Communication: Simulated tempering with fast on-the-fly weight determination

Enhancing torsional sampling using fully adaptive simulated tempering

Enhanced sampling algorithms are indispensable when working with highly disconnected multimodal distributions. An important application of these is the conformational exploration of particular internal degrees of freedom of molecular systems. However, despite the existence of many commonly used enhanced sampling algorithms to explore these internal motions, they often rely on system-dependent parameters, which negatively impact efficiency and reproducibility. Here, we present fully adaptive simulated tempering (FAST), a variation of the irreversible simulated tempering algorithm, which continuously optimizes the number, parameters, and weights of intermediate distributions to achieve maximally fast traversal over a space defined by the change in a predefined thermodynamic control variable such as temperature or an alchemical smoothing parameter. This work builds on a number of previously published methods, such as sequential Monte Carlo, and introduces a novel parameter optimization procedure that can, in principle, be used in any expanded ensemble algorithms. This method is validated by being applied on a number of different molecular systems with high torsional kinetic barriers. We also consider two different soft-core potentials during the interpolation procedure and compare their performance. We conclude that FAST is a highly efficient algorithm, which improves simulation reproducibility and can be successfully used in a variety of settings with the same initial hyperparameters.

Efficient Sampling of Cavity Hydration in Proteins with Nonequilibrium Grand Canonical Monte Carlo and Polarizable Force Fields

Prediction of the hydration levels of protein cavities and active sites is important to both mechanistic analysis and ligand design. Due to the unique microscopic environment of these buried water molecules, a polarizable model is expected to be crucial for an accurate treatment of protein internal hydration in simulations. Here we adapt a nonequilibrium candidate Monte Carlo approach for conducting grand canonical Monte Carlo simulations with the Drude polarizable force field. The GPU implementation enables the efficient sampling of internal cavity hydration levels in biomolecular systems. We also develop an enhanced sampling approach referred to as B-walking, which satisfies detailed balance and readily combines with grand canonical integration to efficiently calculate quantitative binding free energies of water to protein cavities. Applications of these developments are illustrated in a solvent box and the polar ligand binding site in trypsin. Our simulation results show that including electronic polarization leads to a modest but clear improvement in the description of water position and occupancy compared to the crystal structure. The B-walking approach enhances the range of water sampling in different chemical potential windows and thus improves the accuracy of water binding free energy calculations.

Binding and Kinetic Analysis of Human Protein Phosphatase PP2A Interactions with Caspase 9 Protein and the Interfering Peptide C9h

The serine/threonine phosphatase PP2A and the cysteine protease Caspase 9 are two proteins involved in physiological and pathological processes, including cancer and apoptosis. We previously demonstrated the interaction between Caspase 9 and PP2A and identified the C9h peptide, corresponding to the binding site of Caspase 9 to PP2A. This interfering peptide can modulate Caspase 9/PP2A interaction leading to a strong therapeutic effect in vitro and in vivo in mouse models of tumor progression. In this manuscript, we investigate (I) the peptide binding to PP2A combining docking with molecular dynamics and (II) the secondary structure of the peptide using CD spectroscopy. Additionally, we compare the binding affinity, using biolayer interferometry, of the wild-type protein PP2A with Caspase 9 and vice versa to that observed between the PP2A protein and the interfering peptide C9h. This result strongly encourages the use of peptides as new therapeutics against cancer, as shown for the C9h peptide already in clinical trial.

Molecular Dynamics Simulation Studies on the Aggregation of Amyloid-β Peptides and Their Disaggregation by Ultrasonic Wave and Infrared Laser Irradiation

Alzheimer’s disease is understood to be caused by amyloid fibrils and oligomers formed by aggregated amyloid-β (Aβ) peptides. This review article presents molecular dynamics (MD) simulation studies of Aβ peptides and Aβ fragments on their aggregation, aggregation inhibition, amyloid fibril conformations in equilibrium, and disruption of the amyloid fibril by ultrasonic wave and infrared laser irradiation. In the aggregation of Aβ, a β-hairpin structure promotes the formation of intermolecular β-sheet structures. Aβ peptides tend to exist at hydrophilic/hydrophobic interfaces and form more β-hairpin structures than in bulk water. These facts are the reasons why the aggregation is accelerated at the interface. We also explain how polyphenols, which are attracting attention as aggregation inhibitors of Aβ peptides, interact with Aβ. An MD simulation study of the Aβ amyloid fibrils in equilibrium is also presented: the Aβ amyloid fibril has a different structure at one end from that at the other end. The amyloid fibrils can be destroyed by ultrasonic wave and infrared laser irradiation. The molecular mechanisms of these amyloid fibril disruptions are also explained, particularly focusing on the function of water molecules. Finally, we discuss the prospects for developing treatments for Alzheimer’s disease using MD simulations.

Enhanced sampling without borders: on global biasing functions and how to reweight them

Molecular dynamics (MD) simulations are a powerful tool to follow the time evolution of biomolecular motions in atomistic resolution. However, the high computational demand of these simulations limits the timescales of motions that can be observed. To resolve this issue, so called enhanced sampling techniques are developed, which extend conventional MD algorithms to speed up the simulation process. Here, we focus on techniques that apply global biasing functions. We provide a broad overview of established enhanced sampling methods and promising new advances. As the ultimate goal is to retrieve unbiased information from biased ensembles, we also discuss benefits and limitations of common reweighting schemes. In addition to concisely summarizing critical assumptions and implications, we highlight the general application opportunities as well as uncertainties of global enhanced sampling.

Simulated tempering with irreversible Gibbs sampling techniques

We present here two novel algorithms for simulated tempering simulations, which break the detailed balance condition (DBC) but satisfy the skewed detailed balance to ensure invariance of the target distribution. The irreversible methods we present here are based on Gibbs sampling and concern breaking DBC at the update scheme of the temperature swaps. We utilize three systems as a test bed for our methods: a Markov chain Monte Carlo simulation on a simple system described by a one-dimensional double well potential, the Ising model, and molecular dynamics simulations on alanine pentapeptide (ALA5). The relaxation times of inverse temperature, magnetic susceptibility, and energy density for the Ising model indicate clear gains in sampling efficiency over conventional Gibbs sampling techniques with DBC and also over the conventionally used simulated tempering with the Metropolis-Hastings (MH) scheme. Simulations on ALA5 with a large number of temperatures indicate distinct gains in mixing times for inverse temperature and consequently the energy of the system compared to conventional MH. With no additional computational overhead, our methods were found to be more efficient alternatives to the conventionally used simulated tempering methods with DBC. Our algorithms should be particularly advantageous in simulations of large systems with many temperature ladders, as our algorithms showed a more favorable constant scaling in Ising spin systems as compared with both reversible and irreversible MH algorithms. In future applications, our irreversible methods can also be easily tailored to utilize a given dynamical variable other than temperature to flatten rugged free energy landscapes.

Aggregation of disease-related peptides

Protein misfolding and aggregation of amyloid proteins is the fundamental cause of more than 20 diseases. Molecular mechanisms of the self-assembly and the formation of the toxic aggregates are still elusive. Computer simulations have been intensively used to study the aggregation of amyloid peptides of various amino acid lengths related to neurodegenerative diseases. We review atomistic and coarse-grained simulations of short amyloid peptides aimed at determining their transient oligomeric structures and the early and late aggregation steps.

Coarse-grained dynamic RNA titration simulations

Electrostatic interactions play a pivotal role in many biomolecular processes. The molecular organization and function in biological systems are largely determined by these interactions. Owing to the highly negative charge of RNA, the effect is expected to be more pronounced in this system. Moreover, RNA base pairing is dependent on the charge of the base, giving rise to alternative secondary and tertiary structures. The equilibrium between uncharged and charged bases is regulated by the solution pH, which is therefore a key environmental condition influencing the molecule's structure and behaviour. By means of constant-pH Monte Carlo simulations based on a fast proton titration scheme, coupled with the coarse-grained model HiRE-RNA, molecular dynamic simulations of RNA molecules at constant pH enable us to explore the RNA conformational plasticity at different pH values as well as to compute electrostatic properties as local pK _a values for each nucleotide.

Molecular simulations by generalized-ensemble algorithms in isothermal-isobaric ensemble

Generalized-ensemble algorithms are powerful techniques for investigating biomolecules such as protein, DNA, lipid membrane, and glycan. The generalized-ensemble algorithms were originally developed in the canonical ensemble. On the other hand, not only temperature but also pressure is controlled in experiments. Additionally, pressure is used as perturbation to study relationship between function and structure of biomolecules. For this reason, it is important to perform efficient conformation sampling based on the isothermal-isobaric ensemble. In this article, we review a series of the generalized-ensemble algorithms in the isothermal-isobaric ensemble: multibaric-multithermal, pressure- and temperature-simulated tempering, replica-exchange, and replica-permutation methods. These methods achieve more efficient simulation than the conventional isothermal-isobaric simulation. Furthermore, the isothermal-isobaric generalized-ensemble simulation samples conformations of biomolecules from wider range of temperature and pressure. Thus, we can estimate physical quantities more accurately at any temperature and pressure values. The applications to the biomolecular system are also presented.

Amyloid-β(29-42) Dimeric Conformations in Membranes Rich in Omega-3 and Omega-6 Polyunsaturated Fatty Acids

The omega-3 and omega-6 polyunsaturated fatty acids are two important components of cell membranes in human brains. When incorporated into phospholipids, omega-3 slows the progression of Alzheimer's disease (AD), whereas omega-6 is linked to increased risk of AD. Little is known on the amyloid-β (Aβ) conformations in membranes rich in omega-3 and omega-6 phospholipids. Herein, the structural properties of the Aβ_29-42 dimer embedded in both fatty acid membranes were comparatively studied to a 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphocholine (POPC) bilayer using all-atom molecular dynamics (MD) simulations. Starting from α-helix, both omega-6 and omega-3 membranes promote new orientations and conformations of the dimer, in agreement with the observed dependence of Aβ production upon addition of these two fatty acids. This conformational result is corroborated by atomistic MD simulations of the dimer of the 99 amino acid C-terminal fragment of amyloid precursor protein spanning the residues 15-55. Starting from β-sheet, omega-6 membrane promotes helical and disordered structures of Aβ_29-42 dimer, whereas omega-3 membrane preserves the β-sheet structures differing however from those observed in POPC. Remarkably, the mixture of the two fatty acids and POPC depicts another conformational ensemble of the Aβ_29-42 dimer. This finding demonstrates that variation in the abundance of the molecular phospholipids, which changes with age, modulates membrane-embedded Aβ oligomerization.

Optimal updating magnitude in adaptive flat-distribution sampling

We present a study on the optimization of the updating magnitude for a class of free energy methods based on flat-distribution sampling, including the Wang-Landau (WL) algorithm and metadynamics. These methods rely on adaptive construction of a bias potential that offsets the potential of mean force by histogram-based updates. The convergence of the bias potential can be improved by decreasing the updating magnitude with an optimal schedule. We show that while the asymptotically optimal schedule for the single-bin updating scheme (commonly used in the WL algorithm) is given by the known inverse-time formula, that for the Gaussian updating scheme (commonly used in metadynamics) is often more complex. We further show that the single-bin updating scheme is optimal for very long simulations, and it can be generalized to a class of bandpass updating schemes that are similarly optimal. These bandpass updating schemes target only a few long-range distribution modes and their optimal schedule is also given by the inverse-time formula. Constructed from orthogonal polynomials, the bandpass updating schemes generalize the WL and Langfeld-Lucini-Rago algorithms as an automatic parameter tuning scheme for umbrella sampling.

Multi-scale simulations of biological systems using the OPEP coarse-grained model

Biomolecules are complex machines that are optimized by evolution to properly fulfill or contribute to a variety of biochemical tasks in the cellular environment. Computer simulations based on quantum mechanics and atomistic force fields have been proven to be a powerful microscope for obtaining valuable insights into many biological, physical, and chemical processes. Many interesting phenomena involve, however, a time scale and a number of degrees of freedom, notably if crowding is considered, that cannot be explored at an atomistic resolution. To bridge the gap between reality and simulation, many different advanced computational techniques and coarse-grained (CG) models have been developed. Here, we report some applications of the CG OPEP protein model to amyloid fibril formation, the response of catch-bond proteins to two types of fluid flow, and interactive simulations to fold peptides with well-defined 3D structures or with intrinsic disorder.

What Can Human-Guided Simulations Bring to RNA Folding?

Inspired by the recent success of scientific-discovery games for predicting protein tertiary and RNA secondary structures, we have developed an open software for coarse-grained RNA folding simulations, guided by human intuition. To determine the extent to which interactive simulations can accurately predict 3D RNA structures of increasing complexity and lengths (four RNAs with 22-47 nucleotides), an interactive experiment was conducted with 141 participants who had very little knowledge of nucleic acids systems and computer simulations, and had received only a brief description of the important forces stabilizing RNA structures. Their structures and full trajectories have been analyzed statistically and compared to standard replica exchange molecular dynamics simulations. Our analyses show that participants gain easily chemical intelligence to fold simple and nontrivial topologies, with little computer time, and this result opens the door for the use of human-guided simulations to RNA folding. Our experiment shows that interactive simulations have better chances of success when the user widely explores the conformational space. Interestingly, providing on-the-fly feedback of the root mean square deviation with respect to the experimental structure did not improve the quality of the proposed models.

Locally weighted histogram analysis and stochastic solution for large-scale multi-state free energy estimation

The weighted histogram analysis method (WHAM) including its binless extension has been developed independently in several different contexts, and widely used in chemistry, physics, and statistics, for computing free energies and expectations from multiple ensembles. However, this method, while statistically efficient, is computationally costly or even infeasible when a large number, hundreds or more, of distributions are studied. We develop a locally WHAM (local WHAM) from the perspective of simulations of simulations (SOS), using generalized serial tempering (GST) to resample simulated data from multiple ensembles. The local WHAM equations based on one jump attempt per GST cycle can be solved by optimization algorithms orders of magnitude faster than standard implementations of global WHAM, but yield similarly accurate estimates of free energies to global WHAM estimates. Moreover, we propose an adaptive SOS procedure for solving local WHAM equations stochastically when multiple jump attempts are performed per GST cycle. Such a stochastic procedure can lead to more accurate estimates of equilibrium distributions than local WHAM with one jump attempt per cycle. The proposed methods are broadly applicable when the original data to be "WHAMMED" are obtained properly by any sampling algorithm including serial tempering and parallel tempering (replica exchange). To illustrate the methods, we estimated absolute binding free energies and binding energy distributions using the binding energy distribution analysis method from one and two dimensional replica exchange molecular dynamics simulations for the beta-cyclodextrin-heptanoate host-guest system. In addition to the computational advantage of handling large datasets, our two dimensional WHAM analysis also demonstrates that accurate results similar to those from well-converged data can be obtained from simulations for which sampling is limited and not fully equilibrated.

On the use of mass scaling for stable and efficient simulated tempering with molecular dynamics

Simulated tempering (ST) is a generalized-ensemble algorithm that employs trajectories exploring a range of temperatures to effectively sample rugged energy landscapes. When implemented using the molecular dynamics method, ST can require the use of short time steps for ensuring the stability of trajectories at high temperatures. To address this shortcoming, a mass-scaling ST (MSST) method is presented in which the particle mass is scaled in proportion to the temperature. Mass scaling in the MSST method leads to velocity distributions that are independent of temperature and eliminates the need for velocity scaling after the accepted temperature updates that are required in conventional ST simulations. The homogeneity in time scales with changing temperature improves the stability of simulations and allows for the use of longer time steps at high temperatures. As a result, the MSST is found to be more efficient than the standard ST method, particularly for cases in which a large temperature range is employed. © 2016 Wiley Periodicals, Inc.

Communication: Multiple atomistic force fields in a single enhanced sampling simulation

The main concerns of biomolecular dynamics simulations are the convergence of the conformational sampling and the dependence of the results on the force fields. While the first issue can be addressed by employing enhanced sampling techniques such as simulated tempering or replica exchange molecular dynamics, repeating these simulations with different force fields is very time consuming. Here, we propose an automatic method that includes different force fields into a single advanced sampling simulation. Conformational sampling using three all-atom force fields is enhanced by simulated tempering and by formulating the weight parameters of the simulated tempering method in terms of the energy fluctuations, the system is able to perform random walk in both temperature and force field spaces. The method is first demonstrated on a 1D system and then validated by the folding of the 10-residue chignolin peptide in explicit water.

Enhancing pairwise state-transition weights: A new weighting scheme in simulated tempering that can minimize transition time between a pair of conformational states

Simulated tempering (ST) is a widely used enhancing sampling method for Molecular Dynamics simulations. As one expanded ensemble method, ST is a combination of canonical ensembles at different temperatures and the acceptance probability of cross-temperature transitions is determined by both the temperature difference and the weights of each temperature. One popular way to obtain the weights is to adopt the free energy of each canonical ensemble, which achieves uniform sampling among temperature space. However, this uniform distribution in temperature space may not be optimal since high temperatures do not always speed up the conformational transitions of interest, as anti-Arrhenius kinetics are prevalent in protein and RNA folding. Here, we propose a new method: Enhancing Pairwise State-transition Weights (EPSW), to obtain the optimal weights by minimizing the round-trip time for transitions among different metastable states at the temperature of interest in ST. The novelty of the EPSW algorithm lies in explicitly considering the kinetics of conformation transitions when optimizing the weights of different temperatures. We further demonstrate the power of EPSW in three different systems: a simple two-temperature model, a two-dimensional model for protein folding with anti-Arrhenius kinetics, and the alanine dipeptide. The results from these three systems showed that the new algorithm can substantially accelerate the transitions between conformational states of interest in the ST expanded ensemble and further facilitate the convergence of thermodynamics compared to the widely used free energy weights. We anticipate that this algorithm is particularly useful for studying functional conformational changes of biological systems where the initial and final states are often known from structural biology experiments.

Simulated tempering based on global balance or detailed balance conditions: Suwa-Todo, heat bath, and Metropolis algorithms

Simulated tempering (ST) is a useful method to enhance sampling of molecular simulations. When ST is used, the Metropolis algorithm, which satisfies the detailed balance condition, is usually applied to calculate the transition probability. Recently, an alternative method that satisfies the global balance condition instead of the detailed balance condition has been proposed by Suwa and Todo. In this study, ST method with the Suwa-Todo algorithm is proposed. Molecular dynamics simulations with ST are performed with three algorithms (the Metropolis, heat bath, and Suwa-Todo algorithms) to calculate the transition probability. Among the three algorithms, the Suwa-Todo algorithm yields the highest acceptance ratio and the shortest autocorrelation time. These suggest that sampling by a ST simulation with the Suwa-Todo algorithm is most efficient. In addition, because the acceptance ratio of the Suwa-Todo algorithm is higher than that of the Metropolis algorithm, the number of temperature states can be reduced by 25% for the Suwa-Todo algorithm when compared with the Metropolis algorithm.

Exploring biomolecular dynamics and interactions using advanced sampling methods

Molecular dynamics (MD) and Monte Carlo (MC) simulations have emerged as a valuable tool to investigate statistical mechanics and kinetics of biomolecules and synthetic soft matter materials. However, major limitations for routine applications are due to the accuracy of the molecular mechanics force field and due to the maximum simulation time that can be achieved in current simulations studies. For improving the sampling a number of advanced sampling approaches have been designed in recent years. In particular, variants of the parallel tempering replica-exchange methodology are widely used in many simulation studies. Recent methodological advancements and a discussion of specific aims and advantages are given. This includes improved free energy simulation approaches and conformational search applications.

Ab initio RNA folding

RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, the experimental determination of RNA structures through x-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, the need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties, when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding.

Folding Atomistic Proteins in Explicit Solvent Using Simulated Tempering

Following a previous report on a coarse-grained protein model in implicit solvent, we applied simulated tempering (ST) with on-the-fly Helmholtz free energy (weight factors) determination to the folding or aggregation of seven proteins with the CHARMM, OPLS, and AMBER protein, and the SPC and TIP3P water force fields. For efficiency and reliability, we also performed replica exchange molecular dynamics (REMD) simulations on the alanine di- and deca-peptide, and the dimer of the Aβ16-22 Alzheimer's fragment, and used experimental data and previous simulation results on the chignolin, beta3s, Trp-cage, and WW domain peptides of 10-37 amino acids. The sampling with ST is found to be more efficient than with REMD for a much lower CPU cost. Starting from unfolded or extended conformations, the WW domain and the Trp-cage peptide fold to their NMR structures with a backbone RMSD of 2.0 and 1 Å. Remarkably, the ST simulation explores transient non-native topologies for Trp-cage that have been rarely discussed by other simulations. Our ST simulations also show that the CHARMM22* force field has limitations in describing accurately the beta3s peptide. Taken together, these results open the door to the study of the configurations of single proteins, protein aggregates, and any molecular systems at atomic details in explicit solvent using a single normal CPU. They also demonstrate that our ST scheme can be used with any force field ranging from quantum mechanics to coarse-grain and atomistic.

Protein Simulations in Fluids: Coupling the OPEP Coarse-Grained Force Field with Hydrodynamics

A novel simulation framework that integrates the OPEP coarse-grained (CG) model for proteins with the Lattice Boltzmann (LB) methodology to account for the fluid solvent at mesoscale level is presented. OPEP is a very efficient, water-free and electrostatic-free force field that reproduces at quasi-atomistic detail processes like peptide folding, structural rearrangements, and aggregation dynamics. The LB method is based on the kinetic description of the solvent in order to solve the fluid mechanics under a wide range of conditions, with the further advantage of being highly scalable on parallel architectures. The capabilities of the approach are presented, and it is shown that the strategy is effective in exploring the role of hydrodynamics on protein relaxation and peptide aggregation. The end result is a strategy for modeling systems of thousands of proteins, such as in the case of dense protein suspensions. The future perspectives of the multiscale approach are also discussed.

Fluctuation Flooding Method (FFM) for accelerating conformational transitions of proteins

A powerful conformational sampling method for accelerating structural transitions of proteins, "Fluctuation Flooding Method (FFM)," is proposed. In FFM, cycles of the following steps enhance the transitions: (i) extractions of largely fluctuating snapshots along anisotropic modes obtained from trajectories of multiple independent molecular dynamics (MD) simulations and (ii) conformational re-sampling of the snapshots via re-generations of initial velocities when re-starting MD simulations. In an application to bacteriophage T4 lysozyme, FFM successfully accelerated the open-closed transition with the 6 ns simulation starting solely from the open state, although the 1-μs canonical MD simulation failed to sample such a rare event.

The OPEP protein model: from single molecules, amyloid formation, crowding and hydrodynamics to DNA/RNA systems

The OPEP coarse-grained protein model has been applied to a wide range of applications since its first release 15 years ago. The model, which combines energetic and structural accuracy and chemical specificity, allows the study of single protein properties, DNA-RNA complexes, amyloid fibril formation and protein suspensions in a crowded environment. Here we first review the current state of the model and the most exciting applications using advanced conformational sampling methods. We then present the current limitations and a perspective on the ongoing developments.

Understanding amyloid fibril nucleation and aβ oligomer/drug interactions from computer simulations

Evolution has fine-tuned proteins to accomplish a variety of tasks. Yet, with aging, some proteins assemble into harmful amyloid aggregates associated with neurodegenerative diseases, such as Alzheimer's disease (AD), which presents a complex and costly challenge to our society. Thus, far, drug after drug has failed to slow the progression of AD, characterized by the self-assembly of the 39-43 amino acid β-amyloid (Aβ) protein into extracellular senile plaques that form a cross-β structure. While there is experimental evidence that the Aβ small oligomers are the primary toxic species, standard tools of biology have failed to provide structures of these transient, inhomogeneous assemblies. Despite extensive experimental studies, researchers have not successfully characterized the nucleus ensemble, the starting point for rapid fibril formation. Similarly scientists do not have atomic data to show how the compounds that reduce both fibril formation and toxicity in cells bind to Aβ42 oligomers. In this context, computer simulations are important tools for gaining insights into the self-assembly of amyloid peptides and the molecular mechanism of inhibitors. This Account reviews what analytical models and simulations at different time and length scales tell us about the dynamics, kinetics, and thermodynamics of amyloid fibril formation and, notably, the nucleation process. Though coarse-grained and mesoscopic protein models approximate atomistic details by averaging out unimportant degrees of freedom, they provide generic features of amyloid formation and insights into mechanistic details of the self-assembly process. The thermodynamics and kinetics vary from linear peptides adopting straight β-strands in fibrils to longer peptides adopting in parallel U shaped conformations in fibrils. In addition, these properties change with the balance between electrostatic and hydrophobic interactions and the intrinsic disorder of the system. However, simulations suggest that the critical nucleus size might be on the order of 20 chains under physiological conditions. The transition state might be characterized by a simultaneous change from mixed antiparallel/parallel β-strands with random side-chain packing to the final antiparallel or parallel states with the steric zipper packing of the side chains. Second, we review our current computer-based knowledge of the 3D structures of inhibitors with Aβ42 monomer and oligomers, a prerequisite for developing new drugs against AD. Recent extensive all-atom simulations of Aβ42 dimers with known inhibitors such as the green tea compound epigallocatechin-3-gallate and 1,4-naphthoquinon-2-yl-l-tryptophan provide a spectrum of initial Aβ42/inhibitor structures useful for screening and drug design. We conclude by discussing future directions that may offer opportunities to fully understand nucleation and further AD drug development.

A hybrid MD-kMC algorithm for folding proteins in explicit solvent

We present a novel hybrid MD-kMC algorithm that is capable of efficiently folding proteins in explicit solvent. We apply this algorithm to the folding of a small protein, Trp-Cage. Different kMC move sets that capture different possible rate limiting steps are implemented. The first uses secondary structure formation as a relevant rate event (a combination of dihedral rotations and hydrogen-bonding formation and breakage). The second uses tertiary structure formation events through formation of contacts via translational moves. Both methods fold the protein, but via different mechanisms and with different folding kinetics. The first method leads to folding via a structured helical state, with kinetics fit by a single exponential. The second method leads to folding via a collapsed loop, with kinetics poorly fit by single or double exponentials. In both cases, folding times are faster than experimentally reported values, The secondary and tertiary move sets are integrated in a third MD-kMC implementation, which now leads to folding of the protein via both pathways, with single and double-exponential fits to the rates, and to folding rates in good agreement with experimental values. The competition between secondary and tertiary structure leads to a longer search for the helix-rich intermediate in the case of the first pathway, and to the emergence of a kinetically trapped long-lived molten-globule collapsed state in the case of the second pathway. The algorithm presented not only captures experimentally observed folding intermediates and kinetics, but yields insights into the relative roles of local and global interactions in determining folding mechanisms and rates.

Effects of Zn2+ binding on the structural and dynamic properties of amyloid β peptide associated with Alzheimer's disease: Asp1 or Glu11?

Extensive experimental and computational studies have suggested that multiple Zn(2+) binding modes in amyloid β (Aβ) peptides could exist simultaneously. However, consistent results have not been obtained for the effects of Zn(2+) binding on Aβ structure, dynamics, and kinetics in particular. Some key questions such as why it is so difficult to distinguish the polymorphic states of metal ions binding to Aβ and what the underlying rationale is, necessitate elucidation. In this work, two 3N1O Zn(2+) binding modes were constructed with three histidines (His(6), His(13), and His(14)), and Asp(1)/Glu(11) of Aβ40 coordinated to Zn(2+). Results from molecular dynamics simulations reveal that the conformational ensembles of different Zn(2+)-Aβ40 complexes are nonoverlapping. The formation of turn structure and, especially, the salt bridge between Glu(22)/Asp(23) and Lys(28) is dependent on specific Zn(2+) binding mode. Agreement with available NMR observations of secondary and tertiary structures could be better achieved if the two simulation results are considered together. The free energy landscape constructed by combining both conformations of Aβ40 indicates that transitions between distinct Aβ40 conformations thar are ready for Zn(2+) binding could be possible in aqueous solution. Markov state model analyses reveal the complex network of conformational space of Aβ40 modeulated by Zn(2+) binding, suggesting various misfolding pathways. The binding free energies evaluated using a combination of quantum mechanics calculations and the MM/3D-RISM method suggest that Glu(11) is the preferred oxygen ligand of Zn(2+). However, such preference is dependent on the relative populations of different conformations with specific Zn(2+) binding modes, and therefore could be shifted when experimental or simulation conditions are altered.

Effect of the Tottori familial disease mutation (D7N) on the monomers and dimers of Aβ40 and Aβ42

Recent experiments have shown that the mutation Tottori (D7N) alters the toxicity, assembly and rate of fibril formation of the wild type (WT) amyloid beta (Aβ) Aβ40 and Aβ42 peptides. We used all-atom molecular dynamics simulations in explicit solvent of the monomer and dimer of both alloforms with their WT and D7N sequences. The monomer simulations starting from a random coil and totaling 3 μs show that the D7N mutation changes the fold and the network of salt bridges in both alloforms. The dimer simulations starting from the amyloid fibrillar states and totaling 4.4 μs also reveal noticeable changes in terms of secondary structure, salt bridge, and topology. Overall, this study provides physical insights into the enhanced rate of fibril formation upon D7N mutation and an atomic picture of the D7N-mediated conformational change on Aβ40 and Aβ42 peptides.

Importance of the ion-pair interactions in the OPEP coarse-grained force field: parametrization and validation

We have derived new effective interactions that improve the description of ion-pairs in the OPEP coarse-grained force field without introducing explicit electrostatic terms. The iterative Boltzmann inversion method was used to extract these potentials from all atom simulations by targeting the radial distribution function of the distance between the center of mass of the side-chains. The new potentials have been tested on several systems that differ in structural properties, thermodynamic stabilities and number of ion-pairs. Our modeling, by refining the packing of the charged amino-acids, impacts the stability of secondary structure motifs and the population of intermediate states during temperature folding/unfolding; it also improves the aggregation propensity of peptides. The new version of the OPEP force field has the potentiality to describe more realistically a large spectrum of situations where salt-bridges are key interactions.