Fluctuations, gene circuit architecture and stem cell quiescence

Abstract

Biological development is a complex process in which, from a single cell, a whole multicellular organism arises. The formation of this intrincate structures requires a very precise regulation in space and time. This regulation involves a network of proteins and genes that interact. These interactions give rise to nonlinear behaviours, of the same kind that physicists have studied in other systems. Furthermore, cellular processes are often subject to fluctuations, a problem that has been studied by out of equilibrium statistical mechanics. These facts mean that the tools from nonlinear physics and statistical mechanics are suitable to study problems in the biological context and, at the same time, these problems are of interest to physcists.

In this thesis we study small gene circuits that generate bistability, the property of having two stable states upon the same input. In the first part of the thesis, we study at a theoretical level how the architecture of these circuits interacts with stochasticity. We first study a simple autoactivating Positive Feedback Loop, in which a protein activates its own production. We compare how fluctuations affect the system when they are added as a simple perturbation to the deterministic system (additive noise) or when they are derived from the dynamics of the system (multiplicative noise). We also show that multiplicative noise is able to reproduce the experimentally observed result of asymmetric stochastic switching, in which it is easier to escape from a high concentration state to a low concentration state than vice versa. We also compare how noise from diferent sources affects five bistable circuits with different architectures, and find that the sensitivity of the stability of the states to each noise source depends greatly on the circuit considered. This suggests that they could be found in different biological contexts and functions.

In a second part of the thesis, we study the quiescent centre of plant {\em Arabidopsis Thaliana}. This quiescent centre is formed by a group of stem cells that organize the different stem cell types surrounding them, and have the property of rarely dividing called quiescence. Thanks to a collaboration with the plant developmental biology group led by Dr. Ana I. Ca\-no-Delgado at Center for Research in Agricultural Genomics (CRAG), we are able to study a gene circuit that regulates quiescence. Our collaborators discovered BRAVO, a protein that regulates quiescence, and unveiled its interactions with BES1, that regulates many proteins according to the signalling of the Brassinosteroid hormone family and promotes divisions (releasing quiescence). Our mathematical modelling shows that the dimerization of BRAVO and BES1 enables strongly opposed states of these proteins, ensuring unequivocal regulation of quiescence, and a sharp transition from a [HIGH BRAVO, LOW BES1] state to a [LOW BRAVO, HIGH BES1] state upon Brassinosteroid signalling. We also add to this module a third protein, WOX5, that is only expressed in the quiescent centre and has been shown to directly regulate quiescence, and find that this opposed states and sharp transitions are preserved.

El desarrollo biológico es un proceso complejo en que, de una sola célula, surgen las intrincadas estructuras de un organismo multicelular. Para ello, la red de genes y proteínas responsable de todos los procesos celulares tiene que actuar de un modo muy preciso tanto en el espacio como en el tiempo. La dinámica de esta red da lugar a comportamientos no triviales que, además del interés obvio para la biología, son de interés para la física, por ser comunes a sistemas que tradicionalmente han sido estudiados por esta disciplina.

Esta tesis explora dos de estos comportamientos en determinados contextos. Por un lado la multiestabilidad, la capacidad largamente conocida por la física no lineal de mostrar más de un estado estable ante una sola condición externa. Por otro lado, las fluctuaciones que aparecen en las escalas espaciales y temporales de las células, cuyo comportamiento estocástico ha sido estudiada por la física estadística de no equilibrio. La primera parte de la tesis estudia como pequeñas redes genéticas con arquitecturas distintas, pero todas capaces de multiestabilidad, se comportan en la presencia de fluctuaciones de distintos orígenes.

La segunda parte de la tesis se centra en un sistema biológico real, el centro quiescente de la planta Arabidopsis thaliana. Este grupo de células madre se divide muy raramente. En colaboración con el grupo experimental de la Dra. Ana I. Caño-Delgado, estudiamos como las interacciones no lineales entre el gen BRAVO (descubierto por nuestros colaboradores) y otros integran las señales de las hormonas brasinoesteroides para regular estas divisiones.