ATM-FBA: Automatic Thresholding to Minimize Deviation Between Flux State and Gene Expression State

Gene expression data can be employed to improve constraint-based analyses, e.g., to predict metabolic fluxes in differentiated cells of multicellular organisms and tumor cells. Over the last decade, many such methods have been proposed. However, the conversion of expression data to flux constraints is challenging, as expression data is noisy and the exact relationship between expression and flux is complicated by many-to-many relationships of genes and reactions, non-linear kinetics with unknown parameters, and unknown metabolite concentrations. Some of the proposed methods use arbitrary thresholds to define discrete gene activity states {Shlomi 2008}, while others try to correlate flux to expression levels. The performance of a large range of such methods has been compared to parsimonious FBA and was found to be unsatisfactory.

Here, we introduce a novel algorithm, ATM-FBA, applicable to transcriptomic or proteomic data. ATM-FBA builds a mixed integer linear programming (MILP) problem by adding an integer variable for each gene to indicate its expression state (ON/OFF) and an integer variable for each catalyzed reaction to indicate if it carries a significant flux. The thresholds for expression state and flux activity are variables that are part of the optimization. Accordingly, the gene-protein-reaction (GPR) rules are converted to constraints inside the MILP problem. The MILP objective is to minimize the disagreement between the flux state and the corresponding expression state or to minimize the disagreement between predicted gene state (depending on predicted flux state) and measured gene state. There are two types of disagreement. The first occurs when the flux is low while the corresponding gene expression is high (unused expression); the second occurs when a flux is high while the corresponding expression is low (insufficient expression). We allow different weights for these two types of disagreement, as we expect unused expression (which might, for example, indicate post-transcriptional regulation) to be less problematic than insufficient expression.

We compared the performance of ATM-FBAto existing methods using a benchmark dataset recently published by {Machado 2014}.The optimal solution set the gene expression threshold to quantile 0.92 and the flux threshold to be between 0.65 and 1.0. The disagreement between predicted and measured flux is on average 4%. Using the previously published benchmark, our method results in the smallest normalized standard error among all methods tested.

ATM-FBA will be added to sybilEFBA, an extension to the sybil open source library for constraint-based modeling in R(available from http://cran.r-project.org/).

References

Amer Desouki A: sybilEFBA. [ http://CRAN.R-project.org/package=sybilEFBA webcite]

Machado, D., & Herrgård, M. (2014). Systematic evaluation of methods for integration of transcriptomic data into constraint-based models of metabolism. PLoS Comput. Biol, 10, e1003580.

Shlomi, T., Cabili, M. N., Herrgård, M. J., Palsson, B. Ø., & Ruppin, E. (2008). Network-based prediction of human tissue-specific metabolism. Nature biotechnology, 26(9), 1003-1010.