Organizations: PsiDagger, San Diego, CA · Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA · Department of Chemistry and The PULSE Institute, Stanford University, Stanford, CA · SLAC National Accelerator Laboratory, Menlo Park, CA
The classic paradigm of structural biology is that the sequence of a biomolecule (protein, nucleic acid, lipid, etc) determines its conformation (shape) which determines its biological function. Protein folding programs like AlphaFold address this paradigm by predicting the single best conformation given a sequence that defines the molecule. However, biomolecules are not static structures, and their conformational ensemble determines their function. We present the Polyformer -- a generative framework for thermodynamic modeling of polymeric molecules. Given the sequence and temperature (or another thermodynamic variable), the Polyformer generates conformations faithful to the molecule's thermodynamic conformational ensemble. It is the first generative model that solves three problems simultaneously: how does a molecule fold, what is its conformational ensemble, and how does the conformational ensemble change as we change physical temperature. As a concrete test case, we apply Polyformer to protein domains with 50-111 residues and report good agreement of model predictions to Molecular Dynamics (MD) trajectories.
Figures & tables
Figure 1: Polyformer is a DiT conditioned on molecular sequence and temperature that generates conformation ensembles of protein backbones in a temperature-dependent way.
Figure 2: Comparison of Molecular Dynamics and Polyformer sampled conformation ensembles for domain 1g2rA00. Best matching pair of conformations is highlighted. The ensembles of conformations sampled by Polyformer are quite similar to Molecular Dynamics across all five temperatures.
Figure 3: Comparison of Molecular Dynamics and Polyformer sampled conformation ensemble for domain 1g2rA00. (a) Ramachandran plots comparing the distribution of ψ and ϕ dihedral angles. (b) RMSF plots comparing fluctuations along the back bone. (c) Plots comparing distributions of Rg . Across all three metrics, polyformer matches molecular dynamics pretty well.
Figure 4: Comparison of mean (solid points) and standard deviation (error bars) of Rg obtained by mdCATH and Polyformer ensemble sampling of domain lg2A00, showing good agreement.
Figure 5: Comparison of mean Rg obtained by mdCATH and Polformer ensemble sampling across all domains in the testing set and all temperatures in mdCATH dataset. The plots show good, but imperfect correlation.
Appendix figures & tables9 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 6: Comparison of Molecular Dynamics and Polyformer sampled conformation ensembles, same as Fig. 2 but for domain 3g0vA00.
Figure 7: Quantitative comparison of Polyformer and Molecular Dynamics sampled conformation ensemble, same as Fig. 3 but for domain 3g0vA00.
Figure 8: Performance of Polyformer without ESM-2 embedding. Compare with Fig. 2 in the main text.
Figure 9: Performance of Polyformer without ESM-2 embedding on domain 1g2rA00. Compare with Fig. 3 in the main text.
Figure 10: Performance of Polyformer without ESM-2 embedding on domain 3g0vA00. Compare with Fig. 7 in the appendix.
Figure 11: Performance of Polyformer without ESM-2 embedding. Compare with Fig. 5 in the main text.
Figure 12: Performance of SimplFold. Compare with Fig. 2 in the main text. Because SimpleFold tends to predict one dominant conformation, we have not highlighted the matching pair in the SimpleFold panel. For both domains, SimpleFold predicted two structures that did not match the other 298 strcutures and appear as thinner lines.
Figure 13: Performance of SimpleFold. Compare with Fig. 3 in the main text.
Figure 14: CDF of inverse of the learned reciprocal vectors (orange) and PDF of the C α -C α distances shaded blue. Observe that most of the inverse reciprocal vector magnitudes span the range of C α -C α distance.
Department of Computer Science, Columbia University, NY, USA · Department of Systems Biology, Columbia University, NY, USA · Department of Computer Science, Princeton University, Princeton, NJ, USA