## 2 Materials and Methods
### Measurement of the Antioxidant Activity of Bread Made with Flour-Bran Blends  
To analyze any changes in the antioxidant activity of the bread during the bread-making process, the total antioxidant activity of the bread crust and crumb was measured by DPPH and ABTS radical scavenging activities according to the method described by [PERSON] and [PERSON] [12]. To determine DPPH radical scavenging activity, DPPH (1,2-diphenyl-1-picryl hydrazyl) solution (60 \(\upmu\)mol/L) (3.9 mL) and bread extract (0.1 mL) were mixed and reacted at 25 \({}^{\circ}\)C for 30 min (t = 30). The absorbance was measured at 515 nm using a spectrophotometer (X-ma 6100 PC, Human Corporation, Seoul, Korea). For the sample-free group, absorbance was measured by mixing 3.9 mL of DPPH solution and 0.1 mL of 80% methanol. DPPH radical scavenging activity (%) was calculated using the absorbance (Asample t = 30) value of the sample-added group and the absorbance (Asample t = 0) value of the sample-free group. The graph of trolox concentration versus DPPH radical scavenging activity was plotted as the standard curve, and the DPPH value on a dry weight basis (dwb) was expressed as \(\upmu\)mol TE (trolox equivalents)/100 g.  
For determining ABTS radical scavenging activity, ABTS [2,2'-azino-bi (3-ethylbenzothazoline-6-sulfonic acid), 7 mm] (Sigma, Mannheim, Germany) solution and 2.45 mm K2S2O8 (Sigma, St. Louis, MO, USA) solution were mixed 1:1 for 2 min and then reacted in the dark for 12 h. After diluting 1 mL of ABTS solution to 50 mL, absorbance was measured by mixing 1.85 mL of this solution with 0.1 mL of the extract of bread crumb and crust with methanol. The ABTS radical scavenging activity (%) was calculated using the absorbance (Asample t = 30) value of the sample-added group and the absorbance (Asample t = 0) value of the sample-free group. The graph of trolox concentration versus ABTS radical scavenging activity was plotted as the standard curve, and the ABTS value on a dry weight basis (dwb) was expressed as \(\upmu\)mol TE (trolox equivalents)/100 g (dryw).  
Experimental Design for Optimizing the Processing Conditions of Bread Made of Flour-Bran Blends at 30% Bran  
Additionally, a response surface methodology with a Design Expert program (version 10.0, Stat-Ease, Inc., Minneapolis, MN, USA) was used to identify significant processing factors and optimize the water amount in formulation, dough mixing and fermentation conditions to improve the quality of bread made with the flour-bran blend while enhancing its antioxidant activity. The flour-bran blend with 30% bran was used because the bran percentage in the blend was higher than that in the whole wheat flour (approximately 20%). Based on a central composite design for making bread with the flour-bran blend at 30% bran, three factors as independent variables were selected and the levels for each factor were: water amount (55, 75 g), mixing time (2, 5 min), fermentation time (50, 90 min). A center point (65 g water, 3.5 min mixing time, and 70 min fermentation time) was also included. Overall, bread baking under seventeen conditions (by setting \(\alpha\) point to 1.5) (Table 1) was conducted as described above and in random order. The bread quality was analyzed by bread moisture, color, height, volume, and firmness.