  In this research, we study biological networks at different scales: a gene
autoregulatory network at the single-cell level and the gut microbiota at the
population level.
  Proteins are the main actors in cells, they are the building blocks, act as
enzymes and antibodies. The production of proteins is mediated by transcription
factors. In some cases, a protein acts as its own transcription factor, this is
called autoregulation. It is known that autorepression speeds up the response
and that autoactivation can lead to multiple stable equilibria. In this thesis,
we study the effects of the combination of activation and repression in
autoregulation, as a case study we investigate the possible dynamics of the
leucine responsive protein B of the archaeon Sulfolobus solfataricus (Ss-LrpB),
a protein that regulates itself in a unique and non-monotonic way via three
binding boxes. We examine for which conditions this type of network leads to
oscillations or bistability.
  In the second part, much larger biological systems are considered. Ecological
systems, among which the human gut microbiome, are characterized by
heavy-tailed abundance profiles. We study how these distributions can arise
from population-based models by adding saturation effects and linear noise.
Moreover, we examine different characteristics of experimental time series of
microbial communities, such as the noise color and neutrality of the
biodiversity, and look at the influence of the parameters on these
characteristics. With the first research topic we want to lay a foundation for
the understanding of non-monotonic gene regulation and take the first steps
toward synthetic biology in archaea. In the second part of the thesis, we
investigate experimental time series from complex ecosystems and seek
theoretical models reproducing all observed characteristics in view of building
predictive models.
