Mathematical Analysis of Bacterial Growth in the Presence of Toxins David Martin, David Gohlke, Jonathan Caguiat, George

1. Mathematical Analysis of Bacterial Growth in the Presence of Toxins David Martin, David Gohlke, Jonathan Caguiat, George Yates Youngstown State University, Youngstown OH, 44555 Abstract This poster describes research done by the authors during the 2005 SURE (Summer Undergraduate Research Experience) program at Youngstown State University, funded by the National Science Foundation (grant DUE 0337558). This work examined the effects of the toxin selenite on bacteria, and how these effects were changed by the presence of the amino acid cysteine. Specifically, the effects on strains of Stenotrophomonas maltophilia and Escherichia coli were examined. The research confirmed the toxicity of selenite and the ability of cysteine to counteract these effects under certain conditions. Mechanism Selenite is believed to be brought into the cell and broken down into the ion selenide. If cysteine is not available, the cell “accidentally” uses the selenide to create the amino acid selenocysteine via the pathway which normally would produce cysteine. The disproportionately high concentration of selenocysteine and the resultant deficiency of cysteine can be poisonous to cells. However, if cysteine is readily available, then the cell has no need to try and create it, and the selenide is ignored. This buildup of selenide gives the solution a reddish hue. A hypothesized pathway of this incorporation is shown in the diagram to the right. Growth Curves Finding an estimate of how many bacteria exist at each hour makes it possible to plot population as a function of time. This is known as a growth curve, and from this curve, one can create a mathematical model explaining what happens in a sample. This allows one to predict results and notice if a sample is growing strangely. If an anomaly is found, one can examine it in detail, uncovering a mistake or modifying the theory of how the bacteria grow. The growth curves of three samples from June 23 have three distinct shapes from growing in different environments. The constants in the graphs were estimated by using the Solver tool in Microsoft Excel. When in the presence of a toxin, a certain fraction of the total bacteria will die in a given time. This occurs in the presence of selenite without cysteine. This gives the differential equation, which has the solution N = N0e-at. Pathway showing incorporation of selenite into cell (adapted from Müller, Heider, Böck) In optimal conditions, the bacteria undergo exponential growth; after a few hours, this growth slows down noticeably, asymptotically approaching the carrying capacity of the medium. This tempered exponential growth is known as the logistic curve. It has differential equation , and the closed form of . The growth curve of the sample in the presence of both cysteine and selenite can be approximated by assuming that the bacteria gains resistance after reproducing. The original bacteria in the sample have no resistance to selenite, however, their progeny do, and they grow logistically. A first order approximation of the number of bacteria is given by the equation: Procedure The results on this poster come from experiments performed on June 23 and July 6, 2005. For the first experiment, M-9 minimal medium was used for growth of S. maltophilia. The second experiment required the addition of Casamino acids to the medium to grow the HB101 strain of E. coli. The cultures were grown under 4 conditions: neither cysteine nor selenite, cysteine without selenite, selenite without cysteine, and both cysteine and selenite. The concentrations of cysteine and selenite, when present, were 40 mg/mL and 40mM, respectively. Hourly measurements of bacterial concentration and optical density were made for each sample. The bacterial concentration of each sample was obtained by preparing dilutions of the solution and spreading them on agar plates. The plates were incubated overnight, allowing each bacterium to grow into a visible colony. The next morning, the bacterial concentration (in colony forming units per milliliter, or CFU/mL) was extrapolated based on the number of colonies present. Plotting the concentration as a function of time, we can obtain a growth curve. The use of growth curves to mathematically model bacterial populations is explained to the right. The optical density of a sample can be measured by using a calibrated colorimeter. This quick reading often correlates closely to bacterial concentration or gives additional information about our sample. 132 agar plates of bacteria: one day of data collection Absorbance The Klett colorimeter was used to measure the absorbance of light at specific frequencies (or ranges of frequencies). This allowed for the measurement of the “redness” of our sample. Unless something occurs to make the samples more red than they should be, then the value recorded from the apparatus should be directly related to the number of bacteria. However, since the selenite is being broken down into selenide, the sample is far more red than it otherwise would be. Conclusions S. maltophilia was shown to thrive in the proper growing conditions and die in the presence of selenite; however, the bacteria are able to survive in the presence of selenite if cysteine is also available. Acknowledgements First, we would like to thank the National Science Foundation (grant number DUE 0337558) for their funding of this research. We would also like to thank Steve Vadia for his assistance in the laboratory. Also, we would like to thank the other SURE participants and advisors, especially Drs. Jay Kerns and Thomas Smotzer, for their suggestions during the weekly meetings. References [1] M Bébien, G Lagniel, J Garin, D Touati, A Verméglio, J Labarre. Involvement of Superoxide Dismutases in the Response of Escherichia coli to Selenium Oxides. Journal of Bacteriology, Mar. 2002 p. 1556-1564. [2] J Caguiat. Ph.D. thesis / log book [3] R Dungan, SR Yates, W Frankenberger. Transformations of selenate and selenite by Stenotrophomonas maltophilia isolated from a seleniferous agricultural drainage pond sediment. Enviromental Microbiology (2003) 5(4) 287-295. [4] C Garbisu, T Ishii, T Leighton, BB Buchanan. Bacterial reduction of selenite to elemental selenium. Chemical Geology 132 (1996) 199-204. [5] CPL Grady, HC Lim. Biological Wastewater Treatment. [6] Harvard Medical School. Short Protocols in Molecular Biology, 2nd edition. [7] S Müller, J Heider, A Böck. The path of unspecific incorporation in Escherichia coli.Arch Microbiol, 1997, 168:421-427. [8] R Turner, JH Weine, DE Taylor. Selenium metabolism in Escherichia coli. BioMetals 1998, 11, 223-227. As long as the sample is not becoming artificially red, Klett readings can be used to approximate the bacterial concentration. In this case, reddening shows that the bacteria is reducing the selenite, possibly making it useful for bioremediation. S. maltophilia usually grows clear (right), however if grown in the presence of cysteine and selenite, the red hue of elemental selenium can be seen (left). To the left is a graph of the Klett reading as a function of time for the samples on June 23. The sample with only selenite dies, and therefore breaks down very little selenite. The samples without selenite become cloudy from the presence of bacteria, contributing to reasonably high readings, however the high values are from this cloudiness, not the sample becoming redder. The sample grown in cysteine and selenite continued to redden overnight from continued breakdown of selenite, reaching a Klett value of over 1200 by the next morning. Results from July 6 determined the phenotype of the HB101 strain of E. coli, with and without the plasmid pOR1. This plasmid is hypothesized to give resistance to selenite when the bacteria is grown in the presence of cysteine. In these experiments, this plasmid did indeed give E. coli (HB101) the same phenotype as the more hardy S. maltophilia. Because of this, HB101 could also be used for bioremediation, though its slower growth may make this infeasible. In these Klett readings, the redness of the sample grown in the presence of cysteine and selenite increases faster than the number of bacteria, while the other two samples have readings proportional to the total number of bacteria.