Mathematical Models for Expansive Growth of Cells with Walls

Bioengineering Laboratory, Department of Mechanical Engineering, University of Colorado Denver, Colorado 80217-3364 USA

^⋆ Corresponding author. E-mail: joseph.ortega@ucdenver.edu

Abstract

Plants, algae, and fungi are essential for nearly all life on earth. Through photosynthesis, plants and algae convert solar energy to chemical energy in the form of organic compounds that sustains essentially all life on earth. In addition, plants and algae convert the carbon dioxide produced by respiring organisms to oxygen that is needed for respiration. Fungi decompose complex organic compounds produced by respiring organisms so that molecules can be recycled in photosynthesis and respiration. Plants, algae, and fungi have one important feature in common, their cells have walls. Expansive growth and its regulation are central to the life and development of plant, algal, and fungal cells, i.e. cells with walls. In recent decades there has been an explosion of information relevant to expansive growth of cells with walls. Mathematical models have been constructed in an attempt to organize and evaluate this information, to gain insight, to evaluate hypotheses, and to assist in the selection and development of new experimental studies. In this article some of the mathematical models constructed to study expansive growth of cells with walls are reviewed. It is nearly impossible to review all relevant research conducted in this area. Instead, the review focuses on the development of mathematical equations that have been used to model expansive growth, morphogenesis, and growth rate regulation of cells with walls. Also, relevant experimental findings are reviewed, conceptual models are presented, and suggestions for future research are proposed. The authors have attempted to provide an overview that is accessible to researchers that are not working in this field.