When the IM-MS spectra of individual isomers were used to deconvolute a binary mixture, we observed a non-linear correlation between relative weight and molar fraction (Figure , Figures S3). Such non-linearity cannot be explained by the deconvolution procedure as the convexity of the calibration curve varies for different pairs of isomers and in some cases is even linear (Figure ). We also found that the non-linear behavior depends on the type of binary mixture analyzed, not the total di-Ub concentration (Figure ). Similar behavior has been previously observed for β-amyloid peptides bearing isomerized aspartic acid residues. In this case, the basic version of multiple linear regression analysis was used to determine the relative weights of each isomer in the spectrum. The weights were then adjusted to obtain the actual molar fractions. We thought we could apply similar logic to obtain the molar fractions of individual di-Ub isomers. Using the 'response factor' 𝑘𝑘 𝑖𝑖 , the absolute intensity of a single di-Ub isomer can be related to the total concentration (C) and molar fraction (𝜒𝜒 𝑖𝑖 ) of that isomer. In principle, 𝑘𝑘 𝑖𝑖 depends on the (i) overall ion yield in ESI and (ii) the probability that a particular isomer is protonated during ionization. Although the absolute value of 𝑘𝑘 fluctuates with the total ion current of ESI, we can assume that the ratio of 𝑘𝑘 values for different isomers (𝑝𝑝 𝑖𝑖𝑗𝑗 = 𝑘𝑘 𝑖𝑖 /𝑘𝑘 𝑗𝑗 for 𝑖𝑖 and 𝑗𝑗 isomers) remains constant. Based on this assumption, the relative weights (𝑞𝑞 𝑖𝑖 = 𝑤𝑤 𝑖𝑖 /(𝑤𝑤 𝑖𝑖 + 𝑤𝑤 𝑗𝑗 ) and 𝑞𝑞 𝑗𝑗 = 𝑤𝑤 𝑗𝑗 /(𝑤𝑤 𝑖𝑖 + 𝑤𝑤 𝑗𝑗 ) ) of di-Ub isomers "𝑖𝑖" and "𝑗𝑗" after deconvolution in the IM spectrum should depend on the molar fractions according to (Equation