CellTarget: a convex optimisation approach to discover cellular objectives.

Metabolic network models are widely used in systems and synthetic biology to study cellular metabolism from microbes to mammals. However, their application to mammalian cells remains limited by the scarcity of intracellular flux measurements relative to network size. As a result, mammalian metabolic models are typically underdetermined and require optimisation-based assumptions to be solved. Unlike microbial systems, mammalian cells do not generally operate under growth-maximising objectives, making objective specification particularly challenging. To address this limitation, we propose CellTarget, an algorithm for inferring cellular objectives directly from experimental flux data. CellTarget combines a convex Flux Balance Analysis (FBA) module with an error-minimisation module that iteratively adjusts objective coefficients to improve agreement between predicted and measured fluxes. Gradients are obtained via implicit differentiation of the convex FBA optimisation problem, enabling backpropagation of the inferred objective coefficients and joint optimisation of both modules. CellTarget is evaluated across producer and non-producer Chinese Hamster Ovary (CHO) cell lines, growth phases, objective dimensionalities and both reduced and genome-scale networks. Across all settings, CellTarget yields accurate forward flux predictions and outperforms a benchmark inverse FBA method. The results reveal substantial non-identifiability of cellular objectives, with predictive accuracy driven more strongly by network constraints than by objective specificity.