Preface

Historically, mathematical models have been essential to understand plant physiology [12]. They provided rules that could be applied to predict crop growth and yield in the field, made farm management more efficient and helped to increase productivity. For example, the ‘law of minimum’ proposed by Liebig in 1840, states that crop yield is limited by the availability of a most deficient nutrient. Farmers would then simply need to identify requirements for each nutrient in order to obtain optimal yield. Liebig’s law formalised plant requirements in a simple and quantitative fashion and allowed generations of farmers to optimise the application of fertilisers. Unfortunately, complex biological functions of plants cannot be described as a superposition of independent environmental effects in the way Liebig described plant nutrition. Plants possess complex self-organised molecular machineries and exhibit a wide range of responses. For example, sensing proteins in root apical meristems are involved in the detection of nutrients and cascades of signals are triggered to stimulate lateral root proliferation in nutrient patches [13, 21]. Although shoot architectures follow more predictable growth patterns, e.g. phyllotactic arrangement of leaves, they also arise from multiple interactions and feedbacks between cells, tissues and organs [24]. Flowering time in a plant, for example, results from subtle interactions between circadian clock genes regulating day-night sensing and the physiology of photosynthesis and carbon allocation [8]. Early computational biologists understood the limitations of classical agronomic and physiological modelling and initiated alternative approaches. Lindenmayer, a botanist interested in growth patterns of algae and trees, proposed in 1968 a framework named ‘L-systems’ to formalise rules for the development of plant architectures [30]. It became possible to model interactions between plant architecture and the environment, a concept now termed ‘Functional Structural Plant Models’ [14, 16]. In 1969 Korn also noticed that since plant growth and functions are determined by individual cells, the cellular structures of a tissue must be incorporated [25]. In his first model, Korn described the development of a plant tissue from a simple stochastic cell cycle model. The field of plant modelling has grown considerably over the last decades and the concepts of Korn and Lindenmayer evolved. Architectural models now incorporate plant physiology explicitly and are combined with models of the environment to account for, e.g. nutrient transport in soil and light interception [7, 9]. New computational cellular models are able to simulate thousands of cells [34], and include autonomous genetic regulatory networks, the sensing and response to hormonal signals as well as turgor pressure driven expansion [10,20]. Modelling languages such as the ‘Systems Biology Markup Language’ have been developed to model metabolic pathways [31]. Because plants are immobile they must be able to sense their environment and adapt to numerous external cues. Responses to environmental signals are actioned at the cell level, where biological processes are broken down into chains and networks of biochemical reactions. Long range signals between cells are also required to coordinate activities. Signalling molecules, named hormones, are produced and