A Bayesian approach for structure learning in oscillating regulatory networks

Oscillations lie at the core of many biological processes, from the cell cycle, to circadian oscillations and developmental processes. Time-keeping mechanisms are essential to enable organisms to adapt to varying conditions in environmental cycles, from day/night to seasonal. Transcriptional regulatory networks are one of the mechanisms behind these biological oscillations. However, while identifying cyclically expressed genes from time series measurements is relatively easy, determining the structure of the interaction network underpinning the oscillation is a far more challenging problem. Here, we explicitly leverage the oscillatory nature of the transcriptional signals and present a method for reconstructing network interactions tailored to this special but important class of genetic circuits. Our method is based on projecting the signal onto a set of oscillatory basis functions using a Discrete Fourier Transform. We build a Bayesian Hierarchical model within a frequency domain linear model in order to enforce sparsity and incorporate prior knowledge about the network structure. Experiments on real and simulated data show that the method can lead to substantial improvements over competing approaches if the oscillatory assumption is met, and remains competitive also in cases it is not

Inference of the genetic network regulating lateral root initiation in Arabidopsis thaliana

Regulation of gene expression is crucial for organism growth, and it is one of the challenges in Systems Biology to reconstruct the underlying regulatory biological networks from transcriptomic data. The formation of lateral roots in Arabidopsis thaliana is stimulated by a cascade of regulators of which only the interactions of its initial elements have been identified. Using simulated gene expression data with known network topology, we compare the performance of inference algorithms, based on different approaches, for which ready-to-use software is available. We show that their performance improves with the network size and the inclusion of mutants. We then analyse two sets of genes, whose activity is likely to be relevant to lateral root initiation in Arabidopsis, by integrating sequence analysis with the intersection of the results of the best performing methods on time series and mutants to infer their regulatory network. The methods applied capture known interactions between genes that are candidate regulators at early stages of development. The network inferred from genes significantly expressed during lateral root formation exhibits distinct scale-free, small world and hierarchical properties and the nodes with a high out-degree may warrant further investigation

The Local Edge Machine: inference of dynamic models of gene regulation

We present a novel approach, the Local Edge Machine, for the inference of regulatory interactions directly from time-series gene expression data. We demonstrate its performance, robustness, and scalability on in silico datasets with varying behaviors, sizes, and degrees of complexity. Moreover, we demonstrate its ability to incorporate biological prior information and make informative predictions on a well-characterized in vivo system using data from budding yeast that have been synchronized in the cell cycle. Finally, we use an atlas of transcription data in a mammalian circadian system to illustrate how the method can be used for discovery in the context of large complex networks.Department of Applied Mathematic

Mathematical modelling plant signalling networks

During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This sub-cellular analysis paves the way for more comprehensive mathematical studies of hormonal transport and signalling in a multi-scale setting

Identifying stochastic oscillations in single-cell live imaging time series using Gaussian processes

Multiple biological processes are driven by oscillatory gene expression at different time scales. Pulsatile dynamics are thought to be widespread, and single-cell live imaging of gene expression has lead to a surge of dynamic, possibly oscillatory, data for different gene networks. However, the regulation of gene expression at the level of an individual cell involves reactions between finite numbers of molecules, and this can result in inherent randomness in expression dynamics, which blurs the boundaries between aperiodic fluctuations and noisy oscillators. Thus, there is an acute need for an objective statistical method for classifying whether an experimentally derived noisy time series is periodic. Here we present a new data analysis method that combines mechanistic stochastic modelling with the powerful methods of non-parametric regression with Gaussian processes. Our method can distinguish oscillatory gene expression from random fluctuations of non-oscillatory expression in single-cell time series, despite peak-to-peak variability in period and amplitude of single-cell oscillations. We show that our method outperforms the Lomb-Scargle periodogram in successfully classifying cells as oscillatory or non-oscillatory in data simulated from a simple genetic oscillator model and in experimental data. Analysis of bioluminescent live cell imaging shows a significantly greater number of oscillatory cells when luciferase is driven by a {\it Hes1} promoter (10/19), which has previously been reported to oscillate, than the constitutive MoMuLV 5' LTR (MMLV) promoter (0/25). The method can be applied to data from any gene network to both quantify the proportion of oscillating cells within a population and to measure the period and quality of oscillations. It is publicly available as a MATLAB package.Comment: 36 pages, 17 figure

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

Modeling And Identification Of Differentially Regulated Genes Using Transcriptomics And Proteomics Data

Photosynthetic organisms are complex dynamical systems, showing a remarkable ability to adapt to different environmental conditions for their survival. Mechanisms underlying the coordination between different cellular processes in these organisms are still poorly understood. In this dissertation we utilize various computational and modeling techniques to analyze transcriptomics and proteomics data sets from several photosynthetic organisms. We try to use changes in expression levels of genes to study responses of these organisms to various environmental conditions such as availability of nutrients, concentrations of chemicals in growth media, and temperature. Three specific problems studied here are transcriptomics modifications in photosynthetic organisms under reduction-oxidation: redox) stress conditions, circadian and diurnal rhythms of cyanobacteria and the effect of incident light patterns on these rhythms, and the coordination between biological processes in cyanobacteria under various growth conditions. Under redox stresses caused by high light treatments, a strong transcriptomic level response, spread across many biological processes, is discovered in the cyanobacterium Synechocystis sp. PCC 6803. Based on statistical tests, expression levels of about 20% of genes in Synechocystis 6803 are identified as significantly affected due to influence of high light. Gene clustering methods reveal that these responses can mainly be classified as transient and consistent responses, depending on the duration of modified behaviors. Many genes related to energy production as well as energy utilization are shown to be strongly affected. Analysis of microarray data under two stress conditions, high light and DCMU treatment, combined with data mining and motif finding algorithms led to a discovery of novel transcription factor, RRTF1 that responds to redox stresses in Arabidopsis thaliana. Time course transcriptomics data from Cyanothece sp. ATCC 51142 have shown strong diurnal rhythms. By combining multiple experimental conditions and using gene classification algorithms based on Fourier scores and angular distances, it is shown that majority of the diurnal genes are in fact light responding. Only about 10% of genes in the genome are categorized as being circadian controlled. A transcription control model based on dynamical systems is employed to identify the interactions between diurnal genes. A phase oscillator network is proposed to model the behavior of different biological processes. Both these models are shown to carry biologically meaningful features. To study the coordination between different biological processes to various environment and genetic modifications, an interaction model is derived using Bayesian network approach, combining all publicly available microarray data sets for Synechocystis sp. PCC 6803. Several novel relationships between biological processes are discovered from the model. Model is used to simulate several experimental conditions, and the response of the model is shown to agree with the experimentally observed behaviors

Modeling Non-Linear Dynamic Phenomena in Biochemical Networks

Facilitated by the development of high-throughput techniques, the focus of biological research has changed in the last decades from the investigation of single cell components to a system-level approach, which aims at an understanding of interactions between these cell components. This objective requires modeling and analysis methods for these regulatory networks. In this thesis, we investigate mechanisms causing qualitative dynamic behaviors of regulatory subsystems. For this purpose, we introduce a differential equation model based on underlying molecular binding reactions, whose parameters are estimated using time series concentration data. In the first part, the model is applied to subsystems with qualitatively different dynamic behaviors: The response of the Mycobacterium tuberculosis to DNA damages is described as the relaxation of a system to its steady state after external perturbation. Specific repression of genes in Escherichia coli by the global regulator protein H-NS is explained by the interrelation of feedback mechanisms. In order to prevent overfitting, a typical problem in network inference from experimental data, we introduce an approach based on Bayesian statistics, which includes prior knowledge about the system in terms of prior probability distributions. This approach is applied to simulated data and to the regulatory network of the Saccharomyces cerevisiae cell cycle. Motivated by results on the yeast cell cycle, the second part of this thesis investigates the robustness of periodic behavior in regulatory networks. The model presented belongs to a class of differential equations whose solutions tend to converge to a steady state. Accordingly, periodic behavior is not robust with respect to parameter variations. We explain this phenomenon by applying a bifurcation analysis and investigating the stability of steady states. It is shown that large time scale differences and an inclusion of time-delays can stabilize sustained oscillations, and we postulate that they are important to maintain oscillations in biological systems