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Corner Structural Motifs in Proteins S S symmetry Article Use of the Molecular Dynamics Method to Investigate the Stability of α-α-Corner Structural Motifs in Proteins Vladimir R. Rudnev 1,2, Liudmila I. Kulikova 1,3, Anna L. Kaysheva 2,*, Alexander V. Efimov 4 and Dmitry A. Tikhonov 1,3 1 Institute of Theoretical and Experimental Biophysics, Russian Academy of Sciences, 142290 Pushchino, Russia; [email protected] (V.R.R.); [email protected] (L.I.K.); [email protected] (D.A.T.) 2 V.N. Orekhovich Institute of Biomedical Chemistry, 119121 Moscow, Russia 3 Institute of Mathematical Problems of Biology RAS-the Branch of Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, 142290 Pushchino, Russia 4 Institute of Protein Research, Russian Academy of Sciences, 142290 Pushchino, Russia; efi[email protected] * Correspondence: [email protected]; Tel.: +7-(499)-764-98-78 Abstract: This study investigated the stability of structural motifs via molecular dynamics, using α-α-corners as an example. A molecular dynamics experiment was performed on a sample of α-α-corners selected by the authors from the PDB database. For the first time during a molecular dynamics experiment, we investigated the characteristics of structural motifs by describing their geometry, including the interplanar distance, area of polygon of the helices projections intersection, and torsion angles between axes of helices in helical pairs. The torsion angles for the constriction amino acids in the equilibrium portion of the molecular dynamics trajectory were analyzed. Using the molecular dynamics method, α-α-corners were found to be autonomous structures that are stable Citation: Rudnev, V.R.; Kulikova, in aquatic environments. L.I.; Kaysheva, A.L.; Efimov, A.V.; Tikhonov, D.A. Use of the Molecular Keywords: structural motifs of proteins; helical pairs; stability; molecular dynamics Dynamics Method to Investigate the Stability of α-α-Corner Structural Motifs in Proteins. Symmetry 2021, 13, 1193. https://doi.org/10.3390/ 1. Introduction sym13071193 Simple structural motifs are a current focus of researchers. These consist of two Academic Editor: Francesco Merlino elements of the secondary structure, which are characterized by unique folding of the polypeptide chain in space. This interest in structural motifs is due to the uniqueness of the Received: 12 June 2021 structures and their ability to act as focuses in the process of protein folding [1]. Structural Accepted: 28 June 2021 motifs can be used as starting structures to identify possible folds in a polypeptide chain Published: 2 July 2021 when modeling protein structures. They can also be used as stable structures in studies to predict the tertiary structure of a protein. Publisher’s Note: MDPI stays neutral Previously, Efimov [1] presented a classification of structural motifs, including two with regard to jurisdictional claims in α-helices, with unique folds of the polypeptide chain in space (α-α-corners, α-α-hairpins, published maps and institutional affil- and L-shaped and V-shaped structures). Types of helical pairs are presented in the Figure1 . iations. The α-α-hairpin motif is a supersecondary structure comprising two adjacent α-helices in the chain, which are constricted and packed antiparallel. The hairpin can be left or right, depending on how the second α-helix is located relative to the first. The length of the constrictions between the helices can also differ, and each standard α-α-hairpin contains Copyright: © 2021 by the authors. hydrophobic, hydrophilic, and glycine residues at strictly defined locations [2]. Licensee MDPI, Basel, Switzerland. Supersecondary L- and V-shaped structures are formed by two helices. Proline plays This article is an open access article a special role in the formation of L-shaped structures and promotes a link between two distributed under the terms and α-helices. Similar to studs, L-shaped structures can be right-handed or left-handed [3]. conditions of the Creative Commons V-shaped structures are also very similar to α-α-hairpins, in which the unconnected ends of Attribution (CC BY) license (https:// α-helices are very far from each other; they also appear as L-shaped structures. In V-shaped creativecommons.org/licenses/by/ structures, α-helices have a length that does not exceed three to four turns. 4.0/). Symmetry 2021, 13, 1193. https://doi.org/10.3390/sym13071193 https://www.mdpi.com/journal/symmetry Symmetry 2021, 13, x FOR PEER REVIEW 2 of 14 Symmetry 2021, 13, 1193 2 of 12 Figure 1. Types of the helical pairs, including two α-helices, with unique folds of the polypeptide Figurechain 1. Types in space. of the helical pairs, including two α-helices, with unique folds of the polypeptide chain in space. One of the most common structural motifs in homologous and non-homologous Theproteins α-α-hairpin is the α motif-α-corner is a supersecondary [4]. This supersecondary structure comprising structure is two formed adjacent by two α-hel- adjacent ices inα -helicesthe chain, along which the are polypeptide constricted chain, and connectedpacked antiparallel. by a constriction The hairpin and packed can be orthogonally left or right,in depending space. In proteins,on how αthe-α -cornerssecond α occur-helix in is the located form ofrelative a left supercoil.to the first. Their The sequences length of have the constrictionsa definite arrangement between the in helices chains can of hydrophobic,also differ, and hydrophilic, each standard and α glycine-α-hairpin residues. con- The tains sidehydrophobic, chains of residueshydrophilic, buried and in glycine the hydrophobic residues at core strictly are hydrophobic.defined locations Hydrophilic [2]. side Supersecondarychains or other polar L- and groups V-shaped can be structures recessed intoare formed a hydrophobic by two corehelices. (or otherProline hydrophobic plays a specialenvironment) role in the formation if they participate of L-shaped in the structures formation and of promotes hydrogen a link or ionic between bonds two [1 ].α- Thus, helices.each Similarα-helix to must studs, have L-shaped at least structures one hydrophobic can be residueright-handed per turn; or inleft-handed this case, hydrophobic [3]. V- shapedresidues structures should are bealso located very similar on one to side α-α of-hairpins, the α-helix in which and form the aunconnected continuous hydrophobicends of α-helicescluster are [ 4very]. far from each other; they also appear as L-shaped structures. In V- shaped structures,Previously α-helices [5–8], we have investigated a length that the geometricdoes not exceed characteristics three to four of double-helical turns. struc- Onetures. of Importantthe most common characteristics structural of helical motifspairs in homologous include inter-helical and non-homologous distances, the pro- torsion teins anglesis the α between-α-corner helical [4]. This axes insupersecondary helical pairs, the structure number is of formed amino acidsby two between adjacent helixes, α- the heliceslength along of the the polypeptide helixes, and chain, the area connected and perimeter by a constriction of the intersection and packed of helicalorthogonally projections. in space.In a previousIn proteins, study α-α [-corners9], we formulated occur in the rules form for theof a classification left supercoil. of Their double-helical sequences motifs have baseda definite on thearrangement geometric in and chains spatial of characteristicshydrophobic, hydrophilic, of their packing. and glycine residues. The side chainsIn proteins, of residuesα-helices buried are in tightlythe hydrophobic packed. Two core αare-helices hydrophobic. are packed Hydrophilic most densely side chainswhen thereor other is an polar antiparallel, groups can perpendicular, be recessed andinto canteda hydrophobic orientation core between (or other the hy- helices; drophobicexamples environment) of such packing if they include participate the supersecondary in the formation structures of hydrogenα-α-corners, or ionicα -bondsα-hairpins, [1]. Thus,and L-shapedeach α-helix and must V-shaped have structuresat least one (Figure hydrophobic1). The most residue studied per turn;α-α-corners in this case, are those hydrophobicwith short residues constrictions. should be The located constriction on one representsside of the theα-helix disordered and form part a continuous of the molecule, hydrophobicand each cluster amino [4]. acid residue within the constriction has a certain conformation from Previouslythe allowed [5–8], regions we on investigated the Ramachandran the geometric map. Since characteristics the conformational of double-helical change in the structures.molecule Important chain is characteristics significant (close of helical to rotation), pairs include the conformations inter-helical ofdistances, residues the in thetor- short sion anglesconstriction between are helical clamped axes within in helical a narrower pairs, the range. number These of patternsamino acids were between noted in he- [4] and lixes, requirethe length a comprehensive of the helixes, study and the and area statistical and perimeter analysis. of the intersection of helical projections.Many In a smallprevious proteins study exist[9], we that form compriseulated onlyrules onefor the or twoclassification known structural of double- motifs, α α helicalindicating motifs based that on such the structuralgeometric motifsand spatial are stablecharacteristics [4]. The of stability their packing. of - -corners was demonstrated indirectly in 1993 by Canadian researchers F. Tsai and J. Sherman (Univer- Symmetry
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