On gene regulatory networks and data fitting

Sammanfattning: Living organisms can be viewed as complex biological machines. In order to function, they must regulate their internal mechanism to do the right thing, at the right time, and in the right amount. Part of this regulation is encoded in gene regulatory networks. These are built up of genes which produce special proteins (transcription factors, tf) that regulate other tf-producing genes. Thus a network is formed with genes (nodes) linked together by their mutual regulation (edges).By constructing simplified models, we investigate such gene networks. The models allow us to probe general principles behind what shapes these networks (paper II), as well as specific networks such as that which endows the plant Arabidopsis thaliana with the ability to predict dawn and dusk (paper III). We also present a model for dynamically generating transcriptional networks which encode function from a single variable-length binary representation of dna (string of ones and zeroes). This gives a natural way for the network to evolve by mutations. However, performing a meaningful and efficient crossover operation on two dna strings of different length becomes a challenge. We address this by introducing a heuristic algorithm, which we compare against existing methods (paper IV).Additionally, we present a correct error estimation for the popular least squares method that is valid also for nonlinear functions applied to highly correlated data (paper I). For model fitting to correlated data, one has previously been constrained to use either a maximum likelihood approach, which leads to strong bias in the estimated parameters, or a least squares approach, which gives an incorrect error estimate. We also derive the first order contribution of the bias for both the maximum likelihood and the least squares method, and introduce a minimum variance function fitting method suited for Brownian motion.