Evaluation of expected absolute error affecting the maximum specific growth rate for random relative error of cell concentration

Abstract

Borzani's [(1994) World Journal of Microbiology and Biotechnology10, 475–476] idea of evaluation of absolute error affecting the 'maximum specific growth rate' (ESGR), calculated on the basis of the first and the last time points of the entire experimental time period, is generalized to the real-life situations where the relative errors of cell concentration cannot be assumed to be constant during the experiment. Visualizing the entire experimental time period as to comprise of several successive, mutually exclusive and exhaustive time intervals, we compute specific growth rates (SGRs) for each of these time intervals. Defining maximum of these SGR values as MSGR in contrast to Borzani's ESGR our aim is to study the effect of the expected absolute error on SGRs of different intervals. This will reveal the discrepancy between the true and observed MSGRs. Assuming the relative error distribution on (0,1) to be rectangular and symmetric truncated normal with mean at 0.5 and suitable variance, the expected values of the absolute errors are evaluated and numerically tabulated using the software packages MATHEMATICA and S-PLUS. Our results thus hold for situations involving varying relative errors where Borzani's results cannot be applied. A discussion with a concrete numerical example on the misidentification of the MSGR interval due to the effect of the random relative measuremental errors reveals to an experimental biologist that ignorance of this fact may lead to his/her entire experiment being futile.