Modeling and dissecting bidirectional feedback in gene-metabolite systems using the CausalFlux method

Predicting cellular behaviors, a central task in systems biology and metabolic engineering, can be enhanced through integrative modeling of processes such as gene regulation and metabolism. Information flow from gene regulation (modeled via a gene regulatory network) to metabolism (modeled via a genome-scale metabolic model) is well-studied, but the reciprocal regulation of genes by metabolites is less explored. We introduce CausalFlux, a method that models bidirectional feedback between genes and metabolites, in order to predict steady-state reaction fluxes under wild-type (WT) or perturbed (e.g., gene knockout/KO) conditions. CausalFlux does so by iteratively performing causal surgery on a Bayesian gene regulatory network and constraint-based analysis of a coupled metabolic model. CausalFlux enabled us to assess the impact of two-way feedback in several testbed models and real-world biological systems by comparing its predictions to those of TRIMER, a state-of-the-art model of gene-to-metabolite one-way feedback. Incorporating bidirectional feedback, as in CausalFlux, improved the Spearman correlation between actual and predicted fluxes in 92% of the 39 distinct simulation conditions relative to TRIMER. For predicting growth/no-growth phenotype following single-gene KOs in E. coli, CausalFlux achieved a balanced accuracy of 0.79 in identifying essential genes, and TRIMER achieved 0.71 for the same task, again highlighting the importance of modeling two-way feedback. In ablation studies that further dissect the role of specific metabolite[->]gene feedback edges in E. coli, the F1 scores of gene essentiality predictions decreased by 7.5% and 13% upon ablation of feedback edges from any metabolite to the crp gene and the 10 metabolic feedback genes with the highest influence on the KO genes, respectively. Finally, we highlight the application of CausalFlux to predict the essentiality of several hundred genes under different media conditions. Overall, our findings show that CausalFlux can crucially utilize information on feedback metabolites to predict trends in reaction fluxes and qualitative (growth/no-growth) outcomes; thereby encouraging future systems modeling efforts to carefully incorporate not only gene-to-metabolite but also metabolite-to-gene interactions. AvailabilityCode pertaining to the CausalFlux method, and its benchmarking and application is publicly available at: https://github.com/BIRDSgroup/CausalFlux. Author summaryThe myriad processes within a living cell, such as gene regulation or metabolism, are tightly interconnected. Modeling these interconnected processes can offer a deeper mechanistic understanding of cellular behaviors, as well as guide efforts that engineer the metabolic output of a cell. In this work, we develop a novel integrated model of gene regulation and metabolism that incorporates bidirectional feedback between these two processes, via the concept of metabolite-induced causal surgery on a gene regulatory network and gene-induced constraints on the fluxes of metabolic reactions. Our model, which we call CausalFlux, represents an advance over most existing models that capture just the one-way gene-to-metabolism feedback (i.e., genes coding for enzymes that control metabolic reactions). Our CausalFlux methodology opens up an unique opportunity to quantify the impact of two-way feedback in gene-metabolite systems, via comparison of CausalFluxs predictions to those of TRIMER, a published model incorporating one-way feedback alone. For predicting reaction fluxes in testbed models and essential genes in E. coli, quantitative comparison of the performance of CausalFlux vs. TRIMER showed that accounting for two-way feedback leads to more accurate and biologically meaningful predictions. CausalFlux also enabled us to quantify the effect of two-way feedback by comparing prediction performance before and after ablation of certain feedback edges from metabolites to genes. Overall, our findings highlight the importance of modeling gene regulation and metabolism as two-way interconnected systems within a living cell, and encourage future works to incorporate gene{leftrightarrow}metabolite feedback into their analyses.