Applications of the Cluster Method for Biological Systems

This Chapter deals with ab initio studies of Biological Systems treated as large clusters of molecular and atomic entities. After a brief review of the theoretical background, with special focus on Hartree-Fock theory and many-body methods, the advantages of the choice of Gaussian basis sets will be analyzed. Convergence criteria to be discussed include the number of variational basis states used and the actual sizes of the molecular clusters under investigation. The main part of the Chapter centers around a discussion of the application of the cluster method to various types of biological systems and the particular issues that need to be considered for each system. Comparisons with experimental data are made where available.

[1]  M. Stoneking Single nucleotide polymorphisms: From the evolutionary past. . . , 2001, Nature.

[2]  T. P. Das,et al.  First-Principles Theory of Muon and Muonium Trapping in the Protein Chain of Cytochrome c and Associated Hyperfine Interactions , 2001 .

[3]  A. N. Enyashin,et al.  DNA-wrapped carbon nanotubes , 2007 .

[4]  Shibayama,et al.  Disordered magnetism at the metal-insulator threshold in nano-graphite-based carbon materials , 2000, Physical review letters.

[5]  D. F. Koenig The structure of a-chlorohemin , 1965 .

[6]  T. P. Das,et al.  Ab initio molecular orbital studies of the positive muon and muonium in 4-arylmethyleneamino-TEMPO derivatives , 2000 .

[7]  T. P. Das,et al.  Investigation of electron distribution and hyperfine properties of hemin by first-principles Hartree-Fock self-consistent field procedure , 1992 .

[8]  C. Slichter Principles of magnetic resonance , 1963 .

[9]  Michael S. Strano,et al.  Optical Detection of DNA Conformational Polymorphism on Single-Walled Carbon Nanotubes , 2006, Science.

[10]  R. Turner,et al.  Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[11]  T. P. Das,et al.  Hemoglobin magnetism in aqueous solution probed by muon spin relaxation and future applications to brain research , 2007, Proceedings of the Japan Academy. Series B, Physical and biological sciences.

[12]  H. Fellner-Feldegg,et al.  Electron spectroscopy with monochromatized x-rays. , 1972, Science.

[13]  G. Lang,et al.  Mössbauer effect in some haemoglobin compounds. , 1966, Journal of molecular biology.

[14]  T. P. Das,et al.  Relativistic many-body approach to hyperfine interaction in rare earths: Explanation of experimental result in europium , 1977 .

[15]  A. Reina,et al.  Graphene as a sub-nanometer trans-electrode membrane , 2010, Nature.

[16]  S. Ogawa,et al.  Extended X-ray absorption fine structure determination of iron nitrogen distances in haemoglobin , 1978, Nature.

[17]  R. Nesbet Configuration interaction in orbital theories , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[18]  H. Gray,et al.  RATES OF HEME OXIDATION AND REDUCTION IN RU(HIS33)CYTOCHROME C AT VERY HIGH DRIVING FORCES , 1996 .

[19]  T. P. Das,et al.  Many-body calculation of the electric field gradient in the aluminum atom , 1976 .

[20]  H. G. Drickamer,et al.  Effect of Pressure on the Mössbauer Resonance in Ionic Compounds of Iron , 1967 .

[21]  Neil Peterman,et al.  DNA translocation through graphene nanopores. , 2010, Nano letters.

[22]  Michael E Phelps,et al.  Systems Biology and New Technologies Enable Predictive and Preventative Medicine , 2004, Science.

[23]  K. Yoshikawa,et al.  DNA Dissolves Single-walled Carbon Nanotubes in Water , 2003 .

[24]  R. Drago,et al.  Electron delocalization in paramagnetic metallocenes. II. Extended Hueckel Molecular orbital calculations , 1969 .

[25]  M. Perutz,et al.  The crystal structure of human deoxyhaemoglobin at 1.74 A resolution. , 1984, Journal of molecular biology.

[26]  R. Benesch,et al.  The Chemistry of the Bohr Effect I. THE REACTION OF N-ETHYL MALEIMIDE WITH THE OXYGEN-LINKED ACID GROUPS OF HEMOGLOBIN , 1961 .

[27]  J. T. Rodgers,et al.  Discrimination among individual Watson-Crick base pairs at the termini of single DNA hairpin molecules. , 2003, Nucleic acids research.

[28]  C. D. Coryell,et al.  The Magnetic Properties and Structure of Hemoglobin, Oxyhemoglobin and Carbonmonoxyhemoglobin , 1936, Proceedings of the National Academy of Sciences.

[29]  F. Pratt,et al.  Intra- and inter-molecular electron transfer in cytochrome c and myoglobin observed by the muon spin relaxation method , 2000 .

[30]  H. Wickman,et al.  Mössbauer isomer shifts , 1979 .

[31]  D. Deamer,et al.  Nanopores and nucleic acids: prospects for ultrarapid sequencing. , 2000, Trends in biotechnology.

[32]  Jeffrey Goldstone,et al.  Derivation of the Brueckner many-body theory , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[33]  G. Lang Mössbauer spectroscopy of haem proteins , 1970, Quarterly Reviews of Biophysics.

[34]  A. Chakravarti Single nucleotide polymorphisms: . . .to a future of genetic medicine , 2001, Nature.

[35]  H. Gray,et al.  Solution structure of oxidized horse heart cytochrome c. , 1997, Biochemistry.

[36]  P. Jeffrey Hay,et al.  Gaussian basis sets for molecular calculations. The representation of 3d orbitals in transition‐metal atoms , 1977 .

[37]  Sahoo,et al.  Hartree-Fock cluster investigation of 67Zn nuclear quadrupole interaction in zinc oxide. , 1991, Physical review. B, Condensed matter.

[38]  A. Joachimiak,et al.  Determinants of repressor/operator recognition from the structure of the trp operator binding site , 1994, Nature.

[39]  M. Cohen Nuclear Quadrupole Spectra in Solids , 1954 .

[40]  T. P. Das,et al.  Theory of orbital contributions to magnetic hyperfine fields in hemoglobin derivatives—application to azidomyoglobin , 1989 .

[41]  T. P. Das,et al.  Many-body theory of the nuclear quadrupole coupling in the boron atom , 1975 .

[42]  D. Sánchez-Portal,et al.  The SIESTA method for ab initio order-N materials simulation , 2001, cond-mat/0111138.

[43]  G. Romani,et al.  Magnetic properties of oxyhemoglobin. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[44]  H. Postma,et al.  Rapid sequencing of individual DNA molecules in graphene nanogaps. , 2008, Nano letters.

[45]  G. Feher,et al.  ELECTRON NUCLEAR DOUBLE RESONANCE (ENDOR) INVESTIGATION ON MYOGLOBIN AND HEMOGLOBIN * , 1973, Annals of the New York Academy of Sciences.

[46]  C. Johnson Hyperfine field of 57Fe in hemin , 1966 .

[47]  J. Philo,et al.  Diamagnetism of human apo-, oxy-, and (carbonmonoxy)hemoglobin. , 1984, Biochemistry.

[48]  Kehr,et al.  Direct stochastic theory of muon spin relaxation in a model for trans-polyacetylene. , 1992, Physical review. B, Condensed matter.

[49]  T. P. Das,et al.  First-principles study of muon and muonium trapping in the protein chain of cytochrome c , 2003 .

[50]  L. Pauling Covalence of atoms in the heavier transition metals. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[51]  W. Cao,et al.  Rapid timescale processes and the role of electronic surface coupling in the photolysis of diatomic ligands from heme proteins. , 2004, Faraday discussions.

[52]  V. Heine,et al.  Contribution of Core Polarization to the Atomic Hyperfine Structure and Knight Shift of Li and Na , 1959 .

[53]  Stefano Sanvito,et al.  Towards molecular spintronics , 2005, Nature materials.

[54]  W. Caughey,et al.  Mössbauer spectroscopy of heme and hemin compounds. , 1965, Proceedings of the National Academy of Sciences of the United States of America.

[55]  M. Perutz,et al.  Stereochemistry of iron in deoxyhaemoglobin , 1982, Nature.

[56]  T. P. Das,et al.  Hyperfine interactions and relaxivities in divalent and trivalent aquoion systems , 1989 .

[57]  J. Peisach,et al.  Analogous effect of protons and inositol hexaphosphate on the alteration of structure of nitrosyl fetal human hemoglobin. , 1978, Biochemistry.

[58]  T. P. Das,et al.  THEORY OF CORE-ELECTRON CONTRIBUTIONS TO HYPERFINE INTERACTIONS , 1964 .

[59]  R. Hoffmann An Extended Hückel Theory. I. Hydrocarbons , 1963 .

[60]  R. Ahuja,et al.  Physisorption of nucleobases on graphene : Density-functional calculations , 2007, 0704.1316.

[61]  George M. Church,et al.  Genomes for all. , 2006, Scientific American.

[62]  R. Ahuja,et al.  Functionalized nanopore-embedded electrodes for rapid DNA sequencing , 2007, 0708.4011.

[63]  E. Karlsson Solid State Phenomena: As Seen by Muons, Protons, and Excited Nuclei , 1995 .

[64]  T. P. Das,et al.  Ab initio determination of /sup 57/Fe/sup m/ quadrupole moment from Moessbauer data , 1981 .

[65]  P. J. Bray,et al.  Nuclear Quadrupole Resonances of As75 , 1955 .

[66]  Z. Herman,et al.  A theoretical investigation of the magnetic and ground-state properties of model oxyhemoglobin complexes , 1980 .

[67]  T. P. Das,et al.  Relativistic configuration interaction using many-body techniques. Hyperfine interaction in Gd3+ , 1978 .

[68]  A. Szabo,et al.  Modern quantum chemistry , 1982 .

[69]  Probing Electron Transfer in DNA – New Life Science with Muons , 2001 .

[70]  D. H. Vincent,et al.  Direction of the Effective Magnetic Field at the Nucleus in Ferromagnetic Iron , 1960 .

[71]  T. P. Das,et al.  Accurate Values of Nuclear Magnetic Moments of Francium Isotopes , 1982 .

[72]  L. Walker,et al.  Dimensionality of spin fluctuations in highly anisotropic TCNQ salts , 1976 .

[73]  Yoshitsugu Shiro,et al.  1.25 A resolution crystal structures of human haemoglobin in the oxy, deoxy and carbonmonoxy forms. , 2006, Journal of molecular biology.

[74]  G. Feher,et al.  Electron nuclear double resonance studies on heme proteins: determination of the interaction of Fe 3+ with its ligand nitrogens in metmyoglobin. , 1972, Biochimica et biophysica acta.

[75]  T. P. Das,et al.  Influence of coulomb corrections in the self-consistent charge extended Hückel (SCCEH) procedure on hyperfine properties of biological molecules , 1987 .

[76]  M. Klein,et al.  Probing the structure of DNA-carbon nanotube hybrids with molecular dynamics. , 2007, Nano letters.

[77]  M. M. Harris,et al.  Progress in stereochemistry , 1954 .

[78]  F. London,et al.  Zur Theorie und Systematik der Molekularkräfte , 1930 .

[79]  E. Schempp,et al.  Nuclear Quadrupole Coupling Constants , 1969 .

[80]  Jean-Christophe Charlier,et al.  pi-stacking interaction between carbon nanotubes and organic molecules , 2005 .

[81]  G. Volkoff,et al.  FURTHER CALCULATIONS ON THE NUCLEAR RESONANCE SPECTRUM OF Al27 IN SPODUMENE , 1954 .

[82]  B. Delley,et al.  Interaction between zigzag single-wall carbon nanotubes and polymers: a density-functional study. , 2005, The Journal of chemical physics.

[83]  J. Peisach AN INTERIM REPORT ON ELECTRONIC CONTROL OF OXYGENATION OF HEME PROTEINS * , 1975, Annals of the New York Academy of Sciences.

[84]  L. Adamowicz,et al.  Multiple site proton affinities of methylated nucleic acid bases , 1996 .

[85]  S. Vitale,et al.  Reexamination of the evidence for paramagnetism in oxy- and carbonmonoxyhemoglobins. , 1985, Proceedings of the National Academy of Sciences of the United States of America.

[86]  E. Mitchell,et al.  Muon Spin Rotation Spectroscopy Principles and Applications in Solid State Physics , 1985 .

[87]  R. Herber Chemical Applications of Mossbauer Spectroscopy , 1968 .

[88]  Y. Maeda,et al.  Sign and Orientation Determination of the Principal Axis of the Electric Field Gradient in Fe57 Enriched Deoxygenated Myoglobin Single Crystals , 1974 .

[89]  M. Paoli,et al.  Crystal structure of T state haemoglobin with oxygen bound at all four haems. , 1996, Journal of molecular biology.

[90]  Ming Zheng,et al.  DNA sequence motifs for structure-specific recognition and separation of carbon nanotubes , 2009, Nature.

[91]  David L. Beveridge,et al.  Approximate molecular orbital theory , 1970 .

[92]  A. Klug Rosalind Franklin and the double helix , 1974, Nature.

[93]  T. Yonetani,et al.  High magnetic field Mössbauer studies of deoxymyoglobin, deoxyhemoglobin, and synthetic analogues. , 1979, Biochimica et Biophysica Acta.

[94]  T. P. Das,et al.  Investigation of the hyperfine properties of deoxy hemoglobin based on its electronic structure obtained by Hartree-Fock-Roothan procedure , 2008 .

[95]  J. Chien Electron paramagnetic resonance study of the stereochemistry of nitrosylhemoglobin. , 1969, The Journal of chemical physics.

[96]  L. Pauling Magnetic properties and structure of oxyhemoglobin. , 1977, Proceedings of the National Academy of Sciences of the United States of America.

[97]  Ben F. Luisi,et al.  Stereochemistry of cooperative mechanisms in hemoglobin , 1987 .

[98]  K. Richter,et al.  Introducing Molecular Electronics , 2005 .

[99]  W. Nieuwpoort,et al.  CALIBRATION CONSTANT FOR FE-57 MOSSBAUER ISOMER-SHIFTS DERIVED FROM ABINITIO SELF-CONSISTENT-FIELD CALCULATIONS ON OCTAHEDRAL FEF6 AND FE(CN)6 CLUSTERS , 1978 .

[100]  F. Crick,et al.  Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid , 1953, Nature.

[101]  A. Abragam,et al.  Electron paramagnetic resonance of transition ions , 1970 .

[102]  J. Peisach,et al.  ELECTRON PARAMAGNETIC RESONANCE STUDIES OF IRON PORPHIN AND CHLORIN SYSTEMS * , 1973, Annals of the New York Academy of Sciences.

[103]  T. H. Dunning Gaussian basis functions for use in molecular calculations. Contraction of (12s9p) atomic basis sets for the second row atoms , 1970 .

[104]  T. P. Das,et al.  Origin of observed changes in 14N hyperfine interaction accompanying R → T transition in nitrosylhemoglobin , 1979 .

[105]  H. Fink,et al.  Electrical conduction through DNA molecules , 1999, Nature.

[106]  R. Grant,et al.  Mössbauer effect in hemoglobin and some iron-containing biological compounds. , 1965, Biophysical journal.

[107]  Michael Zwolak,et al.  Electronic signature of DNA nucleotides via transverse transport. , 2004, Nano letters.

[108]  R. S. Mulliken Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I , 1955 .

[109]  Tara Prasad Das,et al.  Relativistic quantum mechanics of electrons , 1973 .

[110]  Tara Prasad Das,et al.  Nuclear Quadrupole Resonance Spectroscopy , 1959 .

[111]  Ravindra Pandey,et al.  First-principles study of physisorption of nucleic acid bases on small-diameter carbon nanotubes , 2007, Nanotechnology.

[112]  D. Branton,et al.  Microsecond time-scale discrimination among polycytidylic acid, polyadenylic acid, and polyuridylic acid as homopolymers or as segments within single RNA molecules. , 1999, Biophysical journal.

[113]  Marc Gershow,et al.  DNA molecules and configurations in a solid-state nanopore microscope , 2003, Nature materials.

[114]  K Sakamoto,et al.  Molecular computation by DNA hairpin formation. , 2000, Science.

[115]  J. Ferrer,et al.  Spin and molecular electronics in atomically generated orbital landscapes , 2006 .

[116]  D. Tank,et al.  Brain magnetic resonance imaging with contrast dependent on blood oxygenation. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[117]  T. P. Das,et al.  Critical appraisal of electronic structure of metmyoglobin. 14N and 57Fe hyperfine interactions. , 1977, Biochimica et biophysica acta.

[118]  Alan Gelperin,et al.  DNA-decorated carbon nanotubes for chemical sensing. , 2005 .

[119]  F. Bechstedt,et al.  Attracted by long-range electron correlation: adenine on graphite. , 2005, Physical review letters.

[120]  Michael J. Frisch,et al.  MP2 energy evaluation by direct methods , 1988 .

[121]  T. P. Das,et al.  First-principles study of muonium in A- and B-form DNA , 2006 .

[122]  G. Volkoff,et al.  A THEORETICAL INVESTIGATION OF THE NUCLEAR RESONANCE ABSORPTION SPECTRUM OF Al27 IN SPODUMENE , 1953 .

[123]  Nino Russo,et al.  Protonation of thymine, cytosine, adenine, and guanine DNA nucleic acid bases: Theoretical investigation into the framework of density functional theory , 1998, J. Comput. Chem..

[124]  T. P. Das,et al.  Theory of exchange splitting of core levels in x‐ray photoemission spectroscopy of hemin , 1975 .

[125]  G. M. Smith,et al.  The chemistry of the Bohr effect. II. Some properties of hemoglobin H. , 1961, The Journal of biological chemistry.

[126]  H. Dehmelt,et al.  Kernquadrupolfrequenzen in festem Dichloräthylen , 2004, Naturwissenschaften.

[127]  M. Zheng,et al.  DNA-assisted dispersion and separation of carbon nanotubes , 2003, Nature materials.

[128]  D. Branton,et al.  Rapid nanopore discrimination between single polynucleotide molecules. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[129]  伊藤 厚子 G. K. Shenoy and F. E. Wagner編: Mossbauer Isomer Shifts, North-Holland, Amsterdam and New York, 1978, 956ページ, 23×15.5cm, 33,600円. , 1980 .

[130]  S. Ogawa Brain magnetic resonance imaging with contrast-dependent oxygenation , 1990 .

[131]  Kanetada Nagamine,et al.  Introductory Muon Science , 2003 .

[132]  T. P. Das,et al.  Theory of isomer shift in hemin , 1976 .

[133]  C. Eckart The Application of Group theory to the Quantum Dynamics of Monatomic Systems , 1930 .

[134]  L. Elkin Rosalind Franklin and the double helix , 2003 .

[135]  K. J. Duff Calibration of the isomer shift for 57 Fe , 1974 .

[136]  H. P. Kelly Correlation Effects in Atoms , 1963 .

[137]  M. Dresselhaus,et al.  Structure-Based Carbon Nanotube Sorting by Sequence-Dependent DNA Assembly , 2003, Science.

[138]  E. Kaufmann,et al.  The electric field gradient in noncubic metals , 1979 .

[139]  T. P. Das,et al.  Electron States in Ferromagnetic Iron. II. Wave-Function Properties , 1971 .

[140]  Michael Zwolak,et al.  Fast DNA sequencing via transverse electronic transport. , 2006, Nano letters.

[141]  D. R. Hartree,et al.  The calculation of atomic structures , 1959 .

[142]  Grégory Pandraud,et al.  DNA translocation through graphene nanopores. , 2010, Nano letters.

[143]  M. Burns,et al.  Nanopore sequencing technology: nanopore preparations. , 2007, Trends in biotechnology.

[144]  Jan Andzelm,et al.  Gaussian Basis Sets for Molecular Calculations , 2012 .

[145]  A. Becke A New Mixing of Hartree-Fock and Local Density-Functional Theories , 1993 .

[146]  C. Scholes,et al.  Electron nuclear double resonance from high- and low-spin ferric hemoglobins and myoglobins , 1979 .

[147]  A. R. Srinivasan,et al.  The nucleic acid database. A comprehensive relational database of three-dimensional structures of nucleic acids. , 1992, Biophysical journal.

[148]  C. Dean ZEEMAN SPLITTING OF NUCLEAR QUADRUPOLE RESONANCES , 1954 .

[149]  Vinod Kumar Khanna,et al.  Existing and emerging detection technologies for DNA (Deoxyribonucleic Acid) finger printing, sequencing, bio- and analytical chips: A multidisciplinary development unifying molecular biology, chemical and electronics engineering , 2007 .

[150]  C. Ho,et al.  Magnetic field and temperature induced line broadening in the hyperfine-shifted proton resonances of myoglobin and hemoglobin. , 1977, Journal of the American Chemical Society.

[151]  K. Gersonde,et al.  Proton nuclear magnetic resonance hyperfine shifts as indicators of tertiary structural changes accompanying the Bohr effect in monomeric insect hemoglobins. , 1978, Biochemistry.

[152]  R. Bersohn Nuclear Electric Quadrupole Spectra in Solids , 1952 .

[153]  A. D. McLean,et al.  Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z=11–18 , 1980 .

[154]  M. Karplus,et al.  Electronic structure of cyanide complexes of hemes and heme proteins. , 1971, Journal of molecular biology.

[155]  W. Marshall The Unrestricted Hartree-Fock Method , 1961 .

[156]  W. Lipscomb,et al.  Theory of Polyhedral Molecules. I. Physical Factorizations of the Secular Equation , 1962 .

[157]  P. Hubbard,et al.  Laying the foundation for understanding muon implantation in DNA: ab initio DFT calculations of the nucleic acid base muonium adducts , 2003 .

[158]  T. P. Das,et al.  Theory of origin of hyperfine interactions in atomic systems , 1987 .

[159]  F. Seela,et al.  Replacement of Canonical DNA Nucleobases by Benzotriazole and 1,2,3‐Triazolo[4,5‐d]pyrimidine: Synthesis, Fluorescence, and Ambiguous Base Pairing , 2005 .

[160]  E. S. Chang,et al.  Many-Body Approach to the Atomic Hyperfine Problem. I. Lithium-Atom Ground State , 1968 .

[161]  H. Lefebvre-Brion,et al.  Calculation of the Magnetic Hyperfine Constant of the Nitrogen Atom , 1961 .

[162]  D. Branton,et al.  Characterization of individual polynucleotide molecules using a membrane channel. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[163]  T. P. Das,et al.  Electronic structure of ferricytochrome c and associated hyperfine interactions , 1983 .

[164]  D. Scherlis,et al.  Structure and spin-state energetics of an iron porphyrin model: An assessment of theoretical methods , 2002 .