GPMelt: A hierarchical Gaussian process framework to explore the dark meltome of thermal proteome profiling experiments
Fig 2
Implementation of the hierarchical GP model using the multi-task GP regression framework.
The three-level hierarchical model (Eq (8)) is illustrated on a hypothetical protein presenting different numbers of replicates in the control and treatment conditions, under the simplifying assumption of synchronous observations for all replicates of all conditions. (A) A visualization of the model. Melting curves are fitted to observations of each replicate (bottom level). The condition-wise melting curves (second level) captures the underlying melting behaviours common to replicates of a condition. These condition-wise melting curves can be seen as deviations from the protein-wise melting curve depicted on the top of the hierarchy. (B) Schematic visualisation of the resulting covariance matrix Σ, expressed as a special matrix product between Ky, the sum of the index kernels, and the correlation matrix Kt,λ(T, T), evaluated at the set of temperatures T = (T1, …, T10). This decomposition of the matrix links the hierarchical GP model to the multi-task GP regression framework. Under the simplifying assumption of synchronous observations, the matrix product is a kronecker product. This product is easier to visualize than the Hadamard product obtained in case of asynchronous observations (see Appendix B in S1 File for details).