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Chapter D2 - Fundamental theory

from Part D - Hydrodynamics

Published online by Cambridge University Press:  05 November 2012

Igor N. Serdyuk ,
Nathan R. Zaccai  and
Joseph Zaccai
Igor N. Serdyuk
Affiliation:
Institute of Protein Research, Moscow
Nathan R. Zaccai
Affiliation:
University of Bristol
Joseph Zaccai
Affiliation:
Institut de Biologie Structurale, Grenoble
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Summary

Historical review

1845

G. Stokes showed that the translational friction for a sphere is proportional to its radius, and to the viscosity of its surrounding solvent. In 1856 he demonstrated that for small angular velocity the rotation of the sphere may be characterised by a single parameter, which is proportional to the linear dimensions cubed.

1893

D. Edwardes calculated two frictional coefficients of the rotation for an ellipsoid of revolution: one for rotation around the axis of revolution and another for rotation around a direction normal to the first. In 1906 A. Einstein showed that rotation of the sphere in Stokes' approximation may be characterised by a single constant which has the dimensions of time. In 1928 R. Gans used the Edwardes frictional coefficients for an ellipsoid of revolution to calculate the ratios of the principal relaxation times to the relaxation time of a sphere of equal volume. In 1936 F. (Francis) Perrin presented equations that give the three rotational coefficients and three rotational relaxation times as functions of the dimensions of a three-axis ellipsoid. These equations could not be expressed in terms of elementary functions. In 1960 L. D. Favro showed that diffusion coefficients related to the rotational motion of a general particle involve five relaxation times; when two of the diffusion coefficients are equal the number of relaxation times is reduced to three. In 1977 E. Small and I. Isenberg solved Perrin's equations for the rotational diffusion of a general ellipsoid using a numerical integration procedure.

Type
Chapter
Information
Methods in Molecular Biophysics
Structure, Dynamics, Function
 , pp. 268 - 317
Publisher: Cambridge University Press
Print publication year: 2007

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References

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Garcia de la Torre, J., Carrasco, B., and Harding, S. E. (1997). SOLPRO: theory and computer program for the prediction of SOLution PROperties of rigid macromolecules and bioparticles. Eur Biophys J. 25, 361–372.CrossRefGoogle ScholarPubMed
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Swanson, E., Teller, D. C., and Haen, C. (1978). The low Reynolds number translation friction of ellipsoids, cylinders, dumbbells, and hollow spherical caps. Numerical testing of the validity of the modified Oseen tensor in computing the friction of objects modelled as beads on a shell. J. Chem. Phys., 68, 5097–5102.CrossRefGoogle Scholar
Carrasco, B., and Garcia de la Torre, J. (1999). Hydrodynamic properties of rigid particles: comparison of different modelling and computational procedures. Biophys. J, 75, 3044–3057.CrossRefGoogle Scholar
Allison, S. A. (2001). Boundary element modelling of biomolecular transport. Bioph. Chem., 93, 197–213.CrossRefGoogle Scholar
Hubbard, J. B., and Douglas, J. F. (1993). Hydrodynamic friction of arbitrarily shaped Brownian particles. Phys. Rev., 47, 2983–2986.Google ScholarPubMed
Zhou, H.-X. (1995). Calculation of translational friction and intrinsic viscosity. I. General formulation for arbitrarily shaped particles. Biophys. J., 69, 2286–2297.CrossRefGoogle ScholarPubMed
Venable, R. M., and Pastor, R. W. (1988). Frictional models for stochastic simulations of proteins. Biopolymers, 27, 1001–1014.CrossRefGoogle ScholarPubMed
Garcia de la Torre, J., Huertas, M. L., and Carrasco, B. (2000). Calculation of hydrodynamic properties of globular proteins from their atomic level structure. Biophys. J., 78, 719–730.CrossRefGoogle ScholarPubMed
Garcia de la Torre, J. (1994). Hydrodynamics of segmentally flexible macromolecules. Eur. Biophys. J., 23, 307–322.CrossRefGoogle Scholar
Tsvetkov, V. N. (1989). Rigid-chain polymers. Hydrodynamic and Optical Properties in Solution. New York: Consultants Bureau.Google Scholar
Hearst, J. E. (1963). Rotary diffusion constants of stiff-chain macromolecules. J. Chem. Phys., 38, 1062–1065.CrossRefGoogle Scholar
Garcia de la Torre, J., and Bloomfield, V. A. (1981). Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications. Quart. Rev. of Biophys., 14, 81–139.CrossRefGoogle ScholarPubMed
Hagerman, P. J., and Zimm, B. (1981). Monte Carlo approach to the analysis of wormlike chains. Biopolymers, 20, 1481–1502.CrossRefGoogle Scholar
Harding, S. E. (1995). On the hydrodynamic analysis of macromolecular conformation. Biophys. Chem., 55, 69–93.CrossRefGoogle ScholarPubMed
Garcia de la Torre, J. (1994). Hydrodynamics of segmentally flexible macromolecules. Eur. Biophys. J., 23, 307–322.CrossRefGoogle Scholar
Allison, S. (1999). Low Reynolds number transport properties of axisymmetric particles employing stick and slip boundary conditions. Macromolecules, 32, 5304–5312.CrossRefGoogle Scholar
Garcia de la Torre, J., and Bloomfield, V. A. (1981). Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications. Quart. Rev. Biophys., 14, 81–13D2.CrossRefGoogle ScholarPubMed
Garcia de la Torre, J. (1988). Hydrodynamic properties of macromolecular assemblies. In Dynamic Properties of Biomolecular Assemblies, eds. Harding, S. E. and Rowe, A. J., pp. 3–31. Nottingham: The Royal Society.Google Scholar
Swanson, E., Teller, D. C., and Haen, C. (1978). The low Reynolds number translation friction of ellipsoids, cylinders, dumbbells, and hollow spherical caps. Numerical testing of the validity of the modified Oseen tensor in computing the friction of objects modelled as beads on a shell. J. Chem. Phys., 68, 5097–5102.CrossRefGoogle Scholar
Carrasco, B., and Garcia de la Torre, J. (1999). Hydrodynamic properties of rigid particles: comparison of different modelling and computational procedures. Biophys. J, 75, 3044–3057.CrossRefGoogle Scholar
Allison, S. A. (2001). Boundary element modelling of biomolecular transport. Bioph. Chem., 93, 197–213.CrossRefGoogle Scholar
Hubbard, J. B., and Douglas, J. F. (1993). Hydrodynamic friction of arbitrarily shaped Brownian particles. Phys. Rev., 47, 2983–2986.Google ScholarPubMed
Zhou, H.-X. (1995). Calculation of translational friction and intrinsic viscosity. I. General formulation for arbitrarily shaped particles. Biophys. J., 69, 2286–2297.CrossRefGoogle ScholarPubMed
Venable, R. M., and Pastor, R. W. (1988). Frictional models for stochastic simulations of proteins. Biopolymers, 27, 1001–1014.CrossRefGoogle ScholarPubMed
Garcia de la Torre, J., Huertas, M. L., and Carrasco, B. (2000). Calculation of hydrodynamic properties of globular proteins from their atomic level structure. Biophys. J., 78, 719–730.CrossRefGoogle ScholarPubMed
Garcia de la Torre, J. (1994). Hydrodynamics of segmentally flexible macromolecules. Eur. Biophys. J., 23, 307–322.CrossRefGoogle Scholar
Tsvetkov, V. N. (1989). Rigid-chain polymers. Hydrodynamic and Optical Properties in Solution. New York: Consultants Bureau.Google Scholar
Hearst, J. E. (1963). Rotary diffusion constants of stiff-chain macromolecules. J. Chem. Phys., 38, 1062–1065.CrossRefGoogle Scholar
Garcia de la Torre, J., and Bloomfield, V. A. (1981). Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications. Quart. Rev. of Biophys., 14, 81–139.CrossRefGoogle ScholarPubMed
Hagerman, P. J., and Zimm, B. (1981). Monte Carlo approach to the analysis of wormlike chains. Biopolymers, 20, 1481–1502.CrossRefGoogle Scholar
Harding, S. E. (1995). On the hydrodynamic analysis of macromolecular conformation. Biophys. Chem., 55, 69–93.CrossRefGoogle ScholarPubMed
Garcia de la Torre, J. (1994). Hydrodynamics of segmentally flexible macromolecules. Eur. Biophys. J., 23, 307–322.CrossRefGoogle Scholar
Allison, S. (1999). Low Reynolds number transport properties of axisymmetric particles employing stick and slip boundary conditions. Macromolecules, 32, 5304–5312.CrossRefGoogle Scholar

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