An Improved Systematic Method for Constructing Enzyme-Constrained Genome-Scale Metabolic Models Using a Protein-Chemical Transformer

Enzyme-constrained genome-scale metabolic models (ecGEMs) have improved Flux Balance Analysis (FBA) by incorporating enzyme turnover numbers ($k_{cat}$s). Since in-vivo $k_{cat}$ data is costly to obtain and therefore scarce, we present a novel multi-modal transformer-based approach with cross-attention to predict $k_{cat}$ values for Escherichia. coli using enzyme amino acid sequences and SMILES annotations of reaction substrates. For heteromeric enzymes, we evaluate multiple subunit $k_{cat}$ aggregation strategies. We benchmark ecGEMs constructed with these strategies against current state-of-the-art models using experimental growth rates, Carbon-13 fluxes, and enzyme abundances, and prior to any calibration outperform or match existing methods. We also devise a new calibration method using flux control coefficients (derivatives of log flux with respect to log $k_{cat}$), which we show to be identical to enzyme cost at the FBA optimum. Using these coefficients, we identify 8 key $k_{cat}$ values to recalibrate using experimental data, subsequently achieving superior performance to the current state-of-the-art with 81\% fewer calibrations.