Folding simulations of three proteins having all α-helix,all β-strand and α/β-structures

We performed folding simulations of three proteins using four force fields, AMBER parm96, AMBER parm99, CHARMM 27 and OPLS-AA/L, in order to examine the features of these force fields. We studied three proteins, protein A (all α-helix), cold-shock protein (all β-strand) and protein G (α/β-structures), for the folding simulations. For the simulation, we used the simulated annealing molecular dynamics method, which was performed 50 times for each protein using the four force fields. The results showed that the secondary-structure-forming tendencies are largely different among the four force fields. AMBER parm96 favours β-bridge structures and extended β-strand structures, and AMBER parm99 favours α-helix structures and 3₁₀-helix structures. CHARMM 27 slightly favours α-helix structures, and there are also π-helix and β-bridge structures. OPLS-AA/L favours α-helix structures and 3₁₀-helix structures.     

Analysis of the conformational profile of trishomocubane amino acid dipeptide

4-Amino-(D3)-trishomocubane-4-carboxylic acid is a constrained alpha-amino acid residue that exhibits promising conformational characteristics, i.e., helical and beta-turns. As part of the development of conformational guidelines for the design of peptides and protein surrogates, the conformational energy calculations on trishomocubane using molecular mechanics and ab initio methods are presented. The C(alpha) carbon of trishomocubane forms part of the cyclic structure, and consequently a peptidic environment was simulated with an acetyl group on its N-terminus and a methylamide group on its C-terminus. Ramachandran maps computed at the molecular mechanics level using the standard AMBER (parm94) force field libraries compared reasonably well with the corresponding maps computed at the Hartree Fock level, using the 6-31G* basis set. Trishomocubane peptide (Ac-Tris-NHMe) is characterized by four low energy conformers corresponding to the C7ax, C7eq, 3(10), and alpha(L) helical structures.     

Energy landscape of a peptide consisting of alpha-helix, 3(10)-helix, beta-turn, beta-hairpin, and other disordered conformations

The energy landscape of a peptide [Ace-Lys-Gln-Cys-Arg-Glu-Arg-Ala-Nme] in explicit water was studied with a multicanonical molecular dynamics simulation, and the AMBER parm96 force field was used for the energy calculation. The peptide was taken from the recognition helix of the DNA-binding protein, c-MYB: A rugged energy landscape was obtained, in which the random-coil conformations were dominant at room temperature. The CD spectra of the synthesized peptide revealed that it is in the random state at room temperature. However, the 300 K canonical ensemble, Q(300K), contained alpha-helix, 3(10)-helix, beta-turn, and beta-hairpin structures with small but notable probabilities of existence. The complete alpha-helix, imperfect alpha-helix, and random-coil conformations were separated from one another in the conformational space. This means that the peptide must overcome energy barriers to form the alpha-helix. The overcoming process may correspond to the hydrogen-bond rearrangements from peptide-water to peptide-peptide interactions. The beta-turn, imperfect 3(10)-helix, and beta-hairpin structures, among which there are no energy barriers at 300 K, were embedded in the ensemble of the random-coil conformations. Two types of beta-hairpin with different beta-turn regions were observed in Q(300K). The two beta-hairpin structures may have different mechanisms for the beta-hairpin formation. The current study proposes a scheme that the random state of this peptide consists of both ordered and disordered conformations. In contrast, the energy landscape obtained from the parm94 force field was funnel like, in which the peptide formed the helical conformation at room temperature and random coil at high temperature.     

Determination method of the balance of the secondary-structure-forming tendencies of force fields

We propose a new method of optimisation of backbone torsion-energy parameters in the force field for molecular simulations of protein systems. This method is based on the idea of balancing the secondary-structure-forming tendencies, namely, those of α-helix and β-sheet structures. We perform a minimisation of the backbone dihedral angle-based root-mean-square deviation of the helix and β structure regions in many protein structures. As an example, we optimised the backbone torsion-energy parameters of AMBER parm96 force field using 100 protein molecules from the Protein Data Bank. We then performed folding simulations of α-helical and β-hairpin peptides, using the optimised force field. The results imply that the new force-field parameters give structures more consistent with the experimental implications than the original AMBER parm96 force field.     

Controlling the secondary-structure-forming tendencies of proteins by a backbone torsion-energy term

We examined a new backbone torsion-energy term proposed by us in the force field for protein systems. This torsion-energy term is represented by a double Fourier series in two variables, namely the backbone dihedral angles φ and ψ. It gives a natural representation of the torsion energy in the Ramachandran space in the sense that any two-dimensional energy surface periodic in both φ and ψ can be expanded by the double Fourier series. We can then easily control secondary-structure-forming tendencies by modifying the torsion-energy surface. For instance, we can increase or decrease the α-helix-forming-tendencies by lowering or raising the torsion-energy surface in the α-helix region and likewise increase or decrease the β-sheet-forming tendencies by lowering or raising the surface in the β-sheet region in the Ramachandran space. We applied this torsion-energy modification method to six force fields, AMBER parm94, AMBER parm96, AMBER parm99, CHARMM27, OPLS-AA and OPLS-AA/L, and demonstrated that our modifications of the torsion-energy terms resulted in the expected changes of secondary-structure-forming tendencies by performing folding simulations of α-helical and β-hairpin peptides.     

On the Bioactive Conformation of a Small Peptide and its Set of Thermodynamically Accessible Conformations

Abstract

In order to investigate the relationship between the bioactive conformation of a peptide and its set of thermodynamically accessible structures in solution, the conformational profile of the tetrapeptide Ac-Pro-Ala-Pro-Tyr-OH was characterized by computational methods. Search of the conformational space was performed within the molecular mechanics framework using the AMBER4.0 force field with an effective dielectric constant of 80. Unique structures of the peptide were compared with its bioactive conformation for the protein Streptomyces griseus Protease A, as taken from the crystal structure of the enzyme-peptide complex. The results show that the bound conformation is close to one of the unique conformations characterized in the conformational search of the isolated peptide. Moreover, the lowest energy minimum characterized in the conformational search exhibits large deviations when compared to the bound conformation of the crystal structure.     

Force field influences in beta-hairpin folding simulations

All-atom force fields are now routinely used for more detailed understanding of protein folding mechanisms. However, it has been pointed out that use of all-atom force fields does not guarantee more accurate representations of proteins; in fact, sometimes it even leads to biased structural distributions. Indeed, several issues remain to be solved in force field developments, such as accurate treatment of implicit solvation for efficient conformational sampling and proper treatment of backbone interactions for secondary structure propensities. In this study, we first investigate the quality of several recently improved backbone interaction schemes in AMBER for folding simulations of a beta-hairpin peptide, and further study their influences on the peptide's folding mechanism. Due to the significant number of simulations needed for a thorough analysis of tested force fields, the implicit Poisson-Boltzmann solvent was used in all simulations. The chosen implicit solvent was found to be reasonable for studies of secondary structures based on a set of simulations of both alpha-helical and beta-hairpin peptides with the TIP3P explicit solvent as benchmark. Replica exchange molecular dynamics was also utilized for further efficient conformational sampling. Among the tested AMBER force fields, ff03 and a revised ff99 force field were found to produce structural and thermodynamic data in comparably good agreement with the experiment. However, detailed folding pathways, such as the order of backbone hydrogen bond zipping and the existence of intermediate states, are different between the two force fields, leading to force field-dependent folding mechanisms.     

Peptoid conformational free energy landscapes from implicit-solvent molecular simulations in AMBER

To test the accuracy of existing AMBER force field models in predicting peptoid conformation and dynamics, we simulated a set of model peptoid molecules recently examined by Butterfoss et al. (JACS 2009, 131, 16798-16807) using QM methods as well as three peptoid sequences with experimentally determined structures. We found that AMBER force fields, when used with a Generalized Born/Surface Area (GBSA) implicit solvation model, could accurately reproduce the peptoid torsional landscape as well as the major conformers of known peptoid structures. Enhanced sampling by replica exchange molecular dynamics (REMD) using temperatures from 300 to 800 K was used to sample over cis-trans isomerization barriers. Compared to (Nrch)5 and cyclo-octasarcosyl, the free energy of N-(2-nitro-3-hydroxyl phenyl)glycine-N-(phenyl)glycine has the most "foldable" free energy landscape, due to deep trans-amide minima dictated by N-aryl sidechains. For peptoids with (S)-N (1-phenylethyl) (Nspe) side chains, we observe a discrepancy in backbone dihedral propensities between molecular simulations and QM calculations, which may be due to force field effects or the inability to capture n --> n* interactions. For these residues, an empirical phi-angle biasing potential can "rescue" the backbone propensities seen in QM. This approach can serve as a general strategy for addressing force fields without resorting to a complete reparameterization. Overall, this study demonstrates the utility of implicit-solvent REMD simulations for efficient sampling to predict peptoid conformational landscapes, providing a potential tool for first-principles design of sequences with specific folding properties.     

Comparison of force fields for Alzheimer's A : A case study for intrinsically disordered proteins

Intrinsically disordered proteins are essential for biological processes such as cell signalling, but are also associated to devastating diseases including Alzheimer's disease, Parkinson's disease or type II diabetes. Because of their lack of a stable three‐dimensional structure, molecular dynamics simulations are often used to obtain atomistic details that cannot be observed experimentally. The applicability of molecular dynamics simulations depends on the accuracy of the force field chosen to represent the underlying free energy surface of the system. Here, we use replica exchange molecular dynamics simulations to test five modern force fields, OPLS, AMBER99SB, AMBER99SB*ILDN, AMBER99SBILDN‐NMR and CHARMM22*, in their ability to model Aβ₄₂, an intrinsically disordered peptide associated with Alzheimer's disease, and compare our results to nuclear magnetic resonance (NMR) experimental data. We observe that all force fields except AMBER99SBILDN‐NMR successfully reproduce local NMR observables, with CHARMM22* being slightly better than the other force fields.     

α/310-Helix transitions in α-methylalanine homopeptides: Conformational transition pathway and potential of mean force

The conformational transition between the α- and 3₁₀-helical states of α-methylalanine homopeptides is studied with molecular mechanics. Conformational transition pathways for Ace-(MeA)_n-NMe with n = 7, 9, and 11 are obtained with the algorithms of Elber and co-workers [R. Czerminski & R. Elber (1990) International Journal of Quantum Chemistry, Vol. 24, pp. 167–186; A. Ulitsky & R. Elber (1990) Journal of Chemical Physics, Vol. 92, pp. 1510–1511]. The free energy surface, or potential of mean force, for the conformational transition of Ace-(MeA)₉-NMe is calculated from molecular dynamics simulations, and a method is presented for the decomposition of the free energy surface into the constituent energetic and entropic terms, via the calculation of the required temperature derivatives in situ. For the AMBER/OPLS model employed here, the conformational transition pathways each contain a single 3₁₀-helical-like transition state, and the transition state potential energy relative to the 3₁₀-conformation is 3 kcal/mol, independent of peptide length. Entropic stabilization in the barrier region significantly lowers the activation free energies for the forward and reverse transitions from the estimates of the barrier heights based simply on potential energy alone. © 1994 John Wiley & Sons, Inc.     

Effects of force fields on the conformational and dynamic properties of amyloid β(1‐40) dimer explored by replica exchange molecular dynamics simulations

The conformational space and structural ensembles of amyloid beta (Aβ) peptides and their oligomers in solution are inherently disordered and proven to be challenging to study. Optimum force field selection for molecular dynamics (MD) simulations and the biophysical relevance of results are still unknown. We compared the conformational space of the Aβ(1‐40) dimers by 300 ns replica exchange MD simulations at physiological temperature (310 K) using: the AMBER‐ff99sb‐ILDN, AMBER‐ff99sb*‐ILDN, AMBER‐ff99sb‐NMR, and CHARMM22* force fields. Statistical comparisons of simulation results to experimental data and previously published simulations utilizing the CHARMM22* and CHARMM36 force fields were performed. All force fields yield sampled ensembles of conformations with collision cross sectional areas for the dimer that are statistically significantly larger than experimental results. All force fields, with the exception of AMBER‐ff99sb‐ILDN (8.8 ± 6.4%) and CHARMM36 (2.7 ± 4.2%), tend to overestimate the α‐helical content compared to experimental CD (5.3 ± 5.2%). Using the AMBER‐ff99sb‐NMR force field resulted in the greatest degree of variance (41.3 ± 12.9%). Except for the AMBER‐ff99sb‐NMR force field, the others tended to under estimate the expected amount of β‐sheet and over estimate the amount of turn/bend/random coil conformations. All force fields, with the exception AMBER‐ff99sb‐NMR, reproduce a theoretically expected β‐sheet‐turn‐β‐sheet conformational motif, however, only the CHARMM22* and CHARMM36 force fields yield results compatible with collapse of the central and C‐terminal hydrophobic cores from residues 17‐21 and 30‐36. Although analyses of essential subspace sampling showed only minor variations between force fields, secondary structures of lowest energy conformers are different.     

Characterization of the conformational domains of bradykinin by computational methods

The AMBER 4.0 force field was used to perform a characterization of the conformational profile of the nonapeptide bradykinin. A thorough conformational search was carried out using molecular dynamics as sampling technique, by computing cycles of high (900 K) and low (300 K) temperature trajectories. A total of 2400 minima were generated and subsequently clustered using the root-mean-square of the backbone dihedral angles as criterium. After the use of a tolerance value of 20deg;, the conformations were clustered in 233 unique conformations with energies up to 40 kcal/mol above the lowest minimum. The analysis of the low-energy conformations indicate that the peptide exhibits a high tendency to adopt a β-turn at the C-terminus and a propensity to adopt a bent structure at the N-terminus. These results are in agreement with the experimental evidence reported in the literature and provide detailed information necessary to understand the conformational preferences of the peptide.     

Towards a molecular dynamics consensus view of B-DNA flexibility

We present a systematic study of B-DNA flexibility in aqueous solution using long-scale molecular dynamics simulations with the two more recent versions of nucleic acids force fields (CHARMM27 and parmbsc0) using four long duplexes designed to contain several copies of each individual base pair step. Our study highlights some differences between pambsc0 and CHARMM27 families of simulations, but also extensive agreement in the representation of DNA flexibility. We also performed additional simulations with the older AMBER force fields parm94 and parm99, corrected for non-canonical backbone flips. Taken together, the results allow us to draw for the first time a consensus molecular dynamics picture of B-DNA flexibility.     

Free energy landscapes of peptides by enhanced conformational sampling

The free energy landscapes of peptide conformations in water have been observed by the enhanced conformational sampling method, applying the selectively enhanced multicanonical molecular dynamics simulations. The conformations of the peptide dimers, -Gly-Gly-, -Gly-Ala-, -Gly-Ser-, -Ala-Gly-, -Asn-Gly-, -Pro-Gly-, -Pro-Ala-, and -Ala-Ala-, which were all blocked with N-terminal acetyl and C-terminal N-methyl groups, were individually sampled with the explicit TIP3P water molecules. From each simulation trajectory, we obtained the canonical ensemble at 300 K, from which the individual three-dimensional landscape was drawn by the potential of mean force using the three reaction coordinates: the backbone dihedral angle, psi, of the first amino acid, the backbone dihedral angle, phi, of the second amino acid, and the distance between the carbonyl oxygen of the N-terminal acetyl group and the C-terminal amide proton. The most stable state and several meta-stable states correspond to extended conformations and typical beta-turn conformations, and their free energy values were accounted for from the potentials of mean force at the states. In addition, the contributions from the intra-molecular energies of peptides and those from the hydration effects were analyzed. Consequently, the stable beta-turn conformations in the free energy landscape were consistent with the empirically preferred beta-turn types for each amino acid sequence. The thermodynamic values for the hydration effect were decomposed and they correlated well with the empirical values estimated from the solvent accessible surface area of each molecular conformation during the trajectories. The origin of the architecture of protein local fragments was analyzed from the viewpoint of the free energy and its decomposed factors.     

General trends of dihedral conformational transitions in a globular protein

Dihedral conformational transitions are analyzed systematically in a model globular protein, cytochrome P450cam, to examine their structural and chemical dependences through combined conventional molecular dynamics (cMD), accelerated molecular dynamics (aMD) and adaptive biasing force (ABF) simulations. The aMD simulations are performed at two acceleration levels, using dihedral and dual boost, respectively. In comparison with cMD, aMD samples protein dihedral transitions approximately two times faster on average using dihedral boost, and ～3.5 times faster using dual boost. In the protein backbone, significantly higher dihedral transition rates are observed in the bend, coil, and turn flexible regions, followed by the β bridge and β sheet, and then the helices. Moreover, protein side chains of greater length exhibit higher transition rates on average in the aMD‐enhanced sampling. Side chains of the same length (particularly N_χ = 2) exhibit decreasing transition rates with residues when going from hydrophobic to polar, then charged and aromatic chemical types. The reduction of dihedral transition rates is found to be correlated with increasing energy barriers as identified through ABF free energy calculations. These general trends of dihedral conformational transitions provide important insights into the hierarchical dynamics and complex free energy landscapes of functional proteins. Proteins 2016; 84:501–514. © 2016 Wiley Periodicals, Inc.     

Force field impact and spin-probe modeling in molecular dynamics simulations of spin-labeled T4 lysozyme

Several attempts have been made to compute electron paramagnetic resonance (EPR) spectra of biomolecules, using motional models or simulated trajectories to describe dynamics. Ideally, the simulated trajectories should capture fast (picosecond) snapshots of spin-probe rotations accurately, while being lengthy enough to ensure a proper Fourier integration of the time-domain signal. It is the interplay of the two criteria that poses computational challenges to the method. In this context, an analysis of the spin-probe and protein conformational sampling and equilibration, with different force fields and with explicit solvent, may be a useful attempt. The present work reports a comparative study of the effect of the molecular dynamics (MD) force field on conformational sampling and equilibration in two spin-labeled T4 lysozyme (T4L) variants, N40C and K48C. Ensembles of 10× 3 ns-trajectories per variant and per force field (OPLS/AMBER and AMBER99) are analyzed for a reliable assessment of convergence and sampling. It is found that subtle site-dependent differences in spin-probe rotations and torsions are more readily captured in the AMBER99 trajectories than in the OPLS/AMBER simulations. On the other hand, sampling and equilibration are found to be better with the OPLS/AMBER force field at equal trajectory lengths.Figure: Left panel: The spin-probe R1 ring and the spin-probe Euler angles , and . Middle panel: Illustration of the diffusion in a cone model for the spin-probe motion: snapshots of helix B and of the R1 ring in N40C, taken at 0.3 ps intervals from AMBER trajectory 1. Right panel: The N40C mutant with the spin label (solid mode), solvated in a cubic box.     

Computational study of the conformational preferences of the (R)-8-amino-pentacyclo[5.4.0.0(2,6).0(3,10).0(5,9)]undecane-8-carboxylic acid monopeptide.

alpha-Amino acids are important building blocks for the synthesis of a large number of bioactive compounds and pharmaceutical drugs. However, a literature survey revealed that no theoretical conformational study of alpha-amino acids with cage carbon frameworks has been performed to date. This paper reports the results of a conformational study on the (R)-8-amino-pentacyclo[5.4.0.0(2,6).0(3,10).0(5,9)]undecane-8-carboxylic acid monopeptide (cage monopeptide), using molecular mechanics and ab initio methods. The in vacuo Ramachandran maps computed using the different parameterizations of the AMBER force field show the C7eq structure as the most favourable conformation, in contrast to the C7ax structure, that is the lowest energy conformation at the ab initio level. Analysis of these maps reveals the helical preference for the monopeptide and provides the potential for the cage residue to be incorporated into constrained peptide analogues.     

Conformational study of a nine residue fragment of the antigenic loop of foot-and-mouth disease virus.

The nine-residue peptide Ac-TASARGDLA-NHMe was selected as model peptide in order to understand the conformational features of the antigenic loop of foot-and-mouth disease virus (FMDV). A throughout exploration of the conformational space has been carried out by means of molecular dynamics (MD) and energy minimization. The calculations have been carried out using the AMBER force field. Solvent effects have been included by an effective dielectric constant of epsilon = 4r. The lowest energy conformation presents a secondary structure constituted by an alpha-helix at the N-terminal end followed by two gamma-turns in the central region. The rest of the accessible minima found present also a high tendency to form gamma-turns. Finally, a 100 ps MD trajectory calculation at 298 K suggest a stability of the secondary structure elements of the lowest energy conformation.     

Ab initio construction of polypeptide fragments: Accuracy of loop decoy discrimination by an all-atom statistical potential and the AMBER force field with the Generalized Born solvation model

The accuracy of model selection from decoy ensembles of protein loop conformations was explored by comparing the performance of the Samudrala-Moult all-atom statistical potential (RAPDF) and the AMBER molecular mechanics force field, including the Generalized Born/surface area solvation model. Large ensembles of consistent loop conformations, represented at atomic detail with idealized geometry, were generated for a large test set of protein loops of 2 to 12 residues long by a novel ab initio method called RAPPER that relies on fine-grained residue-specific phi/psi propensity tables for conformational sampling. Ranking the conformers on the basis of RAPDF scores resulted in selected conformers that had an average global, non-superimposed RMSD for all heavy mainchain atoms ranging from 1.2 A for 4-mers to 2.9 A for 8-mers to 6.2 A for 12-mers. After filtering on the basis of anchor geometry and RAPDF scores, ranking by energy minimization of the AMBER/GBSA potential energy function selected conformers that had global RMSD values of 0.5 A for 4-mers, 2.3 A for 8-mers, and 5.0 A for 12-mers. Minimized fragments had, on average, consistently lower RMSD values (by 0.1 A) than their initial conformations. The importance of the Generalized Born solvation energy term is reflected by the observation that the average RMSD accuracy for all loop lengths was worse when this term is omitted. There are, however, still many cases where the AMBER gas-phase minimization selected conformers of lower RMSD than the AMBER/GBSA minimization. The AMBER/GBSA energy function had better correlation with RMSD to native than the RAPDF. When the ensembles were supplemented with conformations extracted from experimental structures, a dramatic improvement in selection accuracy was observed at longer lengths (average RMSD of 1.3 A for 8-mers) when scoring with the AMBER/GBSA force field. This work provides the basis for a promising hybrid approach of ab initio and knowledge-based methods for loop modeling.     

Refinement of the AMBER force field for nucleic acids: improving the description of alpha/gamma conformers

We present here the parmbsc0 force field, a refinement of the AMBER parm99 force field, where emphasis has been made on the correct representation of the alpha/gamma concerted rotation in nucleic acids (NAs). The modified force field corrects overpopulations of the alpha/gamma = (g+,t) backbone that were seen in long (more than 10 ns) simulations with previous AMBER parameter sets (parm94-99). The force field has been derived by fitting to high-level quantum mechanical data and verified by comparison with very high-level quantum mechanical calculations and by a very extensive comparison between simulations and experimental data. The set of validation simulations includes two of the longest trajectories published to date for the DNA duplex (200 ns each) and the largest variety of NA structures studied to date (15 different NA families and 97 individual structures). The total simulation time used to validate the force field includes near 1 mus of state-of-the-art molecular dynamics simulations in aqueous solution.