Thermal Proteome Profiling (TPP)

• Thermal Proteome Profiling (TPP) is a quantitative method that maps protein stability changes across a temperature gradient to assess ligand binding, pathway inhibition, and proteome perturbations.
• It employs both classic sigmoidal fitting and advanced Gaussian process models, like Thermal Tracks, to capture diverse melting curve shapes and provide statistically calibrated hit detection.
• TPP enables robust analysis of proteome dynamics under drug treatment and environmental stress, offering actionable insights into protein function and regulatory mechanisms.

Thermal Proteome Profiling (TPP) is a quantitative technique for assaying proteome-wide thermal stability landscapes. By measuring the soluble fraction of thousands of proteins across a temperature gradient, TPP enables inferences about protein–ligand binding, pathway inhibition, drug engagement, genetic or environmental perturbation effects, and large-scale proteostasis alterations. Analytical methods for TPP must quantify differential thermal stability while accommodating complex melting behaviors and providing statistically calibrated hit identification. Recent advances, notably the Thermal Tracks framework, have introduced robust Gaussian process–based modeling to address limitations inherent in prior sigmoidal curve–centric approaches, enabling unbiased and flexible proteome-wide thermal stability analyses (Hevler et al., 13 Aug 2025).

1. Canonical Analysis Workflows in TPP

Standard TPP analysis fits each protein’s solubility profile as a function of temperature to a three- or four-parameter sigmoidal curve, typically a Boltzmann function:

$y(T) = A + \frac{B - A}{1 + \exp((T - T_m)/s)}$

where $T_m$ is the melting temperature, $A$ and $B$ are low/high plateaus, and $s$ controls slope. Hit calling is generally driven by comparing $T_m$ between control and perturbation ($\Delta T_m$) using $t$- or $z$-tests across replicates.

Nonparametric alternatives, such as NPARC, still constrain the fit to sigmoidal-type curves, comparing the entire fit via ANOVA-style $F$-statistics. Both methods empirically estimate their null distributions by pooling statistics across all proteins, assuming that most proteins are unaffected ($H_0$). This pool forms the empirical null, capping the fraction of significant hits at $\sim$5% under large, true proteome-wide shifts, even if true positives exceed this limit. Furthermore, these approaches mischaracterize proteins with non-sigmoidal melting due to structural or functional features (e.g., membrane proteins, phase-separating proteins) (Hevler et al., 13 Aug 2025).

2. Gaussian Process Framework in Thermal Tracks

Thermal Tracks resolves these core issues using protein-wise Gaussian process (GP) models with squared-exponential (RBF) kernels. For each protein $i$, the latent melting curve $f_i(T)$ is modeled as:

$f_i(T) \sim GP(0,\ k(T, T'))$

where

$$k(T, T') = \sigma^2 \exp\left(-\frac{(T - T')^2}{2\ell^2}\right)$$

and $\ell$ denotes the length scale (smoothness), $\sigma^2$ the marginal variance. Observed soluble fractions $y_i(T)$ are modeled as $y_i(T) = f_i(T) + \epsilon$, with Gaussian noise $\epsilon \sim \mathcal{N}(0, \sigma_e^2)$.

Crucially, the null distribution is generated analytically by sampling from the joint GP prior fitted under $H_0$, pooling all trace data from control and perturbation, rather than relying on empirical nulls. This strategy produces unbiased nulls regardless of the true hit rate, particularly for experiments with widespread proteome perturbation (Hevler et al., 13 Aug 2025).

3. Hit Identification and Statistical Calibration

Protein-specific differential stability is tested by contrasting two models:

• Null ($H_0$): one GP fitted jointly to all replicates/conditions.
• Alternative ($H_1$): two independent GPs, one each for control and perturbation.

The likelihood-ratio statistic is calculated as

$\Lambda = -2 \cdot (mll_{H_0} - mll_{H_1})$

where $mll$ denotes the marginal log-likelihood. To derive empirical $p$-values, synthetic datasets are generated by sampling from the joint GP posterior predictive (using kernel hyperparameters at their Type II MLE). The distribution of $\Lambda$ under these samples forms the null against which observed $\Lambda$ values are compared.

False discovery rate (FDR) is controlled via the Benjamini–Hochberg procedure applied to per-protein $p$-values. This eliminates the ad hoc 5% ceiling on hit rates imposed by empirical null pooling, allowing detection of arbitrarily large affected fractions (Hevler et al., 13 Aug 2025).

4. Modeling Non-Sigmoidal Melting Curves

Gaussian process modeling imposes no parametric constraint on the melting curve shape, provided only that curves are smooth with scale $\ell$. Consequently, Thermal Tracks accurately fits melting behaviors such as:

• Plateaus or nonmonotonic transitions,
• Multiphase or biphasic drops (e.g., phase-separating protein NUCKS1),
• Stiffening-then-collapsing profiles (e.g., E. coli membrane proteins exposed to Mg$^{2+}$).

In these contexts, parametric sigmoidal or NPARC models often misfit or fail, whereas Thermal Tracks reconstructs complex profiles and thus, uncovers biologically relevant shifts otherwise undetectable (Hevler et al., 13 Aug 2025).

5. Quantitative Benchmarks and Comparative Performance

Thermal Tracks' approach has been benchmarked on datasets with known ground-truth targets. On a staurosporine dataset (176 known kinases out of 4,505 proteins), both Thermal Tracks and NPARC recover 55 known targets at BH FDR $<0.05$; GPMelt recovers 48. In p-value calibration, Thermal Tracks displays near-uniform histograms, indicating valid calibration, while NPARC and GPMelt are skewed or conservative.

In proteome-wide perturbation (ATP-TPP), Thermal Tracks detects 366 of 753 known ATP binders from 4,772 proteins, compared to GPMelt’s 336 and NPARC's 97 at matched FDR threshold. Additionally, under global or environmental perturbations, its hit rate scales with true effects rather than remaining artificially capped (Hevler et al., 13 Aug 2025).

Dataset	Thermal Tracks	NPARC	GPMelt
Staurosporine (known hits)	55	55	48
ATP-TPP (known hits)	366	97	336

6. Implementation and Practical Considerations

Thermal Tracks is implemented in Python using the GPyTorch library. The standard workflow involves fitting independent GP models per protein per condition and a joint model under $H_0$. Hyperparameters ($\ell$, $\sigma^2$, $\sigma_e^2$) should be initialized as follows: $\ell$ at about half the temperature range, $\sigma^2$ matching the scaled variance of intensities, and $\sigma_e^2$ either given a broad Gamma prior or initialized to a small fraction of $\sigma^2$. Type II maximum likelihood automatically optimizes these hyperparameters.

The per-protein GP fitting, likelihood computation, and null sampling for significance estimation are all computationally tractable for standard-scale TPP datasets (e.g., 5,000 proteins $\times$ 8–12 temperatures) on desktop hardware (15–30 minutes). For substantially larger datasets, sparse GP or inducing-point methods are suggested to reduce computational complexity from $O(n^3)$ per protein to $O(nm^2),\ m \ll n$ (Hevler et al., 13 Aug 2025).

A core code block for implementation is as follows:

import torch import gpytorch class MeltGP(gpytorch.models.ExactGP): def __init__(self, train_x, train_y, likelihood): super().__init__(train_x, train_y, likelihood) self.mean_module = gpytorch.means.ConstantMean() self.covar_module = gpytorch.kernels.ScaleKernel( gpytorch.kernels.RBFKernel() ) def forward(self, x): mean_x = self.mean_module(x) covar_x = self.covar_module(x) return gpytorch.distributions.MultivariateNormal(mean_x, covar_x) train_x = temperatures.unsqueeze(-1) train_y_ctrl = obs_ctrl train_y_pert = obs_pert lik_ctrl = gpytorch.likelihoods.GaussianLikelihood() lik_pert = gpytorch.likelihoods.GaussianLikelihood() model_ctrl = MeltGP(train_x, train_y_ctrl, lik_ctrl) model_pert = MeltGP(train_x, train_y_pert, lik_pert) model_joint = MeltGP(torch.cat([train_x, train_x]), torch.cat([train_y_ctrl, train_y_pert]), gpytorch.likelihoods.GaussianLikelihood())

7. Current Limitations and Future Extensions

While exact GP modeling is feasible for standard TPP datasets, computational scalability remains a constraint for extremely large proteomes or for high-resolution temperature sampling. In such scenarios, sparse GP or inducing-point approximations offer potential reductions in computational demand.

Posterior predictive effect sizes, such as the area between melting curves across conditions, can be directly fed to downstream enrichment analyses (e.g., GSEA). Integrative extensions are possible, with multi-output GPs facilitating joint modeling of thermal profiles and other omics (phosphoproteomics, metabolomics). Automated linkage of effect sizes to pathway resources (e.g., KEGG, Reactome) can further streamline biological interpretation.

A plausible implication is that future TPP analytics may routinely incorporate flexible probabilistic models beyond rigid parametric forms, enabling higher-resolution biological discovery in both targeted and global perturbation contexts. Thermal Tracks and related frameworks thus represent a generalizable foundation for unbiased, extensible proteome stability analysis (Hevler et al., 13 Aug 2025).