P98: Utilization of the Maclaurin series as a Novel Approach to Determine Microbial Kinetics

The Maclaurin series is a form of the Taylor expansion series that involves the convergence of functions centered around zero. In this study, the quadratic expression on the right hand side of the logistic equation is modified with an appropriate Maclaurin series to model the microbial growth, as shown in Equation (1). The Maclaurin series is constructed by using two parameters relating to microbial kinetics, the specific rate of increase r and the maximum measured value M of all the signal values P(t).

This series converges when P is less than or equal to M/2. With additional calculations, the series applies to data sets outside of these conditions, to include all logistic and semi-logistic data. To make calculations of specific rates much simpler and precise, the expanded form was condensed into the closed form (Equation (2)):

                                                                                           (2) 

When the series' approximations of rate were compared to those of the graphical method, the resultant differences between the two methods always fell within 10%. Experimental data for this study was obtained by culturing Photorhabdus luminescens in a synthetic medium under various conditions utilizing a Sartorius stedim Biostat^® A plus fermentation system.