Nonlinear and spatial dynamics for multicellular organisms

Abstract

The development of living systems, from their conception to their death, involves a very tight coordination between gene expression in time and space. The processes involved in such an unfolding do not solely depend on the interactions between genes, but also on the environment the organism is embedded in, partly random and unpredictable, partly constructed by the organism itself. Indeed, no embryo grows without a warm womb or a protected egg. Understanding development is understanding how diverse functions or phenotypic traits arise from these relationships. In this thesis we have studied some of these biological processes mainly in plants. The approach we take to these problems is that of systems biology, the theoretical framework that studies the interactions between the constituent parts of organisms, be they molecules, genes or cells, and how these relations lead to emergent behaviours which cannot be understood through the study of the parts alone. The main goal is to understand, through this theoretical approach, the biological processes involved in cellular decision-making, whether they are related to the division, differentiation, or generation of molecular signals. The first part of the thesis focuses on the regulatory interactions between BRAVO and WOX5, two transcription factors involved in the regulation of quiescent cells in the stem cell niche of the Arabidopsis thaliana root. By combining theoretical modelling with experimental evidence, we find that these two factors interplay both at the transcriptional and post-transcriptional level, and they involve the formation of a complex. Owing to the convergence of the two transcription factors at the quiescent center, we propose a simple mechanism for regulating cell division and find that the formation of the BRAVO-WOX5 complex can be relevant. We also consider the effect of space in the regulations between BRAVO and WOX5, finding that the movement of WOX5 can be relavant to explain the expression patterns observed experimentally. The second part has focused on the role of genetic circuits operating in coupled cellular lattices by the diffusion of one of the molecules, and how these interactions can generate spatial patterns of different cell types. We first apply this approach to the formation of rhizoid precursor cell patterns in the epidermis of the Marchantia polymorpha plant. Rhizoids are thin outgrowths which appear at the interface between the plant main body and the substrate, and extend distally into the soil effectively increasing the total surface area for water and nutrient absorption. The formation of rhizoids in the epidermis of Marchantia is known to be regulated by several factors, but how the specific spatial distribution emerges from a field of epidermal cells is poorly understood. Building on recent experiments, we propose that rhizoid patterns appear from the interactions between the microRNA FRH1 and the rhizoid-promoting transcription factor RSL1, in a feedback circuit of activator-inhibitor type, where RSL1 activates FRH1, and FRH1 diffuses and represses the activity of RSL1. We find that our theoretical predictions precisely match those of the experiments, underscoring the capabilities of the model. We then study the spatiotemporal behaviours of a small genetic circuit capable of displaying diverse spatiotemporal behaviours, including bistability, oscillations and pattern formation. The circuit is based on the mixed feedback loop, a genetic circuit overrepresented in statistical analyses of gene and protein interaction databases. It consists of the transcriptional repression of a gene by another, plus the formation of a reversible complex between the proteins coded by the two genes. Through dynamical systems theory and bifurcation analysis, we find the conditions for each regime to appear and emphasize the multi-functional nature of the circuit, a feature embodying an increasingly common theme in developmental and evolutionary systems biology, namely the importance of small circuits capable of performing multiple, qualitatively different functions, which arise from the circuit’s topology but depend on the specific external context of which the circuit is embedded. The ultimate goal of systems biology is to understand life at its most basic level. As complex systems par excellence, living organisms have characteristics that cannot be reduced only to the behaviors of their parts. Instead, it is the nature of its systems that characterizes its most iconic idiosyncrasies, from the internal functioning of a cell to the complicated structure of the nervous system.

El desenvolupament dels éssers vius, des de la seva concepció fins la seva mort, implica una estreta coordinació de l'expressió gènica en el temps i l'espai. Els processos implicats en aquest desplegament no depenen únicament de les interaccions entre gens, sinó també de l’entorn, en part aleatori i impredictible, en part construït pel propi organisme. Cap embrió creix sense un ventre calent o un ou protegit. Entendre el desenvolupament és entendre com les diverses funcions o trets fenotípics sorgeixen d'aquestes relacions. En aquesta tesi hem estudiat alguns d’aquests processos biològics principalment en plantes. L’enfocament amb el qual afrontem aquests problemes és el de la biologia de sistemes, el marc teòric que estudia les interaccions entre les parts constituents dels organismes, siguin molècules, gens o cèl·lules. L’objectiu principal és entendre, mitjançant aquest enfocament teòric, els processos biològics involucrats en la presa de decisions cel·lulars, ja estiguin relacionades amb la divisió, la diferenciació, o la generació de senyals moleculars. La primera part de la tesi es centra en les interaccions reguladores entre BRAVO i WOX5, dos factors de transcripció implicats en la regulació de les cèl·lules quiescents al nínxol de cèl·lules mare de l'arrel d'Arabidopsis thaliana. La segona part s'ha centrat en el paper dels circuits genètics que operen en xarxes cel·lulars acoblades per la difusió d'una de les molècules, i com aquestes interaccions poden generar patrons espaials de diferents tipus cel·lulars. Apliquem aquest enfocament a la formació de patrons de cèl·lules precursores de rizoides a l'epidermis de la planta Marchantia polymorpha, per una banda, i en un circuit genèric multifuncional, per l’altra. L'objectiu final de la biologia de sistemes és entendre la vida en el seu nivell més fonamental. Com a sistemes complexos per excel·lència, els organismes vius presenten característiques que no es poden reduir només als comportaments de les seves parts. En canvi, és la naturalesa dels seus sistemes la que caracteritza les seves idiosincràsies més icòniques, des del funcionament intern d'una cèl·lula fins a l'estructura complicada del sistema nerviós.