Implicit Solvent Models and the Energy Landscape for Aggregation of the Amyloidogenic KFFE Peptide

Exploiting Sequence-Dependent Rotamer Information in Global Optimization of Proteins

Rotamers, namely amino acid side chain conformations common to many different peptides, can be compiled into libraries. These rotamer libraries are used in protein modeling, where the limited conformational space occupied by amino acid side chains is exploited. Here, we construct a sequence-dependent rotamer library from simulations of all possible tripeptides, which provides rotameric states dependent on adjacent amino acids. We observe significant sensitivity of rotamer populations to sequence and find that the library is successful in locating side chain conformations present in crystal structures. The library is designed for applications with basin-hopping global optimization, where we use it to propose moves in conformational space. The addition of rotamer moves significantly increases the efficiency of protein structure prediction within this framework, and we determine parameters to optimize efficiency.

Early aggregation mechanism of Aβ16-22 revealed by Markov state models

Aβ_16-22 is believed to have critical role in early aggregation of full length amyloids that are associated with the Alzheimer's disease and can aggregate to form amyloid fibrils. However, the early aggregation mechanism is still unsolved. Here, multiple long-term molecular dynamics simulations combining with Markov state model were used to probe the early oligomerization mechanism of Aβ_16-22 peptides. The identified dimeric form adopted either globular random-coil or extended β-strand like conformations. The observed dimers of these variants shared many overall conformational characteristics but differed in several aspects at detailed level. In all cases, the most common type of secondary structure was intermolecular antiparallel β-sheets. The inter-state transitions were very frequent ranges from few to hundred nanoseconds. More strikingly, those states which contain fraction of β secondary structure and significant amount of extended coiled structures, therefore exposed to the solvent, were majorly participated in aggregation. The assembly of low-energy dimers, in which the peptides form antiparallel β sheets, occurred by multiple pathways with the formation of an obligatory intermediates. We proposed that these states might facilitate the Aβ_16-22 aggregation through a significant component of the conformational selection mechanism, because they might increase the aggregates population by promoting the inter-chain hydrophobic and the hydrogen bond contacts. The formation of early stage antiparallel β sheet structures is critical for oligomerization, and at the same time provided a flat geometry to seed the ordered β-strand packing of the fibrils. Our findings hint at reorganization of this part of the molecule as a potentially critical step in Aβ aggregation and will insight into early oligomerization for large β amyloids.

Modeling and simulation of protein-surface interactions: achievements and challenges

Understanding protein-inorganic surface interactions is central to the rational design of new tools in biomaterial sciences, nanobiotechnology and nanomedicine. Although a significant amount of experimental research on protein adsorption onto solid substrates has been reported, many aspects of the recognition and interaction mechanisms of biomolecules and inorganic surfaces are still unclear. Theoretical modeling and simulations provide complementary approaches for experimental studies, and they have been applied for exploring protein-surface binding mechanisms, the determinants of binding specificity towards different surfaces, as well as the thermodynamics and kinetics of adsorption. Although the general computational approaches employed to study the dynamics of proteins and materials are similar, the models and force-fields (FFs) used for describing the physical properties and interactions of material surfaces and biological molecules differ. In particular, FF and water models designed for use in biomolecular simulations are often not directly transferable to surface simulations and vice versa. The adsorption events span a wide range of time- and length-scales that vary from nanoseconds to days, and from nanometers to micrometers, respectively, rendering the use of multi-scale approaches unavoidable. Further, changes in the atomic structure of material surfaces that can lead to surface reconstruction, and in the structure of proteins that can result in complete denaturation of the adsorbed molecules, can create many intermediate structural and energetic states that complicate sampling. In this review, we address the challenges posed to theoretical and computational methods in achieving accurate descriptions of the physical, chemical and mechanical properties of protein-surface systems. In this context, we discuss the applicability of different modeling and simulation techniques ranging from quantum mechanics through all-atom molecular mechanics to coarse-grained approaches. We examine uses of different sampling methods, as well as free energy calculations. Furthermore, we review computational studies of protein-surface interactions and discuss the successes and limitations of current approaches.

Energy Landscapes and Global Optimization of Self-Assembling Cyclic Peptides

Self-assembled cyclic peptide nanotubes have attracted much attention because of their antimicrobial properties. Here, we present calculations on the formation of cyclic peptide dimers using basin-hopping and discrete path sampling. We present an analysis of the basin-hopping move sets that most efficiently explore the conformations of cyclic peptides. Group rotation moves, in which sections of the ring are rotated as a rigid body, are the most effective for cyclic peptides containing up to 20 residues. For cyclic peptide dimers, we find that a combination of group rotation intramolecular moves and rigid body intermolecular moves performs well. Discrete path sampling calculations on the cyclic peptide dimers show significant differences in the dimerization of hexa- and octapeptides.

Mechanism of amyloid-β fibril elongation

Amyloid-β is an intrinsically disordered protein that forms fibrils in the brains of patients with Alzheimer's disease. To explore factors that affect the process of fibril growth, we computed the free energy associated with disordered amyloid-β monomers being added to growing amyloid fibrils using extensive molecular dynamics simulations coupled with umbrella sampling. We find that the mechanisms of Aβ40 and Aβ42 fibril elongation have many features in common, including the formation of an obligate on-pathway β-hairpin intermediate that hydrogen bonds to the fibril core. In addition, our data lead to new hypotheses for how fibrils may serve as secondary nucleation sites that can catalyze the formation of soluble oligomers, a finding in agreement with recent experimental observations. These data provide a detailed mechanistic description of amyloid-β fibril elongation and a structural link between the disordered free monomer and the growth of amyloid fibrils and soluble oligomers.

Protein structure prediction: assembly of secondary structure elements by basin-hopping

The prediction of protein tertiary structure from primary structure remains a challenging task. One possible approach to this problem is the application of basin-hopping global optimization combined with an all-atom force field. In this work, the efficiency of basin-hopping is improved by introducing an approach that derives tertiary structures from the secondary structure assignments of individual residues. This approach is termed secondary-to-tertiary basin-hopping and benchmarked for three miniproteins: trpzip, trp-cage and ER-10. For each of the three miniproteins, the secondary-to-tertiary basin-hopping approach successfully and reliably predicts their three-dimensional structure. When it is applied to larger proteins, correctly folded structures are obtained. It can be concluded that the assembly of secondary structure elements using basin-hopping is a promising tool for de novo protein structure prediction.

Comparison of volume and surface area nonpolar solvation free energy terms for implicit solvent simulations

Implicit solvent models for molecular dynamics simulations are often composed of polar and nonpolar terms. Typically, the nonpolar solvation free energy is approximated by the solvent-accessible-surface area times a constant factor. More sophisticated approaches incorporate an estimate of the attractive dispersion forces of the solvent and∕or a solvent-accessible volume cavitation term. In this work, we confirm that a single volume-based nonpolar term most closely fits the dispersion and cavitation forces obtained from benchmark explicit solvent simulations of fixed protein conformations. Next, we incorporated the volume term into molecular dynamics simulations and find the term is not universally suitable for folding up small proteins. We surmise that while mean-field cavitation terms such as volume and SASA often tilt the energy landscape towards native-like folds, they also may sporadically introduce bottlenecks into the folding pathway that hinder the progression towards the native state.

Protein structure prediction using global optimization by basin-hopping with NMR shift restraints

Computational methods that utilize chemical shifts to produce protein structures at atomic resolution have recently been introduced. In the current work, we exploit chemical shifts by combining the basin-hopping approach to global optimization with chemical shift restraints using a penalty function. For three peptides, we demonstrate that this approach allows us to find near-native structures from fully extended structures within 10,000 basin-hopping steps. The effect of adding chemical shift restraints is that the α and β secondary structure elements form within 1000 basin-hopping steps, after which the orientation of the secondary structure elements, which produces the tertiary contacts, is driven by the underlying protein force field. We further show that our chemical shift-restraint BH approach also works for incomplete chemical shift assignments, where the information from only one chemical shift type is considered. For the proper implementation of chemical shift restraints in the basin-hopping approach, we determined the optimal weight of the chemical shift penalty energy with respect to the CHARMM force field in conjunction with the FACTS solvation model employed in this study. In order to speed up the local energy minimization procedure, we developed a function, which continuously decreases the width of the chemical shift penalty function as the minimization progresses. We conclude that the basin-hopping approach with chemical shift restraints is a promising method for protein structure prediction.

Connecting macroscopic observables and microscopic assembly events in amyloid formation using coarse grained simulations

The pre-fibrillar stages of amyloid formation have been implicated in cellular toxicity, but have proved to be challenging to study directly in experiments and simulations. Rational strategies to suppress the formation of toxic amyloid oligomers require a better understanding of the mechanisms by which they are generated. We report Dynamical Monte Carlo simulations that allow us to study the early stages of amyloid formation. We use a generic, coarse-grained model of an amyloidogenic peptide that has two internal states: the first one representing the soluble random coil structure and the second one the -sheet conformation. We find that this system exhibits a propensity towards fibrillar self-assembly following the formation of a critical nucleus. Our calculations establish connections between the early nucleation events and the kinetic information available in the later stages of the aggregation process that are commonly probed in experiments. We analyze the kinetic behaviour in our simulations within the framework of the theory of classical nucleated polymerisation, and are able to connect the structural events at the early stages in amyloid growth with the resulting macroscopic observables such as the effective nucleus size. Furthermore, the free-energy landscapes that emerge from these simulations allow us to identify pertinent properties of the monomeric state that could be targeted to suppress oligomer formation.

A number of normally soluble proteins can form amyloid structures in a process associated with neurodegenerative diseases such as Alzheimer's and Parkinson's diseases. Mature amyloid structures consist of large fibrils containing thousands of individual proteins aggregated into linear nanostructures; there is increasing evidence, however, that the toxic species responsible for neurodegeneration are not the mature fibrils themselves but rather lower molecular weight precursors commonly known as amyloid oligomers. Unfortunately, these early oligomers are commonly thermodynamically unstable and of nanometer scale dimensions, factors which make them highly challenging to probe in detail in experiments. We have used computer simulations of a model inspired by Alzheimer's Abeta peptide to investigate the early stages of protein aggregation. The results that we obtain were shown to fit Oosawa's polymerization theory, a finding which allows us to provide a connection between the microscopic molecular parameters and macroscopic growth. One crucial parameter is size of the nucleus, i.e. the basic oligomer existing at origin of the formation of each fiber. We have revealed a path for the formation of this nucleus and validate its size by several methods. Our results provide fundamental information for influencing the early stages of amyloid formation in a rational manner.

Scanning tunneling microscopy reveals single-molecule insights into the self-assembly of amyloid fibrils

Many severe diseases are associated with amyloid fibril deposits in the body caused by protein misfolding. Structural information on amyloid fibrils is accumulating rapidly, but little is known about the assembly of peptides into fibrils at the level of individual molecules. Here we investigate self-assembly of the fibril-forming tetrapeptides KFFE and KVVE on a gold surface under ultraclean vacuum conditions using scanning tunneling microscopy. Combined with restrained molecular dynamics modeling, we identify peptide arrangements with interesting similarities to fibril structures. By resolving individual peptide residues and revealing conformational heterogeneities and dynamics, we demonstrate how conformational correlations may be involved in cooperative fibril growth. Most interestingly, intermolecular interactions prevail over intramolecular interactions, and assembly of the phenyl-rich KFFE peptide appears not to be dominated by π-π interactions. This study offers interesting perspectives for obtaining fundamental single-molecule insights into fibril formation using a surface science approach to study idealized model systems.

Structures of the amyloid β-peptides Aβ1-40 and Aβ1-42 as influenced by pH and a D-peptide

In this simulation study, we present a comparison of the secondary structure of the two major alloforms of the Alzheimer's peptide (Aβ(1-40) and Aβ(1-42)) on the basis of molecular dynamics (MD) simulations on thea microsecond time scale using the two GROMOS96 force fields ffG43a2 and ffG53a6. We observe peptide and force-field related differences in the sampled conformations of Aβ(1-40) and Aβ(1-42), which we characterize in terms of NMR chemical shifts calculated from the MD trajectories and validate against the corresponding experimental NMR results. From this analysis, we can conclude that ffG53a6 is better able to model the structural propensities of Aβ(1-40) and Aβ(1-42) than ffG43a2. Furthermore, we provide a description of the influences of pH and binding of D3, a 12-residue D-enantiomeric peptide with demonstrated antiamyloid effects, on the structure of Aβ(1-42). We demonstrate that, under slightly acidic conditions, protonation of the three histidine residues in Aβ(1-42) promotes the formation of β-sheets via a reduction in electrostatic repulsion between the two terminal regions. Our studies further reveal that the binding between D3 and Aβ(1-42) is driven by electrostatic interactions between negatively charged Aβ(1-42) residues and the five positively charged arginine residues of D3. The binding of D3 was found to induce large conformational changes in the amyloid peptide, with a reduction in β-sheet units being the most significant effect recorded, possibly explaining the observed amyloid-inhibiting properties of the D-peptide.

Modeling the self-assembly of the cellulosome enzyme complex

Most bacteria use free enzymes to degrade plant cell walls in nature. However, some bacteria have adopted a different strategy wherein enzymes can either be free or tethered on a protein scaffold forming a complex called a cellulosome. The study of the structure and mechanism of these large macromolecular complexes is an active and ongoing research topic, with the goal of finding ways to improve biomass conversion using cellulosomes. Several mechanisms involved in cellulosome formation remain unknown, including how cellulosomal enzymes assemble on the scaffoldin and what governs the population of cellulosomes created during self-assembly. Here, we present a coarse-grained model to study the self-assembly of cellulosomes. The model captures most of the physical characteristics of three cellulosomal enzymes (Cel5B, CelS, and CbhA) and the scaffoldin (CipA) from Clostridium thermocellum. The protein structures are represented by beads connected by restraints to mimic the flexibility and shapes of these proteins. From a large simulation set, the assembly of cellulosomal enzyme complexes is shown to be dominated by their shape and modularity. The multimodular enzyme, CbhA, binds statistically more frequently to the scaffoldin than CelS or Cel5B. The enhanced binding is attributed to the flexible nature and multimodularity of this enzyme, providing a longer residence time around the scaffoldin. The characterization of the factors influencing the cellulosome assembly process may enable new strategies to create designers cellulosomes.

Symmetrization of the AMBER and CHARMM force fields

The AMBER and CHARMM force fields are analyzed from the viewpoint of the permutational symmetry of the potential for feasible exchanges of identical atoms and chemical groups in amino and nucleic acids. In each case, we propose schemes for symmetrizing the potentials, which greatly facilitate the bookkeeping associated with constructing kinetic transition networks via geometry optimization.

Relationship between population of the fibril-prone conformation in the monomeric state and oligomer formation times of peptides: insights from all-atom simulations

Despite much progress in understanding the aggregation process of biomolecules, the factors that govern its rates have not been fully understood. This problem is of particular importance since many conformational diseases such as Alzheimer, Parkinson, and type-II diabetes are associated with the protein oligomerization. Having performed all-atom simulations with explicit water and various force fields for two short peptides KFFE and NNQQ, we show that their oligomer formation times are strongly correlated with the population of the fibril-prone conformation in the monomeric state. The larger the population the faster the aggregation process. Our result not only suggests that this quantity plays a key role in the self-assembly of polypeptide chains but also opens a new way to understand the fibrillogenesis of biomolecules at the monomeric level. The nature of oligomer ordering of NNQQ is studied in detail.

Principles governing oligomer formation in amyloidogenic peptides

Identifying the principles that describe the formation of protein oligomers and fibrils with distinct morphologies is a daunting problem. Here we summarize general principles of oligomer formation gleaned from molecular dynamics simulations of Abeta-peptides. The spectra of high free energy structures sampled by the monomer provide insights into the plausible fibril structures, providing a rationale for the 'strain phenomenon.' Heterogeneous growth dynamics of small oligomers of Abeta(16-22), whose lowest free energy structures are like nematic droplets, can be broadly described using a two-stage dock-lock mechanism. In the growth process, water is found to play various roles depending on the oligomer size, and peptide length, and sequence. Water may be an explicit element of fibril structure linked to various fibril morphologies.

Calculation of protein heat capacity from replica-exchange molecular dynamics simulations with different implicit solvent models

The heat capacity has played a major role in relating microscopic and macroscopic properties of proteins and their disorder-order phase transition of folding. Its calculation by atomistic simulation methods remains a significant challenge due to the complex and dynamic nature of protein structures, their solvent environment, and configurational averaging. To better understand these factors on calculating a protein heat capacity, we provide a comparative analysis of simulation models that differ in their implicit solvent description and force-field resolution. Our model protein system is the src Homology 3 (SH3) domain of alpha-spectrin, and we report a series of 10 ns replica-exchange molecular dynamics simulations performed at temperatures ranging from 298 to 550 K, starting from the SH3 native structure. We apply the all-atom CHARMM22 force field with different modified analytical generalized Born solvent models (GBSW and GBMV2) and compare these simulation models with the distance-dependent dielectric screening of charge-charge interactions. A further comparison is provided with the united-atom CHARMM19 plus a pairwise GB model. Unfolding-folding transition temperatures of SH3 were estimated from the temperature-dependent profiles of the heat capacity, root-mean-square distance from the native structure, and the fraction of native contacts, each calculated from the density of states by using the weighted histogram analysis method. We observed that, for CHARMM22, the unfolding transition and energy probability density were quite sensitive to the implicit solvent description, in particular, the treatment of the protein-solvent dielectric boundary in GB models and their surface-area-based hydrophobic term. Among the solvent models tested, the calculated melting temperature varied in the range 353-438 K and was higher than the experimental value near 340 K. A reformulated GBMV2 model of employing a smoother molecular-volume dielectric interface was the most accurate in reproducing the native conformation and a two-state folding landscape, although the melting transition temperature did not show the smallest deviation from experiment. For the lower-resolution CHARMM19/GB model, the simulations failed to yield a bimodal energy distribution, yet the melting temperature was observed to be a good estimate of higher-resolution simulation models. We also demonstrate that a careful analysis of a relatively long simulation is necessary to avoid trapping in local minima and to find a true thermodynamic transition temperature.

What determines the structure and stability of KFFE monomers, dimers, and protofibrils?

The self-assembly of the KFFE peptide was studied using replica exchange molecular dynamics simulations with a fully atomic description of the peptide and explicit solvent. The relative roles of the aromatic residues and oppositely charged end groups in stabilizing the earliest oligomers and the end-products of aggregation were investigated. beta and non-beta-peptide conformations compete in the monomeric state as a result of a balancing between the high beta-sheet propensity of the phenylalanine residues and charge-charge interactions that favor non-beta-conformations. Dimers are present in beta- and non-beta-sheet conformations and are stabilized primarily by direct and water-mediated charge-charge interactions between oppositely charged side chains and between oppositely charged termini, with forces between aromatic residues playing a minor role. Dimerization to a beta-sheet, fibril-competent state, is seen to be a cooperative process, with the association process inducing beta-structure in otherwise non-beta-monomers. We propose a model for the KFFE fibril, with mixed interface and antiparallel sheet and strand arrangements, which is consistent with experimental electron microscopy measurements. Both aromatic and charge-charge interactions contribute to the fibril stability, although the dominant contribution arises from electrostatic interactions.

Stability of single sheet GNNQQNY aggregates analyzed by replica exchange molecular dynamics: antiparallel versus parallel association

Protein and peptide aggregation into amyloid plaques is associated with a large variety of neurodegenerative diseases. The definition of the molecular bases of these pathologies is hampered by the transient nature of pre-fibrillar small-oligomers that are considered the toxic species. The ability of the peptide GNNQQNY to form amyloid-like structures makes it a good model to investigate the complex processes involved into amyloid fiber formation. By employing full atomistic replica exchange molecular dynamics simulations, we constructed the free energy surface of small assemblies of GNNQQNY to gain novel insights into the fiber formation process. The calculations suggest that the peptide exhibits a remarkable tendency to form both parallel and antiparallel beta-sheets. The data show that GNNQQNY preference for parallel or antiparallel beta-sheets is governed by a subtle balance of factors including assemblies' size, sidechain-sidechain interactions and pH. The samplings analysis provides a rationale to the observed trends.