The Mathematical Biology of Diatoms

5Mathematical Basis for Diatom Growth Modeling

Dariush Sardari

Department of Medical Radiation Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

Abstract

A physical-mathematical perspective on population growth of diatoms is presented. Depending on the conceptual needs, biomolecular interpretations are invoked. Beginning with the simple exponential growth of population, the mathematical approach is carried out on differential equations with time-varying coefficients. With decreasing growth rate coefficient, population reaches saturation at its maximum. There are various magnitudes of growth rate corresponding to different sizes of diatoms. Taking into consideration nutrient uptake and metabolism as well as internal structures and phenomena of diatoms, models with different degrees of complexity have been developed with their outlooks presented here. Monod and Michaelis-Menten models are mostly based on kinetics of growth and nutrient uptake. Droop, Aquaphy, and mechanistic models consider internal cell structure and go beyond to enzymatic and molecular reaction phenomena.

Keywords: Marine biology, cell modeling, diatom growth, mathematical models, differential equations

5.1 Introduction

Diatoms are single cell algae that are surrounded by a cell wall made of silica (hydrated silicon dioxide). The diameter in various types of diatoms ranges from 1 to 200 µm [5.25] [5.46]. Diatoms can divide more rapidly than other phytoplanktons. During their physiologic ...