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Coarse-graining is a powerful tool for extending the reach of dynamic models of proteins and other biological macromolecules. Topological coarse-graining, in which biomolecules or sets thereof are represented via graph structures, is a particularly useful way of obtaining highly compressed representations of molecular structures, and simulations operating via such representations can achieve substantial computational savings. A drawback of coarse-graining, however, is the loss of atomistic detail—an effect that is especially acute for topological representations such as protein structure networks (PSNs). Here, we introduce an approach based on a combination of machine learning and physically-guided refinement for inferring atomic coordinates from PSNs. This “neural upscaling” procedure exploits the constraints implied by PSNs on possible configurations, as well as differences in the likelihood of observing different configurations with the same PSN. Using a 1 μs atomistic molecular dynamics trajectory of Aβ1–40, we show that neural upscaling is able to effectively recapitulate detailed structural information for intrinsically disordered proteins, being particularly successful in recovering features such as transient secondary structure. These results suggest that scalable network-based models for protein structure and dynamics may be used in settings where atomistic detail is desired, with upscaling employed to impute atomic coordinates from PSNs. 

Amyloid fibril formation is central to the etiology of a wide range of serious human diseases, such as Alzheimer’s disease and prion diseases. Despite an ever growing collection of amyloid fibril structures found in the Protein Data Bank (PDB) and numerous clinical trials, therapeutic strategies remain elusive. One contributing factor to the lack of progress on this challenging problem is incomplete understanding of the mechanisms by which these locally ordered protein aggregates self-assemble in solution. Many current models of amyloid deposition diseases posit that the most toxic species are oligomers that form either along the pathway to forming fibrils or in competition with their formation, making it even more critical to understand the kinetics of fibrillization. A recently introduced topological model for aggregation based on network Hamiltonians is capable of recapitulating the entire process of amyloid fibril formation, beginning with thousands of free monomers and ending with kinetically accessible and thermodynamically stable amyloid fibril structures. The model can be parameterized to match the five topological classes encompassing all amyloid fibril structures so far discovered in the PDB. This paper introduces a set of network statistical and topological metrics for quantitative analysis and characterization of the fibrillization mechanisms predicted by the network Hamiltonian model. The results not only provide insight into different mechanisms leading to similar fibril structures, but also offer targets for future experimental exploration into the mechanisms by which fibrils form.