Background: Online measurement technique with Carbon Nuclear Magnetic Resonance (13C-NMR) spectroscopy enables the researcher to collect high quality biological time series data. The resulting data contains more information than snapshop data. It can potentially be used to make comparisons between molecular profiles of perturbed cells and controls which have vastly extended the understanding of healthy and pathological functioning of cells. Despite this promise, biological data are sparse, which immediately creates statistical challenges that have not been addressed in a systematic fashion. In this work, we propose sound statistical methods for assessing the significance of differences between relatively sparse biological time series data. In this research we analyze in vivo NMR time series measurements in baker’s yeast Saccharomyces cerevisiae. In particular, we investigate the effect of temperature on the rate of change of glucose concentration with respect to time.
Biological Methods: Six strains of Saccharomyces cerevisiae JK93dα cells were grown until an OD600 of 2 in G0 minimal medium supplemented with 0.2% yeast extract, in a 5-liter fermentor, corresponding to normal conditions. For heat stress conditions, the cells were grown under control conditions until an OD600 of approximately 1.3; at this point the temperature was increased to 39ºC and the cells allowed to grow for a further 40 min to a final OD600 of 2. Cells were harvested, centrifuged, washed and re-suspended in 50 mM KPi buffer containing 6 % (v/v) 2H2O and antifoam agent. The cell suspension was transferred to an 80-mL fermentor, maintained at 30ºC, and connected to a 10-mm NMR tube by a circulating system The culture was pumped through the NMR tube at a rate of 30 mL/min and the pH was maintained at 6.5 by automatic addition of NaOH or HCl. At time zero, [1â€‘13C]glucose was added and the glucose concentration monitored by 13C-NMR until substrate depletion, with a time resolution of 30 sec. Afterwards, the temperature was raised to 39°C, and a second pulse of glucose was added. Once glucose was exhausted, the temperature was set back to 30°C and a third pulse of glucose supplied. Glucose concentration monitored by 13C-NMR until substrate depletion, with a time resolution of 30 sec.
Statistical Methods: The rate of change of glucose concentration for the six strains of Saccharomyces cerevisiae JK93dα cells were recorded for equal intervals of time 0.5min apart for the three temperature conditions, namely: normal (30ºC), heat stress (39ºC), and recovery (30ºC). The data points were plotted for each temperature with experiment type considered as the grouping factor, from which we speculated that nonlinear mixed effects regression model would fit the data. The data was eventually fit to three nonlinear mixed effects models to select the best model based on the model building process proposed by Pinheiro and Bates (2004). Parameters of the best model fit were estimated by maximum likelihood estimation method. We then test the overall effect of temperature on the rate of change of glucose concentration (represented through the best model) by the ANOVA method. We also perform the pairwise analyses for the three different temperatures.
Results: Of the three models selected, the three-parameter logistic model turned out to be the best model with highly significant and stable parameter estimates. Results also show that, overall, temperature significantly affects the rate of glucose concentration with respect to time at the 5% significance level. For the three temperature conditions; normal, heat stress and recovery, all pairwise comparisons were found to be significant at the 5% significant level implying that each temperature affects the rate of glucose concentration with respect to time differently from the other.Public Link: http://fm.ocrss.louisville.edu/clients/hscro/conspectus/searchview.php?ID=2055