Analytical Ultracentrifugation VI

167 Pages·2002·4.768 MB·English

by  W. Mächtle, M. D. Lechner (auth.), W. Borchard, A. Straatmann (eds.)

Progress in Colloid and Polymer Science • Volume 119 • 2002
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Progress in Colloid and Polymer Science
Editors: F. Kremer, Leipzig and G. Lagaly, Kiel
Volume 119 • 2002
Analytical
Ultracentrifugation VI
Volume Editors:
W. Borchard and A. Straatmann
Springer
IV
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Progr Colloid Polym Sci (2002) 119: V
© Springer-Verlag 2002
Since 1978 symposia on Analytical Ultracentrifugation have been performed in Germany, where now the 12th
meeting has taken place in Duisburg fi'om March 1st to 2nd 2001. As in the years before various fields of
ultracentrifugation were covered concerning general theory, research problems in biochemistry, biophysical
chemistry, macromolecular chemistry, size distributions of particles interacting systems, hydrodynamics and
applications to crosslinked swollen systems. In addition a new evaluating software was presented. The development
of the ultracentrifugal technique in the last years is mainly characterized by an enhanced treatment of online available
data from optical detection systems and also the development of a new analytical ultracentrifuge of Beckman
equipped with maintenance-free drives.
Twenty contributions of the recent conference have been selected for publication. They are arranged as can be
taken from the contents corresponding mainly the groupings of posters and lectures during the meeting.
The 12th international symposium on Analytical Ultracentrifugation was generously sponsored by BASF
(Ludwigshafen), Bayer AG (Leverkusen), Degussa AG Coatings and Colorants (Marl) and Beckman Coulter GmbH
(Mfinchen). Thus it was possible to support colleagues from Eastern countries of Europe to cover a small part of their
travel expenses. We express our thanks to the companies. Especially we reward the numerous unnamed reviewers for
helping to improve the contributions of this special volume of Progress in Colloid and Polymer Science.
W. Borchard
A. Straatmann
Progr Colloid Polym Sci (2002) 119: VI-VII
© Springcr-Verhig 2002
¥
Preface ...............................................
Technical and Methodological Investigations
M~ichtle W, Lechner MD: Evaluation of equilibrimn and nonequilibrium density gradients in an
analytical ultracentrifuge by calibration with marker particles .....
Lucas G, B6rger L, C61fen H: Solubility equilibrium gradients in the analytical ultracentrifuge: an
approach towards the isolation of critical crystal nuclei in solution 11
Polymers, Colloids and Supramolecular Systems
Lavrenko P, Yevlampiev K, Hybrid polymer heterogeneity and boundary profile in a low-speed
Volokhova D: sedimentation experiment ................................. 19
Tziatzios C, Precup AA, Weidl CH, Studies on the partial specific volume of a poly(ethylene glycol)
Schubert UH, Schuck P, derivative in different solvent systems ........................ 24
Durchschlag H, Mfichtle W,
van den Brock JA, Schubert D:
Vogel V, Langer K, Balthasar S, Characterization of serum albumin nanoparticles by sedimentation
Schuck P, M/ichtle W, Haase W, velocity analysis and electron microscopy ..................... 31
Broek van den JA, Tziatzios C,
Schubert D:
Pavlov GM, Michailova NA, Properties of a membrane-forming polymer, poly(1-trimethylgermyl-1-
Korneeva EV, propyne), in dilute solutions ............................... 37
Yevlampieva NP, Rjumtsev El,
Khotimsky VS, Litvinova EG,
Chirkova MV:
Biological Systems
Bozdky Z, Ftil6p L, Jfinoki G: Combination of preparative and analytical ultracentrifugation methods
for the investigation of low-density lipoprotein aliquots to prepare
radioactive-labelled o-lipoproteins ........................... 43
Berth G, C61fen H, Dautzenberg H: Physicochemical and chemical characterisation of chitosan in dilute
aqueous solution ........................................ 50
Errington N, Mistry P, Rowe AJ: Protein hydration varies with protein crowding and with applied
pressure: a sedimentation velocity study ...................... 58
Straatmann A, Borchard W: Determination of thermodynamic properties of sodium alginate
from bacteria and seaweeds in aqueous solutions ............... 64
Interacting Systems
Chebotareva NA, Andreeva IE, Self-association of phosphorylase kinase from rabbit skeletal muscle
Makeeva VF, Kurganov BI, in the presence of natural osmolyte, trimethylamine N-oxide ...... 70
Livanova NB, Harding SE:
Mayer G, Anderka O, Ludwig B, The state of association of the cytochrome bc~ complex from
Schubert D: Paracoccus denitrificans in solutions of dodecyl maltoside ......... 77
Wandrey Ch, Grigorescu G, Study of polyelectrolyte complex formation applying the synthetic
Hunkeler D: boundary technique of analytical ultracentrifugation ............ 84
vii
Thermodynamics
Kisters D, Straatmann A, The sedimentation behaviour of gels the generalised Lamm
Borchard W: differential equation ..................................... 92
Borchard W, C61fen H, Kisters D, Evidence for phase transitions of aqueous gelatin gels in a centrifugal
Straatmann A: field .................................................. 101
Wills P, Winzor D: Exact theory of sedimentation equilibrium made useful .......... 113
Hydrodynamics
Durchschlag H, Zipper P: Correlations between crystallographic, small-angle scattering and
hydrodynamic data of biopolymers .......................... 121
Durchschlag H, Zipper P: Modeling of protein hydration with respect to X-ray scattering and
hydrodynamics ......................................... 131
Zipper P, Krebs A, Durchschlag H: Prediction of hydrodynamic parameters of Lumbricus terrestris
hemoglobin from small-angle X-ray and electron microscopic
structures ............................................. 141
Pavlov GM: Evaluation of draining and volume effects in the interpretation of
hydrodynamic data for linear macromolecules ................. 149
Authors/Title Index ...................................... 159
Key word Index ........................................ 160
ProgrColloidPolymSci(2002)119:1–10
TECHNICAL AND METHODOLOGICAL INVESTIGATIONS
(cid:1)Springer-Verlag2002
Evaluation of equilibrium and nonequilibrium
W. Ma¨chtle
M. D. Lechner
density gradients in an analytical
ultracentrifuge by calibration with marker
particles
Abstract Density gradient measure- systematic study of these deviations
ments inside an analytical ultracen- using a marker nanoparticle system
trifuge (AUC) are an excellent tool of 11 precisely characterized ethyl-
for characterizing nanoparticles in hexyl acrylate/methyl acrylate co-
the 10–1000-nm diameter range. polymer latices with known nearly
Because of its very high resolution equidistantparticledensities.During
(i.e. its fractionation power accord- thisstudywealsolearnedtousethis
ing to the particle density and its 11-marker system as a pragmatic
high precision) it is possible to and simple calibration system for
analyze the chemical nature of aqueous density gradients, thereby
nanoparticles, especially of complex reducing considerably the error of
colloidal mixtures. This means that the measurements in absolute nano-
AUCdensitygradientmeasurements particle densities. Some application
are a kind of particle density spec- examples are presented. One advan-
troscopy. Usually, the relation tageofthenewcalibrationtechnique
between the radial position and is that higher particle densities are
particledensity,q(r),insideanAUC now accessible. Another advantage
density gradient is calculated by is the reduction in the measuring
using the well-known (barometrical) time. We no longer have to wait till
equilibrium equation in the formu- equilibrium is reached (sometimes
lation of Hermans and Ende (1963); up to 90 h!); instead already after
W.Ma¨chtle(&)
however, this equation for an ideal 9 h we get reasonable results. This
Kunststofflaboratorium,
PolymerPhysics,BASFAG bimodal density gradient mixture means our static density gradient
67056Ludwigshafen,Germany fails in some cases. The higher the now approaches a ‘‘dynamic’’ one.
e-mail:[email protected] content of the heavy component,
Tel.:[phone]
andthebiggerthedifferencebetween
Fax:[phone]
the actual density gradient being Key words Analytical ultracentri-
M.D.Lechner formed and the equilibrium gradi- fuge Æ Density gradient Æ Particle
PhysicalChemistry
ent, the bigger the failure or the density Æ Colloidal nanoparticles
UniversityOsnabrueck,Barbarastrasse7
49069Osnabrueck,Germany deviation from ideality. We report a Polymer characterization
and its high precision) it is possible to analyze the
Introduction
chemical nature of nanoparticles, especially of complex
Density gradient measurements inside an analytical colloidal mixtures, and to study reactions on particle
ultracentrifuge (AUC) are an excellent tool for charac- surfaces.
terizingnanoparticlesinthe10–1000-nmdiameterrange In principle, a density gradient inside an AUC
[1–8]. Because of its very high resolution (i.e. its measuringcellisbuiltupbyspinningathighrotorspeed
fractionation power according to the particle density amixtureofalightmaincomponent(mostlywater)anda
2
heavy dissolved component (often a sugar, like metriza- Usually, the relation between the radial position and
mide) till equilibrium is reached. Small amounts of theparticledensity,q(r),insideanAUCdensitygradient
nanoparticles dispersed in this mixture will sediment or is calculated by using the well-known (barometrical)
floatduringthisbuilduptimetoaspecificradialposition equilibriumequationintheformulationofHermansand
inside the cell, where the particle density and the local Ende [9]; however, this equation for an ideal bimodal
gradient density are identical. Mixtures of chemically density gradient mixture fails in some cases. The higher
different nanoparticles are fractionated in this way and the content of the heavy component, and the bigger the
appearatdifferentradius/densitygradientpositions.This difference between the actual density gradient being
isakindofparticledensityspectroscopy.Thisstatementis formed and the equilibrium gradient, the bigger the
illustratedinFig. 1.IntheupperpartofFig. 1themost failure or the deviation from ideality. Deviations also
commonindustriallyimportanthomopolymerlaticesare resultifonechangesfromabimodaltoatrimodaldensity
arranged along a density q-axis, from 0.9 to 1.5 g/cm3, gradientmixturesuchaswater/methanol/metrizamide.
accordingtotheirparticledensity,q,frompolybutadiene Wereporthereasystematicstudyofthesedeviations
to poly(ethylhexyl acrylate) (PEHA), polystyrene (PS), using a marker nanoparticle system of 11 precisely
poly(methyl acrylate) (PMA), poly(vinyl chloride) to characterizedethylhexylacrylate(EHA)/methylacrylate
poly(acrylic acid). By copolymerization, a huge number (MA) copolymer latices with known nearly equidistant
ofcopolymerlaticeswithparticledensitiesin-betweenare particle densities of q¼0.980/1.000/1.021/1.043/1.066/
producible. 1.089/1.114/1.140/1.167/1.196/1.225 g/cm3. During this
Fractionation of a mixture of such latices, at high study we also learned to use this 11-marker system as a
resolution, according to their particle density, could be pragmatic and simple calibration system for aqueous
described as ‘‘particle density spectroscopy’’. This is density gradients, thereby reducing considerably the
exactlywhatispossiblewithAUCdensitygradients.Itis error of the measurements in absolute nanoparticle
demonstrated in the lower part of Fig. 1, that a q range densities and the measuring time. We also describe this
of 0.85–1.4 g/cm3 is really accessible by AUC water/ new marker calibration technique and present some
metrizamide density gradients, not with just one gradi- application examples.
ent, but with a set of nine gradients with different
metrizamide contents from 5 to 25 mass%. For low
particledensitiesoneaddsmethanoltowaterinorderto Theory of AUC density gradients
lower the density of the mixture; for high densities one
replaces normal water by D O. The literature exhibits several possibilities for the deter-
2
mination of the density gradient in an AUC, i.e. the
Fig.1 Particledensitiesofthe
mostcommonhomopolymer
laticesarrangedalongadensity
q-axis(upperpart)andaccessi-
bledensityrangesofninedif-
ferentlycomposedstatic
equilibriumwater/metrizamide
densitygradientsinananalyti-
calultracentrifuge(AUC)(low-
erpart)
3
radialdependenceofthesolutiondensityinsidetheAUC whereuin istheinitialvolumefractionofcomponentk,
k
measuring cell (q–r relation). One of the oldest methods r istherotordistanceatthemeniscusofthecell,r isthe
m b
is the theoretical calculation of the equilibrium density rotor distance at the bottom of the cell and
profilebyHermansandEnde[9];however,theHermans– b¼x2(cid:1)M =q0(cid:2)(cid:1)q0(cid:5)q0(cid:2)=ð2RTÞ ; ð5Þ
Ende equation/theory is restricted to ideal solutions 1 1 1 0
where both the mixing enthalpy and the mixing volume where x is the angular velocity, and M , q0, and q0 are
1 0 1
arezero.Themethod/theoryofHearstandVinograd[10] the molar mass of component 1 and the densities of
requiresdetailed knowledgeofthe chemical potential of components 0 and 1, respectively. R is the gas constant
the components in a solution and has been, up to now, and T the absolute temperature.
restricted to aqueous solutions of several salts. The density of an ideal solution, q, is given by
The procedure of Munk [11] gives an empirical
q¼u q0þu q0 : ð6Þ
relationship with several constants which may be deter- 0 0 1 1
mined with marker polymers of known density and Combining Eqs. (1), (3) and (6) results in the Her-
several equilibrium runs at different rotor speeds. The mans–Ende equation in the q–r from:
methodofLechnerandcoworkers[12–14]calculatesthe
q0þq0aexp(cid:1)br2(cid:2)
density gradient for real solutions. As the resulting q¼ 0 1 : ð7Þ
equation is an implicit function one has to calculate the 1þaexpðbr2Þ
density gradient by regression procedures which can Under the assumption a exp(br2) (cid:6) 1 the following
cause complications in some cases. The direct refracto-
equation holds:
metric q–r determination of the equilibrium and non-
equilibrium density gradient requires a precise baseline q¼q0þq0aexp(cid:1)br2(cid:2) : ð8Þ
0 1
[1,2,15].Thismaybewellestablishedinthecaseoftime-
The following typical example demonstrates that in
dependent dynamic density gradients [2]; however, in
manycasesaexp(br2)(cid:6)1.Lightcomponentwater,with
the case of equilibrium or near-to-equilibrium density
1 mass% alkyl sulfonate added to stabilize the latex
gradients one has to use double-sector cells for the
particles, heavy component metrizamide, q0¼0.9987
establishment of the precise baseline [15]. 0
g/cm3,V0¼18.02cm3/g,q0¼2.1552 g/cm3,V0¼ 370.3
Owing to difficulties with respect to the procedures 0 1 1
cm3/mol, M ¼789.1 g/mol, rotor speed N¼30.000
described earlier we describe in the following a new 1
min)1, rotor distances r ¼5.9 cm and r ¼7.2 cm,
marker calibration method for the evaluation of equi- m b
T¼298 K, b¼8.434Æ10)2 cm)2, a¼1.955 · 10)3, a exp
librium and nonequilibrium density gradients in an
(br2)¼3.382 · 10)3(withr»6,5 cm¼middleofthecell).
AUC. Since the Hermans–Ende equation is the mathe-
Thevalueofaexp(br2)ismuchsmallerthan1.
maticalbasisofthenewprocedureaswell,wegiveabrief
Equation (8) holds for ideal mixtures. For real
outline of the Hermans–Ende theory.
mixtures one has to correct the parameters q0, q0, a
Considering an ideal binary mixture of two compo- 0 1
and b with correction factors or, in other words, to
nentswithindices 0and1theratioofthevolumefractions
replace them by three adjustable parameters a, b and c;
of components 1 and 0, u and u , as a function of the
1 0 this gives
rotordistance,r,wasgivenbyHermansandEnde[9]as
follows: q¼aþbexp(cid:1)cr2(cid:2) : ð9Þ
u =u ¼aexpðbr2Þ ; ð1Þ
1 0
with
! ! Experimental
(cid:3) (cid:3)
u ¼(cid:1)n V0(cid:2) Xn V0 ¼(cid:1)m t0(cid:2) Xm t0 ;
k k k k k k k k k
The following materials were used: double-distilled water, alkyl
k k
sulfonate C –C (BASF, Ludwigshafen, Germany), metrizamide
k ¼0;1 ð2Þ (Nyegaard,1O2 slo2,0 Norway) and PS latex (BASF). The physical
constantsofwater/alkylsulfonate(1mass%)andmetrizamideare
and
given in the theoretical part of this work. All the values and
measurementsreferto25(cid:4)C.
u0þu1 ¼1 ; ð3Þ All the polymer latices used were polymerized with a standard
where n , m , V0 and t0 are the amount of matter, the emulsion polymerization technique in our BASF research labora-
k k k k toriesusingBASFmonomers.ThepropertiesofthePSlaticesshow
mass, the molar volume and the specific volume of the a particle density of q ¼1.055±0.002g/cm3 and a mass-
PM
component k. a is an integration constant for sector- averagediameterofD¼160and210nm.Our11markerparticles
shaped cells, are EHA/MA copolymer latices which were all polymerized
separately. All 11latices hadnearly the same particle diameter of
exp(cid:7)buin(cid:1)r2(cid:5)r2(cid:2)(cid:8)(cid:5)1 200nm,buttheparticle densitiesweredifferent becauseofthe 11
a¼ 1 b m ; ð4Þ
exp(cid:1)br2(cid:2)(cid:5)exp(cid:1)b/inr2þb/inr2(cid:2) different copolymer compositions [wMA¼0/10/20/30/40/50/60/70/
b 1 b 0 m 80/90/100mass%].Theseparticledensities(calculatedtheoretically