MetaboTools: A comprehensive toolbox for analysis of genome-scale metabolic models

Metabolomic data sets provide a direct read-out of cellular phenotypes and are increasingly generated to study biological questions. Our previous work revealed the potential of analyzing extracellular metabolomic data in the context of the metabolic model using constraint-based modeling. Through this work, which consists of a protocol, a toolbox, and tutorials of two use cases, we make our methods available to the broader scientific community. The protocol describes, in a step-wise manner, the workflow of data integration and computational analysis. The MetaboTools comprise the Matlab code required to complete the workflow described in the protocol. Tutorials explain the computational steps for integration of two different data sets and demonstrate a comprehensive set of methods for the computational analysis of metabolic models and stratification thereof into different phenotypes. The presented workflow supports integrative analysis of multiple omics data sets. Importantly, all analysis tools can be applied to metabolic models without performing the entire workflow. Taken together, this protocol constitutes a comprehensive guide to the intra-model analysis of extracellular metabolomic data and a resource offering a broad set of computational analysis tools for a wide biomedical and non-biomedical research community

Control of a train of high purity distillation columns for efficient production of 13C isotopes

It is well-known that high-purity distillation columns are difficult to control due to their ill-conditioned and strongly nonlinear behaviour. The fact that these processes are operated over a wide range of feed compositions and flow rates makes the control design even more challenging. This paper proposes the most suitable control strategies applicable to a series of cascaded distillation column processes. The conditions for control and input-output relations are discusssed in view of the global control strategy. The increase in complexity with increased number of series cascaded distillation column processes is tackled. Uncertainty in the model parameters is discussed with respect to the dynamics of the global train distillation process. The main outcome of this work is insight into the possible control methodologies for this particular class of distillation processes

Integration of Genome Scale Metabolic Networks and gene regulation of metabolic enzymes with Physiologically Based Pharmacokinetics

The scope of Physiologically Based Pharmacokinetic (PBPK) modelling can be expanded by assimilation of the mechanistic models of intracellular processes from Systems Biology field. Genome Scale Metabolic Networks (GSMNs) represent a whole set of metabolic enzymes expressed in human tissues. Dynamic models of the gene regulation of key drug metabolism enzymes are available. Here, we introduce GSMNs and review ongoing work on integration of PBPK, GSMNs and metabolic gene regulation. We demonstrate example models

Four lectures on probabilistic methods for data science

Methods of high-dimensional probability play a central role in applications for statistics, signal processing theoretical computer science and related fields. These lectures present a sample of particularly useful tools of high-dimensional probability, focusing on the classical and matrix Bernstein's inequality and the uniform matrix deviation inequality. We illustrate these tools with applications for dimension reduction, network analysis, covariance estimation, matrix completion and sparse signal recovery. The lectures are geared towards beginning graduate students who have taken a rigorous course in probability but may not have any experience in data science applications.Comment: Lectures given at 2016 PCMI Graduate Summer School in Mathematics of Data. Some typos, inaccuracies fixe

Chordal Decomposition in Rank Minimized Semidefinite Programs with Applications to Subspace Clustering

Semidefinite programs (SDPs) often arise in relaxations of some NP-hard problems, and if the solution of the SDP obeys certain rank constraints, the relaxation will be tight. Decomposition methods based on chordal sparsity have already been applied to speed up the solution of sparse SDPs, but methods for dealing with rank constraints are underdeveloped. This paper leverages a minimum rank completion result to decompose the rank constraint on a single large matrix into multiple rank constraints on a set of smaller matrices. The re-weighted heuristic is used as a proxy for rank, and the specific form of the heuristic preserves the sparsity pattern between iterations. Implementations of rank-minimized SDPs through interior-point and first-order algorithms are discussed. The problem of subspace clustering is used to demonstrate the computational improvement of the proposed method.Comment: 6 pages, 6 figure

Risk Bounds for Learning Multiple Components with Permutation-Invariant Losses

This paper proposes a simple approach to derive efficient error bounds for learning multiple components with sparsity-inducing regularization. We show that for such regularization schemes, known decompositions of the Rademacher complexity over the components can be used in a more efficient manner to result in tighter bounds without too much effort. We give examples of application to switching regression and center-based clustering/vector quantization. Then, the complete workflow is illustrated on the problem of subspace clustering, for which decomposition results were not previously available. For all these problems, the proposed approach yields risk bounds with mild dependencies on the number of components and completely removes this dependence for nonconvex regularization schemes that could not be handled by previous methods