Mathematical Sciences

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Mathematical research at MSU is focused primarily on related topics in pure and applied mathematics. Research programs complement each other and are often applied to problems in science and engineering. Research in statistics encompasses a broad range of theoretical and applied topics. Because the statisticians are actively engaged in interdisciplinary work, much of the statistical research is directed toward practical problems. Mathematics education faculty are active in both qualitative and quantitative experimental research areas. These include teacher preparation, coaching and mentoring for in-service teachers, online learning and curriculum development.

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    Surface micropattern resists bacterial contamination transferred by healthcare practitioners
    (2014-12) Mann, Ethan E.; Mettetal, M. Ryan; May, Rhea M.; Drinker, M. C.; Stevenson, B. C.; Baiamonte, V. L.; Marso, J. M.; Dannemiller, E. A.; Parker, Albert E.; Reddy, Shravanthi T.; Sande, M. K.
    Environmental contamination contributes to an estimated 20-40% of all hospitalacquiredinfections (HAI). Infection control practices continue to improve, butmultipronged approaches are necessary to fully combat the diversity of nosocomialpathogens and emerging multidrug resistant organisms. The Sharkletâ„¢ micropattern,inspired from the microtopography of shark skin, was recently shown to significantlyreduce surface contamination but has not been evaluated in a clinical setting. Thefocus of this study was the transfer of bacteria onto micropatterned surfaces comparedto unpatterned surfaces in a clinical simulation environment involving healthcarepractitioners. Physician volunteers were recruited to participate in an emergencymedicine scenario involving a contact-precaution patient with an acute pulmonaryembolism. Prior to scenario initiation, Staphylococcus aureus was inoculated onto theleg of a simulation mannequin and fresh micropatterned and unpatterned surfacefilms were placed on a code cart, cardiac defibrillator shock button, and epinephrinemedication vial. Six physicians interacted with micropatterned surfaces and fivephysicians interacted with unpatterned surfaces in separate scenarios. Bacterial loadloss from the first contact location (control film over the femoral pulse) to subsequentunpatterned or micropatterned surface test locations was quantified as a log reduction(LR) for each surface type.The code cart, cardiac defibrillator button, and medication vial locations withmicropatterned surfaces resulted in LRs that were larger than the unpatternedLRs by 0.64 (p=0.146), 1.14 (p=0.023), and 0.58 (p=0.083) respectively for eachlocation. The geometric mean CFU/RODAC at the first control surface touched at thefemoral pulse pads ranged from 175-250 CFU/RODAC (95% confidence interval).Thus, the micropatterned LRs were consistently greater than the unpatterned LRs,substantiating the micropattern-dependent reduction of microorganism transfer.Principal component analysis showed that the LRs for the code cart and the cardiacdefibrillator button highly covaried. Thus, a single mean LR was calculated fromthese two locations for each surface type; 5.4 times more bacteria attached to theunpatterned surfaces compared to the micropatterned surfaces (p = 0.058). Thesimulated clinical scenario involving healthcare practitioners demonstrated that themicropatterned surface reduced the transfer of bacterial contamination based onthe larger LRs for the micropatterned surface compared to control surfaces. Furtherinvestigation in hospital rooms where patients are receiving care will ultimately revealthe capability of micropatterned surfaces to minimize the incidence of HAIs.
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    Whole cell kinetics of ureolysis by Sporosarcina pasteurii
    (2015-06) Lauchnor, Ellen G.; Topp, D. M.; Cunningham, Alfred B.; Gerlach, Robin
    Aims Ureolysis drives microbially induced calcium carbonate precipitation (MICP). MICP models typically employ simplified urea hydrolysis kinetics that do not account for cell density, pH effect or product inhibition. Here, ureolysis rate studies with whole cells of Sporosarcina pasteurii aimed to determine the relationship between ureolysis rate and concentrations of (i) urea, (ii) cells, (iii) and (iv) pH (H+ activity). Methods and Results Batch ureolysis rate experiments were performed with suspended cells of S. pasteurii and one parameter was varied in each set of experiments. A Michaelis–Menten model for urea dependence was fitted to the rate data (R2 = 0·95) using a nonlinear mixed effects statistical model. The resulting half-saturation coefficient, Km, was 305 mmol l−1 and maximum rate constant, Vmax, was 200 mmol l−1 h−1. However, a first-order model with k1 = 0·35 h−1 fit the data better (R2 = 0·99) for urea concentrations up to 330 mmol l−1. Cell concentrations in the range tested (1 × 107–2 × 108 CFU ml−1) were linearly correlated with ureolysis rate (cell dependent = 6·4 × 10−9 mmol CFU−1 h−1). Conclusions Neither pH (6–9) nor ammonium concentrations up to 0·19 mol l−1 had significant effects on the ureolysis rate and are not necessary in kinetic modelling of ureolysis. Thus, we conclude that first-order kinetics with respect to urea and cell concentrations are likely sufficient to describe urea hydrolysis rates at most relevant concentrations. Significance and Impact of the Study These results can be used in simulations of ureolysis driven processes such as microbially induced mineral precipitation and they verify that under the stated conditions, a simplified first-order rate for ureolysis can be employed. The study shows that the kinetic models developed for enzyme kinetics of urease do not apply to whole cells of S. pasteurii.
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