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Hydrophobic effect and interaction with the environment
The hydrophobic effect is the fact that a nonpolar molecule (or part of molecule) is incapable of hydrogen bonding with water molecules, thus agglomerate together in aqueous medium and exclude water molecules. It is not an attractive or repulsive force, but rather, it is entropically driven. Each water molecule is able to form four hydrogen bonds with its neighbors, thus in order that a nonpolar molecule dissolves into water, such hydrogen bonds have to be broken. The hydrogen bonding network of water disrupted by the nonpolar molecule will reform, by making a cage, around the molecule. This structure of cage is ordered, and thus is unfavored by the second law of thermodynamics which requires an increase in entropy. Hence, the corresponding free energy is unfavorable. The reorganization of water molecules is easier when the nonpolar surface exposed to the aqueous solution is reduced by aggregating the nonpolar molecules together. The hydrophobic effect plays the most important role in protein folding, compared to other non-covalent interactions. It helps polypeptide chains fold in a relatively compact form with a hydrophobic core.
Besides, due to the polarity of water molecules, amino acids with ionized or polar side chains have a tendency to interact with the aqueous medium through hydrogen bonds (see 1.4.3). This allows proteins to exist in water with a hydrophilic exterior.
About Greek key motifs in !-barrels
Following the standard structure corresponding to the identity permutation, the !-barrels are found more commonly in such a way that the !-strands are paired in an antiparallel manner to each other. Among this, the most popular structures are those containing disjoint Greek key motifs (see Figure 2.6), for which, our approach can efficiently solve the optimization problem.
We study different possible configurations for disjoint Greek key motifs in permutations. For such structures, we can apply the elimination process to the quotient graph of the n-strand barrel graph Gc to construct its tree decomposition. The notations mentioned in this section are those of Section 2.7. The regular expression is used to describe the permutation. We consider the alphabet Σ = {Id, g+, g−}, where Id represents the identity motifs, g+ represents Greek key motifs of form k(k + 3)(k +2)(k +1) and g− represents (k+2)(k +1)k(k +3). A permutation with disjoint Greek key motifs can be written as a word of Σ∗. For example, 14325678=g+Id = Idg−Id, 14327658 = g+g−.
• For $ ∈ H1:
– $ = Id: Gc is a cycle, thus has treewidth 2. The complexity is then O(nN2).
– $ = (1 3) = g−Id: The n-strand barrel graph is an outerplanar graph, thus has treewidth 2 (see Figure 3.5) The complexity is then O(nN2).
Evaluation of the shear numbers
We studied the energy distribution of 17 TMB structures in Escherichia coli taken from setPDBTMB40 (setECOLI40: 1AF6 A, 1BXW A, 1BY3 A, 1FEP A, 1ILZ A, 1PNZ A, 1QJ8 A, 1TLW A, 2F1T A, 2GSK A, 2HDF A, 2IWW A, 2J1N A, 2R4P A, 2WJQ A, 3AEH A, 3GP6 A) with regard to the slant angle, hence the shear number (see Figure 4.2). Most optimal structures incline with an angle of 41◦ −49◦, as observed in databases. This suggests that our model takes well into account the physicochemical properties of TMB structures. It should be also noted that there is no natural way to define the shear number a priori
Table of contents :
Introduction
1 Fundamental reviewofproteins
1.1 Introduction
1.2 Proteins
1.2.1 Amino acids
1.2.2 Properties of amino acids
1.2.3 Peptide bond
1.2.4 Protein
1.2.5 Protein structure
1.3 Transmembrane proteins
1.3.1 Biological membrane
1.3.2 Transmembrane proteins
1.4 Folding energy
1.4.1 Partial charges
1.4.2 Electrostatic interaction
1.4.3 Hydrogen bond
1.4.4 Van der Waals forces and steric repulsion
1.4.5 Hydrophobic effect and interaction with the environment
1.4.6 Torsion energy around peptide bonds
1.4.7 Other interactions
1.5 Protein structure determination
1.5.1 Experimental methods
1.5.2 In silico prediction
2 Folding β-barrels
2.1 Introduction
2.2 Geometric framework for β-barrels
2.3 Physicochemical constraints
2.4 Classification filtering
2.5 Folding problem definition
2.5.1 Vertices
2.5.2 Edges
2.5.3 Energy attributes:
2.5.4 Protein folding problem
2.6 Dynamic programming approach
2.6.1 Solving as the longest path problem
2.6.2 Solving as the longest closed path problem
2.6.3 Generalization
2.7 Complexity on permuted structures
2.7.1 Preliminaries
3 Tree-decomposition basedalgorithm
3.1 Introduction
3.2 Graph-theory background
3.2.1 Tree decomposition
3.2.2 Modular decomposition
3.3 NP-Completeness
3.4 Algorithm for finding barrel structures of minimum energy
3.5 About Greek key motifs in β-barrels
4 Evaluationofperformance ofBBP
4.1 Introduction
4.2 Experimental setup
4.2.1 Software
4.2.2 Datasets
4.3 Implementation details
4.4 Method of evaluation
4.4.1 Concepts on predicted secondary structures
4.4.2 Measures of performance
4.5 Experimental results
4.5.1 Folding
4.5.2 Evaluation of the shear numbers
4.5.3 Influence of the filtering threshold
4.5.4 Evaluation on mutated sequences
4.5.5 Permuted structures
4.5.6 Classification
Conclusion and perspectives
Bibliography
