Summary
Presented here is a procedure for reproducible and statistically valid determinations of starch granule size distributions, and for specifying the determined granule lognormal size distributions using a two-parameter multiplicative form. It is applicable to all granule sizing analyses of gram-scale starch samples for plant and food science research.
Abstract
Starch from all plant sources are made up of granules in a range of sizes and shapes having different occurrence frequencies, i.e., exhibiting a size and a shape distribution. Starch granule size data determined using several types of particle sizing techniques are often problematic due to poor reproducibility or lack of statistical significance resulting from some insurmountable systematic errors, including sensitivity to granule shapes and limits of granule-sample sizes. We outlined a procedure for reproducible and statistically valid determinations of starch granule size distributions using the electrical sensing zone technique, and for specifying the determined granule lognormal size distributions using an adopted two-parameter multiplicative form with improved accuracy and comparability. It is applicable to all granule sizing analyses of gram-scale starch samples, and, therefore, could facilitate studies on how starch granule sizes are molded by the starch biosynthesis apparatus and mechanisms; and how they impact properties and functionality of starches for food and industrial uses. Representative results are presented from replicate analyses of granule size distributions of sweetpotato starch samples using the outlined procedure. We further discussed several key technical aspects of the procedure, especially, the multiplicative specification of granule lognormal size distributions and some technical means for overcoming frequent aperture blockage by granule aggregates.
Introduction
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 morphology4,5,6,7, structure8,9 and development10,11 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, wheat13,14, 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 species3,14,16. 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 images12,20, or averages of equivalent sphere diameters3. In other cases, the granule size distributions were specified by using size ranges21,22, the distribution mean volume or mean diameter (sphere equivalent, weighted by number, volume, or surface area) assuming a normal distribution14,23,24,25,26. 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 σg) 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.
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Protocol
1. Preparation of starch samples
- Prepare two (or three) gram-scale replicate starch samples from starch-accumulating tissues of various plant species following the established procedures (e.g., potatoes15, sweetpotatoes28, wheat grains13,29, and maize kernels30, etc.).
- Thoroughly wash starch samples with acetone or toluene 3-4x to minimize granule aggregates and dry them completely.
NOTE: Use extraction procedures that yield more than 1 g of starch per preparation. One or two 0.5-g aliquots from each of the three or two replicate extracts, respectively, are sampled for granule sizing analysis of one starch extract.
2. Electrolyte preparation
- Prepare 500 mL of 50 g/L lithium chloride in methanol for four sizing runs for replication starch samples (100 mL per run plus an extra 100 mL). Preferably, make the electrolyte in large-volume batches, e.g., 4 to 8 L at a time, to minimize the concentration variation.
- Cool the container on ice or in a 4 °C cabinet to speed up dissolution of the lithium chloride.
3. Setting up the analyzer
- Choose an aperture tube with a particle diameter range covering the known (in the literature or through trial runs) granule size range of starch samples to be analyzed, e.g., a 100 μm aperture for sweetpotato starches. For starch samples of unknown granule size range, select an appropriate aperture through trial runs using several aperture tubes having overlapping particle diameter ranges.
NOTE: The particle diameter range of an aperture tube is its accurate sizing range between 2 to 60% of, and with an extended sizing range to 80% of its orifice diameter. Table 1 lists properties of three most useful aperture tubes for sizing granules of major crop starches. If the granule size range of a starch sample is wider than the sizing range of a single aperture tube, perform a multi-tube overlap analysis combining up to five particle size distributions measured with apertures of different sizes. Each aperture is identifiable by its diameter and part number labeled on the tube. Its diameter and serial number contained in a barcode on the tube can be scanned into the analyzer software using the Bar Code Reader on the Control Panel of the analyzer. - Chose a 100 or 200 mL analytical beaker (over cuvettes) for the determination of starch granule sizes, and set up automatic stirring (below) to maintain a good granule suspension during measurement.
- Create a Standard Operating Method (SOM) to specify run settings, and a Preferences file for analyzing, viewing, and printing the results. Combine SOM and Preferences file into a Standard Operating Procedure (SOP) as needed.
NOTE: For non-standardizable analyses, use SOM to run the analyses, and adjust the SOM settings between runs through the Edit the SOM window (see below) as needed. After run completion, analyze, view, and print the run results by changing the Preferences as desired. For standardizable granule sizing analyses, use an SOP to run the analyses.- Start the analyzer software. On the Main Manu, click SOP | Create SOM Wizard or Edit the SOM, or on the Status Panel, click Edit SOM. Use the wizard or the Edit the SOM window to select settings for an SOM. Settings typically used for sizing granules of sweetpotato starch samples are summarized in Table 2.
- Save the created SOM to a File in the SOM Wizard-Summary of Settings window, or in the Edit the SOM window.
- On the Main Manu, Click SOP | Create Preferences Wizard or Edit Preferences. Use the wizard or tabs in the Preferences edit window to select preference settings as those in Table 3 or others as desired.
- Save the selected Preferences to a file in the Create Preferences Wizard-Summary of Settings window or in the Edit Preferences window.
- On the Main Menu, click SOP | Create SOP Wizard. Following the step-by-step guide of the wizard, enter a description, select the SOM and Preferences file to create and save an SOP.
4. Granule sizing analyses of the starch samples
- Prepare the Analyzer
- Turn on the analyzer, open the software in the computer and verify the Ready status at the top of the Status Panel after its automatic connection to the analyzer.
- Fill the electrolyte jar with electrolyte, empty the waste jar if necessary.
- Properly install and secure the chosen aperture tube following the guide in the user’s manual. For an uncalibrated new aperture tube, calibrate it following the step-by-step guide under Calibration | Calibrate Aperture on the Main Menu. For a calibrated aperture tube, verify the calibration following the step-by-step guide of the Change Aperture Tube Wizard under the Run or Calibration | Verify Aperture Calibration on the Main Menu.
- Unlock the assay platform by pushing the lock-release clip (on the middle front of the left sample compartment wall) and manually lower the platform to the bottom. Place an analytical beaker containing 100 mL of electrolyte on the platform, move the stirrer to the stirring position, and manually raise the platform to the self-locking upper position to immerse the aperture tube and stirrer in the electrolyte.
- Click Fill on the bottom instrument Toolbar to have the analyzer automatically fill the system with the electrolyte and click Flush to have the analyzer automatically flush the system.
- Load the SOM by clicking SOP | Load an SOM on the Main Menu, and use the SOM to run an analysis without a Preferences file. Alternatively, load an SOP by clicking SOP | Load an SOP on the Main Menu or Load SOP on the Status Panel, and use the SOP to run an analysis.
- If using an SOP, click SOP | SOM Info or Preference Info on the Main Menu to verify the SOM and Preference settings. Click Sample | Enter Sample Info on the Main Menu or Edit Info on the Status Panel to enter the sample information for the run.
- Prepare starch-methanol sample and sizing suspensions
- Weigh two or one 0.5 g sample from each of the two or three replicate starch extracts, respectively.
- Add each of the 0.5 g starch aliquots to 5 mL methanol in a 50 mL conical centrifuge tube, and fully disperse starch granules using several pulses of low intensity ultrasound (12–24 W/cm2) from an ultrasonic processor.
- Using a disposable transfer pipette, apply one small drop of the starch-methanol suspension (~0.2 mL) to the 100 mL of 50 g/L LiCl methanol electrolyte under constant stirring in the beaker. Close the sample compartment door.
- Perform a sizing run
- Click Preview in the bottom Instrument Toolbar to start a preview run. On the Status Panel, verify that the dynamically displayed concentration bar is in green, and shows a 5 to 8% nominal concentration range for the suspension.
- Click Stop on the bottom Toolbar to stop the Preview run. If necessary, dilute the starch-electrolyte suspension by replacing an aliquot of the suspension with the electrolyte, and then repeat a Preview run.
NOTE: The 5% to 8% nominal concentration range of the suspension is critical for completion of a run without stoppage due to aperture blockage by aggregated granules. If needed, adjust the drop-sample size, and/or the concentration of the starch-methanol suspension to make a new starch-electrolyte suspension having the nominal concentration in the optimal range. - After the verification, click Start on the bottom Toolbar to start the run. The analyzer automatically completes the run once the total count of sized granules, which is displayed along with the run time on the Status Panel in a run, reaches the set Total Count (125,000 or 250,000) by the Control Mode of the SOM. Depending on the suspension concentration (within 5-8% range or lower), a single run takes 2 to 5 min or more.
NOTE: When the analyzer automatically detects an aperture blockage per blockage detection settings of the SOM, it will abort the run, flush to unblock the aperture and start a new run. This blockage action is set to maximally repeat for four times before the analyzer cancels the run operation. This run-aborting blockage problem may be overcome by using two technical methods as noted in Table 2 and detailed in the discussion. - If needed, perform a technical repeat run (see Table 2 and detailed in Discussion) using the same starch-electrolyte suspension by simply clicking Start or Repeat on the bottom Toolbar.
- After completion of a run or repeat runs, empty the beaker, rinse it with methanol, and refill it with 100 mL fresh electrolyte solution for the next run.
- During a run, if an Extended Size Range notification dialog appears when the count of granules larger than 60 µm exceeds 0.1% of the total count (per the SOM setting), click Run 60% to 80% for running an extended dynamic sizing range to 80% of the aperture diameter.
NOTE: The Extended Size Range setting controls actions for granules larger than 60% of the aperture diameter (100 µm, in this case). The setting in the SOM specifies inclusion of starch granules larger than 60 µm when their counts reach over 0.1% of the total count. The completion of the run is still controlled by the total count, and may take slightly less time than otherwise without inclusion of the larger granules totaling less than 0.1% (presumed statically insignificant amount) of the total count.
- Analyze the run results
- If an SOM was used to control the runs, select Preferences settings as desired for viewing, printing, and statistical analyses of the results using the Create Preferences Wizard or the Edit Preferences under the SOP on the Main Menu.
- Overlay results from multiple runs on a single graph for comparison.
- Click Overlay on the Main Toolbar or File | Overlay on the Main Menu to access the Overlay window. Navigate to and select multiple desired result files in the Files box, click Add to move them to the Selected Files box, and click OK to overlay the selected results on a single graph.
- To add a file to an open overlay, click RunFile | Open for Overlay on the Run Menu to access the Overlay window, navigate to the desired file, and click to add.
- Average results from replicate analyses (2 extracts x 2 starch-sampling or 3 extracts x 1 starch-sampling), and view or print the average granule size distribution and statistics in a list or graph.
- On the Main Menu, click File | FileTool | Average to open the Average window. Navigate to and select multiple desired result files in the Files box, click Add to move them to the Selected Files box, and click OK to average the selected results and display the average on a single graph.
- To include an additional result file in an average distribution, on the Run Menu, click RunFile | Open and Add to Average to open the Add to Average window, navigate to and add the file. The new average appears on the graph in the Run (result) window or listing.
5. Specifying the average distribution
- In the Run-Menu window displaying the average distribution, click Calculate | Averaged Statistics on the Run Menu to open the statistics summary window, which displays the average statistics in rows, and the graph statistics for the average distribution in the columns.
- Use the graphic geometric mean (
) and S.D. (s*) in the graph statistics column to specify the average distribution in the x/ s* form. Calculate the CV measuring variations among the averaged replicate distributions by dividing the mean (µ, the same as the of the average distribution) of the geometric means of the averaged distributions with the average S.D. (σ) listed in the average statistics row.
NOTE: The average S.D. (for µ) assessing variations among the means of the replicate distributions is different from the graphic geometric S.D. (for) measuring the spread of the average distribution.
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Representative Results
To validate the procedure, and demonstrate reproducibility of the determined granule size distribution, we performed replicate sizing analyses of sweetpotato starch samples. We prepared replicate (S1 and S2) starch samples from field-grown sweetpotatoes of a breeding line SC1149-19 at a similar developmental age using a previously described procedure28. From each starch extract, two 0.5 g aliquots (a and b) were sampled, suspended in 5 mL of methanol and sonicated with several pulses of low-energy ultrasound to break up aggregates. Each of the two pairs of starch-methanol suspensions was drop-sampled to make a starch-electrolyte suspension, which was then sized twice (technical repeat runs) using the above outlined SOM for a total count of 125,000 granules each. For each single sizing run, once the total count reaches over ~65,000 and ~125,000, the graphic geometric S.D. (s*) and geometric mean ( ) of the displayed differential volume-size distribution no longer significantly change, respectively. Each pair of the repeat runs using one starch-methanol suspension was merged after completion for a total sizing count of 250,000.
Figure 1 shows differential volume-percentage volume-equivalent-sphere-diameter distributions (S1a, S1b, S2a and S2b) for the four replicate sizing analyses of the sweetpotato starch samples, and their average distribution. The CV for the average of geometric means of the four replicate distributions was 3.75 %, demonstrating an excellent reproducibility of the sizing results. Each of the four replicate distributions was determined from a very large sampling size of 250,000 granules, far exceeding the minimal counts (~65,000 and ~125,000) above which the graphic geometric S.D. (s*) and geometric mean () of the displayed differential volume-size distribution in a single sizing run no longer significantly change. Therefore, the determined replicate volume-size distributions were all statistically valid. For better accuracy and comparability (discussed below) of the specification of determined lognormal granule size distributions, all these distributions were specified by using their graphic geometric means () and S.D. (s*) in a x/ (multiply and divide) s* form as listed on the graph. Please note that the granule size distribution of the sweetpotato starch has been rigorously fitted to be lognormal as previously described28.
Figure 1: Lognormal differential volume-percentage volume-equivalent-sphere size distributions from replicate sizing analyses of sweetpotato starch samples. The sampling scheme for the four replicate sizing analyses were detailed in the result. The four distributions (S1a, S1b, S2a and S2b) from replicate analyses and their average were overlaid and specified using the x/ (multiply and divide) s* form. Please click here to view a larger version of this figure.
Figure 2 shows the average (or mean) cumulative (<) number- and volume-percentage size distributions of the four replicate sizing analyses, which were transformation views of the average differential volume-percentage size distribution. The comparison between the cumulative number and volume percentages of starch granules showed that granules having smaller volume-equivalent-sphere diameters accounted for much larger percentages of the total count than the total volume. For example, the numbers of granules having volume-equivalent-sphere diameters smaller or equal to 9.976 µm accounted for 48.53% of the total count, yet only 5.854% of the total volume.
Figure 2: Average cumulative (<) number- and volume-percentage size distributions of starch granules from the four replicate sizing analyses of sweetpotato starch samples. The two distributions are transformation views of the average size distribution in Figure 1. The graph compares the cumulative (<) number (left Y-axis) to volume (right Y-axis) percentages of starch granules having volume-equivalent-sphere sizes lower or equal to particular size bins. Please click here to view a larger version of this figure.
| Aperture Diameter (μm) | Particle Diameter Range (µm) | Particle Volume Range (µm3) |
| 50 | 1.0 - 40 | 0.524 - 33.5 x 103 |
| 70 | 1.4 - 56 | 1.44 - 92.0 x 103 |
| 100 | 2.0 - 80 | 4.19 - 268 x 103 |
Table 1: Three most useful aperture tubes for sizing granules of starches from crop species.
| SOM Settings | Selection | |
| Description | SOM description | Sizing Starch Granules |
| SOM author | - | |
| Sample description | Sweetpotato starch samples | |
| Electrolyte | 50 g L-1 Lithium Chloride | |
| Dispersant | No | |
| Aperture | 100 μm | |
| Control Mode | Control Mode | Total Count [250,000] or [125,000]a |
| Waste Tank | When 80% full | |
| Run Settings | Enter sample info | Yes |
| Number of runs | 1 (or 2, for repeat runs) | |
| Flush aperture tube before run | Yes | |
| Flush aperture tube after run | Yes | |
| Save file | Yes, including pulse data | |
| Export data | Yes | |
| Print report | Yes | |
| Compare to sample specifications | No | |
| View | Size | |
| Stirrer Settings | Sample beaker | 100 ml Multisizer 4 ST |
| Use stirrer | Yes | |
| Speed | [15], CW (clock wise) | |
| Stirrer position | Automatic | |
| Threshold, Current and Gain | Sizing threshold | 2 μm |
| Aperture current | 1600 mA | |
| Preamp gain | 2 | |
| Extended size range b | When count [> 0.1%] of total count | |
| Pulse to Size Settings | Size bins | 400 |
| Size range | 2 to 60 μm | |
| Bin spacing | Log diameter | |
| Coincidence correction | Yes | |
| Pulse Edit | No | |
| Concentration | Sample amount | 0.2 ml |
| Density | - | |
| Use pre-dilution factor | - | |
| Analytic volume | - | |
| Electrolyte volume | 100 ml | |
| Use dilution factor | No | |
| Blockage | Blockage detection | Automatic (From start of run) |
| Default blockage detection: when count rate <20%, Aperture rate >40%, or concentration spike >40%. | ||
| Blockage action | Cancel, unblock and restart,Up to [4] times | |
| Show icon | Yes | |
| Blockage monitor | Count rate | |
| a: If repeated unblock and restart could not get the larger-count run completed, make two repeat runs of sizing a lower total count of 125,000 each from the same starch-electrolyte suspension, and merge the results of the repeat runs by using [MergeRuns] under [FileTools] of [File] in the Main Menu. Alternatively, replace the starch-electrolyte suspension with a new one having a lower nominal concentration (2-5%). When preparing a new drop-sample starch-electrolyte suspension, pulse-sonicate the starch-methanol suspension again to break up more aggregates. | ||
| b: The Extended Size Range controls actions for granules larger than 60% of the aperture diameter (100 µm in this SOM). The setting specifies inclusion of starch granules larger than 60 µm when their counts are larger than 0.1% of the total count. | ||
Table 2: Typical SOM settings for controlling sizing runs for sweetpotato starch samples.
| Preference Settings | Selection | |
| Printed Reports | Sample info | Sample, Run Number, Size Bins, Total Counts |
| Size graphs | Differential Volume %, Log X Axis, Smooth by Groups of Seven | |
| Size statistics | Volume, Volume % | |
| Average statistics | Total Amount, Mean, S.D. | |
| Overlay statistics | Total Amount, Mean, S.D. | |
| Listing | Columns: Bin Number, Bin Diameter (center), Diff. Number, Diff. Number %, Diff. Volume %. | |
| Bin Grouping: Bin Group Size 7, All Bins, Sum Bins in Group. | ||
| Statistics | Type | Geometrica |
| Range | All | |
| Results to print | Range, Total Amount, Mean, S.D., 95% Confidence Limits | |
| Results on graph | Range: All, Total Amount, Mean, S.D. | |
| Averaging and Trend | Average weightingb | Volume % |
| Distributionc | Differential | |
| Limits | 2 S.D. | |
| Pulse averaging | Use Convert Pulses to Size Range | |
| Export | Data items | Sample Information, Statistics, Average Statistics, Size Listing |
| Export extension | .xls | |
| Number format | 123456.78 | |
| Data format | Tab Delimited | |
| Export folder | Current Folder | |
| Page setup | Include Custom Title, Print Graphs using Screen Color Include Date | |
| Graph size: | Half Page | |
| Graph Option | Display: | Screen and Color Printer |
| Line color | (Default) | |
| Line style | (Default) | |
| Legend | Top Right | |
| Size | (Default) | |
| Graph style | Step | |
| Limit style | Curve | |
| Fonts and Colors | Default Fonts and Default Colors or as desired. | |
| View Options | Default view | Size, Graph |
| Size X axis | Diameter | |
| Measuring | Particles | |
| Liter Symbol | L (mL, μL, fL) | |
| Multisizer pulse data | Graph at most 5010 pulses, List at most 5010 pulses | |
| Volume units | μm3 | |
| Numbers | 123456.78 | |
| a: The geometric mean and S.D. statistics specified here are graphic ones that define the scale and shape of the determined differential volume-percentage equivalent-sphere size distribution. They are used to specify the lognormal distribution in the x ̅* x/ s* form. | ||
| b: The average weighting refers to how results from multiple runs are averaged by different weighting options. Change these settings in the Run Menu for different averaging and view options. | ||
| c: Select [Calculate] to open [ Average Statistics] in the [Run Menu] to see the average statistics in rows, the graph statistics for the average distribution in the “Mean” column. | ||
Table 3: Typical preference settings for view, analyses and print of results from sizing runs for sweetpotato starch samples.
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Discussion
The outlined procedure has resolved some critical issues in several existing methods for starch granule size analyses, including inappropriate 1D or 2D sizing of 3D granules, distortion of sizing measurements due to none-uniform granule shapes, poor reproducibility and dubious statistical validity due to limited granule-sample sizes, inaccurate or improper specification (especially the use of the average size) of granule sizes in the presence of both granule shape and none-normal size distributions. It uses the ESZ technique that measures 3D sizes (volume) of starch granules and is unresponsive to granule shapes. The design to derive the average granule size distribution from replicate analyses having a very large granule-sample size (4 x 250,000) not only renders the result statistically valid and more reproducible, but also technically mitigates measurement distortions by aggregated and damaged granules to improve sizing accuracy (explained below). As demonstrated in the representative results, the CV for the average of geometric means of replicate distributions determined using the procedure is usually smaller than 5%, indicating a satisfactory reproducibility of the results. Furthermore, the multiplicative specification of both the scale () and shape (s*) of the lognormal granule volume-equivalent-sphere size distribution more accurately depicts the true nature of distributed granule sizes in a starch sample, and is straightforward to use and universally comparable among granule sizing analyses of starches from same or different sources. Therefore, the procedure enables more accurate, reproducible, and statistically valid determination of starch granule sizes, and proper specification of determined granule lognormal size distributions. It is applicable to all granule sizing analyses of gram-scale starch samples, and could become an essential tool for studies on how starch granule dimensions are molded by the starch biosynthesis apparatus and mechanisms in plant starch-accumulating tissues, and how they impact properties and functionalities of starches for food and industrial uses.
Starch granules are stereo particles having mostly non-spherical shapes so that their sizes must be defined and measured in 3D terms. Thus, the volumes of starch granules best define their sizes, and the volume-equivalent-sphere diameter is the only single 1D size parameter that can be used to properly describe the granule 3D sizes since no stereo objects other than sphere can be defined with a single 1D size parameter. Furthermore, starch granules from all plant species possess a set of shapes with various occurrence frequencies. In the presence of such a shape distribution, any particle sizing techniques that are responsive to particle shapes, e.g., the laser diffraction technique, are not suited for reproducible and statistically valid determinations of starch granule size distributions, as the system error inherent to these techniques cannot be easily corrected with a shape factor. In fact, the error rate (CV) among replicate analyses of granule sizes from the same sweetpotato starch sample using the laser diffraction technique could reach as high as 15-20%28, indicating very poorly reproducible sizing results. Unfortunately, the impact of granule shapes on sizing starch granules have been mostly overlooked, which resulted in a large body of dubious starch granule size data acquired using shape-responsive particle sizing techniques in the literature.
The two-parameter multiplicative specification defines both the scale () and the shape (s*) of lognormal distributions, and is thus far more precise and meaningful than a single descriptor of mean size or a size range26. The multiplicative x/ s*, x/ (s*)2, and x/ (s*)3 intervals, corresponding to 
± s, ± 2s, and ± 3s intervals of a normal distribution, covers approximately 68.3%, 95.5%, and 99.7% confidence intervals of a lognormal distribution, respectively27. The geometric mean ( ) and S.D. ( s* ) of a lognormal granule size distribution correspond to the graphic geometric mean and S.D. of the size distribution curve, which are calculated by the analyzer software and can be selected to display on the on-screen size graph during a sizing run or analyses of results. It is, therefore, rather convenient, and simple to use the multiplicative specification. Additionally, the and s* have been demonstrated to have different physiological implications associated with the starch biosynthesis apparatus28. The granule volume-size distributions of starches from various plant species may well be all lognormal since the formation of starch granules in plant starch-accumulating tissues falls into an unconstrained evolving complex system31 or an intracellular catalytic reaction network32 characteristic of a lognormal distribution. The bimodal granule size distributions of starches from some plant species, such as those from wheat13,14, could be regarded as two lognormal distributions. Therefore, the multiplicative specification of granule lognormal volume-equivalent-sphere size distributions may also allow a statistically valid universal comparison of granule sizes determined from starches of various plant sources and by different measurements, as the is in the form of volume-equivalent-sphere diameter and s* is demensionless.
An appropriate total granule-sizing count for the analysis of a starch (in methanol) sample, which represents the granule sample size, is most critical to successful determination of the granule size distribution of statistical significance for the starch sample. In the case of sweetpotato starch samples, once the total count in a single run reaches over ~65,000 and ~125,000, the graphic geometric S.D. ( s*) and geometric mean ( ) of the displayed differential volume-size distribution curve no longer significantly change, respectively, indicating minimal counts for the s* and of statistical significance. The sampling redundancy in sizing 250,000 granules for a starch-methanol sample in the procedure is intended to discount for the aggregated and damaged granules in the sized granule pool. Even assuming that the aggregated and damaged or broken granules accounted for 50% of the total count of 250,000 granules in a completed run or two merged repeat runs, the graphic geometric S.D. and mean of the determined distribution would not have been significantly impacted as they would have been anchored by the intact granules of half of the total count. Furthermore, the more volume-size reduction of the damaged or broken granules, the less impact they have on the distribution. This is because smaller granules take a larger number percentage, but smaller volume percentages of the total sized granules. As demonstrated by the comparison between number and volume cumulative distributions for the same average distribution in Figure 2, starch granules with an equivalent-sphere diameter smaller than or equal to 9.967 µm accounted for about 48.53% of the total number, but only 5.854% of the total volume. Thus, any damaged or broken-down granules less than 10 µm would have a very small impact on the differential volume-percentage size distribution. For starch samples of other plant sources, an appropriate total count for their sizing analyses can be the one doubling the minimal count over which the graphic geometric mean ( ) of the displayed size distribution in a trial run no longer significantly change.
Technically, the most critical step for a sizing run is to drop a proper amount of the starch-methanol suspension to the electrolyte for an optimal range of 5 to 8% nominal concentration for the starch-electrolyte suspension. To reach the goal, the drop size and the concentration of the starch-methanol suspension may have to be adjusted through trial runs. Concentrations of the starch-electrolyte suspensions higher than the optimal range increase risks of reduced sizing precision, and frequent aperture blockages leading to run abortions, which could make it very difficult to complete a run. But, too low a concentration (e.g. <2%) of the starch-electrolyte suspension may prolong a run too much, and distort frequencies of granules in various size bins due to non-random sampling of granules, which could lead to an unacceptable error rate (the average CV > 5%) for a replicate analysis. The total count for a sizing run also has a major impact on the optimal concentration of a starch-electrolyte suspension, hence on the amount and concentration of the starch-methanol added. The larger the total count for a run, the longer the time for the completion of the run, and thus the more risks for aperture blockages leading to run abortions. The problem of aperture blockage by aggregates worsens when aperture tubes of smaller diameters are used for starch granules of smaller sizes, which makes it very difficult to analyze small starch granules (< 2 µm). This is indeed the major drawback or limitation of the procedure. The aperture blockage problem could be alleviated to a certain extent using some technical means. One may use more sonication to break up aggregates (inevitably more damaged granules as well) in a starch-methanol suspension, and/or a diluted starch-electrolyte suspension at 2-5% nominal concentrations. Alternatively, one may use technical repeat runs of sizing the minimal total count for stable s* and of the size distributions for a starch type (e.g. about 125,0000 counts for sweetpotato starch) from the same starch-electrolyte suspension, and merge the results of the repeat runs. Each of the four replicate distributions (S1a, S1b, S2a and S2b) shown in Figure 1 were from two merged technical repeat runs of sizing 125,000 granules each from the same starch-electrolyte suspension. Both methods need to be well tested, as they may increase the replication error rate to an unacceptable level (i.e., the average CV > 5%).
Technical and biological replicate sizing analyses of starch samples from plant sources under similar physiological conditions improve the reproducibility and accuracy of the determined average granule size distribution. Practically, three or four biological replicates of starch samples may be independently extracted from the same tissue under a specific condition. But, we previously found that there was no significant difference in error rates (CV and Standard Errors for the average), and and s* between the average granule size distribution derived from distributions of four biological replicates (i.e., one sizing x one suspension x 4 extracts) and the one from those of two technical sampling each from two biological replicates (i.e., one sizing x 2 starch-methanol suspensions x 2 extracts)28. Thus, biological replicate samples could be reduced to two, at least for the sweetpotato starch. Other steps and technical parameters that could be modified or adjusted were specifically noted below each of the steps or the particular parameter in the procedure.
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Disclosures
The authors have nothing to disclose
Acknowledgments
This work is partly supported by the Cooperative Agriculture Research Center, and Integrated Food Security Research Center of the College of Agriculture and Human Sciences, Prairie View A&M University. We thank Hua Tian for his technical support.
Materials
| Name | Company | Catalog Number | Comments |
| Analytical beaker | Beckman Coulter Life Sciences | A35595 | Smart-Technology (ST) beaker |
| Aperture tube, 100 µm | Beckman Coulter Life Sciences | A36394 | For the MS4E |
| Disposable transfer pipettor, | Fisher Scientific (Fishersci.com) | 13-711-9AM | Other disposable transfer pipettors with similar orifice can also be used. |
| Fisherbrand Conical Polypropylene Centrifuge Tubes, 50 ml | Fisher Scientific (Fishersci.com) | 05-539-13 | Any other similar types of tubes can be used. |
| Glass beakers, 150 to 250 ml | Fisher Scientific (Fishersci.com) | 02-540K | These beakers are used to contain methanol for washing the aperture tube and stirrer between runs. |
| LiCl | Fisher Chemical | L121-100 | |
| Methanol | Fisher Chemical | A412-500 | Buy in bulk as the analysis uses a large quantity of methanol. |
| Mettler Toledo ML-T Precision Balances | Mettler Toledo | 30243412 | Any other precision balance with a readability 0.01 g to 1 mg will work. |
| Multisizer 4e Coulter Counter | Beckman Coulter Life Sciences | B23005 | The old model, Multisizer 3 can also be used with slight adjustment of parameters. The 4e model comes with a 100 μm aperture tube. Other aperture tubes of different diameter can be purchased separately from the company. |
| Ultrasonic processor UP50H | Hielscher Ultrasound Technology | UP50H | Other laboratory sonicator having a low-power (<50 Watt) output can be also used. Both MS1 and MS2 sonotrodes for the particular sonicator can be used to disperse starch granules in 5 ml methanol. Always use the lowest setting first, 20% amplitude and 0.1 or 0.2 cycle, and raise the setting if aggregates persist in suspension. |
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