Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T21:00:25.132Z Has data issue: false hasContentIssue false

Forward scattering of light, X-rays and neutrons

Published online by Cambridge University Press:  17 March 2009

Henryk Eisenberg
Affiliation:
Laboratory of Molecular Biology, National Institute of Arthritis, Metabolism and Digestive Diseases, National Institutes of Health, Bethesda, Maryland 20205 and Polymer Department, The Weizmann Institute of Science, Rehovot, Israel76100*

Extract

The central points of this paper can now be summarized. We consider here, for simplicity only, vanishing particle concentration. In equilibrium sedimentation equation (6) applies. The density increment is a measurable quantity. It can either be introduced into equation (6) to calculate M2, or it can be analysed by equations (7) and (8) to provide additional information on specific volumes and solute interactions.

Light scattering is determined by the analogous equation (20). The refractive index increment is also experimentally accessible and its structure (not considered here) is similar to that of the density increment. Small angle X-ray scattering is determined by equation (31) and the electron density increment which appears in this equation cannot be directly determined by experiment. Yet it can be obtained in straightforward fashion from the mass density increment, by equation (34). Similarly, in the case of neutron scattering (equation (38)), the scattering length density increment is obtained from the mass density increment by equation (40), or it may now be directly evaluated by neutron interferometry.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1981

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

X. REFERENCES

Aggerbeck, L., Yates, M., Tardieu, A. & Luzzati, V. (1978). Density contrast studies of macromolecules in solution. Cross verification of X-ray scattering and pycnometry experiments. J. appl. Crystallogr. 69, 466472.CrossRefGoogle Scholar
Bacon, G. E. (1962). Neutron Diffraction. London: Oxford University Press.Google Scholar
Benoit, H. & Wippler, C. (1960). Angular distribution of light scattered by a solution of copolymers. J. chem. Phys. 57, 524527.Google Scholar
Berne, B. J. & Pecora, R. (1976). Dynamic Lzght Scattering. New York: John Wiley.Google Scholar
Bushuk, W. & Benoit, H. (1958). Light scattering studies of copolymers. I. Effect of heterogeneity of chain composition on the molecular weight. Can. J. Chem. 36, 16161626.Google Scholar
Casassa, E. F. & Eisenberg, H. (1964). Thermodynamic analysis of multicomponent solutions. Adv. Protein Chem. 19, 287395.CrossRefGoogle ScholarPubMed
Cohen, G. & Eisenberg, H. (1965). Light scattering of water, deuterium oxide, and other pure liquids. J. chem. Phys. 43, 38813887.CrossRefGoogle Scholar
Cohen, G. & Eisenberg, H. (1968). Deoxyribonucleate solutions: sedimentation in a density gradient, partial specific volumes, density and refractive index increments, and preferential interactions. Biopolymers 6, 10771100CrossRefGoogle Scholar
Cotton, J. P. & Benoit, H. (1975) Study of the contrast and its influence on the determination of the scattered intensity and the radius of gyration in heterogeneous macromolecular systems. J. Physique 36, 905910.CrossRefGoogle Scholar
Debye, P. (1944) Light scattering in solutions. J. appl. Phys. 15, 338342.CrossRefGoogle Scholar
Des, Cloiseaux J. & Jannink, G. (1980). Contrasts in multicomponent systems. Physica 102 A, 120130.Google Scholar
Doughty, D. A. (1979) Isopiestic compositions of aqueous ionic surfactant systems as a measure of preferential interactions. Application to the determination of micelle aggregation numbers by equilibrium sedimentation. J. Phys. Chem. 83, 26212627.CrossRefGoogle Scholar
Edelstein, S. J. & Schachman, H. K. (1973). Measurement of partial specific volume by sedimentation equilibrium in H2O-D2O solutions. Meth. Enzym. 27 D, 8298.CrossRefGoogle ScholarPubMed
Einstein, A. (1910). Theory of the opalescence of homogeneous fluids and their mixtures in the vicinity of the critical state. Annln Physik. [4], 33, 12751298.CrossRefGoogle Scholar
Eiseneerg, H. (1962). Multicomponent polyelectrolyte solutions. Part I. Thermodynamic equations for light scattering and sedimentation. J. chem. Phys. 36, 18371843.CrossRefGoogle Scholar
Eisenberg, H. (1972). Light scattering and some aspects of small angle X-ray scattering. In Procedures in Nucleic Acid Research (ed. Cantoni, G. I. and Davies, D. R.), pp. 137175. New York: Harper and Row.Google Scholar
Eisenberg, H. (1976). Biological Macromolecules and Polyelectrolytes in Solution. London: Oxford University Press.Google Scholar
Eisenberg, H. & Cohen, G. (1968). An interpretation of the low angle X-ray scattering of DNA solutions. J. molec. Biol. 37, 355362. Erratum (1969), 42, 607.CrossRefGoogle ScholarPubMed
Eisenberg, H. & Felsenfeld, G. (1981). Hydrodynamic studies of the interaction between nucleosome core particles and core histones. J. molec. Biol., in press.CrossRefGoogle Scholar
Eisenberg, H., Haik, Y., Jfft, J., Leicht, W., Mevarech, M. & Pundak, S. (1978). Interactions of proteins and nucleic acids with solutes in concentrated solutions of monovalent salts, relating to hydration, structural transitions and inactivation of halophilic malate and glutamate dehydrogenase. In Energetics and Structure of Halophilic Microorganisms (ed. Caplan, S. R. and Ginzburg, M.), pp. 1332. Amsterdam: Elsevier/North Holland.Google Scholar
Ewart, R. H., Roe, C. P., Debye, P. & McCartney, J. R. (1946). The determination of polymeric molecular weights by light scattering in solvent-precipitant systems. J. chem. Phys. 14, 687695.CrossRefGoogle Scholar
Finch, J. T., Lutter, L. C., Rhodes, D., Brown, R. S., Rushton, B., Levitt, M. & Klug, A. (1977). Structure of nucleosome core particles of chromatin. Nature, Lond. 269, 2936.CrossRefGoogle ScholarPubMed
Hearst, J. E. & Schmid, C. W. (1973). Density gradient sedimentation equilibrium. Meth. Enzym. 27 D, 111127.CrossRefGoogle ScholarPubMed
Ibel, K. & Stuhrmann, H. G. (1975). Comparison of neutron and X-ray scattering of dilute myoglobin solutions. J. molec. Biol. 93, 255265.CrossRefGoogle ScholarPubMed
Jacrot, B. (1976). The study of biological structures by neutron scattering from solution. Rep. Prog. Phys. 39, 911953.CrossRefGoogle Scholar
Jannink, G., Nierlich, M. & Williams, C. (1980). Variation of contrast and polyelectrolytes in solution. C. r. hebd. Séanc. Acad. Sci. Paris B 29, 8386.Google Scholar
Kam, Z. (1977). Determination of macromolecular structure in solution by spatial correlation of scattering fluctuations. Macromolecules 10, 927934.CrossRefGoogle Scholar
Luzzati, V. & Tardieu, A. (1980). Recent developments in solution X-ray scattering. A. Rev. Biophys. Bioeng. 9, 129.CrossRefGoogle ScholarPubMed
McGhee, J. D. & Felsenfeld, G. (1980). Nucleosome structure. A. Rev. Biochem. 49, 11151156.CrossRefGoogle ScholarPubMed
McGhee, J. D., Felsenfeld, G. & Eisenberg, H. (1980). Nucleosome structure and conformational changes. Biophys. J. 32, 261270.CrossRefGoogle ScholarPubMed
Meselson, M. & Stahl, F. W. (1958). The replication of DNA in Escherichia coli. Proc. natn. Acad. Sci. U.S.A. 44, 671682.Google ScholarPubMed
Meselson, M. & Stahl, F. W. & Vinograd, J. (1957). Equilibrium sedimentation of macromolecules in density gradients. Proc. natn. Acad. Sci. U.S.A. 43, 581588.CrossRefGoogle ScholarPubMed
Müller, K., Laggner, P., Glatter, O. & Kostner, G. (1978). The structure of human plasma low density lipoprotein B. An X-ray small angle scattering study. Eur. J. Biochem. 82, 7390.CrossRefGoogle ScholarPubMed
Pardon, J. F., Worcester, D. L., Wooley, J. C., Cotter, R. I., Lilley, D. M. J. & Richards, B. M. (1977). The structure of the chromatin core particle in solution. Nucl. Acids Res. 4, 31993214.CrossRefGoogle ScholarPubMed
Rattle, H. W. E., Kneale, G. G., Baldwin, J. P., Matthews, H. R., Crane-Robinson, C., Cary, P. D., Carpenter, B. G., Suau, P. & Bradbury, E. M. (1979). Histone complexes, nucleosomes, chromatin and cell-cycle dependent modifications of histones. In Chromatin Structure and Function (ed. Nicolini, C. A.), pp. 451513. New York: Plenum Press.CrossRefGoogle Scholar
Reisler, E. & Eisenberg, H. (1969). Interpretation of equilibrium sedimentation measurements of proteins in guanidine hydrochloride solutions. Partial volumes, density increments, and the molecular weight of the subunits of Rabbit Muscle Aldolase. Biochemistry 8, 45724578.CrossRefGoogle ScholarPubMed
Reisler, E., Haik, Y. & Eisenberg, H. (1977). Bovine serum albumin in aqueous guanidine hydrochloride solutions. Preferential and absolute interactions and comparison with other systems. Biochemistry 16, 197203.CrossRefGoogle ScholarPubMed
Schelten, J., Schlecht, P., Schmatz, W. & Mayer, A. (1972). Neutron small angle scattering of hemoglobin. J. biol. Chem. 247, 54365441.CrossRefGoogle ScholarPubMed
Smoluchowski, M. (1908). Molecular kinetic theory of the opalescence of gases in the critical state, as well as some related phenomena. Annln Physik. [4], 25, 205226.Google Scholar
Smoluchowski, M. (1912). On the opalescence of gases in the critical state. Phil. Mag. [6], 23, 165173.CrossRefGoogle Scholar
Stuhrmann, H. B. (1974). Neutron small-angle scattering of biological macromolecules in solution. J. appl. Crystallogr. 7, 173178.CrossRefGoogle Scholar
Stuhrmann, H. B. & Kirste, R. G. (1965). Elimination of intraparticle background scattering for small angle X-ray scattering of compact particles (proteins). Z. Phys. Chem. Frankfurt. 46, 247250.CrossRefGoogle Scholar
Suau, P., Kneale, G. G., Braddock, G. W., Baldwin, J. P. & Bradbury, E. M. (1977). A low resolution model for the chromatin core particle by neutron scattering. Nucl. Acids Res. 4, 37693786.CrossRefGoogle ScholarPubMed
Tardieu, A. (1979). Some comments on the article. The structure of human plasma low density lipoprotein B. Eur. J. Biochem. 96, 621624.CrossRefGoogle ScholarPubMed
Voordouw, G. & Eisenberg, H. (1978). Binding of additional histones to chromatin core particles. Nature, Lond. 273, 446448.CrossRefGoogle ScholarPubMed
Wise, D. S., Karlin, A. & Schoenborn, B. P. (1979). An analysis by low angle neutron scattering of the structure of the acetylcholine receptor from Torpedo californica in detergent solution. Biophys. J. 28, 473496.CrossRefGoogle ScholarPubMed