A Geometric Clustering Tool (AGCT) to robustly unravel the inner cluster structures of time-series gene expressions.

Systems biology aims at holistically understanding the complexity of biological systems. In particular, nowadays with the broad availability of gene expression measurements, systems biology challenges the deciphering of the genetic cell machinery from them. In order to help researchers, reverse engineer the genetic cell machinery from these noisy datasets, interactive exploratory clustering methods, pipelines and gene clustering tools have to be specifically developed. Prior methods/tools for time series data, however, do not have the following four major ingredients in analytic and methodological view point: (i) principled time-series feature extraction methods, (ii) variety of manifold learning methods for capturing high-level view of the dataset, (iii) high-end automatic structure extraction, and (iv) friendliness to the biological user community. With a view to meet the requirements, we present AGCT (A Geometric Clustering Tool), a software package used to unravel the complex architecture of large-scale, non-necessarily synchronized time-series gene expression data. AGCT capture signals on exhaustive wavelet expansions of the data, which are then embedded on a low-dimensional non-linear map using manifold learning algorithms, where geometric proximity captures potential interactions. Post-processing techniques, including hard and soft information geometric clustering algorithms, facilitate the summarizing of the complete map as a smaller number of principal factors which can then be formally identified using embedded statistical inference techniques. Three-dimension interactive visualization and scenario recording over the processing helps to reproduce data analysis results without additional time. Analysis of the whole-cell Yeast Metabolic Cycle (YMC) moreover, Yeast Cell Cycle (YCC) datasets demonstrate AGCT's ability to accurately dissect all stages of metabolism and the cell cycle progression, independently of the time course and the number of patterns related to the signal. Analysis of Pentachlorophenol iduced dataset demonstrat how AGCT dissects data to identify two networks: Interferon signaling and NRF2-signaling networks.

Time-dependent product-form Poisson distributions for reaction networks with higher order complexes.

It is well known that stochastically modeled reaction networks that are complex balanced admit a stationary distribution that is a product of Poisson distributions. In this paper, we consider the following related question: supposing that the initial distribution of a stochastically modeled reaction network is a product of Poissons, under what conditions will the distribution remain a product of Poissons for all time? By drawing inspiration from Crispin Gardiner's "Poisson representation" for the solution to the chemical master equation, we provide a necessary and sufficient condition for such a product-form distribution to hold for all time. Interestingly, the condition is a dynamical "complex-balancing" for only those complexes that have multiplicity greater than or equal to two (i.e. the higher order complexes that yield non-linear terms to the dynamics). We term this new condition the "dynamical and restricted complex balance" condition (DR for short).

Mechanistic analysis of challenge-response experiments.

We present an application of mechanistic modeling and nonlinear longitudinal regression in the context of biomedical response-to-challenge experiments, a field where these methods are underutilized. In this type of experiment, a system is studied by imposing an experimental challenge, and then observing its response. The combination of mechanistic modeling and nonlinear longitudinal regression has brought new insight, and revealed an unexpected opportunity for optimal design. Specifically, the mechanistic aspect of our approach enables the optimal design of experimental challenge characteristics (e.g., intensity, duration). This article lays some groundwork for this approach. We consider a series of experiments wherein an isolated rabbit heart is challenged with intermittent anoxia. The heart responds to the challenge onset, and recovers when the challenge ends. The mean response is modeled by a system of differential equations that describe a candidate mechanism for cardiac response to anoxia challenge. The cardiac system behaves more variably when challenged than when at rest. Hence, observations arising from this experiment exhibit complex heteroscedasticity and sharp changes in central tendency. We present evidence that an asymptotic statistical inference strategy may fail to adequately account for statistical uncertainty. Two alternative methods are critiqued qualitatively (i.e., for utility in the current context), and quantitatively using an innovative Monte-Carlo method. We conclude with a discussion of the exciting opportunities in optimal design of response-to-challenge experiments.

Network-based empirical Bayes methods for linear models with applications to genomic data.

Empirical Bayes methods are widely used in the analysis of microarray gene expression data in order to identify the differentially expressed genes or genes that are associated with other general phenotypes. Available methods often assume that genes are independent. However, genes are expected to function interactively and to form molecular modules to affect the phenotypes. In order to account for regulatory dependency among genes, we propose in this paper a network-based empirical Bayes method for analyzing genomic data in the framework of linear models, where the dependency of genes is modeled by a discrete Markov random field defined on a predefined biological network. This method provides a statistical framework for integrating the known biological network information into the analysis of genomic data. We present an iterated conditional mode algorithm for parameter estimation and for estimating the posterior probabilities using Gibbs sampling. We demonstrate the application of the proposed methods using simulations and analysis of a human brain aging microarray gene expression data set.

Computationally derived points of fragility of a human cascade are consistent with current therapeutic strategies.

The role that mechanistic mathematical modeling and systems biology will play in molecular medicine and clinical development remains uncertain. In this study, mathematical modeling and sensitivity analysis were used to explore the working hypothesis that mechanistic models of human cascades, despite model uncertainty, can be computationally screened for points of fragility, and that these sensitive mechanisms could serve as therapeutic targets. We tested our working hypothesis by screening a model of the well-studied coagulation cascade, developed and validated from literature. The predicted sensitive mechanisms were then compared with the treatment literature. The model, composed of 92 proteins and 148 protein-protein interactions, was validated using 21 published datasets generated from two different quiescent in vitro coagulation models. Simulated platelet activation and thrombin generation profiles in the presence and absence of natural anticoagulants were consistent with measured values, with a mean correlation of 0.87 across all trials. Overall state sensitivity coefficients, which measure the robustness or fragility of a given mechanism, were calculated using a Monte Carlo strategy. In the absence of anticoagulants, fluid and surface phase factor X/activated factor X (fX/FXa) activity and thrombin-mediated platelet activation were found to be fragile, while fIX/FIXa and fVIII/FVIIIa activation and activity were robust. Both anti-fX/FXa and direct thrombin inhibitors are important classes of anticoagulants; for example, anti-fX/FXa inhibitors have FDA approval for the prevention of venous thromboembolism following surgical intervention and as an initial treatment for deep venous thrombosis and pulmonary embolism. Both in vitro and in vivo experimental evidence is reviewed supporting the prediction that fIX/FIXa activity is robust. When taken together, these results support our working hypothesis that computationally derived points of fragility of human relevant cascades could be used as a rational basis for target selection despite model uncertainty.