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GPMelt: A hierarchical Gaussian process framework to explore the dark meltome of thermal proteome profiling experiments
Fig 3
Principle of GPMelt in presence of multiple conditions.
(SI: Scaled Intensity) Fitting the full model (A, B) is enough to access all the information required to test all possible null hypotheses. The illustration is based on protein SFRS9 of the Dasatinib dataset [1]. The aim of this experiment is to determine changes in melting behaviours upon dasatinib treatment, a BCR-ABL inhibitor. In the experimental set up, the control condition (no treatment) is compared to two treatment concentrations, 0.5μM and 5μM. For clarity in the figure, treatment concentration of 0.5μM is referred to as condition “C1” and treatment concentration of 5μM is referred to as “C2”. Control condition is abbreviated by “Ctrl”. (A,B and D): Full model 
. (A) Hierarchical model corresponding to Eq (8), in which each condition (middle row) is assumed to present a distinct melting behaviour, this behaviour being a deviation from the main protein-wise melting behaviour (top row, blue curve). The fitting of the observations (last row) under this model provides estimated values for output-scales σh, σg and 
. Similarly as in Fig 2, the estimated output-scales can be represented using the index kernels of the multi-task regression framework, as depicted in panel (B). Under this model, the likelihood of the observations is given by 
(D) and further detailed in Appendix C in S1 File. (A.C1 to E.C1): Comparing treatment C1 with control. We aim to compare the melting behaviour of this protein in the control condition (green curve) vs the treatment condition C1 (orange curve). A visualisation of this comparison is provided in panel (C.C1). Under the proposed testing framework, the joint model 
assumes that treatment C1 and control conditions have the same melting dynamic, and group them into a “joint” condition (grey curves in (A.C1, C.C1)). (B.C1) Mathematically, this joint model is obtained by changing the structure of the index kernel corresponding to the condition level. More precisely, the “joint” condition, grouping “C1” and “Ctrl”, is represented by the upper block in the matrix. Importantly, the values of the output-scales σh, σg and 
remain unchanged: there is no need to re-estimate the parameters of this model. Moreover, the modelling of condition “C2” is not affected by this joint model, as can be seen in (A.C1) and (B.C1). (D.C1) The likelihood of the observations under this model is given by 
. (E.C1) The statistic Λ used to statistically assess the significance of melting behaviour changes is given by ΛCtrl vs C1. (A.C2 to E.C2): Comparing treatment C2 with control. Similarly, we illustrate the procedure to compare the protein’s melting behaviours between treatment C2 (pink curve) and control (green curve) conditions. Under this model, conditions “C2” and “Ctrl” are grouped together in the “joint” condition, while condition “C1” is unaffected (A.C2, B.C2). Melting behaviours changes are depicted in panel (C.C2). The likelihood of the observations under this model, 
(D.C2), and the associated statistic ΛCtrl vs C2 (E.C2) are given.
doi: https://doi.org/10.1371/journal.pcbi.1011632.g003