Computational approaches to the modelling of topological and dynamical aspects of biochemical networks

Abstract

Els mecanismes de regulaci o de les c el lules poden ser modelats per controlar i entendre la biologia cel lular. Diferents nivells d'abstracci o s'utilitzen per descriure els processos biol ogics. En aquest treball s'han utilitzat grafs i equacions diferencials per modelar les interaccions cel lulars tant qualitativament com quantitativa. En aquest treball s'han analitzat dades d'interacci o i activitat de diferents organismes, E. coli i S. cerevisiae: xarxes d'interacci o prote na-prote na, de regulaci o de la transcripci o, i metab oliques, aix com per ls d'expressi o gen omica i prote omica. De la rica varietat de mesures de grafs, una variable important d'aquestes xarxes biol ogiques es la distribuci o de grau, i he aplicat eines d'an alisi estad stica per tal de caracteritzar-la. En tots els casos estudiats les distribucions de grau tenen una forma de cua pesada, per o la majoria d'elles presenten difer encies signi catives respecte un model de llei de pot encia, d'acord amb proves estad stiques. D'altra banda, cap de les xarxes podrien ser assignades de forma inequvoca a cap distribuci o testejada. Pel que fa a un nivell m es microsc opic, hem utilitzat equacions diferencials per estudiar la din amica de models de diversos sistemes bioqu mics. En primer lloc, una eina de programari anomenada ByoDyn ha estat creada des de zero. L'eina permet realitzar simulacions deterministes i estoc astiques, analitzar models mitjan cant estimaci o de par ametres, sensibilitat i an alisi d'identi cabilitat, aix com dissenyar optimament experiments. S'ha creat una interf cie web que ofereix la possibilitat d'interactuar amb el programa d'una manera gr a ca, independentment de la con guraci o de l'usuari, permetent l'execuci o del programa en diferents entorns computacionals. Finalment, hem aplicat un protocol de disseny experimental optim en un model multicel lular de l'embriog enesi en vertebrats.

Regulatory mechanisms of cells can be modelled to control and under- stand cellular biology. Di erent levels of abstraction are used to describe biological processes. In this work we have used graphs and di erential equations to model cellular interactions qualitatively and quantitatively. From di erent organisms, E. coli and S. cerevisiae, we have analysed data available for they complete interaction and activity networks. At the level of interaction, the protein-protein interaction network, the tran- scriptional regulatory networks and the metabolic network have been studied; for the activity, both gene and protein pro les of the whole or- ganism have been examined. From the rich variety of graph measures, one of primer importance is the degree distribution. I have applied sta- tistical analysis tools to such biological networks in order to characterise the degree distribution. In all cases the studied degree distributions have a heavy-tailed shape, but most of them present signi cant di erences from a power-law model according to a statistical test. Moreover, none of the networks could be unequivocally assigned to any of the tested distribution. On the other hand, in a more ne-grained view, I have used di erential equations to model dynamics of biochemical systems. First, a software tool called ByoDyn has been created from scratch incorporating a fairly complete range of analysis methods. Both deterministic and stochas- tic simulations can be performed, models can be analysed by means of parameter estimation, sensitivity, identi ability analysis, and optimal ex- perimental design. Moreover, a web interface has been created that pro- vides with the possibility interact with the program in a graphical man- ner, independent of the user con guration, allowing the execution of the program at di erent computational environments. Finally, we have ap- plied a protocol of optimal experimental design on a multicellular model of embryogenesis.