*2.4. Influence of Buckwheat Milling Fractions Addition on the Falling Number Values*

The Falling number index (FN) value, determined at least in duplicate using the standard method (ICC 107/1) and FN device (Perten Instruments AB, Stockholm, Sweden), was performed. The method is a viscometer assay, based on the rapid gelatinization of a flour suspension in a boiling water bath and the measurement of its liquefaction by *α*-amylase. FN index value gives an estimation of the *α*-amylase activity from the wheat-buckwheat flour.

#### *2.5. Dough Rheology Assessed by Mixolab*

The influence of buckwheat flour milling fractions and the level added on the rheological properties of composite flours dough was assessed using a Mixolab analyzer (Chopin, Tripette et Renaud, Paris, France) and ICC-Standard Methods No. 173 (ICC, 2010) by applying the standard Chopin+ protocol, as described in previous studies [31,32]. For all wheat-buckwheat flour samples, the first stage was determined by the following mixing parameters: water absorption, WA (%), dough development time, DT (min), and dough stability, ST (min). In the following stages, the minimum torque C2 (N·m), related to protein reduction due to temperature rise; peak torque, C3 (N·m), related to starch gelatinization; minimum torque C4 (N·m), as the stability of hot-formed gel; maximum torque, C5 (N·m), as a starch retrogradation measure during dough cooling were recorded. From the Mixolab curve registered, the differences between torques C1 and C2 (C1-2), C3 and C2 torques (C2-3), C3 and C4 torques (C3-4), and C4 and C5 torques (C4-5) associated with protein weakening, starch gelatinization, cooking stability and starch retrogradation were also determined.

#### *2.6. Factorial Design and Statistics*

A full factorial design was used to study the main and interaction effect of replacing wheat flour with buckwheat milling fractions on the responses, Falling number (FN) index, water absorption of composite flour, and Mixolab properties. The studied factors were three buckwheat flour particle sizes (large, medium, and small) and the level added in wheat

flour (0, 5, 10, 15, and 20%). An experimental design that consists of fifteen combinations (Table 1) was conducted. The simultaneous effect of these two factors on the responses was investigated through the response surface methodology (RSM) in conjunction with the desirability function approach. RSM is a powerful technique mainly used in the design and innovation of bakery products, and to find the optimum level of formulation factors [34,40] or the optimal processing conditions [41].


**Table 1.** Factors and their level in experimental design.

The quadratic polynomial regression model (Equation (1)) was proposed for all responses. In the equation, Y represents the response and the regression coefficients represented by bo—coefficient of intercept, b1, b2—coefficient of linear terms, b11, b22 coefficient of quadratic terms, and b12—coefficient of interactions between effects of A (particle size of buckwheat flour) and B (level of buckwheat flour added in wheat flour) factors.

$$\mathbf{Y} = \mathbf{b}\_0 + \mathbf{b}\_1 \cdot \mathbf{A} + \mathbf{b}\_2 \cdot \mathbf{B} + \mathbf{b}\_{11} \cdot \mathbf{A}^2 + \mathbf{b}\_{22} \cdot \mathbf{B}^2 + \mathbf{b}\_{12} \cdot \mathbf{A} \cdot \mathbf{B} \tag{1}$$

The multiple linear regression analysis was applied to fit the data obtained for each response to linear, two-factor interactions, quadratic and 2FI models. The most adequately model to predict data variation for each factor was found through a sequential *F*-test, coefficients of determination (*R*2), adjusted coefficients of determination (*Adj.- R*2). To evaluate the significant differences (*p* < 0.05) between the samples, one-way ANOVA and Tukey's HSD post-hoc test was used to describe means with 95% confidence. All the analysis was determined in duplicate. These analyses were performed using Stat Ease Design-Expert 12.00 software (Stat-Ease, Inc., Minneapolis, MN, USA) (trial version), and the relationships between composite flour and chemical characterization and functional properties were verified using XLSTAT 2020.2 software (Addinsoft, Paris, France, 2020). To establish the optimal value of the factors, buckwheat flour particle size and addition level, the multiple responses methodology was used to adequately predict the models. For the numerical optimization applied in this study, the desired goal established for each response included: dough stability (ST) at maximum value, starch retrogradation (C5-4) was minimized and the level of the other responses which have been taken into account in this research were maintain within studied limits. The one-way analysis of variance (ANOVA) was performed by using XLSTAT 2020.2 software (Addinsoft, Paris, France, 2020) to test if the effect of the particle sizes on the physicochemical and functional properties of buckwheat flour was significant (*p* < 0.05).
