*2.3. Rheological Measurements*

The rheological characteristics of starches (RS, PoS and PeS) and starch–betanin pastes were analyzed by an MCR 302 rheometer (Anton-Paar, Graz, Austria) with a parallel-plate measuring system, according to He et al. [15]. In brief, the gels of starch and starch–betanin pastes obtained from Section 2.2 were transferred to a rheometer plate with a probe type of PP50 and a gap of 1 mm. The pastes were equilibrated at ambient temperature for 5 min before measurement.

#### 2.3.1. Steady Shear Analysis

The changes in shear stress of the samples were measured within the range of increasing shear rate from 0.01 to 1000 s−<sup>1</sup> and then decreasing shear rate from 1000 to 0.01 s−<sup>1</sup> by referencing the method of Zhu et al. [16]. The total area of the hysteresis loops, referring to the region of shuttle between the up and down curve of the fluid properties, was integrated using the Origin software (Version 8.0, Microcal Inc., Northampton, MA, USA). The obtained curve was fitted with the power law model for fitting:

$$
\sigma = \mathbb{K} \cdot \gamma^n
$$

where *σ* is the shear stress (Pa), *γ* is the shear rate (s−1), *K* is the consistency coefficient (Pa·sn), and *<sup>n</sup>* is the flow behavior index (*<sup>n</sup>* < 1 for a shear-thinning fluid and *<sup>n</sup>* = 1 for a Newtonian fluid).

#### 2.3.2. Dynamic Rheological Analysis

Firstly, deformation sweep tests were carried out to determine the maximum deformation attainable by all samples, and the strain γ ranged from 0.01% to 100% at a constant frequency of 1 Hz. The linear viscoelastic region for all samples was in the strain range of 0.1~1.6%. An oscillatory frequency sweep measurement was conducted at room temperature with 1% strain (within the linear viscoelastic (LVE) region of all samples), and a frequency range of 0.1~20.8 Hz was selected according to the previous method [17,18]. The storage modulus (G- ) and loss modulus (G") were obtained, and the loss factor tanδ (G"/G- ) was calculated according to the modulus.

#### *2.4. The Chromaticity Value Analysis*

The chromaticity value of the samples was measured by a colorimeter (CM-5, Ke Sheng Instrument Co., Ltd., Shanghai). Before measurement, the instrument was calibrated with the black and the white board. During measurement, the 10 g sample obtained from Section 2.2 was moved into the sample plate to record the *L\** value (brightness), *a*\* value (red-green) and *b*\* value (yellowish-blue).

#### *2.5. X-ray Diffraction (XRD)*

The crystalline properties of the native starches, retrograded starches and starch– betanin samples were determined by a diffractometer (D8 ADVANCEX, BRUKER, Germany) according to a previous study [19]. The samples were scanned from 5 to 40◦ (2θ) at a scan step size of 0.02◦ (2θ). The relative crystallinity was calculated as the ratio of the area of the crystal region to total area using the Origin software with the following equation:

$$Relative\ crystallization\ (\%) = \frac{A\_c}{A\_c + A\_a} \times 1000$$

where *Ac* and *Aa* represent the crystalline and amorphous areas.

#### *2.6. Fourier Transform-Infrared (FT-IR) Spectroscopy*

Spectroscopic properties of starches, betanin and starch–betanin samples were characterized by using an FT-IR spectrometer (Thermo Nicolet-5700, Nicolet, Rhinelander, WI, USA) according to the study by Li et al. [20]. The retrograded starch or starch–betanin samples (1–3 mg) were ground with KBr (140 mg) with an agate mortar, and then compressed into disk-shaped pellets. The FT-IR spectra were recorded over the range of 4000 to 400 cm−1. Raw spectra were deconvoluted by using Omnic 8.0 software to obtain 1047/1022 cm−<sup>1</sup> and 995/1022 cm−<sup>1</sup> values.

#### *2.7. Differential Scanning Calorimetry (DSC)*

The thermal properties of starches (RS, PoS and PeS) and starch–betanin samples were analyzed by using DSC (7000X, HITACHI, Japan) based on a previous study [21]. Samples (2–3 mg) were accurately weighed and placed in an aluminum pan. Distilled water was added to the pan, and the mass ratio of sample/water was 1:2. The samples were heated from 40 to 100 ◦C at a rate of 10 ◦C/min, and the empty pan was used as the reference. The onset (To), peak (Tp), conclusion (Tc) temperature and gelatinization enthalpy (Δ*Hg*) were obtained from the DSC curve. The retrograded samples obtained from Section 2.2 were lyophilized and milled. Then the retrograded starch–betanin samples were reheated in the same conditions to determine the retrogradation enthalpy (Δ*Hr*). Finally, the degree of retrogradation rate *R* was calculated according to the ratio of Δ*Hr* and Δ*Hg*.
