Biomechanics of anther opening
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Many influential papers are published each year on the fundamental role that genetics plays in plant growth and development. However, despite the beautifully written and illustrated On Growth and Form by D'Arcy Wentworth Thompson (1917) being published nearly 100 years ago, it could be argued that the role of physics during developmental processes is still a somewhat neglected field. Yet genetic processes do not happen in isolation, and it is the complex interplay between genetics, physics and the environment that is the true backdrop against which these processes occur (Niklas, 1992). It is therefore especially welcome to read ‘A biomechanical model of anther opening reveals the roles of dehydration and secondary thickening’ by Nelson et al. in this issue of New Phytologist (pp. 1030–1037), where an elegantly simple mathematical formulation of anther opening illustrates how these three factors act together during the vital process. Not only does this paper highlight the importance of biophysical processes, it further highlights the importance and power of theoretical approaches to biological problems.
‘The mechanism, as well as the mathematical model itself, is comparatively simple, yet it is compelling to note that it is able to closely capture the true geometry of an opening anther.’
The anther is a crucial part of the stamen containing the microsporangia. Anthers are commonly two lobed and attached to the filament portion of the stamen. The correct timing of pollen release is clearly vital to maximizing reproductive success, and this timing is regulated in part by the development of pollen grains and in part by the dehiscence (opening) of the anther (Bonner & Dickinson, 1989). Anther opening occurs through a complex interplay between biological processes, such as cell differentiation, and physical processes, such as cell wall thickening in the endothecium (D'Arcy & Keating, 1996). The process is facilitated by enzymatic digestion, anisotropic growth and dehydration. These processes combined generate tensile stresses and cause tissue breaking and opening.
As well as being of interest scientifically, it is important both economically and agriculturally that we gain a thorough understanding of anther opening. Even short periods of elevated temperature may strongly influence the fertility of many plant species. For example, within rice, dehiscence of the anther is disrupted by air temperatures above 33°C (Satake & Yoshida, 1978). Mean diurnal temperatures of 35°C can cause zero yields in rice, and the same has also been predicted for maize. Many other examples exist where agricultural yields can be severely compromised by the disruption of anther opening in tough environmental conditions.
A vital first step to the creation of crops more tolerant to adverse climates is a thorough understanding of the processes involved. In the case of anther opening, this requires the study of the system's genetics and mechanics, and, more importantly, the study of how these two paradigms interact.
The study group system
Before talking about some of the scientific highlights of the paper, it is worth commenting on the interesting history behind the development of the paper. The paper was initiated during the fourth Study Group on Mathematics in the Plant Sciences, held at the University of Nottingham in January 2011. The study group is based on the highly successful industrial study groups that have been a feature of the UK applied mathematics community for decades, and it is expertly organized by the Centre for Plant Integrative Biology (CPIB).
The format of the study group is as follows. A small group (typically five) of experimental biologists begin the week by each presenting a different problem that is central to their field of study, where they feel progress might be made by taking a mathematical approach. For the rest of the week, the theoreticians split up into groups to see what progress they can make, presenting their results at the end and writing a subsequent report.
There are a number of attractive features to this sort of conference. First, it allows scientists and mathematicians with a wide range of experience to see how their peers might tackle problems when encountering them for the first time. Second, it highlights the wide variety of problems in the plant sciences that are suitable for mathematical modelling and where significant progress can be made in a short time (and, of course, the most fruitful problems may yield new collaborations, grants and scientific papers). Nelson et al.'s article is an excellent example of the latter.
Development of the model
Due to the importance of anther opening both scientifically and agriculturally, it is perhaps surprising that this is the first theoretical model of opening that has been presented. The authors proceed by considering a simplified two-dimensional case and neglect variation along the axis. The anther itself is modelled as a bilayer consisting of the endothecium and epidermis. The process of dehydration, which is instrumental in the initiation of dehiscence, is represented as a reduction in the natural length of the epidermis alone. The endothecium and epidermis are not able to slip with respect to each other, and so differential contraction results in an anther geometry that is dependent upon the natural length of the epidermis. From this, the authors are able to predict the likely two-dimensional geometry of the anther as a function of dehydration. This is also combined with secondary thickening of the cell wall (Dawson et al., 1999), which is also modelled in the paper. The mechanism, as well as the mathematical model itself, is comparatively simple, yet it is compelling to note that it is able to closely capture the true geometry of an opening anther. The whole model is described by a family of eight parameters, with five of the eight experimentally measured in previous work.
Highlights of the model and its future impact
A key result for the paper is the suggestion that epidermal dehydration alone can be sufficient to create the transition from a closed to an open anther, with good qualitative agreement to the observed intermediate geometries. This puts anther opening on a similar footing to other mechanisms which have already been suggested, such as the formation of pine cone scales (Dawson et al., 1997) and wheat awns (Elbaum et al., 2007). A further interesting observation is the apparent importance of biological bilayer systems, and experimental work confirms the central importance of the bilayer to this process.
An obvious but certainly non-trivial extension to this work would be to consider the full three-dimensional problem by relaxing the assumption that the material properties and geometry do not change along the axis. A number of authors have already considered these sorts of models for a variety of other systems, and the general approach consists of a numerically intensive simulation of the elastomechanics. (Gladilin et al., 2007).
The future of biophysical modelling
Nelson et al.'s paper is a compelling example of the insights that can be gained when elegantly simple mathematical models can be brought to bear on important problems in plant biology. It is likely to become increasingly important to high-impact plant sciences that coupling between scales (cell, tissue, organ, organism and population), approaches (genetic, physical and environmental) and disciplines (experimental, mathematical and computational) must be considered. The plant study groups organized at CPIB, as well as Nelson et al.'s article, are an excellent example of the progress that can be made when these approaches are combined. It is important that in the future we are not only working in interdisciplinary teams, but training the next generation of scientists to be interdisciplinary individuals who are equally at home with both theoretical and experimental biology.