Interpreting NMR Data for β-Peptides Using Molecular Dynamics Simulations

Quest for New Generation Biocompatible Materials: Tailoring β-Peptide Structure and Interactions via Synergy of Experiments and Modelling

Peptide-based self-assembly has been used to produce a wide range of nanostructures. While most of these systems involve self-assembly of α-peptides, more recently β-peptides have also been shown to undergo supramolecular self-assembly, and have been used to produce materials for applications in tissue engineering, cell culture and drug delivery. In order to engineer new materials with specific structure and function, theoretical molecular modelling can provide significant insights into the collective balance of non-covalent interactions that drive the self-assembly and determine the structure of the resultant supramolecular materials under different conditions. However, this approach has only recently become feasible for peptide-based self-assembled nanomaterials, particularly those that incorporate non α-amino acids. This perspective provides an overview of the challenges associated with computational modelling of the self-assembly of β-peptides and the recent success using a combination of experimental and computational techniques to provide insights into the self-assembly mechanisms and fully atomistic models of these new biocompatible materials.

Identifying the Coiled-Coil Triple Helix Structure of β-Peptide Nanofibers at Atomic Resolution

Peptide self-assembly represents a powerful bottom-up approach to the fabrication of nanomaterials. β³-Peptides are non-natural peptides composed entirely of β-amino acids, which have an extra methylene in the backbone, and we reported fibers derived from the self-assembly of β³-peptides that adopt 14-helical structures. β³-Peptide assemblies represent a class of stable nanomaterials that can be used to generate bio- and magneto-responsive materials with proteolytic stability. However, the three-dimensional structure of many of these materials remains unknown. To develop structure-based criteria for the design of β³-peptide-based biomaterials with tailored function, we investigated the structure of a tri-β³-peptide nanoassembly by molecular dynamics simulations and X-ray fiber diffraction analysis. Diffraction data was collected from aligned fibrils formed by Ac-β³[LIA] in water and used to inform and validate the model structure. Models with 3-fold radial symmetry resulted in stable fibers with a triple-helical coiled-coil motif and measurable helical pitch and periodicity. The fiber models revealed a hydrophobic core and twist along the fiber axis arising from a maximization of contacts between hydrophobic groups of adjacent tripeptides on the solvent-exposed fiber surface. These atomic structures of macroscale fibers derived from β³-peptide-based materials provide valuable insight into the effects of the geometric placement of the side chains and the influence of solvent on the core fiber structure which is perpetuated in the superstructure morphology.

Validation of Molecular Simulation: An Overview of Issues

Computer simulation of molecular systems enables structure-energy-function relationships of molecular processes to be described at the sub-atomic, atomic, supra-atomic, or supra-molecular level. To interpret results of such simulations appropriately, the quality of the calculated properties must be evaluated. This depends on the way the simulations are performed and on the way they are validated by comparison to values Q^exp of experimentally observable quantities Q. One must consider 1) the accuracy of Q^exp , 2) the accuracy of the function Q(r^N ) used to calculate a Q-value based on a molecular configuration r^N of N particles, 3) the sensitivity of the function Q(r^N ) to the configuration r^N , 4) the relative time scales of the simulation and experiment, 5) the degree to which the calculated and experimental properties are equivalent, and 6) the degree to which the system simulated matches the experimental conditions. Experimental data is limited in scope and generally corresponds to averages over both time and space. A critical analysis of the various factors influencing the apparent degree of (dis)agreement between simulations and experiment is presented and illustrated using examples from the literature. What can be done to enhance the validation of molecular simulation is also discussed.

Interpretation of Seemingly Contradictory Data: Low NMR S2 Order Parameters Observed in Helices and High NMR S2 Order Parameters in Disordered Loops of the Protein hGH at Low pH

At low pH, human growth hormone (hGH) adopts a partially folded state, in which the native helices are maintained, but the long loop regions and side-chain packing become disordered. Some of the S² order parameters for backbone N-H vectors derived from NMR relaxation measurements on hGH at low pH initially seem contradictory. Three isolated residues (15, 20, and 171) in helices A and D exhibit low order parameter values (<0.5) indicating flexibility, whereas residue 143 in the centre of a long flexible loop region has a high order parameter (0.82). Using S² order parameter restraining MD simulations, this paradox has been resolved. Low S² values in helices are due to the presence of a mixture of 3₁₀ -helical and α-helical hydrogen bonds. High S² values in relatively disordered parts of a protein may be due to fluctuating networks of hydrogen bonds between the backbone and the side chains, which restrict the motion of N-H bond vectors.

Helix stability of oligoglycine, oligoalanine, and oligo-β-alanine dodecamers reflected by hydrogen-bond persistence

Helices are important structural/recognition elements in proteins and peptides. Stability and conformational differences between helices composed of α- and β-amino acids as scaffolds for mimicry of helix recognition has become a theme in medicinal chemistry. Furthermore, helices formed by β-amino acids are experimentally more stable than those formed by α-amino acids. This is paradoxical because the larger sizes of the hydrogen-bonding rings required by the extra methylene groups should lead to entropic destabilization. In this study, molecular dynamics simulations using the second-generation force field, AMOEBA (Ponder, J.W., et al., Current status of the AMOEBA polarizable force field. J Phys Chem B, 2010. 114(8): p. 2549-64.) explored the stability and hydrogen-bonding patterns of capped oligo-β-alanine, oligoalanine, and oligoglycine dodecamers in water. The MD simulations showed that oligo-β-alanine has strong acceptor+2 hydrogen bonds, but surprisingly did not contain a large content of 3(12) -helical structures, possibly due to the sparse distribution of the 3(12) -helical structure and other structures with acceptor+2 hydrogen bonds. On the other hand, despite its backbone flexibility, the β-alanine dodecamer had more stable and persistent <3.0 Å hydrogen bonds. Its structure was dominated more by multicentered hydrogen bonds than either oligoglycine or oligoalanine helices. The 3(1) (PII) helical structure, prevalent in oligoglycine and oligoalanine, does not appear to be stable in oligo-β-alanine indicating its competition with other structures (stacking structure as indicated by MD analyses). These differences are among the factors that shape helical structural preferences and the relative stabilities of these three oligopeptides.

Differential Flap Dynamics in Wild-type and a Drug Resistant Variant of HIV-1 Protease Revealed by Molecular Dynamics and NMR Relaxation

In the rapidly evolving disease of HIV drug resistance readily emerges, nullifying the effectiveness of therapy. Drug resistance has been extensively studied in HIV-1 protease where resistance occurs when the balance between enzyme inhibition and substrate recognition and turn-over is perturbed to favor catalytic activity. Mutations which confer drug resistance can impact the dynamics and structure of both the bound and unbound forms of the enzyme. Flap+ is a multi-drug-resistant variant of HIV-1 protease with a combination of mutations at the edge of the active site, within the active site, and in the flaps (L10I, G48V, I54V, V82A). The impact of these mutations on the dynamics in the unliganded form in comparison with the wild-type protease was elucidated with Molecular Dynamic simulations and NMR relaxation experiments. The comparative analyses from both methods concur in showing that the enzyme's dynamics are impacted by the drug resistance mutations in Flap+ protease. These alterations in the enzyme dynamics, particularly within the flaps, likely modulate the balance between substrate turn-over and drug binding, thereby conferring drug resistance.

Assessing and refining molecular dynamics simulations of proteins with nuclear magnetic resonance data

The sophistication of the force fields, algorithms and hardware used for molecular dynamics (MD) simulations of proteins is continuously increasing. No matter how advanced the methodology, however, it is essential to evaluate the appropriateness of the structures sampled in a simulation by comparison with quantitative experimental data. Solution nuclear magnetic resonance (NMR) data are particularly useful for checking the quality of protein simulations, as they provide both structural and dynamic information on a variety of temporal and spatial scales. Here, various features and implications of using NMR data to validate and bias MD simulations are outlined, including an overview of the different types of NMR data that report directly on structural properties and of relevant simulation techniques. The focus throughout is on how to properly account for conformational averaging, particularly within the context of the assumptions inherent in the relationships that link NMR data to structural properties.

Investigating how peptide length and a pathogenic mutation modify the structural ensemble of amyloid beta monomer

The aggregation of amyloid beta (Aβ) peptides plays an important role in the development of Alzheimer's disease. Despite extensive effort, it has been difficult to characterize the secondary and tertiary structure of the Aβ monomer, the starting point for aggregation, due to its hydrophobicity and high aggregation propensity. Here, we employ extensive molecular dynamics simulations with atomistic protein and water models to determine structural ensembles for Aβ(42), Aβ(40), and Aβ(42)-E22K (the Italian mutant) monomers in solution. Sampling of a total of >700 microseconds in all-atom detail with explicit solvent enables us to observe the effects of peptide length and a pathogenic mutation on the disordered Aβ monomer structural ensemble. Aβ(42) and Aβ(40) have crudely similar characteristics but reducing the peptide length from 42 to 40 residues reduces β-hairpin formation near the C-terminus. The pathogenic Italian E22K mutation induces helix formation in the region of residues 20-24. This structural alteration may increase helix-helix interactions between monomers, resulting in altered mechanism and kinetics of Aβ oligomerization.

Secondary Structure Assignment of Amyloid-β Peptide Using Chemical Shifts

The distinct conformational dependence of chemical shifts caused by α-helices and β-sheets renders NMR chemical shift analysis a powerful tool for the structural determination of proteins. However, the time scale of NMR experiments can make a secondary structure assignment of highly flexible peptides or proteins, which may be converting between conformational substates, problematic. For instance the amyloid-β monomer, according to NMR chemical shifts, adopts a predominately random coil structure in aqueous solution (with <3% α-helical content). Molecular dynamics simulations, on the other hand, suggest that α-helical content can be significant (10-25%). In this paper, we explore the possible reasons for this discrepancy and show that the different results from experiments and theory are not necessarily mutually exclusive but may reflect a general problem of secondary structure assignment of conformationally flexible biomolecules.

Establishing effective simulation protocols for beta- and alpha/beta-peptides. III. Molecular mechanical model for acyclic beta-amino acids

All-atom molecular mechanics (MM) force field parameters are developed for the backbone of acyclic beta-amino acid using an improved version of the multiobjective evolutionary algorithm (MOEA). The MM model is benchmarked using beta(3)-homo-Alanine (beta(3)-hAla) diamide in water with SCC-DFTB/MM simulations as the reference. Satisfactory agreements are found between the MM and SCC-DFTB/MM results regarding the distribution of key dihedral angles for the beta(3)-hAla diamide in water. The MM model is further applied to a beta-hepta-peptide in methanol solution. The calculated NOE values and (3)J coupling constants averaged over different trajectories are consistent with experimental data. By contrast, simulations using parameters directly transferred from the CHARMM22 force field for proteins lead to much worse agreement, which highlights the importance of careful parameterization for non-natural peptides, for which the improved MOEA is particularly useful. Finally, as an initial application of the new force field parameters, the behaviors of a short random copolymer consisting of beta amino acids in bulk solution and membrane/water interface are studied using a generalized Born implicit solvent model (GBSW). Results for four selected sequences show that segregation of hydrophobic and cationic groups occur easily at the membrane/solution interface for all sequences. The sequence that features alternating short blocks exhibits signs of lower stability at the interface compared to other sequences. These results confirm the hypothesis in recent experimental studies that beta-amino-acid based random copolymers can develop a high degree of amphiphilicity without regular three-dimensional structure.

Using one-step perturbation to predict the effect of changing force-field parameters on the simulated folding equilibrium of a beta-peptide in solution

Computer simulation using molecular dynamics is increasingly used to simulate the folding equilibria of peptides and small proteins. Yet, the quality of the obtained results depends largely on the quality of the force field used. This comprises the solute as well as the solvent model and their energetic and entropic compatibility. It is, however, computational very expensive to perform test simulations for each combination of force-field parameters. Here, we use the one-step perturbation technique to predict the change of the free enthalpy of folding of a beta-peptide in methanol solution due to changing a variety of force-field parameters. The results show that changing the solute backbone partial charges affects the folding equilibrium, whereas this is relatively insensitive to changes in the force constants of the torsional energy terms of the force field. Extending the cut-off distance for nonbonded interactions beyond 1.4 nm does not affect the folding equilibrium. The same result is found for a change of the reaction-field permittivity for methanol from 17.7 to 30. The results are not sensitive to the criterion, e.g., atom-positional RMSD or number of hydrogen bonds, that is used to distinguish folded and unfolded conformations. Control simulations with perturbed Hamiltonians followed by backward one-step perturbation indicated that quite large perturbations still yield reliable results. Yet, perturbing all solvent molecules showed where the limitations of the one-step perturbation technique are met. The evaluated methodology constitutes an efficient tool in force-field development for molecular simulation by reducing the number of required separate simulations by orders of magnitude.

Methods of NMR structure refinement: molecular dynamics simulations improve the agreement with measured NMR data of a C-terminal peptide of GCN4-p1

The C-terminal trigger sequence is essential in the coiled-coil formation of GCN4-p1; its conformational properties are thus of importance for understanding this process at the atomic level. A solution NMR model structure of a peptide, GCN4p16-31, encompassing the GCN4-p1 trigger sequence was proposed a few years ago. Derived using a standard single-structure refinement protocol based on 172 nuclear Overhauser effect (NOE) distance restraints, 14 hydrogen-bond and 11 phi torsional-angle restraints, the resulting set of 20 NMR model structures exhibits regular alpha-helical structure. However, the set slightly violates some measured NOE bounds and does not reproduce all 15 measured (3)J(H(N)-H(Calpha))-coupling constants, indicating that different conformers of GCN4p16-31 might be present in solution. With the aim to resolve structures compatible with all NOE upper distance bounds and (3)J-coupling constants, we executed several structure refinement protocols employing unrestrained and restrained molecular dynamics (MD) simulations with two force fields. We find that only configurational ensembles obtained by applying simultaneously time-averaged NOE distance and (3)J-coupling constant restraining with either force field reproduce all the experimental data. Additionally, analyses of the simulated ensembles show that the conformational variability of GCN4p16-31 in solution admitted by the available set of 187 measured NMR data is larger than represented by the set of the NMR model structures. The conformations of GCN4p16-31 in solution differ in the orientation not only of the side-chains but also of the backbone. The inconsistencies between the NMR model structures and the measured NMR data are due to the neglect of averaging effects and the inclusion of hydrogen-bond and torsional-angle restraints that have little basis in the primary, i.e. measured NMR data.

Synthesis and immunosuppressive activity of new cyclolinopeptide A analogs modified with beta-prolines

Immune response suppressors are used in the medical praxis to prevent graft rejection after organ transplantation and in the therapy of some autoimmune diseases. As a continuation of our previous work searching for new, effective suppressors devoid of toxicity, we present the synthesis, conformational analysis, and biological activity of nonapeptides 1-6, analogs of naturally existing immunomodulatory peptide CLA. New CLA analogs were modified with (S)-beta(2)-iso-proline 7 or (S)-beta(3)-homo-proline 8, respectively. The conformational influence of the beta-iso-proline and beta-homo-proline building blocks was analyzed by NMR spectroscopy. Peptides 1-6 exist as a mixture of four isomers due to cis/trans isomerization of the Xxx-Pro peptide bond. The major isomers of peptides 1, 3, and 4 contain all peptide bonds of the trans geometry. The geometry of the proline-proline bond of the second populated isomer of peptides 3 and 4 is cis. The proline-proline peptide bond is cis for the major isomers of peptides 2, 5, and 6. The peptides were tested for their ability to suppress the proliferative response of mouse splenocytes to T- and B-cell mitogens and the secondary humoral immune response to sheep erythrocytes in vitro in parallel with a reference drug-cyclosporine A. The immunoregulatory actions of the peptides depended on the position and content of proline isomers and were, with some exceptions, strongly inhibitory at the highest dose tested (100 microg/ml). In addition, the peptides were practically devoid of toxicity at that dose. In conclusion, the replacement of Pro by beta-Pro may be useful for fine-tuning CLA immunosuppressive potency and undesirable toxicity.

Theoretical analysis of secondary structures of beta-peptides

Unlike alpha-amino acids, peptides formed from beta-amino acids (beta-peptides) display stability toward enzymatic degradation and may form turns and helices with as few as four residues. Because both the C alpha and C beta of the beta-amino acid may bear substituents, a large number of beta-amino acids can be synthesized. Beta-peptides form various well-defined secondary structures, including 14-helix, 12-helix, 10/12-helix, 10-helix, 8-helix, turn structures, sheets, and hairpins. For all of these reasons, beta-amino acids have been increasingly used as building blocks for molecular design and pharmaceutical applications. To explain the conformational features of beta-peptides, several quantum mechanics and molecular dynamics studies that rationalize the observed conformational features have been reported. However, a systematic account that unifies various factors critical to the conformational features is still lacking. In this Account, we present a detailed analysis of the conformational features of various beta-peptides. We start by studying the basic local conformational features of beta-peptides using di- and tripeptide models. Then, various secondary structures of unsubstituted beta-peptides with differing numbers of residues are investigated using a repeating unit approach to derive the intrinsic backbone conformational features. We find that the 10/12-helix is intrinsically most stable for the beta-peptide backbone. The 14-helix, 12-helix, and 10-helix structures have similar stabilities for beta-peptide backbones of four to six residues. The substituent effects on the stabilities of beta-peptide secondary structures are then analyzed. Combined with the substituent effect and the intrinsic backbone preferences, all experimental observations of secondary structure formation can be understood. For example, the 10/12-helix is favored for like-beta(2)/beta(3)-peptides, unlike-beta(3)/beta(3)-peptides, and beta(3)/beta-hGly-peptides because these substitution patterns do not cause steric problems for the 10/12-helix. Beta(3)-peptides, beta(2)-peptides, and beta (2,3)-peptides favor the 14-helix because the substituents in these peptides benefit the 14-helix the most but significantly destabilize the 10/12-helix. Because the 10/12-helix is intrinsically favored and has two favorable positions in each residue for substituents, many more hybrid beta-peptides are predicted to exist in this secondary structure, which suggests the need for further experiments. These results are valuable for determining the best use of these building blocks in the design of well-structured molecules with desirable chemical functions.

Establishing effective simulation protocols for beta- and alpha/beta-peptides. II. Molecular mechanical (MM) model for a cyclic beta-residue

All-atom molecular mechanical (MM) force field parameters are developed for a cyclic beta-amino acid, amino-cyclo-pentane-carboxylic acid (ACPC), using a multi-objective evolutionary algorithm. The MM model is benchmarked using several short, ACPC-containing alpha/beta-peptides in water and methanol with SCC-DFTB (self consistent charge-density functional tight binding)/MM simulations as the reference. Satisfactory agreements are found between the MM and SCC-DFTB/MM results regarding the distribution of key dihedral angles for the tetra-alpha/beta-peptide in water. For the octa-alpha/beta-peptide in methanol, the MM and SCC-DFTB/MM simulations predict the 11- and 14/15-helical form as the more stable conformation, respectively; however, the two helical forms are very close in energy (2-4 kcal/mol) at both theoretical levels, which is also the conclusion from recent NMR experiments. As the first application, the MM model is applied to an alpha/beta-pentadeca-peptide in water with both explicit and implicit solvent models. The stability of the peptide is sensitive to the starting configuration in the explicit solvent simulations due to their limited length ( approximately 10-40 ns). Multiple ( approximately 20 x 20 ns) implicit solvent simulations consistently show that the 14/15-helix is the predominant conformation of this peptide, although substantially different conformations are also accessible. The calculated nuclear Overhauser effect (NOE) values averaged over different trajectories are consistent with experimental data, which emphasizes the importance of considering conformational heterogeneity in such comparisons for highly dynamical peptides.

Molecular simulation as an aid to experimentalists

Computer-based molecular simulation techniques are increasingly used to interpret experimental data on biomolecular systems at an atomic level. Direct comparison between experiment and simulation is, however, seldom straightforward. The available experimental data are limited in scope and generally correspond to averages over both time and space. A critical analysis of the various factors that may influence the apparent degree of agreement between the results of simulations and experimentally measured quantities is presented and illustrated using examples from recent literature.

Foldamers as versatile frameworks for the design and evolution of function

Foldamers are sequence-specific oligomers akin to peptides, proteins and oligonucleotides that fold into well-defined three-dimensional structures. They offer the chemical biologist a broad pallet of building blocks for the construction of molecules that test and extend our understanding of protein folding and function. Foldamers also provide templates for presenting complex arrays of functional groups in virtually unlimited geometrical patterns, thereby presenting attractive opportunities for the design of molecules that bind in a sequence- and structure-specific manner to oligosaccharides, nucleic acids, membranes and proteins. We summarize recent advances and highlight the future applications and challenges of this rapidly expanding field.

The Structure of the Alzheimer Amyloid β 10-35 Peptide Probed through Replica-Exchange Molecular Dynamics Simulations in Explicit Solvent

The conformational states sampled by the Alzheimer amyloid beta (10-35) (Abeta 10-35) peptide were probed using replica-exchange molecular dynamics (REMD) simulations in explicit solvent. The Abeta 10-35 peptide is a fragment of the full-length Abeta 40/42 peptide that possesses many of the amyloidogenic properties of its full-length counterpart. Under physiological temperature and pressure, our simulations reveal that the Abeta 10-35 peptide does not possess a single unique folded state. Rather, this peptide exists as a mixture of collapsed globular states that remain in rapid dynamic equilibrium with each other. This conformational ensemble is dominated by random coil and bend structures with insignificant presence of an alpha-helical or beta-sheet structure. The 3D structure of Abeta 10-35 is seen to be defined by a salt bridge formed between the side-chains of K28 and D23. This salt bridge is also observed in Abeta fibrils and our simulations suggest that monomeric conformations of Abeta 10-35 contain pre-folded structural motifs that promote rapid aggregation of this peptide.

Simulation of an all-β3-icosapeptide containing the 20 proteinogenic side chains: Effect of temperature, pH, counterions, solvent, and force field on helix stability

Simulations of various beta-peptides have in the last years clarified several issues concerning peptide folding equilibria and interpretation of experimental data, especially from NMR and CD spectroscopy. These simulations involved different temperatures, pH-values, ionic strengths, solvents, and force-field parameters, but a variation of these factors for one beta-peptide has not yet been done. To investigate the influence of varying these factors, we analyze the helix stability of an all-beta3-icosapeptide bearing all 20 proteinogenic amino acid side chains, which is experimentally observed to fold into a 3(14)-helix in methanol but not in water. Structural aspects, such as hydrogen-bonded rings and salt bridges, are discussed and a comparison with NMR primary (NOE distance bounds and 3J-values) and secondary (NMR derived model structures) data is made. We further investigate the reasons for the 3(14)-helix stability/instability in methanol/water. Of all factors studied, the presence of counterions seems to be the one inducing most significant effects in the simulations.

Helices and other secondary structures of β- and γ-peptides

The principal secondary structural motifs adopted by peptides assembled from beta-amino acid units are discussed: the 14-, 12-, 10-, 12/10-, and 8-helices, as well as the hairpin turn, extended structures, stacks, and sheets. Features that promote a particular folding propensity are outlined and illustrated by structures determined in solution (NMR) and in the solid-state (x-ray). The N-C(beta)-C(alpha)-CO dihedral angles from molecular dynamics simulations, which are indicative of a particular secondary structure, are presented. A brief description of a helix and a turn of gamma-peptides is also given.