Mathematical Sciences

Permanent URI for this communityhttps://scholarworks.montana.edu/handle/1/48

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.

Browse

Author: search.filters.author.Gerlach, Robin

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    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.
  • Thumbnail Image
    Item
    Estimation of a biofilm-specific reaction rate: kinetics of bacterial urea hydrolysis in a biofilm
    (2015-09) Connolly, James M.; Jackson, Benjamin; Rothman, Adam P.; Klapper, Isaac; Gerlach, Robin
    Background/Objectives: Biofilms and specifically urea-hydrolysing biofilms are of interest to the medical community (for example, urinary tract infections), scientists and engineers (for example, microbially induced carbonate precipitation). To appropriately model these systems, biofilm-specific reaction rates are required. A simple method for determining biofilm-specific reaction rates is described and applied to a urea-hydrolysing biofilm. Methods: Biofilms were grown in small silicon tubes and influent and effluent urea concentrations were determined. Immediately after sampling, the tubes were thin sectioned to estimate the biofilm thickness profile along the length of the tube. Urea concentration and biofilm thickness data were used to construct an inverse model for the estimation of the urea hydrolysis rate. Results/Conclusions: It was found that urea hydrolysis in Escherichia coli MJK2 biofilms is well approximated by first-order kinetics between urea concentrations of 0.003 and 0.221 mol/l (0.186 and 13.3 g/l). The first-order rate coefficient (k1) was estimated to be 23.2±6.2 h−1. It was also determined that advection dominated the experimental system rather than diffusion, and that urea hydrolysis within the biofilms was not limited by diffusive transport. Beyond the specific urea-hydrolysing biofilm discussed in this work, the method has the potential for wide application in cases where biofilm-specific rates must be determined.
Copyright (c) 2002-2022, LYRASIS. All rights reserved.