipus de patrons són formats degut al efecte de la inhibició lateral. La inhibició lateral és un fenomen en el qual cèl·lules precursores equivalents intenten adoptar un cert estat o destí cel·lular per a diferenciar-se en un tipus cel·lular en particular, i al mateix temps inhibeixen a les seves cèl·lules veïnes que adquireixin aquest mateix estat. Aquest procés dinàmic dóna lloc a un patró fi, on les cèl·lules que han finalment adoptat l’estat desitjat vénen rodejades per cèl·lules que són inhibides, i que acabaran diferenciant-se en un tipus cel·lular diferent. Aquest tipus de patró es troba en una àmplia varietat de teixits animals, com ara en la retina ,i en l’oïda interna de vertebrats, i en l’ull de la mosca Drosophila