Team:Alberta/Project/gradient

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Diffusion Coefficients
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In order to produce and reproduce a predictable gradient that can be manipulated, a diffusion coefficient must be obtained. Diffusion coefficients come in the form of a unit area over a unit time, and are in relation to both the solvent and solute utilized in the experiment. So far, we have focused on finding a coefficient between Ampicillin and Agar gel using equation (a).
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(a)1
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By isolating D from the equation and obtaining values for minimum inhibitory concentration (MIC), concentration (c), zone radius (x), and time (t), we were able to produce a number of fairly similar diffusion coefficients.
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The equation
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The equation (a) is based off of a differential equation used to model one dimensional diffusion. However, this particular equation can be used to model the diffusion of an antibiotic from a well or disk in the center of an agar medium, where the MIC is the minimum concentration to prevent visible cell growth, and the zone is an effect of diffusion causing a ‘front’ of MIC to move through the agar, increasing the radius of said zone with time.
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However, the equation (a) is used to model diffusion if the concentration in the disk or well remains constant throughout the process, which it unfortunately does not, as the solute is wicked up by the agar gel and completely disappears from the well. This effect causes a discrepancy in the zone sizes that can be found over different periods of time between the actual results and the modeled results, and the value sets are only similar very soon after diffusion has begun. This is shown in two contrasting animations of diffusion gradients measured in concentration by distance from the center of the plate after diffusing for different amounts of time (the curve has been simplified into a line so that the graphs will simply illustrate the aforementioned concept)
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Predicted:
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<iframe width="420" height="315" src="http://www.youtube.com/embed/5H3KnWzZi9s" frameborder="0" allowfullscreen></iframe>
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Actual:
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<iframe width="420" height="315" src="http://www.youtube.com/embed/HXWlirnQ9tY" frameborder="0" allowfullscreen></iframe>
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The experiment
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To compensate for the difference in modeled diffusion and actual diffusion, no plates used for results were diffused for longer than 2 days. Taking into account our maximum accuracy of measurement and the maximum size of zone we saw, there were only 50 different lengths of zone size we could measure, while the longest amount of time we measured was around 172000 seconds or about 2 days, and so our results produced a range of values. Using the equation, we created a diffusion constant calculator to get a range of values. With this range of  constants corresponding to different time values, we are able to create an order of magnitude which will allow us to make reasonable hypotheses on how diffusion will occur.
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In our experiment, we made up 8 plates with equal concentrations and volumes of ampicillin in a centre well over a period of 42 hours, plated them all with E. coli at the same time, and saw zones for all plates within 8 hours of plating the E. coli. This also corresponded to the approximate time that cells become visible on the plate during exponential phase. Our end value was approximately 1.5e2µm2/s. Throughout the process we developed a number of protocols that can be utilized to find diffusion constants for other antibiotics or molecules that we may need to use in gradients for our final product.
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Establishing and modeling chemical gradients
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1-Bonev, B., Hooper, J., and Parisot, J., Principles of assessing bacterial susceptibility to antibiotics using the agar diffusion method, Journal of Antimicrobial Chemotherapy, v. 61, i. 6, p. 1295-1301
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Latest revision as of 19:12, 26 September 2012

   Team Alberta




Establishing and modeling chemical gradients

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