Integration of gene expression data into genome-scale metabolic models

Abstract

A framework for integration of transcriptome data into stoichiometric metabolic models to obtain improved flux predictions is presented. The key idea is to exploit the regulatory information in the expression data to give additional constraints on the metabolic fluxes in the model. Measurements of gene expression from chemostat and batch cultures of Saccharomyces cerevisiae were combined with a recently developed genome-scale model, and the computed metabolic flux distributions were compared to experimental values from carbon labeling experiments and metabolic network analysis. The integration of expression data resulted in improved predictions of metabolic behavior in batch cultures, enabling quantitative predictions of exchange fluxes as well as qualitative estimations of changes in intracellular fluxes. A critical discussion of correlation between gene expression and metabolic fluxes is given.

Introduction

Following the developments in genomics there has been an increased focus on the behavior of complete biological systems. In such integrative analysis, also referred to as systems biology (Kitano, 2000; Ideker et al., 2001; Nielsen and Olsson, 2002), biological data from all levels of metabolism, from genome to metabolome, are combined in order to view the studied organism as a whole rather than investigating the single components of the system. In order to integrate the wealth of information, mathematical models play an important role, and systems biology is therefore often associated with quantitative investigation of the biological system under study.

Several mathematical modeling frameworks have been developed to describe and to analyze the metabolic behavior of an organism or a living cell (Gombert and Nielsen, 2000; Arkin, 2001). One of these approaches is stoichiometric modeling, which relies on mass balances over intracellular metabolites and the assumption of pseudo-steady-state conditions to determine intracellular metabolic fluxes. The information contained in a stoichiometric model itself results in an underdetermined linear equation system, which is not enough to calculate a unique flux distribution, and the models are therefore combined with additional experimental data or assumptions to yield a well-defined flux map. Examples of applications are, for instance, calculation of metabolic fluxes for a specific experiment (Aiba and Matsuoka, 1979; Christensen and Nielsen, 2000), and prediction of how phenotypic behavior is affected by genetic or environmental changes (Varma et al., 1993; Edwards and Palsson, 2000; Stuckrath et al., 2002; Segre et al., 2002).

An advantage with stoichiometric modeling is that it is based on well-known stoichiometric coefficients and that it does not require determination of parameters like kinetic constants. With the increasing amount of biological knowledge in public databases, it is therefore relatively straightforward to construct detailed metabolic models, and in recent years large-scale models primarily based on genome sequence information have been developed. The modeled organisms include the prokaryotes Haemophilus influenzae, Escherichia coli, Helicobacter pylori (Edwards and Palsson (1999), Edwards and Palsson (2000); Schilling et al., 2002), and most recently the eukaryote Saccharomyces cerevisiae (Forster et al., 2003). These models have a few hundred to over thousand reactions and are typically used for computational studies, for instance systematic insertion or deletion of heterologous reactions to obtain improved metabolic properties (Burgard and Maranas, 2001). A common approach is the so-called flux balance analysis where metabolic behavior is simulated under the assumption that the cells exhibit optimal growth (Varma and Palsson, 1994). For prokaryotes this assumption seems to hold true in many cases (Edwards et al., 2001) and recently it was demonstrated experimentally that sub-optimal growing cells could be evolved to the predicted optimal phenotype (Ibarra et al., 2002).

The price to pay for the simplicity of stoichiometric models is that no information on metabolic regulation is included. For instance, the S. cerevisiae model readily provides a good prediction of phenotypic behavior in glucose-limited aerobic and anaerobic chemostats (Famili et al., 2003). However, unless further information is supplied it is difficult to describe batch cultivations where the glucose levels are high and regulatory phenomena, referred to as glucose repression (Ronne, 1995; Gancedo, 1998; Johnston, 1999), drastically decrease respiration, biomass yield, etc. To improve the flux estimates, one can provide additional physiological information, such as experimentally measured uptake rates or knowledge about enzyme activities, to constrain the range of possible flux distributions.

Covert et al. (2001) suggested how the stoichiometric modeling framework could be extended with an overlaid transcriptional regulatory network using a Boolean logic formalism. This was later applied to a moderate size model for the central carbon metabolism in E. coli (Covert and Palsson, 2002). Apart from the fact that many regulatory phenomena cannot be accurately described by Boolean logic, this approach is at present primarily limited by the available knowledge on regulatory processes. As an alternative, we here investigate the possibilities to benefit from genome-wide measurements of transcription, e.g., using DNA or oligonucleotide microarrays. We discuss how such measurements can be combined with genome-scale stoichiometric models, thereby incorporating information on transcriptional regulation and hence improving prediction performance. Examples where gene expression data, from batch and chemostat cultivations of S. cerevisiae, are combined with the recently developed yeast model (Forster et al., 2003) are given, and the results are compared to experimental values obtained in Gombert et al. (2001) using ¹³C-labeling experiments.