ProteinDF is a program designed for attaining all-electron calculations on proteins. It adopts the density functional method which uses gaussian-type functions in the calculation and the object-oriented technology in the programming, respectively. The all-electron calculation on cytochrome c was achieved in 2000, and the research is now advancing in FSIS and RSS21 projects supported by the program of the Ministry of Education, Culture, Sports, Science and Technology. The computational size, speed, and stability have greatly improved. In this paper, we introduce the current status and future view of ProteinDF and its interface which plays a key role for practical use.
A theoretical framework called QM/MM (Quantum Mechanics/Molecular Mechanics) is attracting considerable attention as a new approach to the handling of large scale bio-related molecules like proteins in membrane and solution. In the scheme, molecular regions of interest are described in quantum mechanical terms and the rest of the complex molecular system in classical manner, i.e., molecular mechanics. Since computational effort for the QM region increases roughly in proportion to the third power of the number of atoms, computational time is drastically decreased by choosing the QM space as small as possible. In this article, the basic concept of the QM/MM theory and a new attempt to overcome their problems in actual simulations are given. An application to new drug design is introduced, which has been developed in the BioGrid project organized by Osaka University and others.
The application of quantum theory to the investigation of large bio-molecular systems may require an alternative general theory of many-body problems. Straightforward extension of rather established quantum chemical methodologies may encounter serious problems both theoretically and technically. In order to fulfill the required precision for bio-science, the representation of space in simulation is critical. For next generation quantum chemistry, there should be more refined tools than Gaussian basis functions which have been used over half a century. Preliminary application of multi-resolution multi-wavelet basis functions proved its efficiency in the prediction of molecular properties such as polarizability.
Kitaura et al. (Chem. Phys. Lett.312, 319-324 (1999)) have proposed an ab initio fragment molecular orbital (FMO) method by which large molecules such as proteins can be easily treated with chemical accuracy. In the ab initio FMO method, a molecule or a molecular cluster is divided into fragments, and the MO calculations on the fragments (monomers) and the fragment pairs (dimers) are performed to obtain the total energy that is expressed as a summation of the fragment energies and inter-fragment interaction energies (IFIEs). In this paper, we provide a brief description of the ab initio FMO method and demonstrate recent applications in the nano-bio field.
This review introduces the application of the Fragment molecular orbital (FMO) method. The ABINIT-MP and BioStation Viewer programs have been used for such applications. The FMO method was applied for problems of transcriptional regulation, including interactions of nuclear receptor, ligand, transcription factor, and DNA. Detailed interactions between biomolecules and the roles of each amino acid residue were revealed through analyses of inter-fragment interaction energy (IFIE), charge distribution, and orbital configuration. Electrostatic and van der Waals dispersion interactions were found to be equally important in molecular recognition. It was found that the inclusion of electron correlation was essential to obtain appropriate pictures. Other applications such as the photo-excitation process are also introduced.
Numerical methods for the eigenvalue problem of second-order ordinary differential equations are presented. One is the discretized matrix eigenvalue method and another is the shooting method. In the former method, derivative with respect to spatial coordinate is discretized, thus the ordinary differential equation is transformed into matrix eigenvalue problems, then the matrix eigenvalue problems are solved numerically. The latter method has three steps. Firstly, initial values for the eigenvalue and eigenfunction at both ends are obtained by using the discretized matrix eigenvalue method. Secondly, the initial-value problem is solved using new, highly accurate formulas of the linear multistep method. Thirdly, the eigenvalue is properly corrected at the matching point. The efficiency of the proposed methods is demonstrated by their applications to bound states for the one-dimensional harmonic oscillator and anharmonic oscillators, the Morse potential and the modified Pöschl-Teller potential in quantum mechanics.
We have been developing a computational tool to obtain the molecular orbitals for large molecules such as proteins and molecular clusters without excessive calculation costs. In our method, the entire Fock matrix is generated using density matrix obtained from the fragment molecular orbital method, which is applicable to large systems and suitable for parallel processing. To solve the large scale generalized eigenproblem, we use the Sakurai-Sugiura method. This method solves several liner equations which have large granularity and is well suited to master-worker type execution. It is sufficient for parallel processing on computers of distributed memory parallel architecture. The method is favorable for calculation of only a small number of eigenvalues and corresponding eigenvectors of a large scale matrix. Our method has high parallelization efficiency and the communication cost is negligible to the total calculation costs. Thus, this is one of the right applications for using Grid technology. Elapsed times to obtain MOs close to HOMO-LUMO of Lysozyme (129 amino-acid residues and solvent molecules, total 8258 atoms) with FMO/HF/STO-3G (20758 basis functions)) and model DNA (40 A-T base pairs, total 2636 atoms with FMO/HF/STO-3G (10108 basis functions)) are less than about 5 hours and 1 hour, respectively, on only 128 Dual Opteron cluster. The position of HOMO and LUMO in the Lysozyme and water cluster case is strongly dependent on distribution and the number of solvent water molecules. Careful treatment for solvent molecules is required to have consistent results. In the case of model DNA, HOMO and LUMO are located at the center and the terminal of the DNA chain, respectively.