Application of evolutionary algorithm methods to polypeptide folding: comparison with experimental results for unsolvated Ac-(Ala-Gly-Gly)5-LysH+

Surrogate Based Genetic Algorithm Method for Efficient Identification of Low-Energy Peptide Structures

Identification of the most stable structure(s) of a system is a prerequisite for the calculation of any of its properties from first-principles. However, even for relatively small molecules, exhaustive explorations of the potential energy surface (PES) are severely hampered by the dimensionality bottleneck. In this work, we address the challenging task of efficiently sampling realistic low-lying peptide coordinates by resorting to a surrogate based genetic algorithm (GA)/density functional theory (DFT) approach (sGADFT) in which promising candidates provided by the GA are ultimately optimized with DFT. We provide a benchmark of several computational methods (GAFF, AMOEBApro13, PM6, PM7, DFTB3-D3(BJ)) as possible prescanning surrogates and apply sGADFT to two test case systems that are (i) two isomer families of the protonated Gly-Pro-Gly-Gly tetrapeptide (Masson, A.; J. Am. Soc. Mass Spectrom.2015, 26, 1444-1454) and (ii) the doubly protonated cyclic decapeptide gramicidin S (Nagornova, N. S.; J. Am. Chem. Soc.2010, 132, 4040-4041). We show that our GA procedure can correctly identify low-energy minima in as little as a few hours. Subsequent refinement of surrogate low-energy structures within a given energy threshold (≤10 kcal/mol (i), ≤5 kcal/mol (ii)) via DFT relaxation invariably led to the identification of the most stable structures as determined from high-resolution infrared (IR) spectroscopy at low temperature. The sGADFT method therefore constitutes a highly efficient route for the screening of realistic low-lying peptide structures in the gas phase as needed for instance for the interpretation and assignment of experimental IR spectra.

Going clean: structure and dynamics of peptides in the gas phase and paths to solvation

The gas phase is an artificial environment for biomolecules that has gained much attention both experimentally and theoretically due to its unique characteristic of providing a clean room environment for the comparison between theory and experiment. In this review we give an overview mainly on first-principles simulations of isolated peptides and the initial steps of their interactions with ions and solvent molecules: a bottom up approach to the complexity of biological environments. We focus on the accuracy of different methods to explore the conformational space, the connections between theory and experiment regarding collision cross section evaluations and (anharmonic) vibrational spectra, and the challenges faced in this field.

A Study of Ion-Neutral Collision Cross Section Values for Low Charge States of Peptides, Proteins, and Peptide/Protein Complexes

Here, we report ion-helium collision cross sections (CCS) for a number of peptide, small protein, and peptide/protein ionic complexes. The CCS values reported here are compared to previously reported results.[1, 2] We also compare values for low charge state species, i.e., [M + H](+) and [M + 2H](2+), formed by MALDI with values for high charge state species formed by ESI, and the measured CCSs are compared with predicted CCS for solid-state and solution phase structures and calculated structures obtained by using a protein-protein structure algorithm generator, based on a combined Biomolecular complex Generation with Global Evaluation and Ranking[3] and Multi Dimensional Scaling[4].

The contributions of molecular framework to IMS collision cross-sections of gas-phase peptide ions

Molecular dynamics (MD) is an essential tool for correlating collision cross-section data determined by ion mobility spectrometry (IMS) with candidate (calculated) structures. Conventional methods used for ion structure determination rely on comparing the measured cross-sections with the calculated collision cross-section for the lowest energy structure(s) taken from a large pool of candidate structures generated through multiple tiers of simulated annealing. We are developing methods to evaluate candidate structures from an ensemble of many conformations rather than the lowest energy structure. Here, we describe computational simulations and clustering methods to assign backbone conformations for singly-protonated ions of the model peptide (NH(2)-Met-Ile-Phe-Ala-Gly-Ile-Lys-COOH) formed by both MALDI and ESI, and compare the structures of MIFAGIK derivatives to test the 'sensitivity' of the cluster analysis method. Cluster analysis suggests that [MIFAGIK + H](+) ions formed by MALDI have a predominantly turn structure even though the low-energy ions prefer partial helical conformers. Although the ions formed by ESI have collision cross-sections that are different from those formed by MALDI, the results of cluster analysis indicate that the ions backbone structures are similar. Chemical modifications (N-acetyl, methylester as well as addition of Boc or Fmoc groups) to MIFAGIK alter the distribution of various conformers; the most dramatic changes are observed for the [M + Na](+) ion, which show a strong preference for random coil conformers owing to the strong solvation by the backbone amide groups.

Pendular proteins in gases and new avenues for characterization of macromolecules by ion mobility spectrometry

Polar molecules align in electric fields when the dipole energy (proportional to field intensity E x dipole moment p) exceeds the thermal rotational energy. Small molecules have low p and align only at inordinately high E or upon extreme cooling. Many biomacromolecules and ions are strong permanent dipoles that align at E achievable in gases and room temperature. The collision cross-sections of aligned ions with gas molecules generally differ from orientationally averaged quantities, affecting ion mobilities measured in ion mobility spectrometry (IMS). Field asymmetric waveform IMS (FAIMS) separates ions by the difference between mobilities at high and low E and hence can resolve and identify macroion conformers based on the mobility difference between pendular and free rotor states. The exceptional sensitivity of that difference to ion geometry and charge distribution holds the potential for a powerful method for separation and characterization of macromolecular species. Theory predicts that the pendular alignment of ions in gases at any E requires a minimum p that depends on the ion mobility, gas pressure, and temperature. At ambient conditions used in current FAIMS systems, p for realistic ions must exceed approximately 300-400 Debye. The dipole moments of proteins statistically increase with increasing mass, and such values are typical above approximately 30 kDa. As expected for the dipole-aligned regime, FAIMS analyses of protein ions and complexes of approximately 30-130 kDa show an order-of-magnitude expansion of separation space compared with smaller proteins and other ions.

Proton transfer-induced conformational changes and melting in designed peptides in the gas phase

The conformations of protonated RA15K, RA20K and RA15H (R = arginine, A = alanine, K = lysine, and H = histidine) have been examined in the gas phase as a function of temperature. These peptides were designed so that intramolecular proton transfer will trigger conformational changes between a helix (proton sequestered at the C-terminus) and globule (proton sequestered at the N-terminus). Kinetically controlled structural transitions occur below 400 K (from helix to globule for RA15H, and from globule to helix for RA15K and RA20K). As the temperature is raised, the compact globule found at room temperature expands, accesses more configurations, and becomes entropically favored. At around 500 K, the RA15K and RA20K helices undergo a melting transition. The transition is broad, as expected for a phase transition in a finite system, and becomes narrower as the peptide size increases. In the helical conformation, the two basic residues are well separated; as a result, the proton transfer necessary to drive the melting transition probably involves a mobile proton. For doubly protonated RA15K, a dumbbell-like conformation (resulting from repulsion between the two protonated basic residues) is found at high temperature.

Genetic algorithms for protein conformation sampling and optimization in a discrete backbone dihedral angle space

We have investigated protein conformation sampling and optimization based on the genetic algorithm and discrete main chain dihedral state model. An efficient approach combining the genetic algorithm with local minimization and with a niche technique based on the sharing function is proposed. Using two different types of potential energy functions, a Go-type potential function and a knowledge-based pairwise potential energy function, and a test set containing small proteins of varying sizes and secondary structure compositions, we demonstrated the importance of local minimization and population diversity in protein conformation optimization with genetic algorithms. Some general properties of the sampled conformations such as their native-likeness and the influences of including side-chains are discussed.

Helices and Sheets in vacuo

The structures and properties of unsolvated peptides large enough to possess secondary structure have been examined by experiments and simulations. Some of the factors that stabilize unsolvated helices and sheets have been identified. The charge, in particular, plays a critical role in stabilizing alpha-helices and destabilizing beta-sheets. Some helices are much more stable in vacuum than in aqueous solution. Factors like helix propensity, context, and the incorporation of specific stabilizing interactions have been examined. The helix propensities in vacuum differ from those found in solution. Studies of the hydration of unsolvated peptides can be performed one water molecule at a time. The first few water molecules only bind weakly to unsolvated peptides, and they bind much more strongly to some conformations than to others. The most favorable binding locations are not the protonation sites, but clefts or pockets where a water molecule can establish a network of hydrogen bonds. Non-covalent interactions between secondary structure elements leads to the formation of tertiary structure. Helical peptides assemble into complexes with a variety of intriguing structures. The intramolecular coupling of helices to make antiparallel coiled-coil geometries has also been investigated with model peptides.

Developing a move-set for protein model refinement

MOTIVATION

A wide variety of methods for the construction of an atomic model for a given amino acid sequence are known, the more accurate being those that use experimentally determined structures as templates. However, far fewer methods are aimed at refining these models. The approach presented here carefully blends models created by several different means, in an attempt to combine the good quality regions from each into a final, more refined, model.

RESULTS

We describe here a number of refinement operators (collectively, 'move-set') that enable a relatively large region of conformational space to be searched. This is used within a genetic algorithm that reshuffles and repacks structural components. The utility of the move-set is demonstrated by introducing a cost function, containing both physical and other components guiding the input structures towards the target structure. We show that our move-set has the potential to improve the conformation of models and that this improvement can be beyond even the best template for some comparative modelling targets.

AVAILABILITY

The populus software package and the source code are available at http://bmm.cancerresearchuk.org/~offman01/populus.html.

Structural Behavior and Self-Assembly of Lennard-Jones Clusters on Rigid Surfaces

The phase behavior and surface pattern formation for intermediate size Lennard-Jones clusters on rigid surfaces are examined. We use a parallel tempering Monte Carlo algorithm, in the canonical ensemble. Tempering is done over the temperature domain in most of the calculations. A two-dimensional temperature and Hamiltonian tempering algorithm is also implemented, to examine its usefulness in investigating this type of problem. In general, we observe gas phase systems as they undergo a condensation transition on the surface, followed by a freezing transition. The final solid state pattern formed by the cluster on the surface is the result of a number of competing effects. First, there is a competition between attraction within the cluster and that between cluster and surface atoms. Second, a monolayer of Lennard-Jones atoms tends to pack in a hexadic geometry. This geometry is frustrated on a surface with a different symmetry. The molecular organization of the substrate has a serious impact on the cluster packing. The surface morphology and the size mismatch between cluster and surface atoms, along with the relative interaction strengths, determine which of the effects prevail. When the surface atoms are small enough, the interactions within the cluster determine the symmetry of the pattern. In such a case, the substrate behaves similarly to a continuous surface, and the low-temperature pattern is a hexadic monolayer. When the sizes of the surface and cluster atoms are comparable, the low-temperature adsorbed geometry mimics the substrate symmetry. On a face-centered cubic surface, face-centered cubic monolayers or droplets are obtained.

Left-Handed and Ambidextrous Helices in the Gas Phase

We have used ion mobility mass spectrometry to study the effect of d-residues on helix formation in unsolvated alanine-based peptides. The right-handed helix of AC-A15K + H+ is significantly disrupted when five or more of the natural L-residues are randomly replaced with D-residues. On the other hand, when a block of L-residues is replaced with D-residues, an unusual ambidextrous structure with helical segments of opposite chirality is formed. A peptide with all D-residues forms a left-handed helix.