Application of the Method of Steepest Ascent to the Response Surface of the Nitrate-Nitrite Reductase Activity in Salivary Sediment

¹ Biostatistical Unit, University of Oklahoma School of Medicine, and the Dental Section, Oklahoma Medical Research Institute, Oklahoma City, Oklahoma

A study was undertaken to determine the optimum conditions for, and interrelations of, temperature, pH, and concentration of electron donor on the rate of nitrate reduction by the nitrate-nitrite reductase systems in a pooled sample of salivary sediment. By varying the conditions of pH, temperature, and electron donor concentration (yeast extract), the minimum reduction time was established in four sequential sets of experiments. The method employed was that of steepest ascent, which consisted of two phases: first, the establishment of the response surface and the conditions for the optimum and, second, the calculation of the associated contour lines. Three linear approximations of the response surface and their subsequent paths of steepest ascent were utilized in locating the near-optimal region. A fourth and final linear approximation was augmented by additional experimental points such that the property of rotatability was preserved and a second-order approximation of the response surface possible. This method permitted the calculation of the response surface from a much smaller number of experiments than would have been necessary with a complete factorial experiment or by the single-factor method. It also provided the opportunity for the recognition of possible interactions between the variables. While the three variables examined were found to influence the enzyme activity, temperature contributed the predominating influence above pH 6.0 and electron donor concentration of 0.7 mg/ml. Through the utilization of the determined response surface, the estimated optimal conditions were found to be pH, 6.98; temperature, 45.9° C.; and electron donor concentration (yeast extract), 0.97 mg/ml. The basis for the construction of the design for the study was discussed and the details of the statistical analysis presented.