Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-13T12:38:06.825Z Has data issue: false hasContentIssue false
  • English
  • Français

Protein dynamics: comparison of simulations with inelastic neutron scattering experiments

Published online by Cambridge University Press:  17 March 2009

J. C. Smith
J. C. Smith
Affiliation:
Section de Biophysique des Protéines et des Membranes, Département de Biologie Cellulaire et Moléculaire, CEN-Saclay, 91191 Gif-sur-Yvette, France
Get access Rights & Permissions [Opens in a new window]

Extract

To deepen our understanding of the principles determining the folding and functioning of globular proteins the determination of their three-dimensional structures must be supplemented with the characterization of their internal motions. Although dynamical events in proteins occur on time-scale ranging from femtoseconds to at least seconds, the physical properties of globular proteins are such that picosecond (ps) time-scale motions make a particularly important contribution to the internal fluctuations of the atoms from their mean positions.

Type
Research Article
Information
Quarterly Reviews of Biophysics , Volume 24 , Issue 3 , August 1991 , pp. 227 - 291
Copyright
Copyright © Cambridge University Press 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aamodt, R., Case, K. M., Rosenbaum, M. & Zweiful, P. F. (1962). Quasiclassical treatment of neutron scattering. Phys. Rev. 126 (3), 1165–1167.CrossRefGoogle Scholar
Adams, D. (1979). Computer simulation of ionic systems: the distorting effects of the boundary conditions. Chem. Phys. Lett. 62, 329–332.CrossRefGoogle Scholar
Agmon, N. & Hopfield, J. J. (1983). CO binding to heme proteins: A model for barrier height distributions and slow conformational changes. J. chem. Phys. 79 (4), 2042–2053CrossRefGoogle Scholar
Aharony, A., Alexander, S., Entin-Wohlman, O. & Orbach, R. (1985). Scaling approach to phonon-fracton crossover. Phys. Rev. B31, 2565–2567CrossRefGoogle ScholarPubMed
Ahlstrom, P., Teleman, O., Jonsson, B. & Forsen, S. (1987). Molecular dynamics simulation of parvalbumin in aqueous solution. J. Am. chem. Soc. 109, 1541–1551.CrossRefGoogle Scholar
Alcala, J. R., Gratton, E. & Prendergast, F. G. (1987). Interpretation of fluorescence decays in proteins using continuous lifetime distributions. Biophys. J. 51, 925–936.CrossRefGoogle Scholar
Alexander, S. & Orbach, R. (1982). Density of states on fractals: fractons. J. Phys. Lett. 43, L 625–631.CrossRefGoogle Scholar
Allen, J. P., Colvin, J. T., Stinson, D. G., Flynn, P. & Stapleton, H. J. (1982). Protein conformation from electron spin relaxation data. Biophys. J. 38, 299–310.CrossRefGoogle ScholarPubMed
Anderson, J., Ullo, J. J. & Yip, S. (1987). Molecular dynamics of hydrocarbon molecules in condensed phases. II. Benzene. J. chem. Phys. 86 (7), 4078–4089.CrossRefGoogle Scholar
Aqvist, J., Van Gunsteren, W. F., Leijonmarck, M. & Tapia, O. (1985). A molecular dynamics study of the C-terminal fragment of the L7/L12 ribosomal protein. Secondary structure motion in a 150 picosecond trajectory. J. molec. Biol. 183, 461–477.CrossRefGoogle Scholar
Ataka, M. & Tanaka, S. (1979). Far-infrared spectrum of crystalline lysozyme. Biopolymers 18, 507–516.CrossRefGoogle ScholarPubMed
Barnes, J. D. (1973). Inelastic neutron scattering study of the ‘rotator’ phase transition in n-nonadecane. J. chem. Phys. 58,5193–5201.CrossRefGoogle Scholar
Bartunik, H. D., Jolles, P., Berthou, J. & Dianoux, A. J. (1982). Intramolecular low-frequency vibrations in lysozyme by neutron time-of-flight spectroscopy. Biopolymers 21, 43–50.CrossRefGoogle ScholarPubMed
Bauer, K., Jagodzinski, H., Dorner, B. & Grimm, H. (1971). Inelastic nature of the diffuse X-ray scattering near the α-β transition in quartz. Physica Status Solidi B48, 437–443.CrossRefGoogle Scholar
Bauminger, E. R., Cohen, S. G., Nowik, I., Ofer, S. & Yariv, J. (1983). Dynamics of heme iron in crystals of metmyoglobin and deoxymyoglobin. Proc. natn. Acad. Sci. U.S.A. 80, 736–740.CrossRefGoogle ScholarPubMed
Bauminger, E. R., Cohen, S. G., Ofer, S. & Bachrach, U. (1982). Study of storage iron in cultured chick embryo fibroblasts and rat glioma cells, using Moessbauer spectroscopy. Biochim. biophys. Acta 720, 133–140.CrossRefGoogle Scholar
Bee, M. (1988). Quasielastic Neutron Scattering: Principles and Applications in Solid State Chemistry, Biology and Materials Science. Bristol and Philadelphia: Adam Hilger.Google Scholar
Beetz, C. A. & Ascarelli, G. (1976). The low-frequency vibrational modes of an RNA: Poly(I)–Poly(C). Biopolymers 15, 2299–2301.CrossRefGoogle Scholar
Beetz, C. A. & Ascarelli, G. (1982). Far-infrared absorption of nucleotides and Poly(I).Poly(C) RNA. Biopolymers 21, 1569–1586.CrossRefGoogle Scholar
Bell, S. & Crighton, J. S. (1984). Locating transition states, J. chem. Phys. 80, 2464–2475.CrossRefGoogle Scholar
Bellisent-Funel, M.-C., Teixera, J., Chen, S. H., Dorner, B., Middendorf, H. & Crespi, L. (1989). Low-frequency collective modes in dry and hydrated proteins. Biophys. J. 56, 713–716.CrossRefGoogle Scholar
Bengtzelius, U., Gotze, W. & Sjolander, A. (1984). Dynamics of supercooled liquids and the glass transition. J. Phys. C17, 5915–5934.Google Scholar
Bennett, W. S. & Steitz, T. A. (1980). Structure of a complex between yeast hexokinase A and glucose. II. Detailed comparisons of conformation and active site configuration with the native hexokinase B monomer and dimer. J. molec. Biol. 140, 211–230.CrossRefGoogle ScholarPubMed
Berens, P. H. & Wilson, K. R. (1981). Molecular dynamics and spectra. 1. Diatomic rotation and vibration. J. chem. Phys. 74 (9), 4872–4882.CrossRefGoogle Scholar
Berney, C. V., Renugopalakrishnan, V. & Bhatnagar, . (1987). Collagen; an inelastic neutron scattering study of low-frequency vibrational modes. Biophys. J. 52, 343–345.CrossRefGoogle ScholarPubMed
Bialek, W. & Goldstein, R. F. (1985). Do vibrational spectroscopies uniquely describe protein dynamics? The case for myoglobin. Biophys. J. 48, 1027–1044.CrossRefGoogle ScholarPubMed
Bone, S. & Pethig, R. (1985). Dielectric studies of protein hydration and hydration-induced flexibility. J. molec. Biol. 181, 323–326.CrossRefGoogle ScholarPubMed
Boon, J. P. & Yip, S. (1980). Molecular Hydrodynamics. New York: McGraw-Hill.Google Scholar
Brooks, C. L. (1987). Thermodynamics of ionic solvation: the influence of long-range truncation on the thermodynamics of aqueous ionic solutions. J. chem. Phys. 86, 5156–5162.CrossRefGoogle Scholar
Brooks, B. & Karplus, M. (1983). Harmonic dynamics of proteins: normal modes and fluctuations in bovine pancreatic trypsin inhibitor. Proc. natn. Acad. Sci. U.S.A. 80, 6571–6575CrossRefGoogle ScholarPubMed
Brooks, B. & Karplus, M. (1985). Normal modes for specific motions of macromolecules: application to the hinge-bending motion of lysozyme. Proc. natn. Acad. Sci. U.S.A. 82, 4995–4999.CrossRefGoogle Scholar
Brooks, C. L. III & Karplus, M. (1989). Solvent effects on protein motion and protein effects on solvent motion. Dynamics of the active site region of lysozyme. J. molec. Biol. 208, 159–181.CrossRefGoogle ScholarPubMed
Brooks, B., Bruccoleri, R., Olafson, B., States, D., Swaminathan, S. & Karplus, M. (1983). Charmm: a program for macromolecular energy, minimisation and dynamics calculations. J. comp. Chem. 4, 187–217.CrossRefGoogle Scholar
Brooks, C. L. III, Karplus, M. & Pettitt, B. M. (1988). Proteins. A theoretical perspective of dynamics, structure and thermodynamics. Adv. chem. Physics 71, (Eds. I. Prigogine & S. Rice) Wiley.CrossRefGoogle Scholar
Brooks, C. L. III, Pettitt, B. M. & Karplus, M. (1985). Structural and energetic effects of truncating long-range interactions in polar fluids. J. chem. Phys. 83, 5897–5908.CrossRefGoogle Scholar
Brown, R. G., Erfurth, S. C., Small, E. W. & Peticolas, W. L. (1972). Conformationally dependent low-frequency motions of proteins by laser Raman spectroscopy. Proc. natn. Acad. Set. U.S.A. 69 (6), 1467–1469.CrossRefGoogle ScholarPubMed
Bruccoleri, R. E., Karplus, M. & McCammon, J. A. (1986). The hinge-bending mode of a lysozyme-inhibitor complex. Biopolymers 25, 1767–1802.CrossRefGoogle ScholarPubMed
Burkert, U. & Allinger, N. (1982). Molecular Mechanics. ACS monograph. American Chemical Society.Google Scholar
Campbell, B. F., Chance, M. R. & Friedman, J. M. (1987). Linkage of functional and structural heterogeneity in proteins: Dynamic hole burning in carboxymyoglobin. Science, Wash. 238, 373–376.CrossRefGoogle ScholarPubMed
Campbell, I. D., Dobson, C. M. & Williams, R. J. P. (1978). Structures and energetics of proteins and their active sites. Adv. chem. Phys. 39, 55–107.Google Scholar
Careri, E. & Gratton, E. (1986). The statistical time correlation approach to enzyme action: the role of hydration. In The Fluctuating Enzyme (ed. Welch, G. Rickey). New York: Wiley.Google Scholar
Caspar, D. J. D., Clarage, J., Salunke, D. M. & Clarage, M. (1988). Liquid-like movements in crystalline insulin. Nature, Lond. 332, 659–662.CrossRefGoogle ScholarPubMed
Champeney, D. C. & Dean, C. W. (1975). Molecular vibrations in glassy glycerol measured by Moessbauer scattering. J. Phys. C8, 1276–1284.Google Scholar
Chou, K. C. (1983 a). Low-frequency vibrations of helical structures in protein molecules. Biochem. J. 209, 573–580.CrossRefGoogle ScholarPubMed
Chou, K. C. (1983b). Identification of low-frequency modes in protein molecules. Biochem. J. 215, 465–469.CrossRefGoogle ScholarPubMed
Chou, K. C. (1984). Biological functions of low-frequency vibrations (phonons). III. Helical structures and microenvironment. Biophys. J. 45, 881–890.CrossRefGoogle ScholarPubMed
Clementi, E., Corongiu, G., Aida, M., Niesar, V. & Kneller, G. (1990). In ‘MOTECC: Modern Techniques in Computational Chemistry’ (Ed. Clementi, E.). Escom: Leiden.CrossRefGoogle Scholar
Cohen, S. G., Bauminger, E. R., Nowik, I., Ofer, S. & Yariv, J. (1981). Dynamics of the iron-containing core in crystals of the iron-storage protein, ferritin, through Moessbauer spectroscopy. Phys. Rev. Lett. 46, 1244–1248.CrossRefGoogle Scholar
Conroy, H. (1967). Molecular Schrodinger equation. VIII. A new method for the evaluation of multidimensional integrals. J. chem. Phys. 47 (12), 5307–5318.CrossRefGoogle Scholar
Craig, R. R. (1981). Structural Dynamics. New York: Wiley.Google Scholar
Csiba, T., Janninck, G., Durand, D., Papoular, R., LAPP, A., Auvray, L., Boue, F., Cotton, J. P. & Borsali, R. (1991). Diffusion in semi-dilute polymer solutions. A complementary experiment. J. Phys., Paris. (In the Press.)Google Scholar
Currat, R. & Pynn, R. (1979). In Treatise on Materials Science and Technology (ed. Kostorz, G.), vol. 15 New York: Academic Press.Google Scholar
Cusack, S. (1986). Low frequency motion in proteins and its study by inelastic neutron scattering. Comm. molec. cell. Biophys. 3 (4), 243–271.Google Scholar
Cusack, S. (1989). Low frequency dynamics of proteins studied by inelastic neutron scattering. In The Enzyme Catalysis Process (ed. Cooper, A.Houben, J. L. and Chien, L. C.), pp. 103–122. Plenum.CrossRefGoogle Scholar
Cusack, S. & Doster, W. (1990). Temperature dependence of the low frequency dynamics of myoglobin. Measurement of the vibrational frequency distribution by inelastic neutron scattering. Biophys. J. 58, 243–251.CrossRefGoogle ScholarPubMed
Cusack, S., Smith, J., Finney, J., Karplus, M. & Trewhella, J. (1986). Low frequency dynamics of proteins studied by neutron time-of-flight spectroscopy. Physica 136 B, 256–259.Google Scholar
Cusack, S., Smith, J., Finney, J. L. & Karplus, M. (1988). Inelastic neutron scattering analysis of picosecond internal protein dynamics. Comparison of harmonic theory with experiment, J. molec. Biol. 202, 903–908.CrossRefGoogle ScholarPubMed
Czerminski, R. & Elber, R. (1989). Reaction path study of conformational transitions and helix formation in a tetrapeptide. Proc. natn. Acad. Sci. U.S.A. 86, 6963–6967.CrossRefGoogle Scholar
Dattagupta, S. & Reiter, G. F. (1985). Neutron scattering from a quantum oscillator subject to noise. Phys. Rev. A 31 (2), 1034–1038.CrossRefGoogle ScholarPubMed
Davidson, D. W. & Cole, R. H. (1950). Dielectric relaxation in glycerol. J. chem. Phys. 18, 1417–1419.CrossRefGoogle Scholar
Debye, P. (1912). Zur Theorie der spezifischen Warmen. Annln Phys. 39, 789–839.CrossRefGoogle Scholar
De Raedt, B. & Michel, K. H. (1979). Dynamics of molecular impurities in crystals. Phys. Rev. B 19, 767–782.CrossRefGoogle Scholar
Dianoux, A. J., Hervet, H. & Volino, F. (1977). The problem of orientational order in tilted smectic phases: a high resolution neutron quasi-elastic study. J. Phys., Paris 38, 809–816.Google Scholar
Dianoux, A. J., Volino, F. & Hervet, H. (1975). Incoherent scattering law for neutron quasielastic scattering in liquid crystals. Molec. Phys. 20, 1181–1194.CrossRefGoogle Scholar
Dobson, C. M. & Karplus, M. (1986). Internal motion in proteins: Nuclear magnetic resonance measurements and dynamic simulations. Meth. Enzym. 131, 362–389.CrossRefGoogle ScholarPubMed
Dorner, B. (1982). Coherent inelastic neutron scattering in lattice dynamics. In Tracts in Modern Physics, vol. 93. Heidelberg: Springer-Verlag.Google Scholar
Doster, W. (1989). On the mechanism of ligand binding to myoglobin. The role of structural fluctuations. Eur. Biophys. J. 17, 217–220.CrossRefGoogle ScholarPubMed
Doster, W., Bachleitner, A., Dunau, R., Hiebl, M. & Luscher, E. (1986). Thermal properties of water in myoglobin crystals and solutions at subzero temperatures. Biophys. J. 50, 213–219.CrossRefGoogle ScholarPubMed
Doster, W., Cusack, S. & Petry, W. (1989). Dynamical transition of myoglobin revealed by inelastic neutron scattering. Nature, Lond. 337, 754–756.CrossRefGoogle ScholarPubMed
Doster, W., Cusack, S. & Petry, W. (1990). Dynamic instability of liquidlike motions in a globular protein observed by inelastic neutron scattering. Phys. Rev. Lett. 65 (8), 1080–1083.CrossRefGoogle Scholar
Doucet, J. & Benoit, J. P. (1987). Molecular dynamics studied by analysis of the X-ray diffuse scattering from lysozyme crystals. Nature, Lond. 337, 190–192.CrossRefGoogle Scholar
Drexel, W. & Peticolas, W. L. (1978). Neutron scattering spectroscopy of the α- and β-forms of poly-L-alanine. Motion of the methyl side chain. Biopolymers 14, 715–721.CrossRefGoogle Scholar
Dunitz, J. D., Schomaker, V. & Trueblood, K. N. (1988). Interpretation of atomic displacement parameters form diffraction studies of crystals. J. phys. Chem. 92 (4), 856–867.CrossRefGoogle Scholar
Edsall, J. T. & Mackenzie, H. A. (1978). Water and Proteins. I. The significance and structure of water; its interaction with electrolytes and non-electrolytes. Adv. Biophys. 10, 137.Google ScholarPubMed
Edsall, J. T. & Mackenzie, H. A. (1983). Water and Proteins II. The location and dynamics of water in protein systems and its relation to their stability and properties. Adv. Biophys. 16, 53–183.CrossRefGoogle ScholarPubMed
Elber, R. (1990). Calculation of the potential of mean force using molecular dynamics with linear constraints: an application to a conformational transition in a solvated dipeptide. J. chem. Phys. 93 (6), 4312–4321.CrossRefGoogle Scholar
Elber, R. & Karplus, M. (1986). Low-frequency modes in proteins: use of the effective-medium approximation to interpret the fractal dimension observed in electron-spin relaxation measurements. Phys. Rev. Letts. 56 (4), 394–397.CrossRefGoogle ScholarPubMed
Elber, R. & Karplus, M. (1987 a). Multiple conformational states of proteins: A molecular dynamics analysis of myoglobin. Science, Wash. 235, 318–321.CrossRefGoogle ScholarPubMed
Elber, R. & Karplus, M. (1987 b). A method for determining reaction paths in large molecules: Application to myoglobin. Chem. Phys. Letts. 139, 375–380.CrossRefGoogle Scholar
Finney, J. L. & Poole, P. L. (1984). Protein hydration and enzyme activity: The role of hydration-induced conformation and dynamic changes in the activity of lysozyme. Comments molec. Cell. Biophys. 2, 129–151.Google Scholar
Frauenfelder, H., Parak, F. & Young, R. D. (1988). Conformational substates in proteins. A. Rev. Biophys. biophys. Chem. 17, 451–479.CrossRefGoogle ScholarPubMed
Frauenfelder, H., Petsko, G. & Tsernoglou, D. (1979). Temperature dependent X-ray diffraction as a probe of protein structural dynamics. Nature, Lond. 280, 558–563.CrossRefGoogle ScholarPubMed
Frauenfelder, H. & Wolynes, P. (1985). Rate theories and puzzles in heme-protein kinetics. Science, Wash. 229, 337–345.CrossRefGoogle ScholarPubMed
Frick, B., Richter, D., Petry, W. & Buchenau, U. (1988). Study of the glass transition order parameter in amorphous polybutadiene by incoherent neutron scattering. Z. Phys. B70, 73–79.CrossRefGoogle Scholar
Garcia, A. E. & Soumpasis, D. M. (1989). Harmonic vibrations and thermodynamic stability of a DNA oligomer on monovalent salt solution. Proc. natn. Acad. Sci. U.S.A. 86, 3160–3164.CrossRefGoogle ScholarPubMed
Genzel, L., Keilmann, F., Martin, T. P., Winterling, G., Yacoby, Y., Frohlich, H. & Makinen, M. (1976). Low-frequency Raman spectra of lysozyme. Biopolymers 15, 219–225.CrossRefGoogle ScholarPubMed
Genzel, L., Kremer, F., Poglitsch, A. & Bechtold, G. (1983). Relaxation processes on a picosecond timescale in hemoglobin and poly(L-alanine). Biopolymers 22, 1715–1729.CrossRefGoogle Scholar
Gibson, K. D. & Scheraga, H. A. (1967). Minimization of polypeptide energy. I. Preliminary structures of bovine pancreatic ribonuclease S-peptide. Proc. natn. Acad. Sci. U.S.A. 58, 420–427.CrossRefGoogle ScholarPubMed
Giordano, R., Salvato, G., Wanderlingh, F. & Wanderlingh, U. (1990). Quasielastic and inelastic neutron scattering in macromolecular solutions. Phys. Rev. A 41 (2), 689–696.CrossRefGoogle ScholarPubMed
Gō, N. (1990). A theorem on amplitudes of thermal atomic fluctuations in large molecules assuming specific conformations calculated by normal mode analysis. Biophys. Chem. 35, 105–112.CrossRefGoogle ScholarPubMed
Gō, N., Noguti, T. & Nishikawa, T. (1983). Dynamics of a small globular protein in terms of low-frequency vibrational modes. Proc. natn. Acad. Sci. U.S.A. 80, 3696–3700.CrossRefGoogle ScholarPubMed
Goldanskii, V. & Krupyanskii, Y. F. (1989). Protein and protein-bound water dynamics studied by Rayleigh scattering of Moessbauer radiation (RSMR). Q. Rev. Biophys. 22 (1), 39–92.CrossRefGoogle Scholar
Gordon, R. G. (1968). Correlation functions for molecular motion. Adv. Mag. Reson. 3, 1–42.CrossRefGoogle Scholar
Grote, R. F. & Hynes, J. T. (1982). Energy diffusion-controlled reactions in solution. J. chem. Phys. 77, 3736–3743.CrossRefGoogle Scholar
Harrison, R. W. (1984). Variational calculation of the normal modes of a large macromolecule: methods and some initial results. Biopolymers 23, 2943–2949.CrossRefGoogle ScholarPubMed
Harrison, S. C., Olson, A. J., Schutt, C. E., Winkler, F. K. & Bricogne, G. (1978). Tomato bushy stunt virus at 2·9 Å resolution. Nature, Lond. 276, 368–373.CrossRefGoogle ScholarPubMed
Hartmann, H., Parak, F., Steigemann, W., Petsko, G. A., Ringe-Ponzi, D. & Frauenfelder, H. (1982). Conformational substates in a protein: structure and dynamics of metmyoglobin at 80 K. Proc. natn. Acad. Sci. U.S.A. 79, 4967–4971.CrossRefGoogle Scholar
Harvey, S. C. (1989). Treatment of electrostatic effects in macromolecular modelling. Proteins: Struct. Funct. Genetics 5, 78–92.CrossRefGoogle Scholar
Hochstrasser, R. M. & Negus, D. K. (1984). Picosecond fluorescence decay of tryptophans in myoglobin. Proc. natn. Acad. Sci. U.S.A. 81, 4399–4403.CrossRefGoogle ScholarPubMed
Huber, R., Kukla, D., Ruhlmann, A., Epp, O. & Formanek, H. (1970). The basic trypsin inhibitor of bovine pancreas, 1. Structure analysis and conformation of the polypeptide chain. Naturwissenschaften 57, 389–392.CrossRefGoogle Scholar
Hudson, B. S. & Harris, D. (1990). T4 phage lysozyme: a protein designed for understanding tryptophan photophysics. In Time-resolved Laser Spectroscopy in Biochemistry II (ed. Lakowicz, J. R.Eftink, M. R.Nordlund, T. M.Ross, J. B. A. and Steiner, R. F.). SPIE. Vol. 124, pp. 80–91.CrossRefGoogle Scholar
Hudson, B. S., Ludescher, R. D., Ruggiero, A., Harris, D. L. & Johnson, I. (1987). Fluoresence anisotropy decay determinations of rapid reorientational motion: Complications in the interpretation of bilayer acyl-chain and protein tryptophan dynamics. Comm. molec. cell. Biophys. 4, 171–188.Google Scholar
Hudson, B., Warshel, A. & Gordon, R. G. (1974). Molecular inelastic neutron scattering: computational methods using consistent force fields. J. chem. Phys. 61 (7), 2930–2939.CrossRefGoogle Scholar
Ichiye, T. & Karplus, M. (1983). Fluorescence depolarisation of tryptophan residues in proteins: a molecular dynamics study. Biochemistry 22, 2884–2893.CrossRefGoogle ScholarPubMed
Ichiye, T. & Karplus, M. (1987). Anisotropy and anharmonicity of atomic fluctuations in proteins: analysis of a molecular dynamics simulation. Proteins: Struct. Funct. Genet. 2 236–259.CrossRefGoogle ScholarPubMed
Ichiye, T. & Karplus, M. (1988). Anisotropy and anharmonicity of atomic fluctuations in proteins: implications for X-ray analysis. Biochemistry 27, 3487–3497.CrossRefGoogle ScholarPubMed
Jacrot, B., Cusack, S., Dianoux, A. J. & Engelman, D. M. (1982). Inelastic neutron scattering analysis of hexokinase and its modification on binding of glucose. Nature, Lond. 300, 85–86.CrossRefGoogle ScholarPubMed
Jortner, J. & Ulstrup, J. (1979). Dynamics of nonadiabatic atom transfer in biological systems. Carbon monoxide binding to hemoglobin, J. Am. Chem. Soc. 11 (14), 3744–3754.CrossRefGoogle Scholar
Karplus, M. & Kushick, J. (1981). Method for estimating the configurational entropy of macromolecules. Macromolecules 14, 325–332.CrossRefGoogle Scholar
Karplus, M. & Petsko, G. (1990). Molecular dynamics simulations in biology. Nature, Lond. 347, 631–639.CrossRefGoogle ScholarPubMed
Kauzmann, W. (1957). Quantum Chemistry. New York: Academic Press.Google Scholar
Keller, H. & Debrunner, P. G. (1980). Evidence for conformational and diffusional mean square displacements in frozen aqueous solutions of oxymyoglobin. Phys. Rev. Lett. 54, (1) 68–71.CrossRefGoogle Scholar
Kittel, C. (1956). Solid State Physics, 2nd ed. New York: Wiley.Google Scholar
Knapp, E. W., Fischer, S. F. & Parak, F. (1982). Protein dynamics from Moessbauer spectra. The temperature dependence. J. phys. Chem. 86, 5042–5047.CrossRefGoogle Scholar
Knapp, E. W., Fischer, S. F. & Parak, F. (1983). The influence of protein dynamics on Moessbauer spectra. J. chem. Phys. 78 (7), 4701–4711.CrossRefGoogle Scholar
Kneller, G. (1991). Superposition of molecular structures using quaternions. Molecular Simulations. (In the Press.)CrossRefGoogle Scholar
Krumhansl, J. A. (1986). Vibrational anomalies are not generally due to fractal geometry: comments on proteins. Phys. Rev. Lett. 56, 2696–2699.CrossRefGoogle Scholar
Kuczera, K., Kuriyan, J. & Karplus, M. (1990). Temperature dependence of the structure and dynamics of myoglobin. A simulation approach, J. molec. Biol. 213, 351–373.CrossRefGoogle ScholarPubMed
Kuntz, I. S. & Kauzmann, W. (1973). Hydration of proteins and polypeptides. Adv. Prot. Chem. 28, 239–345.Google Scholar
Kuriyan, J., Petsko, G., Levy, R. M. & Karplus, M. (1986 a). Effect of anisotropy and anharmonicity on protein crystallographic refinement. An evaluation of molecular dynamics. J. molec. Biol. 190, 227–254.CrossRefGoogle ScholarPubMed
Kuriyan, J., Wilz, S., Karplus, M. & Petsko, G. A. (1986 b). X-ray refinement of carbon-monoxy (Fe II)-myoglobin at 1·5 Å resolution. J. molec. Biol. 192, 133–154.CrossRefGoogle ScholarPubMed
Lagant, P., Vergoten, G., Fleury, G. & Loucheux-Lefebvre, M.-H. (1984 a). Vibrational normal modes of folded prolyl-containing peptides. Application to β turns. Eur.J. Biochem. 139, 149–154.CrossRefGoogle ScholarPubMed
Lagant, P., Vergoten, G., Fleury, G. & Loucheux-Lefebvre, M.-H. (1984 b). Raman spectroscopy and normal vibrations of peptides. Characteristic normal modes of a type II β turn. Eur. J. Biochem. 139, 137–148.CrossRefGoogle ScholarPubMed
Lamm, G. & Szabo, A. (1986). Langevin modes of macromolecules. J. chem. Phys. 85 (12), 7334–7348.CrossRefGoogle Scholar
Lanczos, C. (1950). An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Natl. Bur. Stand. 45, 255–282.CrossRefGoogle Scholar
Leadbetter, A. J. & Lechner, R. E. (1979). Neutron scattering studies. In The Plastically Crystalline State (ed. Sherwood, J. N.). Chichester: Wiley.Google Scholar
Leutheusser, E. (1984). Dynamical model of the liquid–glass transition. Phys. Rev. A, 29 (5), 2765–2773.CrossRefGoogle Scholar
Levitt, M., Sander, C. & Stern, P. S. (1985). Protein normal mode dynamics: trypsin inhibitor, crambin, ribonuclease and lysozyme. J. molec. Biol. 181 (3), 423–447.CrossRefGoogle Scholar
Levitt, M. & Sharon, R. (1988). Accurate simulation of protein dynamics in solution. Proc. natn. Acad. Sci. U.S.A. 85, 7557–7561.CrossRefGoogle ScholarPubMed
Levy, R. M., Karplus, M. & McCammon, J. A. (1981 a). Increase of 13C NMR relaxation times in proteins due to picosecond motional averaging. J. Am. chem. Soc. 103, 994–996.CrossRefGoogle Scholar
Levy, R. M., Karplus, M. & Wolynes, P. G. (1981 b). NMR relaxation parameters in molecules with internal motion: exact Langevin trajectory results compared with simplified relaxation models, J. Am. chem. Soc. 103, 5998–6011.CrossRefGoogle Scholar
Levy, R. M., Srinivasan, A. R., Olson, W. K. & McCammon, J. A. (1984). Quasiharmonic method for studying very low frequency modes in proteins. Biopolymers 23, 1099–1112.CrossRefGoogle ScholarPubMed
Levy, R. M. & Szabo, A. (1982). Initial fluoresence depolarisation of tyrosines in proteins. J. Am. chem. Soc. 104, 2073–2075.CrossRefGoogle Scholar
Linderstrom-Lang, K. U. & Schellman, J. A. (1959). Protein structure and enzyme activity. Enzymes 1, 443.Google Scholar
Lipari, G., Szabo, A. & Levy, R. M. (1982). Protein dynamics and NMR relaxation; comparison of simulations with experiment. Nature, Lond. 300, 197–198.CrossRefGoogle Scholar
Loncharich, R. J. & Brooks, B. (1989). The effects of truncating long-range forces on protein dynamics. Proteins: Struct. Funct. Genet. 6, 32–45.CrossRefGoogle ScholarPubMed
Loncharich, R. J. & Brooks, B. (1990). Temperature dependence of dynamics of hydrated myoglobin. Comparison of force field calculations with neutron scattering data. J. molec. Biol. 215, 439–455.CrossRefGoogle ScholarPubMed
Lovesey, S. (1984). Theory of Neutron Scattering from Condensed Matter. International Series of Monographs on Physics, no. 72. Oxford Science Publications. Oxford: Clarendon.Google Scholar
Ludescher, R. D., Peting, L., Hudson, S. & Hudson, B. (1987). Time-resolved fluorescence anisotropy for systems with lifetime and dynamic heterogeneity. Biophys. Chem. 28, 59–75.CrossRefGoogle ScholarPubMed
McCammon, J. A. & Harvey, S. C. (1987). Dynamics of Proteins and Nucleic Acids. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
McCammon, J. A. & Northrup, S. H. (1981). Gated binding of ligands to proteins. Nature, Lond. 293, 316–317.CrossRefGoogle ScholarPubMed
McCammon, J. A., Gelin, B. R., Karplus, M. & Wolynes, P. G. (1976). The hinge-bending mode in lysozyme. Nature, Lond. 262, 325–326.CrossRefGoogle ScholarPubMed
McDonald, R. C., Steitz, T. A. & Engelmann, D. M. (1979). Yeast hexokinase in solution exhibits a large conformational change on binding glucose or glucose-6-phosphate. Biochemistry 18, 338–342.CrossRefGoogle ScholarPubMed
McQuarrie, D. (1976). Statistical Mechanics. New York: Harper and Row.Google Scholar
Madden, P. A. & Impey, R. W. (1986). On the infrared and Raman spectra of water in the region 5–200 cm−1. Chem. Phys. Letts. 123 (6), 502–506.CrossRefGoogle Scholar
Madura, J. & Pettitt, B. M. (1988). Effects of Truncating long range interactions in aqueous ionic solution simulations. Chem. Phys. Lett. 150, 105–108.CrossRefGoogle Scholar
Maier, B. (1983). Neutron Facilities at the ILL High Flux Reactor. Grenoble: Institut Laue-Langevin.Google Scholar
Mao, B., Pear, M. R., McCammon, J. A. & Northrup, S. H. (1982). Molecular dynamics of ferrocytochrome C: anharmonicity of atomic displacements. Biopolymers 21, 1979–1989.CrossRefGoogle ScholarPubMed
Mayo, K. H., Kucheida, D., Parak, F. & Chien, J. C. W. (1983). Structural dynamics of human deoxyhemoglobin and hemochrome investigated by nuclear gamma resonance absorption (Moessbauer) spectroscopy. Proc. natn. Acad. Sci. U.S.A. 80, 5294–5296.CrossRefGoogle Scholar
Mayo, K. H., Parak, F. & Moessbauer, R. L. (1981). Observations of elastic and quasielastic nuclear gamma resonance absorption in hemoglobin crystals. Phys. Lett. 82A, 468–470.CrossRefGoogle Scholar
Middendorf, H. D. (1984). Biophysical applications of quasi-elastic and inelastic neutron scattering. Rev. Biophys. Bioengng. 13, 425–451.CrossRefGoogle ScholarPubMed
Middendorf, H. D. & Randall, J. T. (1985). Neutron spectroscopy and protein dynamics. In Structure and Motion; Membranes, Nucleic Acids and Proteins (ed. Clementi, E. and Sarma, R. H.). Adenine Press.Google Scholar
Moon, R. M. & West, C. D. (1986). A next generation steady state neutron source. Physica 137 B, 347–358.Google Scholar
Moon, R. M. & West, C. D. (1989). The advanced neutron source. Physica 156 and 157, 522–524.CrossRefGoogle Scholar
Mountain, R. D. & Basu, P. K. (1983). Temperature-dependence of the dynamic structure factor and the stability of a supercooled liquid: a molecular dynamics study of liquid rubidium. Phys. Rev. A 28, 370–372.CrossRefGoogle Scholar
Munro, I., Pecht, I. & Stryer, L. (1979). Subnanosecond motions of tryptophan residues in proteins. Proc. natn. Acad. Sci. U.S.A. 76, 56–60.CrossRefGoogle ScholarPubMed
Nelligan, W. B., Lepoire, D. J., Brun, T. O. & Kleb, R. (1987). Inelastic neutron scattering study of the torsional and CCC bend frequencies in the solid n-alkanes, ethane-hexane. J. chem. Phys. 87 (5), 2447–2454.CrossRefGoogle Scholar
Nienhaus, G., Heinzl, J., Huenges, E. & Parak, F. (1989). Protein crystal dynamics studied by time resolved analysis of X-ray diffuse scattering. Nature, Lond. 338, 665–666.CrossRefGoogle Scholar
Nijboer, B. R. A. & Rahman, A. (1966). Time expansion of correlation functions and the theory of slow neutron scattering. Physica 32, 415–432.CrossRefGoogle Scholar
Nishikawa, T. & Gō, N. (1987). Normal modes of vibration in bovine pancreatic trypsin inhibitor and its mechanical property. Proteins: Struct. Funct. Genet. 2, 308–329.CrossRefGoogle ScholarPubMed
Noguti, T. & Gō, N. (1983). Dynamics of globular proteins in terms of dihedral angles. J. Phys. Soc. Jap. 52, 3283–3288.CrossRefGoogle Scholar
Noguti, T. & Gō, N. (1989 a). Structural basis of hierarchical multiple substates of a protein. I. Introduction. Proteins: Struct. Funct. Genet. 5, 97–103.CrossRefGoogle ScholarPubMed
Noguti, T. & Gō, N. (1989 b). Structural basis of hierarchical multiple substates of a protein. II. Monte Carlo simulation of native thermal fluctuations and energy minimisation. Proteins: Struct. Funct. Genet. 5, 104–112.CrossRefGoogle Scholar
Noguti, T. & Gō, N. (1989 c). Structural basis of hierarchical multiple substates of protein. III. Side chain and main chain local conformations. Proteins: Struct. Funct. Genet. 5, 113–124.CrossRefGoogle ScholarPubMed
Noguti, T. & Gō, N. (1989 d). Structural basis of hierarchical multiple substates of a protein. IV. Rearrangements in atom packing and local deformations. Proteins: Struct. Funct. Genet. 5, 125–131.CrossRefGoogle ScholarPubMed
Noguti, T. & Gō, N. (1989 e). Structural basis of hierarchical multiple substates of a protein. V. Nonlocal deformations. Proteins: Struct. Funct. Genet. 5, 132–138.CrossRefGoogle ScholarPubMed
Northrup, S. H., Zarrin, F. & McCammon, J. A. (1982). Rate theory for gated diffusion-influenced ligand binding to proteins, J. phys. Chem. 86, 2314–2321.CrossRefGoogle Scholar
Nowik, I., Bauminger, E. R., Cohen, S. G. & Ofer, S. (1985). Spectral shapes of Moessbauer absorption and incoherent neutron scattering from harmonically bound nuclei in Brownian motion: application to macromolecular systems. Phys. Rev. A31 (4). 2291–2299.CrossRefGoogle Scholar
Orbach, R. (1986). Dynamics of fractal networks. Science, Wash. 231, 814–819.CrossRefGoogle ScholarPubMed
Peemoeller, H., Yeomans, F. G., Kydon, D. W. & Sharp, A. R. (1986). Water molecule dynamics in hydrated lysozyme. A deuteron magnetic resonance study. Biophys J. 49, 943–948.CrossRefGoogle ScholarPubMed
Peticolas, W. (1979). Low frequency vibrations and the dynamics of proteins and peptides. Meth. Enzymol. 61, 425–458.CrossRefGoogle Scholar
Pickover, C. A., McKay, D. B., Engelman, D. M. & Steitz, T. A. (1979). Substrate binding closes the cleft between the domains of yeast phosphoglycerate kinase. J. biol. Chem. 254, 11323–11329.CrossRefGoogle ScholarPubMed
Poglitsch, A., Kremer, F. & Genzel, L. (1984). Picosecond relaxations in hydrated lysozyme observed by mm-wave spectroscopy. J. molec. Biol. 173, 137–142.CrossRefGoogle ScholarPubMed
Post, C. B., Dobson, C. M. & Karplus, M. (1989). A molecular dynamics analysis of protein structural elements. Proteins: Struct. Funct. Genet. 5, 337–354.CrossRefGoogle ScholarPubMed
Poole, P. L. & Finney, J. L. (1983). Hydration-induced conformational and flexibility changes in lysozyme at low water content. Int. J. Biol. Macromolecules 5, 308–310.CrossRefGoogle Scholar
Powell, B. M. & Martel, P. (1979). Low frequency intermolecular modes in deuterated α-glycine. Chem. Phys. Lett. 67, 165–167.CrossRefGoogle Scholar
Powell, B. M. & Martel, P. (1981). Hydrogen bonding in DNA base complexes. Biophys. J. 34, 311–323.CrossRefGoogle ScholarPubMed
Rahman, A. (1963). Intermediate scattering function in slow neutron scattering. Phys. Rev. 130 (4), 1334–1346.CrossRefGoogle Scholar
Rahman, A., Singwi, K. S. & Sjolander, A. (1962 a). Theory of slow neutron scattering by liquids. I. Phys. Rev. 126, 986–996.CrossRefGoogle Scholar
Rahman, A., Singwi, K. S. & Sjolander, A. (1962 b). Stochastic model of a liquid and cold neutron scattering. II. Phys. Rev. 126, 997–1004.CrossRefGoogle Scholar
Remington, S., Wiegand, G. & Huber, R. (1982). Crystallographic refinement and atomic models of two different forms of citrate synthase at 2·7 and 1·7 Å resolution. J. molec. Biol. 158, 111–152.CrossRefGoogle ScholarPubMed
Richter, D., Stuhn, B., Ewen, B. & Nerger, D. (1987). Collective relaxation of star polymers – A neutron spin-echo study. Phys. Rev. Lett. 58 (23), 2462–2465.CrossRefGoogle ScholarPubMed
Ringe, D. & Petsko, G. A. (1985). Mapping protein dynamics by X-ray diffraction. Prog. Biophys. molec. Biol. 45, 197–235.CrossRefGoogle ScholarPubMed
Rojewska, D. & Elber, R. (1990). Molecular dynamics study of secondary structure motions in proteins: application to myohemerythrin. Proteins: Struct. Funct. Genet. 7, 265–279.CrossRefGoogle ScholarPubMed
Rosenbaum, M. & Zweifel, P. F. (1965). Quasiclassical theory of neutron scattering. Phys. Rev. 137 (2B), 271–284.CrossRefGoogle Scholar
Rupley, J. A., Gratton, E. & Careri, E. (1983). Water and globular proteins. Trends biochem. Sci. 8, 18–22.CrossRefGoogle Scholar
Sanejouand, Y. H. (1990). Ph.D. thesis, Université Paris Sud, Orsay France.Google Scholar
Sears, V. F. (1966). The law of corresponding states and cold neutron scattering by liquids. Can. J. Phys. 44, 867–875.CrossRefGoogle Scholar
Sharp, K. A. & Honig, B. (1990). Electrostatic interactions in macromolecules: theory and applications. Rev. Biophys. biophys. Chem. 19, 301–332.CrossRefGoogle ScholarPubMed
Smith, J., Cusack, S., Pezzeca, U., Brooks, B. & Karplus, M. (1986 b). Inelastic neutron scattering analysis of low frequency motion in proteins: a normal mode study of the bovine pancreatic trypsin inhibitor. J. chem. Phys. 85 (6), 3636–3654.CrossRefGoogle Scholar
Smith, J., Cusack, S., Poole, P. & Finney, J. (1987). Direct measurement of hydration-related dynamic changes in lysozyme using inelastic neutron scattering spectroscopy. J. Biomol. Struct. Dyn. 4 (4), 583–587.CrossRefGoogle ScholarPubMed
Smith, J., Cusack, S., Tidor, B. & Karplus, M. (1990 a). Inelastic neutron scattering analysis of low-frequency motions in proteins: harmonic and damped harmonic models of bovine pancreatic trypsin inhibitor. J. chem. Phys. 93 (5), 2974–2991.CrossRefGoogle Scholar
Smith, J. L., Hendrickson, W. A., Honzatko, R. B. & Sherriff, S. (1986 a). Structural heterogeneity in protein crystals. Biochemistry 25, 5018–5027.CrossRefGoogle ScholarPubMed
Smith, J., Kuczera, K. & Karplus, M. (1990 b). Dynamics of myoglobin: comparison of simulation results with neutron scattering spectra. Proc. natn. Acad. Sci. U.S.A. 87, 1601–1605.CrossRefGoogle ScholarPubMed
Smith, J., Kuczera, K., Tidor, B., Doster, W., Cusack, S. & Karplus, M. (1989). Internal dynamics of globular proteins: comparison of neutron scattering measurements and theoretical models. Physica B 156, 157, 437–443.CrossRefGoogle Scholar
Stoeckli, H., Furrer, A., Schonenburger, Ch., Meier, B. H., Ernst, R. & Anderson, I. (1986). Dynamics of hydrogen bonds in carboxylic acids. Physica 136B, 161–164.Google Scholar
Strang, G. & Fix, G. J. (1973). An Analysis of the Finite Element Method. Englewood Cliffs, N.J.: Prentice Hall.Google Scholar
Suck, J. B., Perepezko, J. H., Andersen, I. E. & Angell, C. A. (1981). Temperature dependence of the dynamic structure factor for supercooled Sn1−xpbx alloys: a test of instability theories for the liquid–solid phase transition. Phys. Rev. Lett. 47, 424–427.CrossRefGoogle Scholar
Thacher, T., Ganesan, S., Askar, A. & Rabitz, H. (1986). A hybrid approach to modeling the dynamics of macromolecules. J. chem. Phys. 85 (6), 3655–3667.CrossRefGoogle Scholar
Tomkinson, J. (1988). The effect of recoil on the inelastic neutron scattering spectra of molecular vibrations. Chem. Phys. 127, 445–449.CrossRefGoogle Scholar
Trantham, E. C., Rorschach, H. E., Clegg, J. S., Hazlewood, C. F., Nicklow, R. M. & Wakabayashi, N. (1984). Diffusive properties of water in Artemia cysts as determined from quasi-elastic neutron scattering spectra. Biophys. J. 45, 927–937.CrossRefGoogle ScholarPubMed
Ullo, J. J. & Yip, S. (1985). Dynamical transition in a dense fluid approaching structural arrest. Phys. Rev. Lett. 54 (14).CrossRefGoogle Scholar
Ullo, J. J. & Yip, S. (1986). Molecular dynamics simulation of hydrocarbon molecules in condensed phases. 1. Liquid n-butane, J. chem. Phys. 85 (7), 4056–4064.CrossRefGoogle Scholar
Van Gunsteren, W. F. & Karplus, M. (1981). Effect of constraints on the dynamics of macromolecules. Macromolecules 15, 1528–1544.CrossRefGoogle Scholar
Van Gunsteren, W. F. & Karplus, M. (1982). Protein dynamics in solution and in a crystalline environment: a molecular dynamics study. Biochemistry 21 (10), 2259–2274.CrossRefGoogle Scholar
Van Hove, L. (1954). Correlations in space and time and Born approximation scattering in systems of interacting particles. Phys. Rev. 95, 249–262.CrossRefGoogle Scholar
Van Hove, L. (1958). A remark on the time-dependent pair distribution. Physica 24, 404–408.CrossRefGoogle Scholar
Venable, R. M. & Pastor, R. W. (1988). Frictional models for stochastic simulations of proteins. Biopolymers 27, 1001–1014.CrossRefGoogle ScholarPubMed
Wagner, G. & Wuthrich, K. (1986). Observation of internal mobility of proteins by nuclear magnetic resonance in solution. Meth. Enzym. 131 L, 307–326.CrossRefGoogle Scholar
Wang, M. C. & Uhlenbeck, G. E. (1945). On the theory of Brownian motion: II. Rev. mod. Phys. 17, 323–342.CrossRefGoogle Scholar
Weidlich, T., Lindsay, S. M. & Rupprecht, A. (1988). Counterion effects on the structure and dynamics of solid DNA. Phys. Rev. Lett. 61, 1674–1677.CrossRefGoogle ScholarPubMed
Weidlich, T., Powell, J. W., Genzel, L. & Rupprecht, A. (1990). Counterion effects on the far-IR vibrational spectra of Poly(rI).Poly(rC). Biopolymers 30, 477–480.CrossRefGoogle Scholar
Wendolski, J. J. & Matthew, J. B. (1989). Molecular dynamics effects on protein electrostatics. Proteins: Struct. Funct. Genet. 5, 313–321.CrossRefGoogle Scholar
White, J. L., Hackert, M. L., Buehner, M., Adams, M. J., Ford, G. C., Lentz, P. J. JR., Smiley, I. E., Steindel, S. J. & Rossman, M. G. (1976). A comparison of the structures of apo dogfish M4 lactate dehydrogenase and its ternary complexes, J. molec. Biol. 102, 759–779.CrossRefGoogle ScholarPubMed
Williams, G. P., Hirschmugl, C. L., Kneedler, E. M., Sullivan, E. A., Siddons, D. P., Chabal, Y. J., Hoffman, F. & Moeller, K. D. (1989). Infrared synchrotron radiation measurements at Brookhaven. Rev. Sci. Instrum. 60 (7), 2176–2178CrossRefGoogle Scholar
Willis, B. T. M. & Pryor, W. (1975). Thermal Vibrations in Crystallography. Cambridge: Cambridge University Press.Google Scholar
Windsor, C. G. (1981). Pulsed Neutron Scattering. London: Taylor and Francis.Google Scholar
Wlodawer, A., Deisenhofer, J. & Huber, R. (1987). Comparison of two highly refined structures of bovine pancreatic trypsin inhibitor. J. molec. Biol. 193, 145–156.CrossRefGoogle ScholarPubMed
Yarwood, J., Shuttleworth, T., Hasted, J. B. & Nanba, T. (1984). A new radiation source for the infrared region. Nature, Lond. 312, 742–744.CrossRefGoogle Scholar
Young, L., Prabhu, V. V. & Prohofsky, E. W. (1989). Calculation of far-infrared absorption in polymer DNA. Phys. Rev. A 39, 3173–3180.CrossRefGoogle ScholarPubMed
Young, R. D. & Bowne, S. F. (1984). Conformational substates and barrier height distributions in ligand binding to heme proteins. J. chem. Phys. 81 (8), 3730–3738.CrossRefGoogle Scholar
Zemach, A. C. & Glauber, R. J. (1956). Dynamics of neutron scattering by molecules. Phys. Rev. 101 (1), 118–129.CrossRefGoogle Scholar
Zwanzig, R. (1965). Time correlation functions and transport coefficients in statistical mechanics. A. Rev. phys. Chem. 16, 67–99.CrossRefGoogle Scholar