Team:BCCS-Bristol/Modeling-Parameters

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Modelling Parameters

Bacteria

Attribute	Value	Strain	Justification	Reference
Length	2μm	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±0.2μm. But University of Alberta datasheet is specifically for MG1655.	[http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi University of Alberta]
Diameter	0.8μm	MG1655		[http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi University of Alberta]
Shape	Circle r =0.714μm	MG1655	Actually 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]
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 University of Alberta]
Swimming Speed	50μms^-1	MG1655	University 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. 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^-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 K_d 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 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_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 T_tumbling 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 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] [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 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).'
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]
Relationship between tumbling angle and time
Speed while Tumbling	0μm.s^-1	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]
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^-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]
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^-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 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]
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] [http://parts2.mit.edu/wiki/index.php/University_of_California_San_Francisco_2006 UCSF wiki]
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]
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]

GRN Modelling

k_{Mp_{|| 2.4 x 10^-1 min^{-1^{|| Rate of mCherry protein translation || Due to diffucultly in finding mCherry modelling parameters, exsisting GFP parameters have been used. ||}}}}

Parameter	Value	Description	Reference
C_pMax	Unknown (varied in the program)	Maximal CpxR protein concentration
k_Cp	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.]
theta_Cpx	1 x 10^-9 M ESTIMATED	Threshold for pCpxR promoter Hill Function	iGEM 2008 KULeuven
m_Cpx	1.0	Co-operativity of pCpxR promoter Hill function
d_Im	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.]
k_Ip	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.]
d_Ip	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.]
d_Gm	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 ]
k_Gp	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]
d_Gp	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.]
A_prod	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.]
d_A	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 ]
D_A	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.]
k_Tp	0.08min^-1	Maximal Transcription rate of ptetR promoter	[http://parts.mit.edu/igem07/index.php/Imperial/imperial/cell-free/characterisation iGEM 2007Imperial College London]
d_Rm	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.]
k_Rp	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.]
d_Rp	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.]
k_LuxR	0.11 min^-1	Maximal transcription rate of LuxR promoter	iGEM 2008 KULeuven
&theta_LuxR	1.5 x 10^-9 M	Threshold for LuxR pR promoter Hill function	iGEM 2008 KULeuven
m_LuxR	1.6	Co-operativity of LuxpR promoter Hill function	iGEM 2008 KULeuven
&rho_C	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 ]
d_C	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 ]
d_Mm	1.65 x 10^-3 min^-1	Degradation rate of LuxR/AHL complex	Due to diffucultly in finding mCherry modelling parameters, exsisting GFP parameters have been used.
d_Mp	2.14 x 10^-4 min^-1	Degradation rate of mCherry protein	Due to diffucultly in finding mCherry modelling parameters, exsisting GFP parameters have been used.