Abstract
While pattern formation is studied in various areas of biology, little is known about the noise leading to variations between individual realizations of the pattern. One prominent example for de novo pattern formation in plants is the patterning of trichomes on Arabidopsis leaves, which involves genetic regulation and cell-to-cell communication. These processes are potentially variable due to, e.g., the abundance of cell components or environmental conditions. To elevate the understanding of regulatory processes underlying the pattern formation it is crucial to quantitatively analyze the variability in naturally occurring patterns. Here, we review recent approaches toward characterization of noise on trichome initiation. We present methods for the quantification of spatial patterns, which are the basis for data-driven mathematical modeling and enable the analysis of noise from different sources. Besides the insight gained on trichome formation, the examination of observed trichome patterns also shows that highly regulated biological processes can be substantially affected by variability.
Highlights
Some studies have been published that focus on models with a stochastic component, e.g., the stochastic Boolean network model for root hairs (Savage et al, 2008) or floral morphogenesis (Alvarez-Buylla et al, 2008) or noise in the initiation of new organs in phyllotaxis (Mirabet et al, 2012)
Others examine the effect of noise on patterning using stochastic differential equations (Sagués et al, 2007)
A rich tradition exists in studying the effect of noise on pattern formation using abstract sets of equations, only few studies from developmental biology can be found where the effect of intracellular noise and/or cell-to-cell variability on a developing pattern or structure was systematically taken into account (Little et al, 2013)
Summary
Mathematical modeling has been used to study various biological patterning processes, such as trichomes and root hairs (Savage et al, 2008; Benítez et al, 2011), cell sizes in sepals (Roeder et al, 2010), hair follicles (Sick et al, 2006), fruit fly development (Reeves et al, 2006), and other systems (Othmer et al, 2009; Peltier and Schaffer, 2010) It has only recently become more popular to investigate the variance or variability within a system and to discuss the consequences of noise (see Box 1) (Kærn et al, 2005; Swain and Longtin, 2006; Maheshri and O’Shea, 2007; Wilkinson, 2009; Sánchez et al, 2013). Statistical methods are needed which are suitable for the available type and amount of data and the studied system
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