Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-09T15:31:40.975Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications

Published online by Cambridge University Press:  17 March 2009

José García de la Torre  and
Victor A. Bloomfield
José García de la Torre
Affiliation:
Departamento de Qulmica-FIsica, Faculdad de Ciencias, Universidad de Extremadura, Badajoz, Spain
Victor A. Bloomfield
Affiliation:
Department of Biochemistry, University of Minnesota, St Paul, Minnesota 55108†
Get access Rights & Permissions [Opens in a new window]

Extract

Among the Various methods for characterizing macromolecules in solution, hydrodynamic techniques play a major role. Since the advent of the ultracentrifuge and the development of viscometric apparatus, sedimentation coefficients and intrinsic viscosities have been extensively used to learn about the size and shape of synthetic and biological polymers. More recently, refined techniques such as quasielastic light scattering, transient electric birefringence and fluorescence anisotropy decay have made it possible to obtain in a simple and rapid way quantitative information of high precision on the translational and rotational brownian dynamics of dissolved macromolecules.

Type
Research Article
Information
Quarterly Reviews of Biophysics , Volume 14 , Issue 1 , February 1981 , pp. 81 - 139
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

REFERENCES

Abdel-Khalik, S. I. & Bird, R. B. (1975). Estimation of the zero shear rate viscosity for dilute solution of rigid macromolecules with complex configurations. Biopolymers 14, 1915–1932.CrossRefGoogle Scholar
Allen, F. (1981). Bacteriophage. In Molecular Electrooptics (ed. Krause, S.). New York: Plenum. (In the Press.)Google Scholar
Andrews, P. R. & Jeffrey, P. D. (1976). The use of sedimentation coefficients to distinguish between models for protein oligomers. Biophys. Chem. 4, 93–102.CrossRefGoogle ScholarPubMed
Andrews, P. R. & Jeffrey, P. D. (1980). Calculated sedimentation ratios for assemblies of two, three, four and five spatially equivalent protomers. Biophys. Chem. II, 49–59.CrossRefGoogle Scholar
Baran, G. J. & Bloomfield, V. A. (1978). Tail-fiber attachment in bacteriophage T4D studied by quasielastic light scattering-band electrophoresis. Biopolymers 17, 2015–2028.CrossRefGoogle ScholarPubMed
Belford, G. G., Belford, R. L. & Weber, G. (1972). Dynamics of fluorescence polarization in macromolecules. Proc. natn. Acad. Sci. U.S.A. 69, 1392–1393.CrossRefGoogle Scholar
Bernengo, J. C., Bezot, P., Bezot, C., Roux, B. & Marion, C. (1980). Hydrodynamical properties of nucleosomes. Paper presented at the NATO Advanced Study Institute on Molecular Electrooptics, Troy, NY, 14–24 07.Google Scholar
Bloomfield, V. A., Dalton, W. O. & VanHolde, K. E. Holde, K. E. (1967 a). Frictional coefficients of multisubunit structures. I. Theory. Biopolymers 5, 135–148.CrossRefGoogle ScholarPubMed
Bloomfield, V. A. & Filson, D. P. (1968). Shell model calculations of translational and rotational frictional coefficients. J. Polym. Sci. C25, 73–83.Google Scholar
Bloomfield, V. A., GarciaDe La Torre, J. De La Torre, J. & Wilson, R. W. (1979). Rotational diffusion coefficients of complex macromolecules. In Electrooptics and Dielectrics of Macromoleculesand Colloids (ed. Jennings, B. R.), pp. 183–195. New York: Plenum.CrossRefGoogle Scholar
Bloomfield, V. A., VanHolde, K. E. Holde, K. E. & Dalton, W. O. (1967 b). Frictional coefficients of multisubunit structures. II. Application to proteins and viruses. Biopolymers 5, 149–159.CrossRefGoogle ScholarPubMed
Blum, J. J. & Hines, M. (1979). Biophysics of flagellar motility. Q. Rev. Biophys. 12, 103–180.CrossRefGoogle ScholarPubMed
Boontje, W., Greve, J. & Blok, J. (1977). Transient electric birefringence of T-even bacteriophages. III. T2L and T6 with retracted fibres compared to T4B. Biopolymers 16, 551–573.CrossRefGoogle ScholarPubMed
Boontje, W., Gaive, J. & Blok, J. (1978). Transient electric birefringence of T-even bacteriophages. IV. T2Lo and T6 with extended tail fibres. Biopolymers 17, 2689–2702.CrossRefGoogle Scholar
Brenner, H. (1967). Coupling between the translational and rotational Brownian motions of rigid particles of arbitrary shape. J. Colloid & Interface Sci. 23, 407–436.CrossRefGoogle Scholar
Broersma, S. (1960 a). Rotational diffusion constant of a cylindrical particle. J. Chem. Phys. 32, 1626–1631.CrossRefGoogle Scholar
Broersma, S. (1960 b). Viscous force constant for a closed cylinder. J. Chem. Phys. 32, 1632–1635.CrossRefGoogle Scholar
Burgers, J. M. (1938). Second Report on Viscosity and Plasticity, chap. 3. Amsterdam: Nordemann.Google Scholar
Chang, A. T. & Wu, T. Y. (1971). A note on the helical movement of microorganisms. Proc. R. Soc. Lond. B 178, 327–416.Google Scholar
Eden, D. (1980). Transient electric birefringence of rodlike DNA. The effect of ionic strength and length. Paper presented at the NATO ASI on Molecular Electro-optics, Troy, N.Y. 14–24 07.Google Scholar
Felderhof, B. U. (1978). Hydrodynamic interaction between two spheres. Physica A 89, 373–384.CrossRefGoogle Scholar
Felderhof, B. U. & Deutch, J. M. (1975).Frictional properties of dilute polymer solutions. I. Rotational friction coefficient. J. Chem. Phys. 62, 2391–2397.CrossRefGoogle Scholar
Felsenfeld, G. (1978). Chromatin. Nature, Lond. 271, 115–122.CrossRefGoogle ScholarPubMed
Filson, D. P. & Bloomfield, V. A. (1967). Shell model calculations of rotational diffusion coefficients. Biochemistry, N.Y. 6, 1650–1658.CrossRefGoogle ScholarPubMed
Filson, D. P. & Bloomfield, V. A. (1968). The conformation of polysomes in solution. Biochim. biophys. Acta 155, 169–182.CrossRefGoogle Scholar
GarcíaBernal, J. M. Bernal, J. M. & GarciaDe La Torre, J. De La Torre, J. (1980). Transport properties and hydrodynamic centers of rigid macromolecules with arbitrary shape. Biopolymers, 19, 751–766.Google Scholar
GarcíaBernal, J. M. Bernal, J. M. & GarciaDe La Torre, J. De La Torre, J. (1981). Transport properties of oligomeric subunit structures. Biopolymers 20. (In the Press.)Google Scholar
GarcíaDe La Torre, J. De La Torre, J. & Bloomfield, V. A. (1977 a). Hydrodynamic properties of macromolecular complexes. I. Translation. Biopolymers 16, 1747–1763.Google Scholar
GarcíaDe La Torre, J. De La Torre, J. & Bloomfield, V. A. (1977 b). Hydrodynamic properties of macromolecular complexes. II Rotation. Biopolymers 16, 1765–1778.Google Scholar
GarcíaDe La Torre, J. De La Torre, J. & Bloomfield, V. A. (1977 c). Hydrodynamic properties of macromolecular complexes. III. Bacterial viruses. Biopolymers 16, 1779–1793.Google Scholar
GarcíaDe La Torre, J. De La Torre, J. & Bloomfield, V. A. (1977 d). Hydrodynamic theory of swimming of flagellated microorganisms. Biophys. J. 20, 49–67.Google Scholar
GarcíaDe La Torre, J. De La Torre, J. & Bloomfield, V. A. (1978). Hydrodynamic properties of macromolecular complexes. IV. Intrinsic viscosity theory with application to once-broken rods and multisubunit proteins. Biopolymers 17, 1605–1627.Google Scholar
GarcíaDe La Torre, J. De La Torre, J. & Bloomfield, V. A. (1980). The conformation of myosin in dilute solution as estimated from hydrodynamic properties. Biochemistry, N.Y. 19, 5118–5123.CrossRefGoogle Scholar
Happel, J. & Brenner, H. (1973). Low Reynolds number hydrodynamics, chap. 5. Leyden: Nordhoff.Google Scholar
Harvey, S. C. (1978). Diffusion of hinged particles: An exception to the Einstein relation. J. chem. Phys. 69, 3426–3427.CrossRefGoogle Scholar
Harvey, S. C. (1979 a). Transport properties of particles with segmental flexibility. I. Hydrodynamic resistance and diffusion of a freely hinged particle. Biopolymers 18, 1081–1104.CrossRefGoogle Scholar
Harvey, S. C. (1979 b). Experimental detection of macromolecular flexibility by observation of time-dependent diffusion coefficients. J. chem. Phys. 71, 4221–4226.CrossRefGoogle Scholar
Harvey, S. C. & Cheung, H. C. (1980). Transport properties of particles with segmental flexibility. II. Decay of fluorescence polarization anisotropy from hinged macromolecules. Biopolymers 19, 913–930.CrossRefGoogle Scholar
Harvey, S. C. & GarciaDe La Torre, J. De La Torre, J. (1980). Co-ordinate systems for modelling the hydrodynamic resistance and diffusion coefficients of irregularly shaped rigid macromolecules. Macromolecules 13. (In the Press.)CrossRefGoogle Scholar
Hearst, J. E. (1963). Rotary diffusion constants of stiff-chain macromolecules. J. chem. Phys. 38, 1062–1065.CrossRefGoogle Scholar
Hearst, J. E. (1964). Intrinsic viscosity of stiff-chain macromolecules. J. chem. Phys. 40, 1506–1509.CrossRefGoogle Scholar
Hearst, J. E. & Stockmaye, W. H. (1962). Sedimentation constants of broken chains and wormlike coils. J. chem. Phys. 37, 1425–1433.CrossRefGoogle Scholar
Hearst, J. E. & Tagami, Y. (1965). Shear dependence of the intrinsic viscosity of rigid distributions of segment with cylindrical symmetry. J. chem. Phys. 42, 4149–4151.CrossRefGoogle Scholar
Hearst, J. E. & Tagami, Y. (1967). Erratum: ‘Shear dependence of the intrinsic viscosity of rigid distributions of segments with cylindrical symmetry’. J. chem. Phys. 46, 3030.Google Scholar
Holwill, M. E. J. & Burge, R. E. (1963). A hydrodynamic study of the motility of flagellated bacteria. Archs Biochem. Biophys. 101, 249–260.CrossRefGoogle ScholarPubMed
Hopman, P. C. & Koopmans, G. (1979). Molecular weights of the slow and fast forms of TaL bacteriophage. Biopolymers 18, 1551–1553.CrossRefGoogle Scholar
Hopman, P. C. & Koopmans, G. (1980).Influence of double scattering in determination of rotational diffusion coefficients by depolarized dynamic light scattering: application to the bacteriophages T7 and T4B. Biopolymers 19, 1241–1255.CrossRefGoogle Scholar
Iwata, K. (1979). Viscoelastic properties of rigid and semiflexible particles in solution. I. J. chem. Phys. 71, 931–943.CrossRefGoogle Scholar
Kirkwood, J. G. (1954). The general theory of irreversible processes in solutions of macromolecules. J. Polym. Sci. 12, 1–12.CrossRefGoogle Scholar
Kirkwood, J. G. (1949). The statistical mechanical theory of irreversible processes in solutions of flexible macromolecules. Red. Tray. chim. 68, 649–761.CrossRefGoogle Scholar
Kirkwood, J. G. & Riseman, J. (1948). The intrinsic viscosities and diffusion constants of flexible macromolecules in solution. J. chem. Phys. 16, 565–573.CrossRefGoogle Scholar
Kornberg, R. D. (1977). Structure of chromatin. A. Rev. Biochem, 46, 931–954.CrossRefGoogle ScholarPubMed
Kramers, H. A. (1946). The behavior of macromolecules in inhomogeneous flow. J. chem. Phys. 14, 415–424.CrossRefGoogle Scholar
Kuntz, I. D. Jr & Kauzmann, W. (1974). Hydration of proteins and polypeptides. Adv. Protein Chem. 28, 239–345.CrossRefGoogle ScholarPubMed
Lighthill, M. J. (1975). Mathematical biofluid dynamics, chap. 3. Society for Industrial and Applied Mathematics, Philadelphia, PA.CrossRefGoogle Scholar
Lim, T. K., Baran, G. J. & Bloomfield, V. A. (1977). Measurement of diffusion coefficient and electrophoretic mobility with a quasielastic light scattering band-electrophoresis apparatus. Biopolymers 16, 1473–1488.CrossRefGoogle Scholar
Mccammon, J. A., Deutch, J. M. & Felderitoff, B. U. (1975 a). Frictional properties of multisubunit structures. Biopolymers 14, 2613–2623.CrossRefGoogle Scholar
Mccammon, J. A., Deutch, J. M. & Felderitoff, B. U. (1975 b). Low values of the Scheraga–Mendelkern β parameter for proteins. An explanation based on porous sphere hydrodynamics. Biopolymers 14, 2479–2487.CrossRefGoogle Scholar
Mccammon, J. A. & Deutch, J. M. (1976). Frictional properties of non- spherical multisubunit structures. Application to tubules and cylinders. Biopolymers 15, 1397–1408.CrossRefGoogle Scholar
Mellado, P. & GarcíaDe La Torre, J. De La Torre, J. (1981). Steady state and transient electric birefringence of solution of bent rod macromolecules. (Manuscript in preparation.)Google Scholar
Nakajima, H. & Wada, Y. (1977). A general method for evaluation of diffusion constants, dilute-solution viscoelasticity, and the dielectric property of a rigid macromolecule with an arbitrary configuration. Biopolymers 16, 875–893.CrossRefGoogle ScholarPubMed
Nakajima, H. & Wada, Y. (1978). A general method for the evaluation of diffusion constants, dilute-solution viscoelasticity and the complex dielectric constant of a rigid macromolecule with an arbitrary configuration. II. Biopolymers 17, 2291–2307.CrossRefGoogle Scholar
Newman, J., Swinney, H. L. & Day, L. A. (1977). Hydrodynamic properties and structure of fd virus. J. Molec. Biol. 116, 593–606.CrossRefGoogle ScholarPubMed
Norisuye, T., Motokawa, M. & Fujita, H. (1979). Wormlike chains near the rod limit: Translational friction coefficient. Macromolecules 12, 320–323.CrossRefGoogle Scholar
Oseen, C. W. (1927). Hydrodynamik. Leipzig: Academisches Verlag.Google Scholar
Pauling, L. (1960). The Nature of the Chemical Bond. New York: Cornell.Google Scholar
Perrin, F. (1934). Mouvement brownien d'un ellipsoïde. I. Dispersion diélectrique pour des molecules ellipsoïdales. J. Phys. Radium 5, 497–511.CrossRefGoogle Scholar
Perrin, F. (1936). Mouvement brownien d'un ellipsoïde. II. Rotation libre et dépolarisation des fluorescences. Translation et diffusion de molécules ellipsoïdales. J. Phys. Radium 7, 1–11.CrossRefGoogle Scholar
Ramsay-Shaw, B. & Schmitz, K. S. (1976). Quasielastic light scattering by biopolymers. Conformation of chromatin multimers. Biochim. biophys. Res. Comm. 73, 224–232.CrossRefGoogle Scholar
Ramsay-Shaw, B. & Schmitz, K. S. (1979). In Chromatin Structure and Function, part B (ed. Nicoli, C. A.), pp. 427–438. New York: Plenum.CrossRefGoogle Scholar
Riseman, J., & Kirkwood, J. G. (1950). The intrinsic viscosity, translational and rotational diffusion constants of rodlike macromolecules. J. Chem. Phys. 19, 512–516.CrossRefGoogle Scholar
Rotne, J. & Prager, S. (1969). Variational treatment of hydrodynamic interaction on polymers. J. chem. Phys. 50, 4831–4837.CrossRefGoogle Scholar
Rouse, P. E. (1953). A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. chem. Phys. 21, 1272–1280.CrossRefGoogle Scholar
Scfieraga, H. (1955). Non-Newtonian viscosity of solutions of ellipsoidal particles. J. chem. Phys. 23, 1526–1532.CrossRefGoogle Scholar
Scheraga, H. & Mandelkern, L. (1953). Consideration of the hydrodynamic properties of proteins. J. Am. chem. Soc. 75, 179–184.CrossRefGoogle Scholar
Schmitz, K. S. (1977). Hydrodynamic shielding of spherical subunits in macromolecular complexes. Biopolymers 16, 2635–2640.CrossRefGoogle Scholar
Schmitz, K. S. & Ramsay-Shaw, B. (1977 a). Chromatin conformation: a systematic analysis of helical parameters from hydrodynamic data. Biopolymers 16, 2619–2633.CrossRefGoogle ScholarPubMed
Schmitz, K. S. & Ramsay-Shaw, B. (1977 b). Hydrodynamic evidence in support of spacer regions in chromatin. Science, N. Y. 197, 661–663.CrossRefGoogle ScholarPubMed
Simha, R. (1940). The influence of Brownian movements on the viscosity of solutions. J. Phys. Chem. 44, 25–34.CrossRefGoogle Scholar
Stellwagen, N. (1980). The electric birefringence of restriction enzyme fragments of DNA: optical factor, electric polarizability and relaxation times as a function of molecular weight. Paper presented at the NATO ASI on Molecular Electro-optics, Troy, N.Y. 14–24 07.Google Scholar
Swanson, E., Teller, D. C. & De, Haen C. (1978). The low Reynolds number translational friction of ellipsoids, cylinders, dumbells and hollow spherical caps. Numerical testing of the validity of the modified Oseen tensor in computing the friction of objects modelled as beads on the shell. J. chem. Phys. 68, 5097–5102.CrossRefGoogle Scholar
Swanson, E.Teller, D. C. & De, Haen C. (1980). Creeping flow translational resistance of rigid assemblies of spheres. J. chem. Phys. 72, 1623–1628.CrossRefGoogle Scholar
Teller, D. C. & De, Haen C. (1975). The sedimentation behavior of oligomeric proteins. Fedn. Proc. Fed. Am. Socs. exp. Biol. 34, 598.Google Scholar
Teller, D. C., Swanson, E. & De, Haen C. (1979). The translational friction coefficient of proteins. Adv. Enzymol. 61, 103–124.Google ScholarPubMed
Tirado, M. M. & Garcí De La Torre, J. (1979). Translational friction coefficients of rigid, symmetric top macromolecules. Application to circular cylinders. J. chem. Phys. 71, 2581–2588.CrossRefGoogle Scholar
Tirado, M. M. & García, De La Torre J. (1980). Rotational diffusion of rigid, symmetric top macromolecules. Application to circular cylinders. J. chem. Phys. 73. (In the Press.)CrossRefGoogle Scholar
Tsuda, K. (1969). Intrinsic viscosity of rigid complex macromolecules. Bull. chem. Soc. Japan 42, 850.CrossRefGoogle Scholar
Tsuda, K. (1970a). Intrinsic viscosity of rigid complex macromolecules. Rheol. Acta 9, 509–516.CrossRefGoogle Scholar
Tsuda, K. (1970b). Hydrodynamic properties of rigid complex macromolecules. Polym. J. I, 66–631.Google Scholar
Van, Holde K. E. (1971). Physical Biochemistry, chap. 4. Englewood Cliffs: Prentice-Hall.Google Scholar
Wegener, W. A. (1980a). Diffusion coefficients for rigid macromolecules with irregular shapes that allow rotational–translational coupling. Biopolymers 19. (In the Press.)Google Scholar
Wegener, W. A. (1980b). The hydrodynamic resistance and diffusion coefficients of a flexible hinged rod. Biopolymers 19. (In the Press.)CrossRefGoogle Scholar
Wegener, W. A., Dowben, R. M. & Koester, V. J. (1979). Time-dependent birefringence, linear dichroism, and optical rotation resulting from rigid-body rotational diffusion. J. chem. Phys. 70, 622–632.CrossRefGoogle Scholar
Wegener, W. A., Koester, V. J. & Dowben, R. M. (1978). Fluorescence polarization of macromolecules with segmental flexibility. Biophys. J. 21, 114a.Google Scholar
Welch, J. B. & Bloomfleld, V. A. (1978). Concentration-dependent isomerization of bacteriophage T2L. Biopolymers 17, 2001–2014.CrossRefGoogle ScholarPubMed
Wilemski, G. (1977). Conformation dependent transport coefficients of once-broken rods. Macromolecules 10, 28–34.CrossRefGoogle Scholar
Wilson, R. W. & Bloomfield, V. A. (1979a). Hydrodynamic properties of macromolecular complexes. V. Improved calculation of rotational diffusion coefficient and intrinsic viscosity. Biopolymers 18, 1205–1211.CrossRefGoogle Scholar
Wilson, R. W. & Bloomfield, V. A. (1979b). Rotational effects in quasi- elastic laser light scattering from T-even bacteriophage. Biopolymers 18, 1543–1549.CrossRefGoogle Scholar
Yamakawa, H. (1970). Transport properties of polymer chains in dilute solutions. Hydrodynamic interaction. J. chem. Phys. 53, 436–443.CrossRefGoogle Scholar
Yamaakawa, H. (1971). Modern Theory of Polymer Solutions. New York: Harper & Row.Google Scholar
Yamakawa, H. (1975). Viscoelastic properties of straight circular macromolecules in dilute solution. Macromolecules 8, 339–342.CrossRefGoogle Scholar
Yamakawa, H. & Fujii, M. (1973). Translational friction coefficient of wormlike chains. Macromolecules 6, 407–414.CrossRefGoogle Scholar
Yamakawa, H. & Tanaka, G. (1972). Translational diffusion coefficients of rodlike polymers: Application of the modified Oseen tensor. J. chem. Phys. 57, 1537–1542.CrossRefGoogle Scholar
Yamakawa, H. & Yamaki, J. (1972). Translational diffusion coefficients of plane-polygonal polymers: Application of the modified Oseen tensor. J. chem. Phys. 57, 1542–1546.CrossRefGoogle Scholar
Yamakawa, H. & Yamaki, J. (1973). Application of Kirkwood theory of transport in polymer solutions to rigid assemblies of beads. J. chem. Phys. 58, 2049–2055.CrossRefGoogle Scholar
Yamakawa, H., Yoshizaki, T. & Fujii, M. (1977). Transport coefficients of helical wormlike chains. I. Characteristic helices. Macromolecules 10, 934–943.CrossRefGoogle Scholar
Yguerabide, J., Epstein, H. F. & Stryer, L. (1970). Segmental flexibility in an antibody molecule. J. molec. Biol. 51, 573–590.CrossRefGoogle Scholar
Yoshixaki, T. & Yamakawa, H. (1980). Dynamics of spheroid–cylindrical molecules in dilute solutions. J. chem. Phys. 72, 57–69.CrossRefGoogle Scholar
Yu, H. & Stockmayer, W. H. (1967). Intrinsic viscosity of a once-broken rod. J. chem. Phys. 47, 1369–1373.CrossRefGoogle ScholarPubMed
Zimm, B. H. (1956). Dynamics of polymer molecules in dilute solution: Viscoelasticity, flow birefringence and dielectric loss. J. chem. Phys. 24, 269–278.CrossRefGoogle Scholar
Zimm, B. H. (1980). Chain molecule hydrodynamics by the Monte Carlo method and the validity of the Kirkwood–Riseman approximation. Macromolecules 13, 592–602.CrossRefGoogle Scholar
Zwanzig, R., Kiefer, J. & Weiss, G. H. (1968). On the validity of the Kirk-wood–Riseman theory. Proc. natn. Acad. Sci. U.S.A. 60, 381–386.CrossRefGoogle ScholarPubMed