Time varying causal network reconstruction of a mouse cell cycle.

BACKGROUND: Biochemical networks are often described through static or time-averaged measurements of the component macromolecules. Temporal variation in these components plays an important role in both describing the dynamical nature of the network as well as providing insights into causal mechanisms. Few methods exist, specifically for systems with many variables, for analyzing time series data to identify distinct temporal regimes and the corresponding time-varying causal networks and mechanisms. RESULTS: In this study, we use well-constructed temporal transcriptional measurements in a mammalian cell during a cell cycle, to identify dynamical networks and mechanisms describing the cell cycle. The methods we have used and developed in part deal with Granger causality, Vector Autoregression, Estimation Stability with Cross Validation and a nonparametric change point detection algorithm that enable estimating temporally evolving directed networks that provide a comprehensive picture of the crosstalk among different molecular components. We applied our approach to RNA-seq time-course data spanning nearly two cell cycles from Mouse Embryonic Fibroblast (MEF) primary cells. The change-point detection algorithm is able to extract precise information on the duration and timing of cell cycle phases. Using Least Absolute Shrinkage and Selection Operator (LASSO) and Estimation Stability with Cross Validation (ES-CV), we were able to, without any prior biological knowledge, extract information on the phase-specific causal interaction of cell cycle genes, as well as temporal interdependencies of biological mechanisms through a complete cell cycle. CONCLUSIONS: The temporal dependence of cellular components we provide in our model goes beyond what is known in the literature. Furthermore, our inference of dynamic interplay of multiple intracellular mechanisms and their temporal dependence on one another can be used to predict time-varying cellular responses, and provide insight on the design of precise experiments for modulating the regulation of the cell cycle.

Attractor Ranked Radial Basis Function Network: A Nonparametric Forecasting Approach for Chaotic Dynamic Systems.

The curse of dimensionality has long been a hurdle in the analysis of complex data in areas such as computational biology, ecology and econometrics. In this work, we present a forecasting algorithm that exploits the dimensionality of data in a nonparametric autoregressive framework. The main idea is that the dynamics of a chaotic dynamical system consisting of multiple time-series can be reconstructed using a combination of different variables. This nonlinear autoregressive algorithm uses multivariate attractors reconstructed as the inputs of a neural network to predict the future. We show that our approach, attractor ranked radial basis function network (AR-RBFN) provides a better forecast than that obtained using other model-free approaches as well as univariate and multivariate autoregressive models using radial basis function networks. We demonstrate this for simulated ecosystem models and a mesocosm experiment. By taking advantage of dimensionality, we show that AR-RBFN overcomes the shortcomings of noisy and short time-series data.

Time-varying causal inference from phosphoproteomic measurements in macrophage cells.

Cellular signaling circuitry in eukaryotes can be studied by analyzing the regulation of protein phosphorylation and its impact on downstream mechanisms leading to a phenotype. A primary role of phosphorylation is to act as a switch to turn "on" or "off" a protein activity or a cellular pathway. Specifically, protein phosphorylation is a major leit motif for transducing molecular signals inside the cell. Errors in transferring cellular information can alter the normal function and may lead to diseases such as cancer; an accurate reconstruction of the "true" signaling network is essential for understanding the molecular machinery involved in normal and pathological function. In this study, we have developed a novel framework for time-dependent reconstruction of signaling networks involved in the activation of macrophage cells leading to an inflammatory response. Several signaling pathways have been identified in macrophage cells, but the time-varying causal relationship that can produce a dynamic directed graph of these molecules has not been explored in detail. Here, we use the notion of Granger causality, and apply a vector autoregressive model to phosphoprotein time-course data in RAW 264.7 macrophage cells. Through the reconstruction of the phosphoprotein network, we were able to estimate the directionality and the dynamics of information flow. Significant interactions were selected through statistical hypothesis testing ( t-test) of the coefficients of a linear model and were used to reconstruct the phosphoprotein signaling network. Our approach results in a three-stage phosphoprotein network that represents the evolution of the causal interactions in the intracellular signaling pathways.