BACKGROUND: Mixture model on graphs (MMG) is a probabilistic model that integrates network topology with (gene, protein) expression data to predict the regulation state of genes and proteins. It is remarkably robust to missing data, a feature particularly important for its use in quantitative proteomics. A new implementation in C and interfaced with R makes MMG extremely fast and easy to use and to extend. AVAILABILITY: The original implementation (Matlab) is still available from http://www.dcs.shef.ac.uk/~guido/; the new implementation is available from http://wrightlab.group.shef.ac.uk/people_noirel.htm, from CRAN, and has been submitted to BioConductor, http://www.bioconductor.org/.

MOTIVATION: A fundamental task in systems biology is the identification of groups of genes that are involved in the cellular response to particular signals. At its simplest level, this often reduces to identifying biological quantities (mRNA abundance, enzyme concentrations, etc.) which are differentially expressed in two different conditions. Popular approaches involve using t-test statistics, based on modelling the data as arising from a mixture distribution. A common assumption of these approaches is that the data are independent and identically distributed; however, biological quantities are usually related through a complex (weighted) network of interactions, and often the more pertinent question is which subnetworks are differentially expressed, rather than which genes. Furthermore, in many interesting cases (such as high-throughput proteomics and metabolomics), only very partial observations are available, resulting in the need for efficient imputation techniques. RESULTS: We introduce Mixture Model on Graphs (MMG), a novel probabilistic model to identify differentially expressed submodules of biological networks and pathways. The method can easily incorporate information about weights in the network, is robust against missing data and can be easily generalized to directed networks. We propose an efficient sampling strategy to infer posterior probabilities of differential expression, as well as posterior probabilities over the model parameters. We assess our method on artificial data demonstrating significant improvements over standard mixture model clustering. Analysis of our model results on quantitative high-throughput proteomic data leads to the identification of biologically significant subnetworks, as well as the prediction of the expression level of a number of enzymes, some of which are then verified experimentally. AVAILABILITY: MATLAB code is available from http://www.dcs.shef.ac.uk/~guido/software.html

In this work, the problem of metabolic flux estimation is formulated as a problem of parameter estimation from incomplete labelling data. The expectation/conditional maximisation (ECM) algorithm is used to determined a maximum-likelihood (ML) estimate because of its simplicity and stable convergence. We propose to simplify a nonlinear inverse problem, generally numerically solved by an iterative optimisation algorithm, to a linear regression problem which is arrived at from a linear-in-the-parameter formulation during a partial optimisation process of the ECM algorithm. Three linear least square algorithms, the ordinary least squares (LS), the total least squares (TLS) and the constrained least squares (CLS), have been tested to solve the linear regression in this step. Using simulations, resulting parameter estimates and errors in flux estimation are compared and evaluated. The performance of the algorithms are investigated under two scenarios; when the labelling data are corrupted by a wide range of noise and when the labelling data are incompletely observed. Results suggest that the estimates from the ECM algorithm using CLS produce results superior to other combinations and have potential to be refined to improve its performance in metabolic flux estimation

Metabolic flux analysis is important for metabolic system regulation and intracellular pathway identification. A popular approach for intracellular flux estimation involves using 13C tracer experiments to label states that can be measured by nuclear magnetic resonance spectrometry or gas chromatography mass spectrometry. However, the bilinear balance equations derived from 13C tracer experiments and the noisy measurements require a nonlinear optimization approach to obtain the optimal solution. In this paper, the flux quantification problem is formulated as an error-minimization problem with equality and inequality constraints through the 13C balance and stoichiometric equations. The stoichiometric constraints are transformed to a null space by singular value decomposition. Self-adaptive evolutionary algorithms are then introduced for flux quantification. The performance of the evolutionary algorithm is compared with ordinary least squares estimation by the simulation of the central pentose phosphate pathway. The proposed algorithm is also applied to the central metabolism of Corynebacterium glutamicum under lysine-producing conditions. A comparison between the results from the proposed algorithm and data from the literature is given. The complexity of a metabolic system with bidirectional reactions is also investigated by analyzing the fluctuations in the flux estimates when available measurements are varied.

MOTIVATION: Metabolic flux analysis via a (13)C tracer experiment has been achieved using a Monte Carlo method with the assumption of system noise as Gaussian noise. However, an unbiased flux analysis requires the estimation of fluxes and metabolites jointly without the restriction on the assumption of Gaussian noise. The flux distributions under such a framework can be freely obtained with various system noise and uncertainty models. RESULTS: In this paper, a stochastic generative model of the metabolic system is developed. Following this, the Markov Chain Monte Carlo (MCMC) approach is applied to flux distribution analysis. The disturbances and uncertainties in the system are simplified as truncated Gaussian multiplicative models. The performance in a real metabolic system is illustrated by the application to the central metabolism of Corynebacterium glutamicum. The flux distributions are illustrated and analyzed in order to understand the underlying flux activities in the system. AVAILABILITY: Algorithms are available upon request.

Metabolic fluxes have been regarded as an important quantity for metabolic engineering as they reveal cause-effect relationships between genetic modifications and resulting changes in metabolic activity and are used as a prerequisite for the design of optimal whole cell biocatalysts. The intracellular fluxes must be estimated due to the inability to measure them directly. A particular useful technique involves the use of /sup 13/C-enriched substrates and the measurement of label distribution generated for each intermediate to uncover all unmeasured fluxes by solving the label balance equations, e.g. isotopomer balances, at steady state. However, the formation of these equations typically requires tedious algebraic manipulation and in many cases the resulting equations must be solved numerically, due to the nonlinearity and high dimensionality. Here we present three different evolutionary algorithm (EA) based approaches in combination with the least squares algorithm to show the applicability of EAs in metabolic flux quantification. The performance of the algorithms are illustrated and discussed through the simulation of the cyclic pentose phosphate network in a noisy environment and the identifiability problem is also considered.