Network Hamiltonian models reveal pathways to amyloid fibril formation

Abstract

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.

Chemical Properties Determine Solubility and Stability in βγ‐Crystallins of the Eye Lens

“…[241] 2D IR spectroscopy has been used to observe the divergence of different fibril polymorphs in human islet amyloid polypeptide (hIAPP) from a common intermediate in solution, [242] and to monitor the transformation of Aβ oligomers to fibrils. [243] A recently developed topological classification for amyloid fibril structures [244,245] could also be extended to provide a more systematic description of β-sheet oligomers and non-amyloid aggregates.…”

Continuous Time Graph Processes with Known ERGM Equilibria: Contextual Review, Extensions, and Synthesis

“…In systems with a well-defined temperature, these behave very differently.) Versions of this interpretation have (with varying degrees of specificity and attention to physical detail) been used by a number of researchers as tools or metaphors to study or explain ERGM behavior (e.g Häggström and Jonasson, 1999;Park and Newman, 2004;Robins et al, 2005;Radin and Yin, 2013;Butts, 2021), and by others as physical models in their own right (Grazioli et al, 2019;Yu et al, 2020).…”

“…For instance, the choicemotivated SAOMs and competing rate-motivated LERGMs can both lead to the same degenerate graph distributions as CTERGMs and Differential Stability processes. Sometimes, as per Yu et al (2020), this is in fact an empirically realistic outcome; for most social networks, however, degeneracy is usually pathological. What we can glean from the present work is that -at least for processes of the type studied here -degeneracy should be understood as arising from the graph potential rather than the processes operating on it.…”

“…Although relatively few general frameworks of this type have been extensively studied, at least one (the stochastic actor-oriented models, or SAOMs) is arguably among the most successful and widely used families of models in the social sciences (see, e.g., Snijders (2001); Steglich et al (2010); Burk et al (2007); Sijtsema et al (2010); de la Haye et al (2011); Weerman (2011); Schaefer and Kreager (2020) among many others). Work using other continuous time graph processes has also found applications both within (Koskinen and Snijders, 2007;Koskinen et al, 2015;Stadtfeld et al, 2017;Hoffman et al, 2020) and beyond (Grazioli et al, 2019;Yu et al, 2020) the social sciences, suggesting the potential for further advances.…”

Neural Upscaling from Residue-Level Protein Structure Networks to Atomistic Structures

“…Recent work, however, has suggested the potential of graph-theoretic models for molecular structure and dynamics. For instance, Grazioli et al [ 9 ], Yu et al [ 28 ] use Hamiltonians defined on graphs representing the structures of protein aggregates to model the equilibrium structures and kinetics of amyloid fibrils and associated aggregation states (with vertices representing individual proteins, and edges indicating bound interactions). On a smaller scale, Grazioli et al [ 8 ] used a closely related approach to model transient structure in intrinsically disordered proteins (IDPs), using residue-level protein structure networks (PSNs) in which each vertex represents a residue and edges represent inter-residue contacts.…”