Secondary structure and assignment

The peptide backbone of each amino acid residue has three conformational degrees of freedom, namely the main chain torsions ω (peptide bond), ϕ (C-N-C_α-C) and ψ (N-C_α-C-N). The planarity of the peptide bond (partial double bond character) restrictsω to 180 degrees. For a cis peptide bond in proline residues one can find also 0 degrees. The accessible conformational space even for a small protein will therefore be enormously large, let alone for proteins of tens or even hundreds of residues [2].

However, the local (secondary) structure of the peptide main chain is very ordered in the folded state and organized in repeating patterns [12]. This is due to a tight local packing and the extensive hydrogen bond formation between (intra-)backbone donor (NH) and acceptor (C=O) atoms. The different amino acid propensities for certain secondary structure conformations indicate the important role of the side chains in defining the regular secondary structure motifs (e.g. β-sheets are rich in valine, isoleucine and poor in glycine and proline) [200].

As in many other biological processes, the main structural changes in peptide folding and self-association occur on the level of secondary structure, with a particular prevalence of β-sheet conformations in the latter case [4,201]. Given the atomic coordinates of a protein or peptide structure one seeks to obtain a consistent assignment of secondary structure elements in an automated fashion. I therefore briefly review the basic principles of the two popular assignment methods DSSP [202] and STRIDE [203], which were used for secondary structure classification in this thesis.

DSSP (Dictionary of Secondary Structure of Proteins). The DSSP algo-rithm [202] assigns secondary structure elements purely based on calculations of backbone-backbone hydrogen bond energetics. The hydrogen bond coulomb energy E is approximated by the term

where the partial charges q₁ = 0.42,q₂ = 0.20 and the constantf = 1390 kJ/mol. To identify a hydrogen bond, a cutoff with an energy E of less than -2.1 kJ/mol is applied.

Eight types of secondary structure are recognized by DSSP depending on the pattern of hydrogen bonds. A repetitive sequence of hydrogen bonds in which the donor residue is three, four, or five residues later in the backbone define a 3₁₀-, α- and π-helix, respectively.

Hydrogen bond pairs in β-sheet structures are classified as parallel and antiparallel bridges;

extended (repeating) sets of hydrogen bond pairs of the same type are equivalent to aβ-sheet.

Remaining types are turn (featuring a hydrogen bond typical of a helix) and bend motifs for a region of high curvature.

STRIDE (STRuctural IDEntification). The assignment of individual secondary structural elements in STRIDE [203] are based on a more complex expression of hydrogen bond energy and in addition to DSSP, on empirical ϕ-ψ torsional angle criteria.

The term for the total hydrogen bond energy E_hb reads E_hb=E_r·E_t·E_p,

with E_r being a distance-dependent 8-6 potential similar to a Lennard-Jones potential with optimal distances of 3 Å (NO) for the backbone hydrogen bond. E_t and E_p are angular dependent factors, which define the optimized hydrogen bond geometry. The terminal residues are assigned with secondary structure through reliance on torsional angles. The individual secondary structural elements are mapped into the same classes (helix, sheet, coil) as those reported by DSSP.

Secondary structure propensities in peptide

folding simulations: A systematic comparison of molecular mechanics interaction schemes

• D. Matthes and B. L. de Groot, Biophys. J. 2009, 97, 599-608.

Summary

A systematic study directed toward the secondary structure propensity and sampling behavior in peptide folding simulations with eight different molecular dynamics force field variants in explicit solvent is presented. It reports on the combinational result of force field, water model, and electrostatic interaction schemes and compare to available experimental characterization of five studied model peptides in terms of reproduced structure and dynamics. The total simulation time exceeded 18 µs and included simulations that started from both folded and extended conformations. Despite remaining sampling issues, a number of distinct trends in the folding behavior of the peptides emerged. Pronounced differences in the propensity of finding prominent secondary structure motifs in the different applied force fields suggest that problems point in particular to the balance of the relative stabilities of helical and extended conformations.

3.1 Introduction

Molecular dynamics (MD) simulations are routinely utilized to study the folding dynamics of peptides and small proteins as well as biomolecular aggregation. The critical constituents of such molecular mechanics studies are the validity of the underlying physical models together with the assumptions of classical dynamics and a sufficient sampling of the conformational space. In order to verify and validate simulation results, a careful comparison of the simulation outcome directly to experimental data is mandatory (e.g., obtained by NMR, CD or infrared spectroscopy) [204].

Comprehensive reports on applications, improvements and remaining challenges of empirical force field based simulation methods, the choice of water model and electrostatic interaction schemes to study biomolecular systems have been discussed in the literature [147–152].

Within the framework of MD force fields, particular importance is directed to the consistent and proper parameterization of the atomistic interactions, with the functional formulation of the bonded and nonbonded forces often similar among nonpolarizable MD schemes. The latest ef-forts to improve the accuracy of the popular and commonly used force fields AMBER [155,156], CHARMM [158], GROMOS96 [161] and OPLS [164] mainly focused on refining parameters for the torsional potentials of the protein backbone in order to balance the conformational equilib-rium between extended and helical structures.

A recent comparative study using selected variants of the AMBER, CHARMM, GROMOS96 and OPLS force fields reported on converging results for folded proteins between the different compared models. It was suggested that there is an apparent consensus view of protein dynamics [168]. In that study simulations of relatively short lengths were performed and the natively folded state was used as starting point, possibly biasing the results [168].

For folding simulations such a systematic test has not been carried out so far, although with growing computer power several approaches towards the in silico folding problem for peptides and small proteins, both using an implicit or explicit representation of the solvent environment, have been presented [108,205–210]. Given an efficient sampling of conformational space and access to sufficient simulation timescales, one should expect to sample conformational ensembles close to the natively most populated states in solution, even when starting from peptide conformations away from the native structure. Hence, the application of biomolecular simulations offers the unique opportunity to study and predict complex processes in detail that underlie the protein folding thermodynamics and kinetics. For instance, the early events of peptide and protein folding, marked by established and stabilized secondary structure motifs [201].

A realistic preferential formation and representation of secondary structure is therefore a critical prerequisite for the successful study of in silico folding and aggregation.

Thus the question of overall peptide folding representation in different force fields prompted us to investigate the folding behavior and secondary structure formation at the microsecond timescale of a number of prototypic peptides in different MD force fields.

Here, the results of peptide folding and secondary structure formation for five model peptides (two β-hairpins, two α-helical peptides and the Trp-cage) in five state of the art force fields and different schemes for calculating electrostatic interactions are presented.

Extensive MD simulations in explicit water, starting from both extended and prefolded structures are presented that address the folding thermodynamics and sampling characteristics of the different interaction schemes.