A stochastic multicellular model identifies biological watermarks from disorders in self-organized patterns of phyllotaxis.

Yassin Refahi,Minna Pulkkinen,Géraldine Brunoud,Teva Vernoux,Alain Jean-Marie,Christophe Godin,Etienne Farcot

doi:10.7554/elife.14093

Abstract

Exploration of developmental mechanisms classically relies on analysis of pattern regularities. Whether disorders induced by biological noise may carry information on building principles of developmental systems is an important debated question. Here, we addressed theoretically this question using phyllotaxis, the geometric arrangement of plant aerial organs, as a model system. Phyllotaxis arises from reiterative organogenesis driven by lateral inhibitions at the shoot apex. Motivated by recurrent observations of disorders in phyllotaxis patterns, we revisited in depth the classical deterministic view of phyllotaxis. We developed a stochastic model of primordia initiation at the shoot apex, integrating locality and stochasticity in the patterning system. This stochastic model recapitulates phyllotactic patterns, both regular and irregular, and makes quantitative predictions on the nature of disorders arising from noise. We further show that disorders in phyllotaxis instruct us on the parameters governing phyllotaxis dynamics, thus that disorders can reveal biological watermarks of developmental systems.

Highlights

Developmental systems strikingly produce regular patterns and analysis of eukaryote development has classically been focused on regularities as the main source of information to understand these complex systems
We demonstrate that disorders in phyllotactic patterns instruct us on the parameters governing the dynamics of phyllotaxis
As permutations have been notably reported in Arabidopsis (Besnard et al, 2014; Guedon et al, 2013; Landrein et al, 2015; Refahi et al, 2011) and in sunflower (Couder, 1998), we sampled a variety of unrelated species in the wild and searched for permutations

Summary

Introduction

Developmental systems strikingly produce regular patterns and analysis of eukaryote development has classically been focused on regularities as the main source of information to understand these complex systems. It is becoming increasingly evident that intrinsic molecular noise is an inherent property of biological systems (Elowitz et al, 2002; Kupiec, 1997; Lander, 2011) (Itoh et al, 2000) In this case, disorders observed during development could be informative on the origin of noise and on the underlying developmental mechanisms that propagate the noise. Disorders observed during development could be informative on the origin of noise and on the underlying developmental mechanisms that propagate the noise We address this question theoretically using phyllotaxis, the remarkably regular geometric organization of plant aerial organs (such as leaves and flowers) along the stem, as a model system (Appendix section 1). Rooted in early works of pioneers such as (Bonnet, 1754; Braun, 1831; Bravais and Bravais, 1837) and after decades of research, the idea that

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