Modeling and predicting super-secondary structures of transmembrane beta-barrel proteins Thuong van Du Tran To cite this version: Thuong van Du Tran. Modeling and predicting super-secondary structures of transmembrane beta-barrel proteins. Bioinformatics [q-bio.QM]. Ecole Polytechnique X, 2011. English. NNT : 2011EPXX0104. pastel-00711285 HAL Id: pastel-00711285 https://pastel.archives-ouvertes.fr/pastel-00711285 Submitted on 23 Jun 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THESE` pr´esent´ee pour obtenir le grade de DOCTEUR DE L’ECOLE´ POLYTECHNIQUE Sp´ecialit´e: INFORMATIQUE par Thuong Van Du TRAN Titre de la th`ese: Modeling and Predicting Super-secondary Structures of Transmembrane β-barrel Proteins Soutenue le 7 d´ecembre 2011 devant le jury compos´ede: MM. Laurent MOUCHARD Rapporteurs Mikhail A. ROYTBERG MM. Gregory KUCHEROV Examinateurs Mireille REGNIER M. Jean-Marc STEYAERT Directeur Laboratoire d’Informatique UMR X-CNRS 7161 Ecole´ Polytechnique, 91128 Plaiseau CEDEX, FRANCE Composed with LATEX !c Thuong Van Du Tran. All rights reserved. Contents Introduction 1 1Fundamentalreviewofproteins 5 1.1 Introduction................................... 5 1.2 Proteins..................................... 5 1.2.1 Aminoacids............................... 5 1.2.2 Properties of amino acids . 6 1.2.3 Peptidebond .............................. 10 1.2.4 Protein ................................. 12 1.2.5 Proteinstructure............................ 16 1.3 Transmembraneproteins. 20 1.3.1 Biological membrane . 20 1.3.2 Transmembrane proteins . 21 1.4 Foldingenergy ................................. 24 1.4.1 Partial charges . 25 1.4.2 Electrostatic interaction . .. 25 1.4.3 Hydrogen bond . 25 1.4.4 Van der Waals forces and steric repulsion . ... 27 1.4.5 Hydrophobic effect and interaction with the environment ..... 28 1.4.6 Torsion energy around peptide bonds . 29 1.4.7 Otherinteractions ........................... 29 1.5 Proteinstructuredetermination. ..... 29 1.5.1 Experimentalmethods. 29 1.5.2 In silico prediction ........................... 30 2Foldingβ-barrels 33 2.1 Introduction................................... 33 2.2 Geometric framework for β-barrels ...................... 33 2.3 Physicochemicalconstraints . .... 35 2.4 Classificationfiltering ........................... .. 38 2.5 Foldingproblemdefinition. .. 39 i Contents 2.5.1 Vertices ................................. 39 2.5.2 Edges .................................. 39 2.5.3 Energyattributes: ........................... 40 2.5.4 Protein folding problem . 42 2.6 Dynamic programming approach . 43 2.6.1 Solving as the longest path problem . 43 2.6.2 Solving as the longest closed path problem . ... 43 2.6.3 Generalization . 44 2.7 Complexityonpermutedstructures. .... 49 2.7.1 Preliminaries .............................. 49 3Tree-decompositionbasedalgorithm 57 3.1 Introduction................................... 57 3.2 Graph-theory background . 57 3.2.1 Tree decomposition . 58 3.2.2 Modular decomposition . 60 3.3 NP-Completeness................................ 60 3.4 Algorithm for finding barrel structures of minimum energy......... 63 3.5 About Greek key motifs in β-barrels ..................... 68 4EvaluationofperformanceofBBP 75 4.1 Introduction................................... 75 4.2 Experimentalsetup............................... 75 4.2.1 Software................................. 75 4.2.2 Datasets................................. 75 4.3 Implementationdetails. .. 78 4.4 Methodofevaluation.............................. 80 4.4.1 Concepts on predicted secondary structures . ..... 80 4.4.2 Measures of performance . 82 4.5 Experimentalresults ............................. 84 4.5.1 Folding ................................. 85 4.5.2 Evaluation of the shear numbers . 86 4.5.3 Influenceofthefilteringthreshold . .. 86 4.5.4 Evaluation on mutated sequences . 89 4.5.5 Permutedstructures . 92 4.5.6 Classification . 92 Conclusion and perspectives 94 Bibliography 97 ii List of Figures 1.1 Isomers L and D of amino acids . 6 1.2 The 20 amino acids. The side chains are in red. ..... 7 1.3 Peptide bond geometry in trans configuration . 12 1.4 Torsion angles between two peptide plans . ..... 13 1.5 Ramachandran plot for the outer membrane protein A (PDB:1BXW) . 14 1.6 Structure of collagen (PDB:1BKV) . ... 14 1.7 Structure of myoglobin (PDB:1A6M) . ... 15 1.8 Structureof insulinereceptor (PDB:1GAG) . ...... 15 1.9 Structure of an α-helix............................. 17 1.10 Antiparallel pairing (a) and parallel pairing (b) of β-strands . 17 1.11 Characteristics of a β-sheet........................... 18 1.12 Tertiary structure (a) and super-secondary structure (b) of the cystic fi- brosis transmembrane conductance regulator (PDB:1R0W) . ...... 19 1.13 Quaternary structure of human hemoglobin (PDB:1MKO) . ........ 19 1.14 Illustration of a biological membrane and embedded membrane proteins. 21 1.15 Transmembrane proteins: (1) a single transmembrane hydrophobic α-helix -bitopicmembraneprotein,(2)severaltransmembranehydrophobic α- helices, (3) transmembrane β-barrelprotein.. 22 1.16 Bacteriorhodopsin in purple membrane (PDB:2BRD) . ........ 23 1.17 Outer membrane protein X (PDB:1QJ8) . ... 24 1.18 Hydrogen bonds represented in dash lines: (a) between water molecules and (b) between carboxylic and amino groups. δ+ and δ− are positive and negative partial charges, respectively. ...... 27 2.1 The simplified geometry of a β-barrel, a schematic planar view for 6 strands (strand 1 is duplicated for clarity). Thick lines denote the peptide bonds that link consecutive amino acids along their strand. Thin lines denote the hydrogen bonds that link the amino acids of two adjacent strands. In this example, the shear number is S =8,whichistheordinaldistancebetween amino acids A and B.Wenotethatallknownβ-barrels have a positive shear number [80]andareslanted“totheright”,asillustratedhere. 34 iii List of Figures 2.2 A schematic planar representation of 3 β-strands in a transmembrane β- barrel. The black residues direct their side chains toward the membrane and white ones toward the channel. The first and third strands are upward and the second one is downward.Thefirstandsecondstrandsareodd outward and the third one is odd inward.................... 36 2.3 The distribution of average hydrophobicity index of the hydrophilic side of the membrane spanning β-strands from PDBTM40 (see Section 4.2).. 37 2.4 The distribution of average hydrophobicity index of the hydrophobic side of the membrane spanning β-strands from PDBTM40 (see Section 4.2).. 37 2.5 A short example of the graph structure. Edge (v1,v2)isnotallowed,since the two corresponding substrings overlap. Edges (v2,v3)or(v2,v6)arenot allowed, since the substrings in between are respectively too short for a turnortoolongforaloop,etc. 40 2.6 Different views of a β-barrel with a Greek key motif 3654, σ =123654 . 42 2.7 A permuted β-barrel with a Greek key motif 5436, σ =125436 . 44 2.8 Schema of sets conf k corresponding to σ = {1, 2, 5, 4, 3, 6} ......... 46 ∗ th 2.9 Relation ∆k and its transitive closure ∆k on the k substructure . 47 2.10 Illustration for property 2.7 .......................... 48 3.1 A graph and a tree decomposition of width 3 . ... 59 3.2 A path decomposition of width 3 of the graph in 3.1 ............ 59 3.3 A graph and its modular decomposition are on the left. The quotient graphisontheright............................... 61 3.4 The β-barrel(a), Gc(b) and the tree/path decomposition(c) of σ =1432 5678...................................... 63 3.5 Gc(a) and its tree decomposition(b) of σ =32145678......... 69 3.6 Gc(a), its quotient graph(b) and its tree decomposition(c) of σ =3214 76581110912. 70 3.7 Gc(a), its quotient graph(b) and its tree decomposition(c) of σ =1432 5678...................................... 70 3.8 Gc(a) and its tree decomposition(b) of σ =12345876......... 71 3.9 Gc(a), its quotient graph(b) and its tree decomposition(c) of σ =1432 58769121110. 71 3.10 Gc(a), its quotient graph(b) and its tree decomposition(c) of σ =1254 36987101112. 72 3.11 Gc(a) and its tree decomposition(b) of σ =12345671098 ...... 72 3.12 Gc(a), its quotient graph(b) and its tree decomposition(c) of σ =1236 54710981112. 73 3.13 The reduced graph G+− for g+g−(a) and its tree decomposition of width 3(b) ....................................... 73 4.1 Comparison of BBP and TMBpro on structure prediction results. 87 iv List of Figures hS 4.2 Energy distribution of setECOLI40, θ =arctandn ............ 88 4.3 MCC of mutated setECOLI40 ........................ 90 4.4 F-score of mutated setECOLI40 ....................... 91 4.5 Distribution of 7! permutations on E. Coli OmpA 1BXW 8-strand barrel 93 4.6 Distribution of 7! permutations on E. Coli OmpX 1QJ8 8-strand barrel . 93 v List of Figures vi List of Tables 1.1 Hydrophobicscales............................... 8 1.2 Polarity, flexibility and other physicochemical parameters of amino acids . 9 1.3 Partial charges from the Gromos force field for standard amino acids. e is the absolute value of elementary charge unit.