Enzymes conjugated with nanoparticles (e.g., Au) are increasingly important in diverse areas including biosensing, nanocircuitry design and biocatalysis. Research on synthesis and characterization of bioconjugates has been prolific in recent years, especially for single enzyme-nanoparticle conjugates.

The construction of bioconjugates of two or more types of enzymes requires the consideration of additional factors such as the relative location of each type of enzyme (i.e., binding all types of enzymes in the same nanoparticle (multicomponent conjugates) or different types of enzymes on separate nanoparticles (single component conjugates)). In fact, experimental results show that the use of even the same crowding agent (PEG) has a differing effect on the sequential activity of two enzymes carrying out consecutive reactions (i.e., malate dehydrogenase and citrate synthase) in two different bioconjugate constructs. In one case (both enzymes bound on the same nanoparticle) the sequential activity increases almost linearly with PEG concentration whereas in the other case (each enzyme type is located on separate nanoparticles) the sequential activity remains almost constant.

In this work, we present a mathematical model to elucidate the mechanism behind these experimental observations. The model is based on a reaction-diffusion mechanism and an experimentally determined description of the effect of PEG on the kinetics of the considered enzymes. We observe a quantitatively good agreement between the proposed model and experimental results. The proposed modeling framework can be readily extended to systems involving a relatively large number of enzymes and it can offer a rational guide for designing synthetic metabolic pathways using enzyme-nanoparticle bioconjugates.