4.5. Estimation of the Hydrodynamic Radius by SEC

The hydrodynamic radii (Stokes radii, R_S) of the proteins were estimated by analytical SEC using a Superose 6 Increase 10/300 column (Cytiva, Marlborough, MA, USA). Hepes Buffered Saline (HBS, 20 mM Hepes pH 7, 150 mM NaCl) was used as elution buffer unless differently indicated. Typically, 250 μL of purified protein at 2.5 mg mL⁻¹ were injected.

The Stokes radii of proteins eluted from the SEC column were deduced from a calibration curve obtained using globular proteins of known R_S (Thyroglobulin: 85 Å, Ferritin: 61 Å, Aldolase: 48.1 Å, Conalbumin: 36.4 Å, Carbonic anhydrase: 23 Å, RNAse A: 16.4 Å and Aprotinin: 13.5 Å)

The R_S (in Å) of a natively folded (Rs^NF), fully unfolded state in urea (R_S^U) and natively unfolded premolten globule (PMG) (R_S^PMG) protein with a molecular mass (MM) (in Daltons) were calculated according to [47]:

The Rs^NF, R_S^U and R_S^PMG expected for a natively folded, and fully unfolded and PMG dimeric form of a protein with molecular mass MM were calculated according to Equations (1)–(3) by replacing (log MM) with (log 2 × MM).

The R_S of an IDP with N residues was also calculated according to [90] using either the simple power law model:

where R₀ = 2.49 and ν = 0.509, or the sequence-based model:

where A = 1.24, P_Pro = fractional proline content, B = 0.904, C = 0.00759, |Q| = absolute value of the difference between the total number of negatively charged and positively charged residues, D = 0.963, S_his = 0.901 (correction factor for histidine tag).

The compaction index (CI) is expressed as according to [129]:

This parameter, which allows comparison between proteins of different lengths, in principle varies between 0 and 1, with 0 indicating minimal compaction and 1 maximal compaction.