BackgroundMixed graphical models (MGMs) are graphical models learned over a combination of continuous and discrete variables. Mixed variable types are common in biomedical datasets. MGMs consist of a parameterized joint probability density, which implies a network structure over these heterogeneous variables. The network structure reveals direct associations between the variables and the joint probability density allows one to ask arbitrary probabilistic questions on the data. This information can be used for feature selection, classification and other important tasks.ResultsWe studied the properties of MGM learning and applications of MGMs to high-dimensional data (biological and simulated). Our results show that MGMs reliably uncover the underlying graph structure, and when used for classification, their performance is comparable to popular discriminative methods (lasso regression and support vector machines). We also show that imposing separate sparsity penalties for edges connecting different types of variables significantly improves edge recovery performance. To choose these sparsity parameters, we propose a new efficient model selection method, named Stable Edge-specific Penalty Selection (StEPS). StEPS is an expansion of an earlier method, StARS, to mixed variable types. In terms of edge recovery, StEPS selected MGMs outperform those models selected using standard techniques, including AIC, BIC and cross-validation. In addition, we use a heuristic search that is linear in size of the sparsity value search space as opposed to the cubic grid search required by other model selection methods. We applied our method to clinical and mRNA expression data from the Lung Genomics Research Consortium (LGRC) and the learned MGM correctly recovered connections between the diagnosis of obstructive or interstitial lung disease, two diagnostic breathing tests, and cigarette smoking history. Our model also suggested biologically relevant mRNA markers that are linked to these three clinical variables.ConclusionsMGMs are able to accurately recover dependencies between sets of continuous and discrete variables in both simulated and biomedical datasets. Separation of sparsity penalties by edge type is essential for accurate network edge recovery. Furthermore, our stability based method for model selection determines sparsity parameters faster and more accurately (in terms of edge recovery) than other model selection methods. With the ongoing availability of comprehensive clinical and biomedical datasets, MGMs are expected to become a valuable tool for investigating disease mechanisms and answering an array of critical healthcare questions.

We apply the "weighted ensemble" (WE) simulation strategy, previously employed in the context of molecular dynamics simulations, to a series of systems-biology models that range in complexity from a one-dimensional system to a system with 354 species and 3680 reactions. WE is relatively easy to implement, does not require extensive hand-tuning of parameters, does not depend on the details of the simulation algorithm, and can facilitate the simulation of extremely rare events. For the coupled stochastic reaction systems we study, WE is able to produce accurate and efficient approximations of the joint probability distribution for all chemical species for all time t. WE is also able to efficiently extract mean first passage times for the systems, via the construction of a steady-state condition with feedback. In all cases studied here, WE results agree with independent "brute-force" calculations, but significantly enhance the precision with which rare or slow processes can be characterized. Speedups over "brute-force" in sampling rare events via the Gillespie direct Stochastic Simulation Algorithm range from ~10(12) to ~10(18) for characterizing rare states in a distribution, and ~10(2) to ~10(4) for finding mean first passage times.

The long-term goal of connecting scales in biological simulation can be facilitated by scale-agnostic methods. We demonstrate that the weighted ensemble (WE) strategy, initially developed for molecular simulations, applies effectively to spatially resolved cell-scale simulations. The WE approach runs an ensemble of parallel trajectories with assigned weights and uses a statistical resampling strategy of replicating and pruning trajectories to focus computational effort on difficult-to-sample regions. The method can also generate unbiased estimates of non-equilibrium and equilibrium observables, sometimes with significantly less aggregate computing time than would be possible using standard parallelization. Here, we use WE to orchestrate particle-based kinetic Monte Carlo simulations, which include spatial geometry (e.g., of organelles, plasma membrane) and biochemical interactions among mobile molecular species. We study a series of models exhibiting spatial, temporal and biochemical complexity and show that although WE has important limitations, it can achieve performance significantly exceeding standard parallel simulation—by orders of magnitude for some observables.

There is intense interest in mapping the tissue-specific binding sites of transcription factors in the human genome to reconstruct gene regulatory networks and predict functions for noncoding genetic variation. DNase-seq footprinting provides a means to predict the genome-wide binding sites for hundreds of transcription factors (TFs) simultaneously. However, despite the public availability of DNase-seq data for hundreds of samples, there is neither a unified analytical workflow nor a publicly accessible database providing the locations of footprints across all available samples. Here, we describe the implementation of a workflow for uniform processing of footprints using two state-of-the-art footprinting algorithms: Wellington and HINT. Our workflow then scans footprints for 1,530 sequence motifs to predict binding sites for 1,515 human transcription factors. We tested our workflow using 21 DNase-seq experiments of lymphoblastoid cell lines, generated by the ENCODE project. We trained a machine learning model to predict TF binding sites, integrating footprints with additional biologically-related features. This model achieved a maximum MCC of 0.423 and an AUC of 0.943 compared to ENCODE ChIP-seq data for 62 TFs in the same cell type. We applied our workflow to detect footprints in 206 DNase-seq experiments from ENCODE, spanning 27 human tissues. These footprints describe an expansive landscape of TF occupancy in the human genome. Across all tissues, we detected high-quality footprints spanning 9.8% of all nucleotides in the human genome with scores found to enrich for true positives. The highest tissue-specific coverage was observed for samples in the brain (4.4%), followed by extra-embryonic structure (2.6%) and skin (2.4%). In addition, we report a more lenient footprinting call set, providing some evidence of TF occupancy in at least one tissue for 34% of all genomic positions. Our cloud-based workflow and a database with all footprints and TF binding site predictions are available at www.trena.org.