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Team:XMU-China/Project Modelling mmmodel
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\(\frac{{{\rm{dC}}}}{{{\rm{dt}}}} = \frac{{{{\rm{\alpha }}_{\rm{C}}}}}{{1 + {{\left( {{\rm{L}}/{{\rm{\beta }}_{\rm{L}}}} \right)}^{{{\rm{m}}_1}}}}} - {{\rm{\gamma }}_{\rm{C}}} \cdot {\rm{C}}\) | \(\frac{{{\rm{dC}}}}{{{\rm{dt}}}} = \frac{{{{\rm{\alpha }}_{\rm{C}}}}}{{1 + {{\left( {{\rm{L}}/{{\rm{\beta }}_{\rm{L}}}} \right)}^{{{\rm{m}}_1}}}}} - {{\rm{\gamma }}_{\rm{C}}} \cdot {\rm{C}}\) | ||
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Revision as of 18:24, 17 October 2014
MICROSCOPIC MOTION MODEL
Flagella can rotate in two ways: clockwise (CW) and counter-clockwise (CCW). The both determine the motion of E. coli. When FliM binds with cheY-P, the flagella rotate CW and the bacterium moves more randomly which seems that E. coli is tumbling. On the other hand, when the dephosphated cheY binds with FliM, the flagella rotate CCW and bacterium swims smooth. At the macro level, they run in certain direction.
cheZ and cheA control the level of phosphorylation of cheY. cheZ dephosphates cheY-P while cheA phosphates cheY. Reaction can be described using the following equations .With steady state approximation, the concentration ratio of cheY to cheY-P could be calculated (Table 2).
![](http://convert.wenku.baidu.com/rtcs/image?md5sum=5b52e46721865cde07b5048b24c16313.docx&l=webapp&ipr={"t":"img","w":"552.93","h":"308.00","dataType":"png","c":"word\/media\/image1.png"})
![](http://convert.wenku.baidu.com/rtcs/image?md5sum=5b52e46721865cde07b5048b24c16313.docx&l=webapp&ipr={"t":"img","w":"553.70","h":"78.24","dataType":"jpeg","c":"word\/media\/image2.jpeg"})
Table 1. Flagella’ motion
![](http://convert.wenku.baidu.com/rtcs/image?md5sum=5b52e46721865cde07b5048b24c16313.docx&l=webapp&ipr={"t":"img","w":"553.70","h":"195.78","dataType":"png","c":"word\/media\/image3.png"})
It has been reported that the concentration of cheY-P can be used to predict drift velocity of E. coli. [7] By given concentration of cheZ and equations above, we can calculate the concentration ratio of cheY to cheY-P. While the concentration of cheY-P can be calculated by given cheZ (ZT). The motion caused by chemotaxis can be predicted by following equation. With following equation, drift velocity could be calculated.
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\(\frac{{{\rm{dC}}}}{{{\rm{dt}}}} = \frac{{{{\rm{\alpha }}_{\rm{C}}}}}{{1 + {{\left( {{\rm{L}}/{{\rm{\beta }}_{\rm{L}}}} \right)}^{{{\rm{m}}_1}}}}} - {{\rm{\gamma }}_{\rm{C}}} \cdot {\rm{C}}\) |
(5) |
![](http://convert.wenku.baidu.com/rtcs/image?md5sum=5b52e46721865cde07b5048b24c16313.docx&l=webapp&ipr={"t":"img","w":"553.73","h":"383.83","dataType":"png","c":"word\/media\/image5.png"})
As a result, the relation between intracellular and macroscopic motion is built. Thus utilizing all above modeling, we can simulate the motion of E. coli. Meanwhile, we can predict any parameter with enough measurable parameters given.
References
1. Tindall, M. J., Porter, S. L., Wadhams, G. H., Maini, P. K. & Armitage, J. P. Spatiotemporal modelling of cheY complexes in Escherichia coli chemotaxis. Prog. Biophys. Mol. Biol. 100, 40–46 (2009)
http://www.ncbi.nlm.nih.gov/pubmed/?term=Spatiotemporal+modelling+of+cheY+complexes+in+Escherichia+coli+chemotaxis.
2. www.pdn.cam.ac.uk/groups/comp-cell/Rates.html
3. Silversmith, R., Levin, M., Schilling, E., Bourret, R., 2008. Kinetic characterization of catalysis by the chemotaxis phosphatase cheZ. J. Biol. Chem. 283, 756–765.
http://www.ncbi.nlm.nih.gov/pubmed/?term=Kinetic+characterization+of+catalysis+by+the+chemotaxis+phosphatase+cheZ
4. Sourjik, V., Berg, H., 2002a. Binding of the Escherichia coli response regulator cheY to its target measured in vivo by fluorescence resonance energy transfer. Proc. Natl. Acad. Sci. U.S.A. 99, 12669–12674.
http://www.ncbi.nlm.nih.gov/pubmed/?term=Binding+of+the+Escherichia+coli+response+regulator+cheY+to+its+target+measured+in+vivo+by+fluorescence+resonance+energy+transfer
5. Y. S. Dufour, X. Fu, L. Hernandez-Nunez, and T. monet, “Limits of Feedback Control in Bacterial Chemotaxis,” PLoS Comput. Biol., vol. 10, 2014
http://www.ncbi.nlm.nih.gov/pubmed/?term=Limits+of+Feedback+Control+in+Bacterial+Chemotaxis
