Fig. 1

Overview of the approach used in the study. A Artificial pathway used in the study by replicating the topology of the mevalonate pathway for limonene synthesis. Arrows refer to reaction. Dash lines represent feed-forward inhibition, whereas mixed dash and dot lines indicate feedback inhibition. B Formulation of separate reaction kinetics for the pathway [generalized mass action (GMA), Michaelis–Menten (MM), linear-logarithmic (Linlog), and convenience kinetics (CK)]. C Time-series data for metabolite concentrations x(t) is generated by using the formulated reaction kinetics to simulate reaction progressions through time. The empirical net reaction rate for each metabolite at a given timepoint is then interpreted as the slope of its concentration in time. Separately, the dynamic concentration of enzyme participants e(t) is each determined by a specific hyperbolic Hill function. D The mean square error (MSE) between empirical net reaction rates and the predicted values based on the kinetic formulation is then minimized as an objective function in kinetic parameter hyperspace. The corresponding parameter values are then reported as an estimation. E The quality of the parameter estimations is then assessed using 4 criteria/considerations: if the coefficient-of-determinant is greater than or equal to 0.9 and is consistently so for three different seed runs, the computational cost (by using the number of generations required for optimization as a proxy), and the degree of reproducibility of the underlying reaction dynamics with the estimated parameters. F Five widely available evolutionary algorithms (EAs) are then screened for their capacity to estimate the parameters of the different kinetic formulations. The initial screening is done using datapoints at 15 min intervals with no measurement noise. Further evaluations are conducted for selected EAs in estimating GMA and MM parameters at increasing measurement noise and datapoint spacing. The effect of taking parameter averages based on different seed solutions as well as data augmentation is also evaluated. Metabolites AcCoA, acetyl-coenzyme A; AcAcCoA, acetoacetyl-coenzyme A; HMGCoA, 3-hydroxy-3-methylglutaryl-coenzyme A; Mev, mevalonate; MevP, phosphomevalonate; MevPP, diphosphomevalonate; IPP, isopentenyl pyrophosphate; DMAPP, dimethylallyl pyrophosphate; GPP, geranyl pyrophosphate Enzymatic reactions AtoB, acetoacetyl-CoA thiolase; HMGS, hydroxymethylglutaryl-CoA Synthase, HMGR, 3-hydroxy-3-methyl-glutaryl-coenzyme A reductase; MK, mevalonate kinase; PMK, phosphomevalonate kinase; PMD, phosphomevalonate decarboxylase; IDI, isopentenyl-pyrophosphate delta-isomerase; GPPS, geranyl pyrophosphate synthase; LS, limonene synthase