Flux Balance Analysis (FBA) has been used in the past to analyze microbial metabolic networks. Typically, FBA is used to study the metabolic flux at a particular steady state of the system. However, there are many situations where the reprogramming of the metabolic network is important. Therefore, the dynamics of these metabolic networks have to be studied. In this paper, we have extended FBA to account for dynamics and present two different formulations for dynamic FBA. These two approaches were used in the analysis of diauxic growth in Escherichia coli. Dynamic FBA was used to simulate the batch growth of E. coli on glucose, and the predictions were found to qualitatively match experimental data. The dynamic FBA formalism was also used to study the sensitivity to the objective function. It was found that an instantaneous objective function resulted in better predictions than a terminal-type objective function. The constraints that govern the growth at different phases in the batch culture were also identified. Therefore, dynamic FBA provides a framework for analyzing the transience of metabolism due to metabolic reprogramming and for obtaining insights for the design of metabolic networks.

Annotated genome sequences can be used to reconstruct whole-cell metabolic networks. These metabolic networks can be modelled and analysed (computed) to study complex biological functions. In particular, constraints-based in silico models have been used to calculate optimal growth rates on common carbon substrates, and the results were found to be consistent with experimental data under many but not all conditions. Optimal biological functions are acquired through an evolutionary process. Thus, incorrect predictions of in silico models based on optimal performance criteria may be due to incomplete adaptive evolution under the conditions examined. Escherichia coli K-12 MG1655 grows sub-optimally on glycerol as the sole carbon source. Here we show that when placed under growth selection pressure, the growth rate of E. coli on glycerol reproducibly evolved over 40 days, or about 700 generations, from a sub-optimal value to the optimal growth rate predicted from a whole-cell in silico model. These results open the possibility of using adaptive evolution of entire metabolic networks to realize metabolic states that have been determined a priori based on in silico analysis.

The Escherichia coli MG1655 genome has been completely sequenced. The annotated sequence, biochemical information, and other information were used to reconstruct the E. coli metabolic map. The stoichiometric coefficients for each metabolic enzyme in the E. coli metabolic map were assembled to construct a genomespecific stoichiometric matrix. The E. coli stoichiometric matrix was used to define the system's characteristics and the capabilities of E. coli metabolism. The effects of gene deletions in the central metabolic pathways on the ability of the in silico metabolic network to support growth were assessed, and the in silico predictions were compared with experimental observations. It was shown that based on stoichiometric and capacity constraints the in silico analysis was able to qualitatively predict the growth potential of mutant strains in 86% of the cases examined. Herein, it is demonstrated that the synthesis of in silico metabolic genotypes based on genomic, biochemical, and strain-specific information is possible, and that systems analysis methods are available to analyze and interpret the metabolic phenotype.bioinformatics ͉ metabolism ͉ genotype-phenotype relation ͉ flux balance analysis T he complete genome sequence for a number of microorganisms has been established (The Institute for Genomic Research at www.tigr.org). The genome sequencing efforts and the subsequent bioinformatic analyses have defined the molecular ''parts catalogue'' for a number of living organisms. However, it is evident that cellular functions are multigeneic in nature, thus one must go beyond a molecular parts catalogue to elucidate integrated cellular functions based on the molecular cellular components (1). Therefore, to analyze the properties and the behavior of complex cellular networks, one needs to use methods that focus on the systemic properties of the network. Approaches to analyze, interpret, and ultimately predict cellular behavior based on genomic and biochemical data likely will involve bioinformatics and computational biology and form the basis for subsequent bioengineering analysis.In moving toward the goal of developing an integrated description of cellular processes, it should be recognized that there exists a history of studying the systemic properties of metabolic networks (2) and many mathematical methods have been developed to carry out such studies. These methods include approaches such as metabolic control analysis (3, 4), flux balance analysis (FBA) (5-7), metabolic pathway analysis (8-11, 69), cybernetic modeling (12), biochemical systems theory (13), temporal decomposition (14), and so on. Although many mathematical methods and approaches have been developed, there are few comprehensive metabolic systems for which detailed kinetic information is available and where such detailed analysis can be carried out (see refs. 15-17 for a few noteworthy exceptions).To analyze, interpret, and predict cellular behavior, each individual step in a biochemical network must be described, normally with a rate equati...

A significant goal in the post-genome era is to relate the annotated genome sequence to the physiological functions of a cell. Working from the annotated genome sequence, as well as biochemical and physiological information, it is possible to reconstruct complete metabolic networks. Furthermore, computational methods have been developed to interpret and predict the optimal performance of a metabolic network under a range of growth conditions. We have tested the hypothesis that Escherichia coli uses its metabolism to grow at a maximal rate using the E. coli MG1655 metabolic reconstruction. Based on this hypothesis, we formulated experiments that describe the quantitative relationship between a primary carbon source (acetate or succinate) uptake rate, oxygen uptake rate, and maximal cellular growth rate. We found that the experimental data were consistent with the stated hypothesis, namely that the E. coli metabolic network is optimized to maximize growth under the experimental conditions considered. This study thus demonstrates how the combination of in silico and experimental biology can be used to obtain a quantitative genotype-phenotype relationship for metabolism in bacterial cells.