## 2 Materials and Methods
### Glass Transition Temperature  
Modulated DSC experiments were carried out using TA Instruments Q200 differential scanning calorimeter (New Castle, DE, USA). Modulated differential scanning calorimetry (MDSC) was used to determine the glass transition temperature of the selected samples (freeze-dried gels: P0%, P25%, P25%DE and air-dried as well as vacuum-dried gels: P40%De-MC) in the range of water activity 0-0.75. The cell was purged with dry nitrogen (at 50 mL/min) and temperature calibration was performed on an empty oven with an application of standard pure indium and distilled water. The sapphire standard was tested for calibration of specific heat capacity. An empty hermetically sealed aluminium pan was used as a reference. The samples of mass 10-15 mg were hermetically sealed in aluminium pans and cooled from room temperature to \(-90\) \({}^{\circ}\)C at 5 \({}^{\circ}\)C/min, then equilibrated for 5 min. During MDSC procedures, the samples were scanned from \(-90\) to 150 \({}^{\circ}\)C at parameters: a constant heating rate of 2 \({}^{\circ}\)C/min, an amplitude of \(\pm 1\) \({}^{\circ}\)C, period of modulation \(-60\) s. The obtained data were analysed with respect to the total, reversible and non-reversible heat flow [28; 42; 43]. TA Instruments Universal Analysis software was applied to determine the onset, midpoint and endpoint of transition. The midpoint of the glass transition was  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Equation** & **Description** \\ \hline [PERSON] [39] & \(u=\dfrac{F}{(1-a_{w})^{G}}-\dfrac{F}{1+a_{w}{}^{H}}\) & (3) & \(F,G,H\)—constants \\ \hline [PERSON] [40] & \(u=Aa_{w}{}^{D}+Ba_{w}{}^{E}\) & (4) & \(A,B,D,E\)—constants \\ \hline [PERSON] [41] & \(a_{w}=exp\left(\dfrac{-\delta}{u^{H}}\right)\) & (5) & \(g,n\)—constants \\ \hline \hline \multicolumn{3}{c}{**Statistical parameters**} \\ \hline \({}^{\prime}\)RMS & \(RMS=\sqrt{\dfrac{\sum_{i=1}^{N}\left(\dfrac{u_{c}-u_{p}}{u_{c}}\right)^{2}}{N}} 100\%\) & (6) & \(u_{c}\)—an experimental value of water content, \(u_{p}\)—the predicted value of water content, \(N\)—number of observations \\ \hline \(P\) & \(P=\dfrac{\sum_{i=1}^{N}\left|\dfrac{u_{c}-u_{p}}{u_{c}}\right|}{N}100\%\) & (7) & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Cont.  
selected as the transition temperature. The mean value and standard deviation of the glass transition were calculated based on three replicates of measurements.  
The Gordon-Taylor model [44] and Roos model [45] represented by Equations (8) and (9) were used to describe changes of \(T_{g}\) with water content and water activity. The goodness fit was estimated based on \(R^{2}\), \(RMS\) and parameter \(P\).  
\[T_{g}=\frac{(1-x_{w})T_{gs}+kx_{w}T_{gw}}{(1-x_{w})+kx_{w}} \tag{8}\]  
where: \(T_{gs}\), \(T_{gw}\), \(T_{g}\)--glass transition temperatures of solids, water, and their mixture, respectively; \(x_{w}\)--mass fraction of water; \(k\)--the Gordon-Taylor model parameter.  
\[T_{g}=Aa_{w}+B \tag{9}\]  
where: \(a_{w}\)--water activity; \(A\), \(B\)--parameters of the Roos model.  
The critical water content \(x_{wc}\) and critical water activity \(a_{wc}\) were defined as the values of these parameters at which the glass transition temperature was equal to the storage temperature of 25 \({}^{\circ}\)C.  
A one-way ANOVA test (Tukey's method) was applied to determine the significance of differences among samples at the 95% significance level for constants.