1：Experimental Design and Method Selection:

The study investigates re-entrant condensation of BSA with trivalent salts using UV-Vis, fluorescence, TRPL spectroscopy, and DLS to analyze optical responses and hydrodynamic properties.

2：Sample Selection and Data Sources:

BSA solutions of 5, 15, and 25 mg/ml were prepared in Milli-Q water. YCl3 and LaCl3 salts were dissolved in these solutions with concentrations varied from 0 to 20 mM.

3：List of Experimental Equipment and Materials:

Equipment includes Shimadzu UV-1800 Spectrophotometer for UV-Vis, JASCO FP-8500 fluorescence spectrofluorometer for emission spectra, Eddinburg Instrument fluorometer (model FSP920 with 290 nm LED source) for TRPL, and Malvern Zeta sizer Nano series (nano ZS90) with He-Ne laser (λ = 633 nm) and avalanche photodiode detector for DLS. Materials include BSA (Product No. A2153), YCl3 (Product No. 464317), and LaCl3 (Product No. 31820) from Sigma-Aldrich.

4：Experimental Procedures and Operational Workflow:

UV-Vis and fluorescence spectra were taken at specific wavelengths. TRPL measurements used time-domain technique with excitation at 290 nm and emission at 338 nm. DLS measurements were performed at a 90° detection angle to measure autocorrelation functions for diffusion coefficients and hydrodynamic sizes.

5：Data Analysis Methods:

TRPL data were analyzed using FAST software with two-point data analysis for lifetimes. DLS data were analyzed using cumulant analysis to obtain average decay constants and polydispersity. Stokes-Einstein relationship was used to calculate hydrodynamic radius from diffusion coefficients.