Integration of Transcriptomic Data and Metabolic Models for Expression-Informed Flux-Balance Analysis

Any method that integrates transcriptomic data with flux-balance analysis (FBA) modeling must make two fundamental decisions: how to interpret transcript levels as indicators of gene activity; and how to use gene activity assertions to constrain the FBA solution space. For example, the GIMME algorithm (Becker and Palsson, 2008) uses a transcript level threshold to partition gene activity into discrete “off” and “on” states, then inactivates reactions associated with genes that are “off.” In contrast, E-Flux (Colijn et al., 2009) computes a continuous measure of gene activity by determining the percentage of each gene’s maximum transcript level observed in a particular experiment, then constrains maximum flux through the gene’s associated reactions by the same percentage. Most methods also include a penalty function to minimize deviation from the imposed constraints in case a solution cannot be found without violating the constraints.

Our research addresses the first decision by using transcriptomic data across a wide set of experimental conditions to calculate the probability that each gene is active in each particular condition (e.g., low probability = “off”, high probability = “on”). We have developed a statistical model for gene activity as a mixture of two Gaussian distributions with different means and variances, corresponding to the “off” and “on” states. We model the joint distribution across two or more co-regulated genes as a mixture of multivariate normal distributions with an unconstrained variance-covariance matrix. To evaluate this model, we have obtained compendia of cross-normalized gene expression experiments (e.g., M3D) for model organisms with published metabolic models (e.g., E. coli, iJO1366, 907 experiments;  S. oneidensis, iMR1_799, 245 experiments). Recognizing that not all genes fit this two-state model, either because of constitutive expression, or because of insufficient variability of experimental conditions in the compendia, we screen for genes with low expression variability and low Bayesian Information Criteria (BIC) values. Using information about which genes are likely to be co-expressed (e.g., operons, regulons, pathways), we estimate the mean and standard deviation of each gene’s “off” and “on” states across all experiments, and subsequently calculate the posterior probability of each gene being active in each experiment.

We address the second decision by penalizing deviations from the expected gene activity states in proportion to the calculated posterior probabilities. For each gene that is likely to be active, the penalty accrues if the associated reactions do not carry flux during the FBA simulation. Likewise, for each gene that is unlikely to be active, the penalty accrues if the associated reactions do carry flux during the FBA simulation. Thus we attempt to simultaneously achieve the desired objective (e.g., biomass maximization) while minimizing the deviation from expected gene activity states.

We are currently examining techniques for validating our methods. Preliminary results show that deviations from calculated posterior probabilities during FBA simulations may be useful for correcting and gapfilling metabolic models. We hope to use our methods to discover gene functions, and to predict experimental conditions that are likely to induce gene expression variability for genes with low variability in the compendia.