Team:BCCS-Bristol/Modeling-Parameters
From 2008.igem.org
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. | University of Alberta |
Diameter | 0.8μm | MG1655 | 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. | University of Alberta |
Mass | 1.02x10^{-13}g | MG1655 | Given 1x10^{-12}g for cell wet weight. Dividing this by gravity (=9.81) gives mass. | University of Alberta |
Swimming Speed | 50μms^{-1} | MG1655 | University Alberta's datasheet gives 50μms^{-1}. However, Swimming speed is affected by:
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. | University of Alberta 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) | 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 T_{0} , 1s^{-1} e.g. b>0 don't tumble. b< 0, tumble at a rate of 1s^{-1} | Temporal comparisons in bacterial chemotaxis Quantitative analysis of signalling networks 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. | Chemotaxis in E. coli anaylsed by three-dimensions AgentCell: a digital single-cell assay for bacterial chemotaxis 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). | 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. | 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 | Chemotaxis in E. Coli anaylsed by three-dimensional tracking Persistence of direction increases the drift velocity of run and tumble chemotaxis 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. | Chemotaxis in E. Coli anaylsed by three-dimensional tracking On Torque and Tumbling in Swimming E. coli 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 | 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. | Chemotaxis in E. Coli anaylsed by three-dimensional tracking 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 | 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. | The rotary motor of bacterial flagella., On Torque and Tumbling in swimming Escherichia coli |
GRN Modelling
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 | 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 | 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 | 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 | 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 | Efficient GFP mutations profoundly affect mRNA transcription and translation rates | |
k_{Gp } | 2.4 x 10^{-1} min^{-1 } | Rate of GFP protein translation | Quantitative measurement of green fluorescent protein expression | |
d_{Gp } | 2.14 x 10^{-4} min^{-1 } | Degradation rate of GFP protein | 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 | [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 | A synthetic multicellular system for programmed pattern formation | |
D_{A } | 0.23s^{-1 } | Diffusion coefficient of AHL | 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 | iGEM 2007Imperial College London | |
d_{Rm } | 3.6 x 10^{-1} min^{-1 } | Degradation rate of LuxR mRNA | 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 | 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 | 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 | A synthetic multicellular system for programmed pattern formation | |
d_{C } | 0.0231 min^{-1 } | Degradation rate of mCherry mRNA | 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 difficulty in finding mCherry modelling parameters, exsisting GFP parameters have been used. | |
k_{Mp } | 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. | |
d_{Mp } | 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. |