Protein refolding versus aggregation: computer simulations on an intermediate-resolution protein model

Oligomer Formation by Physiologically Relevant C-Terminal Isoforms of Amyloid β-Protein

Alzheimer's disease (AD) is a neurological disorder associated with amyloid β-protein (Aβ) assembly into toxic oligomers. In addition to the two predominant alloforms, Aβ1-40 and Aβ1-42, other C-terminally truncated Aβ peptides, including Aβ1-38 and Aβ1-43, are produced in the brain. Here, we use discrete molecular dynamics (DMD) and a four-bead protein model with amino acid-specific hydropathic interactions, DMD4B-HYDRA, to examine oligomer formation of Aβ1-38, Aβ1-40, Aβ1-42, and Aβ1-43. Self-assembly of 32 unstructured monomer peptides into oligomers is examined using 32 replica DMD trajectories for each of the four peptides. In a quasi-steady state, Aβ1-38 and Aβ1-40 adopt similar unimodal oligomer size distributions with a maximum at trimers, whereas Aβ1-42 and Aβ1-43 oligomer size distributions are multimodal with the dominant maximum at trimers or tetramers, and additional maxima at hexamers and unidecamers (for Aβ1-42) or octamers and pentadecamers (for Aβ1-43). The free energy landscapes reveal isoform- and oligomer-order specific structural and morphological features of oligomer ensembles. Our results show that oligomers of each of the four isoforms have unique features, with Aβ1-42 alone resulting in oligomers with disordered and solvent-exposed N-termini. Our findings help unravel the structure-function paradigm governing oligomers formed by various Aβ isoforms.

Effects of Cell-Adhesive Ligand Presentation on Pentapeptide Supramolecular Assembly and Gelation: Simulations and Experiments

The extracellular matrix (ECM) is a complex, hierarchical material containing structural and bioactive components. This complexity makes decoupling the effects of biomechanical properties and cell-matrix interactions difficult, especially when studying cellular processes in a 3D environment. Matrix mechanics and cell adhesion are both known regulators of specific cellular processes such as stem cell proliferation and differentiation. However, more information is required about how such variables impact various neural lineages that could, upon transplantation, therapeutically improve neural function after a central nervous system injury or disease. Rapidly Assembling Pentapeptides for Injectable Delivery (RAPID) hydrogels are one biomaterial approach to meet these goals, consisting of a family of peptide sequences that assemble into physical hydrogels in physiological media. In this study, we studied our previously reported supramolecularly-assembling RAPID hydrogels functionalized with the ECM-derived cell-adhesive peptide ligands RGD, IKVAV, and YIGSR. Using molecular dynamics simulations and experimental rheology, we demonstrated that these integrin-binding ligands at physiological concentrations (3-12 mm) did not impact the assembly of the KYFIL peptide system. In simulations, molecular measures of assembly such as hydrogen bonding and pi-pi interactions appeared unaffected by cell-adhesion sequence or concentration. Visualizations of clustering and analysis of solvent-accessible surface area indicated that the integrin-binding domains remained exposed. KYFIL or AYFIL hydrogels containing 3 mm of integrin-binding domains resulted in mechanical properties consistent with their non-functionalized equivalents. This strategy of doping RAPID gels with cell-adhesion sequences allows for the precise tuning of peptide ligand concentration, independent of the rheological properties. The controllability of the RAPID hydrogel system provides an opportunity to investigate the effect of integrin-binding interactions on encapsulated neural cells to discern how hydrogel microenvironment impacts growth, maturation, or differentiation.

Soluble State of Villin Headpiece Protein as a Tool in the Assessment of MD Force Fields

Protein self-assembly plays an important role in cellular processes. Whereas molecular dynamics (MD) represents a powerful tool in studying assembly mechanisms, its predictions depend on the accuracy of underlying force fields, which are known to overly promote protein assembly. We here examine villin headpiece domain, HP36, which remains soluble at concentrations amenable to MD studies. The experimental characterization of soluble HP36 at concentrations of 0.05 to 1 mM reveals concentration-independent 90% monomeric and 10% dimeric populations. Extensive all-atom MD simulations at two protein concentrations, 0.9 and 8.5 mM, probe the HP36 dimer population, stability, and kinetics of dimer formation within two MD force fields, Amber ff14SB and CHARMM36m. MD results demonstrate that whereas CHARMM36m captures experimental HP36 monomer populations at the lower concentration, both force fields overly promote HP36 association at the higher concentration. Moreover, contacts stabilizing HP36 dimers are force-field-dependent. CHARMM36m produces consistently higher HP36 monomer populations, lower association rates, and weaker dependence of these quantities on the protein concentration than Amber ff14SB. Nonetheless, the highest monomer populations and dissociation constants are observed when the TIP3P water model in Amber ff14SB is replaced by TIP4P/2005, showcasing the critical role of the water model in addressing the protein solubility problem in MD.

Five-Site Model for Brownian Dynamics Simulations of a Molecular Walker in Three Dimensions

Motor proteins play an important role in many biological processes and have inspired the development of synthetic analogues. Molecular walkers, such as kinesin, dynein, and myosin V, fulfill a diverse set of functions including transporting cargo along tracks, pulling molecules through membranes, and deforming fibers. The complexity of molecular motors and their environment makes it difficult to model the detailed dynamics of molecular walkers over long time scales. In this work, we present a simple, three-dimensional model for a molecular walker on a bead-spring substrate. The walker is represented by five spherically symmetric particles that interact through common intermolecular potentials and can be simulated efficiently in Brownian dynamics simulations. The movement of motor protein walkers entails energy conversion through ATP hydrolysis while artificial motors typically rely on a local conversion of energy supplied through external fields. We model energy conversion through rate equations for mechanochemical states that couple positional and chemical degrees of freedom and determine the walker conformation through interaction potential parameters. We perform Brownian dynamics simulations for two scenarios: In the first, the model walker transports cargo by walking on a substrate whose ends are fixed. In the second, a tethered motor pulls a mobile substrate chain against a variable force. We measure relative displacements and determine the effects of cargo size and retarding force on the efficiency of the walker. We find that, while the efficiency of our model walker is less than for the biological system, our simulations reproduce trends observed in single-molecule experiments on kinesin. In addition, the model and simulation method presented here can be readily adapted to biological and synthetic systems with multiple walkers.

Amyloid Oligomers: A Joint Experimental/Computational Perspective on Alzheimer's Disease, Parkinson's Disease, Type II Diabetes, and Amyotrophic Lateral Sclerosis

Protein misfolding and aggregation is observed in many amyloidogenic diseases affecting either the central nervous system or a variety of peripheral tissues. Structural and dynamic characterization of all species along the pathways from monomers to fibrils is challenging by experimental and computational means because they involve intrinsically disordered proteins in most diseases. Yet understanding how amyloid species become toxic is the challenge in developing a treatment for these diseases. Here we review what computer, in vitro, in vivo, and pharmacological experiments tell us about the accumulation and deposition of the oligomers of the (Aβ, tau), α-synuclein, IAPP, and superoxide dismutase 1 proteins, which have been the mainstream concept underlying Alzheimer's disease (AD), Parkinson's disease (PD), type II diabetes (T2D), and amyotrophic lateral sclerosis (ALS) research, respectively, for many years.

Spatial Stochastic Intracellular Kinetics: A Review of Modelling Approaches

Models of chemical kinetics that incorporate both stochasticity and diffusion are an increasingly common tool for studying biology. The variety of competing models is vast, but two stand out by virtue of their popularity: the reaction-diffusion master equation and Brownian dynamics. In this review, we critically address a number of open questions surrounding these models: How can they be justified physically? How do they relate to each other? How do they fit into the wider landscape of chemical models, ranging from the rate equations to molecular dynamics? This review assumes no prior knowledge of modelling chemical kinetics and should be accessible to a wide range of readers.

Configurational contribution to the Soret effect of a protein ligand system : An investigation with density-of-states simulations

Many of the biological functions of proteins are closely associated with their ability to bind ligands and change conformations in response to changing conditions. Since binding state and conformation of a protein affect its response to a temperature gradient, they may be probed with thermophoresis. In recent years, thermophoretic techniques to investigate biomolecular interactions, quantify ligand binding, and probe conformational changes have become established. To develop a better understanding of the mechanisms underlying the thermophoretic behavior of proteins and ligands, we employ a simple, off-lattice model for a protein and ligand in explicit solvent. To investigate the partitioning of the particles in a temperature gradient, we perform Wang-Landau-type simulations in a divided simulation box and construct the density of states over a two-dimensional state space. This method gives us access to the entropy and energy of the divided system and allows us to estimate the configurational contribution to the Soret coefficient. In this work, we focus on dilute solutions of hydrophobic proteins and investigate the effect of ligand binding on their thermophoretic behavior. We find that our simple model captures important aspects of protein-ligand interactions and allows us to relate the binding energy to the change in Soret coefficient upon ligand binding.

Molecular dynamics study of structure, folding, and aggregation of poly-glycine-alanine (Poly-GA)

Poly-glycine-alanine (poly-GA) proteins are widely believed to be one of the main toxic dipeptide repeat molecules associated with amyotrophic lateral sclerosis (ALS) and frontotemporal dementia diseases. Using discontinuous molecular dynamics simulation and an all-atom model of the proteins, we study folding, stability, and aggregation of poly-GA. The results demonstrate that poly-GA is an aggregation-prone protein that, after a long enough time, forms β-sheet-rich aggregates that match recent experiment data and that two unique helical structures are formed very frequently, namely, β-helix and double-helix. The details of the two structures are analyzed. The analysis indicates that such helical structures are stable and share the characteristics of both α-helices and β-sheets. Molecular simulations indicate that identical phenomena also occur in the aggregation of poly-glycine-arginine (poly-GR). Therefore, we hypothesize that proteins of type (GX)_n in which X may be any non-glycine amino acid and n is the repeat length may share the same folding structures of β-helix and double-helix and that it is the glycine in the repeat that contributes the most to this characteristic. Molecular dynamics simulation with continuous interaction potentials and explicit water molecules as the solvent supports the hypothesis. To our knowledge, this is the first molecular dynamics simulation of the phenomena involving poly-GA and poly-GR proteins.

Effect of the geometry of confining media on the stability and folding rate of α -helix proteins

Protein folding in confined media has attracted wide attention over the past 15 years due to its importance to both in vivo and in vitro applications. It is generally believed that protein stability increases by decreasing the size of the confining medium, if the medium's walls are repulsive, and that the maximum folding temperature in confinement is in a pore whose size D ₀ is only slightly larger than the smallest dimension of a protein's folded state. Until recently, the stability of proteins in pores with a size very close to that of the folded state has not received the attention it deserves. In a previous paper [L. Javidpour and M. Sahimi, J. Chem. Phys. 135, 125101 (2011)], we showed that, contrary to the current theoretical predictions, the maximum folding temperature occurs in larger pores for smaller α-helices. Moreover, in very tight pores, the free energy surface becomes rough, giving rise to a new barrier for protein folding close to the unfolded state. In contrast to unbounded domains, in small nanopores proteins with an α-helical native state that contain the β structures are entropically stabilized implying that folding rates decrease notably and that the free energy surface becomes rougher. In view of the potential significance of such results to interpretation of many sets of experimental data that could not be explained by the current theories, particularly the reported anomalously low rates of folding and the importance of entropic effects on proteins' misfolded states in highly confined environments, we address the following question in the present paper: To what extent the geometry of a confined medium affects the stability and folding rates of proteins? Using millisecond-long molecular dynamics simulations, we study the problem in three types of confining media, namely, cylindrical and slit pores and spherical cavities. Most importantly, we find that the prediction of the previous theories that the dependence of the maximum folding temperature T _f on the size D of a confined medium occurs in larger media for larger proteins is correct only in spherical geometry, whereas the opposite is true in the two other geometries that we study. Also studied is the effect of the strength of the interaction between the confined media's walls and the proteins. If the walls are only weakly or moderately attractive, a complex behavior emerges that depends on the size of the confining medium.

Dynamics of proteins aggregation. II. Dynamic scaling in confined media

In this paper, the second in a series devoted to molecular modeling of protein aggregation, a mesoscale model of proteins together with extensive discontinuous molecular dynamics simulation is used to study the phenomenon in a confined medium. The medium, as a model of a crowded cellular environment, is represented by a spherical cavity, as well as cylindrical tubes with two aspect ratios. The aggregation process leads to the formation of β sheets and eventually fibrils, whose deposition on biological tissues is believed to be a major factor contributing to many neuro-degenerative diseases, such as Alzheimer's, Parkinson's, and amyotrophic lateral sclerosis diseases. Several important properties of the aggregation process, including dynamic evolution of the total number of the aggregates, the mean aggregate size, and the number of peptides that contribute to the formation of the β sheets, have been computed. We show, similar to the unconfined media studied in Paper I [S. Zheng et al., J. Chem. Phys. 145, 134306 (2016)], that the computed properties follow dynamic scaling, characterized by power laws. The existence of such dynamic scaling in unconfined media was recently confirmed by experiments. The exponents that characterize the power-law dependence on time of the properties of the aggregation process in spherical cavities are shown to agree with those in unbounded fluids at the same protein density, while the exponents for aggregation in the cylindrical tubes exhibit sensitivity to the geometry of the system. The effects of the number of amino acids in the protein, as well as the size of the confined media, have also been studied. Similarities and differences between aggregation in confined and unconfined media are described, including the possibility of no fibril formation, if confinement is severe.

Dynamics of proteins aggregation. I. Universal scaling in unbounded media

It is well understood that in some cases proteins do not fold correctly and, depending on their environment, even properly-folded proteins change their conformation spontaneously, taking on a misfolded state that leads to protein aggregation and formation of large aggregates. An important factor that contributes to the aggregation is the interactions between the misfolded proteins. Depending on the aggregation environment, the aggregates may take on various shapes forming larger structures, such as protein plaques that are often toxic. Their deposition in tissues is a major contributing factor to many neuro-degenerative diseases, such as Alzheimer's, Parkinson's, amyotrophic lateral sclerosis, and prion. This paper represents the first part in a series devoted to molecular simulation of protein aggregation. We use the PRIME, a meso-scale model of proteins, together with extensive discontinuous molecular dynamics simulation to study the aggregation process in an unbounded fluid system, as the first step toward MD simulation of the same phenomenon in crowded cellular environments. Various properties of the aggregates have been computed, including dynamic evolution of aggregate-size distribution, mean aggregate size, number of peptides that contribute to the formation of β sheets, number of various types of hydrogen bonds formed in the system, radius of gyration of the aggregates, and the aggregates' diffusivity. We show that many of such quantities follow dynamic scaling, similar to those for aggregation of colloidal clusters. In particular, at long times the mean aggregate size S(t) grows with time as, S(t) ∼ t^z, where z is the dynamic exponent. To our knowledge, this is the first time that the qualitative similarity between aggregation of proteins and colloidal aggregates has been pointed out.

Assembly of Triblock Amphiphilic Peptides into One-Dimensional Aggregates and Network Formation

Peptide assembly plays a key role in both neurological diseases and development of novel biomaterials with well-defined nanostructures. Synthetic model peptides provide a unique platform to explore the role of intermolecular interactions in the assembly process. A triblock peptide architecture designed by the Hartgerink group is a versatile system which relies on Coulomb interactions, hydrogen bonding, and hydrophobicity to guide these peptides' assembly at three different length scales: β-sheets, double-wall ribbon-like aggregates, and finally a highly porous network structure which can support gels with ≤1% by weight peptide concentration. In this study, by using molecular dynamics simulations of a structure based implicit solvent coarse grained model, we analyzed this hierarchical assembly process. Parametrization of our CG model is based on multiple-state points from atomistic simulations, which enables this model to represent the conformational adaptability of the triblock peptide molecule based on the surrounding medium. Our results indicate that emergence of the double-wall β-sheet packing mechanism, proposed in light of the experimental evidence, strongly depends on the subtle balance of the intermolecular forces. We demonstrate that, even though backbone hydrogen bonding dominates the early nucleation stages, depending on the strength of the hydrophobic and Coulomb forces, alternative structures such as zero-dimensional aggregates with two β-sheets oriented orthogonally (which we refer to as a cross-packed structure) and β-sheets with misoriented hydrophobic side chains are also feasible. We discuss the implications of these competing structures for the three different length scales of assembly by systematically investigating the influence of density, counterion valency, and hydrophobicity.

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

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

Impact of sequence on the molecular assembly of short amyloid peptides

The goal of this work is to understand how the sequence of a protein affects the likelihood that it will form an amyloid fibril and the kinetics along the fibrillization pathway. The focus is on very short fragments of amyloid proteins since these play a role in the fibrillization of the parent protein and can form fibrils themselves. Discontinuous molecular dynamics simulations using the PRIME20 force field were performed of the aggregation of 48-peptide systems containing SNQNNF (PrP (170-175)), SSTSAA (RNaseA(15-20)), MVGGVV (Aβ(35-40)), GGVVIA (Aβ(37-42)), and MVGGVVIA (Aβ(35-42)). In our simulations SNQQNF, SSTTSAA, and MVGGVV form large numbers of fibrillar structures spontaneously (as in experiment). GGVVIA forms β-sheets that do not stack into fibrils (unlike experiment). The combination sequence MVGGVVIA forms less fibrils than MVGGVV, hindered by the presence of the hydrophobic residues at the C-terminal. Analysis of the simulation kinetics and energetics reveals why MVGGVV forms fibrils and GGVVIA does not, and why adding I and A to MVGGVVIA reduces fibrillization and enhances amorphous aggregation into oligomeric structures. The latter helps explain why Aβ(1-42) assembles into more complex oligomers than Aβ(1-40), a consequence of which is that it is more strongly associated with Alzheimer's disease.

Coarse-grained modeling of protein second osmotic virial coefficients: sterics and short-ranged attractions

A series of coarse-grained models, with different levels of structural resolution, were tested to calculate the steric contributions to protein osmotic second virial coefficients (B(22,S)) for proteins ranging from small single-domain molecules to large multidomain molecules, using the recently developed Mayer sampling method. B(22,S) was compared for different levels of coarse-graining: four-beads-per-amino-acid (4bAA), one-bead-per-amino-acid (1bAA), one-sphere-per-domain (1sD), and one-sphere-per-protein (1sP). Values for the 1bAA and 4bAA models were quantitatively indistinguishable for both spherical and nonspherical proteins, and the agreement with values from all-atom models improved with increasing protein size, making the CG approach attractive for large proteins of biotechnological interest. Interestingly, in the absence of detailed structural information, the hydrodynamic radius (R(h)) along with a simple 1sP approximation provided reasonably accurate values for B(22,S) for both globular and highly asymmetric protein structures, while other 1sP approximations gave poorer agreement; this helps to justify the currently empirical practice of estimating B(22,S) from R(h) for large proteins such as antibodies. The results also indicate that either 1bAA or 4bAA CG models may be good starting points for incorporating short-range attractions. Comparison of gD-crystallin B(22) values including both sterics and short-range attractions shows that 1bAA and 4bAA models give equivalent results when properly scaled to account for differences in the number of surface beads in the two CG descriptions. This provides a basis for future work that will also incorporate long-ranged electrostatic attractions and repulsions.

DPD Simulation of Protein Conformations: From α-Helices to β-Structures

We suggest a coarse-grained model for DPD simulations of polypeptides in solutions. The model mimics hydrogen bonding that stabilizes α-helical and β-structures using dissociable Morse bonds between quasiparticles representing the peptide groups amenable to hydrogen bonding. We demonstrate the capabilities of the model by simulating transitions between coil-like, globular, α-helical, and β-hairpin configurations of model peptides, varying Morse potential parameters, the hydrophobicities of residue side chains, and pH, which determines the charges of residue side chains. We construct a model triblock polypeptide mimicking the sequence of residues α-synuclein at two different pHs. The conformations of this model polypeptide depend on pH similarly to the behavior observed experimentally. The suggested approach to accounting for hydrogen bond formation within the general DPD framework may make the DPD method a competitive alternative to CGMD for modeling equilibrium and dynamic properties of proteins and polypeptides, especially during their transport in confined environments.

Confinement in nanopores can destabilize α-helix folding proteins and stabilize the β structures

Protein folding in confined media has attracted wide attention over the past decade due to its importance in both in vivo and in vitro applications. Currently, it is generally believed that protein stability increases by decreasing the size of the confining medium, if its interaction with the confining walls is repulsive, and that the maximum folding temperature in confinement occurs for a pore size only slightly larger than the smallest dimension of the folded state of a protein. Protein stability in pore sizes, very close to the size of the folded state, has not however received the attention that it deserves. Using detailed, 0.3-ms-long molecular dynamics simulations, we show that proteins with an α-helix native state can have an optimal folding temperature in pore sizes that do not affect the folded-state structure. In contradiction to the current theoretical explanations, we find that the maximum folding temperature occurs in larger pores for smaller α-helices. In highly confined pores the free energy surface becomes rough, and a new barrier for protein folding may appear close to the unfolded state. In addition, in small nanopores the protein states that contain the β structures are entropically stabilized, in contrast to the bulk. As a consequence, folding rates decrease notably and the free energy surface becomes rougher. The results shed light on many recent experimental observations that cannot be explained by the current theories, and demonstrate the importance of entropic effects on proteins' misfolded states in highly confined environments. They also support the concept of passive effect of chaperonin GroEL on protein folding by preventing it from aggregation in crowded environment of biological cells, and provide deeper clues to the α → β conformational transition, believed to contribute to Alzheimer's and Parkinson's diseases. The strategy of protein and enzyme stabilization in confined media may also have to be revisited in the case of tight confinement. For in silico studies of protein folding in confined media, use of non-Go potentials may be more appropriate.

Fibrillization propensity for short designed hexapeptides predicted by computer simulation

Assembly of normally soluble proteins into ordered aggregates, known as amyloid fibrils, is a cause or associated symptom of numerous human disorders, including Alzheimer's and the prion diseases. Here, we test the ability of discontinuous molecular dynamics (DMD) simulations based on PRIME20, a new intermediate-resolution protein force field, to predict which designed hexapeptide sequences will form fibrils, which will not, and how this depends on temperature and concentration. Simulations were performed on 48-peptide systems containing STVIIE, STVIFE, STVIVE, STAIIE, STVIAE, STVIGE, and STVIEE starting from random-coil configurations. By the end of the simulations, STVIIE and STVIFE (which form fibrils in vitro) form fibrils over a range of temperatures, STVIEE (which does not form fibrils in vitro) does not form fibrils, and STVIVE, STAIIE, STVIAE, and STVIGE (which do not form fibrils in vitro) form fibrils at lower temperatures but stop forming fibrils at higher temperatures. At the highest temperatures simulated, the results on the fibrillization propensity of the seven short de novo designed peptides all agree with the experiments of López de la Paz and Serrano. Our results suggest that the fibrillization temperature (temperature above which fibrils cease to form) is a measure of fibril stability and that by rank ordering the fibrillization temperatures of various sequences, PRIME20/DMD simulations could be used to ascertain their relative fibrillization propensities. A phase diagram showing regions in the temperature-concentration plane where fibrils are formed in our simulations is presented.

Computer simulation study of amyloid fibril formation by palindromic sequences in prion peptides

We simulate the aggregation of large systems containing palindromic peptides from the Syrian hamster prion protein SHaPrP 113-120 (AGAAAAGA) and the mouse prion protein MoPrP 111-120 (VAGAAAAGAV) and eight sequence variations: GAAAAAAG, (AG)(4) , A8, GAAAGAAA, A10, V10, GAVAAAAVAG, and VAVAAAAVAV The first two peptides are thought to act as the Velcro that holds the parent prion proteins together in amyloid structures and can form fibrils themselves. Kinetic events along the fibrillization pathway influence the types of structures that occur and variations in the sequence affect aggregation kinetics and fibrillar structure. Discontinuous molecular dynamics simulations using the PRIME20 force field are performed on systems containing 48 peptides starting from a random coil configuration. Depending on the sequence, fibrillar structures form spontaneously over a range of temperatures, below which amorphous aggregates form and above which no aggregation occurs. AGAAAAGA forms well organized fibrillar structures whereas VAGAAAAGAV forms less well organized structures that are partially fibrillar and partially amorphous. The degree of order in the fibrillar structure stems in part from the types of kinetic events leading up to its formation, with AGAAAAGA forming less amorphous structures early in the simulation than VAGAAAAGAV. The ability to form fibrils increases as the chain length and the length of the stretch of hydrophobic residues increase. However as the hydrophobicity of the sequence increases, the ability to form well-ordered structures decreases. Thus, longer hydrophobic sequences form slightly disordered aggregates that are partially fibrillar and partially amorphous. Subtle changes in sequence result in slightly different fibril structures.

Elucidation of amyloid beta-protein oligomerization mechanisms: discrete molecular dynamics study

Oligomers of amyloid beta-protein (Abeta) play a central role in the pathology of Alzheimer's disease. Of the two predominant Abeta alloforms, Abeta(1-40) and Abeta(1-42), Abeta(1-42) is more strongly implicated in the disease. We elucidated the structural characteristics of oligomers of Abeta(1-40) and Abeta(1-42) and their Arctic mutants, [E22G]Abeta(1-40) and [E22G]Abeta(1-42). We simulated oligomer formation using discrete molecular dynamics (DMD) with a four-bead protein model, backbone hydrogen bonding, and residue-specific interactions due to effective hydropathy and charge. For all four peptides under study, we derived the characteristic oligomer size distributions that were in agreement with prior experimental findings. Unlike Abeta(1-40), Abeta(1-42) had a high propensity to form paranuclei (pentameric or hexameric) structures that could self-associate into higher-order oligomers. Neither of the Arctic mutants formed higher-order oligomers, but [E22G]Abeta(1-40) formed paranuclei with a similar propensity to that of Abeta(1-42). Whereas the best agreement with the experimental data was obtained when the charged residues were modeled as solely hydrophilic, further assembly from spherical oligomers into elongated protofibrils was induced by nonzero electrostatic interactions among the charged residues. Structural analysis revealed that the C-terminal region played a dominant role in Abeta(1-42) oligomer formation whereas Abeta(1-40) oligomerization was primarily driven by intermolecular interactions among the central hydrophobic regions. The N-terminal region A2-F4 played a prominent role in Abeta(1-40) oligomerization but did not contribute to the oligomerization of Abeta(1-42) or the Arctic mutants. The oligomer structure of both Arctic peptides resembled Abeta(1-42) more than Abeta(1-40), consistent with their potentially more toxic nature.

Multistep aggregation pathway of human interleukin-1 receptor antagonist: kinetic, structural, and morphological characterization

The complex, multistep aggregation kinetic and structural behavior of human recombinant interleukin-1 receptor antagonist (IL-1ra) was revealed and characterized by spectral probes and techniques. At a certain range of protein concentration (12-27 mg/mL) and temperature (44-48 degrees C), two sequential aggregation kinetic transitions emerge, where the second transition is preceded by a lag phase and is associated with the main portion of the aggregated protein. Each kinetic transition is linked to a different type of aggregate population, referred to as type I and type II. The aggregate populations, isolated at a series of time points and analyzed by Fourier-transform infrared spectroscopy, show consecutive protein structural changes, from intramolecular (type I) to intermolecular (type II) beta-sheet formation. The early type I protein spectral change resembles that seen for IL-1ra in the crystalline state. Moreover, Fourier-transform infrared data demonstrate that type I protein assembly alone can undergo a structural rearrangement and, consequently, convert to the type II aggregate. The aggregated protein structural changes are accompanied by the aggregate morphological changes, leading to a well-defined population of interacting spheres, as detected by scanning electron microscopy. A nucleation-driven IL-1ra aggregation pathway is proposed, and assumes two major activation energy barriers, where the second barrier is associated with the type I --> type II aggregate structural rearrangement that, in turn, serves as a pseudonucleus triggering the second kinetic event.

Retinol-binding site in interphotoreceptor retinoid-binding protein (IRBP): a novel hydrophobic cavity

PURPOSE

Interphotoreceptor retinoid-binding protein (IRBP) appears to target and protect retinoids during the visual cycle. X-ray crystallographic studies had noted a betabetaalpha-spiral fold shared with crotonases and C-terminal protein transferases. The shallow cleft formed by the fold was assumed to represent the retinol-binding site. However, a second hydrophobic site consisting of a highly restricted cavity was more recently appreciated during in silico ligand-docking studies. In this study, the ligand-binding environment within the second module of Xenopus IRBP (X2IRBP) is defined.

METHODS

Pristine recombinant polypeptide corresponding to X2IRBP was expressed in a soluble form and purified to homogeneity without its fusion tag. Phenylalanine was substituted for tryptophan at each of the putative retinol-binding domains (W450F, hydrophobic cavity; W587F, shallow cleft). Binding of 11-cis and all-trans retinol were observed in titrations monitoring retinol fluorescence enhancement, quenching of tryptophan fluorescence, and energy transfer. The effect of oleic acid on retinol binding was also examined.

RESULTS

A ligand-binding stoichiometry of approximately 1:1 was observed for 11-cis and all-trans with K(d) in the tens of nanomolar range. The substitution mutants showed little effect on retinol binding in titrations after fluorescence enhancement. However, the W450F and not the W587F mutant showed a markedly reduced capacity for fluorescence quenching for both 11-cis and all-trans retinol. Oleic acid inhibited the binding of 11-cis and all-trans retinol in an apparent noncompetitive manner.

CONCLUSIONS

The binding site for 11-cis and all-trans retinol is a novel hydrophobic cavity that is highly restrictive and probably distinct from the long chain fatty acid-binding site.

Dynamics of locking of peptides onto growing amyloid fibrils

Sequence-dependent variations in the growth mechanism and stability of amyloid fibrils, which are implicated in a number of neurodegenerative diseases, are poorly understood. We have carried out extensive all-atom molecular dynamics simulations to monitor the structural changes that occur upon addition of random coil (RC) monomer fragments from the yeast prion Sup35 and Abeta-peptide onto a preformed fibril. Using the atomic resolution structures of the microcrystals as the starting points, we show that the RC --> beta-strand transition for the Sup35 fragment occurs abruptly over a very narrow time interval, whereas the acquisition of strand content is less dramatic for the hydrophobic-rich Abeta-peptide. Expulsion of water, resulting in the formation of a dry interface between 2 adjacent sheets of the Sup35 fibril, occurs in 2 stages. Ejection of a small number of discrete water molecules in the second stage follows a rapid decrease in the number of water molecules in the first stage. Stability of the Sup35 fibril is increased by a network of hydrogen bonds involving both backbone and side chains, whereas the marginal stability of the Abeta-fibrils is largely due to the formation of weak dispersion interaction between the hydrophobic side chains. The importance of the network of hydrogen bonds is further illustrated by mutational studies, which show that substitution of the Asn and Gln residues to Ala compromises the Sup35 fibril stability. Despite the similarity in the architecture of the amyloid fibrils, the growth mechanism and stability of the fibrils depend dramatically on the sequence.

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.

Molecular simulation of protein dynamics in nanopores. II. Diffusion

A novel combination of discontinuous molecular dynamics and the Langevin equation, together with an intermediate-resolution model of proteins, is used to carry out long (several microsecond) simulations in order to study transport of proteins in nanopores. We simulated single-domain proteins with the alpha-helical native structure. Both attractive and repulsive interaction potentials between the proteins and the pores' walls are considered. The diffusivity D of the proteins is computed not only under the bulk conditions but also as a function of their "length" (the number of the amino-acid groups), temperature T, pore size, and interaction potentials with the walls. Compared with the experimental data, the computed diffusivities under the bulk conditions are of the correct order of magnitude. The diffusivities both in the bulk and in the pores follow a power law in the length [script-l] of the proteins and are larger in pores with repulsive walls. D(+)/D(-), the ratio of the diffusivities in pores with attractive and repulsive walls, exhibits two local maxima in its dependence on the pore size h, which are attributed to the pore sizes and protein configurations that induce long-lasting simultaneous interactions with both walls of the pores. Far from the folding temperature T(f), D increases about linearly with T, but due to the thermal fluctuations and their effect on the proteins' structure near T(f), the dependence of D on T in this region is nonlinear. We propose a novel and general "phase diagram," consisting of four regions, that describes qualitatively the effect of h, T, and interaction potentials with the walls on the diffusivity D of a protein.

Probing the mechanisms of fibril formation using lattice models

Using exhaustive Monte Carlo simulations we study the kinetics and mechanism of fibril formation using lattice models as a function of temperature (T) and the number of chains (M). While these models are, at best, caricatures of peptides, we show that a number of generic features thought to govern fibril assembly are captured by the toy model. The monomer, which contains eight beads made from three letters (hydrophobic, polar, and charged), adopts a compact conformation in the native state. In both the single-layered protofilament (seen for M10) structures, the monomers are arranged in an antiparallel fashion with the "strandlike" conformation that is perpendicular to the fibril axis. Partial unfolding of the folded monomer that populates an aggregation prone conformation (N(*)) is required for ordered assembly. The contacts in the N(*) conformation, which is one of the four structures in the first "excited" state of the monomer, are also present in the native conformation. The time scale for fibril formation is a minimum in the T-range when the conformation N(*) is substantially populated. The kinetics of fibril assembly occurs in three distinct stages. In each stage there is a cascade of events that transforms the monomers and oligomers to ordered structures. In the first "burst" stage, highly mobile oligomers of varying sizes form. The conversion to the N(*) conformation occurs within the oligomers during the second stage in which a vast number of interchain contacts are established. As time progresses, a dominant cluster emerges that contains a majority of the chains. In the final stage, the aggregation of N(*) particles serve as a template onto which smaller oligomers or monomers can dock and undergo conversion to fibril structures. The overall time for growth in the latter stages is well described by the Lifshitz-Slyazov growth kinetics for crystallization from supersaturated solutions. The detailed analysis shows that elements of the three popular models, namely, nucleation and growth, templated assembly, and nucleated conformational conversion are present at various stages of fibril assembly.

Molecular simulation of protein dynamics in nanopores. I. Stability and folding

Discontinuous molecular dynamics simulations, together with the protein intermediate resolution model, an intermediate-resolution model of proteins, are used to carry out several microsecond-long simulations and study folding transition and stability of alpha-de novo-designed proteins in slit nanopores. Both attractive and repulsive interaction potentials between the proteins and the pore walls are considered. Near the folding temperature T(f) and in the presence of the attractive potential, the proteins undergo a repeating sequence of folding/partially folding/unfolding transitions, with T(f) decreasing with decreasing pore sizes. The unfolded states may even be completely adsorbed on the pore's walls with a negative potential energy. In such pores the energetic effects dominate the entropic effects. As a result, the unfolded state is stabilized, with a folding temperature T(f) which is lower than its value in the bulk and that, compared with the bulk, the folding rate decreases. The opposite is true in the presence of a repulsive interaction potential between the proteins and the walls. Moreover, for short proteins in very tight pores with attractive walls, there exists an unfolded state with only one alpha-helical hydrogen bond and an energy nearly equal to that of the folded state. The proteins have, however, high entropies, implying that they cannot fold onto their native structure, whereas in the presence of repulsive walls the proteins do attain their native structure. There is a pronounced asymmetry between the two termini of the protein with respect to their interaction with the pore walls. The effect of a variety of factors, including the pore size and the proteins' length, as well as the temperature, is studied in detail.

Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin

The computational sampling of rare, large-scale, conformational transitions in proteins is a well appreciated challenge-for which a number of potentially efficient path-sampling methodologies have been proposed. Here, we study a large-scale transition in a united-residue model of calmodulin using the "weighted ensemble" (WE) approach of Huber and Kim. Because of the model's relative simplicity, we are able to compare our results with brute-force simulations. The comparison indicates that the WE approach quantitatively reproduces the brute-force results, as assessed by considering (i) the reaction rate, (ii) the distribution of event durations, and (iii) structural distributions describing the heterogeneity of the paths. Importantly, the WE method is readily applied to more chemically accurate models, and by studying a series of lower temperatures, our results suggest that the WE method can increase efficiency by orders of magnitude in more challenging systems.

Computational models of molecular self-organization in cellular environments

The cellular environment creates numerous obstacles to efficient chemistry, as molecular components must navigate through a complex, densely crowded, heterogeneous, and constantly changing landscape in order to function at the appropriate times and places. Such obstacles are especially challenging to self-organizing or self-assembling molecular systems, which often need to build large structures in confined environments and typically have high-order kinetics that should make them exquisitely sensitive to concentration gradients, stochastic noise, and other non-ideal reaction conditions. Yet cells nonetheless manage to maintain a finely tuned network of countless molecular assemblies constantly forming and dissolving with a robustness and efficiency generally beyond what human engineers currently can achieve under even carefully controlled conditions. Significant advances in high-throughput biochemistry and genetics have made it possible to identify many of the components and interactions of this network, but its scale and complexity will likely make it impossible to understand at a global, systems level without predictive computational models. It is thus necessary to develop a clear understanding of how the reality of cellular biochemistry differs from the ideal models classically assumed by simulation approaches and how simulation methods can be adapted to accurately reflect biochemistry in the cell, particularly for the self-organizing systems that are most sensitive to these factors. In this review, we present approaches that have been undertaken from the modeling perspective to address various ways in which self-organization in the cell differs from idealized models.

Effects of macromolecular crowding on biochemical reaction equilibria: a molecular thermodynamic perspective

A molecular thermodynamic model is developed to investigate the effects of macromolecular crowding on biochemical reactions. Three types of reactions, representing protein folding/conformational isomerization, coagulation/coalescence, and polymerization/association, are considered. The reactants, products, and crowders are modeled as coarse-grained spherical particles or as polymer chains, interacting through hard-sphere interactions with or without nonbonded square-well interactions, and the effects of crowder size and chain length as well as product size are examined. The results predicted by this model are consistent with experimentally observed crowding effects based on preferential binding or preferential exclusion of the crowders. Although simple hard-core excluded-volume arguments do in general predict the qualitative aspects of the crowding effects, the results show that other intermolecular interactions can substantially alter the extent of enhancement or reduction of the equilibrium and can even change the direction of the shift. An advantage of the approach presented here is that competing reactions can be incorporated within the model.

Structure and aggregation of a helix-forming polymer

We have studied the competition between helix formation and aggregation for a simple polymer model. We present simulation results for a system of two such polymers, examining the potential of mean force, the balance between intermolecular and intramolecular interactions, and the promotion or disruption of secondary structure brought on by the proximity of the two molecules. In particular, we demonstrate that proximity between two such molecules can stabilize secondary structure. However, for this model, observed secondary structure is not stable enough to prevent collapse of the system into an unstructured globule.

Effects of chain length on the aggregation of model polyglutamine peptides: molecular dynamics simulations

Aggregation in the brain of polyglutamine-containing proteins is either a cause or an associated symptom of nine hereditary neurodegenerative disorders including Huntington's disease. The molecular level mechanisms by which these proteins aggregate are still unclear. In an effort to shed light on this important phenomenon, we are investigating the aggregation of model polyglutamine peptides using molecular-level computer simulation with a simplified model of polyglutamine that we have developed. This model accounts for the most important types of intra- and inter-molecular interactions-hydrogen bonding and hydrophobic interactions-while allowing the folding process to be simulated in a reasonable time frame. The model is used to examine the folding of isolated polyglutamine peptides 16, 32, and 48 residues long and the folding and aggregation of systems of 24 model polyglutamine peptides 16, 24, 32, 36, 40, and 48 residues long. Although the isolated polyglutamine peptides did form some alpha and beta backbone-backbone hydrogen bonds they did not have as many of these bonds as they would have if they had folded into a complete alpha helix or beta sheet. In one of the simulations on the isolated polyglutamine peptide 48 residues long, we observed a structure that resembles a beta helix. In the multi-chain simulations we observed amorphous aggregates at low temperatures, ordered aggregates with significant beta sheet character at intermediate temperatures, and random coils at high temperatures. We have found that the temperature at which the model peptides undergo the transition from amorphous aggregates to ordered aggregates and the temperature at which the model peptides undergo the transition from ordered aggregates to random coils increase with increasing chain length. Our finding that the stability of the ordered aggregates increases as the peptide chain length increases may help to explain the experimentally observed relation between polyglutamine tract length and aggregation in vitro and disease progression in vivo. We have also observed in our simulations that the optimal temperature for the formation of beta sheets increases with chain length up to 36 glutamine residues but not beyond. Equivalently, at fixed temperature we find a transition from a region dominated by random coils at chain lengths less than 36 to a region dominated by relatively ordered beta sheet structures at chain lengths greater than 36. Our finding of this critical chain length of 36 glutamine residues is interesting because a critical chain length of 37 glutamine residues has been observed experimentally.

Elucidating amyloid beta-protein folding and assembly: A multidisciplinary approach

Oligomeric, neurotoxic amyloid protein assemblies are thought to be causative agents in Alzheimer's and other neurodegenerative diseases. Development of oligomer-specific therapeutic agents requires a mechanistic understanding of the oligomerization process. This is a daunting task because amyloidogenic protein oligomers often are metastable and comprise structurally heterogeneous populations in equilibrium with monomers and fibrils. A single methodological approach cannot elucidate the entire protein assembly process. An integrated multidisciplinary program is required. We discuss here the synergistic application of in hydro, in vacuo, and in silico methods to the study of the amyloid beta-protein, the key pathogenetic agent in Alzheimer's disease.

Protein activity in bacterial inclusion bodies correlates with predicted aggregation rates

Recent data show that protein aggregation as bacterial inclusion bodies does not necessarily imply loss of biological activity. Here, we investigate the effect of a large set of single-point mutants of an aggregation-prone protein on its specific activity once deposited in inclusion bodies. The activity of such aggregates significantly correlates with the predicted aggregation rates for each mutant, suggesting that rationally tuning the kinetic competition between folding and aggregation might result in highly active, inclusion bodies. The exploration of this technology during recombinant protein production would have a significant biotechnological value.

The equilibrium properties and folding kinetics of an all-atom Go model of the Trp-cage

The ultrafast-folding 20-residue Trp-cage protein is quickly becoming a new benchmark for molecular dynamics studies. Already several all-atom simulations have probed its equilibrium and kinetic properties. In this work an all-atom Go model is used to accurately represent the side-chain packing and native atomic contacts of the Trp-cage. The model reproduces the hallmark thermodynamics cooperativity of small proteins. Folding simulations observe that in the fast-folding dominant pathway, partial alpha-helical structure forms before hydrophobic core collapse. In the slow-folding secondary pathway, partial core collapse occurs before helical structure. The slow-folding rate of the secondary pathway is attributed to the loss of side-chain rotational freedom, due to the early core collapse, which impedes the helix formation. A major finding is the observation of a low-temperature kinetic intermediate stabilized by a salt bridge between residues Asp-9 and Arg-16. Similar observations [R. Zhou, Proc. Natl. Acad. Sci. U.S.A. 100, 13280 (2003)] were reported in a recent study using an all-atom model of the Trp-cage in explicit water, in which the salt-bridge stabilized intermediate was hypothesized to be the origin of the ultrafast-folding mechanism. A theoretical mutation that eliminates the Asp-9-Arg-16 salt bridge, but leaves the residues intact, is performed. Folding simulations of the mutant Trp-cage observe a two-state free-energy landscape with no kinetic intermediate and a significant decrease in the folding rate, in support of the hypothesis.