Team:BCCS-Bristol/Modeling-Parameters

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Modelling Parameters


Bacteria

Attribute Value Strain Justification Reference
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-1MG1655University 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

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/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/AThe past second has positive weighting, the previous 3 seconds have negative weighting. E coli compares these concentrations (average occupancy of the receptors) and therefore the memory lasts approximately 3 s. Models reflecting this have been developed 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. Hence b= c 0–1 - c 1–4, If b>0, the cell reduces the tumbling rate to Ttumb from the ambient value T0 (1s-1) e.g. b>0 don\'t tumble. b< tumble at a rate of 1s-1Temporal comparisons 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 "Quantitative analysis of signalling networks"] Motility of Escherichia coli cells in clusters formed by chemotactic aggregation http://web.mit.edu/biophysics/papers/PNAS2003b.pdf
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).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 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 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 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 distributionBerg and Brown Nature 239, 500 - 504 (27 October 1972) http://www.nature.com/nature/journal/v239/n5374/pdf/239500a0.pdf

Swimming Machinery

Attribute Value Strain Justification Reference
Average thrust 0.41±0.23 pNAW4050.41±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

Properties of the media

Attribute Value Strain Justification Reference
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. Intrinsic viscosity η in 0.1M NaNO3 aqueous solution at 45 ◦C is correlated to molecular size of agar through a Mark-Houwink equation, η= 0.07M0.72, where M is the average molecular weight.The rotary motor of bacterial flagella. Physica A 358 (2005) 205–211. http://arjournals.annualreviews.org/doi/pdf/10.1146/annurev.biochem.72.121801.161737 On torque and tumbling in swimming Escherichia coli
Diffusion coefficient of Aspartate.0.033 cm2.h-1N/A0.033 cm2/h is for aspartate at 22°C in 0.15% agar. Another value from the literature, 0.9 x10-5 cm2/s, is for aspartate at 35◦C in 0.3% agar. To calculate diffusion coefficients the following formula can be used D=RT/6πNvr where: R is the gas constant, T is the absolute temperature (Kelvin), N is the number of molecules in a mole (6 x1023), v is the viscosition of the solvent (e.g. 0.001 for water), r= radius of the particle. This formula could be used to calculate the diffusion coefficient at the viscosity used in our experiments.\"Chemotactic Responses of Escherichia coli to Small Jumps of Photoreleased L-Aspartate http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=1300146&blobtype=pdf Response tuning in bacterial chemotaxis http://www.pnas.org/content/96/20/11346.full.pdf\"
Diffusion coefficient of Phenylalanine.3.58 x 10-4 cm 2 min -1N/A[http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TGK-3W38497-D&_user=121739&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000010018&_version=1&_urlVersion=0&_userid=121739&md5=316e71596cb388d2a0cf0de7c15f84fe#fd16 Extraction and re-extraction of phenylalanine by cationic reversed micelles in hollow fibre contactors]
Quorum SignalOHHL (3-oxo-C6-HSL)N/AFrom the quorum sensing system of Vibrio Fischeri produced by LuxI. Molecular weight: 213
Basal (constitutive) rate of AHL production30nmol.hr-1V. fischeriValue was used in a modelling simulation of the Lux system in V. fischeri. Note that the maximum [AHL] is achieved during stationary phase.Kinectics of the AHL regulatory system in a model biofilmsystem: How many bacteria constitute a \"Quorum\"? http://docstore.ingenta.com/cgi-bin/ds_deliver/1/u/d/ISIS/45421751.1/ap/mb/2001/00000309/00000003/art04697/34CECEE65ADECE1112181237349BDA2365FA8246B1.pdf?link=http://bristol.library.ingentaconnect.com/error/delivery&format=pdf
Diffusion coefficient for Quorum signalDaq= 4.9x 10-6 cm2 s-1N/ADaq= 4.9x10-6cm2.s-1 is the diffusion coefficient of 3 oxo-C12 AHL in water, not OHHL as we would be using. Estimations can be calculated using Wilke Chang equation (see Perry\'s Chemical Engineers\' Handbook). De = 1.23x 10-6 cm2 s-1 is the effective diffusion coefficient of 3 oxo-C12 AHL in biofilm. The effect of the chemical, biological and physical environment on quorum sensing in structured microbial communities. Anal Bioanal Chem (2007) 387:371-380. http://www.springerlink.com/content/v36128k24t558820/fulltext.pdf
Threshold concentration of autoinducerUse imperial iGEM value 1nM! ~1 to 10μg.ml-1N/AIn the pattern formation paper fig 2c and d represent a simulation and experimental data respecitively. The graph plots the concentration of AHL required to elicit a visual response (observation of fluorescence). Imperial iGEM team looked at the lower and higher threshold levels of AHL in vivo and in vitro. They also visualised this with expression of GFP. Low threshold 1nM in vivo (estimated the number of plasmids present) in vitro value is only obtained on extrapolation and therefore it is not accurate but predicited to be higher. High threshold is ~1000nM and therefore beyond this level the system does not respond to any further increase, the system is saturated. See graph sheet. Another paper, A novel strategy for the isolation of luxl homologues:evidence for the widespread distribution of a LuxR:Luxl superfamily in enteric bacteria. The V. fischeri sensor for OHHL is very senstive requiring levels of 10ng.ml-1 to inititate transcription. This paper also states that the thresholds differ depending on strain of bacteria and cell densities. The Imperial\'s iGEM team value is the best as it is for MC1000 and therefore most relevent for this project. A synthetic multicellular system for programmed pattern formation. http://www.nature.com/nature/journal/v434/n7037/pdf/nature03461.pdf http://parts.mit.edu/igem07/index.php/Imperial/Infector_Detector/F2620_Comparison A novel strategy for the isolation of luxl homologues: evidence for the widespread distribution of a LuxR:Luxl superfamily in enteric bacteria http://www3.interscience.wiley.com/cgi-bin/fulltext/119307663/PDFSTART
Protein decay (LuxR/AHL)0.0231 min-1A synthetic multicellular system for programmed pattern formation. http://www.nature.com/nature/journal/v434/n7037/pdf/nature03461.pdf
LuxR/AHL activation coefficient0.01µMA synthetic multicellular system for programmed pattern formation. http://www.nature.com/nature/journal/v434/n7037/pdf/nature03461.pdf
LuxR/AHL dimerisation 0.5µM-3.min-1A synthetic multicellular system for programmed pattern formation. http://www.nature.com/nature/journal/v434/n7037/pdf/nature03461.pdf
AHL decay0.01min-1Note that this value is affected by pHA synthetic multicellular system for programmed pattern formation. http://www.nature.com/nature/journal/v434/n7037/pdf/nature03461.pdf
Particle10µm diameter and roundValue obtained from lab teamBacterial flagella-based propulsion and on/off motion control of microscale objects
Particle density1.05g.cm-3N/AValue is for the particles the lab team is using
Diffusion coefficient of 10μm polystyrene bead4.93x10-14 m2/sN/ABacterial flagella-based propulsion and on/off motion control of microscale objects
Drag on 10μm sphere1.4pNN/ABacterial flagella-based propulsion and on/off motion control of microscale objects


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