Predicting synthetic rescues in metabolic networks

Adilson E Motter¹, Natali Gulbahce^2,3,4, Eivind Almaas⁵ & Albert-László Barabási^6,7

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Synopsis

Advances in studies of genome-level cellular networks have highlighted striking properties in their large-scale structure, such as a heavy-tailed connectivity distribution and hierarchical or modular organization (Barabási and Oltvai, 2004). However, to capture functional aspects of biological systems, it is necessary to take into account dynamical processes, such as enzymatic activity in the case of metabolism.

Here, we use metabolic reaction fluxes as a representation of cellular phenotypes to develop network-based strategies to recover metabolic function that may have been lost due to defective genes. A recent study of cascading failures in generic complex networks (Motter, 2004) suggested that these cascades can be mitigated through the intentional removal of selected links. In the context of biological networks, this result raises the rather counterintuitive possibility that damage to cellular phenotypes, such as growth, can be alleviated by the targeted removal or downregulation of selected genes. In this study, we have developed a systematic approach to identify such rescue gene knockouts in genome-wide metabolic networks.

Focusing on the metabolism of single-cell organisms, we demonstrate our approach by computationally analyzing reconstructed metabolic networks of Escherichia coli (Edwards and Palsson, 2000) and Saccharomyces cerevisiae (Duarte et al, 2004). We identify genes whose removal can improve the growth of knockout mutants with reduced growth performance relative to the wild type. This is achieved by forcing the cell to either bypass the functions affected by the initial gene loss or to compensate for the lost function. In the extreme case of mutants with zero growth, our analysis predicts that it is sometimes possible to identify single genes whose removal will make it possible for the organism to regain the ability to grow. Consequently, our results suggest the possibility of synthetic-rescue genes, and thus, promise to represent a paradigm shift in the study of gene essentiality.

Figure 1 is a schematic description of our framework to identify possible cases of metabolic rescue. It is based on a combination of the constraint-based approach of flux balance analysis (FBA) (Edwards and Palsson, 2000) and the related method of minimization of metabolic adjustment (MOMA) (Segrè et al, 2002). Simply stated, FBA is a computational technique that identifies possible steady-state reaction fluxes in genome-scale metabolic networks, and MOMA is a variant that predicts postmutational flux states.

Figure 1

Schematic illustration of the consequences of gene deletion on the organism's growth rate. (A) The growth rate following the deletion of an enzyme-encoding gene often drops, but after many generations may recover to a new optimal value not very different from the original one (red line). The optimal growth rate before and after the deletion is predicted by FBA (black and green dotted lines). The blue line indicates the predicted buffering effect of additional gene deletions: by deleting appropriately selected additional genes, the suboptimal growth rate shortly after gene deletions is higher than without the rescue deletions. (B–E) The effect of rescue deletions on the fluxes of a metabolic network, where M₁ ... M₄ represent metabolites and the width of the arrows represents the strength of individual fluxes.

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We use MOMA to predict the growth of mutants, since the decrease in an organism's growth rate that often follows a gene deletion frequently could be just a transient effect: experiments in fixed media show that after many generations both wild-type and mutant strains typically increase their growth rate (Edwards and Palsson, 2000; Fong and Palsson, 2004) through the accumulation of appropriate regulatory changes and mutations that bring the metabolic system to an optimal steady state. Consequently, FBA is appropriate for predicting the growth phenotype of adapted wild-type strains, as well as the maximum potential for growth recovery in mutant strains.

Our analysis has identified multiple examples of the rescue effect, for both growing and non-growing mutants (Figure 4). We refer to the former case as a suboptimal recovery and the latter as the Lazarus effect. In particular, for E. coli cells in a minimal medium with glucose as the single carbon source, we predict that mutants with the lethal deletion of gene fbaA, pfk, or tpiA can be rescued through the concurrent deletion of other genes (Figure 4A). Sometimes, such as in the case of fbaA mutants in arabinose medium, the Lazarus effect comes along with the deletion of a single additional gene (Figure 4B). Counterintuitively, however, we find that the strength of the recovery generally increases with the number of genes that can be deleted.

Figure 4

The impact of rescue deletions for E. coli (A, B) and S. cerevisiae (C, D) gene-deficient mutants. (A, C) Predicted biomass production before () and after () rescue deletions in glucose minimal media. The mutants are generated through the deletion of the genes shown at the x-axis. We show the results for all mutants with G¹_MOMA<G¹_FBA such that G¹_MOMA0.8 G^wt_FBA and G¹_FBA0.2 G^wt_FBA. If the rescue deletion changes the growth rate from zero to some positive value, we observe the Lazarus effect, applying to suboptimally essential genes (left). If the rescue deletion only enhances the growth rate, we observe a suboptimal recovery (right). The experimental information on the lethality of the original E. coli (Edwards and Palsson, 2000; Gerdes et al, 2003; Baba et al, 2006; PEC, 2007) and S. cerevisiae (Giaever et al, 2002; Steinmetz et al, 2002; SDG, 2007) gene-deficient mutants is indicated with (+) for viable mutants, (-) for non-viable mutants, and (^a) for a gene absent in the databases. (B, D) Same as in (A, C) for single-gene rescue deletions in various media. We show selected mutants with significant biomass improvements after the rescue deletion of a single gene. The rescue deletion is indicated at the top, and the tested media are indicated at the bottom. The abbreviations stand for acetate (Ac), -ketoglutarate (Akg), arabinose (Ara), ethanol (Eth), galactose (Gal), glucose (Glc), glucose anaerobic (Glc^a), glycerol (Gly), lactate (Lac), malate (Mal), mannose (Man), pyruvate (Pyr), rich medium (Rich) (see Supplementary Information), sorbitol (Sor), succinate (Succ), sucrose (Suc), and xylose (Xyl). The biomass fluxes are normalized by the wild-type flux G^wt_FBA in all panels. In units of mmol/g DW-h, the wild-type fluxes for E. coli are 0.187 (Ac), 0.535 (Akg), 0.745 (Ara), 0.908 (Glc), 0.367 (Lac), 0.388 (Mal), 0.908 (Man), 0.303 (Pyr), 2.87 (Rich), 0.418 (Succ), and 1.37 (Suc), while for S. cerevisiae they are 0.189 (Ac), 0.311 (Eth), 0.703 (Gal), 0.819 (Glc), 0.180 (Glc^a), 0.532 (Gly), 1.34 (Rich), 0.798 (Sor), and 0.742 (Xyl). All the genes involved in the rescues of (A, C) are listed in Supplementary Information, while the minimum rescue sets are listed in Supplementary Tables SII and SIII, respectively. The alternative rescue genes for each media in (B, D) are listed along with the corresponding recoveries in Supplementary Information.

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The mechanism underlying the rescue effect is general and does not depend on the specific details of MOMA or FBA. In particular, any computational or experimental methodology that can help estimate metabolic fluxes can be used to identify candidates for rescue deletions. This study thus suggests a promising approach to restore metabolic function and identify genetic compensatory interactions, with potentially important implications for disease treatment research.

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