Folding of a model three-helix bundle protein: a thermodynamic and kinetic analysis

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.

Configurational entropy, transition rates, and optimal interactions for rapid folding in coarse-grained model proteins

Under certain conditions, the dynamics of coarse-grained models of solvated proteins can be described using a Markov state model, which tracks the evolution of populations of configurations. The transition rates among states that appear in the Markov model can be determined by computing the relative entropy of states and their mean first passage times. In this paper, we present an adaptive method to evaluate the configurational entropy and the mean first passage times for linear chain models with discontinuous potentials. The approach is based on event-driven dynamical sampling in a massively parallel architecture. Using the fact that the transition rate matrix can be calculated for any choice of interaction energies at any temperature, it is demonstrated how each state's energy can be chosen such that the average time to transition between any two states is minimized. The methods are used to analyze the optimization of the folding process of two protein systems: the crambin protein and a model with frustration and misfolding. It is shown that the folding pathways for both systems are comprised of two regimes: first, the rapid establishment of local bonds, followed by the subsequent formation of more distant contacts. The state energies that lead to the most rapid folding encourage multiple pathways, and they either penalize folding pathways through kinetic traps by raising the energies of trapping states or establish an escape route from the trapping states by lowering free energy barriers to other states that rapidly reach the native state.

Nonnative contact effects in protein folding

The folding simulations of three ββα-motifs and β-barrel structured proteins (NTL9, NuG2b, and CspA) were performed to determine the important roles of native and nonnative contacts in protein folding.

Coarse-Grained Protein Model Coupled with a Coarse-Grained Water Model: Molecular Dynamics Study of Polyalanine-Based Peptides

The coupling of a coarse-grained (CG) protein model with the CG water model developed by Marrink et al. (J. Phys. Chem. B 2004, 108, 750) is presented. The model was used in the molecular dynamics studies of Ac-(Ala)6-Xaa-(Ala)7-NHMe, Xaa = Ala, Leu, Val, and Gly. A Gly mutation in the middle of polyalanine is found to destabilize the helix and stabilize the hairpin by favoring a type-II' turn and probably to speed up hairpin folding. The simulations allow us to derive thermodynamic parameters of, in particular, the helical propensities (s) of amino acids in these polyalanine-based peptides. The calculated s values are 1.18 (Ala), 0.84 (Leu), 0.30 (Val), and <0.02 (Gly) at 291 K, in excellent agreement with experimental values (R(2)=0.970). Analyses using a structural approach method show that the helical propensity difference of these amino acids mainly comes from solvation effect. Leu and Val have lower helical propensities than Ala mainly because the larger side chains shield the solvation of helical structures, while Gly has a much poorer helical propensity mainly due to the much better solvation for the coil structures than for the helical structures. Overall, the model is at least about 10(2) times faster than current all-atom MD methods with explicit solvent.

The role of semidisorder in temperature adaptation of bacterial FlgM proteins

Probabilities of disorder for FlgM proteins of 39 species whose optimal growth temperature ranges from 273 K (0°C) to 368 K (95°C) were predicted by a newly developed method called Sequence-based Prediction with Integrated NEural networks for Disorder (SPINE-D). We showed that the temperature-dependent behavior of FlgM proteins could be separated into two subgroups according to their sequence lengths. Only shorter sequences evolved to adapt to high temperatures (>318 K or 45°C). Their ability to adapt to high temperatures was achieved through a transition from a fully disordered state with little secondary structure to a semidisordered state with high predicted helical probability at the N-terminal region. The predicted results are consistent with available experimental data. An analysis of all orthologous protein families in 39 species suggests that such a transition from a fully disordered state to semidisordered and/or ordered states is one of the strategies employed by nature for adaptation to high temperatures.

Polymer uncrossing and knotting in protein folding, and their role in minimal folding pathways

We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would have been required to avoid such events. A depth-first tree search algorithm is applied to find minimal transformations to fold [Formula: see text], [Formula: see text], [Formula: see text], and knotted proteins. In all cases, the extra uncrossing/non-crossing distance is a small fraction of the total distance travelled by a ghost chain. Different structural classes may be distinguished by the amount of extra uncrossing distance, and the effectiveness of such discrimination is compared with other order parameters. It was seen that non-crossing distance over chain length provided the best discrimination between structural and kinetic classes. The scaling of non-crossing distance with chain length implies an inevitable crossover to entanglement-dominated folding mechanisms for sufficiently long chains. We further quantify the minimal folding pathways by collecting the sequence of uncrossing moves, which generally involve leg, loop, and elbow-like uncrossing moves, and rendering the collection of these moves over the unfolded ensemble as a multiple-transformation "alignment". The consensus minimal pathway is constructed and shown schematically for representative cases of an [Formula: see text], [Formula: see text], and knotted protein. An overlap parameter is defined between pathways; we find that [Formula: see text] proteins have minimal overlap indicating diverse folding pathways, knotted proteins are highly constrained to follow a dominant pathway, and [Formula: see text] proteins are somewhere in between. Thus we have shown how topological chain constraints can induce dominant pathway mechanisms in protein folding.

Folding helical proteins in explicit solvent using dihedral-biased tempering

Using a single-trajectory-based tempering method with a high-temperature dihedral bias, we repeatedly folded four helical proteins [α(3)D (PDB ID: 2A3D, 73 residues), α(3)W (1LQ7, 67 residues), Fap1-NR(α) (2KUB, 81 residues) and S-836 (2JUA, 102 residues)] and some of the mutants in explicit solvent within several microseconds. The lowest root-mean-square deviations of backbone atoms from the experimentally determined structures were 1.9, 1.4, 1.0, and 2.1 Å, respectively. Cluster analyses of folding trajectories showed the native conformation usually occupied the most populated cluster. The simulation protocol can be applied to large-scale simulations of other helical proteins on commonly accessible computing platforms.

An effective solvent theory connecting the underlying mechanisms of osmolytes and denaturants for protein stability

An all-atom Gō model of Trp-cage protein is simulated using discontinuous molecular dynamics in an explicit minimal solvent, using a single, contact-based interaction energy between protein and solvent particles. An effective denaturant or osmolyte solution can be constructed by making the interaction energy attractive or repulsive. A statistical mechanical equivalence is demonstrated between this effective solvent model and models in which proteins are immersed in solutions consisting of water and osmolytes or denaturants. Analysis of these studies yields the following conclusions: 1), Osmolytes impart extra stability to the protein by reducing the entropy of the unfolded state. 2), Unfolded states in the presence of osmolyte are more collapsed than in water. 3), The folding transition in osmolyte solutions tends to be less cooperative than in water, as determined by the ratio of van 't Hoff to calorimetric enthalpy changes. The decrease in cooperativity arises from an increase in native structure in the unfolded state, and thus a lower thermodynamic barrier at the transition midpoint. 4), Weak denaturants were observed to destabilize small proteins not by lowering the unfolded enthalpy, but primarily by swelling the unfolded state and raising its entropy. However, adding a strong denaturant destabilizes proteins enthalpically. 5), The folding transition in denaturant-containing solutions is more cooperative than in water. 6), Transfer to a concentrated osmolyte solution with purely hard-sphere steric repulsion significantly stabilizes the protein, due to excluded volume interactions not present in the canonical Tanford transfer model. 7), Although a solution with hard-sphere interactions adds a solvation barrier to native contacts, the folding is nevertheless less cooperative for reasons 1-3 above, because a hard-sphere solvent acts as a protecting osmolyte.

Turbulent phenomena in protein folding

Protein folding and hydrodynamic turbulence are two long-standing challenges, in molecular biophysics and fluid dynamics, respectively. The theories of these phenomena have been developed independently and used different formalisms. Here we show that the protein folding flows can be surprisingly similar to turbulent fluid flows. Studying a benchmark model protein (an SH3 domain), we have found that the flows for the slow folding trajectories of the protein, in which a partly formed N- and C-terminal β sheet hinders the RT loop from attaching to the protein core, have many properties of turbulent flows of a fluid. The flows are analyzed in a three-dimensional (3D) space of collective variables, which are the numbers of native contacts between the terminal β strands, between the RT loop and the protein core, and the rest of the native contacts. We have found that the flows have fractal nature and are filled with 3D eddies; the latter contain strange attractors, at which the tracer flow paths behave as saddle trajectories. Two regions of the space increment have been observed, in which the flux variations are self-similar with the scaling exponent h=1/3, in surprising agreement with the Kolmogorov inertial range theory of turbulence. In one region, the cascade of protein rearrangements is directed from larger to smaller scales (net folding), and in the other, it is oppositely directed (net unfolding). Folding flows for the fast trajectories are essentially "laminar" and do not have the property of self-similarity. Based on the results of our study, we infer, and support this inference by simulations, that the origin of the similarity between the protein folding and turbulent motion of a fluid is in a cascade mechanism of structural transformations in the systems that underlies these phenomena.

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.

Folding processes of the B domain of protein A to the native state observed in all-atom ab initio folding simulations

Reaching the native states of small proteins, a necessary step towards a comprehensive understanding of the folding mechanisms, has remained a tremendous challenge to ab initio protein folding simulations despite the extensive effort. In this work, the folding process of the B domain of protein A (BdpA) has been simulated by both conventional and replica exchange molecular dynamics using AMBER FF03 all-atom force field. Started from an extended chain, a total of 40 conventional (each to 1.0 micros) and two sets of replica exchange (each to 200.0 ns per replica) molecular dynamics simulations were performed with different generalized-Born solvation models and temperature control schemes. The improvements in both the force field and solvent model allowed successful simulations of the folding process to the native state as demonstrated by the 0.80 A C(alpha) root mean square deviation (RMSD) of the best folded structure. The most populated conformation was the native folded structure with a high population. This was a significant improvement over the 2.8 A C(alpha) RMSD of the best nativelike structures from previous ab initio folding studies on BdpA. To the best of our knowledge, our results demonstrate, for the first time, that ab initio simulations can reach the native state of BdpA. Consistent with experimental observations, including Phi-value analyses, formation of helix II/III hairpin was a crucial step that provides a template upon which helix I could form and the folding process could complete. Early formation of helix III was observed which is consistent with the experimental results of higher residual helical content of isolated helix III among the three helices. The calculated temperature-dependent profile and the melting temperature were in close agreement with the experimental results. The simulations further revealed that phenylalanine 31 may play critical to achieve the correct packing of the three helices which is consistent with the experimental observation. In addition to the mechanistic studies, an ab initio structure prediction was also conducted based on both the physical energy and a statistical potential. Based on the lowest physical energy, the predicted structure was 2.0 A C(alpha) RMSD away from the experimentally determined structure.

Probing protein aggregation using discrete molecular dynamics

Understanding the role of biomolecular dynamics in cellular processes leading to human diseases and the ability to rationally manipulate these processes is of fundamental importance in scientific research. The last decade has witnessed significant progress in probing biophysical behavior of proteins. However, we are still limited in understanding how changes in protein dynamics and inter-protein interactions occurring in short length- and time-scales lead to aberrations in their biological function. Bridging this gap in biology probed using computer simulations marks a challenging frontier in computational biology. Here we examine hypothesis-driven simplified protein models in conjunction with discrete molecular dynamics in the study of protein aggregation, implicated in series of neurodegenerative diseases, such as Alzheimer's and Huntington's diseases. Discrete molecular dynamics simulations of simplified protein models have emerged as a powerful methodology with its ability to bridge the gap in time and length scales from protein dynamics to aggregation, and provide an indispensable tool for probing protein aggregation.

Parallel folding pathways in the SH3 domain protein

The transition-state ensemble (TSE) is the set of protein conformations with an equal probability to fold or unfold. Its characterization is crucial for an understanding of the folding process. We determined the TSE of the src-SH3 domain protein by using extensive molecular dynamics simulations of the Go model and computing the folding probability of a generated set of TSE candidate conformations. We found that the TSE possesses a well-defined hydrophobic core with variable enveloping structures resulting from the superposition of three parallel folding pathways. The most preferred pathway agrees with the experimentally determined TSE, while the two least preferred pathways differ significantly. The knowledge of the different pathways allows us to design the interactions between amino acids that guide the protein to fold through the least preferred pathway. This particular design is akin to a circular permutation of the protein. The finding motivates the hypothesis that the different experimentally observed TSEs in homologous proteins and circular permutants may represent potentially available pathways to the wild-type protein.

Generalized simulated annealing applied to protein folding studies

During the last few years, computational simulations based on the atomic description of biological molecules have resulted in significant advances in the comprehension of biological processes. It is well known, however, that a molecular system may have a great number of conformations due to the large number of rotation of degrees of freedom around chemical bonds, leading to several local minima on the energy hypersurface. It has been proposed though, that proteins express their biological function when their structure is close to a conformation with energy global minimum. To help solve the protein-folding problem, we use a new strategy based on Simulated Annealing methods. These methods have been well suited for a large extent of optimization problems, especially those containing many local minima. In fact, this work applies the Generalized Simulated Annealing method (GSA) coupled to the GROMOS96 Molecular Force Field to research the minimum energy conformation of 18-alanine. We show that the q(T) GSA parameter can be used to control the freezing process during the annealing procedure, and to avoid polypeptide chains to be trapped in energy local minima. We scanned the q-values for visiting (q(V)) and accepting (q(A)) functions for q(T) values ranging from 1 to 3, and found the best values to obtain an alpha-helix conformation for the polyalanine peptide, which is the conformation with energy global minimum. Global optimization methods also exemplify a class of applications that requires a large amount of computational resources, being suitable for Grid computing. To implement a Grid computing platform, we developed and tested a Grid environment based on MYGRID middleware, which is a technology that can employ all machines accessed by the user to run the application.

Temperature-dependent folding pathways of Pin1 WW domain: an all-atom molecular dynamics simulation of a Gō model

We study the folding thermodynamics and kinetics of the Pin1 WW domain, a three-stranded beta-sheet protein, by using all-atom (except nonpolar hydrogens) discontinuous molecular dynamics simulations at various temperatures with a Gō model. The protein exhibits a two-state folding kinetics near the folding transition temperature. A good agreement between our simulations and the experimental measurements by the Gruebele group has been found, and the simulation sheds new insights into the structure of transition state, which is hard to be straightforwardly captured in experiments. The simulation also reveals that the folding pathways at approximately the transition temperature and at low temperatures are much different, and an intermediate state at a low temperature is predicted. The transition state of this small beta-protein at its folding transition temperature has a well-established hairpin 1 made of beta1 and beta2 strands while its low-temperature kinetic intermediate has a formed hairpin 2 composed of beta2 and beta3 strands. Theoretical results are compared with other simulation results as well as available experimental data. This study confirms that specific side-chain packing in an all-atom Gō model can yield a reasonable prediction of specific folding kinetics for a given protein. Different folding behaviors at different temperatures are interpreted in terms of the interplay of entropy and enthalpy in folding process.

Multiscale modeling of nucleosome dynamics

Nucleosomes form the fundamental building blocks of chromatin. Subtle modifications of the constituent histone tails mediate chromatin stability and regulate gene expression. For this reason, it is important to understand structural dynamics of nucleosomes at atomic levels. We report a novel multiscale model of the fundamental chromatin unit, a nucleosome, using a simplified model for rapid discrete molecular dynamics simulations and an all-atom model for detailed structural investigation. Using a simplified structural model, we perform equilibrium simulations of a single nucleosome at various temperatures. We further reconstruct all-atom nucleosome structures from simulation trajectories. We find that histone tails bind to nucleosomal DNA via strong salt-bridge interactions over a wide range of temperatures, suggesting a mechanism of chromatin structural organization whereby histone tails regulate inter- and intranucleosomal assemblies via binding with nucleosomal DNA. We identify specific regions of the histone core H2A/H2B-H4/H3-H3/H4-H2B/H2A, termed "cold sites", which retain a significant fraction of contacts with adjoining residues throughout the simulation, indicating their functional role in nucleosome organization. Cold sites are clustered around H3-H3, H2A-H4 and H4-H2A interhistone interfaces, indicating the necessity of these contacts for nucleosome stability. Essential dynamics analysis of simulation trajectories shows that bending across the H3-H3 is a prominent mode of intranucleosomal dynamics. We postulate that effects of salts on mononucleosomes can be modeled in discrete molecular dynamics by modulating histone-DNA interaction potentials. Local fluctuations in nucleosomal DNA vary significantly along the DNA sequence, suggesting that only a fraction of histone-DNA contacts make strong interactions dominating mononucleosomal dynamics. Our findings suggest that histone tails have a direct functional role in stabilizing higher-order chromatin structure, mediated by salt-bridge interactions with adjacent DNA.

Discontinuous molecular dynamics for rigid bodies: Applications

Event-driven molecular dynamics simulations are carried out on two rigid-body systems which differ in the symmetry of their molecular mass distributions. First, simulations of methane in which the molecules interact via discontinuous potentials are compared with simulations in which the molecules interact through standard continuous Lennard-Jones potentials. It is shown that under similar conditions of temperature and pressure, the rigid discontinuous molecular dynamics method reproduces the essential dynamical and structural features found in continuous-potential simulations at both gas and liquid densities. Moreover, the discontinuous molecular dynamics approach is demonstrated to be between 3 and 100 times more efficient than the standard molecular dynamics method depending on the specific conditions of the simulation. The rigid discontinuous molecular dynamics method is also applied to a discontinuous-potential model of a liquid composed of rigid benzene molecules, and equilibrium and dynamical properties are shown to be in qualitative agreement with more detailed continuous-potential models of benzene. The few qualitative differences in the angular dynamics of the two models are related to the relatively crude treatment of variations in the discontinuous repulsive interactions as one benzene molecule rotates by another.

Role of electrostatic interactions in amyloid beta-protein (A beta) oligomer formation: a discrete molecular dynamics study

Pathological folding and oligomer formation of the amyloid beta-protein (A beta) are widely perceived as central to Alzheimer's disease. Experimental approaches to study A beta self-assembly provide limited information because most relevant aggregates are quasi-stable and inhomogeneous. We apply a discrete molecular dynamics approach combined with a four-bead protein model to study oligomer formation of A beta. We address the differences between the two most common A beta alloforms, A beta 40 and A beta 42, which oligomerize differently in vitro. Our previous study showed that, despite simplifications, our discrete molecular dynamics approach accounts for the experimentally observed differences between A beta 40 and A beta 42 and yields structural predictions amenable to in vitro testing. Here we study how the presence of electrostatic interactions (EIs) between pairs of charged amino acids affects A beta 40 and A beta 42 oligomer formation. Our results indicate that EIs promote formation of larger oligomers in both A beta 40 and A beta 42. Both A beta 40 and A beta 42 display a peak at trimers/tetramers, but A beta 42 displays additional peaks at nonamers and tetradecamers. EIs thus shift the oligomer size distributions to larger oligomers. Nonetheless, the A beta 40 size distribution remains unimodal, whereas the A beta 42 distribution is trimodal, as observed experimentally. We show that structural differences between A beta 40 and A beta 42 that already appear in the monomer folding, are not affected by EIs. A beta 42 folded structure is characterized by a turn in the C-terminus that is not present in A beta 40. We show that the same C-terminal region is also responsible for the strongest intermolecular contacts in A beta 42 pentamers and larger oligomers. Our results suggest that this C-terminal region plays a key role in the formation of A beta 42 oligomers and the relative importance of this region increases in the presence of EIs. These results suggest that inhibitors targeting the C-terminal region of A beta 42 oligomers may be able to prevent oligomer formation or structurally modify the assemblies to reduce their toxicity.

Discontinuous molecular dynamics simulation study of polymer collapse

Discontinuous molecular dynamics simulations were used to study the coil-globule transition of a polymer in an explicit solvent. Two different versions of the model were employed, which are differentiated by the nature of monomer-solvent, solvent-solvent, and nonbonded monomer-monomer interactions. For each case, a model parameter lambda determines the degree of hydrophobicity of the monomers by controlling the degree of energy mismatch between the monomers and solvent particles. We consider a lambda-driven coil-globule transition at constant temperature. The simulations are used to calculate average static structure factors, which are then used to determine the scaling exponents of the system in order to determine the theta-point values lambda(theta) separating the coil from the globule state. For each model we construct coil-globule phase diagrams in terms of lambda and the particle density rho. Additionally, we explore for each model the effects of varying the range of the attractive interactions on the phase boundary separating the coil and globule phases. The results are analyzed in terms of a simple Flory-type theory of the collapse transition.

Testing simplified proteins models of the hPin1 WW domain

The WW domain of the human Pin1 protein for its simple topology and large amount of experimental data is an ideal candidate to assess theoretical approaches to protein folding. The purpose of this work is to compare the reliability of the chemically based Sorenson/Head-Gordon (SHG) model and a standard native centric model in reproducing, through molecular dynamics simulations, some of the well known features of the folding transition of this small domain. Our results show that the Gō model correctly reproduces the cooperative, two-state, folding mechanism of the WW-domain, while the SHG model predicts a transition occurring in two stages: a collapse, followed by a structural rearrangement. The lack of a cooperative folding in the SHG simulations appears to be related to the nonfunnel shape of the energy landscape featuring a partitioning of the native valley in subbasins corresponding to different chain chiralities. However, the SHG approach remains more reliable in estimating the phi-values with respect to Gō-like description. This may suggest that the WW-domain folding process is stirred by energetic and topological factors as well, and it highlights the better suitability of chemically based models in simulating mutations.

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.

Multiple folding mechanisms of protein ubiquitin

Based on the C(alpha) Go-type model, the folding kinetics and mechanisms of protein ubiquitin with mixed alpha/beta topology are studied by molecular dynamics simulations. The relaxation kinetics shows that there are three phases, namely the major phase, the intermediate phase and the slowest minor phase. The existence of these three phases are relevant to the phenomenon found in experiments. According to our simulations, the folding at high temperatures around the folding transition temperature T(f) is of a two-state process, and the folding nucleus is consisted of contacts between the front end of alpha-helix and the turn(4). The folding at low temperature (approximately T = 0.8) is also studied, where an A-state like structure is found lying on the major folding pathway. The appearance of this structure is related to the stability of the first part (residue 1-51) of protein ubiquitin. As the temperature decreases, the formation of secondary structures, tertiary structures and collapse of the protein are found to be decoupled gradually and the folding mechanism changes from the nucleation-condensation to the diffusion-collision. This feature indicates a unifying common folding mechanism for proteins. The intermediate phase is also studied and is found to represent a folding process via a long-lived intermediate state which is stabilized by strong interactions between the beta(1) and the beta(5) strand. These strong interactions are important for the function of protein ubiquitin as a molecular chaperone. Thus the intermediate phase is assumed as a byproduct of the requirement of protein function. In addition, the validity of the current Go-model is also investigated, and a lower limited temperature for protein ubiquitin T(limit) = 0.8 is proposed. At temperatures higher than this value, the kinetic traps due to glass dynamics cannot be significantly populated and the intermediate states can be reliably identified although there is slight chevron rollover in the folding rates. At temperature lower than T(limit), however, the traps due to glass dynamics become dominant and may be mistaken for real intermediate states. This limitation of valid temperature range prevents us to reveal the burst phase intermediate in the major folding phase since it might only be stabilized at temperatures lower than T(limit), according to experiments. Our works show that caution must be taken when studying low-temperature intermediate states by using the C(alpha) Go-models.

Ab initio discrete molecular dynamics approach to protein folding and aggregation

Understanding the toxicity of amyloidogenic protein aggregates and designing therapeutic approaches require the knowledge of their structure at atomic resolution. Although solid-state NMR, X-ray diffraction, and other experimental techniques are capable of discerning the protein fibrillar structure, determining the structures of early aggregates, called oligomers, is a challenging experimental task. Computational studies by all-atom molecular dynamics, which provides a complete description of a protein in the solvent, are typically limited to study folding of smaller protein or aggregation of a small number of short protein fragments. We review an efficient ab initio computer simulation approach to protein folding and aggregation using discrete molecular dynamics (DMD) in combination with several coarse-grained protein models and implicit solvent. This approach involves different complexity levels in both the protein model and the interparticle interactions. Starting from the simplest protein model with minimal interactions, and gradually increasing its complexity, while guided by in vitro findings, we can systematically select the key features of the protein model and interactions that drive protein folding and aggregation. Because the method used in this DMD approach does not require any knowledge of the native or any other state of the protein, it can be applied to study degenerative disorders associated with protein misfolding and aberrant protein aggregation. The choice of the coarse-grained model depends on the complexity of the protein and specific questions to be addressed, which are mostly suggested by in vitro findings. Thus, we illustrate our approach on amyloid beta-protein (Abeta) associated with Alzheimer's disease (AD). Despite the simplifications introduced in the DMD approach, the predicted Abeta conformations are in agreement with existing experimental data. The in silico findings also provide further insights into the structure and dynamics of Abeta folding and oligomer formation that are amenable to in vitro testing.

Simple but predictive protein models

The traditional approach to computational biophysics studies of molecular systems is brute force molecular dynamics simulations under the conditions of interest. The disadvantages of this approach are that the time and length scales that are accessible to computer simulations often do not reach biologically relevant scales. An alternative approach, which we call intuitive modeling, is hypothesis-driven and based on tailoring simplified protein models to the systems of interest. Using intuitive modeling, the length and time scales that can be achieved using simplified protein models exceed those of traditional molecular-dynamic simulations. Here, we describe several recent studies that signify the predictive power of simplified protein models within the intuitive-modeling approach.

A Single Disulfide Bond Differentiates Aggregation Pathways of ß2-Microglobulin

Deposition of wild-type beta2-microglobulin (beta2m) into amyloid fibrils is a complication in patients undergoing long-term hemodialysis. The native beta-sandwich fold of beta2m has a highly conserved disulfide bond linking Cys25 and Cys80. Oxidized beta2m forms needle-like amyloid fibrils at pH 2.5 in vitro, whereas reduced beta2m, at acid pH, in which the intra-chain disulfide bond is disrupted, cannot form typical fibrils. Instead, reduced beta2m forms thinner and more flexible filaments. To uncover the difference in molecular mechanisms underlying the aggregation of the oxidized and reduced beta2m, we performed molecular dynamics simulations of beta2m oligomerization under oxidized and reduced conditions. We show that, consistent with experimental observations, the oxidized beta2m forms domain-swapped dimer, in which the two proteins exchange their N-terminal segments complementing each other. In contrast, both dimers and trimers, formed by reduced beta2m, are comprised of parallel beta-sheets between monomers and stabilized by the hydrogen bond network along the backbone. The oligomerized monomers are in extended conformations, capable of further aggregation. We find that both reduced and oxidized dimers are thermodynamically less stable than their corresponding monomers, indicating that beta2m oligomerization is not accompanied by the formation of a thermodynamically stable dimer. Our studies suggest that the different aggregation pathways of oxidized and reduced beta2m are dictated by the formation of distinct precursor oligomeric species that are modulated by Cys25-Cys80 disulfide-bonds. We propose that the propagation of domain swapping is the aggregation mechanism for the oxidized beta2m, while "parallel stacking" of partially unfolded beta2m is the aggregation mechanism for the reduced beta2m.

Thermodynamics of Gō-type models for protein folding

Go-type potentials, based on the inter-residue contacts present in the native structure of a protein, are frequently used to predict dynamic and structural features of the folding pathways through computer simulations. However, the mathematical form used to define the model interactions includes several arbitrary choices, whose consequences are not usually analyzed. In this work, we use a simple off-lattice protein model and a parallel tempering Monte Carlo simulation technique to carry out such analysis, centered in the thermodynamic characteristics of the folding transition. We show how the definition of a native contact has a deep impact on the presence of simple or complex transitions, with or without thermodynamic intermediates. In addition, we have checked that the width of the attractive wells has a profound effect on the free-energy barrier between the folded and unfolded states, mainly through its influence on the entropy of the denatured state.

Scaling Behavior and Structure of Denatured Proteins

An ensemble of random-coil conformations with no persistent structures has long been accepted as the classical model of denatured proteins due to its consistency with the experimentally determined scaling of protein sizes. However, recent NMR spectroscopy studies on proteins at high chemical denaturant concentrations suggest the presence of significant amounts of native-like structures, in contrast to the classical random-coil picture. To reconcile these seemingly controversial observations, we examine thermally denatured states of experimentally characterized proteins by using molecular dynamics simulations. For all studied proteins, we find that denatured states indeed have strong local conformational bias toward native states while a random-coil power law scaling of protein sizes is preserved. In addition, we explain why experimentally determined size of the protein creatine kinase does not follow general scaling. In simulations, we observe that this protein exhibits a stable intermediate state, the size of which is consistent with the reported experimental observation.

Free-energy landscape of the villin headpiece in an all-atom force field

We investigate the landscape of the internal free-energy of the 36 amino acid villin headpiece with a modified basin hopping method in the all-atom force field PFF01, which was previously used to predictively fold several helical proteins with atomic resolution. We identify near native conformations of the protein as the global optimum of the force field. More than half of the twenty best simulations started from random initial conditions converge to the folding funnel of the native conformation, but several competing low-energy metastable conformations were observed. From 76,000 independently generated conformations we derived a decoy tree which illustrates the topological structure of the entire low-energy part of the free-energy landscape and characterizes the ensemble of metastable conformations. These emerge as similar in secondary content, but differ in tertiary arrangement.

Self-similarity and protein chains

Fractal properties of 5526 different protein chains are investigated. Characteristic fractal behavior for different molecular systems is obtained from the fractal dimension analysis, which shows that the dimension is delta=2.47 . This dimension gives a measure of the protein compactness. The present finding indicates that the fractal analysis describes some structural properties of proteins and corroborates the explanation about multifractality in the energy hypersurface.

In silico study of amyloid beta-protein folding and oligomerization

Experimental findings suggest that oligomeric forms of the amyloid beta protein (Abeta) play a critical role in Alzheimer's disease. Thus, elucidating their structure and the mechanisms of their formation is critical for developing therapeutic agents. We use discrete molecular dynamics simulations and a four-bead protein model to study oligomerization of two predominant alloforms, Abeta40 and Abeta42, at the atomic level. The four-bead model incorporates backbone hydrogen-bond interactions and amino acid-specific interactions mediated through hydrophobic and hydrophilic elements of the side chains. During the simulations we observe monomer folding and aggregation of monomers into oligomers of variable sizes. Abeta40 forms significantly more dimers than Abeta42, whereas pentamers are significantly more abundant in Abeta42 relative to Abeta40. Structure analysis reveals a turn centered at Gly-37-Gly-38 that is present in a folded Abeta42 monomer but not in a folded Abeta40 monomer and is associated with the first contacts that form during monomer folding. Our results suggest that this turn plays an important role in Abeta42 pentamer formation. Abeta pentamers have a globular structure comprising hydrophobic residues within the pentamer's core and hydrophilic N-terminal residues at the surface of the pentamer. The N termini of Abeta40 pentamers are more spatially restricted than Abeta42 pentamers. Abeta40 pentamers form a beta-strand structure involving Ala-2-Phe-4, which is absent in Abeta42 pentamers. These structural differences imply a different degree of hydrophobic core exposure between pentamers of the two alloforms, with the hydrophobic core of the Abeta42 pentamer being more exposed and thus more prone to form larger oligomers.

Predictive in Silico All-Atom Folding of a Four-Helix Protein with a Free-Energy Model

We report the predictive all-atom folding of the 60 amino acid four-helix bacterial ribosomal protein (BRP) L20 with a stochastic evolutionary optimization method in a free-energy force field. The energetically best, as well as six of the 10 lowest conformations, converge to a near-native structure. All of the 10 best energy conformations share the secondary structure elements of the native conformation, but differ in their tertiary alignment. The best conformation has a backbone root-mean-square deviation of 4.6 A to the native conformation and reproduces most distance constraints of the NMR experiment to 1.5 A resolution. Starting from random initial conditions, the native content of the simulated population increases more than 60-fold in the course of the simulation. These data demonstrate the feasibility of predictive unbiased all-atom protein folding with present day computational resources for the BRP L20.

New Insights into FAK Signaling and Localization Based on Detection of a FAT Domain Folding Intermediate

Mounting evidence suggests that the focal adhesion targeting (FAT) domain, an antiparallel four-helix bundle, exists in alternative conformations that may modulate phosphorylation, ligand binding, and the subcellular localization of focal adhesion kinase (FAK). In order to characterize the conformational dynamics of the FAT domain, we have developed a novel method for reconstructing the folding pathway of the FAT domain by using discrete molecular dynamics (DMD) simulations, with free energy constraints derived from NMR hydrogen exchange data. The DMD simulations detect a folding intermediate, in which a cooperative unfolding event causes helix 1 to lose helical character while separating from the helix bundle. The conformational dynamic features of helix 1 in the intermediate state of the FAT domain are likely to facilitate Y926 phosphorylation, yet interfere with paxillin binding. The presence of this intermediate state in vivo may promote FAK signaling via the ERK/MAPK pathway and by release of FAK from focal adhesions.

Experimental resolution of early steps in protein folding: testing molecular dynamics simulations

Time-resolved Tyr fluorescence spectroscopy coupled with a laser-induced temperature-jump (T-jump) was employed to follow the folding relaxation dynamics of the B-domain of Staphylococcal protein A. The single Tyr is located in helix 1 (H1) and is a sensitive probe of the structure of this helix and the overall helical bundle structure. The results from this study were compared to those from a complementary infrared T-jump study on this protein [Vu, D. M.; Myers, J. K.; Oas, T. G.; Dyer, R. B. Biochemistry 2004, 43, 3582]. Both methods detect a microsecond process that follows the cooperative relaxation of the helical bundle core. However, a fast process (10-7 s) that follows the relaxation of the individual helices was observed only with the infrared probe. Thus, fast formation of H1 is not observed, but rather H1 forms in the microsecond phase, concomitantly with the docking to (and stabilization by) the other two helices to form the helical bundle structure. This observation validates the results of several previous molecular dynamics simulations that predict H1 formation only in the final assembly of the helix bundle.

An all-atom force field for tertiary structure prediction of helical proteins

We have developed an all-atom free-energy force field (PFF01) for protein tertiary structure prediction. PFF01 is based on physical interactions and was parameterized using experimental structures of a family of proteins believed to span a wide variety of possible folds. It contains empirical, although sequence-independent terms for hydrogen bonding. Its solvent-accessible surface area solvent model was first fit to transfer energies of small peptides. The parameters of the solvent model were then further optimized to stabilize the native structure of a single protein, the autonomously folding villin headpiece, against competing low-energy decoys. Here we validate the force field for five nonhomologous helical proteins with 20-60 amino acids. For each protein, decoys with 2-3 A backbone root mean-square deviation and correct experimental Cbeta-Cbeta distance constraints emerge as those with the lowest energy.

The protein folding 'speed limit'

How fast can a protein possibly fold? This question has stimulated experimentalists to seek fast folding proteins and to engineer them to fold even faster. Proteins folding at or near the speed limit are prime candidates for all-atom molecular dynamics simulations. They may also have no free energy barrier, allowing the direct observation of intermediate structures on the pathways from the unfolded to the folded state. Both experimental and theoretical approaches predict a speed limit of approximately N/100micros for a generic N-residue single-domain protein, with alpha proteins folding faster than beta or alphabeta. The predicted limits suggest that most known ultrafast folding proteins can be engineered to fold more than ten times faster.

Probing the folding and unfolding dynamics of secondary and tertiary structures in a three-helix bundle protein

Fast relaxation kinetics studies of the B-domain of staphylococcal protein A were performed to characterize the folding and unfolding of this small three-helix bundle protein. The relaxation kinetics were initiated using a laser-induced temperature jump and probed using time-resolved infrared spectroscopy. The kinetics monitored within the amide I' absorbance of the polypeptide backbone exhibit two distinct kinetics phases with nanosecond and microsecond relaxation times. The fast kinetics relaxation time is close to the diffusion limits placed on protein folding reactions. The fast kinetics phase is dominated by the relaxation of the solvated helix (nu = 1632 cm(-1)), which reports on the fast relaxation of the individual helices. The slow kinetics phase follows the cooperative relaxation of the native helical bundle core that is monitored by both solvated (nu = 1632 cm(-1)) and buried helical IR bands (nu = 1652 cm(-1)). The folding rates of the slow kinetics phase calculated over an extended temperature range indicate that the core formation of this protein follows a pathway that is energetically downhill. The unfolding rates are much more strongly temperature-dependent indicating an activated process with a large energy barrier. These results provide significant insight into the primary process of protein folding and suggest that fast formation of helices can drive the folding of helical proteins.

Force-Clamp Spectroscopy Monitors the Folding Trajectory of a Single Protein

We used force-clamp atomic force microscopy to measure the end-to-end length of the small protein ubiquitin during its folding reaction at the single-molecule level. Ubiquitin was first unfolded and extended at a high force, then the stretching force was quenched and protein folding was observed. The folding trajectories were continuous and marked by several distinct stages. The time taken to fold was dependent on the contour length of the unfolded protein and the stretching force applied during folding. The folding collapse was marked by large fluctuations in the end-to-end length of the protein, but these fluctuations vanished upon the final folding contraction. These direct observations of the complete folding trajectory of a protein provide a benchmark to determine the physical basis of the folding reaction.

Can Contact Potentials Reliably Predict Stability of Proteins?

The simplest approximation of interaction potential between amino acid residues in proteins is the contact potential, which defines the effective free energy of a protein conformation by a set of amino acid contacts formed in this conformation. Finding a contact potential capable of predicting free energies of protein states across a variety of protein families will aid protein folding and engineering in silico on a computationally tractable time-scale. We test the ability of contact potentials to accurately and transferably (across various protein families) predict stability changes of proteins upon mutations. We develop a new methodology to determine the contact potentials in proteins from experimental measurements of changes in protein's thermodynamic stabilities (DeltaDeltaG) upon mutations. We apply our methodology to derive sets of contact interaction parameters for a hierarchy of interaction models including solvation and multi-body contact parameters. We test how well our models reproduce experimental measurements by statistical tests. We evaluate the maximum accuracy of predictions obtained by using contact potentials and the correlation between parameters derived from different data-sets of experimental (DeltaDeltaG) values. We argue that it is impossible to reach experimental accuracy and derive fully transferable contact parameters using the contact models of potentials. However, contact parameters may yield reliable predictions of DeltaDeltaG for datasets of mutations confined to the same amino acid positions in the sequence of a single protein.

Mechanism for the alpha-helix to beta-hairpin transition

The aggregation of alpha-helix-rich proteins into beta-sheet-rich amyloid fibrils is associated with fatal diseases, such as Alzheimer's disease and prion disease. During an aggregation process, protein secondary structure elements-alpha-helices-undergo conformational changes to beta-sheets. The fact that proteins with different sequences and structures undergo a similar transition on aggregation suggests that the sequence nonspecific hydrogen bond interaction among protein backbones is an important factor. We perform molecular dynamics simulations of a polyalanine model, which is an alpha-helix in its native state and observe a metastable beta-hairpin intermediate. Although a beta-hairpin has larger potential energy than an alpha-helix, the entropy of a beta-hairpin is larger because of fewer constraints imposed by the hydrogen bonds. In the vicinity of the transition temperature, we observe the interconversion of the alpha-helix and beta-sheet states via a random coil state. We also study the effect of the environment by varying the relative strength of side-chain interactions for a designed peptide-an alpha-helix in its native state. For a certain range of side-chain interaction strengths, we find that the intermediate beta-hairpin state is destabilized and even disappears, suggesting an important role of the environment in the aggregation propensity of a peptide.