Replica exchange molecular dynamics simulations of coarse-grained proteins in implicit solvent

CHARMM-GUI Implicit Solvent Modeler for Various Generalized Born Models in Different Simulation Programs

Implicit solvent models are widely used because they are advantageous to speed up simulations by drastically decreasing the number of solvent degrees of freedom, which allows one to achieve long simulation time scales for large system sizes. CHARMM-GUI, a web-based platform, has been developed to support the setup of complex multicomponent molecular systems and prepare input files. This study describes an Implicit Solvent Modeler (ISM) in CHARMM-GUI for various generalized Born (GB) implicit solvent simulations in different molecular dynamics programs such as AMBER, CHARMM, GENESIS, NAMD, OpenMM, and Tinker. The GB models available in ISM include GB-HCT, GB-OBC, GB-neck, GBMV, and GBSW with the CHARMM and Amber force fields for protein, DNA, RNA, glycan, and ligand systems. Using the system and input files generated by ISM, implicit solvent simulations of protein, DNA, and RNA systems produce similar results for different simulation packages with the same input information. Protein-ligand systems are also considered to further validate the systems and input files generated by ISM. Simple ligand root-mean-square deviation (RMSD) and molecular mechanics generalized Born surface area (MM/GBSA) calculations show that the performance of implicit simulations is better than docking and can be used for early stage ligand screening. These reasonable results indicate that ISM is a useful and reliable tool to provide various implicit solvent simulation applications.

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.

Structural and thermodynamical properties of early human amylin oligomers using replica exchange molecular dynamics: mutation effect of three key residues F15, H18 and F23

A schematic representation of a possible oligomerization mechanism of hIAPP. β-Hairpins are proposed to self-assemble into early ordered oligomers by side-to-side association.

PACE Force Field for Protein Simulations. 2. Folding Simulations of Peptides

We present the application of our recently developed PACE force field to the folding of peptides. These peptides include α-helical (AK17 and Fs), β-sheet (GB1m2 and Trpzip2), and mixed helical/coil (Trp-cage) peptides. With replica exchange molecular dynamics (REMD), our force field can fold the five peptides into their native structures while maintaining their stabilities reasonably well. Our force field is also able to capture important thermodynamic features of the five peptides that have been observed in previous experimental and computational studies, such as different preferences for a helix-turn-helix topology for AK17 and Fs, the relative contribution of four hydrophobic side chains of GB1p to the stability of β-hairpin, and the distinct role of a hydrogen bond involving Trp-Hε and a D9/R16 salt bridge in stabilizing the Trp-cage native structure. Furthermore, multiple folding and unfolding events are observed in our microsecond-long normal MD simulations of AK17, Trpzip2, and Trp-cage. These simulations provide mechanistic information such as a "zip-out" pathway of the folding mechanism of Trpzip2 and the folding times of AK17 and Trp-cage, which are estimated to be about 51 ± 43 ns and 270 ± 110 ns, respectively. A 600 ns simulation of the peptides can be completed within one day. These features of our force field are potentially applicable to the study of thermodynamics and kinetics of real protein systems.

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.

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.

The power of coarse graining in biomolecular simulations

Computational modeling of biological systems is challenging because of the multitude of spatial and temporal scales involved. Replacing atomistic detail with lower resolution, coarse grained (CG), beads has opened the way to simulate large-scale biomolecular processes on time scales inaccessible to all-atom models. We provide an overview of some of the more popular CG models used in biomolecular applications to date, focusing on models that retain chemical specificity. A few state-of-the-art examples of protein folding, membrane protein gating and self-assembly, DNA hybridization, and modeling of carbohydrate fibers are used to illustrate the power and diversity of current CG modeling.

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.

Folding and unfolding thermodynamics of the TC10b Trp-cage miniprotein

We examine the folding-unfolding of a variant of the Trp-cage, known as TC10b, and compare structural stability, dynamics, and thermodynamics with that of the TC5b variant, using replica exchange molecular dynamics (REMD). The TC10b variant was designed to have larger helical stability by the substitution of amino acids with greater alpha helical propensities in the N-terminal region. Experiments have shown TC10b to possess larger overall stability than TC5b. Simulations starting from unbiased, unfolded initial conditions are run for 1 μs per replica. The calculations show a higher melting temperature for TC10b than TC5b, and suggest a more ordered folded structure through the elimination of a substate found in the folded ensemble of TC5b. We model the difference in Gibbs free energy, ΔG(P,T), of folding using the bootstrap statistical method, which is used to calculate uncertainties associated with the thermodynamic parameters for both variants of the Trp-cage. We find that while the shape of the area for which the protein is stability folded is elliptical for TC5b, there is a degree of uncertainty associated with that of TC10b, with one model suggesting elliptical and another suggesting hyperbolic. This model suggests that at high pressures, TC5b can experience pressure denaturation, but TC10b may not.

Efficient Parameter Estimation of Generalizable Coarse-Grained Protein Force Fields Using Contrastive Divergence: A Maximum Likelihood Approach

Maximum Likelihood (ML) optimization schemes are widely used for parameter inference. They maximize the likelihood of some experimentally observed data, with respect to the model parameters iteratively, following the gradient of the logarithm of the likelihood. Here, we employ a ML inference scheme to infer a generalizable, physics-based coarse-grained protein model (which includes Go̅-like biasing terms to stabilize secondary structure elements in room-temperature simulations), using native conformations of a training set of proteins as the observed data. Contrastive divergence, a novel statistical machine learning technique, is used to efficiently approximate the direction of the gradient ascent, which enables the use of a large training set of proteins. Unlike previous work, the generalizability of the protein model allows the folding of peptides and a protein (protein G) which are not part of the training set. We compare the same force field with different van der Waals (vdW) potential forms: a hard cutoff model, and a Lennard-Jones (LJ) potential with vdW parameters inferred or adopted from the CHARMM or AMBER force fields. Simulations of peptides and protein G show that the LJ model with inferred parameters outperforms the hard cutoff potential, which is consistent with previous observations. Simulations using the LJ potential with inferred vdW parameters also outperforms the protein models with adopted vdW parameter values, demonstrating that model parameters generally cannot be used with force fields with different energy functions. The software is available at https://sites.google.com/site/crankite/.

Using D-Amino Acids to Delineate the Mechanism of Protein Folding: Application to Trp-cage

Using the miniprotein Trp-cage as a model, we show that D-amino acids can be used to facilitate the delineation of protein folding mechanism. Specifically, we study the folding-unfolding kinetics of three Trp-cage mutants where the native glycine residue near the C-terminus of the α-helix is replaced by a D-amino acid. A previous study showed that these mutations increase the Trp-cage stability, due to a terminal capping effect. Our results show that the stabilizing effect of D-asparagine and D-glutamine originates almost exclusively from a decrease in the unfolding rate, while the D-alanine mutation results in a similar decrease in the unfolding rate, but it also increases the folding rate. Together, these results support a folding mechanism wherein the α-helix formation in the transition state is nucleated at the N-terminus, whereas those long-range native interactions stabilizing this helix are developed at the downhill side of the folding free energy barrier.

Characterization of folding mechanisms of Trp-cage and WW-domain by network analysis of simulations with a hybrid-resolution model

In this study, we apply a hybrid-resolution model, namely, PACE, to characterize the free energy surfaces (FESs) of Trp-cage and a WW-domain variant along with the respective folding mechanisms. Unbiased, independent simulations with PACE are found to achieve together multiple folding and unfolding events for both proteins, allowing us to perform network analysis of the FESs to identify folding pathways. PACE reproduces for both proteins expected complexity hidden in the folding FESs, in particular metastable non-native intermediates. Pathway analysis shows that some of these intermediates are, actually, on-pathway folding intermediates and that intermediates kinetically closest to the native states can be either critical on-pathway or off-pathway intermediates, depending on the protein. Apart from general insights into folding, specific folding mechanisms of the proteins are resolved. We find that Trp-cage folds via a dominant pathway in which hydrophobic collapse occurs before the N-terminal helix forms; full incorporation of Trp6 into the hydrophobic core takes place as the last step of folding, which, however, may not be the rate-limiting step. For the WW-domain variant studied, we observe two main folding pathways with opposite orders of formation of the two hairpins involved in the structure; for either pathway, formation of hairpin 1 is more likely to be the rate-limiting step. Altogether, our results suggest that PACE combined with network analysis is a computationally efficient and valuable tool for the study of protein folding.

PRIMO: A Transferable Coarse-grained Force Field for Proteins

We describe here the PRIMO (PRotein Intermediate Model) force field, a physics-based fully transferable additive coarse-grained potential energy function that is compatible with an all-atom force field for multi-scale simulations. The energy function consists of standard molecular dynamics energy terms plus a hydrogen-bonding potential term and is mainly parameterized based on the CHARMM22/CMAP force field in a bottom-up fashion. The solvent is treated implicitly via the generalized Born model. The bonded interactions are either harmonic or distance-based spline interpolated potentials. These potentials are defined on the basis of all-atom molecular dynamics (MD) simulations of dipeptides with the CHARMM22/CMAP force field. The non-bonded parameters are tuned by matching conformational free energies of diverse set of conformations with that of CHARMM all-atom results. PRIMO is designed to provide a correct description of conformational distribution of the backbone (ϕ/ψ) and side chains (χ1) for all amino acids with a CMAP correction term. The CMAP potential in PRIMO is optimized based on the new CHARMM C36 CMAP. The resulting optimized force field has been applied in MD simulations of several proteins of 36-155 amino acids and shown that the root-mean-squared-deviation of the average structure from the corresponding crystallographic structure varies between 1.80 and 4.03 Å. PRIMO is shown to fold several small peptides to their native-like structures from extended conformations. These results suggest the applicability of the PRIMO force field in the study of protein structures in aqueous solution, structure predictions as well as ab initio folding of small peptides.

Advanced replica-exchange sampling to study the flexibility and plasticity of peptides and proteins

Molecular dynamics (MD) simulations are ideally suited to investigate protein and peptide plasticity and flexibility simultaneously at high spatial (atomic) and high time resolution. However, the applicability is still limited by the force field accuracy and by the maximum simulation time that can be routinely achieved in current MD simulations. In order to improve the sampling the replica-exchange (REMD) methodology has become popular and is now the most widely applied advanced sampling approach. Many variants of the REMD method have been designed to reduce the computational demand or to enhance sampling along specific sets of conformational variables. An overview on recent methodological advances and discussion of specific aims and advantages of the approaches will be given. Applications in the area of free energy simulations and advanced sampling of intrinsically disordered peptides and proteins will also be discussed. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.

Coarse-grained models for protein folding and aggregation

Coarse-grained models for protein folding and aggregation are used to explore large dimension scales and timescales that are inaccessible to all-atom models in explicit aqueous solution. Combined with enhanced configuration search methods, these simplified models with various levels of granularity offer the possibility to determine equilibrium structures, compare folding kinetics and thermodynamics with experiments for single proteins and understand the dynamic assembly of amyloid proteins leading to neurodegenerative diseases. I shall describe recent progress in developing such models, and discuss their potentials and limitations in probing the folding and misfolding of proteins with computer simulations.

Replica exchanging self-guided Langevin dynamics for efficient and accurate conformational sampling

This work presents a replica exchanging self-guided Langevin dynamics (RXSGLD) simulation method for efficient conformational searching and sampling. Unlike temperature-based replica exchanging simulations, which use high temperatures to accelerate conformational motion, this method uses self-guided Langevin dynamics (SGLD) to enhance conformational searching without the need to elevate temperatures. A RXSGLD simulation includes a series of SGLD simulations, with simulation conditions differing in the guiding effect and/or temperature. These simulation conditions are called stages and the base stage is one with no guiding effect. Replicas of a simulation system are simulated at the stages and are exchanged according to the replica exchanging probability derived from the SGLD partition function. Because SGLD causes less perturbation on conformational distribution than high temperatures, exchanges between SGLD stages have much higher probabilities than those between different temperatures. Therefore, RXSGLD simulations have higher conformational searching ability than temperature based replica exchange simulations. Through three example systems, we demonstrate that RXSGLD can generate target canonical ensemble distribution at the base stage and achieve accelerated conformational searching. Especially for large systems, RXSGLD has remarkable advantages in terms of replica exchange efficiency, conformational searching ability, and system size extensiveness.

Kinetics of amyloid aggregation: a study of the GNNQQNY prion sequence

The small amyloid-forming GNNQQNY fragment of the prion sequence has been the subject of extensive experimental and numerical studies over the last few years. Using unbiased molecular dynamics with the OPEP coarse-grained potential, we focus here on the onset of aggregation in a 20-mer system. With a total of 16.9 of simulations at 280 K and 300 K, we show that the GNNQQNY aggregation follows the classical nucleation theory (CNT) in that the number of monomers in the aggregate is a very reliable descriptor of aggregation. We find that the critical nucleus size in this finite-size system is between 4 and 5 monomers at 280 K and 5 and 6 at 300 K, in overall agreement with experiment. The kinetics of growth cannot be fully accounted for by the CNT, however. For example, we observe considerable rearrangements after the nucleus is formed, as the system attempts to optimize its organization. We also clearly identify two large families of structures that are selected at the onset of aggregation demonstrating the presence of well-defined polymorphism, a signature of amyloid growth, already in the 20-mer aggregate.

Protein aggregation plays an important pathological role in numerous neurodegenerative diseases such as Alzheimer's, Parkinson's, Creutzfeldt-Jakob, the Prion disease and diabetes mellitus. In most cases, misfolded proteins are involved and aggregate irreversibly to form highly ordered insoluble macrostructures, called amyloid fibrils, which deposit in the brain. Studies have revealed that all proteins are capable of forming amyloid fibrils that all share common structural features and therefore aggregation mechanisms. The toxicity of amyloid aggregates is however not attributed to the fibrils themselves but rather to smaller more disordered aggregates, oligomers, forming parallel to or prior to fibrils. Understanding the assembly process of these amyloid oligomers is key to understanding their toxicity mechanism in order to devise a possible treatment strategy targeting these toxic aggregates. Our approach here is to computationally study the aggregation dynamics of a 20-mer of an amyloid peptide GNNQQNY from a prion protein. Our findings suggest that the assembly is a spontaneous process that can be described as a complex nucleation and growth mechanism and which can lead to two classes of morphologies for the aggregates, one of which resembles a protofibril-like structure. Such numerical studies are crucial to understanding the details of fast biological processes and complement well experimental studies.

Further optimization of a hybrid united-atom and coarse-grained force field for folding simulations: Improved backbone hydration and interactions between charged side chains

PACE, a hybrid force field which couples united-atom protein models with coarse-grained (CG) solvent, has been further optimized, aiming to improve itse ciency for folding simulations. Backbone hydration parameters have been re-optimized based on hydration free energies of polyalanyl peptides through atomistic simulations. Also, atomistic partial charges from all-atom force fields were combined with PACE in order to provide a more realistic description of interactions between charged groups. Using replica exchange molecular dynamics (REMD), ab initio folding using the new PACE has been achieved for seven small proteins (16 - 23 residues) with different structural motifs. Experimental data about folded states, such as their stability at room temperature, melting point and NMR NOE constraints, were also well reproduced. Moreover, a systematic comparison of folding kinetics at room temperature has been made with experiments, through standard MD simulations, showing that the new PACE may speed up the actual folding kinetics 5-10 times. Together with the computational speedup benefited from coarse-graining, the force field provides opportunities to study folding mechanisms. In particular, we used the new PACE to fold a 73-residue protein, 3D, in multiple 10 - 30 μs simulations, to its native states (C(α) RMSD ~ 0.34 nm). Our results suggest the potential applicability of the new PACE for the study of folding and dynamics of proteins.

Structural, thermodynamical, and dynamical properties of oligomers formed by the amyloid NNQQ peptide: insights from coarse-grained simulations

Characterizing the early formed oligomeric intermediates of amyloid peptides is of particular interest due to their links with neurodegenerative diseases. Here we study the NNQQ peptide, known to display parallel β-strands in amyloid fibrils by x-ray microcrystallography, and investigate the structural, thermodynamical, and dynamical properties of 20 NNQQ peptides using molecular dynamics and replica exchange molecular dynamics simulations coupled to a coarse-grained force field. All simulations are initiated from randomized and fully dispersed monomeric conformations. Our simulations reveal that the phase transition is characterized by a change in the oligomer and β-sheet size distributions and the percentage of mixed parallel/antiparallel β-strands when the sheets are formed. At all temperatures, however, the fraction of parallel β-strands remains low, though there are many association/fragmentation events. This work and a growing body of computational studies provide strong evidence that the critical nucleus goes beyond 20 chains and reordering of the β-strands occurs in larger oligomers.

A convective replica-exchange method for sampling new energy basins

Replica-exchange is a powerful simulation method for sampling the basins of a rugged energy landscape. The replica-exchange method's sampling is efficient because it allows replicas to perform round trips in temperature space, thereby visiting both low and high temperatures in the same simulation. However, replicas have a diffusive walk in temperature space, and the round trip rate decreases significantly with the system size. These drawbacks make convergence of the simulation even more difficult than it already is when bigger systems are tackled. Here, we present a simple modification of the exchange method. In this method, one of the replicas steadily raises or lowers its temperature. We tested the convective replica-exchange method on three systems of varying complexity: the alanine dipeptide in implicit solvent, the GB1 β-hairpin in explicit solvent and the Aβ(25-35) homotrimer in a coarse grained representation. For the highly frustrated Aβ(25-35) homotrimer, the proposed "convective" replica-exchange method is twice as fast as the standard method. It discovered 24 out of 27 free-energy basins in less than 500 ns. It also prevented the formation of groups of replicas that usually form on either side of an exchange bottleneck, leading to a more efficient sampling of new energy basins than in the standard method.

A review of combined experimental and computational procedures for assessing biopolymer structure-process-property relationships

Tailored biomaterials with tunable functional properties are desirable for many applications ranging from drug delivery to regenerative medicine. To improve the predictability of biopolymer materials functionality, multiple design parameters need to be considered, along with appropriate models. In this article we review the state of the art of synthesis and processing related to the design of biopolymers, with an emphasis on the integration of bottom-up computational modeling in the design process. We consider three prominent examples of well-studied biopolymer materials - elastin, silk, and collagen - and assess their hierarchical structure, intriguing functional properties and categorize existing approaches to study these materials. We find that an integrated design approach in which both experiments and computational modeling are used has rarely been applied for these materials due to difficulties in relating insights gained on different length- and time-scales. In this context, multiscale engineering offers a powerful means to accelerate the biomaterials design process for the development of tailored materials that suit the needs posed by the various applications. The combined use of experimental and computational tools has a very broad applicability not only in the field of biopolymers, but can be exploited to tailor the properties of other polymers and composite materials in general.

Thermally induced protein unfolding probed by isotope-edited IR spectroscopy

Infrared (IR) spectroscopy has been widely utilized for the study of protein folding, unfolding, and misfolding processes. We have previously developed a theoretical method for calculating IR spectra of proteins in the amide I region. In this work, we apply this method, in combination with replica-exchange molecular dynamics simulations, to study the equilibrium thermal unfolding transition of the villin headpiece subdomain (HP36). Temperature-dependent IR spectra and spectral densities are calculated. The spectral densities correctly reflect the unfolding conformational changes in the simulation. With the help of isotope labeling, we are able to capture the feature that helix 2 of HP36 loses its secondary structure before global unfolding occurs, in agreement with experiment.

Structural transitions and oligomerization along polyalanine fibril formation pathways from computer simulations

The results of a computer simulation study of the aggregation kinetics of a large system of model peptides with particular focus on the formation of intermediates are presented. Discontinuous molecular dynamic simulations were used in combination with our intermediate-resolution protein model, PRIME, to simulate the aggregation of a system of 192 polyalanine (KA(14) K) peptides at a concentration of 5 mM and a reduced temperature of T* = 0.13 starting from a random configuration and ending in the assembly of a fibrillar structure. The population of various structures, including free monomers, beta sheets, amorphous aggregates, hybrid aggregates, and fibrils, and the transitions between the structures were tracked over the course of 30 independent simulations and averaged together. The aggregation pathway for this system starts with the association of free monomers into small amorphous aggregates that then grow to moderate size by incorporating other free monomers or merging with other small amorphous aggregates. These then rearrange into either small beta sheets or hybrid aggregates formed by association between unstructured chains and beta sheets, both of which grow in size by adding free monomer chains or other small aggregates, one at a time. Fibrillar structures are formed initially either by the stacking of beta sheets, rearrangement of hybrid aggregates or association between beta sheets and hybrid aggregates. They grow by the addition of beta sheets, hybrid aggregates, and other small fibrillar structures. The rearrangement of amorphous aggregates into beta sheets is a critical and necessary step in the fibril formation pathway.

PEP-FOLD: an updated de novo structure prediction server for both linear and disulfide bonded cyclic peptides

In the context of the renewed interest of peptides as therapeutics, it is important to have an on-line resource for 3D structure prediction of peptides with well-defined structures in aqueous solution. We present an updated version of PEP-FOLD allowing the treatment of both linear and disulphide bonded cyclic peptides with 9-36 amino acids. The server makes possible to define disulphide bonds and any residue-residue proximity under the guidance of the biologists. Using a benchmark of 34 cyclic peptides with one, two and three disulphide bonds, the best PEP-FOLD models deviate by an average RMS of 2.75 Å from the full NMR structures. Using a benchmark of 37 linear peptides, PEP-FOLD locates lowest-energy conformations deviating by 3 Å RMS from the NMR rigid cores. The evolution of PEP-FOLD comes as a new on-line service to supersede the previous server. The server is available at: http://bioserv.rpbs.univ-paris-diderot.fr/PEP-FOLD.

Coarse-grain Protein Models

Coarse-graining is a powerful approach for modeling biomolecules that, over the last few decades, has been extensively applied to proteins. Coarse-grain models offer access to large systems and to slow processes without becoming computationally unmanageable. In addition, they are very versatile, enabling both the protein representation and the energy function to be adapted to the biological problem in hand. This review concentrates on modeling soluble proteins and their assemblies. It presents an overview of the coarse-grain representations, of the associated interaction potentials, and of the optimization procedures used to define them. It then shows how coarse-grain models have been used to understand processes involving proteins, from their initial folding to their functional properties, their binary interactions, and the assembly of large complexes.

Distinct dimerization for various alloforms of the amyloid-beta protein: Aβ(1-40), Aβ(1-42), and Aβ(1-40)(D23N)

The Amyloid-beta protein is related to Alzheimer's disease, and various experiments have shown that oligomers as small as the dimer are cytotoxic. Two alloforms are mainly produced: Aβ(1-40) and Aβ(1-42). They have very different oligomer distributions, and it was recently suggested, from experimental studies, that this variation may originate from structural differences in their dimer structures. Little structural information is available on the Aβ dimer, however, and to complement experimental observations, we simulated the folding of the wild-type Aβ(1-40) and Aβ(1-42) dimers as well as the mutated Aβ(1-40)(D23N) dimer using an accurate coarse-grained force field coupled to Hamiltonian-temperature replica exchange molecular dynamics. The D23N variant impedes the salt-bridge formation between D23 and K28 seen in the wild-type Aβ, leading to very different fibrillation properties and final amyloid fibrils. Our results show that the Aβ(1-42) dimer has a higher propensity than the Aβ(1-40) dimer to form β-strands at the central hydrophobic core (residues 17-21) and at the C-terminal (residues 30-42), which are two segments crucial to the oligomerization of Aβ. The free energy landscape of the Aβ(1-42) dimer is also broader and more complex than that of the Aβ(1-40) dimer. Interestingly, D23N also impacts the free energy landscape by increasing the population of configurations with higher β-strand propensities when compared against Aβ(40). In addition, while Aβ(1-40)(D23N) displays a higher β-strand propensity at the C-terminal, its solvent accessibility does not change with respect to the wild-type sequence. Overall, our results show the strong impact of the two amino acids Ile41-Ala42 and the salt-bridge D23-K28 on the folding of the Aβ dimer.

Structures of Aβ17-42 trimers in isolation and with five small-molecule drugs using a hierarchical computational procedure

The amyloid-β protein (Aβ) oligomers are believed to be the main culprits in the cytoxicity of Alzheimer's disease (AD) and p3 peptides (Aβ17-42 fragments) are present in AD amyloid plaques. Many small-molecule or peptide-based inhibitors are known to slow down Aβ aggregation and reduce the toxicity in vitro, but their exact modes of action remain to be determined since there has been no atomic level of Aβ(p3)-drug oligomers. In this study, we have determined the structure of Aβ17-42 trimers both in aqueous solution and in the presence of five small-molecule inhibitors using a multiscale computational study. These inhibitors include 2002-H20, curcumin, EGCG, Nqtrp, and resveratrol. First, we used replica exchange molecular dynamics simulations coupled to the coarse-grained (CG) OPEP force field. These CG simulations reveal that the conformational ensemble of Aβ17-42 trimer can be described by 14 clusters with each peptide essentially adopting turn/random coil configurations, although the most populated cluster is characterized by one peptide with a β-hairpin at Phe19-Leu31. Second, these 14 dominant clusters and the less-frequent fibril-like state with parallel register of the peptides were subjected to atomistic Autodock simulations. Our analysis reveals that the drugs have multiple binding modes with different binding affinities for trimeric Aβ17-42 although they interact preferentially with the CHC region (residues 17-21). The compounds 2002-H20 and Nqtrp are found to be the worst and best binders, respectively, suggesting that the drugs may interfere at different stages of Aβ oligomerization. Finally, explicit solvent molecular dynamics of two predicted Nqtrp-Aβ17-42 conformations describe at atomic level some possible modes of action for Nqtrp.

Flexibility and binding affinity in protein-ligand, protein-protein and multi-component protein interactions: limitations of current computational approaches

The recognition process between a protein and a partner represents a significant theoretical challenge. In silico structure-based drug design carried out with nothing more than the three-dimensional structure of the protein has led to the introduction of many compounds into clinical trials and numerous drug approvals. Central to guiding the discovery process is to recognize active among non-active compounds. While large-scale computer simulations of compounds taken from a library (virtual screening) or designed de novo are highly desirable in the post-genomic area, many technical problems remain to be adequately addressed. This article presents an overview and discusses the limits of current computational methods for predicting the correct binding pose and accurate binding affinity. It also presents the performances of the most popular algorithms for exploring binary and multi-body protein interactions.

Structural basis of folding cooperativity in model proteins: insights from a microcanonical perspective

Two-state cooperativity is an important characteristic in protein folding. It is defined by a depletion of states that lie energetically between folded and unfolded conformations. There are different ways to test for two-state cooperativity; however, most of these approaches probe indirect proxies of this depletion. Generalized-ensemble computer simulations allow us to unambiguously identify this transition by a microcanonical analysis on the basis of the density of states. Here, we present a detailed characterization of several helical peptides obtained by coarse-grained simulations. The level of resolution of the coarse-grained model allowed to study realistic structures ranging from small α-helices to a de novo three-helix bundle without biasing the force field toward the native state of the protein. By linking thermodynamic and structural features, we are able to show that whereas short α-helices exhibit two-state cooperativity, the type of transition changes for longer chain lengths because the chain forms multiple helix nucleation sites, stabilizing a significant population of intermediate states. The helix bundle exhibits signs of two-state cooperativity owing to favorable helix-helix interactions, as predicted from theoretical models. A detailed analysis of secondary and tertiary structure formation fits well into the framework of several folding mechanisms and confirms features that up to now have been observed only in lattice models.

A multiscale approach to characterize the early aggregation steps of the amyloid-forming peptide GNNQQNY from the yeast prion sup-35

The self-organization of peptides into amyloidogenic oligomers is one of the key events for a wide range of molecular and degenerative diseases. Atomic-resolution characterization of the mechanisms responsible for the aggregation process and the resulting structures is thus a necessary step to improve our understanding of the determinants of these pathologies. To address this issue, we combine the accelerated sampling properties of replica exchange molecular dynamics simulations based on the OPEP coarse-grained potential with the atomic resolution description of interactions provided by all-atom MD simulations, and investigate the oligomerization process of the GNNQQNY for three system sizes: 3-mers, 12-mers and 20-mers. Results for our integrated simulations show a rich variety of structural arrangements for aggregates of all sizes. Elongated fibril-like structures can form transiently in the 20-mer case, but they are not stable and easily interconvert in more globular and disordered forms. Our extensive characterization of the intermediate structures and their physico-chemical determinants points to a high degree of polymorphism for the GNNQQNY sequence that can be reflected at the macroscopic scale. Detailed mechanisms and structures that underlie amyloid aggregation are also provided.

The formation of amyloid fibrils is associated with many neurodegenerative diseases such as Alzheimer's, Creutzfeld-Jakob, Parkinson's, the Prion disease and diabetes mellitus. In all cases, proteins misfold to form highly ordered insoluble aggregates called amyloid fibrils that deposit intra- and extracellularly and are resistant to proteases. All proteins are believed to have the instrinsic capability of forming amyloid fibrils that share common specific structural properties that have been observed by X-ray crystallography and by NMR. However, little is known about the aggregation dynamics of amyloid assemblies, and their toxicity mechanism is therefore poorly understood. It is believed that small amyloid oligomers, formed on the aggregation pathway of full amyloid fibrils, are the toxic species. A detailed atomic characterization of the oligomerization process is thus necessary to further our understanding of the amyloid oligomer's toxicity. Our approach here is to study the aggregation dynamics of a 7-residue amyloid peptide GNNQQNY through a combination of numerical techniques. Our results suggest that this amyloid sequence can form fibril-like structures and is polymorphic, which agrees with recent experimental observations. The ability to fully characterize and describe the aggregation pathway of amyloid sequences numerically is key to the development of future drugs to target amyloid oligomers.

HiRE-RNA: a high resolution coarse-grained energy model for RNA

Although RNAs play many cellular functions, the gap between their sequences and 3D structures is increasing and our knowledge of RNA thermodynamics and long time scale dynamics is still limited at an atomic level of detail. In principle, all-atom molecular dynamics (MD) and replica exchange molecular dynamics (REMD) simulations can investigate these issues, but with current computer facilities, these simulations in explicit solvent have been limited to small RNAs and to short times. To move to larger systems, we can resort to coarse-graining. In this study, we present HiRE-RNA, a generic high resolution coarse-grained model for RNA, and report MD and REMD simulations on two RNAs of 22 and 36 nucleotides. Starting from unfolded structures, the 22-mer folds within 1.8 A rmsd from the NMR structure, while the 36-mer folds within 4.6 A rmsd. Current results suggest that further optimization of the HiRE-RNA force field should open the door to a relevant model for studying large RNAs, such as riboswitches, and for predicting 3D structures from secondary structure information.

Effects of G33A and G33I mutations on the structures of monomer and dimer of the amyloid-β fragment 29-42 by replica exchange molecular dynamics simulations

The early formed oligomers of amyloid-β proteins with 40 and 42 amino acids are believed to be the culprits of Alzheimer's disease. Aβ1-42 peptides with alanine and isoleucine mutations of glycine 33 are known to be much less toxic than the wild-type Aβ1-42 and promote the aggregation process in vitro. The fragment Aβ29-42 has also been shown to form fibrils, disrupt Aβ1-42 oligomerization, and inhibit Aβ1-42-induced neurotoxicity. As a first step toward understanding the impact of G33A and G33I mutations on the earliest steps along the Aβ1-42 aggregation pathway, we have studied the structures of the monomer and dimer of Aβ29-42 and its two G33 variants using coarse-grained replica exchange molecular dynamics simulations. These simulations, totaling 15 μs, indicate that both substitutions impact the conformational ensemble of Aβ29-42. For the monomer, the population of the β-hairpin is high for wild-type Aβ29-42, but marginal for Aβ29-42 G33I mutant. The three dimers are also stabilized by different patterns of interaction. The data are discussed in terms of the differences in the aggregation characteristics between wild-type Aβ1-42 and its two G33A and G33I variants.