Characterizing the Distribution of Ppm Gluten in Gluten Free Oatmeal Servings Contaminated with a Wheat Kernel

Oats are often contaminated with rogue kernels of gluten-containing grains like wheat, barley and rye. When producing gluten free oatmeal, possessing an understanding of the consequences of this possibility is prudent, as labeling requirements specify a maximum amount of gluten in terms of ‘parts per million’ (ppm) gluten. Variation in contaminant kernels, along with variation due to measurement itself though, can result in a wide range of possible ppm gluten outcomes in contaminated servings. This research pursues characterization of this variability, highlighting contributors to it, doing so by quantifying distributional outcomes of ppm gluten in wheat kernel contaminated servings. This is done via statistical simulation of wheat kernel contaminated servings, done for a collection of wheat types and incorporating various measurement influences. Results indicate substantial variability in ppm gluten per serving for a given wheat type, as well as between them, with this being compounded by the measurement task itself.


Introduction
Oats are commonly contaminated with gluten containing grains (GCG's) such as wheat, barley and rye (Hernando et al, 2008;Koerner et al, 2011;Thompson, Lee & Grace, 2010). 'Kernel based' contamination like this has recently been found to complicate determination of whether oats labeled gluten free (GF) end up as such on store shelves (Fritz, Chen & Contreras, 2017;. Due to oversights in this regard, much of industry has been mis-diagnosing their GF labeled oat offerings, concluding they are pure when in fact one in every few dozen servings contains a GCG (Fritz, Chen & Contreras, 2017;Chen, Fritz & Ferrini, 2017;Fritz & Chen, 2019). False negative dispositions in this regard affect celiac disease (CD) patients who rely on a GF diet to avoid adverse effects (Leonard, Sapone, Catassi et al., 2017).
Due to the prevalence of contamination and inherent difficulties in assessing oats as GF, it is believed prudent to understand the consequences of GCG contaminated servings. This is addressed here by characterizing the distribution of ppm gluten in servings of pure oats containing a single barley kernel. This is a corollary study to that carried out by the authors where wheat kernels were the GCG of focus (Fritz & Chen, 2017b). A 'divide and conquer' approach has been taken regarding these two GCG contaminates due to inherent differences in these grains along with the dissimilarities in how gluten is assessed due to them.
The approach used here is statistical simulation. With this we first create a virtual barley kernel based on published weight, protein and gluten distributions, and then determine the ppm gluten with this kernel present in a 40g serving of otherwise pure oats. Doing this 25,000 times, provides a distributional assessment of 'actual' gluten in a barley contaminated serving, providing insight into true contamination unencumbered by measurement influences.
As a second analysis, we add influences of measurement, obtaining an 'as measured' assessment by simulating the use of R-Biopharm R5 ELISA testing. Doing this 25,000 times provides a distributional assessment of gluten in a barley contaminated serving as it would be perceived through the lens of measurement.
These two simulated distributions provide new insights into gluten dosing when a barley kernel exists in a serving of oats. Comparison of them provides insights into how measurement affects assessment and what the requirements are in this regard.

Methods -Kernel Variability
It has been widely published that gluten resides in the endosperm of barley in the form of storage proteins called hordeins (Kirkman et al, 1982;Shewry et al, 1985). Given this, there are three variables, believed to directly influence the gluten content of a barley kernel. They are 1) kernel weight (dry basis), 2) % protein in the kernel on a dry weight basis, and 3) % gluten (i.e., hordeins) in the protein. Following a literature search, estimates of distribution parameters for the above-mentioned factors have been shown in Table 1 Nair, 2010Nair, 2010Nair, 2010& Fox, 2011** Kirkman, 1982 * -As per Kirkman et al '82, hordein content tends to vary from 35% -55% so 45% used as an average with stdev to vary roughly across the 35% -55% range.
** -Stdev's obtained via Monte Carlo simulation combining variation in 'line to line' averages with 'kernel to kernel' variability from Fox '11 (for Gairdner cultivar used here as representative of other cultivars) Averages and stdevs shown in Table 1 are parameter estimates reflecting 'kernel to kernel' variability across varietal lines for each of the two barley classification types. The stdev for 'kernel % protein' was not directly found in the literature but derived by combining a 'line to line average' variance component (Nair et al, 2010) with a 'kernel to kernel' variance component (for the Gairdner variety used as a surrogate for other lines) (Fox, 2011). This approach is outlined in Table 2. * -Single kernel characterizaion system hardness index ** -For the Gairdner barley variety used here as a surrogate for other lines (Fox, 2011).
*** -Obtained by sampling across lines for a given row type using Fox '11 kernel to kernel % Protein findings.
The three variables shown in Table 1 are assumed herein to be independent of each other. Research into such relationships was unable to be found in the literature except for protein content relative to dry kernel weight for wheat (Delwiche, 1995), where no relationship was apparent.

Methods -Measurement Variability
Four measurement variables have been utilized in characterizing the ppm gluten in a barley contaminated serving of otherwise gluten-free oatmeal. This was to determine gluten content 'as measured' relative to estimation of 'actual true gluten' exclusive of measurement. These variables are 1) % of overall gluten protein actually assessed, 2) % analytical recovery of the fraction of hordeins assessed, 3) test kit calibration standard and multiplier used, and 4) effects of grinding non-homogeneity (of a barley kernel in oats).
Percentage (%) of overall gluten protein actually assessed has been included, since the R-Biopharn ELISA test kit only measures three of the four barley hordeins, namely the γ, B & C (and not D) components (Shewry et al,'85,Tanner et al,'19). It is assumed to be normally distributed.
Also, percentage (%) analytical recovery of the fraction of hordeins assessed has been included, since no validation for gluten in oats is believed to have been performed, as there's no record of this published by Biopharm up till now (R-Biopharm, 2012). It is also possible that this may vary somewhat 'test to test' as well. It has been assumed to be normally distributed as well.
'Test kit calibration standard and multiplier' is included since this obviously has a profound effect on estimated ppm gluten.
Finally, 'effects of grinding non-homogeneity' is included since this has been shown to inflate gluten ppm test outcome variability, producing a lognormal distribution of gluten test results (Fritz, 2017b.) Following a literature search, estimates of distribution parameters for the above have been shown in Table 3. Note that the stdev of 'analytical recovery' was unable to be found in the literature and has been 'guesstimated' here. Sensitivity analysis around this 'guesstimate' has been performed and will be reported in the results section of this paper.

Methods -Simulation
These seven variables, three being barley characteristics (Table 1) and four measurement variables (Table 3), have been used to simulate servings of gluten-free oatmeal (of 40g size), where each is contaminated with a single barley kernel. These contaminated barley kernels are 'created' based on random selection from the distributions for the three key kernel variables defined in Table 1. Since these kernel characteristics are considered independent of each other, the approach is simply to first 'create' a kernel of a certain dry weight by randomly selecting a weight from the 'dry weight' probability distribution. Then to this '% protein' and '% protein that's gluten' values are applied, with these values being randomly selected from their respective distributions.
So, for a 'true' ppm gluten assessment (exclusive of any measurement influences), the following equation defines each simulated serving's ppm gluten: PPM gluten actual =[(dry weight in g) x ('% Protein'/100) x ('% Protein that's Gluten'/100)]/40g (1) For an 'as measured' assessment of ppm gluten due to barley, there are two steps. The first is to get what we refer to as a 'pre-grind' assessment of gluten and this is then used to obtain the final 'post grind' ppm denoted herein as the 'as measured' value. By 'pre-grind' we mean prior to incorporating variability due to the inability to achieve a homogenous grind of the kernel based gluten in a serving of oats (Fritz et al., 2017b).
Obtaining the 'pre-grind' assessment is done by randomly selecting measurement values for '% protein that will be assessed' and 'analytical recovery' from their respective probability distributions, and then choosing a calibration standard and multiplier to use. Herein we have opted to use a wheat calibration with a multiplier of 1. This is recognized as appropriate practice for barley related gluten in oats (Hernando et al, 2008), although the best multiplier is under debate. Use of a different multiplier would simply convert results by that amount so a conversion factor of 1.0 has been selected here for simplicity.
For the final 'as measured' value, or 'post-grind' ppm value for a serving, the 'PPM gluten pre-grind ' outcome is used as the gluten ppm average of a log-normally distributed collection of 0.25g test results in a 40g serving (Fritz, 2017b.) The natural log of this value is considered the average of a normally distributed random variable whose stdev is then randomly selected from a normal distribution whose parameters are shown in Table 3, namely 0.793 average and 0.082 stdev. These values come from studies conducted previously (Fritz et al., 2017b) although the barley results were not published at that time (as the focus in the previous publication was wheat contamination of oats).
So the final 'as measured' ppm gluten for a serving, denoted as 'PPM gluten post-grind ', is then the anti-log of this log transformed value, defined by: PPM gluten post-grind = e ln(PPM gluten post-grind transformed) So the above is done for 25,000 simulated barley kernels, each in 40g servings of otherwise pure oats. The resultant 25,000 simulated ppm gluten values are then used to characterize the 'as measured' distribution of ppm gluten contamination of a 40g serving of pure oats contaminated with a single kernel of barley. This has been done for each of the two U.S. spring barley types, namely two and 6 row barley.

Data Analysis
Simulation of servings was performed in custom routines created in Excel, Microsoft Office 2013. Table 4 shows the outcomes obtained for 25,000 simulated 40g servings of oats each contaminated with a single 'virtual' barley kernel. The seven barley and measurement variable settings for each simulation are shown on the left-hand side with resultant simulation findings shown on the right-hand side. Rows 1-4 of the table are for two row spring barley and 5-8 for six row cultivars. Rows 1 and 5 are simulated 'actual' outcomes which are estimates of 'true' ppm gluten in 40g contaminated servings. Rows 2-4 and 6-8 then show 'as measured' outcomes for various analytical recoveries. 70%, 80% and 90% analytical recovery simulations have been conducted due to the uncertainty of this variable's average value.

Results
The simulation findings part of the table includes resultant distribution type, parameters for that distribution, % of servings < 20 ppm (a common regulatory maximum for GF labeling) and comparative distribution plots which overlay 'actual' and 'as measured' distributional outcomes. NOTE: For each of these 8 simulations, ten replicates of the same 'settings' were performed. This was to evaluate the stability or lack thereof of the resultant simulation outcomes. Outcomes were found repeatable with less than +/-1 ppm difference in averages obtained and less than +/-3 ppm differences in standard deviations obtained across all eight simulations.

'Actual' PPM Gluten Outcomes
Simulated 'actual' outcomes are shown in rows 1 and 5 in Table 4. These distributions provide insight regarding gluten dosing potential as unencumbered by the influence of measurement. Resultant distributions are normally distributed averaging 57 ppm and 41 ppm gluten with 14 and 12 ppm stdevs for two and six row barley respectively. For both barley type classifications, a single barley kernel in 40g of otherwise pure oats appears likely to produce a non-compliant serving (prob. < 20 ppm being 0.0008 and 0.0225 respectively).
With two row barley averaging 39% higher gluten than six row, we can also infer that different barley classifications can produce significantly different gluten contamination potential. Within both barley classifications we have also observed substantial variability as well, with 95% control limits for these two types spanning 29 to 85 ppm and 33 to 81 ppm gluten respectively. This suggests cultivar to cultivar differences may also exist.
There is a lack of kernel level characterization of weight, protein and hordein fraction research at present, preventing more detailed analyses beyond the broad categories dealt with here. Looking into sub-classifications and more commonly used common cultivars in this way would enable better understanding of barley related gluten contamination of oats.

'As Measured' PPM Gluten Outcomes
Simulated 'as measured' outcomes are shown in rows 2-4 and 6-8 in Table 4. These ppm gluten distributions are intended to reflect what one would 'view' through the lens of measurement. Again, all simulations assume assessment via ELISA R5 using a wheat calibration and 1x multiplier. Resultant distributions are lognormally distributed due to the prevalence of non-homogenous grinding shown to create this circumstance (Fritz, Chen & Contreras, 2017).
Using an 80% average analytical recovery rate, average ppm gluten outcomes obtained are 61 & 44 for two and six row barley respectively. With 70% and 90% recovery rates, these change from 54 to 69 and 39 to 49 ppm gluten for two and six row respectively. Consequently, and as expected, analytical recovery rate is a significant influencer on resultant gluten obtained. Since regulatory dispositions are made regarding ppm gluten content in oats, it is hoped recovery rates for RIDASCREEN Gliadin in oats will be determined to aid assessment accuracy.
The stdev for analytical recovery was a 'guesstimate' as well. This was varied from 1% to 8.5% in simulations (results not shown) to test outcome sensitivity due to this potential variability. Doing so resulted in no change in average ppm gluten and less than 3 ppm change in ppm gluten stdevs across barley types and analytical recoveries evaluated.

'Actual' vs. 'As Measured' PPM Gluten Discussion
Referring to Table 4, simulated 'as measured' average ppm gluten values are comparable to simulated 'actual' average ppm gluten values, this being the case for both two row and 6 row barley types. It appears a recovery rate of around 75% would produce the most similar results for both barley types given a calibration conversion of 1x as assumed here.
Despite being comparable in average though, dissimilarity in distributional shapes, i.e., normally distributed 'actual' outcomes vs. lognormally distributed 'as measured' ones, produce a significant difference in resultant probability of diagnosing contaminated servings as 'compliant'. As mentioned earlier, employing the common < 20 ppm regulatory requirement as a standard , two row and six row barley types are simulated to possess 0.0008 and 0.00225 probabilities of a compliant 40g serving when containing one of their kernels. In contrast though, their 'as measured' counterparts provide probabilities of ~ 0.18 and 0.31 for two and six row barley respectively (using an 80% recovery rate). Assuming the 'actual' simulation results reflect true contamination potential, this equates to false negative rates of ~ 0.18 and 0.28 'as measured'.
Since 'as measured' results are obviously what are used to disposition compliance, false negative potential like this is problematic. This is driven by the inherent inability to homogenously grind gluten in these grains which causes the lognormal distribution of gluten test outcomes. Mitigating this has been addressed though ) and use of a method such as this is encouraged.
Finally, in Table 4, in the rightmost column, calibration mulitpliers needed to provide 'as measured' probabilities of being < 20 ppm equal to those obtained in the 'actual' simulations are provided. These range from 3.75x to 7.0x based on barley type and analytical recovery rate.

Conclusion
Statistical simulation has been used to characterize the ppm gluten in otherwise pure servings of oats. This provides insight regarding potential gluten dosing due to barley contamination. This has also shown how measurement can adversely affect assessment, highlighting the need for inventive methods  to overcome non-homogeneity in grinds, for analytical recovery studies for gliadin in oats to be conducted, and for studies to better ascertain proper conversion factors for gluten in oats due to barley to be pursued.