40,129 research outputs found
Flux imbalance analysis and the sensitivity of cellular growth to changes in metabolite pools
Stoichiometric models of metabolism, such as flux balance analysis (FBA), are classically applied to predicting steady state rates - or fluxes - of metabolic reactions in genome-scale metabolic networks. Here we revisit the central assumption of FBA, i.e. that intracellular metabolites are at steady state, and show that deviations from flux balance (i.e. flux imbalances) are informative of some features of in vivo metabolite concentrations. Mathematically, the sensitivity of FBA to these flux imbalances is captured by a native feature of linear optimization, the dual problem, and its corresponding variables, known as shadow prices. First, using recently published data on chemostat growth of Saccharomyces cerevisae under different nutrient limitations, we show that shadow prices anticorrelate with experimentally measured degrees of growth limitation of intracellular metabolites. We next hypothesize that metabolites which are limiting for growth (and thus have very negative shadow price) cannot vary dramatically in an uncontrolled way, and must respond rapidly to perturbations. Using a collection of published datasets monitoring the time-dependent metabolomic response of Escherichia coli to carbon and nitrogen perturbations, we test this hypothesis and find that metabolites with negative shadow price indeed show lower temporal variation following a perturbation than metabolites with zero shadow price. Finally, we illustrate the broader applicability of flux imbalance analysis to other constraint-based methods. In particular, we explore the biological significance of shadow prices in a constraint-based method for integrating gene expression data with a stoichiometric model. In this case, shadow prices point to metabolites that should rise or drop in concentration in order to increase consistency between flux predictions and gene expression data. In general, these results suggest that the sensitivity of metabolic optima to violations of the steady state constraints carries biologically significant information on the processes that control intracellular metabolites in the cell.Published versio
Efficient Gaussian Sampling for Solving Large-Scale Inverse Problems using MCMC Methods
The resolution of many large-scale inverse problems using MCMC methods
requires a step of drawing samples from a high dimensional Gaussian
distribution. While direct Gaussian sampling techniques, such as those based on
Cholesky factorization, induce an excessive numerical complexity and memory
requirement, sequential coordinate sampling methods present a low rate of
convergence. Based on the reversible jump Markov chain framework, this paper
proposes an efficient Gaussian sampling algorithm having a reduced computation
cost and memory usage. The main feature of the algorithm is to perform an
approximate resolution of a linear system with a truncation level adjusted
using a self-tuning adaptive scheme allowing to achieve the minimal computation
cost. The connection between this algorithm and some existing strategies is
discussed and its efficiency is illustrated on a linear inverse problem of
image resolution enhancement.Comment: 20 pages, 10 figures, under review for journal publicatio
Robust localization methods for passivity enforcement of linear macromodels
In this paper we solve a non-smooth convex formulation for passivity enforcement of linear macromodels using robust localization based algorithms such as the ellipsoid and the cutting plane methods. Differently from existing perturbation based techniques, we solve the formulation based on the direct ℌ∞ norm minimization through perturbation of state-space model parameters. We provide a systematic way of defining an initial set which is guaranteed to contain the global optimum. We also provide a lower bound on the global minimum, that grows tighter at each iteration and hence guarantees δ - optimality of the computed solution. We demonstrate the robustness of our implementation by generating accurate passive models for challenging examples for which existing algorithms either failed or exhibited extremely slow convergenc
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
Inferring Multiple Graphical Structures
Gaussian Graphical Models provide a convenient framework for representing
dependencies between variables. Recently, this tool has received a high
interest for the discovery of biological networks. The literature focuses on
the case where a single network is inferred from a set of measurements, but, as
wetlab data is typically scarce, several assays, where the experimental
conditions affect interactions, are usually merged to infer a single network.
In this paper, we propose two approaches for estimating multiple related
graphs, by rendering the closeness assumption into an empirical prior or group
penalties. We provide quantitative results demonstrating the benefits of the
proposed approaches. The methods presented in this paper are embeded in the R
package 'simone' from version 1.0-0 and later
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