AUTHOR=Amirian Mohammad M. , Irwin Andrew J. , Finkel Zoe V. 

TITLE=Extending the Monod model of microbal growth with memory

JOURNAL=Frontiers in Marine Science

VOLUME=9

YEAR=2022

URL=https://www.frontiersin.org/journals/marine-science/articles/10.3389/fmars.2022.963734

DOI=10.3389/fmars.2022.963734

ISSN=2296-7745

ABSTRACT=<p>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 (<italic>T. pseudonana</italic> and <italic>T. weissflogii</italic>) and prasinophytes (<italic>Micromonas</italic> sp. and <italic>O. tauri</italic>), 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.</p>