Iterative design of training data to control intricate enzymatic reaction networks

Abstract

Kinetic modeling of in vitro enzymatic reaction networks is vital to understand and control the complex behaviors emerging from the nonlinear interactions inside. However, modeling is severely hampered by the lack of training data. Here, we introduce a methodology that combines an active learning-like approach and flow chemistry to efficiently create optimized datasets for a highly interconnected enzymatic reactions network with multiple sub-pathways. The optimal experimental design (OED) algorithm designs a sequence of out-of-equilibrium perturbations to maximize the information about the reaction kinetics, yielding a descriptive model that allows control of the output of the network towards any cost function. We experimentally validate the model by forcing the network to produce different product ratios while maintaining a minimum level of overall conversion efficiency. Our workflow scales with the complexity of the system and enables the optimization of previously unobtainable network outputs.

Quantitative Online Monitoring of an Immobilized Enzymatic Network by Ion Mobility–Mass Spectrometry

“…This is not surprising since the goodness-of-fit scores of the model to the training data show that these species were among those which deviated most (Figure c), indicating that these lower concentration regimes were not adequately mapped by the model and the OED experiment. Regardless, considering that a single OED iteration was previously not sufficient to even approximate the data quantitatively, the predicted concentrations from Figure are remarkably close to the experimental data.…”

“…The quantitative online monitoring approach described in this work nicely complements the active learning workflow we recently reported. , Therefore, we assessed whether the increased information contained in the IMS–MS data would yield a trained model within a single design-build-test cycle for the entire ERN. Compared to previous works, this would drastically simplify the procedure to gain full control over the output of ERNs (see eqs S5–S8).…”

“…Flow chemistry emerges as particularly beneficial for determining network kinetics, facilitating the systematic exploration of a large input space while analyzing the resulting mixture of products. , In a previous work, we streamlined this search with an optimal experimental design (OED) workflow, utilizing an OED algorithm to design maximally informative inflow profiles of metabolites into a flow reactor. − With this tool, we were able to train a model that could reliably control the nucleotide salvage pathway immobilized on beads, comprising 6 enzymes …”

“…Although OED workflows eliminate the need to systematically probe individual reactions, the analysis of ERN products constitutes a bottleneck when it is carried out offline using chromatographic methods. , In our previous work, the offline analysis of ERN products by HPLC resulted in relatively low sampling rates (3–9 min per sample) and limited observability over intermediate metabolites. Because of this, several design-build-test iterations were required to train a model that could control the reactions in the network . To facilitate the optimization of an ERN, it is imperative to employ measurement techniques that fulfill three essential requirements: (i) many intermediates need to be observed quantitatively, including low-concentration species; (ii) the time resolution of the observations needs to be significantly faster than the input changes suggested by the OED algorithm; and (iii) the approach needs to be time- and cost-effective.…”

“…The generation of isotopically 13 C-labeled intermediates in situ enables their quantification using available, nonisotopically labeled standards. We used a similar flow chemistry platform described before, in which we immobilized all enzymes constituting the network on hydrogel beads for compartmentalization in a filtered continuous stirred-tank reactor (CSTR). , Confining enzymatic reactivity to the CSTR prevents the loss of enzymes and allows us to disregard the downstream reactivity after metabolites leave the reactor. The network output was monitored in real time under continuously changing reactor conditions, enabling the collection of quantitative data for individual metabolites at a 550 ms time resolution (∼100,000 data points per experiment).…”