“Rolledupness”: phenotyping leaf rolling in cereals using computer vision and functional data analysis approaches
 X. R. R. Sirault^{1, 2},
 A. G. Condon^{2},
 J. T. Wood^{3}View ORCID ID profile,
 G. D. Farquhar^{1} and
 G. J. Rebetzke^{2}Email author
DOI: 10.1186/s1300701500951
© Sirault et al. 2015
Received: 26 August 2015
Accepted: 19 October 2015
Published: 14 November 2015
Abstract
Background
The flag leaf of a wheat (Triticum aestivum L.) plant rolls up into a cylinder in response to drought conditions and then unrolls when leaf water relations improve. This is a desirable trait for extending leaf area duration and improving grain size particularly under drought. But how do we quantify this phenotype so that different varieties of wheat or different treatments can be compared objectively since this phenotype can easily be confounded with intergenotypic differences in rootwater uptake and/or transpiration at the leaf level if using traditional methods?
Results
We present a new method to objectively test a range of lines/varieties/treatments for their propensity of leaves to roll. We have designed a repeatable protocol and defined an objective measure of leaf curvature called “rolledupness” which minimises confounding factors in the assessment of leaf rolling in grass species. We induced leaf rolling by immersing leaf strips in an osmoticum of known osmotic pressure. Using microphotographs of individual leaf crosssections at equilibrium in the osmoticum, two approaches were used to quantify leaf rolling. The first was to use some properties of the convex hull of the leaf crosssection. The second was to use cubic smoothing splines to approximate the transverse leaf shape mathematically and then use a statistic derived from the splines for comparison. Both approaches resulted in objective measurements that could differentiate clearly between breeding lines and varieties contrasting genetically in their propensity for leaf rolling under water stress. The spline approach distinguished between upward and downward curvature and allowed detailed properties of the rolling to be examined, such as the position on the strip where maximum curvature occurs.
Conclusions
A method applying smoothing splines to skeletonised images of transverse wheat leaf sections enabled objective measurements of intergenotypic variation for hydronastic leaf rolling in wheat. Meancurvature of the leaf crosssection was the measure selected to discriminate between genotypes, as it was straightforward to calculate and easily construed. The method has broad applicability and provides an avenue to genetically dissect the trait in cereals.
Keywords
Leaf water potential Polyethylene glycol (PEG) Mean curvature Convex hull Spline analysis Digital phenotypingBackground
The leaves of many important cereal crops including sorghum, maize, rice and wheat roll (transverse rolling of the leaf lamina along the mid axis) in response to drought conditions then unroll to continue photosynthesis when water is available. This is a trait identified as potentially important in rainfed conditions [1], particularly if late rains occur during grainfilling. It may lead to a delay in the onset of leaf senescence (longer maintenance of leaf area) and thus lead to greater wateruse efficiency. The trait is mainly expressed in the flag leaf [2], which is one of the main organs contributing to grain dry weight [3, 4], a major component of final harvested yield and an important parameter in grain quality.
Significant genotypic variation for leafrolling has been reported within wheat germplasm [2]: leaves of some wheat varieties roll after only mild water stress whereas leaves of other varieties roll only when severely waterstressed. For use in breeding, a measure is required to quantify rolling so that different genotypes and/or different treatments can be compared objectively. Apart from the obvious differences in leaf rolling arising between genotypes from variation due to evaporative demand and/or spatial heterogeneity in soil water content in the field, this phenotype is easily confounded with intergenotypic differences in rootwater uptake and/or transpiration at the leaf level. To understand the leaf rolling phenotype one must be sure of the intrinsic value of the tested lines.
The degree of rolling in the flag leaf is often quantified by using a visual discrete scale of schematic transversal shape (leaf rolling score from 1 ≡ flat to 5 ≡ tightly rolled) [5], or by using a rolling index defined as the ratio of rolled leaf width to unrolled leaf width [6]. The choice between leafrolling score and leaf rolling indices is a tradeoff between a rapid but qualitative measure if using leafrolling scores and a slow but quantitative measure if using rolling indices. Applying a visual score on different plant species requires different transversal references [7] and raises the problem of the definition of leaf rolling. This is particularly relevant since leaf rolling tends not to be homogeneous along the midrib, i.e. the tip is usually more rolled than the middle of the leaf. In addition, visual ratings of different “scorers” cannot be compared or related adequately to each other [8] so there is a need for a repeatable protocol for screening leaf rolling genotypes. Using rolling indices address some of these issues because they are calculated ratios but they are not logistically practical under field conditions and are highly confounded with environmental factors when used in situ.
Results
Development of a data analysis framework for phenotyping leaf rolling
To measure the degree of rolling for the individual strips we considered two approaches as follows:
Convex hull
Smoothing spline functions
From these splines first and second derivatives, \(\dot{x}_{s}\) and \(\dot{y}_{s}\), \(\textit{\"{x}}_{s}\) and \(\textit{\"{y}}_{s}\) of x and y with respect to t at any point along the strip were calculated. The curvature, κ, at a point was estimated by, \(\kappa = \frac{{\textit{\"{y}}_{s} \dot{x}_{s}  \textit{\"{x}}_{s} \dot{y}_{s} }}{{\dot{s}^{3} }}\), where \(\dot{s} = \surd (\dot{x}_{s}^{2} + \dot{y}_{s}^{2} )\).
The length of the strip was estimated by integrating \(\dot{s}\).
With this framework in place, several choices had to be made for analysing the data. These included the degree of smoothing to use and the points at which the curvature was to be estimated. We also had to decide what function we were going to use in the interpretation of the data (e.g. mean curvature over the whole crosssection, or position of the maximum curvature for each strip), and, since not all leaves had the same width, what standardisation, if any, was to be used.
Effect of smoothing and interpolation on inferences
Repeatability of curvature measurements
Use of developed indices to characterize genotypic differences
Means of two measures of rolling: (1) the logarithm of the ratio of leaf strip length divided by the greatest diameter of the convex hull and (2) the mean curvature among rolling groups
Log (length/diagonal)  Mean curvature (mm^{−1})  

Osmotic potential of bathing solution  Osmotic potential of bathing solution  
−0.06 MPa  −1.38 MPa  −2.82 MPa  −0.06 MPa  −1.38 MPa  −2.82 MPa  
Low rollers  0.129  0.049  0.091  −0.137  −0.078  0.022 
High rollers  0.163  0.275  0.683  0.120  0.159  0.452 
It is also interesting to note that errors on mean curvature estimates increased at lower osmotic pressures. This indicated that variance was not homogeneous across osmotic potentials and thus caution needs to be exercised when statistically comparing mean curvature across osmotic potentials. However, increases in standard errors could also be the result of greater mean curvature estimates at lower osmotic potential.
The relationship between the logarithmic index (logarithms of the ratio of length to the longest diameter of the convex hull) and osmotic potential revealed an interesting pattern for the different lines (Fig. 7b). In contrast to breeding lines KJ21 and B403D, that had monotonic increases in their logarithmic indices as osmotic potential decreased, indices for cv. Diamondbird and cv. Silverstar decreased over 2 MPa reaching a minimum at −2.0 and −2.40 MPa, respectively, before increasing. This indicated that the diagonal of the convex hull increased relative to the leaf strip length, implying that the leaf strip was “unrolling” in the first instance. This is consistent with the revolute crosssection of these genotypes at full turgor (Additional file 5). To roll inwards, the leaves of these genotypes had to first flattenout.
Variation in length of the leaf strips
On average, the data indicated that the leafrolling lines KJ21 and KJ41 had longer leaf strips (data not shown). However, the analysis of variance for strip length indicated there were no differences between rolling groups (P = 0.858) but a significant effect of PEG level (P < 0.001). The rolling group × PEG level interaction was also highly significant (P < 0.001) for strip length. This indicated that across PEG levels the length of the strip was not constant, and was actually decreasing or shrinking differentially between groups: the highroller group had a strip length decreasing more at lower leaf water potential than the lowroller group. It is also worth mentioning that leaf lengths for individual lines were statistically different (P < 0.05) (data not shown).
Scaled indices
Comparisons of “scaled” meancurvature, i.e. mean curvature divided by estimated leaf strip length, to mean curvature “unscaled” did not indicate a different pattern between genotypes. Conclusions from the analysis of variance on scaled meancurvature were identical to conclusions for unscaled mean curvature, i.e. highly statistically significant effects of rolling group, PEG concentration (P < 0.001), and of their interaction, i.e. rolling group × PEG concentration (P < 0.001). Mean curvature was thus unaffected by scaling, i.e. the length of the leaf strip was not playing a major role in explaining variation in leaf rolling.
The analysis of variance for the logarithm of the length divided by the greatest diameter of the convex hull with trace(S) = 10 showed the expected effects including statistically significant differences between the lines and the different degrees of leaf dehydration. The convex hull was unaffected by the smoothing and interpolation but the estimation of the length of the strip was affected (data not shown). No significant differences (P > 0.05) were identified for genotypes within a group, indicating that behaviours within a rolling group were similar. At high osmotic potentials, the rolling group comprising breeding lines KJ21 and KJ41 had noticeably higher ratios than the nonrolling group, the differences becoming more pronounced at intermediate and lower osmotic potentials.
Discussion
Unlike the traditional methods for quantifying leaf rolling, i.e. leafrolling scores and rolling indices, quantifying leaf rolling using the approach detailed here with PEG solutions allowed evaluation of diverse genotypes under essentially identical conditions. Measuring leaf rolling using this protocol was independent of external confounding factors such as variation in vapourpressure deficit during the day or field variation in soil water content. It was clearly demonstrated that mean curvature was very sensitive to changes in hydration level and occurred in a monotonic way over a large range of leaf water potentials. This monotonic characteristic makes mean curvature a suitable measure for assessing the ability of a genotype to roll. Monotonic increase in curvature was also reported by Moulia [7] for a single genotype of maize in characterising the mechanics of leaf rolling.
An asymmetry in transverse shapes was observed at full turgor for most lines, i.e. one side was more “rolled” than the other (Fig. 2). Interestingly, when the leaf was at the lowest osmotic potential, i.e. at −2.82 MPa, the side that was initially strongly revolute in cv. Silverstar did not achieve a positive concavity while the other half, which was less revolute at full turgor, did achieve a positive concavity. Equally, the side that was highly rolled in line KJ21 rolled more than the opposite side even at intermediate leaf water potential. This suggested that the transverse shape at full turgor, in particular the degree of positive or negative concavity, restricted to some extent the ability of a leaf to roll. We thus hypothesize that leaf rolling is actually mechanically impeded by the initial degree of transverse curvature at full turgor.
It is still uncertain why “shrinkage” of the strip length was more pronounced in the highrolling group. Two explanations were hypothesised. The first was that this effect is an artefact of the data fitting. Although the recording process was similar between genotypes, the high rollers had greater curvatures around their leaf strip extremities, which the fitted spline functions tended to underestimate. Integrating \(\dot{s}\) may have artificially reduced leaf strip length in the same manner that the smoothing matrix with lower traces lowered estimates of leaf strip length as a result of “oversmoothing”. The second hypothesis was that “shrinkage” is a physiological response to higher level of osmotic stress. Cells of the leaf strip in the leafrolling groups may have been more susceptible to loss of water and lost volume more readily than cells of the nonrolling group, resulting in differential shrinkage between these two groups.
Although mean curvature and the logarithm of the ratio of strip length to maximum diameter of the convex hull were both suitable measures of leaf rolling, mean curvature over the whole strip length was the index of “rolledupness” that will be retained from this study as it is easier to interpret and understand than a logarithmic index. Differences between rollers and nonrollers could also be assessed at full turgor with this metric since genotypes with a high propensity for rolling had positive mean curvatures while genotypes with a lower propensity for rolling had negative curvatures. Finally, mean curvature does not need to be scaled to be meaningful and interpreted, while the logarithmic index requires the calculation of an extra parameter, which is associated with an extra standard error.
For the statistical geneticist seeking mechanisms and underlying genetic control for the leaf rolling phenotype, the method herein has the advantage of being objective and provides measures containing values that are continuously distributed. Although the method was developed to quantify leaf rolling in response to leaf dehydration, there are many other situations where leaf rolling is of interest and where this method could be applied: the assessment of damage caused by insects (e.g. wheat curl mite) [11], or potassium deficiency. The method could also be applied to other cereal crops such as sorghum, rice, maize, durum wheat and barley without having to define a different visual scale for each species.
Conclusions
A method applying cubic smoothing splines to skeletonised images of transverse wheat leaf sections enabled objective measurements of intergenotypic variation for hydronastic leaf rolling in wheat. Meancurvature of the leaf crosssection was the measure selected to discriminate between genotypes, as it was straightforward to calculate and easily construed. The method has broad applicability and provides an avenue to genetically dissect the trait in cereals.
Methods
Plant material
Wheat (Triticum aestivum L.) genotypes KJ41, KJ21, B403D and cultivars Arrino, Diamondbird, Kite, Krichauff, Lang and Silverstar were sown into soilfilled wooden seedling trays (600 mm long × 300 mm wide × 100 mm deep) on 30 August 2004 at CSIRO Black Mountain (Canberra, Australia). Lines KJ41 and KJ21 are two CSIRO inbred breeding lines derived from a cross between line K648R (“roller” phenotype) and cv. Janz (“nonroller” phenotype). They were selected in this study due to their propensity to roll quickly with water deficit as was B403D (“roller” phenotype) while cvs. Silverstar and Diamondbird are usually described as “nonrolling” phenotype. The other four entries were included to randomly represent Australian cultivars without any a priori knowledge of their leaf rolling abilities, although Chara and Krichauff have been observed to roll on a few occasions (Dr N. Fettell, pers. comm.).
Cultural conditions
The seedling tray contained a fertile, compostbased potting mix and was placed outdoors after sowing in order to experience “fieldlike” temperatures and radiation. Each entry was represented by three seeds, sown in a rowcolumn design with three replications (9 lines × 3 reps × 3 trays). The perimeter of the tray was sown with a buffer to minimise border effect. Plants were kept wellwatered and received a standard nutrient solution (modified Hoagland #2 [12]) twice while growing. Only the main stem and two tillers per plant were retained by removing regularly any newly appearing tillers, therefore limiting competition for light and water between plants. All entries reached anthesis, or Z65 [13], within a couple days of each other.
Leaf sampling protocol and PEG treatment
At flowering, the flag leaves of individual plants were sampled by cutting the leaves just below the leaf ligule. Each leaf was then placed in a 15 mL Eppendorf tube filled with tap water and was allowed to rehydrate overnight in a constant temperature room set at 8 °C under low light conditions, so as to attain a fully turgid state. The next day each flag leaf was cut to form a 30 mm segment with the middle of the 30 mm segment being at 30 % of the maximum leaf length (Additional file 3). Preliminary work indicated that this section of the leaf was instrumental in determining the leaf rolling response of the flag leaf. Each 30 mm segment was subsequently cut into ten 3 mm strips at right angles to the central rib. The strips were then subjected to different degrees of dehydration by immersing them in solutions of PEG 3350 (Sigma^{®} Chemical). Polyethylene glycol 3350 was chosen as an osmoticum for the study as it was assumed that its high molecular weight would prevent it from entering the cells by diffusion in the time necessary to reach equilibrium. In all, seven degrees of dehydration were used: −0.06, −0.43, −1.00, −1.38, −1.76, −2.38 and −2.82 MPa. The leaf strips, randomly allocated to the different solutions, were left to equilibrate within the solutions for 4 hours in a constant temperature room, set at 20 degree Celsius, in order to reach thermal and osmotic equilibrium. Strips were placed in a glass Petri dish and covered with tap water or solutions of PEG. Some leaves were left for 3 days in the solutions and did not show further rolling.
Osmotic potentials of Polyethylene glycol 3350 solutions (Π_{PEG}): calibration
For calibration purposes, ten solutions of PEG 3350 were prepared by dissolving from 5–55 g of PEG in 100 g of milliQ Water. A shaker (Bioline) set up at 50 °C and 90 rpm was used to homogenise the PEG solutions for two and a half hours. The solutions were then left to equilibrate overnight in a 20 °C constant temperature room before measuring their osmotic potential. One extra solution consisting of pure milliQ water was also included in the calibration. High concentrations of PEG, i.e. 0.50 and 0.55 g.g^{−1}, were not used for assessing changes in transverse shapes of the leaf strips because it was considered that the viscosity of the solution at those concentrations could mechanically impede the rolling of the strips.
Osmotic potentials of the ten PEG solutions were measured using custombuilt thermocouple psychrometers. Strips (30 × 11 mm) of filter papers (Whatman #2) lining the walls of the psychrometric chambers were soaked with 100 µL of the different PEG solutions. The psychrometric chambers were sealed and left in a constant temperature room, set at 20 °C, for 4 hours to reach thermal and watervapour equilibrium. Osmotic potentials of the solutions were determined using a dew point microvolt meter (Wescor HR33T, Inc Utah, USA) operated in the dew point mode.
The relationship between PEG 3350 and osmotic potential at 20 °C is plotted in Additional file 4. The relationship was fitted by a secondorder polynomial equation and described by the following: Π_{PEG} = −11.517[PEG]^{2}−1.0508[PEG]−0.0342 with Π_{PEG} in MPa and [PEG] in g.g^{−1} of milliQ water.
Microphotographs of leaf transverse shapes
Statistical analysis
The lines and cultivars were divided into four groups according to the expected extent of rolling. The first group, most rolling expected, consisted of breeding lines KJ21 and KJ41, the next was cv. Krichauff only, B403D only, and the remaining group “nonrolling” consisted of cvs Arrino, Diamondbird, Kite, Lang and Silverstar. These groups are later referred to as “rolling group” in text and tables.
A Genstat program (Genstat 9, release 9.1) [14] was used to read the Excel file and for plotting the indexed data. The statistical software R (R, v 2.2.1) [15] was used to fit the convex hull and the spline functions to the data. (Program code is available on request). Smoothing splines were fitted using the R packages stats ‘smooth.spline’ [15]. The function ‘smooth.spline’ fits cubic smoothing spline to the supply data, i.e. the set of (x, y) coordinates describing the leaf transect. Mean curvature for each cross section was obtained by averaging all curvature measurements along each cross section. Calculated variables were analysed using ANOVA and mixed linear models to assess the significance of the differences between treatment, i.e. rolling group and PEG concentration. Genstat was used to fit the different models using ANOVA and REML structure with rolling group, cultivar within rolling group, and PEG concentrations considered as fixed effects and leaf side within replicate within cultivar treated as nested random effects.
Abbreviations
 PEG:

polyethylene glycol
 ANOVA:

analysis of variance
 REML:

restricted maximum likelihood
 cv. :

cultivar
 cvs :

cultivars
Declarations
Authors’ contributions
GJR developed and supplied the genetic material; GJR, AGC, GDF participated in the design of the study; JTW wrote the Genstat and R programs, performed the statistical analysis and helped to draft the manuscript; XRRS conceived the study, designed it, acquired the data, coordinated and wrote the manuscript. All authors read and approved the final manuscript.
Acknowledgements
We thank the Grains Research and Development Corporation of Australia for funding a PhD scholarship for Xavier Sirault.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
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