Contact pair dynamics during folding of two small proteins: chicken villin head piece and the Alzheimer protein beta-amyloid

Can local heating and molecular crowders disintegrate amyloid aggregates?

The present study employs a blend of molecular dynamics simulations and a theoretical model to explore the potential disintegration mechanism of a matured Aβ octamer, aiming to offer a strategy to combat Alzheimer's disease. We investigate local heating and crowding effects on Aβ disintegration by selectively heating key Aβ segments and varying the concentration of sodium dodecyl sulphate (SDS), respectively. Despite initiation of disruption, Aβ aggregates resist complete disintegration during local heating due to rapid thermal energy distribution to the surrounding water. Conversely, although SDS molecules effectively inhibit Aβ aggregation at higher concentration through micelle formation, they fail to completely disintegrate the aggregate due to the exceedingly high energy barrier. To address the sampling challenge posed by the formidable energy barrier, we have performed well-tempered metadynamics simulations. Simulations reveal a multi-step disintegration mechanism for the Aβ octamer, suggesting a probable sequence: octamer → pentamer/hexamer ⇌ tetramer → monomer, with a rate-determining step constituting 45 kJ mol-1 barrier during the octamer to pentamer/hexamer transition. Additionally, we have proposed a novel two-state mean-field model based on Ising spins that offers an insight into the kinetics of the Aβ growth process and external perturbation effects on disintegration. Thus, the current simulation study, coupled with the newly introduced mean-field model, offers an insight into the detailed mechanisms underlying the Aβ aggregation process, guiding potential strategies for effective disintegration of Aβ aggregates.

Interplay between Conformational Heterogeneity and Hydration in the Folding Landscape of a Designed Three-Helix Bundle

Water is known to play a critical role in protein folding and stability. Here we develop and employ a coarse-grained (CG) model to directly explore the role of water in shaping the conformational landscape explored during protein folding. For this purpose, we simulate a designed sequence with binary patterning of neutral and hydrophobic residues, which is capable of folding to a three-helix bundle in explicit water. We find two folded states of this sequence, with rotation of the helices occurring to trade between hydrophobic packing and water expulsion from the core. This work provides insight into the role of water and hydrophobicity in generating competing folded states for a protein.

Hydrophobic hydration driven self-assembly of curcumin in water: similarities to nucleation and growth under large metastability, and an analysis of water dynamics at heterogeneous surfaces

As the beneficial effects of curcumin have often been reported to be limited to its small concentrations, we have undertaken a study to find the aggregation properties of curcumin in water by varying the number of monomers. Our molecular dynamics simulation results show that the equilibrated structure is always an aggregated state with remarkable structural rearrangements as we vary the number of curcumin monomers from 4 to 16 monomers. We find that the curcumin monomers form clusters in a very definite pattern where they tend to aggregate both in parallel and anti-parallel orientation of the phenyl rings, often seen in the formation of β-sheet in proteins. A considerable enhancement in the population of parallel alignments is observed with increasing the system size from 12 to 16 curcumin monomers. Due to the prevalence of such parallel alignment for large system size, a more closely packed cluster is formed with maximum number of hydrophobic contacts. We also follow the pathway of cluster growth, in particular the transition from the initial segregated to the final aggregated state. We find the existence of a metastable structural intermediate involving a number of intermediate-sized clusters dispersed in the solution. We have constructed a free energy landscape of aggregation where the metatsable state has been identified. The course of aggregation bears similarity to nucleation and growth in highly metastable state. The final aggregated form remains stable with the total exclusion of water from its sequestered hydrophobic core. We also investigate water structure near the cluster surface along with their orientation. We find that water molecules form a distorted tetrahedral geometry in the 1st solvation layer of the cluster, interacting rather strongly with the hydrophilic groups at the surface of the curcumin. The dynamics of such quasi-bound water molecules near the surface of curcumin cluster is considerably slower than the bulk signifying a restricted motion as often found in protein hydration layer.

Recent advances in transferable coarse-grained modeling of proteins

Computer simulations are indispensable tools for studying the structure and dynamics of biological macromolecules. Biochemical processes occur on different scales of length and time. Atomistic simulations cannot cover the relevant spatiotemporal scales at which the cellular processes occur. To address this challenge, coarse-grained (CG) modeling of the biological systems is employed. Over the last few years, many CG models for proteins continue to be developed. However, many of them are not transferable with respect to different systems and different environments. In this review, we discuss those CG protein models that are transferable and that retain chemical specificity. We restrict ourselves to CG models of soluble proteins only. We also briefly review recent progress made in the multiscale hybrid all-atom/CG simulations of proteins.

Electronic polarization stabilizes tertiary structure prediction of HP-36

Molecular dynamic (MD) simulations with both implicit and explicit solvent models have been carried out to study the folding dynamics of HP-36 protein. Starting from the extended conformation, the secondary structure of all three helices in HP-36 was formed in about 50 ns and remained stable in the remaining simulation. However, the formation of the tertiary structure was difficult. Although some intermediates were close to the native structure, the overall conformation was not stable. Further analysis revealed that the large structure fluctuation of loop and hydrophobic core regions was devoted mostly to the instability of the structure during MD simulation. The backbone root-mean-square deviation (RMSD) of the loop and hydrophobic core regions showed strong correlation with the backbone RMSD of the whole protein. The free energy landscape indicated that the distribution of main chain torsions in loop and turn regions was far away from the native state. Starting from an intermediate structure extracted from the initial AMBER simulation, HP-36 was found to generally fold to the native state under the dynamically adjusted polarized protein-specific charge (DPPC) simulation, while the peptide did not fold into the native structure when AMBER force filed was used. The two best folded structures were extracted and taken into further simulations in water employing AMBER03 charge and DPPC for 25 ns. Result showed that introducing polarization effect into interacting potential could stabilize the near-native protein structure.

Molecular mechanics

Molecular Mechanics (MM) force fields are the methods of choice for protein simulations, which are essential in the study of conformational flexibility. Given the importance of protein flexibility in drug binding, MM is involved in most if not all Computational Structure-Based Drug Discovery (CSBDD) projects. This paper introduces the reader to the fundamentals of MM, with a special emphasis on how the target data used in the parametrization of force fields determine their strengths and weaknesses. Variations and recent developments such as polarizable force fields are discussed. The paper ends with a brief overview of common force fields in CSBDD.

Molecular dynamics simulations to investigate the aggregation behaviors of the Abeta(17-42) oligomers

The amyloid beta-peptides (Abetas) are the main protein components of amyloid deposits in Alzheimer's disease (AD). Detailed knowledge of the structure and assembly dynamics of Abeta is important for the development of properly targeted AD therapeutics. So far, the process of the monomeric Abeta assembling into oligomeric fibrils and the mechanism underlying the aggregation process remain unclear. In this study, several molecular dynamics simulations were conducted to investigate the aggregation behaviors of the Abeta(17-42) oligomers associated with various numbers of monomers (dimer, trimer, tetramer, and pentamer). Our results showed that the structural stability of the Abeta(17-42) oligomers increases with increasing the number of monomer. We further demonstrated that the native hydrophobic contacts are positive correlated with the beta-sheet contents, indicating that hydrophobic interaction plays an important role in maintaining the structural stability of the Abeta(17-42) oligomers, particularly for those associated with more monomers. Our results also showed that the stability of the C-terminal hydrophobic segment 2 (residues 30-42) is higher than that of the N-terminal hydrophobic segment 1 (residues 17-21), suggesting that hydrophobic segment 2 may act as the nucleation site for aggregation. We further identified that Met35 residue initiates the hydrophobic interactions and that the intermolecular contact pairs, Gly33-Gly33 and Gly37-Gly37, form a stable "molecular notch", which may mediate the packing of the beta-sheet involving many other hydrophobic residues during the early stage of amyloid-like fibril formation.

Construction of an intermediate-resolution lattice model and re-examination of the helix-coil transition: a dynamic Monte Carlo simulation

In protein modeling, spatial resolution and computational efficiency are always incompatible. As a compromise, an intermediate-resolution lattice model has been constructed in the present work. Each residue is decomposed into four basic units, i.e. the α-carbon group, the carboxyl group, the imino group, and the side-chain group, and each basic coarse-grained unit is represented by a minimum cubic box with eight lattice sites. The spacing of the lattice is about 0.56 Å, holding the highest spatial resolution for the present lattice protein models. As the first report of this new model, the helix-coil transition of a polyalanine chain was examined via dynamic Monte Carlo simulation. The period of formed α-helix was about 3.68 residues, close to that of a natural α-helix. The resultant backbone motion was found to be in the realistic regions of the conformational space in the Ramachandran plot. Helix propagation constant and nucleation constant were further determined through the dynamic hydrogen bonding process and torsional angle variation, and the results were used to make comparison between classical Zimm-Bragg theory and Lifson-Roig theory based on the Qian-Schellman relationship. The simulation results confirmed that our lattice model can reproduce the helix-coil transition of polypeptide and construct a moderately fine α-helix conformation without significantly weakening the priority in efficiency for a lattice model.

Estimating free-energy barrier heights for an ultrafast folding protein from calorimetric and kinetic data

Differential scanning calorimetry was used to measure the temperature dependence of the absolute heat capacity of the 35-residue subdomain of the villin headpiece, a protein that folds in 5 mus and is therefore assumed to have a small free-energy barrier separating folded and unfolded states. To obtain an estimate of the barrier height from the calorimetric data, two models, a variable-barrier model and an Ising-like model, were used to fit the heat capacity in excess of the folded state over the temperature range 15-125 degrees C. The variable-barrier model is based on an empirical mathematical form for the density of states, with four adjustable parameters and the enthalpy (H) as a reaction coordinate. The Ising-like model is based on the inter-residue contact map of the X-ray structure with exact enumeration of approximately 10(5) possible conformations, with two adjustable parameters in the partition function, and either the fraction of native contacts (Q) or the number of ordered residues (P) as reaction coordinates. The variable-barrier model provides an excellent fit to the data and yields a barrier height at the folding temperature ranging from 0.4 to 1.1 kcal mol(-1), while the Ising-like model provides a less good fit and yields barrier heights of 2.3 +/- 0.1 kcal mol(-1) and 2.1 +/- 0.1 kcal mol(-1) for the Q and P reaction coordinates, respectively. In both models, the barrier to folding increases with increasing temperature. Assuming a sufficiently large activation energy for diffusion on the free-energy surfaces, both models are consistent with the observation of a temperature-independent folding rate in previously published laser temperature-jump experiments. Analysis of this kinetic data, using an approximate form for the pre-exponential factor of Kramers theory and the 70 ns relaxation time for the fast phase that precedes the unfolding/refolding relaxation to determine the diffusion coefficient, results in a barrier height of 1.6 +/- 0.3 kcal mol-1 for an unspecified reaction coordinate. Although no independent test of the validity of the H, Q, or P reaction coordinates is given, the barrier-height estimates obtained with the three reaction coordinates are in quite good agreement with the value derived from a Kramers analysis of the kinetics that makes no assumptions about the reaction coordinate. However, the higher estimates obtained using Q or P appear more consistent with the finding of barrier-crossing kinetics of a villin mutant that folds in 700 ns, corresponding to a 1.3 kcal mol-1 reduction in the folding barrier relative to wild-type. All of the results suggest that the free-energy barrier to folding is sufficiently low that it should be possible to engineer this protein or find solution conditions that would eliminate the barrier to create the "downhill" folding scenario of Wolynes and Onuchic.

Global optimization and folding pathways of selected alpha-helical proteins

The results of basin-hopping global optimization simulations are presented for four small, alpha-helical proteins described by a coarse-grained potential. A step-taking scheme that incorporates the local conformational preferences extracted from a large number of high-resolution protein structures is compared with an unbiased scheme. In addition, the discrete path sampling method is used to investigate the folding of one of the proteins, namely, the villin headpiece subdomain. Folding times from kinetic Monte Carlo simulations and iterative calculations based on a Markovian first-step analysis for the resulting stationary-point database are in good mutual agreement, but differ significantly from the experimental values, probably because the native state is not the global free energy minimum for the potential employed.

Theoretical investigation of the photoinitiated folding of HP-36

A computational model was developed to examine the phototriggered folding of a caged protein, a protein modified with an organic photolabile cross-linker. Molecular dynamics simulations of the modified 36-residue fragment of subdomain B of chicken villin head piece with a photolabile linker were performed, starting from both the caged and the uncaged structures. Construction of a free-energy landscape, based on principal components as well as on radius of gyration versus root-mean-square deviation, and circular dichroism calculations were employed to characterize folding behavior and structures. The folded structures observed in the molecular dynamics trajectories were found to be similar to that of the wild-type protein, in agreement with the published experimental results. The free-energy landscapes of the modified and wild-type proteins have similar topology, suggesting common thermodynamic/kinetic behavior. The existence of small differences in the free-energy surface of the modified protein from that of the native protein, however, indicates subtle differences in the folding behavior.

Mapping all-atom models onto one-bead Coarse Grained Models: general properties and applications to a minimal polypeptide model

In the one and two beads Coarse Grained (CG) models for proteins, the two conformational dihedrals ϕ and ψ that describe the backbone geometry are no longer present as explicit internal coordinates, thus the information contained in the Ramachandran plot cannot be used directly. We derive an analytical mapping between these dihedrals and the internal variable describing the backbone conformation in the one(two) beads CG models, namely the pseudo-bond angle and pseudo-dihedral between subsequent Cαs. This is used to derive a new density plot that contains the same information as the Ramachandran plot and can be used with the one(two) beads CG models. The use of this mapping is then illustrated with a new one bead polypeptide model that accounts for transitions between α-helices and β-sheets.

Finding pathways between distant local minima

We report a new algorithm for constructing pathways between local minima that involve a large number of intervening transition states on the potential energy surface. A significant improvement in efficiency has been achieved by changing the strategy for choosing successive pairs of local minima that serve as endpoints for the next search. We employ Dijkstra's algorithm [E. W. Dijkstra, Numer. Math. 1, 269 (1959)] to identify the "shortest" path corresponding to missing connections within an evolving database of local minima and the transition states that connect them. The metric employed to determine the shortest missing connection is a function of the minimized Euclidean distance. We present applications to the formation of buckminsterfullerene and to the folding of various biomolecules: the B1 domain of protein G, tryptophan zippers, and the villin headpiece subdomain. The corresponding pathways contain up to 163 transition states and will be used in future discrete path sampling calculations.

High-resolution x-ray crystal structures of the villin headpiece subdomain, an ultrafast folding protein

The 35-residue subdomain of the villin headpiece (HP35) is a small ultrafast folding protein that is being intensely studied by experiments, theory, and simulations. We have solved the x-ray structures of HP35 and its fastest folding mutant [K24 norleucine (nL)] to atomic resolution and compared their experimentally measured folding kinetics by using laser temperature jump. The structures, which are in different space groups, are almost identical to each other but differ significantly from previously solved NMR structures. Hence, the differences between the x-ray and NMR structures are probably not caused by lattice contacts or crystal/solution differences, but reflect the higher accuracy of the x-ray structures. The x-ray structures reveal important details of packing of the hydrophobic core and some additional features, such as cross-helical H bonds. Comparison of the x-ray structures indicates that the nL substitution produces only local perturbations. Consequently, the finding that the small stabilization by the mutation is completely reflected in an increased folding rate suggests that this region of the protein is as structured in the transition state as in the folded structure. It is therefore a target for engineering to increase the folding rate of the subdomain from approximately 0.5 micros(-1) for the nL mutant to the estimated theoretical speed limit of approximately 3 micros(-1).