## 2 Materials and Methods
### Determination of Total Flavonoid Content  
The total flavonoid content in the extract was determined by ultraviolet-visible (UV-Vis) spectrometry (Unico Shanghai Instrument Co., Ltd., Shanghai, China) [16]. The extract solution (1 mL) was taken in a colorimeter tube (10 mL) and sodium nitrite solution (0.3 mL, 5%) was added. The mixture was shaken for 6 min before adding aluminum nitrate solution (0.3 mL, 10%), and the mixture was shaken again for 6 min. Then, sodium hydroxide (4.0 mL, 5%) was added. Finally, the solution volume was adjusted to 10.0 mL by adding deionized water. After 15 min of reaction at ambient temperature, the absorbance was evaluated at 510 nm [17]. Rutin was used as the standard for the calibration curve. The flavonoid content was calculated using the following linear equation based on the calibration curve [Figure 1]:  
\[Y=1.104X,\ R^{2}=0.997 \tag{1}\]  
where \(Y\) is the absorbance and \(X\) is the concentration of flavonoids in the range 0.02-0.40 mg mL\({}^{-1}\).  
Figure 1: Calibration curve for total flavonoid content test.  
Phase Diagram of PEG/(NH\({}_{4}\))\({}_{2}\)SO\({}_{4}\)-Containing Aqueous Two-Phase Systems  
The phase diagram of ATPSs comprising PEG of different molecular weights (MW) and (NH\({}_{4}\))\({}_{2}\)SO\({}_{4}\) was investigated at T = 298 K. The turbidity titration method was used to obtain the phase diagrams of the PEG/(NH\({}_{4}\))\({}_{2}\)SO\({}_{4}\) systems. Deionized water and PEG (MW 400, 600, 1500, 4000, and 6000) were added to a tube before the (NH\({}_{4}\))\({}_{2}\)SO\({}_{4}\) solution was added dropwise. The mixture was shaken using a vortex mixer for 3 min after the addition of each droplet. The mixture became turbid after mixing, and deionized water was added until the turbidity disappeared (Figure S1). Once the mixture became transparent, another drop of (NH\({}_{4}\))\({}_{2}\)SO\({}_{4}\) solution was added and the mixture turned turbid again. The point at which the mixture initially became turbid was taken as the turbidity point. The amounts of (NH\({}_{4}\))\({}_{2}\)SO\({}_{4}\) and deionized water added were measured, and the concentrations of (NH\({}_{4}\))\({}_{2}\)SO\({}_{4}\) and PEG were calculated at different turbidity points. A phase diagram curve was plotted according to the above data. The influences of various process parameters such as (NH\({}_{4}\))\({}_{2}\)SO\({}_{4}\) and PEG concentrations on the volume ratio and flavonoid yield of the ATPS were calculated. Rutin was used as the standard for flavonoid content determination. The partitions of the flavonoids between the various phases were characterized by various parameters, including the partition coefficient (\(K\)), volume ratio (\(P\)), recovery (\(R\)), and extraction yield (\(\gamma\)).  
Partition coefficient (\(K\)) is defined as:  
\[K=\frac{C_{t}}{C_{b}} \tag{2}\]  
where \(C_{t}\) and \(C_{b}\) denote the concentrations of the partitioned substance in the polymer and salt phases, respectively.  
The volumes of the phases (\(V_{t}\) and \(V_{b}\)) can be described by the phase-volume ratio (\(P\)):  
\[P=\frac{V_{t}}{V_{b}} \tag{3}\]  
where \(R\) is the phase volume ratio, \(V_{t}\) is the volume of the top phase, and \(V_{b}\) is the volume of the bottom phase.  
The recovery in the top phase (\(R\)) is defined as:  
\[R=\frac{C_{t}\times V_{t}}{W}\times 100\% \tag{4}\]  
where \(R\) is the flavonoid recovery in the top phase, \(C_{t}\) is the flavonoid concentration in the top phase, and \(W\) is the mass of total flavonoids.  
The total flavonoid extraction yield (mg g\({}^{-1}\)) is defined as:  
\[Y=\frac{C_{t}\times V_{t}}{M_{\textit{leaf}}}\times 100\% \tag{5}\]  
where \(Y\) is the total flavonoid yield, \(C_{t}\) is the flavonoid concentration in the top phase, and \(M_{\textit{leaf}}\) is the mass of _Ginkgo_ leaf.