Dynamical Modeling Techniques for Biological Time Series Data

Doctoral thesis (2019)

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 ... [more ▼]

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. [less ▲]

Dynamical differential expression (DyDE) reveals the period control mechanisms of the Arabidopsis circadian oscillator

in PLoS Computational Biology (2019)

The circadian oscillator, an internal time-keeping device found in most organisms, enables timely regulation of daily biological activities by maintaining synchrony with the external environment. The ... [more ▼]

The circadian oscillator, an internal time-keeping device found in most organisms, enables timely regulation of daily biological activities by maintaining synchrony with the external environment. The mechanistic basis underlying the adjustment of circadian rhythms to changing external conditions, however, has yet to be clearly elucidated. We explored the mechanism of action of nicotinamide in Arabidopsis thaliana, a metabolite that lengthens the period of circadian rhythms, to understand the regulation of circadian period. To identify the key mechanisms involved in the circadian response to nicotinamide, we developed a systematic and practical modeling framework based on the identification and comparison of gene regulatory dynamics. Our mathematical predictions, confirmed by experimentation, identified key transcriptional regulatory mechanisms of circadian period and uncovered the role of blue light in the response of the circadian oscillator to nicotinamide. We suggest that our methodology could be adapted to predict mechanisms of drug action in complex biological systems. [less ▲]

Optimising time-series experimental design for modelling of circadian rhythms: the value of transient data

in IFAC-PapersOnLine (2016, October)

Circadian clocks consist of complex networks that coordinate the daily cycle of most organisms. In light/dark cycles, the clock is synchronized (or entrained) by the environment, which corresponds to a ... [more ▼]

Circadian clocks consist of complex networks that coordinate the daily cycle of most organisms. In light/dark cycles, the clock is synchronized (or entrained) by the environment, which corresponds to a constant rephasing of the oscillations and leads to a steady state regime. Some circadian clocks are endogenous oscillators with rhythms of about 24-hours that persist in constant light or constant darkness. This operating mechanism with and without entrainment provides flexibility and robustness to the clock against perturbations. Most of the clock-oriented experiments are performed under constant photoperiodic regime, overlooking the transitory regime that takes place between light/dark cycles and constant light or darkness. This paper provides a comparative analysis of the informative potential of the transient time-series data with the other regimes for clock modelling. Realistic data were simulated from 2 experimentally validated plant circadian clock models and sliced into several time windows. These windows represent the different regimes that take place before, meanwhile and after the switch to constant light. Then, a network inference tool was used over each window and its capability of retrieving the ground-truth of the network was compared for each window. The results suggest that including the transient data to the network inference technique significally improves its performance. [less ▲]