# IGEM:IMPERIAL/2008/Prototype/Drylab/Modelling the Growth of B.Subtilis

The aim of doing so is to characterise the chassis.

OVERVIEW

In order to model the growth of B.Subtilis, the process was broken down into three main steps where a submodel is produced in MATLAB in each step. Each submodel is an ODE model which can be simulated using MATLAB. The variables in each submodel are modified. So in the final step, a combination of submodel 1 and 2 are incorporated with submodel 3, resulting in a more complex model which illustrates the behaviour of bacterial growth.

STEP 1:

First Submodel

Firstly, to design submodel 1, an ODE model was written and simulated for the growth of the bacterial volume depending on a constant growth rate. Here, it was assumed that the concentration of the nutrient does not influence bacterial growth. Next, the ODE model was modified to take into account the effect the concentration of nutrient inside the bacteria has on the growth rate. This was achieved by using the Hill Function. The Hill function models the cooperativity between a ligand and a macromolecule. So in this case, it models the cooperativity between the bacteria and the nutrients. In the final part of step 1, it was assumed that the internal concentration of nutrients (i.e. the nutrient concentration inside the bacteria) varies with time. This resulted in a new ODE model.

STEP 2:

Second Submodel

At this stage, the modelling of growth was continued by considering the evolution of the internal concentration of nutrients; the diffusion of nutrients through the membrane of the bacteria. Two things were considered in terms of modelling: the geometric model for B-Subtilis and the diffusion model. Several assumptions were made. Firstly, the nutrients are not consumed by the metabolism of the bacteria. Secondly, the bacteria in a colony share the same shape. Therefore, their surface and volume are linked by a relation of the kind S = a V^(2/3)

STEP 3:

To incorporate the consumption of nutrients into the overall model, two more phenomena were embodied into the second submodel to help create an even more realistic model; the increase in bacterial volume, which consumes nutrients and energy and the fact that there is only a finite amount of nutrients as the culture medium has a finite volume. These two phenomena were modelled. Click on the links to see the modelling in more detail. Assumptions: The amount of nutrients required to increase the volume by one unit is independent of the volume and is constant. Also, the external concentration of nutrients remains constant.

STEP 4:

Third Submodel

We are now close to building a more complex model. To do this, the way that the replication machinery switches on is modelled. This model is linked to the internal concentration of nutrients and the growth rate.

A List of ODE needed:

o For controlling the internal concentration of nutrients when

i) the bacteria, modelled as a bag with permeable membrane, has a constant volume and the external medium has a constant concentration

 suggestion of a mathematical description: Fick’s second law (d2c / dx2)

ii) When ‘the bag’ is increasing, such as V(t) = 1 + t. Again, the external medium’s concentration remains constant.

o One that will incorporate the consumption of nutrients by the bacteria