IntroductionUnlike monocots and dicots, many conifers, particularlyPinaceae, form three or more cotyledons. These are arranged in a whorl, or ring, at a particular distance from the embryo tip, with cotyledons evenly spaced within the ring. The number of cotyledons,nc, varies substantially within species, both in clonal cultures and in seed embryos.ncvariability reflects embryo size variability, with larger diameter embryos having highernc. Correcting for growth during embryo development, we extract values for the whorl radius at eachnc. This radius, corresponding to the spatial pattern of cotyledon differentiation factors, varies over three-fold for the naturally observed range ofnc. The current work focuses on factors in the patterning mechanism that could produce such a broad variability in whorl radius. Molecularly, work inArabidopsishas shown that the initiation zone for leaf primordia occurs at a minimum between inhibitor zones of HD-ZIP III at the shoot apical meristem (SAM) tip and KANADI (KAN) encircling this farther from the tip. PIN1-auxin dynamics within this uninhibited ring form auxin maxima, specifying primordia initiation sites. A similar mechanism is indicated in conifer embryos by effects on cotyledon formation with overexpression of HD-ZIP III inhibitors and by interference with PIN1-auxin patterning.MethodsWe develop a mathematical model for HD-ZIP III/KAN spatial localization and use this to characterize the molecular regulation that could generate (a) the three-fold whorl radius variation (and associatedncvariability) observed in conifer cotyledon development, and (b) the HD-ZIP III and KAN shifts induced experimentally in conifer embryos and inArabidopsis.ResultsThis quantitative framework indicates the sensitivity of mechanism components for positioning lateral organs closer to or farther from the tip. Positional shifting is most readily driven by changes to the extent of upstream (meristematic) patterning and changes in HD-ZIP III/KAN mutual inhibition, and less efficiently driven by changes in upstream dosage or the activation of HD-ZIP III. Sharper expression boundaries can also be more resistant to shifting than shallower expression boundaries.DiscussionThe strong variability seen in conifernc(commonly from 2 to 10) may reflect a freer variation in regulatory interactions, whereas monocot (nc= 1) and dicot (nc= 2) development may require tighter control of such variation. These results provide direction for future quantitative experiments on the positional control of lateral organ initiation, and consequently on plant phyllotaxy and architecture.