Balancing Metabolic Homeostasis and Enzyme Cost with Multi-Objective Evolutionary Algorithms

The metabolic fluxes in cells are regulated by metabolites that bind to enzymes and modulate their activities. Metabolites can stabilize their own concentrations by exerting a negative feedback on their production pathways. Although metabolic networks have been studied extensively, many regulation arrows remain unknown. To model the costs and benefits of direct enzyme regulation, we apply multi-objective optimization with one loss function describing how regulation stabilizes the metabolic state against random perturbations and another loss function scoring the extra enzyme amounts required by regulation arrows. Using the number of arrows as a third objective for ease of interpretation, we study how activating and inhibiting arrows should be arranged in the system. Using an evolutionary multi-objective approach, simulating an evolution under biological trade-offs, we explore optimal arrow configurations. Our framework can also be used with other biological objectives, including optimal adaptation or information transmission in metabolic networks, to study their trade-offs with objectives such as energy or enzyme investment in cells.