Team:BCCS-Bristol/Modeling-Parameters

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== Modelling Parameters ==
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* [[Team:BCCS-Bristol/Modeling-Progress#Bacteria|'''Bacteria''']]
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* [[Team:BCCS-Bristol/Modeling-Progress#Run Tumble motion|'''Run Tumble motion''']]
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* [[Team:BCCS-Bristol/Modeling-Progress#Swimming Machinery|'''Swimming Machinery''']]
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=== Bacteria ===
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{| {{table}}
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| align="center" style="background:#f0f0f0;"|'''Bacteria'''
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| align="center" style="background:#f0f0f0;"|''''''
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| align="center" style="background:#f0f0f0;"|''''''
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| align="center" style="background:#f0f0f0;"|''''''
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| align="center" style="background:#f0f0f0;"|''''''
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|-
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| Attribute||Value||Strain||Justification||Reference
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|-
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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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|-
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| Diameter||0.8ìm||MG1655||||http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi
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|-
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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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|-
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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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|-
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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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|-
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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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|-
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| • Temperature
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|-
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| • Culture medium
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|-
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| • Vary strain to strain.
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|-
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| • Experimental methods
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|-
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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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|-
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|
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|}
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=== Run Tumble motion  ===
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{| {{table}}
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| align="center" style="background:#f0f0f0;"|'''Run tumble motion'''
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| align="center" style="background:#f0f0f0;"|''''''
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| align="center" style="background:#f0f0f0;"|''''''
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| align="center" style="background:#f0f0f0;"|''''''
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| align="center" style="background:#f0f0f0;"|''''''
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|-
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| Attribute||Value||Strain||Justification||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
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|-
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| Signalling Complexes http://www.jbc.org/cgi/reprint/281/41/30512\"
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|-
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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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|-
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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           
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|-
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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.
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|-
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|
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|-
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|
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|-
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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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|-
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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).||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf 
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|-
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| Relationship between tumbling angle and time||||||||
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|-
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| 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 
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|-
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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 (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
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|-
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| 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
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|-
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| 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
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|-
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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
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|-
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| Run length UP Serine gradient||2.19±3.43s||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
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|-
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| Run Length DOWN Serine gradient||1.40±1.88s||AW405||Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.6, Berg and Brown)||Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf
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|-
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|
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|}
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=== Swimming Machinery ===
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{| {{table}}
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| align="center" style="background:#f0f0f0;"|'''Average thrust'''
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| align="center" style="background:#f0f0f0;"|'''0.41±0.23 pN'''
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| align="center" style="background:#f0f0f0;"|'''AW405'''
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| align="center" style="background:#f0f0f0;"|'''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.'''
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| align="center" style="background:#f0f0f0;"|'''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'''
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|-
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|
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|}
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Revision as of 11:46, 11 August 2008

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


Modelling Parameters


Bacteria

Bacteria ' ' ' '
AttributeValueStrainJustificationReference
Length2ìmMG1655Values 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
Diameter0.8ìmMG1655http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi
ShapeCircle r =0.714ìmMG1655Actually 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
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
Swimming Speed50ìm.s-1MG1655\"University Alberta\'s datasheet gives 50ìms-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: 1.0ìm and diameter: 0.5ìm) maximum speed occurs at viscosity 8cp. Suggested to be because higher viscosity provides increased energy supply.
• Temperature
• Culture medium
• Vary strain to strain.
• Experimental methods
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

Run Tumble motion

Run tumble motion ' ' ' '
AttributeValueStrainJustificationReference
Aspartate concentration detected by E. coliOver ~5 orders of magnitude, 10nM up to 10mM. Can detect changes of as little as ~0.1%N/AMost 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\"
Temporal comparison of chemotactic gradient4 secondsN/Apast 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 byTemporal 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
Tumbling angleShape parameter 4 Scale parameter 18.32 Location parameter -4.6AW405Appears 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
Tumble angle directionBidirectionalAW405\"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.
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).Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf
Relationship between tumbling angle and time
Speed while Tumbling0μm.s-1AW405Berg 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
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 (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
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 distributionBerg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf
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 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
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 distributionBerg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf
Run length UP Serine gradient2.19±3.43sAW405Exponential 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 distributionBerg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf
Run Length DOWN Serine gradient1.40±1.88sAW405Exponential distribution fitted, this is only an approximate and does not fit exactly (see fig.6, Berg and Brown)Berg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf

Swimming Machinery

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


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