All algal, fungal, and plant cells have walls. These cells with walls undergo expansive growth that can enlarge their volume by as much as 30,000 times their initial volume. Expansive growth is fundamental to the development of these cells and essential to producing growth responses to environment signals that enhance their survival. The cell wall is an exoskeleton that provides shape, physical support, and protection for these cells. However, the cell wall also represents an obstacle to expansive growth. The cell wall is a composite of networks of complex polysaccharides and proteins. Generally, the expanding cell wall is strong and varies in thickness (0.1-1.0 µm). During expansive growth, the cells must produce a significant force to stretch, or deform, their walls to
accommodate larger and larger volumes. All of these cells with walls produce the same force to deform their walls, pressure force. The pressure force produces stresses within the wall causing it to deform. These cells regulate the mechanical properties of their walls to control wall deformation and expansive growth. Experimental and theoretical investigations are beginning to elucidate the many biological, chemical, and physical processes involved in expansive growth and its regulation. This chapter presents conceptual and mathematical frameworks, or models, that are consistent with experimental evidence. These models are used to study and explore the underlying processes and mechanisms involved in expansive growth and regulation of expansive growth. 15.1 IntroductionPlant, algal, and fungal cells have engineered unique solutions to obstacles encountered in their microenvironment. A paramount and fundamental challenge for all cells is the acquisition of energy to run and maintain the many complex chemical and biological processes that are necessary to sustain, maintain, and procreate life. Plant and algal cells have developed and honed unique biological structures (e.g., chloroplasts) and unique chemical processes (e.g., photosynthesis) that capture and convert solar energy to chemical energy in the form of organic compounds that sustain essentially all life on earth. Also, plant and algal cells have developed chemical reactions that convert the carbon dioxide in the atmosphere to oxygen, a molecule that is required for all respiring cells. Fungal cells have developed chemical reactions that decompose complex organic compounds produced by respiring organisms so that the molecules of life can be recycled in photosynthesis and respiration.Another biological process that is unique to plant, algal, and fungal cells is expansive growth. Some plant, algal, and fungal cells can enlarge more than 30,000 times their initial volume (e.g., xylem vessels in plants) and achieve lengths of greater than 10 cm (e.g., fungal sporangiophores). Importantly expansive growth and its regulation are fundamental to development, morphogenesis, and environmental (sensory) responses of plant, algal and fungal cells.