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Intrinsic Viscosity of Macromolecular Solutions Viscometry:

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Annalen der Physik Band 19, 1906, :

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Annalen der Physik Band 34, 1911, :

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Viscosity of biomolecules Simple, straightforward technique for assaying 1.Solution conformation of biomolecules & volume/ solvent association 2.Molecular weight of biomolecules 3.Flexibility Why viscometry?

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1.U-tube (Ostwald or Ubbelohde) 2.Cone & Plate (Couette) Types of Viscometer: Ostwald Viscometer

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1.U-tube (Ostwald or Ubbelohde) 2.Cone & Plate (Couette) Types of Viscometer: Extended Ostwald Viscometer

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1.U-tube (Ostwald or Ubbelohde) 2.Cone & Plate (Couette) Types of Viscometer: Couette-type Viscometer

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Anton-Paar AMVn Rolling Ball viscometer

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Water bath o C Density meter Coolant system Solution Auto-timer

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For normal (Newtonian) flow behaviour: = (F/A) =. (dv/dy) Definition of viscosity: /(dv/dy) units: (dyn/cm 2 )/sec -1 = dyn.sec.cm -2.. = POISE (P) At 20.0 o C, (water) ~ 0.01P

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For normal (Newtonian) flow behaviour: = (F/A) =. (dv/dy) Definition of viscosity: /(dv/dy) units: (dyn/cm 2 )/sec -1 = dyn.sec.cm -2.. = POISE (P) At 20.0 o C, (water) ~ 0.01P shear stress shear rate viscosity

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Viscosity of biomolecular solutions: A dissolved macromolecule will INCREASE the viscosity of a solution because it disrupts the streamlines of the flow:

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We define the relative viscosity r as the ratio of the viscosity of the solution containing the macromolecule,, to that of the pure solvent in the absence of macromolecule, o : r = o no units For a U-tube viscometer, r = ( t/t o ). ( o )

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Reduced viscosity The relative viscosity depends (at a given temp.) on the concentration of macromolecule, the shape of the macromolecule & the volume it occupies. If we are going to use viscosity to infer on the shape and volume of the macromolecule we need to eliminate the concentration contribution. The first step is to define the reduced viscosity red = r – 1)/c If c is in g/ml, units of red are ml/g

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The Intrinsic Viscosity [ ] The next step is to eliminate non-ideality effects deriving from exclusion volume, backflow and charge effects. By analogy with osmotic pressure, we measure red at a series of concentrations and extrapolate to zero concentration: ] = Lim c 0 red ) Units of [ ] are ml/g

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Form of the Concentration Extrapolation 2 main forms Huggins equation: red = [ ] 1 + K H [ ]c) Kraemer equation: (ln r )/c = [ ] 1 - K K [ ]c) K H (no units): HUGGINS CONSTANT K K (no units): KRAEMER CONSTANT

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A variant of the Huggins equation is: red = [ ] 1 + k.c) k : ml/g and another important relation is the SOLOMON- CIUTA relation, essentially a combination of the Huggins and Kraemer lines: ] ~ (1/c). [2 ( r – 1) – 2 ln( r ) ] 1/2 The Solomon-Ciuta equation permits the approximate evaluation of [ ] without a concentration extrapolation.

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Differential Pressure Viscometer: r = 1 + {(4 P).(P i -2 P)} P PiPi

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Intrinsic Viscosity and its relation to macromolecular properties [ ] so found depends on the shape, flexibility and degree of (time- averaged) water-binding, and for non- spherical particles the molecular weight:

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M (g/mol) [ ] (ml/g) Glucose Myoglobin Ovalbumin Hemoglobin Soya-bean 11S Tomato bushy stunt 10.7 x virus Fibrinogen Myosin Alginate GLOBULAR RODS, COILS

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Intrinsic Viscosity and Protein Shape and Hydration [ ] =. v s (1) : Simha-Saito function (function of shape & flexibility) v s : swollen specific volume, ml/g (function of H 2 O interaction) : Einstein value of 2.5 for rigid spheres >2.5 for other shapes v s : volume of hydrated or swollen macromolecule per. unit anhydrous mass = v + ( ) = v. S w : hydration (g H 2 O/g protein) v: partial specific volume (anhydrous volume per unit anhydrous mass)

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[ ] =. v s or [ ] =. {v + ( )} or [ ] =. v. S w So, 3 forms of Eqn. (1): For proteins, v ~ 0.73ml/g, v s ~ 1ml/g, S w ~ 1.4, {For polysacchs, v ~ 0.6ml/g, v s >>1ml/g, S w >>1}

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Getting a shape from the viscosity parameter SIMPLE ELLIPSOIDS OF REVOLUTION: axial ratio: a/b Computer program ELLIPS1 downloadable from

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Getting a shape from the viscosity parameter Computer program ELLIPS2 downloadable from

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For more complicated shapes: BEAD & SHELL MODELS IgE IgG1 /

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GENERAL CONFORMATIONS The three extremes of macromolecular conformation (COMPACT SPHERE, RIGID ROD, RANDOM COIL) are conveniently represented at the corners of a triangle, known as the HAUG TRIANGLE:

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Each extreme has its own characteristic dependence of [ ] on M. Mark-Houwink-Kuhn-Sakurada equation [ ] = K.M a Analagous power law relations exist for sedimentation, diffusion and R g (classical light scattering) s o 20,w = K.M b ; D o 20,w = K.M - ; R g = K.M c ; By determining a (or b, or c) for a homologous series of a biomolecule, we can pinpoint the conformation type

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Globular proteins, a~0.0, polysaccharide, a ~ 0.5 – 1.3 [ ] = K.M a a = 1.8 a = 0 a =

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The intrinsic viscosity is ideal for monitoring conformation change: [ ] (ml/g) T( o C) Denaturation of ribonuclease

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Storage of chitosan (used in nasal drug delivery) Fee et al, 2006 The intrinsic viscosity is also ideal for monitoring stability:

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Demonstration of H-bonding in DNA Creeth, J.M., Gulland J.M. & Jordan, D.O. (1947) J. Chem. Soc

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J.Michael Creeth,

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Follow up reference sources: Serydyuk, I.N., Zaccai, N.R. and Zaccai, J. (2006) Methods in Molecular Biophysics, Cambridge, Chapter D9 Harding, S.E. (1997) "The intrinsic viscosity of biological macromolecules. Progress in measurement, interpretation and application to structure in dilute solution" Prog. Biophys. Mol. Biol 68, Tombs, M.P. and Harding, S.E. (1997) An Introduction to Polysaccharide Biotechnology, Taylor & Francis, ISBN

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