IGEM:IMPERIAL/2008/Prototype/Drylab/Data Analysis/Alt Models
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<a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Motility">Motility Analysis</a>
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</td><td align="center" width="17%" valign="bottom"><ul id="sddm"><a href="http://2008.igem.org/Team:Imperial_College/Notebook"> Notebook </a></ul> </td><td align="center" width="17%" valign="bottom"><ul id="sddm"><a href="http://openwetware.org/wiki/IGEM:IMPERIAL/2008/New/Team"> Our Team </a></ul> </td></tr></table></html> |
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Run Velocity
 The Maxwell-Boltzmann distribution is commonly used to describe molecular speeds, which are under the influence of brownian motion. Although bacteria size does not come close to that of small molecules and in general bacteria motility is controlled by beating flagellar, we cannot ignore the effects of colliding molecules on the micro-sized bacteria.
 The Gaussian or Normal distribution is the most common distribution and is used as the first level of assumption on the distribution of bacteria bacteria characteristics. Most Likely Estimators: [math]\displaystyle{ E \left[ \widehat\mu \right] = \mu, }[/math] and [math]\displaystyle{ E \left[ \widehat{\sigma^2} \right]= \frac{n-1}{n}\sigma^2 }[/math] Tumbling Angle
 The von Mises distribution is a continuous distribution defined on the The von Mises distribution is a continuous probability distribution on the range 0≤x<2π. It may be thought of as the circular analogue of the normal distribution. It is used where a distribution of angles are the result of the addition of many small independent angular deviations, such as target sensing. Since bacteria use various types of chemoreceptors to pick up chemo attractants and repellants, we may assume that the tumbling angle which causes the bacteria to change its direction of motion in response to its environment follows a von Mises distribution. Run and Tumbling Duration
 The exponential distribution is the only continuous memoryless random distribution. If we assume that both the run and tumbling durations are memoryless processes, then they are probably exponentially distributed. Most Likely Estimator: [math]\displaystyle{ \widehat{\lambda} = \frac1{\overline{x}}. }[/math] Other DistributionsThe following table describes the various types of distributions which bacteria motility characteristics may follow. 
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