  We report simulation studies of 33 single intrinsically disordered proteins
(IDPs) using coarse-grained (CG) bead-spring models where interactions among
different amino acids are introduced through a hydropathy matrix and additional
screened Coulomb interaction for the charged amino acid beads. Our simulation
studies of two different hydropathy scales (HPS1, HPS2) [Dignon et al., PLOS
Comp. Biology, 14, 2018, Tesei et al. PNAS, 118, 2021] and the comparison with
the existing experimental data indicates an optimal interaction parameter
$\epsilon = 0.1$ kcal/mol and $0.2$ kcal/mol for the HPS1 and HPS2 hydropathy
scales. We use these best-fit parameters to investigate both the universal
aspects as well as the fine structures of the individual IDPs by introducing
additional characteristics.(i) First, we investigate the polymer specific
scaling relations of the IDPs in comparison to the universal scaling relations
[Bair et al., J. Chem. Phys. 158, 204902 (2023)] for the homopolymers and we
demonstrate that IDPs are broadly characterized with a Flory exponent of 0.56
with the conclusion that conformations of the IDPs interpolate between Gaussian
and 3DSAW chains. (ii) Then we introduce Wilson charge index W that captures
the essential features of charge interactions and distribution in the sequence
space, and (iii) a skewness parameter S that captures the finer shape variation
of the gyration radii distribution related to the charge asymmetry. Finally,
our study of the variation of <$R_g$> as a function of salt concentration
provides another important metric to bring out finer characteristics of the
IDPs which may carry relevant information for the origin of life.
