Advances in flux balance analysis by integrating machine learning and mechanism-based models

The availability of multi-omics data sets and genome-scale metabolic models for various organisms provide a platform for modeling and analyzing genotype-to-phenotype relationships. Flux balance analysis is the main tool for predicting flux distributions in genome-scale metabolic models and various data-integrative approaches enable modeling context-specific network behavior. Due to its linear nature, this optimization framework is readily scalable to multi-tissue or -organ and even multi-organism models. However, both data and model size can hamper a straightforward biological interpretation of the estimated fluxes. Moreover, flux balance analysis simulates metabolism at steady-state and thus, in its most basic form, does not consider kinetics or regulatory events. The integration of flux balance analysis with complementary data analysis and modeling techniques offers the potential to overcome these challenges. In particular machine learning approaches have emerged as the tool of choice for data reduction and selection of most important variables in big data sets. Kinetic models and formal languages can be used to simulate dynamic behavior. This review article provides an overview of integrative studies that combine flux balance analysis with machine learning approaches, kinetic models, such as physiology-based pharmacokinetic models, and formal graphical modeling languages, such as Petri nets. We discuss the mathematical aspects and biological applications of these integrated approaches and outline challenges and future perspectives.