Fig. 1: Illustration of the 2D-TPP experimental setup and our computational analysis approach.

a 2D-TPP protocol: Cells are grown in the presence of n different concentrations of a ligand of interest. Each sample is divided into m aliquots, each of which is subjected to one of m temperatures, and the remaining soluble proteins are extracted. Proteins are digested with trypsin and labeled with TMT, such that one set of TMT labels is used for all concentrations and two adjacent temperatures. w = m/2 MS runs are performed, peptides are identified by database search and quantified signal is aggregated at the protein level. b Illustration of fitted curves under the null and alternative model, and how obtained residuals are used to find proteins significantly altered in thermal stability—and thus potential ligand interactors—via an F-statistic (example fits for the null and alternative model are shown in Supplementary Fig. 1). The q–q plot on the right compares bootstrapped and observed F-statistics. Although the majority of quantiles of the two distributions align, the top observed F-statistics, corresponding to the true positives in the dataset, are shifted off-diagonal. The results can be represented as volcano plots, highlighting significant hits. RSS: residual sum of squares; \({{{\rm{sign}}}}(\kappa )\times \sqrt{{{{{\rm{RSS}}}}}^{0}-{{{{\rm{RSS}}}}}^{1}}\): measure of effect size—how much more variance is explained by the alternative model compared to the null—and direction, i.e., a positive sign for stabilized proteins, negative for destabilized ones; log₂(F-statistic + 1): the transformation is used for visualization purposes only, the addition of 1 guarantees that logarithm-transformed values remain bounded as F approaches 0.