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We have divided the modelling team into 3 sections:
We have divided the modelling team into 3 sections:
#Modelling Genetic Circuits - Erika
#Modelling Genetic Circuits - Erika
#Collecting Motility Data - Yanis
#Modelling ''B.Subtilis'' Growth - Prudence
#Analysis of Motlity Data and Model Fitting - Clinton & Prudence
#Modelling ''B.Subtilis'' Motility
#*Collecting Motility Data - Yanis
#*Analysis of Motlity Data and Model Fitting - Clinton


=[[/ODE_Model | Modelling the Genetic Circuit]]=
=[[/ODE_Model | Modelling the Genetic Circuit]]=
A simple '''[[/ODE_Model | ODE model]]''' was assumed in order to model the concentrations of the interacting proteins.
A simple [[/ODE_Model | ODE model]] was assumed in order to model the concentrations of the interacting proteins.


=Motility Data Collection=
To build the ODE model, each [[IGEM:IMPERIAL/2008/Prototype/Wetlab/test_constructs | test construct]] was [[/ODE_models_of_test_constructs | individually modelled]]. These test construct models can then be combined and the combined models compared to the experimental results from the wetlab.


We plan to capture video footage of ''B. subtilis'' and analyse its motility. Using a tracking software or algorithm, we would be able to determine the position of cells of interest at each frame. From this data, we can derive the run velocity and tumbling angle at each frame.
=[[IGEM:IMPERIAL/2008/Prototype/Drylab/Modelling_the_Growth_of_B.Subtilis| Modelling the Growth of ''B.Subtilis'']]=


However, it is more complicated to derive the run time and tumbling time. If, for some frames the velocity is equal to zero, we may assume that this corresponds to the tumbling phase. Therefore, we can create a new array containing the tumbling duration for each frame. The same can be done for run time. To obtain run/tumbling duration over multiple frames, we have to find a sequence of frames that corresponds to the run phase or tumbling phase, and then sum their durations to determine the duration of the run/tumbling phases.  
=Modelling the Motility of ''B.Subtilis''=


After obtaining data arrays with run/tumbling durations, run velocity and tumbling angle, we can then proceed on to data analysis. 
[[Image:Approach.jpg|300px|thumb|right|Approach to Modelling Motility]]


==Video Methods==
The motility of ''B.Subtilis'' is hypothesised to be affected by various levels of EpsE expression. In order to model motility as a function of EpsE production, we have decided to use video microscopy techniques to analyse the motility of ''B.Subtilis''. We hope to obtain a transfer function model relating EpsE expression to bacterial motility characteristics such as run velocity, run duration, tumbling angle and tumbling duration. This modelling process is shown on the right and has been divided into 3 main sections:


We will be using the Zeiss Axiovert 200 inverted microscope with a fully motorised stage, controlled by Improvision Volocity acquisition software. This system offers a full incubation chamber with temperature and CO2 control, a large range of filter sets from UV to far-red and a highly sensitive 1300x1000 pixel camera for fast low-light imaging.  
#'''[[IGEM:IMPERIAL/2008/Prototype/Drylab/Validation | Validation of Tracking Software ]]'''
#*In order to assess the error associated with tracking algorithms applied to a digitised images sequence, a series of steps were taken to '''[[IGEM:IMPERIAL/2008/Prototype/Drylab/Validation |validate]]''' the tracking software.
#'''[[IGEM:IMPERIAL/2008/Prototype/Drylab/Motility_data_collection|Motility Data Acquisition]]'''
#*Data on run velocity, run duration, tumbling angle and tubmling duration were extracted from coordinate data output provided by the tracking software as part of the process of gathering data.
#'''[[IGEM:IMPERIAL/2008/Prototype/Drylab/Data_Analysis|Model Fitting]]'''
#*Several alternative models were created for the purpose of model fitting. The motility data obtained is then analysed and fitted to alternative models. Preferences will then be assigned to fitted models using probabilistic methods such as Bayesian Analysis.


Video images are captured into memory by the system at a basal video frame rate of 16.3Hz. This can be further increased by performing binning.
=Resources=


== [[IGEM:IMPERIAL/2008/Prototype/Drylab/Validation | Validating the Tracking Software ]] ==
The following are four tutorials which introduce us to data analysis and modelling. The tutorials are focused on the above approach. MATLAB codes used for data analysis can be found in the final link.


For our motility analysis we will be using ImageJ (open source freeware software written by NIH). We have considered a few tracking plugins for ImageJ. The most accurate seems to be SpotTracker written by EPFL ( Ecole Polytechnique Federale de Lausanne), though not written specifically for cell tracking. Thus the need for us to validate the software and delimit its range of operability. This link leads to more on '''[[IGEM:IMPERIAL/2008/Prototype/Drylab/Validation | Software Validation ]]'''.
[[Media:Tutorial_1.pdf | Dry Lab Tutorial 1: Design of a Motility Assay]]
 
=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 hte replication machinery switches on is modelled.  This model is linked to the internal concentration of nutrients and the growth rate.
By combining the two submodels, a simple model is created.
 
= [[IGEM:IMPERIAL/2008/Prototype/Drylab/Data_Analysis| Data Analysis]] =
 
==Resources==
 
The following are four tutorials which introduce us to data analysis and modelling. The tutorials are focused on the above approach.
 
[[IGEM:IMPERIAL/2008/Modelling/Tutorial1 | Dry Lab Tutorial 1: Creating Synthetic Data]]


[[IGEM:IMPERIAL/2008/Modelling/Tutorial2 | Dry Lab Tutorial 2: Statistical Data Analysis]]
[[IGEM:IMPERIAL/2008/Modelling/Tutorial2 | Dry Lab Tutorial 2: Statistical Data Analysis]]
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[[Media:Modelling_Growth_Curve.pdf | Dry Lab Tutorial 4: Modelling the Growth Curve]]
[[Media:Modelling_Growth_Curve.pdf | Dry Lab Tutorial 4: Modelling the Growth Curve]]
[[IGEM:IMPERIAL/2008/Prototype/Drylab/Code| MATLAB Codes]]


=References=
=References=


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Team Strategy

We have divided the modelling team into 3 sections:

  1. Modelling Genetic Circuits - Erika
  2. Modelling B.Subtilis Growth - Prudence
  3. Modelling B.Subtilis Motility
    • Collecting Motility Data - Yanis
    • Analysis of Motlity Data and Model Fitting - Clinton

Modelling the Genetic Circuit

A simple ODE model was assumed in order to model the concentrations of the interacting proteins.

To build the ODE model, each test construct was individually modelled. These test construct models can then be combined and the combined models compared to the experimental results from the wetlab.

Modelling the Growth of B.Subtilis

Modelling the Motility of B.Subtilis

Approach to Modelling Motility

The motility of B.Subtilis is hypothesised to be affected by various levels of EpsE expression. In order to model motility as a function of EpsE production, we have decided to use video microscopy techniques to analyse the motility of B.Subtilis. We hope to obtain a transfer function model relating EpsE expression to bacterial motility characteristics such as run velocity, run duration, tumbling angle and tumbling duration. This modelling process is shown on the right and has been divided into 3 main sections:

  1. Validation of Tracking Software
    • In order to assess the error associated with tracking algorithms applied to a digitised images sequence, a series of steps were taken to validate the tracking software.
  2. Motility Data Acquisition
    • Data on run velocity, run duration, tumbling angle and tubmling duration were extracted from coordinate data output provided by the tracking software as part of the process of gathering data.
  3. Model Fitting
    • Several alternative models were created for the purpose of model fitting. The motility data obtained is then analysed and fitted to alternative models. Preferences will then be assigned to fitted models using probabilistic methods such as Bayesian Analysis.

Resources

The following are four tutorials which introduce us to data analysis and modelling. The tutorials are focused on the above approach. MATLAB codes used for data analysis can be found in the final link.

Dry Lab Tutorial 1: Design of a Motility Assay

Dry Lab Tutorial 2: Statistical Data Analysis

Dry Lab Tutorial 3: Testing the Tracking Software

Dry Lab Tutorial 4: Modelling the Growth Curve

MATLAB Codes

References


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