Trends in Plant Science
Volume 14, Issue 9, September 2009, Pages 467-478
Journal home page for Trends in Plant Science

Review
Feature Review
Mechanics and modeling of plant cell growth

https://doi.org/10.1016/j.tplants.2009.07.006Get rights and content

Cellular expansive growth is one of the foundations of morphogenesis. In plant and fungal cells, expansive growth is ultimately determined by manipulating the mechanics of the cell wall. Therefore, theoretical and biophysical descriptions of cellular growth processes focus on mathematical models of cell wall biomechanical responses to tensile stresses, produced by the turgor pressure. To capture and explain the biological processes they describe, mathematical models need quantitative information on relevant biophysical parameters, geometry and cellular structure. The increased use of mechanical modeling approaches in plant and fungal cell biology emphasizes the need for the concerted development of both disciplines and underlines the obligation of biologists to understand basic biophysical principles.

Section snippets

Mechanical aspects of plant and fungal cell growth

Plant development is the result of three essential processes: cell expansive growth, cell division and cellular differentiation. All three processes have key mechanical aspects that have prompted numerous attempts to generate theoretical, mechanical and biophysical models. In this review, we will focus on cellular expansive growth in walled cells typical for plants, algae and fungi. Given that walled cells rarely migrate, cell expansive growth contributes in dramatic manner to the generation of

Biophysical equations describing cell wall mechanics and expansive growth

To model and predict the inherently mechanical process of cell expansive growth, equations have been derived for the underlying physical processes and coupled to the relevant biological processes with biophysical variables, thereby forming biophysical equations [10]. In the case of the expansive growth of cells with walls, two relevant physical processes are the net rate of water uptake and rate of cell wall deformation, which occurs in response to the cell wall stresses produced by the turgor

Molecular models and the molecular interpretation of biophysical variables

Conceptually, growing (primary) cell walls of algal, fungal and plant cells can be viewed as being composed of a network of microfibrils cross-linked by tethers and embedded into a somewhat amorphous matrix of cell wall materials. Generally, microfibrils are synthesized in the plasma membrane, whereas matrix materials are transported from cellular organelles to the plasma membrane and released to the inner cell wall via exocytosis. The molecular mechanisms by which cell wall materials are

Quantification of physical parameters at cellular level

To supply mathematical models with relevant and accurate input, quantitative values for a number of physical parameters need to be provided. Although educated guesses are often the only recourse, valuable quantitative information is becoming increasingly available by applying various biomechanical and cytomechanical techniques 34, 35, 36. The two central and measurable quantities involved in algal, fungal and plant cell growth are cell wall deformability and hydrostatic pressure. In terms of

Mechanics of anisotropic plant cell growth: the microtubule–cellulose connection

Differentiated plant cells range from simple cylindrical cells (e.g. palisade mesophyll) to star-shaped complex structures (e.g. astrosclereids) 37, 38. The fact that even these complex shapes are determined by the cell wall can easily be demonstrated by enzymatic digestion of the latter resulting in a perfectly spherical protoplast. Because hydrostatic pressure always produces a force perpendicular to the entire surface confining the pressurized compartment the generation of complex geometries

Heterotropic growth behavior

Cellulose-mediated anisotropy in the deformability of the cell wall is generally associated with overall anisotropic cellular expansion. Approximately spherical or polyhedric cells derived from the apical meristem elongate by anisotropic deformation of large portions of their surface. Typically, cells that have differentiated through this mechanism have no sharp concave bends in their surface. Numerous cell types, however, do have such concave bends or exhibit other types of complex geometries.

Single cell mechanics versus tissues

Although individually growing algal cells (internodes, rhizoids), fungal cells (hyphae, sporangiophores) and plant cells (pollen tubes, root hairs, trichomes, moss protonemata) do exist both in nature and in vitro (suspension culture cells), most growth activities in plant cells occur within the context of a tissue. To understand the mechanics of a plant tissue or organ and model their behavior, important additional parameters need to be taken into consideration. These include the connection

Conclusions

Cells must obey the laws of physics; therefore, understanding cell mechanics is fundamental to understanding and explaining growth processes leading to morphogenesis. Theoretical modeling of the mechanical and physical foundations using biophysical variables to couple physical and biological processes has provided a better understanding of growth processes. Future modeling approaches should focus on the relationships between physical and biological processes, incorporating the increasing

Acknowledgements

J.K.E. Ortega acknowledges funding by the National Science Foundation Grant MCB-0640542. A. Geitmann received funding from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT) and the Human Frontier Science Program (HFSP). We are grateful to Firas Bou Daher for assistance on nomenclature issues.

Glossary

Anisotropic material
A material whose properties differ in different directions.
Creep test
The time-dependent strain or extension behavior of a material in response to constant stress.
Elastic material
Material that immediately returns to its original shape after removal of the deforming load or stress.
Isotropic material
A material whose properties are identical in all directions.
Plastic material
Material that retains its deformed shape after the deforming load, or stress, is removed.
Relaxation test
A

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