Inferring time-varying network topologies from gene expression data

Chimera-like states induced by additional dynamic nonlocal wirings

We investigate the existence of chimera-like states in a small-world network of chaotically oscillating identical Rössler systems with an addition of randomly switching nonlocal links. By varying the small-world coupling strength, we observe no chimera-like state either in the absence of nonlocal wirings or with static nonlocal wirings. When we give an additional nonlocal wiring to randomly selected nodes and if we allow the random selection of nodes to change with time, we observe the onset of chimera-like states. Upon increasing the number of randomly selected nodes gradually, we find that the incoherent window keeps on shrinking, whereas the chimera-like window widens up. Moreover, the system attains a completely synchronized state comparatively sooner for a lower coupling strength. Also, we show that one can induce chimera-like states by a suitable choice of switching times, coupling strengths, and a number of nonlocal links. We extend the above-mentioned randomized injection of nonlocal wirings for the cases of globally coupled Rössler oscillators and a small-world network of coupled FitzHugh-Nagumo oscillators and obtain similar results.

Invariance and stability conditions of interlayer synchronization manifold

We investigate interlayer synchronization in a stochastic multiplex hypernetwork which is defined by the two types of connections, one is the intralayer connection in each layer with hypernetwork structure and the other is the interlayer connection between the layers. Here all types of interactions within and between the layers are allowed to vary with a certain rewiring probability. We address the question about the invariance and stability of the interlayer synchronization state in this stochastic multiplex hypernetwork. For the invariance of interlayer synchronization manifold, the adjacency matrices corresponding to each tier in each layer should be equal and the interlayer connection should be either bidirectional or the interlayer coupling function should vanish after achieving the interlayer synchronization state. We analytically derive a necessary-sufficient condition for local stability of the interlayer synchronization state using master stability function approach and a sufficient condition for global stability by constructing a suitable Lyapunov function. Moreover, we analytically derive that intralayer synchronization is unattainable for this network architecture due to stochastic interlayer connections. Remarkably, our derived invariance and stability conditions (both local and global) are valid for any rewiring probabilities, whereas most of the previous stability conditions are only based on a fast switching approximation.

Emergence of synchronization and regularity in firing patterns in time-varying neural hypernetworks

We study synchronization of dynamical systems coupled in time-varying network architectures, composed of two or more network topologies, corresponding to different interaction schemes. As a representative example of this class of time-varying hypernetworks, we consider coupled Hindmarsh-Rose neurons, involving two distinct types of networks, mimicking interactions that occur through the electrical gap junctions and the chemical synapses. Specifically, we consider the connections corresponding to the electrical gap junctions to form a small-world network, while the chemical synaptic interactions form a unidirectional random network. Further, all the connections in the hypernetwork are allowed to change in time, modeling a more realistic neurobiological scenario. We model this time variation by rewiring the links stochastically with a characteristic rewiring frequency f. We find that the coupling strength necessary to achieve complete neuronal synchrony is lower when the links are switched rapidly. Further, the average time required to reach the synchronized state decreases as synaptic coupling strength and/or rewiring frequency increases. To quantify the local stability of complete synchronous state we use the Master Stability Function approach, and for global stability we employ the concept of basin stability. The analytically derived necessary condition for synchrony is in excellent agreement with numerical results. Further we investigate the resilience of the synchronous states with respect to increasing network size, and we find that synchrony can be maintained up to larger network sizes by increasing either synaptic strength or rewiring frequency. Last, we find that time-varying links not only promote complete synchronization, but also have the capacity to change the local dynamics of each single neuron. Specifically, in a window of rewiring frequency and synaptic coupling strength, we observe that the spiking behavior becomes more regular.

Time-Dependent Gene Network Modelling by Sequential Monte Carlo

Most existing methods used for gene regulatory network modeling are dedicated to inference of steady state networks, which are prevalent over all time instants. However, gene interactions evolve over time. Information about the gene interactions in different stages of the life cycle of a cell or an organism is of high importance for biology. In the statistical graphical models literature, one can find a number of methods for studying steady-state network structures while the study of time varying networks is rather recent. A sequential Monte Carlo method, namely particle filtering (PF), provides a powerful tool for dynamic time series analysis. In this work, the PF technique is proposed for dynamic network inference and its potentials in time varying gene expression data tracking are demonstrated. The data used for validation are synthetic time series data available from the DREAM4 challenge, generated from known network topologies and obtained from transcriptional regulatory networks of S. cerevisiae. We model the gene interactions over the course of time with multivariate linear regressions where the parameters of the regressive process are changing over time.

Identifying structures of continuously-varying weighted networks

Identifying network structures from dynamical observations is a fundamental problem currently pervading scientific research on complex systems, as understanding and modeling the structure of a complex network will lead to greater knowledge of its evolutionary mechanisms and to a better understanding of its functional behaviors. Usually, one needs to identify a network's structure through a limited number of observations. Particularly, couplings of many real-world networks are sparse and continuously varying with time. In this study, a new framework is developed via optimization for identifying structures of continuously-varying weighted networks formed by sparsely-connected dynamical systems. Furthermore, a regularization technique is employed to increase the numerical stability of the parameter estimation algorithm. Three numerical examples are provided to illustrate the feasibility and effectiveness of the proposed identification method. In comparison with other existing techniques, the main advantages of our method include its ability to identify structures of continuously-varying weighted networks in addition to static ones, as well as its requirement of a relatively small number of observations. The proposed method has a potential applicability to a variety of evolving complex dynamical networks.

Robust inference of the context specific structure and temporal dynamics of gene regulatory network

Background

Response of cells to changing endogenous or exogenous conditions is governed by intricate molecular interactions, or regulatory networks. To lead to appropriate responses, regulatory network should be 1) context-specific, i.e., its constituents and topology depend on the phonotypical and experimental context including tissue types and cell conditions, such as damage, stress, macroenvironments of cell, etc. and 2) time varying, i.e., network elements and their regulatory roles change actively over time to control the endogenous cell states e.g. different stages in a cell cycle.

Results

A novel network model PathRNet and a reconstruction approach PATTERN are proposed for reconstructing the context specific time varying regulatory networks by integrating microarray gene expression profiles and existing knowledge of pathways and transcription factors. The nodes of the PathRNet are Transcription Factors (TFs) and pathways, and edges represent the regulation between pathways and TFs. The reconstructed PathRNet for Kaposi's sarcoma-associated herpesvirus infection of human endothelial cells reveals the complicated dynamics of the underlying regulatory mechanisms that govern this intricate process. All the related materials including source code are available at http://compgenomics.utsa.edu/tvnet.html.

Conclusions

The proposed PathRNet provides a system level landscape of the dynamics of gene regulatory circuitry. The inference approach PATTERN enables robust reconstruction of the temporal dynamics of pathway-centric regulatory networks. The proposed approach for the first time provides a dynamic perspective of pathway, TF regulations, and their interaction related to specific endogenous and exogenous conditions.

Statistical inference of the time-varying structure of gene-regulation networks

Background

Biological networks are highly dynamic in response to environmental and physiological cues. This variability is in contrast to conventional analyses of biological networks, which have overwhelmingly employed static graph models which stay constant over time to describe biological systems and their underlying molecular interactions.

Methods

To overcome these limitations, we propose here a new statistical modelling framework, the ARTIVA formalism (Auto Regressive TIme VArying models), and an associated inferential procedure that allows us to learn temporally varying gene-regulation networks from biological time-course expression data. ARTIVA simultaneously infers the topology of a regulatory network and how it changes over time. It allows us to recover the chronology of regulatory associations for individual genes involved in a specific biological process (development, stress response, etc.).

Results

We demonstrate that the ARTIVA approach generates detailed insights into the function and dynamics of complex biological systems and exploits efficiently time-course data in systems biology. In particular, two biological scenarios are analyzed: the developmental stages of Drosophila melanogaster and the response of Saccharomyces cerevisiae to benomyl poisoning.

Conclusions

ARTIVA does recover essential temporal dependencies in biological systems from transcriptional data, and provide a natural starting point to learn and investigate their dynamics in greater detail.

Estimating the directed information to infer causal relationships in ensemble neural spike train recordings

Advances in recording technologies have given neuroscience researchers access to large amounts of data, in particular, simultaneous, individual recordings of large groups of neurons in different parts of the brain. A variety of quantitative techniques have been utilized to analyze the spiking activities of the neurons to elucidate the functional connectivity of the recorded neurons. In the past, researchers have used correlative measures. More recently, to better capture the dynamic, complex relationships present in the data, neuroscientists have employed causal measures-most of which are variants of Granger causality-with limited success. This paper motivates the directed information, an information and control theoretic concept, as a modality-independent embodiment of Granger's original notion of causality. Key properties include: (a) it is nonzero if and only if one process causally influences another, and (b) its specific value can be interpreted as the strength of a causal relationship. We next describe how the causally conditioned directed information between two processes given knowledge of others provides a network version of causality: it is nonzero if and only if, in the presence of the present and past of other processes, one process causally influences another. This notion is shown to be able to differentiate between true direct causal influences, common inputs, and cascade effects in more two processes. We next describe a procedure to estimate the directed information on neural spike trains using point process generalized linear models, maximum likelihood estimation and information-theoretic model order selection. We demonstrate that on a simulated network of neurons, it (a) correctly identifies all pairwise causal relationships and (b) correctly identifies network causal relationships. This procedure is then used to analyze ensemble spike train recordings in primary motor cortex of an awake monkey while performing target reaching tasks, uncovering causal relationships whose directionality are consistent with predictions made from the wave propagation of simultaneously recorded local field potentials.