Abstract
Constraint-based models of metabolic networks are typically underdetermined, because they contain more reactions than metabolites. Therefore the solutions to this system do not consist of unique flux rates for each reaction, but rather a space of possible flux rates. By uniformly sampling this space, an estimated probability distribution for each reaction’s flux in the network can be obtained. However, sampling a high dimensional network is time-consuming. Furthermore, the constraints imposed on the network give rise to an irregularly shaped solution space. Therefore more tailored, efficient sampling methods are needed. We propose an efficient sampling algorithm (called optGpSampler), which implements the Artificial Centering Hit-and-Run algorithm in a different manner than the sampling algorithm implemented in the COBRA Toolbox for metabolic network analysis, here called gpSampler. Results of extensive experiments on different genome-scale metabolic networks show that optGpSampler is up to 40 times faster than gpSampler. Application of existing convergence diagnostics on small network reconstructions indicate that optGpSampler converges roughly ten times faster than gpSampler towards similar sampling distributions. For networks of higher dimension (i.e. containing more than 500 reactions), we observed significantly better convergence of optGpSampler and a large deviation between the samples generated by the two algorithms. Availability: optGpSampler for Matlab and Python is available for non-commercial use at: http://cs.ru.nl/~wmegchel/optGpSampler/.
Highlights
Modelling metabolic networks helps to unravel the complex machinery of metabolism within the cell
Our contributions are threefold: (1) we introduce an efficient and effective random sampling algorithm which combines the advantages of ACHR and gpSampler; (2) we propose a new measure to quantify the deviation between samples obtained from two independent sampling runs; (3) we perform a thorough analysis on five metabolic network models
We proposed a new algorithm for uniform sampling of the steady-state solution space of metabolic networks
Summary
Modelling metabolic networks helps to unravel the complex machinery of metabolism within the cell. A classic approach is to model the reaction pathways in a dynamic fashion, using detailed kinetic data. For genome-scale models, often involving hundreds or thousands of reactions and metabolites, it is experimentally prohibitive to obtain the kinetic parameters involved. A constraintbased approach has successfully been applied to model and address a wide range of biological questions in the absence of detailed kinetic data [1,2]. By using a steady-state assumption, a first type of constraint dictates that all metabolite concentrations stay constant over time (mass-balance). A second type of constraint limits the flux rate for each reaction (flux-capacity and directionality). The relation between the m metabolites and n reactions is described in the m|n stoichiometric matrix S. At steady-state, the massbalance and flux capacity constraints can be formulated as in eq (1) and inequality (2) respectively
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