In order to create artificial enzymatic networks capable of increasingly complex behavior, an improved methodology in understanding and controlling the kinetics of these networks is needed. Here, we introduce a Bayesian analysis method allowing for the accurate inference of enzyme kinetic parameters and determination of most likely reaction mechanisms, by combining data from different experiments and network topologies in a single probabilistic analysis framework. This Bayesian approach explicitly allows us to continuously improve our parameter estimates and behavior predictions by iteratively adding new data to our models, while automatically taking into account uncertainties introduced by the experimental setups or the chemical processes in general. We demonstrate the potential of this approach by characterizing systems of enzymes compartmentalized in beads inside flow reactors. The methods we introduce here provide a new approach to the design of increasingly complex artificial enzymatic networks, making the design of such networks more efficient, and robust against the accumulation of experimental errors.

Currente fforts to design functional molecular systems have overlooked the importance of coupling out-ofequilibrium behaviour with changes in the environment. Here, the authors use an oscillating reaction network and demonstrate that the application of environmental forcing, in the form of periodic changes in temperature and in the inflow of the concentrationo fo ne of the network components, removes the dependency of the periodicity of this network on temperature or flow rates and enforces as table periodicity across aw ide range of conditions. Coupling a system to ad ynamic environmentc an thusb eu sed as a simple tool to regulate the output of an etwork. In addition, the authors show that coupling can also induce an increase in behavioural complexity to include quasi-periodic oscillations. Institute for Molecules and Materials, RadboudU niversity Heyendaalseweg 135, 6525 AJ Supporting information and the ORCID identification number(s) for the author(s) of this articlecan be found under: https://doi.

Living systems use enzymatic reaction networks to process biochemical information and make decisions in response to external or internal stimuli. Herein, we present a modular and reusable platform for molecular information processing using enzymes immobilised in hydrogel beads and compartmentalised in a continuous stirred tank reactor. We demonstrate how this setup allows us to perform simple arithmetic operations, such as addition, subtraction and multiplication, using various concentrations of substrates or inhibitors as inputs and the production of a fluorescent molecule as the readout.

Living systems use enzymatic reaction networks to process biochemical information and make decisions in response to external or internal stimuli. Herein, we present a modular and reusable platform for molecular information processing using enzymes immobilised in hydrogel beads and compartmentalised in a continuous stirred tank reactor. We demonstrate how this setup allows us to perform simple arithmetic operations, such as addition, subtraction and multiplication, using various concentrations of substrates or inhibitors as inputs and the production of a fluorescent molecule as the readout.

Kinetic modelling of in vitro constructed enzymatic reaction works is vital to understand and control the complex behaviours emerging from the abundant nonlinear interactions inside. However, modelling 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 inputs and multiple outputs. The optimal experimental design (OED) algorithm designed a sequence of out-of-equilibrium perturbations to maximise the information about the reaction kinetics, yielding a descriptive model that allowed inverse design of the output of the network towards any cost function. We experimentally validated 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 inverse design of previously unobtainable network outputs.