Why model the growth curve?
The aim of modelling the growth curve is to characterise the B. subtilis chassis used in the project. Characterisation increases the predictability of the growth of B. subtilis by determining, for example, its growth rate and the duration of its distinctive growth phases.
How to model the growth curve?
In order to model the growth of B. subtilis, the process was broken down into three main steps, where a separate submodel is produced in MATLAB for each step. Each submodel is an ODE model, which can be simulated using MATLAB. The variables in each submodel can be adjusted according to the boundary conditions (from experimental results).
In the final step, a combination of Submodels 1 and 2 are superposed with Submodel 3, resulting in a more complex model which enhances the accuracy of illustrating bacterial growth. For more details about the submodels, please click on the following link: Media:Modelling_Growth_Curve.pdf. For more information on our modelling strategy, please click on Tutorial for Growth Curve.
The M-file used to generate the model below is located in the Appendices section, its link can be found at the bottom of this page.
The model illustrates the main growth phases the B. subtilis undergoes. These are identified as the lag phase, the exponential phase and the stationary phase. The death phase is a constitutive event and it is possible that it exerts an influence on the three phases discussed below. However, to simplify a complicated model, it is less relevant in this case and therefore is not included in this model.
During the lag phase, the rate of growth is slow due to two main reasons, B. subtilis is absorbing nutrients in the medium and the replication machinery is being switched on. The higher the concentration of nutrients in the medium, the faster the rate of bateria growth.
As a result, the volume of the bacteria increases, followed by an increases in the number of bacteria.
Both colony number and cell volume increase exponentially during this phase. Our model assumes concentration of the nutrients inside the bacteria is constant.
The growth of the colony ceases in number and in volume due to a finite concentration of nutrients, hence its does not have a gradient. Other causes may be death and cell division.
According to the model, the maximum growth of the bacteria is determined by the concentration of nutrients available initially.
To further enhance the accuracy of the model, the following information will be extracted from experimental data:
The model for the growth curve was fitted to the experimental results as shown below. The experimental results is depicted by the red curve, while our model is shown by the green curve. The resource curve was also plotted as a function of time and is shown below. From experimental results, a log graph was plotted to determine the growth rate. The growth rate was then determined from the gradient of the log graph. This value was included when simulating the growth model using MATLAB.
The following constants used to generate the model were found to yield the best fit to experimental results.
GROWTH CONSTANT: A = 1.3494
INITIAL NUTRIENT CONCENTRATION: R_0 = 2
HILL COEFFICIENT: n = 1.25
INITIAL OD = 0.4
CONSTANT: α = 0.64516