Thermodynamics and stability of a beta-sheet complex: molecular dynamics simulations on simplified off-lattice protein models

Investigating the folding mechanism of the N-terminal domain of ribosomal protein L9

Protein folding is a popular topic in the life science. However, due to the limited sampling ability of experiments and simulations, the general folding mechanism is not yet clear to us. In this work, we study the folding of the N-terminal domain of ribosomal protein L9 (NTL9) in detail by a mixing replica exchange molecular dynamics method. The simulation results are close to previous experimental observations. According to the Markov state model, the folding of the protein follows a nucleation-condensation path. Moreover, after the comparison to its 39-residue β-α-β motif, we find that the helix at the C-terminal has a great influence on the folding process of the intact protein, including the nucleation of the key residues in the transition state ensemble and the packing of the hydrophobic residues in the native state.

Energetics of oligomeric protein folding and association

In nature, proteins most often exist as complexes, with many of these consisting of identical subunits. Understanding of the energetics governing the folding and misfolding of such homooligomeric proteins is central to understanding their function and misfunction, in disease or biotechnology. Much progress has been made in defining the mechanisms and thermodynamics of homooligomeric protein folding. In this review, we outline models as well as calorimetric and spectroscopic methods for characterizing oligomer folding, and describe extensive results obtained for diverse proteins, ranging from dimers to octamers and higher order aggregates. To our knowledge, this area has not been reviewed comprehensively in years, and the collective progress is impressive. The results provide evolutionary insights into the development of subunit interfaces, mechanisms of oligomer folding, and contributions of oligomerization to protein stability, function and regulation. Thermodynamic analyses have also proven valuable for understanding protein misfolding and aggregation mechanisms, suggesting new therapeutic avenues. Successful recent designs of novel, functional proteins demonstrate increased understanding of oligomer folding. Further rigorous analyses using multiple experimental and computational approaches are still required, however, to achieve consistent and accurate prediction of oligomer folding energetics. Modeling the energetics remains challenging but is a promising avenue for future advances.

Toward a molecular theory of early and late events in monomer to amyloid fibril formation

Quantitative understanding of the kinetics of fibril formation and the molecular mechanism of transition from monomers to fibrils is needed to obtain insights into the growth of amyloid fibrils and more generally self-assembly multisubunit protein complexes. Significant advances using computations of protein aggregation in a number of systems have established generic and sequence-specific aspects of the early steps in oligomer formation. Theoretical considerations, which view oligomer and fibril growth as diffusion in a complex energy landscape, and computational studies, involving minimal lattice and coarse-grained models, have revealed general principles governing the transition from monomeric protein to ordered fibrillar aggregates. Detailed atomistic calculations have explored the early stages of the protein aggregation pathway for a number of amyloidogenic proteins, most notably amyloid β- (Aβ-) protein and fragments from proteins linked to various diseases. These computational studies have provided insights into the role of sequence, role of water, and specific interatomic interactions underlying the thermodynamics and dynamics of elementary kinetic steps in the aggregation pathway. Novel methods are beginning to illustrate the structural basis for the production of Aβ-peptides through interactions with secretases in the presence of membranes. We show that a variety of theoretical approaches, ranging from scaling arguments to minimal models to atomistic simulations, are needed as a complement to experimental studies probing the principles governing protein aggregation.

Insights Into Crowding Effects on Protein Stability From a Coarse-Grained Model

Proteins aggregate and precipitate from high concentration solutions in a wide variety of problems of natural and technological interest. Consequently, there is a broad interest in developing new ways to model the thermodynamic and kinetic aspects of protein stability in these crowded cellular or solution environments. We use a coarse-grained modeling approach to study the effects of different crowding agents on the conformational equilibria of proteins and the thermodynamic phase behavior of their solutions. At low to moderate protein concentrations, we find that crowding species can either stabilize or destabilize the native state, depending on the strength of their attractive interaction with the proteins. At high protein concentrations, crowders tend to stabilize the native state due to excluded volume effects, irrespective of the strength of the crowder-protein attraction. Crowding agents reduce the tendency of protein solutions to undergo a liquid-liquid phase separation driven by strong protein-protein attractions. The aforementioned equilibrium trends represent, to our knowledge, the first simulation predictions for how the properties of crowding species impact the global thermodynamic stability of proteins and their solutions.

Replica exchange simulations of the thermodynamics of Abeta fibril growth

Replica exchange molecular dynamics and an all-atom implicit solvent model are used to probe the thermodynamics of deposition of Alzheimer's Abeta monomers on preformed amyloid fibrils. Consistent with the experiments, two deposition stages have been identified. The docking stage occurs over a wide temperature range, starting with the formation of the first peptide-fibril interactions at 500 K. Docking is completed when a peptide fully adsorbs on the fibril edge at the temperature of 380 K. The docking transition appears to be continuous, and occurs without free energy barriers or intermediates. During docking, incoming Abeta monomer adopts a disordered structure on the fibril edge. The locking stage occurs at the temperature of approximately 360 K and is characterized by the rugged free energy landscape. Locking takes place when incoming Abeta peptide forms a parallel beta-sheet structure on the fibril edge. Because the beta-sheets formed by locked Abeta peptides are typically off-registry, the structure of the locked phase differs from the structure of the fibril interior. The study also reports that binding affinities of two distinct fibril edges with respect to incoming Abeta peptides are different. The peptides bound to the concave edge have significantly lower free energy compared to those bound on the convex edge. Comparison with the available experimental data is discussed.

Temperature-induced dissociation of Abeta monomers from amyloid fibril

Using all-atom molecular dynamics, we study the temperature-induced dissociation of Abeta monomers from the fibril protofilament. To accelerate conformational sampling, simulations are performed at elevated temperatures and peptide concentrations. By computing free energy disconnectivity graphs we mapped the free energy landscape of monomers on the surface of Abeta fibril. We found that Abeta monomers sample diverse sets of low free energy states with different degrees of association with the fibril. Some of these states have residual amounts of fibril interactions, whereas others lack fibril-like content. Generally, Abeta monomers with partially formed fibril-like interactions have the lowest free energies, but their backbone conformations may differ considerably from those in the fibril interior. Overall, Abeta amyloid protofilaments seem to be highly resistant to thermal dissociation. Monomer dissociation from the fibril edge proceeds via multiple stages and pathways. Our simulation findings are discussed in the context of recent experimental results.

Modeling amyloid fibril formation: a free-energy approach

Amyloid fibrils are structures consisting of many proteins with a well-defined conformation. The formation of these fibrils has been the subject of intense research, largely due to their connection to several diseases. We focus here on the computational studies and discuss these from a free-energy point of view. The fibrillogenic properties of many proteins can be predicted and understood by taking the relevant free energies into account in an appropriate way. This is because both the equilibrium and the kinetic properties of the protein system depend on its free-energy landscape. Advanced simulation techniques can be used to understand the relationship between the free-energy landscape of a protein and its three-dimensional structure and propensity to form amyloid fibrils. We give an overview of existing simulation techniques that operate at a molecular level of detail and that are capable of generating relevant free-energy values. The free energies obtained with these methods can be inserted into a statistical-mechanical or kinetic framework to predict mean fibril properties on length scales and time scales that are inaccessible by molecular-scale simulation methods.

Dissociation of Abeta(16-22) amyloid fibrils probed by molecular dynamics

The mechanisms of deposition and dissociation are implicated in the assembly of amyloid fibrils. To investigate the kinetics of unbinding of Abeta(16-22) monomers from preformed fibrils, we use molecular dynamics (MD) simulations and the structures for Abeta(16-22) amyloid fibrils. Consistent with experimental studies, the dissociation of Abeta(16-22) peptides involves two main stages, locked and docked, after which peptides unbind. The lifetime of the locked state, in which a peptide retains fibril-like structure and interactions, extends up to 0.5 micros under normal physiological conditions. Upon cooperative rupture of all fibril-like hydrogen bonds (HBs) with the fibril, a peptide enters a docked state. This state is populated by disordered random coil conformations and its lifetime ranges from approximately 10 to 200 ns. The docked state is stabilized by hydrophobic side chain interactions, while the contribution from HBs is small. Our simulations also suggest that the peptides located on fibril edges may form stable beta-strand conformations distinct from the fibril "bulk". We propose that such edge peptides can act as fibril caps, which impede fibril elongation. Our results indicate that the interactions between unbinding peptides constitute the molecular basis for cooperativity of peptide dissociation. The kinetics of fibril growth is reconstructed from unbinding assuming the reversibility of deposition/dissociation pathways. The relation of in silica dissociation kinetics to experimental observations is discussed.

Molecular simulation of surfactant-assisted protein refolding

Protein refolding to its native state in vitro is a challenging problem in biotechnology, i.e., in the biomedical, pharmaceutical, and food industry. Protein aggregation and misfolding usually inhibit the recovery of proteins with their native states. These problems can be partially solved by adding a surfactant into a suitable solution environment. However, the process of this surfactant-assisted protein refolding is not well understood. In this paper, we wish to report on the first-ever simulations of surfactant-assisted protein refolding. For these studies, we defined a simple model for the protein and the surfactant and investigated how a surfactant affected the folding behavior of a two-dimensional lattice protein molecule. The model protein and model surfactant were chosen such that we could capture the important features of the folding process and the interaction between the protein and the surfactant, namely, the hydrophobic interaction. It was shown that, in the absence of surfactants, a protein in an "energy trap" conformation, i.e., a local energy minima, could not fold into the native form, which was characterized by a global energy minimum. The addition of surfactants created folding pathways via the formation of protein-surfactant complexes and thus enabled the conformations that fell into energy trap states to escape from these traps and to form the native proteins. The simulation results also showed that it was necessary to match the hydrophobicity of surfactant to the concentration of denaturant, which was added to control the folding or unfolding of a protein. The surfactants with different hydrophobicity had their own concentration range on assisting protein refolding. All of these simulations agreed well with experimental results reported elsewhere, indicating both the validity of the simulations presented here and the potential application of the simulations for the design of a surfactant on assisting protein refolding.

Effect of single-point sequence alterations on the aggregation propensity of a model protein

Sequences of contemporary proteins are believed to have evolved through a process that optimized their overall fitness, including their resistance to deleterious aggregation. Biotechnological processing may expose therapeutic proteins to conditions that are much more conducive to aggregation than those encountered in a cellular environment. An important task of protein engineering is to identify alternative sequences that would protect proteins when processed at high concentrations without altering their native structure associated with specific biological function. Our computational studies exploit parallel tempering simulations of coarse-grained model proteins to demonstrate that isolated amino acid residue substitutions can result in significant changes in the aggregation resistance of the protein in a crowded environment while retaining protein structure in isolation. A thermodynamic analysis of protein clusters subject to competing processes of folding and association shows that moderate mutations can produce effects similar to those caused by changes in system conditions, including temperature, concentration, and solvent composition, that affect the aggregation propensity. The range of conditions where a protein can resist aggregation can therefore be tuned by sequence alterations, although the protein generally may retain its generic ability for aggregation.

Frequencies of hydrophobic and hydrophilic runs and alternations in proteins of known structure

Patterns of alternation of hydrophobic and polar residues are a profound aspect of amino acid sequences, but a feature not easily interpreted for soluble proteins. Here we report statistics of hydrophobicity patterns in proteins of known structure in a current protein database as compared with results from earlier, more limited structure sets. Previous studies indicated that long hydrophobic runs, common in membrane proteins, are underrepresented in soluble proteins. Long runs of hydrophobic residues remain significantly underrepresented in soluble proteins, with none longer than 16 residues observed. These long runs most commonly occur as buried alpha helices, with extended hydrophobic strands less common. Avoiding aggregation of partially folded intermediates during intracellular folding remains a viable explanation for the rarity of long hydrophobic runs in soluble proteins. Comparison between database editions reveals robustness of statistics on aqueous proteins despite an approximately twofold increase in nonredundant sequences. The expanded database does now allow us to explain several deviations of hydrophobicity statistics from models of random sequence in terms of requirements of specific secondary structure elements. Comparison to prior membrane-bound protein sequences, however, shows significant qualitative changes, with the average hydrophobicity and frequency of long runs of hydrophobic residues noticeably increasing between the database editions. These results suggest that the aqueous proteins of solved structure may represent an essentially complete sample of the universe of aqueous sequences, while the membrane proteins of known structure are not yet representative of the universe of membrane-associated proteins, even by relatively simple measures of hydrophobic patterns.

Coarse-grained strategy for modeling protein stability in concentrated solutions. II: phase behavior

We use highly efficient transition-matrix Monte Carlo simulations to determine equilibrium unfolding curves and fluid phase boundaries for solutions of coarse-grained globular proteins. The model we analyze derives the intrinsic stability of the native state and protein-protein interactions from basic information about protein sequence using heteropolymer collapse theory. It predicts that solutions of low hydrophobicity proteins generally exhibit a single liquid phase near their midpoint temperatures for unfolding, while solutions of proteins with high sequence hydrophobicity display the type of temperature-inverted, liquid-liquid transition associated with aggregation processes of proteins and other amphiphilic molecules. The phase transition occurring in solutions of the most hydrophobic protein we study extends below the unfolding curve, creating an immiscibility gap between a dilute, mostly native phase and a concentrated, mostly denatured phase. The results are qualitatively consistent with the solution behavior of hemoglobin (HbA) and its sickle variant (HbS), and they suggest that a liquid-liquid transition resulting in significant protein denaturation should generally be expected on the phase diagram of high-hydrophobicity protein solutions. The concentration fluctuations associated with this transition could be a driving force for the nonnative aggregation that can occur below the midpoint temperature.

Spontaneous fibril formation by polyalanines; discontinuous molecular dynamics simulations

Fibrillary protein aggregates rich in beta-sheet structure have been implicated in the pathology of several neurodegenerative diseases. In this work, we investigate the formation of fibrils by performing discontinuous molecular dynamics simulations on systems containing 12 to 96 model Ac-KA(14)K-NH(2) peptides using our newly developed off-lattice, implicit-solvent, intermediate-resolution model, PRIME. We find that, at a low concentration, random-coil peptides assemble into alpha-helices at low temperatures. At intermediate concentrations, random-coil peptides assemble into alpha-helices at low temperatures and large beta-sheet structures at high temperatures. At high concentrations, the system forms beta-sheets over a wide range of temperatures. These assemble into fibrils above a critical temperature which decreases with concentration and exceeds the isolated peptide's folding temperature. At very high temperatures and all concentrations, the system is in a random-coil state. All of these results are in good qualitative agreement with those by Blondelle and co-workers on Ac-KA(14)K-NH(2) peptides. The fibrils observed in our simulations mimic the structural characteristics observed in experiments in terms of the number of sheets formed, the values of the intra- and intersheet separations, and the parallel peptide arrangement within each beta-sheet. Finally, we find that when the strength of the hydrophobic interaction between nonpolar side chains is high compared to the strength of hydrogen bonding, amorphous aggregates, rather than fibrillar aggregates, are formed.

Structural transitions of confined model proteins: molecular dynamics simulation and experimental validation

Proteins fold in a confined space not only in vivo, i.e., folding assisted by molecular chaperons and chaperonins in a crowded cellular medium, but also in vitro as in production of recombinant proteins. Despite extensive work on protein folding in bulk, little is known about how and to what extent the thermodynamics and kinetics of protein folding are altered by confinement. In this work, we use a Gō-like off-lattice model to investigate the folding and stability of an all beta-sheet protein in spherical cages of different sizes and surface hydrophobicity. We find whereas extreme confinement inhibits correct folding, a hydrophilic cage stabilizes the protein due to restriction of the unfolded configurations. In a hydrophobic cage, however, strong attraction from the cage surface destabilizes the confined protein because of competition between self-aggregation and adsorption of hydrophobic residues. We show that the kinetics of protein collapse and folding is strongly correlated with both the cage size and the surface hydrophobicity. It is demonstrated that a cage of moderate size and hydrophobicity optimizes both the folding yield and kinetics of structural transitions. To support the simulation results, we have also investigated the refolding of hen-egg lysozyme in the presence of cetyltrimethylammoniumbromide (CTAB) surfactants that provide an effective confinement of the proteins by micellization. The influence of the surfactant hydrophobicity on the structural and biological activity of the protein is determined with circular dichroism spectrum, fluorescence emission spectrum, and biological activity assay. It is shown that, as predicted by coarse-grained simulations, CTAB micelles facilitate the collapse of denatured lysozyme, whereas the addition of beta-cyclodextrin-grafted-PNIPAAm, a weakly hydrophobic stripper, dissociates CTAB micelles and promotes the conformational rearrangement and thereby gives an improved recovery of lysozyme activity.

Amyloid β-Peptide Oligomerization in Silico: Dimer and Trimer

Soluble oligomers of Alzheimer's amyloid beta protein (Abeta) may act as effectors of neurotoxicity in early stages of Alzheimer's disease. Detailed information about the structure of Abeta in atomistic level and the dynamics of assembly of monomeric Abeta into oligomeric structures is rather elusive. We have performed replica exchange molecular dynamics (REMD) simulations on the formation of the dimer and trimer of Abeta10-35 peptide. We have observed spontaneous formation of several basic structural units that may act as a template or an intermediate for further aggregation of Alzheimer's Abeta protein. Various conformers, including interlocking structures of experimentally known bend double beta strands, are identified.

Protein oligomerization: how and why

A large fraction of cellular proteins are oligomeric. Protein oligomerization may often be an advantageous feature from the perspective of protein evolution and has probably evolved by a variety of mechanisms. The study of protein oligomerization may provide insights into the early protein environment and the evolution of modern proteins. Oligomeric mini-proteins, short peptides with discrete protein-like structures, may serve as valuable models for understanding features of protein oligomerization.

Coarse-grained strategy for modeling protein stability in concentrated solutions

We present a coarse-grained approach for modeling the thermodynamic stability of single-domain globular proteins in concentrated aqueous solutions. Our treatment derives effective protein-protein interactions from basic structural and energetic characteristics of the native and denatured states. These characteristics, along with the intrinsic (i.e., infinite dilution) thermodynamics of folding, are calculated from elementary sequence information using a heteropolymer collapse theory. We integrate this information into Reactive Canonical Monte Carlo simulations to investigate the connections between protein sequence hydrophobicity, protein-protein interactions, protein concentration, and the thermodynamic stability of the native state. The model predicts that sequence hydrophobicity can affect how protein concentration impacts native-state stability in solution. In particular, low hydrophobicity proteins are primarily stabilized by increases in protein concentration, whereas high hydrophobicity proteins exhibit richer nonmonotonic behavior. These trends appear qualitatively consistent with the available experimental data. Although factors such as pH, salt concentration, and protein charge are also important for protein stability, our analysis suggests that some of the nontrivial experimental trends may be driven by a competition between destabilizing hydrophobic protein-protein attractions and entropic crowding effects.

Kinetics of fibril formation by polyalanine peptides

Ordered beta-sheet complexes, termed amyloid fibrils, are the underlying structural components of the intra- and extracellular fibrillar protein deposits that are associated with a variety of human diseases, including Alzheimer's, Parkinson's, and the prion diseases. In this work, we investigated the kinetics of fibril formation using our newly developed off-lattice intermediate resolution model, PRIME. The model is simple enough to allow the treatment of large multichain systems while maintaining a fairly realistic description of protein dynamics without built-in bias toward any conformation when used in conjunction with constant temperature discontinuous molecular dynamics, a fast alternative to conventional molecular dynamics. Simulations were performed on systems containing 48-96 model Ac-KA14K-NH2 peptides. We found that fibril formation for polyalanines incorporate features that are characteristic of three models, the templated assembly, nucleated polymerization, and nucleated conformational conversion models, but that none of them gave a completely satisfactory description of the simulation kinetics. Fibril formation was nucleation-dependent, occurring after a lag time that decreased with increasing peptide concentration and increased with increasing temperature. Fibril formation appeared to be a conformational conversion process in which small amorphous aggregates --> beta-sheets --> ordered nucleus --> subsequent rapid growth of a small stable fibril or protofilament. Fibril growth in our simulations involved both beta-sheet elongation, in which the fibril grew by adding individual peptides to the end of each beta-sheet, and lateral addition, in which the fibril grew by adding already formed beta-sheets to its side. The initial rate of fibril formation increased with increasing concentration and decreased with increasing temperature.

In silico assembly of Alzheimer's Abeta16-22 peptide into beta-sheets

Recent studies suggest that soluble oligomers of amyloid-forming peptides have toxic effects in cell cultures. In this study, the folding of three Alzheimer's A beta(16-22) peptides have been simulated with the activation-relaxation technique and a generic energy model. Starting from randomly chosen states, the predicted lowest energy structure superposes within 1 A rms deviation from its conformation within the fibrils. This antiparallel structure is found to be in equilibrium with several out-of-register antiparallel beta-sheets and mixed parallel-antiparallel beta-sheets, indicating that full structural order in the fibrils requires larger aggregates. Folding involves the formation of dimers followed by the addition of a monomer and proceeds through a generalized mechanism between disordered and native alignments of beta-strands.

Phase diagrams describing fibrillization by polyalanine peptides

Amyloid fibrils are the structural components underlying the intra- and extracellular protein deposits that are associated with a variety of human diseases, including Alzheimer's, Parkinson's, and the prion diseases. In this work, we examine the thermodynamics of fibril formation using our newly-developed off-lattice intermediate-resolution protein model, PRIME. The model is simple enough to allow the treatment of large multichain systems while maintaining a fairly realistic description of protein dynamics when used in conjunction with constant-temperature discontinuous molecular dynamics, a fast alternative to conventional molecular dynamics. We conduct equilibrium simulations on systems containing 96 Ac-KA14K-NH2 peptides over a wide range of temperatures and peptide concentrations using the replica-exchange method. Based on measured values of the heat capacity, radius of gyration, and percentage of peptides that form the various structures, a phase diagram in the temperature-concentration plane is constructed delineating the regions where each structure is stable. There are four distinct single-phase regions: alpha-helices, fibrils, nonfibrillar beta-sheets, and random coils; and four two-phase regions: random coils/nonfibrillar beta-sheets, random coils/fibrils, fibrils/nonfibrillar beta-sheets, and alpha-helices/nonfibrillar beta-sheets. The alpha-helical region is at low temperature and low concentration. The nonfibrillar beta-sheet region is at intermediate temperatures and low concentrations and expands to higher temperatures as concentration is increased. The fibril region occurs at intermediate temperatures and intermediate concentrations and expands to lower as the peptide concentration is increased. The random-coil region is at high temperatures and all concentrations; this region shifts to higher temperatures as the concentration is increased.

Assembly and kinetic folding pathways of a tetrameric beta-sheet complex: molecular dynamics simulations on simplified off-lattice protein models

We have performed discontinuous molecular dynamic simulations of the assembly and folding kinetics of a tetrameric beta-sheet complex that contains four identical four-stranded antiparallel beta-sheet peptides. The potential used in the simulation is a hybrid Go-type potential characterized by the bias gap parameter g, an artificial measure of a model protein's preference for its native state, and the intermolecular contact parameter eta, which measures the ratio of intermolecular to intramolecular native attractions. The formation of the beta-sheet complex and its equilibrium properties strongly depend on the size of the intermolecular contact parameter eta. The ordered beta-sheet complex in the folded state and nonaligned beta-sheets or tangled chains in the misfolded state are distinguished by measuring the squared radius of gyration Rg2 and the fraction of native contacts Q. The folding yield for the folded state is high at intermediate values of eta, but is low at both small and large values of eta. The folded state at small eta is liquid-like, but is solid-like at both intermediate and large eta. The misfolded state at small eta contains nonaligned beta-sheets and tangled chains with poor secondary structure at large eta. Various folding pathways via dimeric and trimeric intermediates are observed, depending on eta. Comparison with experimental results on protein aggregation indicates that intermediate eta values are most appropriate for modeling fibril formation and small eta values are most appropriate for modeling the formation of amorphous aggregates.