IGEM:IMPERIAL/2008/Prototype/Drylab/Data Analysis: Difference between revisions
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In some cases, we can visually segment the cell's trajectory into two or more separate runs. In the case below, we see that if we fit the cell's trajectory to only one run and a single set of parameters, we do not obtain a satisfactory fit. However, if we introduce an orientation change at approximately frame 75, we are able to obtain a better fit. This fit contains two runs, seperated by a tumble at frame 75, thus generating two sets of parameters for the two runs. | In some cases, we can visually segment the cell's trajectory into two or more separate runs. In the case below, we see that if we fit the cell's trajectory to only one run and a single set of parameters, we do not obtain a satisfactory fit. However, if we introduce an orientation change at approximately frame 75, we are able to obtain a better fit. This fit contains two runs, seperated by a tumble at frame 75, thus generating two sets of parameters for the two runs. | ||
{| border="1" cellpadding="5" cellspacing="0" align="center" | {| border="1" cellpadding="5" cellspacing="0" align="center" | ||
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|Cell trajectory fitted with single run | |'''Cell trajectory fitted with single run''' | ||
|Cell trajectory fitted with two runs | |'''Cell trajectory fitted with two runs''' | ||
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|[[Image:V15Cell6.jpg|thumb|center|300px|100908 Video 15 Cell 2 One Run]] | |[[Image:V15Cell6.jpg|thumb|center|300px|100908 Video 15 Cell 2 One Run]] | ||
Revision as of 03:49, 24 September 2008
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Model Fitting
Alternative Models
Models of run velocity include a Gaussian Distribution, or the Maxwell Distribution which govern the velocities and energies of molecules. An exponential distribution may describe the memoryless characteristic of run duration. We will build up a database of models, for future model fitting.
Mechanical Model
We have created a simple mechanical model of motile bacteria, depicted in the figure below.
Fitting Models to Data
In this first level of inference, we apply Bayes' Theorem. We first assume a particular model, and go on to derive the parameters of our model which maximises the data obtained.
Mechanical Model
The following trajectories were fitted based on the above equations, and corresponding parameters determined:
 |
 |
| A=[-102.2628 -67.2227] B=[362.5003 -92.3339] alpha=0.2500 |
A=[-109.7191 -7.7453] B=[219.2134 -154.1100] alpha=0.4342 |
 |
 |
| A=[57.0606 -29.0868] B=[12.0191 25.8818] alpha=2.4867 |
A=[28.8774 116.5196] B=[-790.7562 -1162.5363] alpha=0.1231 |
In some cases, we can visually segment the cell's trajectory into two or more separate runs. In the case below, we see that if we fit the cell's trajectory to only one run and a single set of parameters, we do not obtain a satisfactory fit. However, if we introduce an orientation change at approximately frame 75, we are able to obtain a better fit. This fit contains two runs, seperated by a tumble at frame 75, thus generating two sets of parameters for the two runs.
| Cell trajectory fitted with single run | Cell trajectory fitted with two runs |
 |
.jpg) |
| A=[164.3967 -56.7380] B=[-1295.3312 991.4668] alpha=0.1442 |
A1=[95.6096 60.9460], A2=[86.4716 -46.1687] B1=[-492.7792 10.5021], B2=[-108.9051 296.9050] alpha1=[0.2430], alpha2=[0.3563] |
Assigning Preferences to Alternative Models
In this second level of inference, we use the evidence contributed by the data to compare fitted models. Using Occam's Razor, we are then able to deduce the best model which fits our data.
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