Dynamical Modeling Techniques for Biological Time Series Data

The present thesis is articulated over two main topics which have in common the modeling
of the dynamical properties of complex biological systems from large-scale time-series
data. On one hand, this thesis analyzes the inverse problem of reconstructing Gene Regulatory
Networks (GRN) from gene expression data. This first topic seeks to reverse-engineer
the transcriptional regulatory mechanisms involved in few biological systems of interest,
vital to understand the specificities of their different responses. In the light of recent mathematical
developments, a novel, flexible and interpretable modeling strategy is proposed
to reconstruct the dynamical dependencies between genes from short-time series data.
In addition, experimental trade-offs and optimal modeling strategies are investigated for
given data availability. Consistent literature on these topics was previously surprisingly
lacking. The proposed methodology is applied to the study of circadian rhythms, which
consists in complex GRN driving most of daily biological activity across many species.
On the other hand, this manuscript covers the characterization of dynamically differentiable
brain states in Zebrafish in the context of epilepsy and epileptogenesis. Zebrafish
larvae represent a valuable animal model for the study of epilepsy due to both their genetic
and dynamical resemblance with humans. The fundamental premise of this research
is the early apparition of subtle functional changes preceding the clinical symptoms of
seizures. More generally, this idea, based on bifurcation theory, can be described by a
progressive loss of resilience of the brain and ultimately, its transition from a healthy
state to another characterizing the disease. First, the morphological signatures of seizures
generated by distinct pathological mechanisms are investigated. For this purpose, a
range of mathematical biomarkers that characterizes relevant dynamical aspects of the
neurophysiological signals are considered. Such mathematical markers are later used to
address the subtle manifestations of early epileptogenic activity. Finally, the feasibility of
a probabilistic prediction model that indicates the susceptibility of seizure emergence over
time is investigated. The existence of alternative stable system states and their sudden
and dramatic changes have notably been observed in a wide range of complex systems
such as in ecosystems, climate or financial markets.