# Collaborations

We joined up with the National University of Singapore iGEM Team to collaborate and help each other with the modelling aspect of our projects.

In order to assist us characterise our star peptide, we asked NUS Singapore to create a simple diffusion simulation on MATLAB. Their diffusion program and our subsequent utilisation of this simulator can be found here.

The NUS Singapore team asked us to help them visualise and compare the simulation and theoretical solutions they developed for their cylindrical diffusion system. Their model involves determining the concentration of a particular molecule in terms of cylindrical coordinates at a particular instance in time. The coordinate system of their model is illustrated below.

NUS Singapore provided us with results from a two-dimensional diffusion simulation they developed. The simulation data contains $r$ and $z$ values for different time steps in the cylindrical bacteria. The initial condition of their model is visualised below, with yellow representing a high concentration and purple representing a low concentration.

Using MATLAB, we were able to provide visual representations for various time steps of their simulation.

From the images displayed above, we can see that the system undergoes diffusion until the concentration field is essentially uniform.

NUS Singapore also provided as with us with the equations for the theoretical solution they had developed to the cyclindrical diffusion problem:

Using the same initial concentration field used in the simulation, we attempted to implement this theoretical solution in MATLAB. Our goal was to vary the number of terms in the series and visualise the resulting concentration fields. Unfortunately, due to some difficulties experienced in the implementation process, we cannot be confident that our results are an accurate representation of the theoretical model provided. In the future, we recommend that an integrator specific to cylindrical coordinates and this model be developed in order for the Kik term to be accurately determined.

Nonetheless, featured below are the concentration fields obtained for different final values of $I$ and $K$ after 10ms. Although these fields are not representative of the theoretical solution, the impact of the number of terms in the series used is still evident. It can therefore be recommended that if this theoretical solution is to be used for further analysis, the maximum number of terms permitted by the available computing power should be used.

$$I = K = 1$$ |
$$I = K = 2$$ |
$$I = K = 3$$ |

$$I = K = 4$$ |
$$I = K = 5$$ |