Network Hamiltonian Models for Unstructured Protein Aggregates, with Application to γD-Crystallin

Abstract

Network Hamiltonian models (NHMs) are a framework for topological coarse-graining of protein–protein interactions, in which each node corresponds to a protein, and edges are drawn between nodes representing proteins that are noncovalently bound. Here, this framework is applied to aggregates of γD-crystallin, a structural protein of the eye lens implicated in cataract disease. The NHMs in this study are generated from atomistic simulations of equilibrium distributions of wild-type and the cataract-causing variant W42R in solution, performed by Wong, E. K.; Prytkova, V.; Freites, J. A.; Butts, C. T.; Tobias, D. J. Molecular Mechanism of Aggregation of the Cataract-Related γD-Crystallin W42R Variant from Multiscale Atomistic Simulations. Biochemistry 2019, 58 (35), 3691–3699. Network models are shown to successfully reproduce the aggregate size and structure observed in the atomistic simulation, and provide information about the transient protein–protein interactions therein. The system size is scaled from the original 375 monomers to a system of 10000 monomers, revealing a lowering of the upper tail of the aggregate size distribution of the W42R variant. Extrapolation to higher and lower concentrations is also performed. These results provide an example of the utility of NHMs for coarse-grained simulation of protein systems, as well as their ability to scale to large system sizes and high concentrations, reducing computational costs while retaining topological information about the system.

Genetic Algorithm for Automated Parameterization of Network Hamiltonian Models of Amyloid Fibril Formation

“…While atomistic classical molecular dynamics simulations can be highly effective for studying molecular motions of individual proteins and nucleic acids, − protein aggregation dynamics leading to amyloid fibril formation involves many individual protein molecules interacting on time scales roughly 9 orders of magnitude beyond the reach of typical molecular dynamics simulations (e.g., 1 μs compared to 1 h). Although enhanced sampling techniques for atomistic molecular dynamics simulations can be used to extend the temporal reach of atomistic molecular dynamics simulations, − time scale deficits of this magnitude typically require the construction of coarse-grained (CG) models, where degrees of freedom deemed unimportant for characterizing the molecular motions of interest are unified into less detailed fundamental components of the system. − Coarse-grained computational models of protein aggregation are useful for suggesting potential mechanisms for amyloid fibril formation at a higher level of detail than what is directly accessible to experiments while remaining grounded in experiments due to computed observables being consistent with experimentally measured observables. ,,− Most coarse-grained models of molecular self-assembly employ a bottom-up approach, wherein the underlying physics driving monomer dynamics at an atomistic level of detail is coarse-grained down to a set of mechanical degrees of freedom deemed essential by the builder of that model. Such approaches yield fibril structures as emergent phenomena from the modeled monomer dynamics.…”

“…This model has been used to propose a mechanism of amyloid fibril formation whereby amyloid fibrils are preceded by the formation of prefibrillar oligomers. 39 Another coarse-grained modeling approach of a similar level of coarseness to the aforementioned work by S ̌aricé t al., 39 i.e., whereby the fundamental interacting bodies are entire protein molecules, is the network Hamiltonian model (NHM), 13,29,36,40,41 which is the focus of the present work.…”

“…42−44 Though not an exhaustive list, some of the leading coarse-grained modeling approaches that have been applied toward studying amyloid fibril formation include: single bead per amino acid models, 11,45,46 midresolution models (multiple beads per residue), 10,15,47−50 the UNRES model, 37,51 the Martini model, 52,53 lattice models, 34,54,55 and network Hamiltonian models. 13,29,36,40,41 Network Hamiltonian Simulations of Amyloid Fibril Formation. Network Hamiltonian models are highly computationally efficient coarse-grained (CG) molecular simulations, which are capable of reproducing multiple known experimental observables (e.g., topological structures measured via NMR and fibril formation growth curves from dye-binding fluorescence kinetics assays 13,28 ), and can provide insights into the complex interactions between proteins that lead to the formation of amyloid fibrils.…”

“…One particularly interesting mechanistic insight into amyloid fibril formation, which was brought to light using network Hamiltonian models by Yu et al, is that fibrillar fraction growth curves for the simple 1-ribbon fibril topology exhibit steady gentle growth compared to the higher ordered structures that display a sharp increase in fibril formation after the initial lag phase. Such developments offer interesting targets for experimental probes involving comparisons between computed fibril fraction growth curves and fibril growth kinetics data obtained via dye-binding fluorescence assays. − Though not an exhaustive list, some of the leading coarse-grained modeling approaches that have been applied toward studying amyloid fibril formation include: single bead per amino acid models, ,, midresolution models (multiple beads per residue), ,,− the UNRES model, , the Martini model, , lattice models, ,, and network Hamiltonian models. ,,,, …”

“… 42 − 44 Though not an exhaustive list, some of the leading coarse-grained modeling approaches that have been applied toward studying amyloid fibril formation include: single bead per amino acid models, 11 , 45 , 46 midresolution models (multiple beads per residue), 10 , 15 , 47 − 50 the UNRES model, 37 , 51 the Martini model, 52 , 53 lattice models, 34 , 54 , 55 and network Hamiltonian models. 13 , 29 , 36 , 40 , 41 …”