Robert J. Flassig

TRANSWESD: inferring cellular networks with transitive reduction

Motivation: Distinguishing direct from indirect influences is a central issue in reverse engineering of biological networks because it facilitates detection and removal of false positive edges. Transitive reduction is one approach for eliminating edges reflecting indirect effects but its use in reconstructing cyclic interaction graphs with true redundant structures is problematic. Results: We present TRANSWESD, an elaborated variant of TRANSitive reduction for WEighted Signed Digraphs that overcomes conceptual problems of existing versions. Major changes and improvements concern: (i) new statistical approaches for generating high-quality perturbation graphs from systematic perturbation experiments; (ii) the use of edge weights (association strengths) for recognizing true redundant structures; (iii) causal interpretation of cycles; (iv) relaxed definition of transitive reduction; and (v) approximation algorithms for large networks. Using standardized benchmark tests, we demonstrate that our method outperforms existing variants of transitive reduction and is, despite its conceptual simplicity, highly competitive with other reverse engineering methods. Contact: klamt@mpi-magdeburg.mpg.de Supplementary information: Supplementary data are available at Bioinformatics online.

Optimal design of stimulus experiments for robust discrimination of biochemical reaction networks

Motivation: Biochemical reaction networks in the form of coupled ordinary differential equations (ODEs) provide a powerful modeling tool for understanding the dynamics of biochemical processes. During the early phase of modeling, scientists have to deal with a large pool of competing nonlinear models. At this point, discrimination experiments can be designed and conducted to obtain optimal data for selecting the most plausible model. Since biological ODE models have widely distributed parameters due to, e.g. biologic variability or experimental variations, model responses become distributed. Therefore, a robust optimal experimental design (OED) for model discrimination can be used to discriminate models based on their response probability distribution functions (PDFs). Results: In this work, we present an optimal control-based methodology for designing optimal stimulus experiments aimed at robust model discrimination. For estimating the time-varying model response PDF, which results from the nonlinear propagation of the parameter PDF under the ODE dynamics, we suggest using the sigma-point approach. Using the model overlap (expected likelihood) as a robust discrimination criterion to measure dissimilarities between expected model response PDFs, we benchmark the proposed nonlinear design approach against linearization with respect to prediction accuracy and design quality for two nonlinear biological reaction networks. As shown, the sigma-point outperforms the linearization approach in the case of widely distributed parameter sets and/or existing multiple steady states. Since the sigma-point approach scales linearly with the number of model parameter, it can be applied to large systems for robust experimental planning. Availability: An implementation of the method in MATLAB/AMPL is available at http://www.uni-magdeburg.de/ivt/svt/person/rf/roed.html. Contact: flassig@mpi-magdeburg.mpg.de Supplementary information: Supplementary data are are available at Bioinformatics online.

A dynamic growth model of Dunaliella salina: Parameter identification and profile likelihood analysis

In this work, a photoautotrophic growth model incorporating light and nutrient effects on growth and pigmentation of Dunaliella salina was formulated. The model equations were taken from literature and modified according to the experimental setup with special emphasis on model reduction. The proposed model has been evaluated with experimental data of D. salina cultivated in a flat-plate photobioreactor under stressed and non-stressed conditions. Simulation results show that the model can represent the experimental data accurately. The identifiability of the model parameters was studied using the profile likelihood method. This analysis revealed that three model parameters are practically non-identifiable. However, some of these non-identifiabilities can be resolved by model reduction and additional measurements. As a conclusion, our results suggest that the proposed model equations result in a predictive growth model for D. salina.

An effective framework for reconstructing gene regulatory networks from genetical genomics data

MOTIVATION Systems Genetics approaches, in particular those relying on genetical genomics data, put forward a new paradigm of large-scale genome and network analysis. These methods use naturally occurring multi-factorial perturbations (e.g. polymorphisms) in properly controlled and screened genetic crosses to elucidate causal relationships in biological networks. However, although genetical genomics data contain rich information, a clear dissection of causes and effects as required for reconstructing gene regulatory networks is not easily possible. RESULTS We present a framework for reconstructing gene regulatory networks from genetical genomics data where genotype and phenotype correlation measures are used to derive an initial graph which is subsequently reduced by pruning strategies to minimize false positive predictions. Applied to realistic simulated genetic data from a recent DREAM challenge, we demonstrate that our approach is simple yet effective and outperforms more complex methods (including the best performer) with respect to (i) reconstruction quality (especially for small sample sizes) and (ii) applicability to large data sets due to relatively low computational costs. We also present reconstruction results from real genetical genomics data of yeast. AVAILABILITY A MATLAB implementation (script) of the reconstruction framework is available at www.mpi-magdeburg.mpg.de/projects/cna/etcdownloads.html CONTACT klamt@mpi-magdeburg.mpg.de.

Probabilistic reactor design in the framework of elementary process functions

Abstract Computational process models in combination with innovative design methodologies provide a powerful reactor design platform. Yet, model-based design is mostly done in a pure deterministic way. Possible uncertainties of the underlying model parameters, prediction errors due to simplifying assumptions regarding the reactor behavior and suboptimal realizations of the design along the reaction coordinate are in general not considered. Here we propose a systematic design approach to directly account for the impact of such variabilities during the design procedure. The three level design approach of Peschel et al. (2010) based on the concept of elementary process functions (EPF) serves as basis. The dynamic optimizations on each level are extended within a probabilistic framework to account for different sources of randomness. The impact of these sources on the performance prediction of a design is quantified and used to robustify the reactor design aiming at a more reliable performance and thus design prediction. The uncertainties of model parameters, non-idealities of the reactor behavior and inaccuracies in the design are included via statistical moments. By means of the sigma point method ( Julier and Uhlmann, 1996 ) random variables are mapped to the design objective space via the nonlinear process model. Importantly, this work introduces a full probabilistic orthogonal collocation approach, i.e. random and stochastic variables can be described. Whereas the former one relates to randomness independent on the reaction time (e.g. kinetic model parameters or initial conditions), the latter one describes stochasticity along the reaction time (e.g. fluctuating pressure or temperature control). As an example process the hydroformylation of 1-dodecene in a thermomorphic solvent system consisting of n -decane and N , N -dimethylformamide is considered. Our probabilistic EPF approach allows designing robust optimal reactors, which operate within an estimated confidence at their expected optimum considering almost any kind of randomness arising in the design procedure. An additional value is that with increased predictive power of the reactor performance its embedding in an overall process is strongly simplified.

Dynamic and Steady State 1-D Model of Mediated Electron Transfer in a Porous Enzymatic Electrode

A 1-D mathematical model of a porous enzymatic electrode exhibiting the mediated electron transfer (MET) mechanism has been developed. As a model system, glucose oxidation catalyzed by immobilized glucose oxidase (GOx) in the presence of a co-immobilized tetrathiafulvalene (TTF) mediator in the porous electrode matrix has been selected. The balance equations for potential fields in the electron- and ion-conducting phases as well as concentration field have been formulated, solved numerically and validated experimentally under steady state conditions. The relevant kinetic parameters of the lumped reaction kinetics have been obtained by global optimization. The confidence intervals (CIs) of each parameter have been extracted from the respective likelihood. The parameter study has shown that the parameters related to mediator consumption/regeneration steps can be responsible for the shift of the reaction onset potential. Additionally, the model has shown that diffusion of the oxidized mediator out of the catalyst layer (CL) plays a significant role only at more positive potentials and low glucose concentrations. Only concentration profiles in different layers influence the electrode performance while other state fields like potential distributions in different phases have no impact on the performance. The concentration profiles reveal that all electrodes work through; the observed limiting currents are diffusion-reaction limiting. The normalized electrode activity decreases with an increase of enzyme loading. According to the model, the reason for this observation is glucose depletion along the CL at higher enzyme loadings. Comparison with experiments advices a decrease of enzyme utilization at higher enzyme loadings.

Reconstruction of large-scale regulatory networks based on perturbation graphs and transitive reduction: improved methods and their evaluation

BackgroundThe data-driven inference of intracellular networks is one of the key challenges of computational and systems biology. As suggested by recent works, a simple yet effective approach for reconstructing regulatory networks comprises the following two steps. First, the observed effects induced by directed perturbations are collected in a signed and directed perturbation graph (PG). In a second step, Transitive Reduction (TR) is used to identify and eliminate those edges in the PG that can be explained by paths and are therefore likely to reflect indirect effects.ResultsIn this work we introduce novel variants for PG generation and TR, leading to significantly improved performances. The key modifications concern: (i) use of novel statistical criteria for deriving a high-quality PG from experimental data; (ii) the application of local TR which allows only short paths to explain (and remove) a given edge; and (iii) a novel strategy to rank the edges with respect to their confidence. To compare the new methods with existing ones we not only apply them to a recent DREAM network inference challenge but also to a novel and unprecedented synthetic compendium consisting of 30 5000-gene networks simulated with varying biological and measurement error variances resulting in a total of 270 datasets. The benchmarks clearly demonstrate the superior reconstruction performance of the novel PG and TR variants compared to existing approaches. Moreover, the benchmark enabled us to draw some general conclusions. For example, it turns out that local TR restricted to paths with a length of only two is often sufficient or even favorable. We also demonstrate that considering edge weights is highly beneficial for TR whereas consideration of edge signs is of minor importance. We explain these observations from a graph-theoretical perspective and discuss the consequences with respect to a greatly reduced computational demand to conduct TR. Finally, as a realistic application scenario, we use our framework for inferring gene interactions in yeast based on a library of gene expression data measured in mutants with single knockouts of transcription factors. The reconstructed network shows a significant enrichment of known interactions, especially within the 100 most confident (and for experimental validation most relevant) edges.ConclusionsThis paper presents several major achievements. The novel methods introduced herein can be seen as state of the art for inference techniques relying on perturbation graphs and transitive reduction. Another key result of the study is the generation of a new and unprecedented large-scale in silico benchmark dataset accounting for different noise levels and providing a solid basis for unbiased testing of network inference methodologies. Finally, applying our approach to Saccharomyces cerevisiae suggested several new gene interactions with high confidence awaiting experimental validation.

Dynamic flux balance modeling to increase the production of high-value compounds in green microalgae

BackgroundPhotosynthetic organisms can be used for renewable and sustainable production of fuels and high-value compounds from natural resources. Costs for design and operation of large-scale algae cultivation systems can be reduced if data from laboratory scale cultivations are combined with detailed mathematical models to evaluate and optimize the process.ResultsIn this work we present a flexible modeling formulation for accumulation of high-value storage molecules in microalgae that provides quantitative predictions under various light and nutrient conditions. The modeling approach is based on dynamic flux balance analysis (DFBA) and includes regulatory models to predict the accumulation of pigment molecules. The accuracy of the model predictions is validated through independent experimental data followed by a subsequent model-based fed-batch optimization. In our experimentally validated fed-batch optimization study we increase biomass and

A guide to automated apoptosis detection: How to make sense of imaging flow cytometry data

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