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This article was submitted to Plant Biophysics and Modeling, a section of the journal Frontiers in Plant Science

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The maize (

The maize (

Recent investigations of maize meristem morphology as a quantitative trait incorporated small numbers of descriptive measurements approximating SAM shape and size for genome-wide association studies (GWAS) and quantitative trait locus (QTL) mapping (

Progress toward the description of complex shapes utilizing Fourier transform methods has enabled unbiased interrogations of biological shape (

Collectively known as teosintes, the wild members of the genus

Beyond the genus

This project utilizes a maize x teosinte (MxT) backcross population to examine the genetic architecture of SAM shape and size (

Germplasm for all experiments was grown in 10 h-day conditions with 27°C daytime and 25°C nighttime temperatures in Percival A100 growth chambers (Percival Scientific, Perry, IA, USA). An intermediate day length was selected to promote maturation of genus

After overnight fixation in FAA, plant tissue was dehydrated through an ethanol dilution series, transferred to a 1:1 mix of ethanol and methyl salicylate, then transferred to methyl salicylate for clearing overnight. Fully cleared tissue was imaged by DIC with Nomarski optics on an Axio Imager.Z10 (Carl Zeiss Microscopy, LLC, Thornwood, NY, USA) with an AxioCam MRc5 camera. We captured near-median longitudinal optical sections using SAM apex contours and primordia appearance as morphological cues. To avoid the analysis of determinant, IMs in our study, we only processed images where the shoot apex displayed recent initiation of leaf primordia, a morphological marker of vegetative SAMs (

Several shoot apex images of anciently diverged plant taxa were collected from high quality publications (Supplementary Data Sheet

A small number of shoot apex images from demonstrative plant taxa were collected from freshly fixed tissues (Supplementary Data Sheet

Near-median DIC images were processed by custom ImageJ macros to extract meristem contours and measures of SAM height and SAM radius (as reported in 10). Using a custom Python script SAM height and radius were used to calculate a table of 8 parabolic estimators: height, radius, height to radius ratio (H/R), volume (Vol.), surface area (Surf. Area), arc length (Arc Len.), parabolic coefficient (Para. Coeff.), and cross-sectional area (Area) (as previously reported in 10).

Shoot apical meristem contours were digitized with an Intuos Draw Tablet (Wacom Technology Corporation, Portland, OR, USA) and used for both linear model fitting with the lm() function and Fourier transform with the Momocs package for R. All traced SAM coordinates were imported as open contours (data type Opn), thinned to 800 evenly spaced pseudo-landmarks, Procrustes aligned, and Fourier transformed by the discrete cosine transform in the Momocs package for R. Discrete cosine transform made use of 12 harmonics, the lowest number of harmonics that sufficiently recaptured variation.

Using publically available genotype information for the MxT population from panzea.org, genotype and phenotype information were processed via the R/qtl package for R. MxT genotypes were coded as BC2S3 and mapped using the Kosambi algorithm. Single QTL were detected using the scanone() function. We used a 95% confidence threshold generated from 10,000 permutations to determine significant QTL. Bayesian 95% confidence QTL intervals were called using the bayesint() function to estimate QTL location.

Descriptive statistical analysis, correlation analysis, Wilcoxon one-sided rank sum test, and two-way ANOVA were carried out using core R packages. Raw data were summarized according to replicate by BLUP + coefficient using the nmle package in R (

Supplementary Data Sheet

We utilized microscopic imaging of 14-day-old seedling vegetative SAMs (described in Materials and Methods) to construct a morphospace of SAM height and radius for the genus

^{∗} indicates SAM with flanking leaf primorida. Scale bar, 50 urn.

We used image-processing to collect two discrete measurements, SAM height and SAM radius and approximate the MxT shoot meristem as a paraboloid surface, the geometric shape yielded from revolving a parabolic curve around its central axis (additionally described in 10). Exploiting the simple geometry of a paraboloid, we used two primary measures to derive eight total parabolic shape estimators: height, radius, height to radius ratio (H/R), volume (Vol.), surface area (Surf. Area), arc length (Arc Len.), parabolic coefficient (Para. Coeff.), and cross-sectional area (Area) (Supplementary Data Sheet

Our previous study analyzed SAM volume (

The remaining 7 parabolic estimators mapped QTL to several chromosomes (

In total, QTL intervals recaptured 11 previously identified SAM-morphology candidate genes implicated by GWAS of maize inbred varieties (Supplementary Data Sheet

Using Fourier- related transform methods, we processed Procrustes-aligned and scaled MxT shoot meristem outlines (Supplementary Image

^{∗} indicates SAM with flanking leaf primorida. //’/, renderings of expected SAM shapes with PC values of -4, -2, 0, 2, and 4 standard deviations from the average recorded SAM shape. Histogram

Using PC1, PC2, and PC3 as quantitative phenotypes, we identified significant QTL for each trait: PC1 identified QTL on chromosomes 2, 4, 7, and 9 (

Despite their similar roles in stem cell maintenance and the production of lateral organs, the shoot apices of anciently diverged plant lineages have remarkable anatomical and transcriptomic differences (^{2} goodness-of-fit scores ranging from 0.838 to 0.997 with a mean of 0.963 and median of 0.975. Interestingly, SAM shape parameters do not significantly separate anciently diverged evolutionary clades (ANOVA,

^{∗} indicates SAM and flanking leaf primorida. R^{2}, goodness-of-fit of parabolic model. Bar, 50 um.

We processed SAM images from 33 wild teosintes and 841 lines from a maize by teosinte (MxT) backcross population to generate a meristem morphospace for the genus

Comprehensive analysis of SAM shape by Fourier methods yielded unexpected and interesting phenotypes for quantitative genetics. We note that the ‘left-leaning’ to ‘right-leaning’ asymmetry identified in PC2 (

Approximating SAM shape and size with a parabolic model has several advantages for quantitative genetics. Parabolic estimates of SAM morphology can be generated by collecting two simple measures, SAM height and radius, whereas Fourier methods requires the careful placement of pseudo-landmarks or outline information generated from laborious manual image tracing or automated image processing of high signal-to-noise SAM micrographs. Despite the increased sensitivity of Fourier methods, we expect that the throughput of approximating SAM morphology with a paraboloid is better suited to large-scale genetic analyses of SAM morphology in maize.

We furthermore demonstrated that shoot apical regions from diverse plant taxa are well fit by parabolic curves. The shoot apices utilized in these comparisons (especially the historical samples) were obtained from plants grown in a wide variety of environmental conditions, which may indeed influence meristem size and/or geometry (

As previous studies in maize have uncovered statistically significant correlations between SAM size and selected adult plant traits (

MS, helped conceive and design the experiments, and edited the manuscript; SL, helped conceive and design the experiments, generated, analyzed, and interpreted the data, and wrote the manuscript. CD, performed imaging and image analyses of the teosinte SAMs.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

We thank L. Comai (UC Davis), for stimulating discussions of the data. We thank K. Niklas (Cornell) for strategic advice in modeling SAMs as paraboloids. Many thanks to the organizers and participants of the 2015 NIMBioS Investigative Workshop: morphological Plant Models for advice on morphometric concepts and techniques. We thank N. Ronning (Cornell) for assistance with plant harvest and image acquisition.

The Supplementary Material for this article can be found online at: