The quantitative comprehension of a metabolic system in its dynamic state is a prerequisite for purposed strain improvement and enzymatic regulation. It is therefore crucial to accurately obtain the extracellular and intracellular metabolite concentrations in vivo in the time scale faster than typical metabolite turn-over rate. Though intracellular metabolite dynamics are addressable by latest rapid sampling technology, the measurements are not satisfactory due to the low percentage of intracellular volume to the total sample volume and often the low concentration levels of most intracellular metabolites. When the examined system is observable, a possible solution to this problem is by means of available statistical estimation approach. Hence, in this paper, the sequential Monte Carlo filter is applied to estimate the intracellular metabolite concentrations with the knowledge of extracellular metabolite concentrations. The application of this algorithm in a synthetic system with simulated data illustrates the applicability of this approach. All the intracellular metabolite concentrations are accurately estimated and the extracellular states are reconstructed from their noisy measurements. The dynamic flux distributions are also obtained and their underlying biological meanings are described

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.