IGEM:IMPERIAL/2008/New/Growth Curve: Difference between revisions

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== Results ==
== Results ==


The variables that affect bacterial growth rate versus time were adjusted to yield a curve similar to that given by experimental data, illustrated as the red curve on the graph.
The variables that affect bacterial growth rate versus time were adjusted to yield a curve similar to that given by experimental data, illustrated as the red curve on the graph.  The variables that were adjusted are the concentration of nutrients and the Hill coefficient.


[[Image:Growth_curve2.tif]]
[[Image:Growth_curve2.tif]]


From experimental results, which can be found under the appendices, a log graph was plotted.  The growth rate was determined from the gradient of the log graph.  This value was included when simulating the growth model using MATLAB.
From experimental results, which can be found under the appendices, a log graph was plotted to aid the determination of the growth rate.  The growth rate was determined from the gradient of the log graph.  This value was included when simulating the growth model using MATLAB.


[[Image:Exp_growth.tif|right]]
[[Image:Exp_growth.tif|right]]

Revision as of 03:29, 19 September 2008

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Growth Curves

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 Model

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.

LAG PHASE

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 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.

EXPONENTIAL PHASE

Both colony number and cell volume increase exponentially during this phase. Our model assumes concentration of the nutrients inside the bacteria is constant.

STATIONARY PHASE

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:

  • Time span of lag phase, stationary phase and exponential phase
  • The growth rate

Results

The variables that affect bacterial growth rate versus time were adjusted to yield a curve similar to that given by experimental data, illustrated as the red curve on the graph. The variables that were adjusted are the concentration of nutrients and the Hill coefficient.

From experimental results, which can be found under the appendices, a log graph was plotted to aid the determination of the growth rate. The growth rate was determined from the gradient of the log graph. This value was included when simulating the growth model using MATLAB.

Graph used to determine the growth rate

From the model, the following constants were found to yield a close match to growth curve given by the experimental results:

GROWTH CONSTANT: a = 1.019

HILL COEFFICIENT: n = 1

Discussion

Dry lab hub

Growth Curve

Genetic Circuit

Motility

Appendices


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