A modified Gompertz model and its MATLAB implementation for microbial growth performance assessment

Abstract

To systematically assess the growth performance of different methanotrophs, microalgae and their cocultures, this work presents an improved four-parameter Zwietering modification of the Gompertz model (4Z model) to extract biologically relevant information using batch growth data. The 4Z model was based on the three-parameter Zwietering modification of the original Gompertz model, with a constant term added to address the discrepancy between model predictions and measurements for the initial period of growth data. The 4Z model provided excellent fits to the batch growth data of different monocultures and cocultures. However, the parameters in the 4Z model are different from the commonly used maximum growth rate and delay time, making interpretation of the results challenging. To facilitate the assessment of different strains, we follow the two-step procedure to extract biologically significant parameters:

1. Estimate the four parameters in the 4Z model using the whole batch growth trajectory.

2. Use the 4Z model prediction of early-stage growth data to estimate the biologically significant parameters in the commonly used exponential growth model.

The estimated biologically significant parameters (maximum growth rate, delay time, and carrying capacity) enabled an unbiased assessment of different strains.