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`CSL EXHIBIT 1052
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`BIOPHYSICAL CHEMISTRY
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`An International Journal devoted to the Physics and Chemistry ofBiological Phenomena
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`The journal is devoted to the interpretation of biological phenomena in terms of the principles and methods of physics and chemistry. [t is
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`receptive to articles which deal with biological molecules and systems. and to papers which treat systems sewing as models for these.
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`Treatments, phenomenological as well as molecular. of the interactions. structure and biological functions of individual biological macro-
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`Page 3 of 14
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`Page 3 of 14
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`

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`BIOPHYSICAL CHEMISTRY
`
`Vol. 85, No. l, 31 May 2000
`
`Abstracted/indexed in Chemical Abstracts. l.S.l. Current Contents (Life Sciences). EMBASE/Excerpta
`Mcdica. PASCAL M. Elsevier BlOBASE/Current Awareness in Biological Sciences
`
`Letter
`Steric effect and effect of metal coordination on the reactivity of nitric oxide with cysteine-containing
`proteins under anaerobic conditions
`C.T. Aravindakurnar, J. Ceulemans. M. De Ley (Belgium)
`
`Viscosity analysis of the temperature dependence at the solution ccnlonnation oi ovalbumin
`K. Monkos (Poland)
`Reaction oi reducing hydroxyl radical adducts of pyrimidine nucleotides with riboflavin and fiavin adenine
`dlnucleotide (FAD) via electron transfer: a pulse radiolysls study
`C. Lu. S. Yao. 2. Han. W. Lin. W. Wang, W. Zhang. N. Lin (China)
`Heat capacity of hydrogen-bonded networks: an altemative view 01 protein folding thermodynamics
`A. Cooper (UK)
`Spontaneous electrical potential oscillation on a filter impregnated with soybean lecithin placed between
`identical solutions of alanine
`D. Cucu. D. MihEilescu (Romania)
`Quenching mechanism of quinolinium-type chloride-sensitive fluorescent indicators
`3. Jayaraman. A.S. Verkman (USA)
`The positive role of voids in the plasma membrane in growth and energetics oi Eschen'chia coll
`S. Natesan. C.N. Madravarao. V. Sitaramam (India)
`The sell-organization of edenoeine 5'-triphosphate and ndenosine 5'-diphosphate in aqueous solution
`as determined from ultraviolet hypochrcmic effects
`F. Feral. E. Galleoo (Spain)
`Klnetics of a ilnite one-dimensional spin system as a model for protein tolding
`T. Kikuchi (Japan)
`
`1
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`7
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`17
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`25
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`41
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`49
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`59
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`79
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`93
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`For more information, see Biophysical Chemistry Homepage:
`
`www.clsevieml/locate/bpc
`
`The table of contents of Biophysical Chemistry is included in ESTOC - Elsevier
`Science Tables of Contents service — which can be accessed on the World Wide
`Web at the following URL addresses:
`httpv/wwwelseviernl/locate/estoc or http://www.elsaviercom/locate/estoc
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`0301-‘622(20000531)85:1;1-x
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`”elm...
`manna-u—n—
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`Page 4 of 14
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`51‘2
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`if};
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`ELSEVlR
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`Biophysical Chemistry 85 (2000) 7—16
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`Bioph sical
`Chemistry
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`www.clsevier.nlllocate/bpc
`
`Viscosity analysis of the temperature dependence of
`the solution conformation of ovalbumin
`
`Karol Monkos“
`
`Department of Biophysics. Silesian MedicalAcademy, H. Jordana I9, 41—808 Zabm 8, Poland
`
`Received l5 September 1999; meived in revised form 27 January 2000; accepted [7 February 2000
`
`Abstract
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`The viscosity of ovalbumin aqueous solutions was studied as a function of temperature and of protein concentra-
`tion. Viscosity-temperature dependence was discussed on the basis of the modified Arrhenius formula at tempera-
`tures ranging from 5 to 55°C. The activation energy of viscous flow for hydrated and unhydrated ovalbumin was
`calculated. Viscosity-concentration dependence, in turn, was discussed on the basis of Mooney equation. It has been
`shown that the shape parameter S decreases with increasing temperature, and self-crowding factor K does not
`depend on temperature. At low concentration limit the numerical values of the intrinsic viscosity and of Huggins
`coefficient were calculated. A master curve relating the specific viscosity 1]“, to the reduced concentration ch], over
`the whole range of temperature, was obtained and the three ranges of concentrations: diluted, semi-diluted and
`concentrated, are discussed. it has been proved that the Mark-Houvink—Kuhn—Sakurada (MHKS) exponent for
`ovalbumin does not depend on temperature. (9 2000 Elsevier Science Ireland Ltd. All rights reserved.
`
`Keywords: Ovalbumin; Activation energy; Intrinsic viscosity; Huggins coefficient; Mark-Houvink-Kuhn-Sakurada exponent
`
`1. Introduction
`
`Ovalbumin is the major globular protein of
`chicken egg white. It is a member of the serpin
`superfamily and is classified as a non-inhibitory
`serpin [1]. Ovalbumin consists of a single polypep-
`tide chain of 385 amino acid residues that folds
`
`
`
`‘Tel; + 48-32-172-30—4l; fax: + 48-32-272-26—72.
`
`into a globular conformation with three B-sheets.
`nine a-helices and three short helical segments of
`three to four residues [2—4]. This globular protein
`contains electrophoretically three distinguishable
`fractions with, respectively,
`two, one and zero
`phosphate groups per molecule. However. they
`possess the same overall native protein conforma-
`tion [5]. The crystal structure of the protein, as
`revealed by X-ray crystallography, indicates that
`the ovalbumin molecule is approximately a tri-
`
`030l-4622/00/S - see front matter © 2000 Elsevier Science Ireland Ltd, All rights reserved.
`I'll: 80301-4622(00)00|27-7
`
`Page 5 of 14
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`

`

`8
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`K Monkos / Biophysical Chemishy 85 (2000) 7—16
`
`
`
`
`
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`
`
`
`
`
`
`
`
`
`
`
`solved fragments. The samples were stored at 4°C
`
`
`
`
`
`
`
`until just prior to Viscometry measurements, when
`
`
`
`
`
`
`
`
`
`
`they were warmed from 5 to 55°C. The pH values
`
`
`
`
`
`
`
`of such prepared samples were approximately 6.4
`
`
`
`
`
`
`and changed only insignificantly during the dilu-
`tion of the solutions.
`
`
`
`
`
`2. 2. Viscometry
`
`
`
`
`
`
`
`
`
`
`
`
`
`Viscometry is still extensively used in many
`
`
`
`
`
`investigations of biological macromolecules in so-
`lution because of its extreme sensitivity and tech—
`
`
`
`
`
`
`
`
`
`
`
`
`
`nical simplicity ([17] and references therein). We
`have used an Ubbelohde-type capillary microvis-
`
`
`
`
`
`cometer with a flow time for water of 28.5 s at
`
`
`
`
`
`
`
`
`
`
`
`25°C. The microviscometer was immersed in a
`
`
`
`
`
`
`
`thermostated water bath at 5—55°C i 005°C. The
`
`
`
`
`
`
`
`
`same viscometer was used for all measurements
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`and was mounted so that it always occupied the
`
`
`
`
`
`
`
`
`same position in the bath. Sample solution was
`
`
`
`
`temperature-equilibrated and passed once
`
`
`
`
`
`
`through the viscometer before any measurements
`
`
`
`
`
`
`
`were made. For most concentrations the viscosity
`
`measurements were done from 5 to 55°C in 5°C
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`intervals. At the temperatures higher than 55°C
`the thermal denaturation of ovalbumin occurs
`
`
`
`
`
`
`
`
`
`
`
`
`
`and the lower protein concentration the higher
`denaturation temperature. The viscosities of the
`
`
`
`
`
`
`ovalbumin solutions were measured for concenv
`
`
`
`
`
`
`
`
`
`
`
`
`trations from 6.16 kg/m3 up to 429.8 kg/m3.
`
`
`
`
`Solutions densities and protein concentrations
`were determined as described earlier [18,19].
`
`
`
`
`
`
`
`
`
`
`3. Results and discussion
`
`
`
`
`
`
`3.1. Viscosity-temperature dependence
`
`
`
`
`
`
`
`
`
`
`
`for aqueous
`Very recently we have proved,
`solutions of bovine serum albumin [20] and hen
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`egg-white lysozyme [19], that the most useful rela-
`
`
`
`
`
`
`
`tion connecting the viscosity with temperature is
`a somewhat modified Arrhenius formula. It has
`
`
`
`
`
`
`
`the form:
`
`
`
`B DT
`—
`n—exp(— +
`
`
`
`
`
`
`
`ES
`+RT)
`
`
`(1)
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`axial ellipsoid with overall dimensions 7 X 4.5 X 5
`
`
`nm [2].
`
`
`Ovalbumin, both native and denatured, has
`
`
`
`
`
`
`
`
`
`
`
`
`
`been the object of physicochemical studies for
`
`
`
`
`
`
`
`
`many years. The studies have based on the exper-
`
`
`
`
`
`
`
`imental techniques such as Viscometry [6—9], 1H-
`
`
`
`
`NMR spectroscopy [10], dielectric spectroscopy
`[11], densimetric and ultrasonic velosimetric titra-
`
`
`
`
`
`tion [12],
`fluorescence and circular dichroism
`
`
`
`
`
`
`
`
`
`
`
`
`[13,14], differential scanning calorimetry [15] and
`
`
`
`
`
`
`Fourier transform infrared spectroscopy [16]. The
`
`
`
`
`
`
`
`results of the investigations give information about
`
`
`
`
`
`the functional properties, protein denaturation,
`
`
`
`
`
`
`hydration and structure of ovalbumin. However,
`
`
`
`
`
`
`
`little attention has been devoted to the hydrody—
`namic properties of ovalbumin. This is especially
`
`
`
`
`
`
`
`the case for the viscosity of ovalbumin solutions,
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`where the results are still fragmentary and limited
`to one temperature.
`
`
`
`
`
`
`
`
`
`
`This work presents the results of viscosity mea-
`
`
`
`
`
`
`surements for ovalbumin aqueous solutions at
`
`
`
`
`
`
`
`
`
`temperatures ranging from 5 to 55°C and at a
`
`
`
`
`
`
`
`
`wide range of concentrations. On the basis of
`
`
`
`
`
`these results the viscosity—temperature and vis-
`
`
`
`
`cosity—concentration relationships are discussed.
`
`
`
`
`
`
`Such rheological quantities as activation energy
`
`
`
`
`
`
`of viscous flow, Simha parameter and self-crowd-
`
`
`
`
`
`
`
`ing factor are calculated. At low concentrations,
`
`
`
`
`
`
`the temperature dependence of the intrinsic vis-
`
`
`
`
`
`
`cosity and of Huggins coefficient
`is presented
`
`
`
`
`
`
`Using the dimensionless parameter [n]c, the exis—
`
`
`
`
`
`
`tence of three characteristic ranges of concentra-
`
`
`
`
`
`
`
`tions is shown. By applying Lefebvre’s equation
`for the relative viscosity in the semi—dilute regime,
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`the MHKS exponent for ovalbumin is evaluated.
`
`
`
`2. Materials and methods
`
`
`
`
`
`2.1. Materials
`
`
`
`
`
`
`
`
`
`Crystallized hen ovalbumin (grade V) was ob-
`
`
`
`
`
`
`
`tained from Sigma Chemical Co. and was used
`
`
`
`
`
`
`without further purification for all the measure-
`
`
`
`
`
`
`
`ments. Aqueous solutions of the ovalbumin were
`
`
`
`
`
`
`
`prepared by dissolving the material
`in distilled
`water. Such solutions were then filtered by means
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`of filter papers in order to remove possible undis—
`
`
`
`Page 6 of 14
`
`Page 6 of 14
`
`

`

`K. Monkos / Biophysical Chemistry 85 (2000) 7-16
`
`9
`
`so
`
`00
`
`7o
`
`_ooo.
`8.
`z.so
`3.»
`goo
`an
`
`1o
`
`0
`
`o
`
`to
`
`ao
`
`so
`
`ma
`
`4o
`
`so
`
`to
`
`Fig. 1. Temperature dependence of the viscosity of ovalbumin aqueous solutions for concentrations c = 246.89 (0), 370.6 (A) and
`397.59 ( x) kg/m‘. The curves show the fit obtained by using Eq. (I) with the parameters: 8 - 35.166, D - 3.632 X 10‘2 K“ and
`E‘ = 46.889 kJ/mol for c = 246.89 kg/m’; B = 46.342. D = 5.392 x 10’: K'1 and E. - 65.288 kJ/mol for c = 370.6 kg/m":
`B = 57.853, D = 7.273 x 10" ‘ K ' and E‘ = 81.367 U/iuol fut t - 397.59 kg/m‘.
`
`where B and D are parameters, 135 is the activa-
`tion energy of viscous flow of solution and R, T
`are gas constant and absolute temperature, re-
`spectively. Fig.
`1 shows the results of viscosity
`measurements at three various concentrations of
`
`ovalbumin. As seen, curves obtained by using the
`function from the above equation give a good fit
`to the experimental points over the whole range
`of temperatures.
`Numerical values of the parameters B, D and
`
`100
`
`oo
`
`s °°
`i 10
`E oo
`
`o so
`‘8
`5 4o
`
`5 so
`3 no
`1o
`
`o
`
`0
`
`o
`
`.
`
`0
`
`so
`
`100
`
`no
`
`zoo
`
`zoo
`
`zoo
`
`:so
`
`too
`
`too
`
`0 [Italm‘S]
`
`Fig. 2. Plot of the solution activation energy E. vs. concentration. (0) experimental points were obtained by using the least squares
`method; the curve shows the fit according to Eq. (2) with the parameters given in the text.
`
`Page 7 of 14
`
`

`

`10
`
`
`K Mankos / Biophysical Chemistry 85 (2000) 7-16
`
`
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`
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`
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`
`
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`
`
`0,12
`
`
`0,1
`
`
`0,08
`
`0.06
`
`
`
`
`
`0.04
`
`
`
`D[1IK]
`
`
`
`0,02
`
`
`
`
`
`
`
`0
`
`
`50
`
`
`100
`
`
`
`150
`
`
`
`300
`
`
`
`350
`
`
`
`400
`
`
`
`450
`
`200
`
`
`c [kglm‘3]
`
`
`Fig. 3. Plot of the coefficients B (X) and D (0) vs. concentration. Experimental points were obtained by using the least squares
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`method; the curves show the fit according to Eqs. (3) and (4), respectively.
`
`
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`
`
`
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`
`
`
`
`
`
`
`
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`
`
`
`
`
`K" and the Eq. (1) gives the viscosity—tempera-
`
`ture relationship for water, where Ew denotes an
`
`
`
`
`
`
`
`activation energy of viscous
`flow of water
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`molecules. The parameters Ep’ Bp and Dp are
`
`
`
`
`
`
`connected with dissolved proteins and, in particu-
`
`
`
`
`
`
`
`
`
`lar, Ep is an activation energy of ovalbumin. In
`
`
`
`
`
`
`
`
`
`
`Eqs. (2)—(4) the quantities Ep, 1;; BP, 1; and DP, 5;,
`respectively, must be taken into account as two
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`adjustable parameters. To establish their values,
`the molecular mass of ovalbumin is needed. By
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`using the least squares method, for Mp = 45 kDa
`
`
`
`
`
`
`
`the following values were obtained: Ep=
`[2],
`
`
`
`
`
`
`
`
`
`6.241 X 10'1 kJ/mol and g— 1928 X10 ’ rn/kg;
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`13=3.45><104 and g=1.991><10 3mj/kg;D
`
`
`
`
`
`
`
`
`
`=6356 K' and g=1.934><10 3 m/kg. As
`
`
`seen in Figs 2 and 3,
`the functions from Eqs.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`(2)44), with the parameters values presented
`
`
`
`
`
`
`above, give good approximation to the experimen-
`tal values. The three values of the effective speci-
`
`
`
`
`
`
`
`
`fic volume obtained above differ each other only
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`slightly and give the average value (1;) = 1.951 X
`
`
`
`
`
`10'3 m3/kg.
`However, as has been shown by various tech-
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`niques [12,21—24], there exists a hydration shell of
`
`
`
`
`
`
`water surrounding the protein molecules in solu-
`tion, which is distinct from bulk water. On the
`
`
`
`
`
`
`
`
`basis of microwave dielectric measurements,
`it
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`ES for all measured concentrations were calcu-
`
`
`
`
`
`
`
`
`
`lated by using the least squares method [20]. The
`results are shown in Figs. 2 and 3. As for bovine
`
`
`
`
`
`
`
`
`
`
`serum albumin and Iysozyme, both activation en-
`
`
`
`
`
`
`
`
`
`
`
`
`
`ergy ES and the parameters B and D monotoni-
`
`cally increase with increasing concentration. The
`
`
`
`
`
`
`
`
`
`
`
`
`
`explanation of this fact
`is given in our earlier
`
`
`
`
`
`
`
`
`
`paper [20]. At the same time, it has been shown
`
`
`
`
`
`
`
`
`that the following relations have to be fulfilled:
`
`ES=a—BC(EP_EW)+E“
`
`(2)
`
`
`
`
`
`
`
`
`
`
`
`C
`
`
`
`
`
`
`B: 01— Bc(BP_BW) +13w
`
`
`
`
`
`C
`D=a_Bc(Dp—Dw)+Dw
`
`
`
`(3)
`
`
`
`(4)
`
`
`
`
`
`
`
`
`where (X = pW MP/MW and B = a}; — 1 The quan-
`
`
`
`
`
`
`
`
`
`tities c, pw, g, MD and Mw denote the solute
`concentration andpwater density in kg/m the
`
`
`
`
`
`
`
`
`
`
`
`
`
`effective specific volume of a protein and the
`
`
`
`
`
`
`molecular masses of the dissolved proteins and
`water, respectively.
`
`
`
`
`
`the parameters Es— E. = 32. 013
`c = 0
`At
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`kJ/mol, B: 3,, =25.,936 D= Dw =2.014X10‘
`
`
`
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`
`
`Page 8 of 14
`
`Page 8 of 14
`
`

`

`K. Marika: /Biophysical Chemistry 85 (2000) 7-16
`
`11
`
`was shown for bovine serum albumin, that it does
`
`not change with temperature [23]. This hydration
`shell must be taken into account when the mass
`
`and volume of the hydrodynamic particle are
`computed, because they influence on the values
`of some experimental parameters. The molecular
`mass of hydrated protein is Mh = Mp(1 + 8) [25],
`where 8 denotes the amount of grams of water
`associated with the protein per gram of protein.
`For globular proteins a value of 03-04 has been
`obtained from experiments and computer simula-
`tions [17] and, in particular, for ovalbumin 8 =
`0.36 [26]. This value is within the range (0.42 :9;
`0.09), which was quite recently found by Harding
`et al.
`[27] on the basis of oovolume measure-
`ments. It gives the molecular mass of hydrated
`ovalbumin Mll = 61.2 kDa. To calculate
`the
`parameters EP, BP. DD and F, in Eqs. (2)-(4) for
`hydrated ovalbumin the Mp should be replaced
`by Mb. By using once more the least squares
`method the following values one can obtain: EP
`=8.487X104 kJ/mol, Bp=4.691><10‘ and D:
`=86.44 K '. It
`is interesting that the effective
`specific volume of a protein g, obtained in this
`we, is exactly the same as obtained earlier. The
`curves in Figs. 2 and 3 are identical for parame-
`ters obtained for both hydrated and unhydrated
`ovalbumin.
`
`3.2. Viscosity-concentration dependence
`
`The most useful relation describing the depen-
`dence of relative viscosity of aqueous solutions of
`globular proteins on concentration is
`that of
`Mooney [28]:
`
`mash—5m.
`
`where TI, ‘fl/‘lo and '10 is the viscosity of the
`solvent. (b is the volume fraction of the dissolved
`
`particles, S denotes the shape parameter and K
`is a self-crowding factor. The volume fraction
`‘1’ =NAVc/Mh, where NA and V are Avogadro’s
`number and the hydrodynamic volume of one
`dissolved particle, respectively. The solute con-
`centration c is in kg/m’. As has been shown in
`our earlier works [19,20], the shape parameter S
`
`and a self-crowding factor K can be written by
`the following equations:
`
`Mw
`S= pNA—V —(BP MB)+(D —D)T
`
`59—15,.
`+T
`
`
`Mw
`Mh
`
`K=(§— prh)NAV
`
`(6)
`
`(7)
`
`Both coefficients can be calculated when the
`
`hydrodynamic volume and mass of the dissolved
`proteins is known. The volume of hydrodynamic
`particle may be calculated from two terms [29]:
`Va V1, + MPS/Npr, where V0 is a volume of the
`unhydrated molecule and the other term denotes
`the volume of the hydration shell.
`As was mentioned earlier the X-ray crystallo-
`graphy revealed that the ovalbumin molecule is
`approximately a tri-axjal ellipsoid with the main
`semiaxes ii = 3.5 nm, b = 2.25 nm and 6“ - 2.5 nm.
`It gives a volume of unhydrated molecule V0 =
`82.467 nm3. For 8 = 0.36, the volume of the hy-
`dration shell is 26.897 nm3 and V= 109.36 nm".
`The hydrodynamic volume of ovalbumin may be
`obtained experimentally, too. As has been shown
`by using high-performance size-exclusion chro-
`matography and intrinsic viscosity measurement,
`the Stokes radius of ovalbumin is 3 run [8]. It
`corresponds to the hydrodynamic volume V= 113
`nm" and is in a good agreement with the value
`given above.
`The numerical values of the shape parameter S
`obtained from Eq. (6) are presented in Table 1.
`As is seen this parameter decreases with increas-
`ing temperature from S = 3.782 (at != 5°C) up to
`S =3.435 (at
`t=55°C). Simha [30] proved for
`hard ellipsoids of revolution (6‘ aé b = 6) immersed
`in a solution, that in the high temperature limit
`i.e. in the case when the orientation of particles is
`completely at random, the factor S depends on
`the axial ratio p = ti/b of the dissolved particles.
`For ellipsoids of revolution for which 1 < p < 15,
`it can be calculated from the asymptotic formula
`[31]:
`
`Page 9 of 14
`
`

`

`12
`
`K. Monko: / Biophysical Chemistry 85 (2000) 7-16
`
`Table l
`The numerical values of the shape parameter S, the intrinsic viscosity [1}] and the Huggins coefficient kl for ovalbumin calculated
`from Eq. (6), Eq. (10) and Eq. (11), respectively
`
`([C l
`
`5
`[1]] X 10‘
`[ma/kg]
`k.
`
`5
`
`3.782
`4.070
`
`10
`
`3.723
`4.007
`
`15
`
`3.669
`3.949
`
`20
`
`3.623
`3.899
`
`25
`
`3.582
`3.855
`
`30
`
`3.545
`3.816
`
`35
`
`3.514
`3.782
`
`40
`
`3.488
`3.754
`
`45
`
`3.466
`3.730
`
`50
`
`3.448
`3.712
`
`55
`
`3.435
`3.697
`
`0.9792
`
`0.9868
`
`0.9938
`
`1.0002
`
`1.0059
`
`1.0112
`
`1.0157
`
`1.0196
`
`1.0229
`
`1.0255
`
`1.0276
`
`s = 2.5 + 0,4075( p _ ”"5“"
`
`(3)
`
`sion of Eq. (5) in the power series of concentra-
`tion yields to the following polynomial:
`
`One can easily calculate from the above rela-
`tion that the high temperature value of S (S=
`3.435) corresponds to the ellipsoid of revolution
`with p = 2.735. The shape parameter S can be
`obtained for tri-axial ellipsoids also [17]. How-
`ever,
`in this case,
`the calculations are very
`troublesome. For unhydrated ovalbumin é/b =
`1.56 and (3/6 = 1.4. To assess the theoretical value
`of S we take their mean value p = 1.48 and it
`gives, from Eq. (8), S = 2.635. Comparison of the
`experimental and theoretical value of 5 shows
`that hydrated ovalbumin is more elongated than
`the unhydrated form. This conclusion is consis-
`tent with the recent results of Harding et a1. [27].
`It means that the hydration shell of water is not a
`uniform monolayer but a patchwork of water
`clusters, covering some atoms in charged groups
`by water layers while leaving some part of the
`protein surface uncovered.
`As is seen from Eq. (7), the self-crowding factor
`K does not depend on temperature. Substitution
`of the hydrodynamic volume Vh = 109.36 11m3 into
`Eq. (7) gives the numerical value K = 1.81. This
`value lies within the range (1.35 -:- 1.91) which was
`obtained, on the basis of purely geometric calcu-
`lations, for rigid spherical particles by Mooney
`[28]. However,
`the measurements
`for bovine
`serum albumin [20] (K = 1.25) and for hen egg-
`white lysozyme [19] (K- 2.91) showed that for
`aspherical particles, the values of K may lie out-
`side of this range.
`The Mooney formula [Eq. (5)] describes (for a
`given temperature) the viscosity—concentration
`dependence from very diluted up to very concen-
`trated solutions. At low concentrations, an expan-
`
`11—“,
`
`=[n][l+k12[n]€+k [11] C + }
`
`(9)
`
`“—91
`C
`is the intrinsic viscosity and
`where [11]= 11111
`1],? = 11, — 1 isHthe specific viscosity. The intrinsic
`viscosity [1]] and the Huggins coefficient k.can
`be calculated from the following expressions [20]:
`
`[n]=f
`
`k,=
`
`E —5,,
`
`-(Bp B—)+(D-—-Dw)T+———————R———PT
`(10)
`
`213
`1
`7 __’_’""""_'"""——EE" +1
`
`(11)
`
`The higher coefficients of expansion k2, k3 and
`so on, are connected with the Huggins coefficient
`kl [19] and are omitted here. As shown earlier,
`the parameters at. 8,, DP and En are different
`for hydrated and unhydrated ovalburnin. How-
`ever, as calculations showed,
`in both cases the
`values of [1]] and k, are identical and they are
`presented in Table 1. It is worth noting that the
`numerical value of the intrinsic viscosity calcu-
`lated from Eq. (10) at z - 25°C