Team:BCCS-Bristol/Modeling-Parameters

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* [[Team:BCCS-Bristol/Modeling-Parameters#Bacteria|'''Bacteria''']]
* [[Team:BCCS-Bristol/Modeling-Parameters#Bacteria|'''Bacteria''']]
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* [[Team:BCCS-Bristol/Modeling-Parameters#Run Tumble motion|'''Run Tumble motion''']]
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* [[Team:BCCS-Bristol/Modeling-Parameters#Run_Tumble_Motion|'''Run Tumble motion''']]
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* [[Team:BCCS-Bristol/Modeling-Parameters#Swimming Machinery|'''Swimming Machinery''']]
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* [[Team:BCCS-Bristol/Modeling-Parameters#GRN_Modelling|'''GRN Modelling''']]
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=== Bacteria ===
=== Bacteria ===
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{| {{table}}
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| align="center" style="background:#f0f0f0;"|'''Bacteria'''
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{| class="bccstable" align="center"  margin-left="40px"
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| align="center" style="background:#f0f0f0;"|''''''
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| align="center" width="10%" style="background:#f0f0f0;"|'''Attribute'''
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| align="center" style="background:#f0f0f0;"|''''''
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| align="center" width="10%" style="background:#f0f0f0;"|'''Value'''
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| align="center" style="background:#f0f0f0;"|''''''
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| align="center" width="10%" style="background:#f0f0f0;"|'''Strain'''
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| align="center" style="background:#f0f0f0;"|''''''
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| align="center" width="40%" style="background:#f0f0f0;"|'''Justification'''
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| align="center" width="30%" style="background:#f0f0f0;"|'''Reference'''
|-
|-
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| Attribute||Value||Strain||Justification||Reference
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| Length||2&#956;m||MG1655||Values come from the University of Alberta’s datasheet on MG1655, produced to aid modelling. There is variability in size between strains - for instance, AW405 length varies between 1.5±0.2&#956;m. But University of Alberta datasheet is specifically for MG1655.||[http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi University of Alberta]
|-
|-
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| Length||2ìm||MG1655||Values come from the University of Alberta’s datasheet on MG1655, produced to aid modelling. There is variability in size between strains - for instance, AW405 length varies between 1.5±0.2ìm. But University of Alberta datasheet is specifically for MG1655.||http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi
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| Diameter||0.8&#956;m||MG1655||||[http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi University of Alberta]
|-
|-
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| Diameter||0.8ìm||MG1655||||http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi
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| Shape||Circle r =0.714&#956;m||MG1655||Actually rod-like. A circle with r= 0.714&#956;m will have equivalent surface area to rod-like.||[http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi University of Alberta]
|-
|-
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| Shape||Circle r =0.714ìm||MG1655||Actually rod-like. A circle with r= 0.714ìm will have equivalent surface area to rod-like.||http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi
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| Mass||1.02x10<sup>-13</sup>g||MG1655||Given 1x10<sup>-12</sup>g for cell wet weight. Dividing this by gravity (=9.81) gives mass. ||[http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi University of Alberta]
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|-
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| Mass||1.02x10-13g||MG1655||Given 1x10-12g for cell wet weight. Dividing this by gravity (=9.81) gives mass. ||http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi
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| Swimming Speed||50&#956;ms<sup>-1</sup>||MG1655||University Alberta's datasheet gives 50&#956;ms<sup>-1</sup>. However, Swimming speed is affected by:
 +
*Viscosity (as viscosity increases the speed increases to some maximum, then decreases as the viscosity increases further. E.coli (strain:KL227 of length: 1.0&#956;m and diameter: 0.5&#956;m) maximum speed occurs at viscosity 8cp.
 +
*Temperature
 +
*Culture medium
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*Vary strain to strain.
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*Experimental methods
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Various papers give different speeds for E. coli (most papers provide information on AW405 with a speed of ~20&#956;ms<sup>-1</sup>). The speed itself is nearly uniform during the run. The wet lab may need to measure this experimentally as we are unaware of the conditions that the speed for MG1655 was obtained. Alberta's value is higher than other values, but this probably because MG1655 is a motile strain.
 +
||[http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi University of Alberta] <br> [http://www3.interscience.wiley.com/cgi-bin/fulltext/71003069/PDFSTART A Method for Measuring Bacterial Chemotaxis Parameters in a Microcapillary]
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|}
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 +
=== Run Tumble Motion ===
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 +
{| class="bccstable"
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| align="center" width="10%" style="background:#f0f0f0;"|'''Attribute'''
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| align="center" width="10%" style="background:#f0f0f0;"|'''Value'''
 +
| align="center" width="10%" style="background:#f0f0f0;"|'''Strain'''
 +
| align="center" width="40%" style="background:#f0f0f0;"|'''Justification'''
 +
| align="center" width="30%" style="background:#f0f0f0;"|'''Reference'''
|-
|-
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| Swimming Speed||50ìm.s-1||MG1655||\"University Alberta\'s datasheet gives 50ìms-1. However, Swimming speed is affected by:
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| Aspartate concentration detected by E. coli||Over ~5 orders of magnitude, 10nM up to 10mM. Can detect changes of as little as ~0.1%||N/A||E. coli detect small changes in concentration of 0.1% via temporal comparisons (4s) over a large range ( 10<sup>-8</sup> to 10<sup>-3</sup> ). Most computer simulations of chemotaxis are based on experimentally determined rates and concentrations. As a result they predict that the minimum detectable concentration of Aspartate is at ~200 nM. Experiments performed by Segall et al. in 1986, exposed tethered E. coli cells to iontophoretically delivered quantities of chemoattractant. These experiments indicated that a change in receptor occupancy of as little as 1/600 could produce an detectable change in swimming behaviour. With a K<sub>d</sub> of 1 µM, this corresponds to a minimum detectable concentration of about 2 nM Aspartate. Wild type E. coli cells can detect <10nM of Asp and respond to Asp concentrations of upto 1mM,(responding to over ~5 orders of magnitude). M)||[http://www.jbc.org/cgi/reprint/281/41/30512 Competitive and Cooperative Interactions in Receptor Signalling Complexes]
|-
|-
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| • Viscosity (as viscosity increases the speed increases to some maximum, then decreases as the viscosity increases further. E.coli (strain:KL227 of length: 1.0ìm and diameter: 0.5ìm) maximum speed occurs at viscosity 8cp. Suggested to be because higher viscosity provides increased energy supply.
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| Temporal comparison of chemotactic gradient||4 seconds||N/A||The past second has positive weighting, the previous 3 seconds have negative weighting. E coli compares past and present concentrations by comparing the average occupancy of the receptors over the 4s. Models reflecting this system have been developed by Segall et al and Schnitzer, cells compare their average receptor occupancy between 4 and 1 s ago  c<sub>1-4</sub> to the average receptor occupancy during the last second  c<sub>0-1</sub> . Hence b= c<sub>0-1</sub>  -  c<sub>1-4</sub> .  If b>0, the cell reduces the tumbling rate to T<sub>tumbling</sub> from the ambient value T<sub>0</sub> , 1s<sup>-1</sup> e.g. b>0 don't tumble. b< 0, tumble at a rate of 1s<sup>-1</sup> ||[http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=387059&blobtype=pdf Temporal comparisons in bacterial chemotaxis]<br> [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TBN-4CVRC68-2&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=470c7fd73fb9ebf4ca43342f365e221f#sec5.1 Quantitative analysis of signalling networks] <br> [http://web.mit.edu/biophysics/papers/PNAS2003b.pdf Motility of Escherichia coli cells in clusters formed by chemotactic aggregation]
|-
|-
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| • Temperature
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| Tumbling angle||Shape parameter 4 Scale parameter 18.32 Location parameter -4.6||AW405||The tumble angle appears not to be dependant on the concentration gradient of chemoattractants/repellents. Nor is there correlation between the length of the run and the change in direction. The program uses a gamma distribution that fits the data collected by Berg and Brown. Several groups though, have observed that the tumble angle is not noramlly distributed but suggest that non-normality was only due to the experimental methods used e.g. in the capillary tube. Tumbling can cause a change in direction when as few as one flagella moves out of the bundle. ||[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. coli anaylsed by three-dimensions] <br> [http://bioinformatics.oxfordjournals.org/cgi/reprint/21/11/2714 AgentCell: a digital single-cell assay for bacterial chemotaxis] <br> [http://jb.asm.org/cgi/reprint/189/5/1756 On Torque and tumbling in swimming Escherichia coli]
|-
|-
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| • Culture medium
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| Tumble angle direction||Bidirectional||AW405||Personal communication with Howard Berg. 'The direction is random, more or less, but there is a slight forward bias. It varies from tumble to tumble.  The turn-angle distribution peaks at 68° rather than 90°. Tumbles turn out to be more complex than believed in 1972.  Motors switch independently, and a tumble can occur if one or just a few motors change their directions of rotation.  Tumbles are short, as judged by the tracking microscope, because they involve filament physics rather than motor physics:  a transformation in polymorphic form, following motor reversal, from normal to semi-coiled.  See  Darnton, N.C., Turner, L., Rojevsky, S. and Berg, H.C.  On torque and tumbling in swimming Escherichia coli, J. Bacteriol. 189, 1756-1764 (2007).'||
|-
|-
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| • Vary strain to strain.
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| Tumbling time||0.14±0.19s||AW405||Exponential distribution fitted (stated to be exponential by Berg and Brown) using only the mean tumble length (not STDEV).||[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking] 
|-
|-
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| • Experimental methods
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| Relationship between tumbling angle and time||||||||
|-
|-
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| Many papers give different and variable speeds (mainly for AW405 ~20ìms-1). The speed itself is nearly uniform during the run. May need to measure experimentally, don\'t know under what conditions University of Alberta. Alberta value is higher than other values, but probably because MG1655 is a motile strain. \"||http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi  Biotechnology and Bioengineering, Volume 51, Issue 1  (p 120-125) http://www3.interscience.wiley.com/cgi-bin/fulltext/71003069/PDFSTART
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| Speed while Tumbling||0μm.s<sup>-1</sup>||AW405||Berg and Brown noted that AW405 slowed/stopped while tumbling.||[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking] 
|-
|-
-
|  
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| Drift during run||23±23°||AW405||Drift was observed. It is what would be expected from rotational diffusion. (at 2.7cp at 32ºC drift was 23±23°). Rotational Brownian motion cause the cell to veer off course, so that in between tumbles the probability density function f of the swimming direction e evolves according to the Fokker-Planck equation.  Drift velocity in steep gradient of attractant ~7 µm.s<sup>-1</sup>(Berg & Turner, 1990. Note our model did not include the effects of drift||[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking] <br> [http://www.springerlink.com/content/d8u27q8430202342/ Persistence of direction increases the drift velocity of run and tumble chemotaxis] <br>  [http://www.pdn.cam.ac.uk/groups/comp-cell/Biophysics.html Bray computer modelling]
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|}
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-
 
+
-
=== Run Tumble motion  ===
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-
 
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-
{| {{table}}
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-
| align="center" style="background:#f0f0f0;"|'''Attribute'''
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-
| align="center" style="background:#f0f0f0;"|'''Value'''
+
-
| align="center" style="background:#f0f0f0;"|'''Strain'''
+
-
| align="center" style="background:#f0f0f0;"|'''Justification'''
+
-
| align="center" style="background:#f0f0f0;"|'''Reference'''
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|-
|-
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| Aspartate concentration detected by E. coli||Over ~5 orders of magnitude, 10nM up to 10mM. Can detect changes of as little as ~0.1%||N/A||Most computer simulations of the chemotaxis pathway based on experimentally determined rates and concentrations predict a minimum detectable concentration of the attractant aspartate of around 200 nM. However, experiments performed by Segall et al. in 1986, in which E. coli cells are tethered to a coverslip were exposed to small quantities of chemoattractant delivered iontophoretically. These experiments indicated that a change in receptor occupancy of as little as 1/600 could produce an detectable change in swimming behaviour. With a Kd of 1 µM, this corresponds to a minimum detectable concentration of about 2 nM aspartate. E. coli cells can adapt to Aspartate concentrations over ~5 orders of magnitude. Wild type E. coli cells can detect <10nM of Asp and respond to gradients upto 1mM of Asp. detect small changes in concentration ( 0.1%) via temporal comparisons ( 4 s) over a large range ( 10-8 to 10-3 M)||\"http://www.pdn.cam.ac.uk/groups/comp-cell/ConfSpread.html  Overview of Mathematical approaches used to model bacterial chemotaxis I: The single cell. www.pdn.cam.ac.uk/groups/comp-cell/Biophysics.html    Competitive and Cooperative Interactions in Receptor Signalling Complexes http://www.jbc.org/cgi/reprint/281/41/30512\"
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| Thrust||Down an Asp gradient 0.41pN, Up an Asp gradient 0.4387pN ||AW405||Average thrust =0.41pN. In the Berg and Brown paper it states that the speed of the bacteria up an aspartate chemotactic gradient increases by 7%. Therefore in our model we shall use the following; thrust DOWN the Asp gradient =0.41pN, up the Asp gradient = 0.4387pN. Data was obtained from 32 AW405s, a strain which has provided the majority of our previous parameters but is not as motile as MG1655. The value was obtained at 23ºC in viscosity 0.93 and 3.07 cP for motility buffer and motility buffer with 0.18% methylcellulose, respectively. The standard deviation is not used as the speed is fixed at 50µm.s<sup>-1</sup> . 0.57pN is the average thrust generated in strain HCB30 (a non tumbling strain). The thrust value was obtained when the imposed flow (U) U=0 at 23ºC. O.41pN was calculated using the resistance force theory treating the flagellar bundle as a single filament. The body was assumed to be prolate elipsoid using values roughly similar to ours, 2μm for length and 0.86μm for diameter. ||[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking] <br> [http://jb.asm.org/cgi/reprint/189/5/1756.pdf On Torque and Tumbling in Swimming E. coli]<br> [http://www.pnas.org/content/103/37/13712.full.pdf+html Swimming efficiency of bacterium E. coli.]
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| Temporal comparison of chemotactic gradient||4 seconds||N/A||past second has positive weighting, previous 3 seconds have negative weighting. E. coli compares the current concentration over the proceeding one second to the concentration observed over the previous 3 s. The memory thus lasts approximately 3 s. Bacterial cells evaluate changes in signal concentrations by a temporal mechanism, in particular by comparing their average number of bound receptors over the past 1 s with their average number during the previous 3 s. In models by Segall et al and Schnitzer, cells compare their average receptor occupancy between 4 and 1 s ago  c 1–4 to the average receptor occupancy during the last second  c 0–1. Henceforth we will refer to this difference as the biaser b= c 0–1 -  c 1–4. If b>0, the cell reduces the tumbling rate from the ambient value by||Temporal comparisions in bacterial chemotaxis http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=387059&blobtype=pdf  http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TBN-4CVRC68-2&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=470c7fd73fb9ebf4ca43342f365e221f#sec5.1
+
|-
|-
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| Tumbling angle||Shape parameter 4 Scale parameter 18.32 Location parameter -4.6||AW405||Appears not to be dependant on the concentration gradient of chemoattractants/repellents. Nor is there correlation between the length of the run and the change in direction. Used a gamma distribution that fitted the data of Berg and Brown. Non normality observed by several groups. Suggestions that non-normality was only due to the experimental methods used e.g. in the capillary tube. Tumbling can cause a change in direction when as few as one filaments moves out of the bundle. The flagella on transition from the bundle to release go from normal (a left-handed helix with a pitch of 2.3  m and a diameter of 0.4  m) to semi coiled (a right-handed helix with half the normal pitch but normal amplitude) and then curly (a right-handed helix with half the normal pitch and half the normal amplitude). This therefore suggests that the tumbling angle has bidirectionality??||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf       Emonet Bioinformatics 2005 21(11):2714-2721    http://bioinformatics.oxfordjournals.org/cgi/reprint/21/11/2714 Darnton, N. C., Turner. L., Rojevsky. S., Berg. H. C., 2007 On Torque and tumbling in swimming Escherichia coli J. Bacteriol 189(5) 1756-1764. http://jb.asm.org/cgi/reprint/189/5/1756           
+
| Isotropic run lengths||0.86±1.18s||AW405||Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.4 Berg and Brown) The standard deviation is the standard deviation of the mean and has not been used in the exponential distribution||[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking]
|-
|-
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| Tumble angle direction||Bidirectional||AW405||\"Personal communication with Howard Berg. \"\"The direction is random, more or less, but there is a slight forward bias. It varies from tumble to tumble. The turn-angle distribution peaks at 68 deg rather than 90 deg.
+
| Run length UP Aspartate gradient||1.07±1.80s||AW405||Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.6, Berg and Brown). The standard deviation is the standard deviation of the mean and has not been used in the exponential distribution. ||[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking] <br> [http://parts2.mit.edu/wiki/index.php/University_of_California_San_Francisco_2006 UCSF wiki]
|-
|-
-
|  
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| Run length DOWN Aspartate gradient||0.8±1.38s||AW405||Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.6, Berg and Brown) The standard deviation is the standard deviation of the mean and has not been used in the exponential distribution||[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking]
|-
|-
-
|  
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| Viscosity||Viscosity of water is 1.002cP at 20°C||N/A||At present the medium being used by the lab is still be discussed. Currently though the medium most resembles water and therefore the water's viscosity value can be used. This allows us to assume that the medium is Newtonian (dilute aqueous medium that doesn’t contain long unbranched molecules such as methylcellulose or polyvinylpyrrolidone. Note that methlycellulose does not alter the run and tumble statistics, only bundle and motor rotation rates are affected by the addition of methylcellulose). If agar were to be used then the medium would be Non-Newtonian. Even though it would be Non- Newtonian John Hogan in passing said that we could assume it is Newtonian.||[http://arjournals.annualreviews.org/doi/pdf/10.1146/annurev.biochem.72.121801.161737 The rotary motor of bacterial flagella.],  [http://jb.asm.org/cgi/reprint/189/5/1756.pdf On Torque and Tumbling in swimming Escherichia coli]
|-
|-
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| Tumbles turn out to be more complex than believed in 1972.  Motors switch independently, and a tumble can occur if one or just a few motors change their directions of rotation.  Tumbles are short, as judged by the tracking microscope, because they involve filament physics rather than motor physics: a transformation in polymorphic form, following motor reversal, from normal to semi-coiled.  See  Darnton, N.C., Turner, L., Rojevsky, S. and Berg, H.C.  On torque and tumbling in swimming Escherichia coli, J. Bacteriol. 189, 1756-1764 (2007).\"\"\"||
+
|}
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 +
=== GRN Modelling ===
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 +
{| class="bccstable"
 +
| align="center" width="10%" style="background:#f0f0f0;"|'''Parameter'''
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| align="center" width="20%" style="background:#f0f0f0;"|'''Value'''
 +
| align="center" width="40%" style="background:#f0f0f0;"|'''Description'''
 +
| align="center" width="30%" style="background:#f0f0f0;"|'''Reference'''
|-
|-
-
| Tumbling time||0.14±0.19s||AW405||Exponential distribution fitted (stated to be exponential by Berg and Brown) using only the mean tumble length (not STDEV).||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf 
+
| C<sub>pMax<sub> ||Unknown (varied in the program)||Maximal CpxR protein concentration||||
|-
|-
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| Relationship between tumbling angle and time||||||||
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| k<sub>Cp<sub> ||0.075min<sup>-1<sup> <br> ESTIMATED ||Maximal transcription rate of pCpxR promoter || [http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=11830644 Surface Sensing and Adhesion of Escherichia Coli controlled by the cpx-signalling pathway.]
|-
|-
-
| Speed while Tumbling||0μm.s-1||AW405||Berg and Brown noted that AW405 slowed/stopped while tumbling.||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf 
+
| theta<sub>Cpx<sub> ||1 x 10<sup>-9</sup> M <br> ESTIMATED ||Threshold for pCpxR promoter Hill Function || [https://2008.igem.org/team:kuleuven iGEM 2008 KULeuven ]||
|-
|-
-
| Drift during run||23±23○||AW405||Drift was observed. It is what would be expected from rotational diffusion. (at 2.7cp at 32ºC drift was 23±23°). Rotational Brownian motion cause the cell to veer off course, so that in between tumbles the probability density function f of the swimming direction e evolves according to the Fokker-Planck equation.  Drift velocity in steep gradient of attractant ~7 µm/s (Berg & Turner, 1990)||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf  http://www.springerlink.com/content/d8u27q8430202342/      http://www.pdn.cam.ac.uk/groups/comp-cell/Biophysics.html
+
| m<sub>Cpx<sub> ||1.0 || Co-operativity of pCpxR promoter Hill function ||||
|-
|-
-
| Isotropic run lengths||0.86±1.18s||AW405||Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.4 Berg and Brown) The standard deviation is the standard deviation of the mean and has not been used in the exponential distribution||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf
+
| d<sub>Im<sub> || 3.6 x 10<sup>-1</sup>  min<sup>-1<sup> || Degradation rate of GFP mRNA ||[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347      Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
|-
|-
-
| Run length UP Aspartate gradient||1.07±1.80s||AW405||Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.6, Berg and Brown). The standard deviation is the standard deviation of the mean and has not been used in the exponential distribution Phenylalanine ( the recruitment chemoattractant) utilises a mutant of the Tar receptor. The mutant Tar receptor has been shown to have comparable chemotactic response to the wild type and therefore the values used for the run lengths of aspartate can also be used for phenylalanine.||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf http://parts2.mit.edu/wiki/index.php/University_of_California_San_Francisco_2006
+
| k<sub>Ip<sub> || 9.6 x 10<sup>-1</sup>  min<sup>-1<sup> || Rate of LuxI protein translation || [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347      Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
|-
|-
-
| Run length DOWN Aspartate gradient||0.8±1.38s||AW405||Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.6, Berg and Brown) The standard deviation is the standard deviation of the mean and has not been used in the exponential distribution||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf
+
| d<sub>Ip<sub> || 1.67 x 10<sup>-2</sup>  min<sup>-1<sup> || Degradation rate of LuxI protein || [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347      Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
|-
|-
-
|  
+
| d<sub>Gm<sub> || 1.65 x 10<sup>-3</sup> min<sup>-1<sup> || Degradation rate of GFP protein || [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T36-42HFN5W-11&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000010018&_version=1&_urlVersion=0&_userid=121739&md5=38be996fd7eb7dc4e71179e9d721b298 Efficient GFP mutations profoundly affect mRNA transcription and translation rates ]
-
|}
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+
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+
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{| {{table}}
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| align="center" style="background:#f0f0f0;"|'''Attribute'''
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| align="center" style="background:#f0f0f0;"|'''Value'''
+
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| align="center" style="background:#f0f0f0;"|'''Strain'''
+
-
| align="center" style="background:#f0f0f0;"|'''Justification'''
+
-
| align="center" style="background:#f0f0f0;"|'''Reference'''
+
|-
|-
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| Aspartate concentration detected by E. coli||Over ~5 orders of magnitude, 10nM up to 10mM. Can detect changes of as little as ~0.1%||N/A||Most computer simulations of the chemotaxis pathway based on experimentally determined rates and concentrations predict a minimum detectable concentration of the attractant aspartate of around 200 nM. However, experiments performed by Segall et al. in 1986, in which E. coli cells are tethered to a coverslip were exposed to small quantities of chemoattractant delivered iontophoretically. These experiments indicated that a change in receptor occupancy of as little as 1/600 could produce an detectable change in swimming behaviour. With a Kd of 1 µM, this corresponds to a minimum detectable concentration of about 2 nM aspartate. E. coli cells can adapt to Aspartate concentrations over ~5 orders of magnitude.  Wild type E. coli cells can detect <10nM of Asp and respond to gradients upto 1mM of Asp. detect small changes in concentration ( 0.1%) via temporal comparisons ( 4 s) over a large range ( 10-8 to 10-3 M)||\"http://www.pdn.cam.ac.uk/groups/comp-cell/ConfSpread.html
+
| k<sub>Gp<sub> || 2.4 x 10<sup>-1</sup> min<sup>-1<sup> || Rate of GFP protein translation || [http://www.springerlink.com/content/p14488p56p37n602/ Quantitative measurement of green fluorescent protein expression]
-
Overview of Mathematical approaches used to model bacterial chemotaxis I: The single cell. Www.pdn.cam.ac.uk/groups/comp-cell/Biophysics.html
+
-
Competitive and Cooperative Interactions in Receptor
+
|-
|-
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| Signalling Complexes http://www.jbc.org/cgi/reprint/281/41/30512\"
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| d<sub>Gp<sub> || 2.14 x 10<sup>-4</sup> min<sup>-1<sup> || Degradation rate of GFP protein || [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347      Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
|-
|-
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| Temporal comparison of chemotactic gradient||4 seconds||N/A||past second has positive weighting, previous 3 seconds have negative weighting. E. coli compares the current concentration over the proceeding one second to the concentration observed over the previous 3 s. The memory thus lasts approximately 3 s. Bacterial cells evaluate changes in signal concentrations by a temporal mechanism, in particular by comparing their average number of bound receptors over the past 1 s with their average number during the previous 3 s. In models by Segall et al and Schnitzer, cells compare their average receptor occupancy between 4 and 1 s ago  c 1–4 to the average receptor occupancy during the last second  c 0–1. Henceforth we will refer to this difference as the biaser b= c 0–1 -  c 1–4. If b>0, the cell reduces the tumbling rate from the ambient value by||Temporal comparisions in bacterial chemotaxis http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=387059&blobtype=pdf  http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TBN-4CVRC68-2&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=470c7fd73fb9ebf4ca43342f365e221f#sec5.1
+
| A<sub>prod<sub> || 3.6 min<sup>-1<sup> || AHL production rate per LuxI enzyme ||[[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347      Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
|-
|-
-
| Tumbling angle||Shape parameter 4 Scale parameter 18.32 Location parameter -4.6||AW405||Appears not to be dependant on the concentration gradient of chemoattractants/repellents. Nor is there correlation between the length of the run and the change in direction. Used a gamma distribution that fitted the data of Berg and Brown. Non normality observed by several groups. Suggestions that non-normality was only due to the experimental methods used e.g. in the capillary tube. Tumbling can cause a change in direction when as few as one filaments moves out of the bundle. The flagella on transition from the bundle to release go from normal (a left-handed helix with a pitch of 2.3  m and a diameter of 0.4  m) to semi coiled (a right-handed helix with half the normal pitch but normal amplitude) and then curly (a right-handed helix with half the normal pitch and half the normal amplitude). This therefore suggests that the tumbling angle has bidirectionality??||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf      Emonet Bioinformatics 2005 21(11):2714-2721    http://bioinformatics.oxfordjournals.org/cgi/reprint/21/11/2714 Darnton, N. C., Turner. L., Rojevsky. S., Berg. H. C., 2007 On Torque and tumbling in swimming Escherichia coli J. Bacteriol 189(5) 1756-1764. http://jb.asm.org/cgi/reprint/189/5/1756           
+
| d<sub>A<sub> || 1 x 10<sup>-2</sup> min<sup>-1<sup> || Degradation rate of AHL molecule ||[http://www.nature.com/nature/journal/v434/n7037/full/nature03461.html A synthetic multicellular system for programmed pattern formation ]
|-
|-
-
| Tumble angle direction||Bidirectional||AW405||\"Personal communication with Howard Berg. \"\"The direction is random, more or less, but there is a slight forward bias. It varies from tumble to tumble.  The turn-angle distribution peaks at 68 deg rather than 90 deg.
+
| D<sub>A<sub> || 0.23s<sup>-1<sup> || Diffusion coefficient of AHL || [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347      Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
|-
|-
-
|  
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| k<sub>Tp<sub> || 0.08min<sup>-1<sup> || Maximal Transcription rate of ptetR promoter || [https://2007.igem.org/Imperial/imperial/cell-free/characterisation iGEM 2007Imperial College London]
|-
|-
-
|  
+
| d<sub>Rm<sub> || 3.6 x 10<sup>-1</sup> min<sup>-1<sup> || Degradation rate of LuxR mRNA || [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347      Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
|-
|-
-
| Tumbles turn out to be more complex than believed in 1972. Motors switch independently, and a tumble can occur if one or just a few motors change their directions of rotation. Tumbles are short, as judged by the tracking microscope, because they involve filament physics rather than motor physics:  a transformation in polymorphic form, following motor reversal, from normal to semi-coiled.  See  Darnton, N.C., Turner, L., Rojevsky, S. and Berg, H.C.  On torque and tumbling in swimming Escherichia coli, J. Bacteriol. 189, 1756-1764 (2007).\"\"\"||
+
| k<sub>Rp<sub> || 9.6 x 10<sup>-1</sup> min<sup>-1<sup> || Rate of Lux protein translation || [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347      Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
|-
|-
-
| Tumbling time||0.14±0.19s||AW405||Exponential distribution fitted (stated to be exponential by Berg and Brown) using only the mean tumble length (not STDEV).||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf 
+
| d<sub>Rp<sub> || 2.31 x 10<sup>-2</sup> min<sup>-1<sup> || Degration rate of LuxR protein ||[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347      Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
|-
|-
-
| Relationship between tumbling angle and time||||||||
+
| k<sub>LuxR<sub> || 0.11 min<sup>-1<sup> || Maximal transcription rate of LuxR promoter || [https://2008.igem.org/team:kuleuven iGEM 2008 KULeuven ]
|-
|-
-
| Speed while Tumbling||0μm.s-1||AW405||Berg and Brown noted that AW405 slowed/stopped while tumbling.||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf 
+
| theta<sub>LuxR<sub> || 1.5 x 10<sup>-9</sup> M || Threshold for LuxR pR promoter Hill function || [https://2008.igem.org/team:kuleuven iGEM 2008 KULeuven ]
|-
|-
-
| Drift during run||23±23○||AW405||Drift was observed. It is what would be expected from rotational diffusion. (at 2.7cp at 32ºC drift was 23±23°). Rotational Brownian motion cause the cell to veer off course, so that in between tumbles the probability density function f of the swimming direction e evolves according to the Fokker-Planck equation.  Drift velocity in steep gradient of attractant ~7 µm/s (Berg & Turner, 1990)||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf  http://www.springerlink.com/content/d8u27q8430202342/      http://www.pdn.cam.ac.uk/groups/comp-cell/Biophysics.html
+
| m<sub>LuxR<sub> || 1.6 || Co-operativity of LuxpR promoter Hill function || [https://2008.igem.org/team:kuleuven iGEM 2008 KULeuven ]
|-
|-
-
| Isotropic run lengths||0.86±1.18s||AW405||Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.4 Berg and Brown) The standard deviation is the standard deviation of the mean and has not been used in the exponential distribution||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf
+
| rho<sub>C<sub> || 0.5 micro M<sup>-3</sup> min<sup>-1</sup> || LuxR/AHL dimerisation ||[http://www.nature.com/nature/journal/v434/n7037/full/nature03461.html A synthetic multicellular system for programmed pattern formation ]
|-
|-
-
| Run length UP Aspartate gradient||1.07±1.80s||AW405||Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.6, Berg and Brown). The standard deviation is the standard deviation of the mean and has not been used in the exponential distribution Phenylalanine ( the recruitment chemoattractant) utilises a mutant of the Tar receptor. The mutant Tar receptor has been shown to have comparable chemotactic response to the wild type and therefore the values used for the run lengths of aspartate can also be used for phenylalanine.||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf http://parts2.mit.edu/wiki/index.php/University_of_California_San_Francisco_2006
+
| d<sub>C<sub> || 0.0231 min<sup>-1<sup> || Degradation rate of mCherry  mRNA ||[http://www.nature.com/nature/journal/v434/n7037/full/nature03461.html A synthetic multicellular system for programmed pattern formation ]
|-
|-
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| Run length DOWN Aspartate gradient||0.8±1.38s||AW405||Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.6, Berg and Brown) The standard deviation is the standard deviation of the mean and has not been used in the exponential distribution||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf
+
| d<sub>Mm<sub> || 1.65 x 10<sup>-3</sup> min<sup>-1<sup> || Degradation rate of LuxR/AHL complex ||Due to difficulty in finding mCherry modelling parameters, exsisting GFP parameters have been used. ||
|-
|-
-
|  
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| k<sub>Mp<sub> || 2.4 x 10<sup>-1</sup> min<sup>-1<sup> || Rate of mCherry protein translation || Due to difficulty in finding mCherry modelling parameters, exsisting GFP parameters have been used. ||
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|}
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=== Swimming Machinery ===
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{| {{table}}
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| align="center" style="background:#f0f0f0;"|'''Attribute'''
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| align="center" style="background:#f0f0f0;"|'''Value'''
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| align="center" style="background:#f0f0f0;"|'''Strain'''
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| align="center" style="background:#f0f0f0;"|'''Justification'''
+
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| align="center" style="background:#f0f0f0;"|'''Reference'''
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|-
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| Average thrust ||0.41±0.23 pN||AW405||0.41±0.23 pN ( standard deviation for 32 bacteria) was obtained from strain AW405, a strain which has provided the majority of our previous parameters but is not MG1655 which is more motile. The value was obtained at 23ºC in viscosity 0.93 and 3.07 cP for motility buffer and motility buffer with 0.18% methylcellulose, respectively. The standard deviation is not used as the speed is fixed at 50µm/s. 0.57pN is the average thrust generated in strain HCB30 (a non tumbling strain). The thrust value was obtained when the imposed flow (U) U=0 at 23ºC. O.41pN was calculated using the resistance force theory treating the flagellar bundle as a single filament. The body was assumed to be prolate elipsoid using values roughly similar to ours, 2μm for length and 0.86μm for diameter.||Darnton, N. C., Turner. L., Rojevsky. S., Berg. H. C., 2007 On Torque and tumbling in swimming Escherichia coli J. Bacteriol 189(5) 1756-1764. http://jb.asm.org/cgi/reprint/189/5/1756  Swimming efficiency of bacterium E. coli. http://www.pnas.org/content/103/37/13712.full.pdf+html
+
| d<sub>Mp<sub> || 2.14 x 10<sup>-4</sup> min<sup>-1<sup> || Degradation rate of mCherry protein || Due to difficulty in finding mCherry modelling parameters, exsisting GFP parameters have been used. ||
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<br>
 
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</div>
 

Latest revision as of 15:38, 26 September 2008

Home The Team The Project Submitted Parts Modelling Wet Lab Calendar Miscellaneous


Modelling Parameters

Bacteria

Attribute Value Strain Justification Reference
Length2μmMG1655Values come from the University of Alberta’s datasheet on MG1655, produced to aid modelling. There is variability in size between strains - for instance, AW405 length varies between 1.5±0.2μm. But University of Alberta datasheet is specifically for MG1655.[http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi University of Alberta]
Diameter0.8μmMG1655[http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi University of Alberta]
ShapeCircle r =0.714μmMG1655Actually rod-like. A circle with r= 0.714μm will have equivalent surface area to rod-like.[http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi University of Alberta]
Mass1.02x10-13gMG1655Given 1x10-12g for cell wet weight. Dividing this by gravity (=9.81) gives mass. [http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi University of Alberta]
Swimming Speed50μms-1MG1655University Alberta's datasheet gives 50μms-1. However, Swimming speed is affected by:
  • Viscosity (as viscosity increases the speed increases to some maximum, then decreases as the viscosity increases further. E.coli (strain:KL227 of length: 1.0μm and diameter: 0.5μm) maximum speed occurs at viscosity 8cp.
  • Temperature
  • Culture medium
  • Vary strain to strain.
  • Experimental methods

Various papers give different speeds for E. coli (most papers provide information on AW405 with a speed of ~20μms-1). The speed itself is nearly uniform during the run. The wet lab may need to measure this experimentally as we are unaware of the conditions that the speed for MG1655 was obtained. Alberta's value is higher than other values, but this probably because MG1655 is a motile strain.

[http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi University of Alberta]
[http://www3.interscience.wiley.com/cgi-bin/fulltext/71003069/PDFSTART A Method for Measuring Bacterial Chemotaxis Parameters in a Microcapillary]

Run Tumble Motion

Attribute Value Strain Justification Reference
Aspartate concentration detected by E. coliOver ~5 orders of magnitude, 10nM up to 10mM. Can detect changes of as little as ~0.1%N/AE. coli detect small changes in concentration of 0.1% via temporal comparisons (4s) over a large range ( 10-8 to 10-3 ). Most computer simulations of chemotaxis are based on experimentally determined rates and concentrations. As a result they predict that the minimum detectable concentration of Aspartate is at ~200 nM. Experiments performed by Segall et al. in 1986, exposed tethered E. coli cells to iontophoretically delivered quantities of chemoattractant. These experiments indicated that a change in receptor occupancy of as little as 1/600 could produce an detectable change in swimming behaviour. With a Kd of 1 µM, this corresponds to a minimum detectable concentration of about 2 nM Aspartate. Wild type E. coli cells can detect <10nM of Asp and respond to Asp concentrations of upto 1mM,(responding to over ~5 orders of magnitude). M)[http://www.jbc.org/cgi/reprint/281/41/30512 Competitive and Cooperative Interactions in Receptor Signalling Complexes]
Temporal comparison of chemotactic gradient4 secondsN/AThe past second has positive weighting, the previous 3 seconds have negative weighting. E coli compares past and present concentrations by comparing the average occupancy of the receptors over the 4s. Models reflecting this system have been developed by Segall et al and Schnitzer, cells compare their average receptor occupancy between 4 and 1 s ago c1-4 to the average receptor occupancy during the last second c0-1 . Hence b= c0-1 - c1-4 . If b>0, the cell reduces the tumbling rate to Ttumbling from the ambient value T0 , 1s-1 e.g. b>0 don't tumble. b< 0, tumble at a rate of 1s-1 [http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=387059&blobtype=pdf Temporal comparisons in bacterial chemotaxis]
[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TBN-4CVRC68-2&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=470c7fd73fb9ebf4ca43342f365e221f#sec5.1 Quantitative analysis of signalling networks]
[http://web.mit.edu/biophysics/papers/PNAS2003b.pdf Motility of Escherichia coli cells in clusters formed by chemotactic aggregation]
Tumbling angleShape parameter 4 Scale parameter 18.32 Location parameter -4.6AW405The tumble angle appears not to be dependant on the concentration gradient of chemoattractants/repellents. Nor is there correlation between the length of the run and the change in direction. The program uses a gamma distribution that fits the data collected by Berg and Brown. Several groups though, have observed that the tumble angle is not noramlly distributed but suggest that non-normality was only due to the experimental methods used e.g. in the capillary tube. Tumbling can cause a change in direction when as few as one flagella moves out of the bundle. [http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. coli anaylsed by three-dimensions]
[http://bioinformatics.oxfordjournals.org/cgi/reprint/21/11/2714 AgentCell: a digital single-cell assay for bacterial chemotaxis]
[http://jb.asm.org/cgi/reprint/189/5/1756 On Torque and tumbling in swimming Escherichia coli]
Tumble angle directionBidirectionalAW405Personal communication with Howard Berg. 'The direction is random, more or less, but there is a slight forward bias. It varies from tumble to tumble. The turn-angle distribution peaks at 68° rather than 90°. Tumbles turn out to be more complex than believed in 1972. Motors switch independently, and a tumble can occur if one or just a few motors change their directions of rotation. Tumbles are short, as judged by the tracking microscope, because they involve filament physics rather than motor physics: a transformation in polymorphic form, following motor reversal, from normal to semi-coiled. See Darnton, N.C., Turner, L., Rojevsky, S. and Berg, H.C. On torque and tumbling in swimming Escherichia coli, J. Bacteriol. 189, 1756-1764 (2007).'
Tumbling time0.14±0.19sAW405Exponential distribution fitted (stated to be exponential by Berg and Brown) using only the mean tumble length (not STDEV).[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking]
Relationship between tumbling angle and time
Speed while Tumbling0μm.s-1AW405Berg and Brown noted that AW405 slowed/stopped while tumbling.[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking]
Drift during run23±23°AW405Drift was observed. It is what would be expected from rotational diffusion. (at 2.7cp at 32ºC drift was 23±23°). Rotational Brownian motion cause the cell to veer off course, so that in between tumbles the probability density function f of the swimming direction e evolves according to the Fokker-Planck equation. Drift velocity in steep gradient of attractant ~7 µm.s-1(Berg & Turner, 1990. Note our model did not include the effects of drift[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking]
[http://www.springerlink.com/content/d8u27q8430202342/ Persistence of direction increases the drift velocity of run and tumble chemotaxis]
[http://www.pdn.cam.ac.uk/groups/comp-cell/Biophysics.html Bray computer modelling]
ThrustDown an Asp gradient 0.41pN, Up an Asp gradient 0.4387pN AW405Average thrust =0.41pN. In the Berg and Brown paper it states that the speed of the bacteria up an aspartate chemotactic gradient increases by 7%. Therefore in our model we shall use the following; thrust DOWN the Asp gradient =0.41pN, up the Asp gradient = 0.4387pN. Data was obtained from 32 AW405s, a strain which has provided the majority of our previous parameters but is not as motile as MG1655. The value was obtained at 23ºC in viscosity 0.93 and 3.07 cP for motility buffer and motility buffer with 0.18% methylcellulose, respectively. The standard deviation is not used as the speed is fixed at 50µm.s-1 . 0.57pN is the average thrust generated in strain HCB30 (a non tumbling strain). The thrust value was obtained when the imposed flow (U) U=0 at 23ºC. O.41pN was calculated using the resistance force theory treating the flagellar bundle as a single filament. The body was assumed to be prolate elipsoid using values roughly similar to ours, 2μm for length and 0.86μm for diameter. [http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking]
[http://jb.asm.org/cgi/reprint/189/5/1756.pdf On Torque and Tumbling in Swimming E. coli]
[http://www.pnas.org/content/103/37/13712.full.pdf+html Swimming efficiency of bacterium E. coli.]
Isotropic run lengths0.86±1.18sAW405Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.4 Berg and Brown) The standard deviation is the standard deviation of the mean and has not been used in the exponential distribution[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking]
Run length UP Aspartate gradient1.07±1.80sAW405Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.6, Berg and Brown). The standard deviation is the standard deviation of the mean and has not been used in the exponential distribution. [http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking]
[http://parts2.mit.edu/wiki/index.php/University_of_California_San_Francisco_2006 UCSF wiki]
Run length DOWN Aspartate gradient0.8±1.38sAW405Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.6, Berg and Brown) The standard deviation is the standard deviation of the mean and has not been used in the exponential distribution[http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf Chemotaxis in E. Coli anaylsed by three-dimensional tracking]
ViscosityViscosity of water is 1.002cP at 20°CN/AAt present the medium being used by the lab is still be discussed. Currently though the medium most resembles water and therefore the water's viscosity value can be used. This allows us to assume that the medium is Newtonian (dilute aqueous medium that doesn’t contain long unbranched molecules such as methylcellulose or polyvinylpyrrolidone. Note that methlycellulose does not alter the run and tumble statistics, only bundle and motor rotation rates are affected by the addition of methylcellulose). If agar were to be used then the medium would be Non-Newtonian. Even though it would be Non- Newtonian John Hogan in passing said that we could assume it is Newtonian.[http://arjournals.annualreviews.org/doi/pdf/10.1146/annurev.biochem.72.121801.161737 The rotary motor of bacterial flagella.], [http://jb.asm.org/cgi/reprint/189/5/1756.pdf On Torque and Tumbling in swimming Escherichia coli]

GRN Modelling

Parameter Value Description Reference
CpMax Unknown (varied in the program)Maximal CpxR protein concentration
kCp 0.075min-1
ESTIMATED 		Maximal transcription rate of pCpxR promoter [http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=11830644 Surface Sensing and Adhesion of Escherichia Coli controlled by the cpx-signalling pathway.]
thetaCpx 1 x 10-9 M
ESTIMATED 		Threshold for pCpxR promoter Hill Function iGEM 2008 KULeuven
mCpx 1.0 Co-operativity of pCpxR promoter Hill function
dIm 3.6 x 10-1 min-1 Degradation rate of GFP mRNA [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347 Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
kIp 9.6 x 10-1 min-1 Rate of LuxI protein translation [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347 Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
dIp 1.67 x 10-2 min-1 Degradation rate of LuxI protein [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347 Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
dGm 1.65 x 10-3 min-1 Degradation rate of GFP protein [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T36-42HFN5W-11&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000010018&_version=1&_urlVersion=0&_userid=121739&md5=38be996fd7eb7dc4e71179e9d721b298 Efficient GFP mutations profoundly affect mRNA transcription and translation rates ]
kGp 2.4 x 10-1 min-1 Rate of GFP protein translation [http://www.springerlink.com/content/p14488p56p37n602/ Quantitative measurement of green fluorescent protein expression]
dGp 2.14 x 10-4 min-1 Degradation rate of GFP protein [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347 Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
Aprod 3.6 min-1 AHL production rate per LuxI enzyme [[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347 Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
dA 1 x 10-2 min-1 Degradation rate of AHL molecule [http://www.nature.com/nature/journal/v434/n7037/full/nature03461.html A synthetic multicellular system for programmed pattern formation ]
DA 0.23s-1 Diffusion coefficient of AHL [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347 Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
kTp 0.08min-1 Maximal Transcription rate of ptetR promoter iGEM 2007Imperial College London
dRm 3.6 x 10-1 min-1 Degradation rate of LuxR mRNA [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347 Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
kRp 9.6 x 10-1 min-1 Rate of Lux protein translation [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347 Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
dRp 2.31 x 10-2 min-1 Degration rate of LuxR protein [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4H4T39N-1&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_version=1&_urlVersion=0&_userid=121739&md5=08a37acb41420b0e80d3cde6ead4a347 Systems Analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants.]
kLuxR 0.11 min-1 Maximal transcription rate of LuxR promoter iGEM 2008 KULeuven
thetaLuxR 1.5 x 10-9 M Threshold for LuxR pR promoter Hill function iGEM 2008 KULeuven
mLuxR 1.6 Co-operativity of LuxpR promoter Hill function iGEM 2008 KULeuven
rhoC 0.5 micro M-3 min-1 LuxR/AHL dimerisation [http://www.nature.com/nature/journal/v434/n7037/full/nature03461.html A synthetic multicellular system for programmed pattern formation ]
dC 0.0231 min-1 Degradation rate of mCherry mRNA [http://www.nature.com/nature/journal/v434/n7037/full/nature03461.html A synthetic multicellular system for programmed pattern formation ]
dMm 1.65 x 10-3 min-1 Degradation rate of LuxR/AHL complex Due to difficulty in finding mCherry modelling parameters, exsisting GFP parameters have been used.
kMp 2.4 x 10-1 min-1 Rate of mCherry protein translation Due to difficulty in finding mCherry modelling parameters, exsisting GFP parameters have been used.
dMp 2.14 x 10-4 min-1 Degradation rate of mCherry protein Due to difficulty in finding mCherry modelling parameters, exsisting GFP parameters have been used.

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