And how can it be used?

Mathematical modelling provides a powerful tool for scientists of all disciplines, allowing inspection and manipulation of a system in ways which are unachievable in the lab. In the context of biology, we can use mathematical models to study the behaviour of a single cell or an entire ecosystem. In fact, inspecting a mathematical model is very much like a laboratory experiment – the main difference being that in modelling, the environment is artificial.

To the right is a short animation showing the model’s graphical output. Red dots represent amyloid plaques, and blue dots show microglia cells. The red circle shows the boundary of a small hypothetical spherical section of the brain. Although the underlying mechanics of this animation are simply mathematical, the behaviour of the plaques and cells is surprisingly representative of the truth. This is the essence of a model.

UCL's iGEM model

The entire downloadable source code for the UCL model can be found on github. Click here, then download and compile the project to play with the iGEM model.

When coupled with computational power, we can use mathematical modelling to produce intricate simulations of a very fine scale. This is exactly what the iGEM team has done this year, in producing a comprehensive model of the plaques and microglia in the brain. With many millions of cells present, mathematical tricks and techniques have been employed in order to allow computation of this highly complex system. For the end-user, this scaffolding is hidden from view: the final result will be a user-friendly windows application.

The user-interface of the application is shown below. This interface hints at the internal operation of the model: a large number of numerical inputs are processed in a way representing the biological mechanics of the system, generating a set of numerical outputs. For example, these outputs could be the coordinates of a single microglia cell with corresponding time values, providing insight into how these cells move. Since almost every numerical factor can be altered by the user, the model can also be used to predict how a particular change would affect the system at large.

Method Overview

The brain is modelled as a 3D homogenous static medium, throughout which small ‘plaques’ are fixed. As far as the model is concerned, these plaques cause Alzheimer’s, and their removal would result in the reversal of the disease’s effects. At the start of the model (t=0), a number of microglia cells will be introduced to the system at a number of distinct points. These will then move throughout the brain, will the overall goal of binding to and removing the plaques.

Every plaque and microglia cell is modelled individually, with the state of the system regularly sampled (roughly every minute). In between samplings, a number of processes take place. The diagram to the right outlines these processes.