Sizes, shapes and interactions of molecules in solution

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1 Sizes, shapes and interactions of molecules in solution Light Scattering Analytical Viscometry Ultracentrifugation Steve Harding, NCMH University of Nottingham

2 1. Molecular weight distribution analysis SEC MALLs and AUC 2. Conformation and flexibility Viscometry, AUC, Light scattering

3 NCMH at Nottingham: A Facility for characterising i sizes/shapes and interactions of macromolecules in solution

5 Lecture 1: Albert Einstein and the Viscosity of Albert Einstein and the Viscosity of Macromolecules

6 Annalen der Physik Band 19, 1906, :

7 Annalen der Physik Band 34, 1911, :

8 Viscometry Intrinsic Viscosity of Macromolecular Solutions

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

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

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

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

13 Anton-Paar AMVn Rolling Ball viscometer

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

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

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

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

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

that of the pure solvent in the absence of macromolecule, η o :

19 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 η red = (η r 1)/c If c is in g/ml, units of η red are ml/g

If we are going to use viscosity to infer on the shape and volume of the macromolecule we need to

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

ec By analogy a with osmotic o pressure, e, we measure η red at a series of

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

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

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

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

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

26 Intrinsic Viscosity and Protein Shape and Hydration [η] = ν. v s (1) ν: Simha-Saito function (function of shape & flexibility) v s : swollen specific volume, ml/g (function of H 2 O interaction) ν: 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 + (δ/ρ ο ) = v. S w δ: hydration (g H 2 O/g protein) v: partial specific volume (anhydrous volume per unit anhydrous mass)

27 So, 3 forms of Eqn. (1): [η] = ν. v s or [η] = ν. {v + (δ/ρ ο )} or [η] = ν. v. S w 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}

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

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

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

31 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:

32 Each extreme has its own characteristic dependence of [η] on M. Mark-Houwink-Kuhn-Sakurada equation [η] = 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 -ε ; R g = K.M c ; d i i ( b )f h l i f By determining a (or b, ε or c) for a homologous series of a biomolecule, we can pinpoint the conformation type

33 [η] = K.M a a = 0 a = a = 1.8 Globular proteins, a~0.0, polysaccharide, a ~

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

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

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

37 J.Michael Creeth,

38 Follow up reference sources: Serydyuk, I.N., Zaccai, N.R. and Zaccai, J. (2006) Methods in Molecular l Biophysics, i 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

SIZE OF A MOLECULE FROM A VISCOSITY MEASUREMENT

Experiment 8, page 1 Version of April 25, 216 Experiment 446.8 SIZE OF A MOLECULE FROM A VISCOSITY MEASUREMENT Theory Viscous Flow. Fluids attempt to minimize flow gradients by exerting a frictional force,