2.4. Determination of Glycan Binding: Calculation of the Dissociation Constant (KD)

Data from native ESI MS measurements were translated into dissociation constants (K_D values). The detailed calculations were based on the equations listed below. A protein (P) and a glycan ligand (L) form a complex through non-covalent interactions leading to a reversible association described by (Equation (1)):

when equilibrium is reached, the K_D can be calculated directly from the concentrations via the law of mass action (Equation (2)):

Theoretically, the K_D is calculated by measuring the concentration of the three components (P_free, L_free, PL) in solution. Usually, these values are only indirectly accessible because they require ligand titration up to binding saturation. However, native MS allows for the directly measurement of P_free and PL, from which L_free can be calculated using the input concentrations. In the present work, the non-covalent interaction was measured in the gas phase assuming identical ESI and detection efficiency for free and glycan-associated proteins, both for the analyte and the reference protein. The peak areas (A) of the non-bound protein ion (Pⁿ⁺) and the bound protein ion (PLⁿ⁺) were used to calculate the ratio (R) as these most accurately reflected the total signal and hence were assumed to be comparable to the ratio of a ligand-bound protein complex and an unbound protein in solution (e.g., equilibrium state). For P dimers, the equations reflect glycan binding to the individual monomers [4] assuming that binding sites on each monomer are equal and independent [21].

Using R described in Equation (3), the K_D calculation can be re-written into Equation (4) with the known initial concentration of glycan ligand [L₀] and protein [P₀], adapted from Sun et al. [5]: