The experimental data comprise R g values of 25 IDPs 22 listed in Table . To compare simulated R g values using the HPS-Urry model with experiments, we ran temperature replica exchange MD simulations for the 25 IDPs at the following temperatures: 300.00 K, 342.94 K, 392.03 K, 448.14 K, 512.29 K, 585.61 K, 669.43 K, 765.25 K, 874.79 K, and 1000 K using the OpenMM package. Each simulation was run for 1 µs with a step size of 10 fs, and conformations were saved every 10 ps. Exchanges between neighboring temperatures were attempted every 1000 steps. The simulation generated 100,000 conformations per IDP at each temperature. Using conformations generated from the simulation at 300 K, we computed the simulated R g values and compared them with experimental results, as shown in Fig. . Notably, there is a systematic deviation between the simulated and experimental R g values. In the following, we will demonstrate how the proposed framework can effectively optimize the HPS-Urry model to enhance its agreement with the experimental data. name R g (nm) label alpha-synuclein 3.31 train NUL 3.00 train K10 4.00 train K44 5.20 train K19 3.50 train K17 3.60 train K27 3.70 train P53 2.87 train ACTR 2.51 train NUS 2.49 train NLS 2.40 train K25 4.40 train K18 3.80 train IBB 3.20 train K23 4.90 train NSP 4.10 test N98 2.86 test N49 1.59 test ProTalpha 3.79 test SH4-UD 2.90 test Sic1 3.21 test K16 3.90 test K32 4.20 test hNHE1cdt 3.63 test Ash1 2.85 test Optimizing hydrophobicity parameters using experimental R g data.