Team:BCCS-Bristol/Modeling-Batch Simulations

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Batch Simulations

Batch simulations allow us to perform statistical analysis on our simulations and in particular look at the affect of altering one or many of the parameters. This will enable us to inform the wet lab team of the optimum conditions for their experiments.

Statistical Analysis

For every simulation statistical analysis will be performed on six aspects:

The direction (angle) the particle has moved towards the chemoattractant.
The distance (x axis) travelled by the particle.
The mean direction (angle) of movement by all particles towards the chemoattractant.
The mean distance (x axis) travelled by all particles.
The mean direction (angle) of bacterial movement towards the chemoattractant
The mean distance (x axis) bacteria travelled.

For each altered parameter 100 simulations (if feasible) will be run with each simulation running for 10 000 time steps containing 1-10 particles.

Methods of Statistical Analysis

Methods of Statistical analysis will include:

T tests to show that results observed due to parameter changes are statistically significant.
Histograms.
Scatter plots.
Means.

Batch Simulations

Parameter	Motivation	Description	Test
Particle Size (Particle size is described by diameter.)	Increasing the surface area of the bead would increase the number of bacteria that could contact the particle at once. With a greater number of bacteria attached the particle is subjected to a greater propulsion force. This would speed up the rate of particle movement towards the goal. But, increasing the surface area of the particle may dramatically retard the movement of the particle through the fluid. Modelling would resolve an optimum balance of speed and retardation due to a large surface area.	Surface Area. The range of values to be tested must primarily have a low Reynolds number for the simulation to remain valid. Another factor to be considered is the availability of certain sized particles. Mass and shape are not going to be altered. Our model is based on the rules of Stokes’ law, which does not include mass. For Stokes’ Law to work Re<<1 (threshold is stated to be roughly around 0.5). The particles used currently by the lab in feasibility studies have very low Reynolds numbers ((1 x 10³ x 1 x 10^-5 x 5 x 10^-6 ) /1 x 10^-3 = 5 x 10^-4 ). Shape is not going to be altered as different shaped particles are not widely available on the market.	1µm -100 µm at 10 µm intervals and 500µm i. 1µm (Re = 5 x 10^-5 ) ii. 50 µm (Re = 2.5 x 10^-3 ) iii. 100 µm (Re = 5 x 10^-3 ) iv. 500 µm (Re = 2.5 x 10^-2 ) v. NOTE R_e values have been calculated using the viscosity of water, 1 x 10^-3 Pa.s, and the density of water, 1000kg.m^-3
Particle Adherence	Does the permanent attachment of bacteria to the particle increase the efficiency of particle movement? Is adherence required for the GRN to work? Does the pattern of coating on the particle have an affect? Does the angle that bacteria attach to the particle have an affect? Is the strength of adhesion between 1 Streptavidin and biotin sufficiently strong that it would prevent the bacteria from detaching once attached? On adhering to the particle can the bacteria still chemotax?	Absence of particle coating Presence of particle coating 1/2 or full particle coating Simple: The bacteria once attached could not dissociate. Complex: The strength of adhesion and the number of adhesions between a bacterium and particle are modelled. Particle adherence is currently modelled as a potential function using two vectors to compute a single vector; the force a particle exerts on bacteria and the distance between the edges of the particle to the edge of the bacteria. The rupture forces between 1 Streptavidin and 1 Biotin at loading rates 198 and 2300pN.s^-1 were 126±2.3 pN and 207±5.8 pN respectively (where mean ± SEM) These values were measured with atomic force microscopy in PBS at 25°C. [http://pubs.acs.org/cgi-bin/article.cgi/bichaw/2000/39/i33/pdf/bi992715o.pdf Energy Landscape of Streptavidin-Biotin complexes measured by Atomic Force Microscopy.] Each Streptavidin is a tetramer with 4 biotin binding sites but contacts 1 biotin. Contact angles of bacteria to surfaces.An example- if water was placed on a hydrophobic surface the contact angle would be greater than 90°. Bacterial adhesion is dependent on: The bacterial surface charge, The solid subtratum (characterised by its surface free energy, high- hydrophilic, low- hydrophobic), The surrounding liquid phase. The bacterial surface charge is dependant on the strain of the organism, changing with growth phase and environmental conditions.[http://www.pubmedcentral.nih.gov/articlerender.fgci?artid=241988 Bubble contact angle method for evaluating substratum interfacial characteristics and its relevance to bacterial attachment.] The lipopolysaccharide surface of E. coli usually contains three components; keto deoxy octulonate, core polysaccharide, and a large O antigen. Each strain has a different composition. Increased LPS lenght increases adhesion. [http://www.engr.psu.edu/ce/enve/publications/2004-Li&Logan-CSB.pdf Bacterial adhesion to glass and metal oxide surfaces]	Coated, non Coated Change coating distribution on the particle. 1/2 or fully coated particle
Bacterial Population Density	Model the exact area that the lab team observes under the microscope to allow direct correlation between the work of the modelling team and wet lab team.
What population density is required to move the particle an observable distance?
How many bacteria are required to move one particle?	Currently the wet lab team commonly uses magifications of 40x and 63x.	Test 1/2, 1, and 2 times the density currently used by the lab.
40x magnification: Currently 24683 bacteria in 0.320 x 0.2257 mm²
1/2 density = 12341 bacteria, 2x density = 49366 bacteria.
63x magnification: Currently 9992 bacteria in 0.2036 x 0.1436 mm²
1/2 density = 4996 bacteria, 2x density = 19984 bacteria mm²
GRN dynamics	Simulations will enable us to check that the dynamics of the GRN are sufficiently quick. It may also be able to refine the GRN by altering elements within the GRN e.g. a promoter and seeing how the dynamics had been affected. The simulation will also be able to tell if the GRN dynamics occur within 1 cell cycle.	Initially this can be modelled by altering the delay. Eventually simulations could lead to the production of an accurate GRN where elements can be individually changed.
The longest delay (r.d.s.) so far is the activation of gene expression downstream of the Cpx promoter following the binding of bacteria to a hydrophobic surface (the particle). A paper, [http://www.pnas.org/content/99/4/2287.full.pdf+html Surface sensing and adhesion of Escherichia coli controlled by the Cpx-signalling pathway] , measures the alteration in expression levels of genes downstream of Cpx. They analyse the activity of lacz, the gene fused downstream of Cpx. To do this they measure the rate of ONPG hydrolysis and use this value as the alteration in activity of gene expression levels. Activity on contact with a hydrophobic surface occurred immediately. “Significant level of activity” is observed after 30 minutes. But the choice of when a “significant level of activity” occurred was not justified. The overall activity increases to a max ~3 fold of the constitutive level, 400-1200 units in 1 hr (note that the activity of a fully activated lac operon is usually 1500 units). The graph of activity had only 3 data points (0, 30 and 60 mins) and therefore the relationship of increase in activity cannot be accurately assumed. Furthermore, the activity of gene expression was measured by the catalysis of ONPG. This value is hard to manipulate for what we need e.g. for significant results to be observed 10 enzymes need to be produced but for there to be sufficient levels of CheW 6700 may need to be produced and therefore “significant" activity may occur in completely different time scales.
Note that this was restricted to cell growth in stationary phase, CpxRA system activation increases rapidly at the end of exponential and start of stationary phase and therefore the Cpx pathway has GROWTH PHASE DEPENDENCE.	Test 30 minute delay
Initial placement of bacteria	Simulations could calculate the optimum distance that the bacteria should be inoculated from the goal.
Viscosity	What viscosity results in the greatest motility of the bacteria?	Viscosity primarily alters the speed of bacteria in our model. In [http://jb.asm.org/cgi/reprint/189/5/1756.pdf Torque and Tumbling] , the addition of methylcellulose resulting in a more viscous media does not alter the run and tumble statistics and any affect seen is only on bundle and motor rotation rates. Unlike Stokesian inert particles where diffusivities are inversely proportional to the medium's viscosity papers have observed that the speed of bacteria in fact increases as viscosity increases to a maximum of 8cP. [http://www3.interscience.wiley.com/cgi-bin/fulltext/71003069/PDFSTART A Method for Measuring Bacterial Chemotaxis Parameters in a Microcapillary] . The best explanation of this is the assumption that flagellar in polar regions are active (e.g. head) and the other flagella stream passively by hydrodynamic drag to the rear. The extra inactive flagella bunched at the pole would contribute to the effective stiffness of the active flagella and thereby increase internal elasticity resulting in maximum efficiency reached at higher viscosities. [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=285562 Effect of Viscosity on Bacterial Motility] Further increases in viscosity result in decreased swimming speed as viscous drag increases. 60cP is the lowest viscosity that renders bacteria immobile. [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=221865 Motility of flagellated bacteria in viscous environments ] This paper in fig 1 shows the relationship between velocity and viscosity for Pseudomonas aerginosa (another flagellated bacteria like E. coli.)Addition of a polymer that increases viscosity improved propulsion efficiency, which surpasses the decline in flagellar rotation rate and therefore the swimming speed increases with increased viscosity. [http://www.biophysj.org/cgi/reprint/83/2/733A Mathematical Explanation of an Increase in Bacterial Swimming Speed with Viscosity in Linear-Polymer Solutions.] This can be mathematically modelled by introducing two apparent viscosities:
1) When the bacteria moves through virtual space is assumed µ_T (T because the motion of the body is tangential to the surface of the body.)
2) µ_N is assumed when the bacterial body moves outside the virtual space (the polymer network must be reconstructed as the virtual space is moving.) (N referring to the direction of the body being normal to the surface of the body.) As the polymer concentration increases the network becomes denser and the ratio of µ_N: µ_T becomes larger.	1cP – 3.2cP
1cP is the viscosity of water
3.2cP is commonly seen in the literature