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Study of the quasicanonical localized orbital method based on protein structures
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10.1063/1.2786998
/content/aip/journal/jcp/127/18/10.1063/1.2786998
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/18/10.1063/1.2786998

Figures

Image of FIG. 1.
FIG. 1.

Outline of the scenario for all-electron calculation for proteins. The whole protein is calculated in several steps. Each line block represents a molecule calculated by the usual canonical MO method. In step 1, MO calculations are carried out on all single amino acids. In step 2, MO calculations are carried out on tripeptides, such as residues 1–3, 2–4, and 3–5,…. The initial guesses for tripeptides are evaluated by combining the results of step 1. In step 3, peptides of several residues are computed by combining the result of the middle residues of the tripeptides derived in step 2. After iterating this type of procedure, the MO calculation is performed on the whole protein.

Image of FIG. 2.
FIG. 2.

The pattern diagrams of hydrogen bond in secondary structure. (a) Alpha helix, (b) antiparallel beta sheet, (c) parallel beta sheet.

Image of FIG. 3.
FIG. 3.

The simplest QCLO scheme for estimating interaction energy between subunits. and stand for fragment. and stands for overlapped region between fragments and . The total energy of fragment and of fragment are calculated in STEP . The total energy of fragment is calculated in STEP . is calculated in order to evaluate interaction energy specially. The interaction energy between nonoverlapping regions is evaluated as difference between total of total energy of STEP and one of STEP . The small interaction energy implies that the frame molecules are divided ideally.

Image of FIG. 4.
FIG. 4.

Structures of test models. (a) The three-dimensional protein structure of model I. The portion drawn by the van der Waals model consists of residues composing the salt bridge. (b) Topological graphic showing the RGD peptide of model I. The colored region represents the residues forming the salt bridge (Asp3 and Arg5). (c) Three-dimensional protein structure of model II. This protein contains two alpha helixes. (d) Topological graphic of model II. The colored region represents the alpha helix (from Ser8 to Glu21 and from Val23 to Gln24). (e) Three-dimensional protein structure of model III. This protein contains an antiparallel beta structure. (f) Topological graphic of model III. The colored region represents the beta sheet (from Cys24 to Asp31, from Gly34 to Cys41, and from Leu52 to Cys55).

Image of FIG. 5.
FIG. 5.

Convergence processes of all-electron calculation in model I. Scenario I-a was performed in three steps using previous method. In step 1, all each amino acid composing protein was calculated. In step 2, tripeptide of 1–3, 2–4,…, 9–11 residues were calculated. In step 3 whole protein was calculated. Scenario I-b was performed using three steps as well as scenario I-a. In the case of scenario I-b, the improved method described in the present paper was employed. In step 1, all each amino acid was calculated and in step 2 tripeptides were calculated and in step 3 whole protein is calculated. However, if a frame molecule had a residue that formed a salt bridge with a molecule in the other frame, the partner residue was also involved in frame molecule. Specifically, all the frame molecules that contained Asp3 or Arg5 involved its salt bridge partner in scenario I-b.

Image of FIG. 6.
FIG. 6.

Convergence processes of all-electron calculation in model II. The shaded area represents residues arranged in an alpha helix (from Ser8 to Glu21 and from Val23 to Gln24). Steps 1, 2, and 4 were carried out in a similar manner in both scenarios. In step 1 all each amino acid was calculated, in step 2 tripeptides were calculated, and in step 4 whole protein is calculated. In step 3 of scenario II-a, the whole molecule was divided into five frame molecules composed of approximately seven residues (residues 1–7, 6–12, 11–17, 16–22, and 21–29). In step 3 of scenario II-b, the residues in the alpha helix were treated as one frame molecule (residues 1–4, 3–7, 6–22, 21–26, and 25–29).

Image of FIG. 7.
FIG. 7.

Convergence processes of all-electron calculation in model III. The shaded areas represent residues that are arranged in beta strands (from Cys24 to Asp31, from Gly34 to Cys41, and from Leu52 to Cys55). Steps 1, 2, and 4 are carried out in a similar manner in both scenarios. In step 1 all each amino acid was calculated, in step 2 tripeptides were calculated, and in step 4 whole protein is calculated. In step 3 of scenario III-a, the calculated frame molecules were peptides of approximately seven residues (residues 23–29, 28–34, 33–39, 38–42, 41–47, 46–53, 52–56). For step 3 of scenario III-b, a polypeptide folded into a beta sheet was treated as a single frame molecule (residues 42–47, 46–53, and ({23–43, and 52–56}). The frame molecule shown as a heavy line in scenario III-b was calculated as a single frame molecule.

Image of FIG. 8.
FIG. 8.

SCF convergence curve of the total energy in the final step in model I. The upper plot shows changes in total energy in SCF iterative calculation. The differences between the initial and final total energies were and in scenarios I-a and I-b, respectively. This indicates that the initial wave functions obtained using scenario I-b are closer to the final solution and are better estimated than those using scenario I-a. The total energy converged from the lower energy side. This is a frequent phenomenon in the RI-based DF method because of the incompleteness of the electron density expanded by auxiliary functions. The lower plot is differences of total energy among iterations. When the difference was below twice, we judged the calculation converged.

Image of FIG. 9.
FIG. 9.

Differences between the initial and final Mulliken atomic charges in the final step in model I. The hatched areas represent residues that form a salt bridge (Asp3 and Arg5). In scenario I-a, a striking difference in the salt bridge residues was observed; this difference was markedly smaller in scenario I-b.

Image of FIG. 10.
FIG. 10.

SCF convergence curve of the total energy in the final step in model II. The upper plot shows changes in total energy in SCF iterative calculation. The differences between the initial and the final total energies were and , using scenarios II-a and II-b, respectively. The lower plot is differences of total energy among iterations.

Image of FIG. 11.
FIG. 11.

Differences in Mulliken atomic charges between the initial guess and convergence in the step 4 of model II. The hatched area represents the alpha helix. In scenario II-a, the most striking differences were observed in the alpha helix region. Differences in the alpha helix were markedly smaller in scenario II-b.

Image of FIG. 12.
FIG. 12.

SCF convergence curve of the total energy in the final step in model III. The upper plot shows changes in total energy in SCF iterative calculation. The difference between the initial and final total energies using scenario III-b was about one-third of that obtained using scenario III-a. The lower plot is differences of total energy among iterations.

Image of FIG. 13.
FIG. 13.

Differences in Mulliken atomic charges between the initial guess and convergence in step 4 of model III. The hatched area represents an antiparallel beta sheet. The most striking differences in atomic charge in scenario III-a were found in the beta sheet residues. In scenario III-b, these significant differences in the beta sheet were markedly smaller because the beta-sheet residues were grouped as a single frame molecule.

Tables

Generic image for table
Table I.

Convergence information for the models.

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/content/aip/journal/jcp/127/18/10.1063/1.2786998
2007-11-12
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Study of the quasicanonical localized orbital method based on protein structures
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/18/10.1063/1.2786998
10.1063/1.2786998
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