Models to reconcile plant science and stochasticity

Plants are modular organisms that exhibit diverse adaptations to variability. This variability can be intrinsic in nature, as in the case of cell shape or division plane stochasticity, protein distribution in a cell, variations in internal mechanical properties etc. . . (Altschuler et al., 2008; Besson and Dumais, 2011). It can also be extrinsic, as with variations in environmental conditions at different time scales (Wolpert et al., 1998; Sultan, 2000; Franklin, 2009; Leyser and Day, 2009). When it comes to rationalizing data acquisition and interpretation, one has the tendency to define what part of the variability is arguably unhelpful stochasticity and what part does in fact contain meaningful information. Systems biology, which combines methodologies from various disciplines, can be used to understand the mechanisms of development. For example, complex network analysis (Lucas et al., 2011), computer simulations (Band et al., 2012) or physical measurements through atomic force microscopy (Milani et al., 2014) can be combined with biological experiments. For instance, such an approach has been able to produce reasonable explanations for how patterning at the meristem level can lead to the stem structure (Prusinkiewicz et al., 1995). Stochasticity in models as a variable or as a methodological tool has been a subject of interest for many years in physics and mathematics (Saguès et al., 2007; Friedrich et al., 2011; Wilkinson, 2011). Studies have already been published in biology but only a few focused on plant development, and are often more recent (for a review of this aspect, see Meyer and Roeder, 2014). Along with a better understanding of growth processes, those studies have also illustrated how our vision of stochasticity was previously too derogatory (Kliebenstein, 2012). Those new methodologies illustrate how stochasticity can be both a consequence and an origin of core mechanisms in development. Here we use specific examples to illustrate how mathematical or computational models are well-suited to the study of stochasticity in plant functions. Moreover, models enable the use of measured phenotypic stochasticity at multiple scales to elucidate the underlying processes. We suggest that models used for such purposes do not need to be overly complex, and various complex models of the same process will in fact converge toward similar conclusions. We will focus our attention on apical meristems and the growth that they generate, where cell–cell interactions underlie the emergence of various interesting properties of the tissues and organs.