Assessment of Two Restraint Potentials for Coarse-Grained Chemical-Cross-Link-Assisted Modeling of Protein Structures.

The influence of distance restraints from chemical cross-link mass spectroscopy (XL-MS) on the quality of protein structures modeled with the coarse-grained UNRES force field was assessed by using a protocol based on multiplexed replica exchange molecular dynamics, in which both simulated and experimental cross-link restraints were employed, for 23 small proteins. Six cross-links with upper distance boundaries from 4 Å to 12 Å (azido benzoic acid succinimide (ABAS), triazidotriazine (TATA), succinimidyldiazirine (SDA), disuccinimidyl adipate (DSA), disuccinimidyl glutarate (DSG), and disuccinimidyl suberate (BS3)) and two types of restraining potentials ((i) simple flat-bottom Lorentz-like potentials dependent on side chain distance (all cross-links) and (ii) distance- and orientation-dependent potentials determined based on molecular dynamics simulations of model systems (DSA, DSG, BS3, and SDA)) were considered. The Lorentz-like potentials with properly set parameters were found to produce a greater number of higher-quality models compared to unrestrained simulations than the MD-based potentials, because the latter can force too long distances between side chains. Therefore, the flat-bottom Lorentz-like potentials are recommended to represent cross-link restraints. It was also found that significant improvement of model quality upon the introduction of cross-link restraints is obtained when the sum of differences of indices of cross-linked residues exceeds 150.

Heat-induced degradation of fibrils: Exponential vs logistic kinetics.

The degradation of fibrils under the influence of thermal fluctuations was studied experimentally by various groups around the world. In the first set of experiments, it was shown that the decay of fibril content, which can be measured by the ThT fluorescence assay, obeys a bi-exponential function. In the second series of experiments, it was demonstrated that when the monomers separated from the aggregate are not recyclable, the time dependence of the number of monomers belonging to the dominant cluster is described by a single-exponential function if the fraction of bound chains becomes less than a certain threshold. Note that the time dependence of the fraction of bound chains can be measured by tryptophan fluorescence. To understand these interesting experimental results, we developed a phenomenological theory and performed molecular simulation. According to our theory and simulations using the lattice and all-atom models, the time dependence of bound chains is described by a logistic function, which slowly decreases at short time scales but becomes a single exponential function at large time scales. The results, obtained by using lattice and all-atom simulations, ascertained that the time dependence of the fibril content can be described by a bi-exponential function that decays faster than the logistic function on short time scales. We have uncovered the molecular mechanism for the distinction between the logistic and bi-exponential behavior. Since the dissociation of the chain from the fibrils requires the breaking of a greater number of inter-chain contacts as compared to the breaking of the beta sheet structure, the decrease in the number of connected chains is slower than the fibril content. Therefore, the time dependence of the aggregate size is logistic, while the two-exponential behavior is preserved for the content of fibrils. Our results are in agreement with the results obtained in both sets of experiments.

Aggregation rate of amyloid beta peptide is controlled by beta-content in monomeric state.

Understanding the key factors that govern the rate of protein aggregation is of immense interest since protein aggregation is associated with a number of neurodegenerative diseases. Previous experimental and theoretical studies have revealed that the hydrophobicity, charge, and population of the fibril-prone monomeric state control the fibril formation rate. Because the fibril structures consist of cross beta sheets, it is widely believed that those sequences that have a high beta content (ß) in the monomeric state should have high aggregation rates as the monomer can serve as a template for fibril growth. However, this important fact has never been explicitly proven, motivating us to carry out this study. Using replica exchange molecular dynamics simulation with implicit water, we have computed ß of 19 mutations of amyloid beta peptide of 42 residues (Aß42) for which the aggregation rate κ has been measured experimentally. We have found that κ depends on ß in such a way that the higher the propensity to aggregation, the higher the beta content in the monomeric state. Thus, we have solved a long-standing problem of the dependence of fibril formation time of the ß-structure on a quantitative level.

Kinetics and mechanical stability of the fibril state control fibril formation time of polypeptide chains: A computational study.

Fibril formation resulting from protein misfolding and aggregation is a hallmark of several neurodegenerative diseases such as Alzheimer's and Parkinson's diseases. Despite much progress in the understanding of the protein aggregation process, the factors governing fibril formation rates and fibril stability have not been fully understood. Using lattice models, we have shown that the fibril formation time is controlled by the kinetic stability of the fibril state but not by its energy. Having performed all-atom explicit solvent molecular dynamics simulations with the GROMOS43a1 force field for full-length amyloid beta peptides Aß40 and Aß42 and truncated peptides, we demonstrated that kinetic stability can be accessed via mechanical stability in such a way that the higher the mechanical stability or the kinetic stability, the faster the fibril formation. This result opens up a new way for predicting fibril formation rates based on mechanical stability that may be easily estimated by steered molecular dynamics.

Preformed template fluctuations promote fibril formation: insights from lattice and all-atom models.

Fibril formation resulting from protein misfolding and aggregation is a hallmark of several neurodegenerative diseases such as Alzheimer's and Parkinson's diseases. Despite the fact that the fibril formation process is very slow and thus poses a significant challenge for theoretical and experimental studies, a number of alternative pictures of molecular mechanisms of amyloid fibril formation have been recently proposed. What seems to be common for the majority of the proposed models is that fibril elongation involves the formation of pre-nucleus seeds prior to the creation of a critical nucleus. Once the size of the pre-nucleus seed reaches the critical nucleus size, its thermal fluctuations are expected to be small and the resulting nucleus provides a template for sequential (one-by-one) accommodation of added monomers. The effect of template fluctuations on fibril formation rates has not been explored either experimentally or theoretically so far. In this paper, we make the first attempt at solving this problem by two sets of simulations. To mimic small template fluctuations, in one set, monomers of the preformed template are kept fixed, while in the other set they are allowed to fluctuate. The kinetics of addition of a new peptide onto the template is explored using all-atom simulations with explicit water and the GROMOS96 43a1 force field and simple lattice models. Our result demonstrates that preformed template fluctuations can modulate protein aggregation rates and pathways. The association of a nascent monomer with the template obeys the kinetics partitioning mechanism where the intermediate state occurs in a fraction of routes to the protofibril. It was shown that template immobility greatly increases the time of incorporating a new peptide into the preformed template compared to the fluctuating template case. This observation has also been confirmed by simulation using lattice models and may be invoked to understand the role of template fluctuations in slowing down fibril elongation in vivo.

Dual effect of crowders on fibrillation kinetics of polypeptide chains revealed by lattice models.

We have developed the lattice model for describing polypeptide chains in the presence of crowders. The influence of crowding confinement on the fibrillation kinetics of polypeptide chains is studied using this model. We observed the non-trivial behavior of the fibril formation time τfib that it decreases with the concentration of crowders if crowder sizes are large enough, but the growth is observed for crowders of small sizes. This allows us to explain the recent experimental observation on the dual effect of crowding particles on fibril growth of proteins that for a fixed crowder concentration the fibrillation kinetics is fastest at intermediate values of total surface of crowders. It becomes slow at either small or large coverages of cosolutes. It is shown that due to competition between the energetics and entropic effects, the dependence of τfib on the size of confined space is described by a parabolic function.

New method for determining size of critical nucleus of fibril formation of polypeptide chains.

A new method for determining the size of critical nucleus of fibril formation of polypeptide chains is proposed. Based on the hypothesis that the fibril grows by addition of a nascent peptide to the preformed template, the nucleus size N(c) is defined as the number of forming template peptides above which the time to add a new monomer becomes independent of the template size. Using lattice models one can show that our method and the standard method which is based on calculation of the free energy, provide the same result for N(c).

Computational Models for the Study of Protein Aggregation.

Protein aggregation has been studied by many groups around the world for many years because it can be the cause of a number of neurodegenerative diseases that have no effective treatment. Obtaining the structure of related fibrils and toxic oligomers, as well as describing the pathways and main factors that govern the self-organization process, is of paramount importance, but it is also very difficult. To solve this problem, experimental and computational methods are often combined to get the most out of each method. The effectiveness of the computational approach largely depends on the construction of a reasonable molecular model. Here we discussed different versions of the four most popular all-atom force fields AMBER, CHARMM, GROMOS, and OPLS, which have been developed for folded and intrinsically disordered proteins, or both. Continuous and discrete coarse-grained models, which were mainly used to study the kinetics of aggregation, are also summarized.

Effect of Surface Roughness on Aggregation of Polypeptide Chains: A Monte Carlo Study.

The self-assembly of amyloidogenic peptides and proteins into fibrillar structures has been intensively studied for several decades, because it seems to be associated with a number of neurodegenerative diseases, such as Alzheimer's and Parkinson's disease. Therefore, understanding the molecular mechanisms of this phenomenon is important for identifying an effective therapy for the corresponding diseases. Protein aggregation in living organisms very often takes place on surfaces like membranes and the impact of a surface on this process depends not only on the surface chemistry but also on its topology. Our goal was to develop a simple lattice model for studying the role of surface roughness in the aggregation kinetics of polypeptide chains and the morphology of aggregates. We showed that, consistent with the experiment, an increase in roughness slows down the fibril formation, and this process becomes inhibited at a very highly level of roughness. We predicted a subtle catalytic effect that a slightly rough surface promotes the self-assembly of polypeptide chains but does not delay it. This effect occurs when the interaction between the surface and polypeptide chains is moderate and can be explained by taking into account the competition between energy and entropy factors.

Factors governing fibrillogenesis of polypeptide chains revealed by lattice models.

Using lattice models we explore the factors that determine the tendencies of polypeptide chains to aggregate by exhaustively sampling the sequence and conformational space. The morphologies of the fibril-like structures and the time scales (τ(fib)) for their formation depend on a balance between hydrophobic and Coulomb interactions. The extent of population of an ensemble of N* structures, which are fibril-prone structures in the spectrum of conformations of an isolated protein, is the major determinant of τ(fib). This observation is used to determine the aggregating sequences by exhaustively exploring the sequence space, thus providing a basis for genome wide search of fragments that are aggregation prone.