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Intrinsic viscosity of macromolecules within the generalized Rotne–Prager–Yamakawa approximation

Published online by Cambridge University Press:  02 June 2017

Pawel J. Zuk ,
Bogdan Cichocki  and
Piotr Szymczak Open the ORCID record for Piotr Szymczak [Opens in a new window]
Pawel J. Zuk
Affiliation:
Department of Mechanics and Physics of Fluids, Institute of Fundamental and Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland
Bogdan Cichocki
Affiliation:
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
Piotr Szymczak*
Affiliation:
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
*
†Email address for correspondence: piotrek@fuw.edu.pl
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Abstract

We develop a generalized Rotne–Prager–Yamakawa approximation for the dipolar components of the inverse friction matrix and use it for calculating the intrinsic viscosity of rigidly connected bead conglomerates. Such bead models are commonly used in the calculation of hydrodynamic properties of macromolecules. We consider both the case of non-overlapping constituent beads as well as overlapping beads of different sizes. We demonstrate the accuracy of the approximation in two test cases and show that it performs well even if the distances between the beads are small or if the beads overlap. Robust performance of this approximation in the case of overlapping beads stems from its correct limiting behaviour at a complete overlap, with one sphere fully immersed in the other. The generalized Rotne–Prager–Yamakawa approximation is thus well suited for evaluation of intrinsic viscosity, which is a key quantity in characterizing molecular conformations of biological macromolecules.

JFM classification

Complex Fluids: Complex Fluids Low-Reynolds-number flows: Low-Reynolds-number flows Mathematical Foundations: Mathematical Foundations
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 822 , 10 July 2017 , R2
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Copyright
© 2017 Cambridge University Press 

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References

Bloomfield, V., Dalton, W. O. & Van Holde, K. E. 1967 Frictional coefficients of multisubunit structures. I. Theory. Biopolymers 5 (2), 135–148.CrossRefGoogle ScholarPubMed
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Annu. Rev. Fluid. Mech. 20, 111–157.Google Scholar
Brenner, H. & O’Neill, M. E. 1972 On the Stokes resistance of multiparticle systems in a linear shear field. Chem. Engng Sci. 27 (7), 1421–1439.Google Scholar
Carrasco, B. & de la Torre, G. J. 1999a Hydrodynamic properties of rigid particles: comparison of different modeling and computational procedures. Biophys. J. 76, 3044–3057.Google Scholar
Carrasco, B. & de la Torre, J. G. 1999b Improved hydrodynamic interaction in macromolecular bead models. J. Chem. Phys. 111, 4817–4826.CrossRefGoogle Scholar
Cichocki, B., Ekiel-Jezewska, M. L. & Wajnryb, E. 2012 Intrinsic viscosity for Brownian particles of arbitrary shape. J. Phys.: Conf. Ser. 392 (1), 012004.Google Scholar
Cichocki, B., Ekiel-Jezewska, M. L. & Wajnryb, E. 2014 Hydrodynamic radius approximation for spherical particles suspended in a viscous fluid: influence of particle internal structure and boundary. J. Chem. Phys. 140 (16), 164902.Google Scholar
Cichocki, B., Felderhof, B. U. & Schmitz, R. 1988 Hydrodynamic interactions between two spherical particles. Physico-Chem. Hydrodyn. 10, 383–403.Google Scholar
Cichocki, B., Felderhof, B. U., Hinsen, K., Wajnryb, E. & Bławzdziewicz, J. 1994 Friction and mobility of many spheres in Stokes flow. J. Chem. Phys. 100, 3780–3790.Google Scholar
Durlofsky, L., Brady, J. F. & Bossis, G. 1987 Dynamic simulation of hydrodynamically interacting particles. J. Fluid Mech. 180, 21–49.CrossRefGoogle Scholar
Harding, S. E. 1997 The intrinsic viscosity of biological macromolecules. Prog. Biophys. Mol. Biol. 68, 207–262.Google Scholar
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.Google Scholar
Pamies, R., Cifre, J. G. H., Martínez, M. C. L. & de la Torre, J. G. 2008 Determination of intrinsic viscosities of macromolecules and nanoparticles. Comparison of single-point and dilution procedures. Colloid Polym. Sci. 286, 1223–1231.CrossRefGoogle Scholar
Privalov, P. L., Griko, Y. V., Venyaminov, S. Y. & Kutyshenko, V. P. 1986 Cold denaturation of myoglobin. J. Mol. Biol. 190 (3), 487–498.Google Scholar
Rallison, J. M. 1978 The effects of Brownian rotations in a dilute suspension of rigid particles of arbitrary shape. J. Fluid Mech. 84 (02), 237–263.CrossRefGoogle Scholar
Rallison, J. M. 1979 The role of rigidity constraints in the rheology of dilute polymer solutions. J. Fluid Mech. 93 (02), 251–279.CrossRefGoogle Scholar
de la Torre, J. G. & Bloomfield, V. A. 1978 Hydrodynamic properties of macromolecular complexes. IV. Intrinsic viscosity theory, with applications to once-broken rods and multisubunit proteins. Biopolymers 17, 1605–1627.CrossRefGoogle Scholar
de la Torre, J. G. & Carrasco, B. 1998 Intrinsic viscosity and rotational diffusion of bead models for rigid macromolecules and bioparticles. Eur. Biophys. J. 27 (6), 549–557.Google Scholar
de la Torre, J. G., del Rio Echenique, G. & Ortega, A. 2007 Improved calculation of rotational diffusion and intrinsic viscosity of bead models for macromolecules and nanoparticles. J. Phys. Chem. B 111, 955–961.Google Scholar
Wajnryb, E., Mizerski, K. A., Zuk, P. J. & Szymczak, P. 2013 Generalization of the Rotne–Prager–Yamakawa mobility and shear disturbance tensors. J. Fluid Mech. 731, R3.Google Scholar
Williams, C., Brochard, F. & Frisch, H. L. 1981 Polymer collapse. Annu. Rev. Phys. Chem. 32, 433–451.CrossRefGoogle Scholar
Zuk, P. J., Wajnryb, E., Mizerski, K. A. & Szymczak, P. 2014 Rotne–Prager–Yamakawa approximation for different-sized particles in application to macromolecular bead models. J. Fluid Mech. 741, R5.CrossRefGoogle Scholar