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

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

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

Recent advances in understanding regulation of the Arabidopsis circadian clock by local cellular environment [version 1; peer review: 3 approved]

Circadian clocks have evolved to synchronise an organism’s physiology with the environmental rhythms driven by the Earth’s rotation on its axis. Over the past two decades, many of the genetic components of the Arabidopsis thaliana circadian oscillator have been identified. The interactions between these components have been formulized into mathematical models that describe the transcriptional translational feedback loops of the oscillator. More recently, focus has turned to the regulation and functions of the circadian clock. These studies have shown that the system dynamically responds to environmental signals and small molecules. We describe advances that have been made in discovering the cellular mechanisms by which signals regulate the circadian oscillator of Arabidopsis in the context of tissue-specific regulation

Recent advances in understanding regulation of the Arabidopsis circadian clock by local cellular environment.

Circadian clocks have evolved to synchronise an organism's physiology with the environmental rhythms driven by the Earth's rotation on its axis. Over the past two decades, many of the genetic components of the Arabidopsis thaliana circadian oscillator have been identified. The interactions between these components have been formulized into mathematical models that describe the transcriptional translational feedback loops of the oscillator. More recently, focus has turned to the regulation and functions of the circadian clock. These studies have shown that the system dynamically responds to environmental signals and small molecules. We describe advances that have been made in discovering the cellular mechanisms by which signals regulate the circadian oscillator of Arabidopsis in the context of tissue-specific regulation

Modelling temperature dependence in the Arabidopsis thaliana circadian clock

The circadian clock is the mechanism responsible for generating and controlling the biological rhythms that occur with 24 h periodicity in most living organisms. This clock allows organisms to anticipate the environmental variation caused by the rotation of the Earth such as the daily light and temperature cycles, providing them adaptive advantages. The circadian clock is a complex network of genes interacting with each other in regulatory processes which have been represented by mathematical models. In the plant Arabidopsis thaliana, the mechanisms by which light regulates the circadian clock have been widely modelled mathematically and implemented computationally permitting to explain experimental observations and to generate hypotheses, which have led experimental investigation. However, the role of temperature and the mechanisms of adaptation to temperature variation are poorly understood, and especially in the scenario of global climate change, modelling a temperature responsive plant clock is of increasing importance. Here we present a framework of temperature dependence for the Arabidopsis circadian clock by applying Arrhenius equations to the most predominant models for the plant system and we additionally propose three minimal models via random parameterisations to explore design principles underlying temperature compensation. By numerical investigation, we conclude that temperature compensation is especially sensitive to degradation processes, and that the combined effect of light and temperature favors the robustness of the clock. We also propose to analyse the plant clock as a whole system and under that perspective we suggest that context graph-theoretic approaches could be a powerful tool to uncover the design principles for temperature mechanisms

Arabidopsis sirtuins and poly( ADP ‐ribose) polymerases regulate gene expression in the day but do not affect circadian rhythms

Abstract: Nicotinamide‐adenine dinucleotide (NAD) is involved in redox homeostasis and acts as a substrate for NADases, including poly(ADP‐ribose) polymerases (PARPs) that add poly(ADP‐ribose) polymers to proteins and DNA, and sirtuins that deacetylate proteins. Nicotinamide, a by‐product of NADases increases circadian period in both plants and animals. In mammals, the effect of nicotinamide on circadian period might be mediated by the PARPs and sirtuins because they directly bind to core circadian oscillator genes. We have investigated whether PARPs and sirtuins contribute to the regulation of the circadian oscillator in Arabidopsis. We found no evidence that PARPs and sirtuins regulate the circadian oscillator of Arabidopsis or are involved in the response to nicotinamide. RNA‐seq analysis indicated that PARPs regulate the expression of only a few genes, including FLOWERING LOCUS C. However, we found profound effects of reduced sirtuin 1 expression on gene expression during the day but not at night, and an embryo lethal phenotype in knockouts. Our results demonstrate that PARPs and sirtuins are not associated with NAD regulation of the circadian oscillator and that sirtuin 1 is associated with daytime regulation of gene expression

Novel methods for biological network inference: an application to circadian Ca2+ signaling network

Biological processes involve complex biochemical interactions among a large number of species like cells, RNA, proteins and metabolites. Learning these interactions is essential to interfering artificially with biological processes in order to, for example, improve crop yield, develop new therapies, and predict new cell or organism behaviors to genetic or environmental perturbations. For a biological process, two pieces of information are of most interest. For a particular species, the first step is to learn which other species are regulating it. This reveals topology and causality. The second step involves learning the precise mechanisms of how this regulation occurs. This step reveals the dynamics of the system. Applying this process to all species leads to the complete dynamical network. Systems biology is making considerable efforts to learn biological networks at low experimental costs. The main goal of this thesis is to develop advanced methods to build models for biological networks, taking the circadian system of Arabidopsis thaliana as a case study. A variety of network inference approaches have been proposed in the literature to study dynamic biological networks. However, many successful methods either require prior knowledge of the system or focus more on topology. This thesis presents novel methods that identify both network topology and dynamics, and do not depend on prior knowledge. Hence, the proposed methods are applicable to general biological networks. These methods are initially developed for linear systems, and, at the cost of higher computational complexity, can also be applied to nonlinear systems. Overall, we propose four methods with increasing computational complexity: one-to-one, combined group and element sparse Bayesian learning (GESBL), the kernel method and reversible jump Markov chain Monte Carlo method (RJMCMC). All methods are tested with challenging dynamical network simulations (including feedback, random networks, different levels of noise and number of samples), and realistic models of circadian system of Arabidopsis thaliana. These simulations show that, while the one-to-one method scales to the whole genome, the kernel method and RJMCMC method are superior for smaller networks. They are robust to tuning variables and able to provide stable performance. The simulations also imply the advantage of GESBL and RJMCMC over the state-of-the-art method. We envision that the estimated models can benefit a wide range of research. For example, they can locate biological compounds responsible for human disease through mathematical analysis and help predict the effectiveness of new treatments

Inference of Gene Regulatory Networks from Single-Cell Transcriptomics by scATA: an All-to-All Approach

Gene regulatory networks (GRNs) model the controlling interactions between genes, where the ex- pression of some genes activate or inhibit the expression of other genes. In the study of biomedical systems, a better understanding of the system can be achieved by knowing the underlying GRN in different conditions (e.g. health/disease or control/mutant). Generally, the underlying GRN of the system is not known, and it is inferred from transcriptomic data by computational methods. Single- cell transcriptomic measurements have been developed and exponentially improved over the last decade. These recent experimental techniques can measure the expression of almost each gene for most of the individual cells in a sample and have been widely used to study the heterogeneity of biological systems. However, there are not many computational methods available to infer GRNs from this type of data and the existing ones suffer from major limitations. Thus, there is a need for the development of computational approaches to infer GRNs from single-cell transcriptomics. The aim of this thesis is to develop a simple and scalable method that can infer GRNs from single-cell transcriptomic time series data by studying pairwise regulations between genes. The presented method, named single-cell All-to-All (scATA), is based on estimating the parameters of a stochastic linear differential equation that describes the regulation between each pair of regulator and target genes, one pair at a time while ignoring other genes. The parameters are estimated by solving an optimization problem that minimizes the Wasserstein distance between the simulated distribution of the target gene and the corresponding time series data. The simulated distribution is obtained by numerically integrating a stochastic differential equation several times to obtain a distribution of the regulated gene trajectories. The developed method was tested on synthetic data simulated from different network models with different sizes and topologies up to 10 genes, with AUROC between 0.65 and 0.91 for 5- genes networks and between 0.54 and 0.71 for 10-genes networks. The shape of the ROC curves show that, with scATA, we are able to identify a few links with high confidence. To evaluate the applicability and performance of the algorithm on experimental data, the method was applied to infer the GRN of a publicly available, single-cell transcriptomic time series data, with a publicly available GRN compiled from literature. The use of this tool can provide new insights into the regulatory mechanism inside biological systems. It can propose novel key connections between genes to be validated experimentally, that, if verified, could be useful in better understanding the underlying system and in developing targeted treatments. This thesis is as proof of concept that dynamical model-based pairwise approaches, previously used in bulk transcriptomics, can also be used for GRN inference using single-cell time series