Derivative processes for modelling metabolic fluxes.

MOTIVATION: One of the challenging questions in modelling biological systems is to characterize the functional forms of the processes that control and orchestrate molecular and cellular phenotypes. Recently proposed methods for the analysis of metabolic pathways, for example, dynamic flux estimation, can only provide estimates of the underlying fluxes at discrete time points but fail to capture the complete temporal behaviour. To describe the dynamic variation of the fluxes, we additionally require the assumption of specific functional forms that can capture the temporal behaviour. However, it also remains unclear how to address the noise which might be present in experimentally measured metabolite concentrations. RESULTS: Here we propose a novel approach to modelling metabolic fluxes: derivative processes that are based on multiple-output Gaussian processes (MGPs), which are a flexible non-parametric Bayesian modelling technique. The main advantages that follow from MGPs approach include the natural non-parametric representation of the fluxes and ability to impute the missing data in between the measurements. Our derivative process approach allows us to model changes in metabolite derivative concentrations and to characterize the temporal behaviour of metabolic fluxes from time course data. Because the derivative of a Gaussian process is itself a Gaussian process, we can readily link metabolite concentrations to metabolic fluxes and vice versa. Here we discuss how this can be implemented in an MGP framework and illustrate its application to simple models, including nitrogen metabolism in Escherichia coli. AVAILABILITY AND IMPLEMENTATION: R code is available from the authors upon request

Derivative processes for modelling metabolic fluxes

Motivation: One of the challenging questions in modelling biological systems is to characterize the functional forms of the processes that control and orchestrate molecular and cellular phenotypes. Recently proposed methods for the analysis of metabolic pathways, for example, dynamic flux estimation, can only provide estimates of the underlying fluxes at discrete time points but fail to capture the complete temporal behaviour. To describe the dynamic variation of the fluxes, we additionally require the assumption of specific functional forms that can capture the temporal behaviour. However, it also remains unclear how to address the noise which might be present in experimentally measured metabolite concentrations. Results: Here we propose a novel approach to modelling metabolic fluxes: derivative processes that are based on multiple-output Gaussian processes (MGPs), which are a flexible non-parametric Bayesian modelling technique. The main advantages that follow from MGPs approach include the natural non-parametric representation of the fluxes and ability to impute the missing data in between the measurements. Our derivative process approach allows us to model changes in metabolite derivative concentrations and to characterize the temporal behaviour of metabolic fluxes from time course data. Because the derivative of a Gaussian process is itself a Gaussian process, we can readily link metabolite concentrations to metabolic fluxes and vice versa. Here we discuss how this can be implemented in an MGP framework and illustrate its application to simple models, including nitrogen metabolism in Escherichia coli

Computational hypothesis generation with genome-side metabolic reconstructions: in-silico prediction of metabolic changes in the freshwater model organism Daphnia to environmental stressors

Computational toxicology is an emerging, multidisciplinary field that uses in-silico modelling techniques to predict and understand how biological organisms interact with pollutants and environmental stressors. Genome-wide metabolic reconstruction (GWMR) is an in-silico modelling technique that aims to represent the metabolic capabilities of an organism. Daphnia is an emerging model species for environmental omics whose underlying biology is still being uncovered. Creating a metabolic reconstruction of Daphnia and applying it in an environmental computational toxicology setting has the potential to aid in understanding its interaction with environmental stressors. Here, the fist GWMR of D. magna is presented, which is built using METRONOME, a newly developed tool for automated GWMR of new genome sequences. Active module identification allows for omics data sets to be integrated into in-silico models and uses optimisation algorithms to find hot-spots within networks that represent areas that are significantly impacted based on a toxicogenomic transcriptomics dataset. Here, a method that uses the active modules approach in a predictive capacity for computational hypothesis generation is introduced to predict unknown metabolic responses to environmentally relevant human-induced stressors. A computational workflow is presented that takes a new genome sequence, builds a GWMR and integrates gene expression data to make predictions of metabolic effects. The aim is to introduce an element of hypothesis generation into the untargeted metabolomics experimental workflow. A study to validate this approach using D. magna as the target organism is presented, which uses untargeted Liquid-Chromatography Mass Spectrometry (LC-MS) to make metabolomics measurements. A software tool MUSCLE is presented that uses multi-objective closed-loop evolutionary optimisation to automatically develop LC-MS instrument methods and is used here to develop the analytical method