# Modelling

When designing our project, we were aware of the novel nature of our scaffold, and thus wanted to develop models of our system in order to better understand its features. Previous experiments in enzyme scaffolds have yielded vastly different results, thus we aimed to create a mathematical model to mimic the effect of scaffolding enzymes. We focused on the effect that distance between enzymes has on the diffusion of an intermediary substrate. As we are employing the prefoldin protein as our enzyme scaffold, we wanted to understand precisely how attaching enzymes via tag-catcher systems would affect the prefoldin, and how the enzymes would interact. Thus, we ran molecular dynamics simulations of our hexameric complex. We took into consideration how our model could be validated experimentally, and ensured all assumptions and boundary conditions could be replicated in a laboratory environment. We believe our models provide a strong point of reference for other teams aiming to design enzyme scaffolding systems.

## Enzyme Kinetics and Diffusion

We modelled the effect of distance between enzymes on reaction rate, by considering the diffusion of the key intermediary substrate. The rates of reaction at each enzyme were controlled by the Michaelis-Menten equation, whilst the diffusion of substrate followed Fick’s law. Thus, the driving force of diffusion in our system was a concentration gradient between enzymes, which changes as the enzymes are brought closer together, or shifted further apart. We found increases of over 5-fold in final product production when enzymes were brought together at a distance that reflects the effect of scaffolding the enzymes on prefoldin.

## Molecular Dynamics

Conducting molecular dynamics simulations allowed us to visualize our scaffold, and determine key physical parameters for use in the mathematical model. We were able to approximate the average distance between enzymes when attached to prefoldin, and thus extract relevant data from our mathematical model. The molecular dynamics confirmed the efficacy of using prefoldin as an enzyme scaffold as the enzymes remained clustered.