Over the last two decades, several simplified protein models (one-bead, two-bead, four-bead and united-atom models) having differing structural resolution and complexity have been developed to study protein aggregation. Native structure-based Go model (33
) have been extensively used to simulate protein folding and aggregation (11
). Inter-particle interactions in the Go model are assigned based on the native state of the protein and are consequently biased towards the native state, thus Go models don't use an ab initio
force field. Recently, explicit modeling of inter-particle interaction potentials such as the hydrophobic and electrostatic salt-bridge interactions in proteins have resulted in accurate protein models having remarkable predictive power (31
). While high-resolution protein models provide accurate structural details, they result in a larger number of beads representing the same protein. Increased computational costs associated with high-resolution models may prohibit simulations of large protein aggregates over experimentally relevant timescales. Thus, there is a necessity to design accurate computational models of proteins having different complexity and detail. In the remainder of this section, we highlight various cases wherein these simplified protein models are used along-with DMD simulations to probe protein aggregation.
4.1. One-bead protein models with Go-like potentials
One of the simplest protein models used to study protein dynamics is the one-bead per residue model, which is based on a representation of each individual amino acid by a single sphere and the protein as a polymer with bead-on-a-string representation (16
) (). Zhou et al
) used DMD simulations of a one-bead model to study first order phase transitions in a homopolymers chain of 64 beads. The authors note that the first order disordered-to-ordered phase transition exhibited by this model homopolymer was analogous to simulating conformational changes in the protein folding process, despite significant differences in the final native state conformations of two species.
Figure 1 Schematic diagrams of (a) the one-bead protein model, (b) the two-bead peptide model, (c) the four bead protein model Solid thick lines represent covalent and peptide bonds. Dashed thin lines denote effective bonds assigned to mimic the tetrahedral constraint (more ...)
Later, Zhou and Karplus (16
) used the one-bead model to study folding of a model three-helix bundle protein (16
). Despite the inherent structural simplicity of the one-bead model, the simulations show experimentally observed transitions from a collapsed state to a native-like topology, whose folding thermodynamics was comparable to all-atom MD simulations by Bockzo and Brooks (43
). These DMD simulations formed one of the early evidences of applicability of simplified models and DMD in probing protein folding and misfolding transitions.
Dokholyan et al.
) demonstrated the ability of one-bead protein models to capture the thermodynamics and kinetics of folding and misfolding transitions in model proteins. The authors also used DMD simulations having Go potential for inter-residue interactions to characterize the folding nucleus of a model 46-residue protein (19
). Dokholyan et al
. observed that few contacts in proteins are essential for mediating the folding kinetics and energetics of the folding transition barrier (19
). The authors also suggested that proteins having similar structures but differing sequence may share common locations of folding nuclei. Biophysical observations derived from these DMD simulations regarding phase transitions upon folding are general and expected to be consistent for folding transitions in other proteins.
) used the one-bead model to perform Langevin dynamics simulation of protein aggregation kinetics of protein G, L and their mutations, each 56 residue long. The author used a simplified off-lattice cooperative folding model (non-Go interactions), representing each protein residue as a single bead. The mutations investigated disrupt hydrophobic interactions in the protein core without significantly changing the overall structure and folding propensities of the two proteins. Moreover, the simulation conditions are chosen to have similar populations of the folded states. The authors note that for simulations with these simplified models, folding cooperativity is the most significant determinant of folding time, estimating the effective population of folding intermediate. Clark observes that aggregates observed in simulations of the one-bead model are less structured as compared to the corresponding native states (44
Chahine and Cheung (37
) used a simplified one-bead per residue protein model to study reversible domain swapping of the p13suc1 protein. MD simulations with a Go-like potential were used to study the p13suc1 dimer formation. Two transition states, the monomer transition state and the dimer transition states are observed in the domain-swapped dimerization process, suggesting a “lock-and-dock” mechanism for p13suc1 dimerization, wherein domain swapping of one strand of a monomer onto an adjoining monomer results in locking of the dimer conformation followed by docking to stabilize the domain-swapped conformation (37
). The authors characterize two populated species coexisting at temperatures significantly lower than the folding transition temperature. The simulations also suggests that folding kinetics of native-like monomer formation will be significantly slower in the course of domain-swapping (37
4.2. Two-bead model applications in protein aggregation
While the one-bead model is able to capture the salient features of protein folding kinetics (19
), the need to obtain structural details of the transition state ensemble (TSE) resulted in the development of the two-bead model of the protein (46
), in which Calpha
atoms were modeled as the constituent protein beads (). Khare et al.
) used the two bead model with Go-type interactions to study folding of SOD1 protein monomer (discussed in section 5.2). Peng et al.
) applied a two-bead protein model with Go-like interactions to study aggregation of Abeta
40 proteins into a fibrillar structure. DMD simulations of the Abeta
40 protein at temperatures exceeding alpha-helix unfolding transition temperature show a conformational transition of the Abeta
40 peptides into multi-layered parallel beta sheets having an interstrand separation of 4.8 Angstroms, in agreement with the structure of the Abeta
40 amyloid fibers derived using electron microscopy (48
). Furthermore, the authors observe the presence of unbound beta sheet edges in the Abeta
40 amyloid aggregates predicted by DMD simulations which may facilitate further aggregation into longer oligomeric species.
Simulations of amphipathic alpha-helix monomer folding demonstrated that the folding process is mediated via a competition between hydrophobicity and hydrogen-bonding interactions in the alpha-helix residues. The temperature dependence of folding kinetics was also dependent on the strength of hydrophobic interactions used in the simulation. Contributions of side-chain entropy and non-backbone hydrogen-bonding to folding kinetics was absent in this model, however, the authors suggested scaling the strength of square-well interactions based on side-chain hydrophobicities to model side chain contributions. Notably, a number of conformations are sampled in the simulations, including non-native topologies, which subsequently lead to misfolded aggregates.
Smith et al.
) studied the conformational transitions of a polyalanine chain to an alpha-helix using DMD simulations of a simplified two-bead protein model with excluded-volume and hydrogen-bonding interactions. The authors note that the (phi, psi) values adopted by the polyalanine chain during the course of conformational transitions in DMD simulation are limited to the valid protein regions in the Ramachandran map and that the formation of is alpha-helices is mediated by backbone hydrogen bonding and is largely cooperative. As opposed to polgyglycine chains, which adopt non-helical topologies, alanine polymers are mostly helical in nature.
4.3. Four-bead model applications in protein aggregation
The four-bead protein model captures significant details of the protein structure and is extensively used for studying protein aggregation using DMD simulations. In this model, three backbone beads N, Calpha
, C and one side-chain bead Cbeta
are used to represent each residue (). Ding et al
) developed a four-bead protein model with hydrogen bonding interactions for DMD simulations. The authors used this protein model to study the temperature dependent conformational transformations of a 16-residue long model polyalanine chain having alpha
-helical native conformation. In the DMD simulations, the authors observe that the alpha
-helix native conformation changes into a partially-stable beta-hairpin conformation. The authors also note an important role of physicochemical nature of the protein environment and hydrophobicity of adjoining residues in governing the aggregation propensity of the polyalanine chain and suggest the presence of sequence-independent backbone hydrogen bonding mediates such conformational transitions. Larger entropy of the beta-hairpin conformation relative to the native alpha-helix stabilizes the beta-hairpin.
Hall and coworkers developed four-bead protein models to study ab initio
DMD simulations of the assembly of 16 residue long amphipathic alpha-helices into a four-helix bundle (51
). The authors performed multiple DMD simulations to accurately sample the conformational space of the monomeric alpha-helix and the tetrameric alpha-helical bundle and describe the tetramer folding landscape (51
). Notably, the conformations explored by the helix monomers and the helical bundle in the DMD simulations were found to be consistent with experiments of DeGrado and coworkers (52
). The authors also report rapid conformational sampling ability of DMD, leading to significant conformational sampling with less computational cost (49
) and the efficacy of the simplified protein model in understanding the dynamics of multi-protein complexes.
Lam et al.
) used DMD simulations of a four-bead protein model with hydrogen bonds and amino-acid specific interactions to study temperature-driven conformational changes in the Amyloid-beta
42 protein. The conformational changes observed in DMD simulations were found to be in good agreement with temperature dependent solution structures of Amyloid-beta
protein determined by Gursky and Aleshkov (57
). Under low temperature conditions, the Abeta
42 protein was found to be mostly globular, however, beta
-rich conformations lacking helical content are observed in simulations at elevated temperatures. While the folded Abeta
42 showed dynamic conformational transitions, turns centered on the Abeta
G25-S26, G37-G38 residues were found to be persistent and important for formation of amyloid fibrils.
Urbanc et al.
) applied a four-bead protein model for the Amyloid-beta
protein to investigate dimer formation in Amyloid-beta
aggregation and probe the oligomerization process of two predominant amyloid-beta
40 and Abeta
42 using DMD. The authors report aggregation of both proteins into oligomers of variable sizes. Dimer conformations were generated using DMD simulations at different constant temperature simulations with the simplified four-bead protein model. These simplified protein conformations were converted into corresponding all-atom representations by superposition against amino-acid structural templates, and subsequent optimization using a Monte Carlo algorithm, resulting in a multiscale model of Abeta
Urbanc et al
) modified the four-bead protein model introducing effective hydrophobic, hydrophilic interactions in addition to the hydrogen bond interactions present in the original model lacking hydropathic interactions (58
). Using this model, the authors investigated folding and oligomerization of the Amyloid-beta
protein using DMD simulations. Both hydrophilic repulsion and hydrophobic attraction were found to be critical for modeling Amyloid-beta
oligomer distributions consistent with experiments by Teplow and coworkers (59
). Notably, oligomers resulting from folding and aggregation simulations of Abeta
monomers displayed variable size distributions, with Abeta
40 oligomers being predominantly dimeric while Abeta
42 forming pentameric oligomers having globular, hydrophobic core (32
). The authors suggest that the presence of Gly-37-Gly-38 turn in Abeta
42, not observed in Abeta
40 plays a crucial role in Abeta
42 pentamer formation. These structural differences between high molecular-weight oligomers of Abeta
40 and Abeta
42 proteins were suggested to cause differences in oligomerization propensities of the two alloforms.
Yun et al.
) used DMD simulation with simplified four-beads per residue protein models to study the electrostatic interactions in Amyloid beta
) protein oligomerization and the role of electrostatic interactions between charged residues in the Abeta
protein. Mechanistic differences between aggregation kinetics of Abeta
40 and Abeta
42 were observed to be based on differences in electrostatic interactions between pairs of charged amino-acids in Abeta
40 and Abeta
42. Differences in protein aggregation propensities resulting from change of polypeptide length is of considerable interest in amyloid research community. The rates of aggregation for Abeta
40 and Abeta
42 proteins, the major components of amyloid plaques formed in Alzheimer's disease, are significantly different. However, the precise mechanisms of these differences in aggregation propensities are not completely understood. The work of Yun et al.
) suggests that electrostatic interactions in Amyloid beta
-protein favor formation of larger oligomeric species in both Abeta
40 and Abeta
42, thereby shifting the oligomer size distribution to larger oligomers. However, the Abeta
40 size distribution remains largely unimodal, while size distribution of Abeta
42 is trimodal, in agreement with experimental findings. Importantly, differences in folded structures of Abeta
40 and Abeta
42 monomers are unaffected by electrostatic interactions. A C-terminus turn, found in Abeta
42 folded structure is absent in Abeta
40, suggesting a key role of the C-terminal tail in Abeta
42 oligomerization. These simulations with simplified protein models also suggest inhibitors targeting the Abeta
42 C-terminal domain may prevent oligomer formation thereby reducing its cytotoxicity.
Smith et al.
) probed the assembly of a prototypical tetrameric alpha-helical bundle using DMD simulations of a simplified four-bead per residue protein model having detailed backbone geometry (three beads modeling the backbone and one bead modeling the side chain). Starting from random coil conformations, DMD simulations of the model monomer amphipathic polypeptides undergo folding transitions resulting in alpha-helical native topologies. Equilibrium between side-chain hydrophobic interactions and backbone hydrogen-bonding mediates the stability of model peptide's alpha-helical native state. The authors observe formation of non-native hydrogen bonds in the course of simulations, resulting in exploration of non-native misfolded conformations, rich in beta
-hairpin, or beta
-sheet motifs). Simulations of tetramers of 16-residue chains result in parallel and anti-parallel tetrameric alpha-helical bundles with hydrophobic side-chains shielded in the bundle interior as the most stable conformation. Low temperature simulations were found to be often trapped in misfolded states because of stronger hydrogen bonding and hydrophobic interactions relative to thermal fluctuations. Notably, structures with non-native and beta
-hydrogen bonds are often observed in tetramer simulations, resulting in non-ideal folding trajectories leading to misfolded states.
Nguyen et al.
) studied the kinetics of polyalanine fibril formation using an intermediate-resolution four-bead per residue protein model, termed PRIME (49
). The model has three beads representing the peptide backbone and one bead representing the side chain atoms. As opposed to the native conformation based Go-model, the PRIME four-bead protein model is devoid of any conformational bias towards native or non-native conformations. In addition to distance, angular and dihedral constraints modeling the protein structure, intra- and inter-molecular hydrogen bonding and hydrophobic interactions are modeled for inter-residue interactions. While DMD simulations of the 48−96 residue long polyalanine chains show that the mechanism of amyloid fibril formation is in agreement with three known models, namely: templated assembly; nucleated polymerization; and nucleated conformational conversion. However, none of these models could alone explain the kinetics of fibril formulation with significant accuracy. The authors suggested that the kinetics of polyalanine conformational conversion is manifested as progression from small amorphous aggregate state to beta
-sheets, which form an ordered nucleus ultimately leading to fibrillar protofilament species. The kinetics of amyloid fibril formation increased with increasing polyalanine concentration as well as decreasing simulation temperature. Furthermore, the simulations indicate that the polyalanine oligomers growth involved beta
-sheet elongation adding polyalanine peptides in the end as well as lateral appending of existing beta-
4.4. United-atom model applications in protein aggregation
The united-atom model represents groups of atoms as novel atom types having physical properties such as particle diameter and inter-particle interactions scaled corresponding to the constituent atoms. Borrguero et al.
) used a detailed unified-atom model representing all atoms except hydrogens and DMD simulations to study the folding dynamics of a 10 residue segment (Ala 21-Ala 30) of the amyloid beta
protein. This segment is suggested to nucleate the folding of monomeric Abeta
protein. The authors report that hydrophobic interactions between constituent Val-24, Lys-28 residues and an equilibrium between electrostatic interactions of Glu-22 and Asp-23 with Lys-28 result in folding of this domain into a stable loop structure. Salt bridge interactions of Asp-23 with Lys-28 was also consistent with Abeta
conformational stability analyses by Ma et al.
) and the NMR-derived model of Abeta
by Petkova et al.
). Different conformations adopted by this 10 residue segment Abeta
), as observed in the NMR solution structure of Abeta
), Protein DataBank accession number: 1HZ3, are shown in . Side chains of residues Glu-22, Asp-23 and Lys-28 are highlighted for clarity. Familial mutations of Alzheimer's disease at the Glu-22 are suggested to change the interactions of Glu-22 with Lys-28, thereby altering the stability of Abeta
folding nucleus (39
). Subsequent long timescale all-atom MD simulations by Cruz et al.
) also confirm the role of hydrophobic and salt bridge interactions in folding dynamics of Abeta
Figure 2 Conformational dynamics of the model Amyloid-β folding nucleus (residues 21−30, derived from Protein DataBank accession number: 1HZ3). Salt bridge interactions between residues Glu22, Asp23 and Lys28 are highlighted. These residues are (more ...)