Analysis and Specification of Starch Granule Size Distributions

Starch granules are the physical structure in which two main reserve homoglucan polymers in plant photosynthesis and storage tissues, the linear or sparsely branched amylose and the highly branched amylopectin, are orderly packed along with some minor components, including lipids and proteins. Starch granules from various plant species exhibit many three-dimensional (3D) shapes (reviewed in ref.^1,2), including spheres, ellipsoids, polyhedrons, platelets, cubes, cuboids, and irregular tubules. Even those from the same tissue or different tissues of the same plant species could have a set of shapes with varying occurrence frequencies. In other words, starch granules from a plant species may have a characteristic statistical shape distribution, rather than a specific shape. The non-uniform and non-spherical granule shapes make it difficult to properly measure and define starch granule sizes. Additionally, starch granules from the same tissues of a plant species are of a range of sizes with different proportions, i.e., exhibiting a characteristic size distribution. This size distribution further complicates the analysis and description of starch granule sizes.

Starch granule sizes have been analyzed using several categories of particle sizing techniques (reviewed in ref.³), including microscopy, sedimentation/steric field-flow fractionation (Sd/StFFF), laser diffraction and electrical sensing zone (ESZ). However, these techniques are not equally suited for the determination of starch granule sizes in the presence of a granule shape and a size distribution. Microscopy, including light, confocal and scanning electron microscopy, is excellent for the studies of morphology^4,5,6,7, structure^8,9 and development^10,11 of starch granules, but hardly suited for defining their size distributions due to some inherent shortcomings. Direct measurements of microscopic granule images or software-assisted image analysis of optical microscopy data (IAOM), which have been used for the determination of granule sizes of starches from several species, including maize¹², wheat^13,14, potato¹⁵ and barley¹⁶, can measure only 1D (usually maximal length) or 2D (surface area) sizes of very limited numbers (tens to a few thousands) of starch granule images. The small granule sampling sizes that are inherently constrained by the techniques could rarely be statistically representative, considering the enormous granule numbers per unit weight of starch (~120 x 10⁶ per gram, assuming all 10 µm spheres at 1.5 g/cm³ density), and, therefore, could lead to the poor reproducibility of the results. The Sd/StFFF technique may have high speed and resolution, and narrow size fractions of starch granules¹⁷, but has been rarely used probably because its accuracy could be severely affected by damages, different shapes, and density of starch granules. The laser diffraction technique is the most widely used, and has been applied for starch granule size analyses for all major crop species^3,14,16. Although the technique has many advantages, it is actually not suited for determinations of starch granule sizes in the presence of a granule shape distribution. Most of the concurrent laser diffraction instruments rely on the Mie light-scattering theory¹⁸ for uniform spherical particles and the modified Mie theory¹⁸ for some other shapes of uniformity. The technique is, therefore, inherently very sensitive to particle shapes, and not entirely suited even for certain shapes of uniformity¹⁹, let alone for starch granules having a set of shapes of varying proportions. The ESZ technique measures the electric field disturbance proportional to the volume of the particle passing through an aperture. It provides granule volume sizes, as well as the number and volume distribution information, etc., at high resolutions. Since the ESZ technique is independent of any optical properties of particles including color, shape, composition or refractive index, and results are very reproducible, it is particularly suited for determining size distributions of starch granules having a set of shapes.

Starch granule sizes have also been defined by using many parameters. They were often simplistically described by average diameters, which in some cases were the arithmetic means of the microscopically measured maximal lengths of 2D images^12,20, or averages of equivalent sphere diameters³. In other cases, the granule size distributions were specified by using size ranges^21,22, the distribution mean volume or mean diameter (sphere equivalent, weighted by number, volume, or surface area) assuming a normal distribution^{14,23,24,25,26}. These descriptors of starch granule sizes from various analyses are of a vastly different nature, and not strictly comparable. It could be very misleading if these “sizes” of starch granules from different species or even the same tissues of the same species were directly compared. Furthermore, the spread (or shape) parameter of the assumed normal distributions, i.e., the standard deviation σ (or graphic standard deviation σ_g) measuring the width of the distribution (i.e., the spread of the sizes), has been ignored in most studies.

To resolve the aforementioned critical issues facing starch granule sizing analyses, we outlined a procedure for reproducible and statistically valid determinations of granule size distributions of starch samples using the ESZ technique, and for properly specifying the determined granule lognormal size distributions using an adopted two-parameter multiplicative form²⁷ with improved accuracy and comparability. For validation and demonstration, we performed replicate granule sizing analyses of sweetpotato starch samples using the procedure, and specified the lognormal differential volume-percentage volume-equivalent-sphere diameter distributions using their graphic geometric means and multiplicative standard deviations s* in a ^x/ (multiply and divide) s* form.