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The corresponding lengths in A are close to 2.77, 2.71 and 2.27 respectively. Also, the terminal hydrogen of the cysteine interact with the carbonyl of the same residue and with that of the nearest residue through two hydrogen bonds with lengths of 2.51 A and 2.19 A respectively. Finally sulfur interacts with the amide hydrogen of the peptide bond and the hydrogen acid is interacting with the carbonyl of the same amino acid. The corresponding lengths in A are in the range of 2.59 and 2.51 respectively. The A2C-n2and A2C -n3 structures are less stable. Energy deviations from A2C-n1 are in the range of 0.5 and 0.6 kcal / mol, respectively. The low instability of these structures can be explained structurally by the number and the nature of the intramolecular bonds characterizing each conformation. structural unit where three intramolecular bonds are built. A hydrogen bond, whose length is fixed and equal to 2.51 A is established between the carbonyl C-terminal residues with one of the amide hydrogen of the same residue. Two other bonds are built from the interaction of the carbonyl of residue i with the amide hydrogen of residue i + 1 from residue N to the C-terminal. The lengths of these bonds are around 2.18 A. Thus one of the structures can be the global minimum of neutral CA2-NHz2. Indeed, the energy gaps of 0.1 and 0.2 kcal / mol for CA2-n2 and CA2-n3, respectively, can be justified by the number of hydrogen bonds in the cysteine residue. Energy deviation from CA2-n1 rises by 0.7 kcal / mol for CA2-n4 and by 3.6 kcal / mol for CA2-n10. The conformational stability decreases with the increase of the formation energy and the variation of the number of intramolecular bonds established within the system.

Figure 11 The corresponding lengths in A are close to 2.77, 2.71 and 2.27 respectively. Also, the terminal hydrogen of the cysteine interact with the carbonyl of the same residue and with that of the nearest residue through two hydrogen bonds with lengths of 2.51 A and 2.19 A respectively. Finally sulfur interacts with the amide hydrogen of the peptide bond and the hydrogen acid is interacting with the carbonyl of the same amino acid. The corresponding lengths in A are in the range of 2.59 and 2.51 respectively. The A2C-n2and A2C -n3 structures are less stable. Energy deviations from A2C-n1 are in the range of 0.5 and 0.6 kcal / mol, respectively. The low instability of these structures can be explained structurally by the number and the nature of the intramolecular bonds characterizing each conformation. structural unit where three intramolecular bonds are built. A hydrogen bond, whose length is fixed and equal to 2.51 A is established between the carbonyl C-terminal residues with one of the amide hydrogen of the same residue. Two other bonds are built from the interaction of the carbonyl of residue i with the amide hydrogen of residue i + 1 from residue N to the C-terminal. The lengths of these bonds are around 2.18 A. Thus one of the structures can be the global minimum of neutral CA2-NHz2. Indeed, the energy gaps of 0.1 and 0.2 kcal / mol for CA2-n2 and CA2-n3, respectively, can be justified by the number of hydrogen bonds in the cysteine residue. Energy deviation from CA2-n1 rises by 0.7 kcal / mol for CA2-n4 and by 3.6 kcal / mol for CA2-n10. The conformational stability decreases with the increase of the formation energy and the variation of the number of intramolecular bonds established within the system.

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Polyalanine gas phase acidities determination and conformational space analysis by genetic algorithm assessment
Polyalanine gas phase acidities determination and conformational space analysis by genetic algorithm assessment
the gas phase (Tan and Ren, 2007; Ren et al., 2009; Morishetti et al., 2010; Shen and Ren, 2012). Cysteine- polyalanine, the subject of this study, consist of two uncharged amino acids namely Cysteine and Alanine. The C- terminal group of each system undergoes a change in the OH group which has been replaced by NHz2 to have a single acid site (AlaCysNH2, AlazCysNH2, AlasCysNH2z, AlasCysNH2 CysAlaNH2 and CysAla2NHz). 1985), to account for electronic effects. Furthermore, an important factor to take into account is the choice of the PES scanning technique. This must indeed be able to locate the global minimum without 'getting caught’ by local minima in the PES area surrounding the starting structure. Several research techniques can be used. The MNC genetic algorithm, developed and reported, allows after a sequence of steps (selection, crossover, mutation and substitution) to explore and exploit a very large conformational search space to converge directly to the proper equilibrium structures. Several factors may influence the convergence of these polypeptides towards the equilibrium structures, the diversity and the multiplication in dihedral angles (HSCC, HNCC, OCCN, HNCO, CNCC, CCNC.,...) vary and depends upon the nature of S,O and N heteroatoms, the acidic hydrogen of the thiol group and the hydrogen of the amine and the amide (Figure 1). ine acidity of an isolated amino acid 1s the most important thermochemical property which influences the structure, the reactivity, folding proteins and peptides as well (Ren et al., 2009). In solution form, the chemistry of this factor may be affected by the solvent; hence the concept of gas phase chemistry where solvent effect is eliminated is required. Acidity of a peptide of an amino acid depends primarily on its position along the peptide chain. A residue located in the N-terminal of a helix is more acidic than the C- terminal one (Ren et al., 2009; Morisheti et al., 2010). The acidity of the isolated amino acids is widely studied in recent years (Jones et al., 2007), while information on the acidity in Studies in model systems with different force fields have shown that the method of molecular mechanics MM is able to properly model the energies of polypeptides (Beachy et al., 1997). For large polypeptides, the MM is not able to accurately model the intramolecular interactions (Beachy et al., 1997). An alternative to this method could be the use of semi empirical procedures, AM1 in this case (Dewar et al.,
the gas phase (Tan and Ren, 2007; Ren et al., 2009; Morishetti et al., 2010; Shen and Ren, 2012). Cysteine- polyalanine, the subject of this study, consist of two uncharged amino acids namely Cysteine and Alanine. The C- terminal group of each system undergoes a change in the OH group which has been replaced by NHz2 to have a single acid site (AlaCysNH2, AlazCysNH2, AlasCysNH2z, AlasCysNH2 CysAlaNH2 and CysAla2NHz). 1985), to account for electronic effects. Furthermore, an important factor to take into account is the choice of the PES scanning technique. This must indeed be able to locate the global minimum without 'getting caught’ by local minima in the PES area surrounding the starting structure. Several research techniques can be used. The MNC genetic algorithm, developed and reported, allows after a sequence of steps (selection, crossover, mutation and substitution) to explore and exploit a very large conformational search space to converge directly to the proper equilibrium structures. Several factors may influence the convergence of these polypeptides towards the equilibrium structures, the diversity and the multiplication in dihedral angles (HSCC, HNCC, OCCN, HNCO, CNCC, CCNC.,...) vary and depends upon the nature of S,O and N heteroatoms, the acidic hydrogen of the thiol group and the hydrogen of the amine and the amide (Figure 1). ine acidity of an isolated amino acid 1s the most important thermochemical property which influences the structure, the reactivity, folding proteins and peptides as well (Ren et al., 2009). In solution form, the chemistry of this factor may be affected by the solvent; hence the concept of gas phase chemistry where solvent effect is eliminated is required. Acidity of a peptide of an amino acid depends primarily on its position along the peptide chain. A residue located in the N-terminal of a helix is more acidic than the C- terminal one (Ren et al., 2009; Morisheti et al., 2010). The acidity of the isolated amino acids is widely studied in recent years (Jones et al., 2007), while information on the acidity in Studies in model systems with different force fields have shown that the method of molecular mechanics MM is able to properly model the energies of polypeptides (Beachy et al., 1997). For large polypeptides, the MM is not able to accurately model the intramolecular interactions (Beachy et al., 1997). An alternative to this method could be the use of semi empirical procedures, AM1 in this case (Dewar et al.,
the gas phase of neutral peptides is still rare (Morisheti et a 2010). The acidity in the gas phase of the studied polypeptides is due to the acidity of the cysteine residu which contains acid thiol site. Therefore, the theoretical study of the equilibrium structures, the acidity in the gas phase and its variation as a function of the position of th cysteine and the number of residues constituting the peptid chain is studied by employing genetic algorithm approach. e y e e fitness. Each chromosome is composed of a set of elements called characteristics or genes. In the study of the conformational space problem of a_ given molecule, individuals correspond to conformations, the genes to dihedral angles and the fitness function to the heat of formation of the system.
the gas phase of neutral peptides is still rare (Morisheti et a 2010). The acidity in the gas phase of the studied polypeptides is due to the acidity of the cysteine residu which contains acid thiol site. Therefore, the theoretical study of the equilibrium structures, the acidity in the gas phase and its variation as a function of the position of th cysteine and the number of residues constituting the peptid chain is studied by employing genetic algorithm approach. e y e e fitness. Each chromosome is composed of a set of elements called characteristics or genes. In the study of the conformational space problem of a_ given molecule, individuals correspond to conformations, the genes to dihedral angles and the fitness function to the heat of formation of the system.
Table 2: Torsion angles of the three conformations which may be the equilibrium structures of the neutral CysAla-NH2 peptide obtained by AM1//GA method
Table 2: Torsion angles of the three conformations which may be the equilibrium structures of the neutral CysAla-NH2 peptide obtained by AM1//GA method
Table 3: Theoretical and experimental AHacia of studied peptides
Table 3: Theoretical and experimental AHacia of studied peptides
Fig. 3: The most stable conformations of the neutral CysAla-NH2 obtained by AM1 // genetic algorithm
Fig. 3: The most stable conformations of the neutral CysAla-NH2 obtained by AM1 // genetic algorithm
Fig. 4: The most stable conformations of the neutral AlaCys-NH2 obtained by AM1 // genetic algorithm
Fig. 4: The most stable conformations of the neutral AlaCys-NH2 obtained by AM1 // genetic algorithm
genome of each individual (conformation) is composed of n dihedral angels (#1, @2,...,pn), in the case of a molecule of n degrees of freedom, whose values represent a location on the PES. The crossover operator used is called interval crossover (Cedeno, 1995). In interval crossover, only one offspring is generated. For each pair of parent genes ~1 and @2, the offspring’s gene is selected at random from the interval [~1- €/2, @2te/2], assuming without loss of generality that ~1<@2, if we use a real encoding as in our case. The parameter ¢ will be called in the following the parameter of interval crossover. The crossover operation is thus performed so that it generates an offspring close to the parents. The mutation is applied to the offspring, generated by the crossover operation, with a probability Pm, while permuting a couple of genes of the offspring selected at random. Table 1 regroups the different control parameters of the algorithm used in this study. This algorithm is implemented in a package of program interfaced with MOPAC (Stewart, 1989) (version 6.0) in order to evaluate the quality of the individual to insert into he population in each iteration. The criterion of evaluation is he energy of the molecule (the heat of formation in our case). The semi-empirical method AM1 is used to accomplish this task. The data file has been conceived so that a constraint is imposed to the values of the dihedral angles defining the degrees of freedom of the conformation generated beforehand randomly. This constraint permits indeed to calculate exactly the energy of the conformation generated during the construction of the initial population and after the application of crossover and eventually the mutation operators as well. Once the algorithm converges after the fixed maximum number of generation, an optimization without constraint is performed in order to release the structure so that the individuals of the same niche converge to the correspondent minimum. t t
genome of each individual (conformation) is composed of n dihedral angels (#1, @2,...,pn), in the case of a molecule of n degrees of freedom, whose values represent a location on the PES. The crossover operator used is called interval crossover (Cedeno, 1995). In interval crossover, only one offspring is generated. For each pair of parent genes ~1 and @2, the offspring’s gene is selected at random from the interval [~1- €/2, @2te/2], assuming without loss of generality that ~1<@2, if we use a real encoding as in our case. The parameter ¢ will be called in the following the parameter of interval crossover. The crossover operation is thus performed so that it generates an offspring close to the parents. The mutation is applied to the offspring, generated by the crossover operation, with a probability Pm, while permuting a couple of genes of the offspring selected at random. Table 1 regroups the different control parameters of the algorithm used in this study. This algorithm is implemented in a package of program interfaced with MOPAC (Stewart, 1989) (version 6.0) in order to evaluate the quality of the individual to insert into he population in each iteration. The criterion of evaluation is he energy of the molecule (the heat of formation in our case). The semi-empirical method AM1 is used to accomplish this task. The data file has been conceived so that a constraint is imposed to the values of the dihedral angles defining the degrees of freedom of the conformation generated beforehand randomly. This constraint permits indeed to calculate exactly the energy of the conformation generated during the construction of the initial population and after the application of crossover and eventually the mutation operators as well. Once the algorithm converges after the fixed maximum number of generation, an optimization without constraint is performed in order to release the structure so that the individuals of the same niche converge to the correspondent minimum. t t
Fig. 7: The most stable conformations of neutral AlaCys-NH> obtained by AM1// genetic algorithm
Fig. 7: The most stable conformations of neutral AlaCys-NH> obtained by AM1// genetic algorithm
Fig. 9: The equilibrium structures of the conjugate base of AlazCys-NH2 optimized by AM1// genetic algorithm (9 a) anc B3LYP / 6-31 ++ G (d, p) (9b)
Fig. 9: The equilibrium structures of the conjugate base of AlazCys-NH2 optimized by AM1// genetic algorithm (9 a) anc B3LYP / 6-31 ++ G (d, p) (9b)
The most stable structure obtained using B3LYP/6-31++G(d,p) (Shen and Ren, 2012)
The most stable structure obtained using B3LYP/6-31++G(d,p) (Shen and Ren, 2012)
Fig. 12: The most stable conformations of neutral AlasCysNH2 obtained using AM1// genetic algorithm
Fig. 12: The most stable conformations of neutral AlasCysNH2 obtained using AM1// genetic algorithm
Fig. 13: The equilibrium structures of conjugated base of AlazCys-NH2 optimized with AM1// genetic algorithm (13, a) and AM1 // simulated annealing (13, b)
Fig. 13: The equilibrium structures of conjugated base of AlazCys-NH2 optimized with AM1// genetic algorithm (13, a) and AM1 // simulated annealing (13, b)
Fig. 14: The equilibrium structures of conjugated base of AlagCys-NH2 optimized with AM1//genetic algorithm (14,a) and AM1// simulated annealing (14,b)
Fig. 14: The equilibrium structures of conjugated base of AlagCys-NH2 optimized with AM1//genetic algorithm (14,a) and AM1// simulated annealing (14,b)
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