Extending the Monod Model of Microbial Growth with Memory

TL;DR

This paper introduces a memory-augmented extension to the Monod model of microbial growth, capturing historical resource effects with fewer variables, validated against empirical data, and offering computational advantages for ecological modeling.

Contribution

The paper develops a Monod model extension incorporating memory effects using fractional calculus, reducing complexity while maintaining accuracy in growth predictions.

Findings

The Monod-memory model accurately estimates growth rate and cell density.

It performs comparably to the Droop model with fewer variables.

Validated with empirical data from diverse phytoplankton species.

Abstract

Monod's model describes the growth of microorganisms using a hyperbolic function of extracellular resource concentration. Under fluctuating or limited resource concentrations this model performs poorly against experimental data, motivating the more complex Droop model with a time-varying internal storage pool. We extend the Monod model to incorporate memory of past conditions, adding a single parameter motivated by a fractional calculus analysis. We show how to interpret the memory element in a biological context and describe its connection to a resource storage pool. Under nitrogen starvation at non-equilibrium conditions, we validate the model with simulations and empirical data obtained from lab cultures of diatoms (T. pseudonana and T. weissflogii) and prasinophytes (Micromonas sp. and O. tauri), globally influential phytoplankton taxa. Using statistical analysis, we show that our Monod-memory model estimates the growth rate, cell density, and resource concentration as well as the Droop model while requiring one less state variable. Our simple model may improve descriptions of phytoplankton dynamics in complex earth system models at a lower computational cost than is presently achievable.