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

Loyal Murphy1, Q Peter He1, Jin Wang1

  • 1Auburn University, Department of Chemical Engineering, Auburn, AL, 36849, USA.

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|October 13, 2025
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Summary

This study introduces an enhanced Gompertz model (4Z model) for analyzing microbial growth, specifically methanotrophs and microalgae. The model accurately predicts growth and extracts key biological parameters for strain assessment.

Keywords:
Gompertz modelMethanotrophsMethanotrophs – microalgae cocultureMicroalgaeMicrobial batch growth

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Area of Science:

  • Microbiology
  • Biotechnology
  • Mathematical Modeling

Background:

  • Accurate assessment of microbial growth is crucial for optimizing bioprocesses.
  • Traditional models may not fully capture initial growth phases.
  • Differentiating performance of methanotrophs and microalgae requires robust analytical tools.

Purpose of the Study:

  • To present an improved four-parameter Zwietering modification of the Gompertz model (4Z model).
  • To extract biologically relevant parameters from batch growth data of methanotrophs and microalgae.
  • To facilitate unbiased assessment of different microbial strains and cocultures.

Main Methods:

  • Application of the 4Z model to batch growth data of monocultures and cocultures.
  • A two-step procedure to extract biologically significant parameters.
  • Estimation of maximum growth rate, delay time, and carrying capacity.

Main Results:

  • The 4Z model demonstrated excellent fits to diverse batch growth data.
  • A novel method was developed to derive standard growth parameters from the 4Z model.
  • Biologically significant parameters were successfully extracted for unbiased strain comparison.

Conclusions:

  • The 4Z model offers a robust approach for analyzing microbial growth dynamics.
  • The developed two-step procedure enables accurate extraction of key biological parameters.
  • This methodology facilitates the systematic assessment and comparison of methanotrophs and microalgae growth performance.