Test for the Presence of Autocorrelation in the Gompertz Model used in the Fitting of the Growth of E. coli Measured using a Real-time Impedimetric Biosensor

Abstract

Biosensor for measuring bacterial concentrations for use biotechnology and the health scienceswould allow a rapid, robust and sensitive real-time monitoring of bacteria. Kim et al [1] hasdeveloped such a method using impedance spectroscopy, and was able to measure in real-timethe concentration of E. coli at 0.01 MHz frequency using impedance changes. We modeled thegrowth kinetics using several nonlinear regression methods and discovered that the modifiedGompertz model is the best model for the growth of the bacterium [2]. Bacterial growth curvesare time-dependent series model and the use of nonlinear regression method relies heavily on theassumption that the residuals must not show autocorrelation. If this assumption is satisfied thanthe test is said to be robust. In this work we perform statistical diagnosis test to test for thepresence of autocorrelation in this model and found out its absence suggesting that the model isrobust enough and adequate.