# Genetic and Environmental Factors Associated to Glutenin Polymer Characteristics of Wheat
## Materials and Methods
### Asymmetric Flow Field-Flow Fractionation (A4F) Multi-Angle Laser Light Scattering (MALLS)  
The principle of the separation technique and the wheat protein extraction protocol were previously described [20; 22]. The polymer samples were analyzed with A4F-MALLS-UV using an Eclipse 3 A4F Separation System controller (Wyatt Technology, Toulouse, France) serially connected to a UV detector and a Wyatt DAWN HELEOS 18-angle MALLS detector (Wyatt Technology, Toulouse, France). The MALLS detector operated at a wavelength of 690 nm. An Agilent 1100 series isocratic pump (Agilent Technologies, Les Ulis, France) with an in-line vacuum degasser and an Agilent 1100 series autosampler delivered the eluent flow and handled the sample injection (30 \(\upmu\)L) into the A4F separation channel. The UV detector was set at 214 nm. At the pump outlet, a regenerated cellulose filter with a pore size of 0.2 \(\upmu\)m (Merck Millipore, Guyancourt, France) was installed, ensuring that particle-free carrier entered the channel. The A4F channel had a trapezoidal geometry (tip-to-tip length of 28.6 cm, and inlet and outlet widths of 2.15 and 0.6 cm, respectively). The spacer nominal thickness was 350 \(\upmu\)m. The ultrafiltration membrane, forming the accumulation wall, was a regenerated cellulose membrane with a nominal cut-off of 10 kDa (Merck Millipore, Guyancourt, France). Validation of the A4F system performance and normalization of MALLS detector was performed with monomeric bovine serum albumin solubilized in the mobile phase (Sigma-Aldrich, Saint-Quentin Fallavier, France). The carrier liquid was sodium phosphate buffer (0.05 M, pH 6.9) containing 0.1% (_w/v_) SDS and was filtered through a 0.1-\(\upmu\)m membrane (Merck Millipore, Guyancourt, France). The fractionation method used a constant detector flow of 1 mL/min and a gradient cross-flow. The method started with a focus time of 0.5 min at a flow rate of 2 mL/min. This step was followed by a focus/injection time of 1.0 min at 0.2 mL/min and a relaxation/focusing time of 0.5 min. Elution then followed at an outflow rate of 1.0 mL/min and with a cross-flow rate decreasing exponentially from 3.0 to 0.0 mL/min for 14 min. Finally, elution at a cross-flow rate of 0.0 mL/min was maintained for 9 min. The recorded MALLS and UV data were processed using Astra software (v. 5.3.4.13, Wyatt Technology, Santa Barbara, CA, USA). The Mw and radius were obtained by fitting the MALLS data using the Berry method, performing a second order fit to the data collected at scattering detectors 5-17. Molar mass and radius can be obtained by MALLS combined with concentration measurements by applying the Rayleigh-Gans-Debye approximation [32] (Equation (1)):  
\[\left(\frac{K^{\mathrm{c}}c_{i}}{R_{\mathrm{\theta}}}=\frac{1}{M_{i}P(\mathrm{ \theta})}+2A_{2}c\right) \tag{1}\]  
where \(R_{\mathrm{\theta}}\) is the excess Rayleigh scattering over and above that of the solvent due to a solute of concentration \(\mathrm{c_{i}}\) for slice i of the fractionated sample. \(K^{\mathrm{*}}\) is an instrumental constant dependent on the wavelength and refractive index increment (dn/dc) of the solute in the particular solvent. \(M_{i}\) is the weight-average molar mass for the solute. \(P(\mathrm{\theta})\) is the scattering function that describes the angular dependence of the scattered light intensity from which the mean square radius \(<\)r2\(>\) is derived. \(A_{2}\) is the second virial coefficient and captures nonideality due to solvent-solute interactions; it is expected to be vanishingly small in a dilute fractionated sample.