# Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat
## 3 Results and Discussion
### The Allelic Diversity of Glutenins had Limited Influence on Polymer Characteristics  
The PLS regression first evidenced that PC and GH had very low, but significant, influences on Mw and PI characteristics (Table 2). Although all experimental plots received optimum nitrogen supply at each location for high grain yield, other agro-climatic conditions may have induced differences in nitrogen absorption and immobilization in spikes. Higher temperatures and droughts are known to reduce nitrogen absorption by the plant and starch content in grains and, also, to shorten the duration of the grain-filling period [33]. The increased PC is, consequently, opposed to higher protein accumulation and polymerization, requiring longer normal accumulation time. Once PC and GH are involved, the PLS regression revealed that LMW-GS diversity contributed two times more to polymer characteristics than HMW-GS. These global contributions of the HMW-GS and LMW-GS to polymer characteristics are in full agreement with the quantitative proportion classically found of the two types of glutenins: i.e., 1/3 and 2/3, respectively. The 31 alleles encoding the HMW-GS and LMW-GS increased the explanation of the phenotypic values by only 17.1%, 25.4%, and 16.8% for Mw, Rw, and PI, respectively. Similar contributions (not shown in [24]) were found for the 28 alleles present in the 68 cultivars experimented in 2008-2010. Among the 14 alleles encoding HMW-GS, the Glu-A1 null allele, all the Glu-B1 alleles, and the subunits Glu-D1 2-12 had negative influences on polymer characteristics. In contrast, the subunits Glu-A1 1, Glu-D1 3-12, and Glu-D1 5-10 increased the three characteristics. For the 17 alleles encoding LMW-GS, Glu-A3 a and b had negative influences, whereas Glu-A3 e or f, noted \"ef\", were positively associated. For the Glu-B3 locus, alleles a, b, and i were negatively associated, whereas g and j were positively associated to the three characteristics. The alleles GluD3 a and c (Glu-D3 b) were negatively (positively) associated to the three characteristics. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Explanatory Variate** & **Mw (\%)** & **Rw (\%)** & **PI = Mw/Mn (\%)** \\ \hline PC + GH & 3.628 * & 0.064 & 0.688 * \\ \hline PC + GH & & & \\  +HMW-GS & 8.846 * & 8.807 * & 5.316 * \\ \hline PC + GH & & & \\  +LMW-GS & 16.465 * & 17.630 * & 14.419 * \\ \hline PC + GH & & & \\  +HMW-GS & 20.781 * & 25.498 * & 17.570 * \\ +LMW-GS & & & \\ \hline PC + GH & & & \\  +HMW-GS & & & \\  +LMW-GS & & & \\  +WatSum May & 28.342 * & 39.350 * & 37.052 * \\  +WatSum Jun & & & \\  +WatSum Jly & & & \\ \hline PC + GH & & & \\  +HMW-GS & & & \\  +LMW-GS & & & \\  +Tmean May & 60.485 * & 73.627 * & 76.441 * \\  +Tmean Jun & & & \\  +Tmean Jly & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Partial least square (PLS) regression: Part of the phenotypic variance of molecular mass (Mw), gyration radius (Rw) and polydispersity index (PI) explained by grain protein concentration (PC), grain hardness (GH), high molecular weight glutenin subunits (HMW-GS) alleles, low molecular weight glutenin subunits (LMW-GS) alleles, cumulative water precipitations (WatSum), and cumulative mean temperatures (Tmean)for the three final months in the 11 experimental fields of wheat crops. The standardized coefficient, described by the PLS regression, for the 14 HMW-GS alleles are shown in Supplemental Figure S3a-c and for the 17 LMW-GS alleles in Supplemental Figure S3d-f. Altogether, PC, GH, and glutenin diversity explained only 20%, 25%, and 17% of the phenotypic diversity of Mw, Rw, and PI, respectively. When rainfalls registered in each experimental location for May, June, and July were introduced into the PLS regression, the total part of the variance explained reached 28.3%, 39.4%, and 37.1%, respectively (Table 2).