31 May 2000
`
`ISSN 0001-422
`
`BiophySical
`Chemistry
`
`An lldlmlftanll Joumll t*W1IIId Ill) , .
`,.,.. Md etr.mlay aiiJiolog/otll PlawJmena
`
`DISPLAY
`
`UNWEIISITY Of ~1\VGTOH
`CHEMISlHY
`JUN 2 1 2000
`
`Page 1 of 14
`
`CSL EXHIBIT 1052
`CSL v. Shire
`
`

`

`BIOPHYSICAL CHEMISTRY
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`An International Journal devoted to the Physics and Chemistry of Biological Phenomena
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`

`

`BIOPHYSICAL CHEMISTRY
`Vol. 85, No.1, 31 May 2000
`
`Abstracted/indexed in Chemical Abstracts, I.S.I. Current Contents (Life Sciences), EMBASE!Excerpta
`Medica, PASCAL M, Elsevier BIOBASE/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. Aravindakumar, J. Ceulemans, M. De Ley (Belgium)
`
`Viscosity analysis of the temperature dependence of the solution conformation of ovalbumin
`K. Monkos (Poland)
`Reaction of reducing hydroxyl radical adducts of pyrimidine nucleotides with riboflavin and flavin adenine
`dinucleotide (FAD) via electron transfer: a pulse radiolysis study
`C. Lu, S. Yao, Z. Han, W. Lin, W. Wang, W. Zhang, N. Lin (China)
`Heat capacity of hydrogen-bonded networks: an alternative view of 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. Mihailescu (Romania)
`Quenching mechanism of quinolinium-type chloride-sensitive fluorescent indicators
`S. Jayaraman, A.S. Verkman (USA)
`The positive role of voids in the plasma membrane in growth and energetics of Escherichia coli
`S. Natesan, C.N. Madhavarao, V. Sitaramam (India)
`The self-organization of adenosine 5'-triphosphate and adenosine 5'-diphosphate in aqueous solution
`as determined from ultraviolet hypochromic effects
`F. Peral, E. Gallego (Spain)
`Kinetics of a finite one-dimensional spin system as a model for protein folding
`T. Kikuchi (Japan)
`
`7
`
`17
`
`25
`
`41
`
`49
`
`59
`
`79
`
`93
`
`For more information, see Biophysical Chemistry Homepage:
`www.elsevier.nl/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
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`!i142
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`Page 4 of 14
`
`

`

`ELSEVIER
`
`Biophysical Chemistry 85 (2000) 7-16
`
`Biophysical
`Chemistry
`
`www.elsevier.nl /locatc/bpc
`
`Viscosity analysis of the temperature dependence of
`the solution conformation of ovalbumin
`
`Karol Monkos*
`
`Department of Biophysics, Silesian Medical Academy, H. Jorda11a 19, +I-808 Zabrze 8, Poland
`
`Received 15 September 1999; received in revised form 27 January 2000; accepted 17 February 2000
`
`Abstract
`
`The viscosity of ovalbumin aqueous solutions was studied as a function of temperature and of protein concentra(cid:173)
`tion. Visco ity- temperature dependence was discussed on the basis of the modified Arrhenius formula at tempera(cid:173)
`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 'Tl,p to the reduced concentration c[ 'T]], 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
`ovalbumjn does not depend on temperature. © 2000 Elsevier Science Ireland Ltd. All rights re erved.
`
`Keywords: Ovalbumin; Activation energy; Intrinsic viscosity; Huggins coefficient; Mark-Houvink- Kuhn - Sakurada exponent
`
`l. Introduction
`
`Ovalbumin is the major globular protein of
`chicken egg white. It is a member of the serpin
`uperfamily and is classified as a non-inhibitory
`erpin [1]. Ovalbumin consists of a single polypep(cid:173)
`tide chain of 385 amino acid residues that folds
`
`• Tel.: +48-32-172-30-41; fax: + 48-32-272-26-72.
`
`into a globular conformation with three [3-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(cid:173)
`tion [5]. The crystal structure of the protein, as
`revealed by X-ray crystallography, indicates that
`the ovalbumin molecule is approximately a tri-
`
`0301-4622/ 00j $- see front matter © 2000 Elsevier Science Ireland Ltd. All rights reserved.
`PII: S 0 3 0 1 - 4 6 2 2 ( 0 0 ) 0 0 I 2 7 - 7
`
`Page 5 of 14
`
`

`

`8
`
`K. Monkos 1 Biophysical Clzemisny 85 (2000) 7- 16
`
`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(cid:173)
`imental techniques such as viscometry [6-9], 1 H(cid:173)
`NMR spectroscopy [10], dielectric spectroscopy
`[11], densimetric and ultrasonic velosimetric titra(cid:173)
`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(cid:173)
`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(cid:173)
`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(cid:173)
`cosity-concentration relationships are discussed.
`Such rheological quantities as activation energy
`of viscous flow, Simha parameter and self-crowd(cid:173)
`ing factor are calculated. At low concentrations,
`the temperature dependence of the intrinsic vis(cid:173)
`cosity and of Huggins coefficient is presented.
`Using the dimensionless parameter [ 1'Jlc, the exis(cid:173)
`tence of three characteristic ranges of concentra(cid:173)
`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(cid:173)
`tained from Sigma Chemical Co. and was used
`without further purification for all the measure(cid:173)
`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-
`
`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(cid:173)
`tion of the solutions.
`
`2. 2. Viscometry
`
`Viscometry is still extensively used in many
`investigations of biological macromolecules in so(cid:173)
`lution because of its extreme sensitivity and tech(cid:173)
`nical simplicity ([17] and references therein). We
`have used an Ubbelohde-type capillary rnicrovis(cid:173)
`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 ± 0.05°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 soc
`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 concen(cid:173)
`trations from 6.16 kgjm3 up to 429.8 kg j m3
`.
`Solutions densities and protein concentrations
`were determined as described earlier [18,19].
`
`3. Results and discussion
`
`3.1. Viscosity-temperature dependence
`
`Very recently we have proved, for aqueous
`solutions of bovine serum albumin [20] and hen
`egg-white lysozyme [19], that the most useful rela(cid:173)
`tion connecting the viscosity with temperature is
`a somewhat modified Arrhenius formula. It has
`the form:
`
`11 = exp(- B + DT + :T)
`
`(1)
`
`Page 6 of 14
`
`

`

`K Monkos I Biophysical Chemist1y 85 (2000) 7-16
`
`9
`
`90
`
`80
`
`70
`
`60
`~
`u
`~50
`~ ·;;;
`8 40
`"' > 30
`
`20
`
`10
`
`0
`
`0
`
`10
`
`20
`
`30
`t[C]
`
`40
`
`50
`
`60
`
`Fig. 1. Temperature dependence of the viscosity of ovalbumin aqueous solutions for concentrations c = 246.89 (e), 370.6 (6.) and
`397.59 ( x) kg j m3 . The curves show the fit obtained by using Eq. (1) with the parameters: B = 35.166, D = 3.632 X 10 - 2 K - 1 and
`E, = 46.889 kJ / mol for c = 246.89 kg j m3; B = 46.342, D = 5.392 X w-:o K - 1 and E, = 65.288 kJ j mol for c = 370.6 kg j m3;
`B = 57.853, D = 7.273 X 10 -:> K - 1 and E, = 81.367 kJ j mol for c = 397.59 kg j m3
`
`where B and D are parameters, £ 5 i the activa(cid:173)
`tion energy of viscous flow of solution and R, T
`are gas constant and absolute temperature, re(cid:173)
`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
`
`90
`
`80
`0
`E 70
`:::;
`~
`>o 60
`.... • 50
`til
`c • c 40
`~
`"' > 30
`t;
`< 20
`
`10
`
`0
`
`0
`
`50
`
`100
`
`150
`
`250
`200
`c [kgfmA3]
`
`300
`
`350
`
`400
`
`450
`
`Fig. 2. Plot of the solution activation energy E, vs. concentration. (e) 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 Monkos 1 Biophysical Chemistry 85 (2000) 7-16
`
`8
`
`70
`
`60
`
`50
`
`40
`
`30
`
`20
`
`10
`
`0
`
`0,12
`
`0,1
`
`0,08
`
`0,06
`
`0,04
`
`0[1/K]
`
`0
`
`50
`
`100
`
`150
`
`200
`250
`c [kg/m"3]
`
`300
`
`350
`
`400
`
`0,02
`450
`
`Fig. 3. Plot of the coefficients B ( X) and D (e) vs. concentration. Experimental points were obtained by using the least squares
`method; the curves show the fit according to Eqs. (3) and (4), respectively.
`
`£ 5 for all measured concentrations were calcu(cid:173)
`lated by using the least squares method [20]. The
`results are shown in Figs. 2 and 3. As for bovine
`serum albumin and lysozyme, both activation en(cid:173)
`ergy £ 5 and the parameters B and D monotoni(cid:173)
`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:
`
`B =
`
`c
`l3 (BP- Bw) + Bw
`a- c
`
`(2)
`
`(3)
`
`(4)
`
`where a= PwMp/ M w and 13 =a~ -1. The quan(cid:173)
`tities c, Pw• ~, MP and Mw denote the solute
`concentration and water density in kgj m3
`, the
`effective specific volume of a protein and the
`molecular masses of the dissolved proteins and
`water, respectively.
`At c = 0
`the parameters E, = E"' = 32.013
`kJj mol, B = Bw = 25.936, D = Dw = 2.014 x 10- 2
`
`K - 1 and the Eq. (1) gives the viscosity-tempera(cid:173)
`ture relationship for water, where Ew denotes an
`activation energy of viscous
`flow of water
`molecules. The parameters E P, BP and DP are
`connected with dissolved proteins and, in particu(cid:173)
`lar, EP is an activation energy of ovalbumin. In
`Eqs. (2)- (4) the quantities EP, ~ ; BP, ~ and DP, ~ '
`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
`[2], the following values were obtained: EP =
`6.241 X 10 4 kJ j mol and ~ = 1.928 X 10 - 3 m3 / kg;
`BP = 3.45 X 10 4 and £ = 1.991 X 10 - 3 m 3 j kg; DP
`= 63.56 K- 1 and £ = 1.934 X 10 - 3 m 3 j kg. As
`seen in Figs. 2 and 3, the functions from Eqs.
`(2)-(4), with the parameters values presented
`above, give good approximation to the experimen(cid:173)
`tal values. The three values of the effective speci(cid:173)
`fic volume obtained above differ each other only
`slightly and give the average value <£) = 1.951 X
`w-3 m3 / kg.
`However, as has been shown by various tech(cid:173)
`niques [12,21-24], there exists a hydration shell of
`water surrounding the protein molecules in solu(cid:173)
`tion, which is distinct from bulk water. On the
`basis of microwave dielectric measurements, it
`
`Page 8 of 14
`
`

`

`K Monkos / 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(l + 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 0.3-0.4 has been
`obtained from experiments and computer simula(cid:173)
`tions [17] and, in particular, for ovalbumin 8 =
`0.36 [26]. This value is within the range (0.42 ±
`0.09), which was quite recently found by Harding
`et al. [27] on the basis of covolume measure(cid:173)
`ments. It gives the molecular mass of hydrated
`ovalbumin M h = 61.2 kDa. To calculate
`the
`parameters EP, BP' DP and ~ in Eqs. (2)-(4) for
`hydrated ovalbumin the MP should be replaced
`by Mh. By using once more the least squares
`method the following values one can obtain: EP
`= 8.487 X 10 4 kJ jmol, BP = 4.691 X 10 4 and DP
`= 86.44 K - 1• It is interesting that the effective
`specific volume of a protein ~' obtained in this
`case, is exactly the same as obtained earlier. The
`curves in Figs. 2 and 3 are identical for parame(cid:173)
`ters obtained for both hydrated and unhydrated
`ovalbumin.
`
`3.2. Viscosity-concentration dependence
`
`The most useful relation describing the depen(cid:173)
`dence of relative viscosity of aqueous solutions of
`globular proteins on concentration is
`that of
`Mooney [28]:
`
`(5)
`
`where 'T], = 'Tl/'Tlo and 'Tlo is the viscosity of the
`solvent. <I> is the volume fraction of the dissolved
`particles, S denotes the shape parameter and K
`is a self-crowding factor. The volume fraction
`<I>= NAVcjMh, where NA and V are Avogadro's
`number and the hydrodynamic volume of one
`dissolved particle, respectively. The solute con(cid:173)
`centration c is in kgj m3. 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:
`
`(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]:
`V = V0 + M p8/ NApw, 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(cid:173)
`graphy revealed that the ovalbumin molecule is
`approximately a tri-axial ellipsoid with the main
`semiaxes a = 3.5 nm, b = 2.25 nm and c = 2.5 nm.
`It gives a volume of unhydrated molecule V0 =
`82.467 nm3
`. For 8 = 0.36, the volume of the hy(cid:173)
`dration shell is 26.897 nm3 and V = 109.36 nm3
`.
`The hydrodynamic volume of ovalbumin may be
`obtained experimentally, too. As has been shown
`by using high-performance size-exclusion chro(cid:173)
`matography and intrinsic viscosity measurement,
`the Stokes radius of ovalbumin is 3 nm [8]. It
`corresponds to the hydrodynamic volume V = 113
`nm 3 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(cid:173)
`ing temperature from s = 3.782 (at t = 5°C) up to
`S = 3.435 (at t = 55°C). Simha [30] proved for
`hard ellipsoids of revolution ca =F b = c) 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 =a jb of the dissolved particle .
`For ellipsoids of revolution for which 1 < p < 15,
`it can be calculated from the asymptotic formula
`[31]:
`
`Page 9 of 14
`
`

`

`12
`
`K. Monkos / Biophysical Chemistry 85 (2000) 7-16
`
`Table 1
`The numerical values of the shape parameter S, the intrinsic viscosity [ 11l and the Huggins coefficient k 1 for ovalbumin calculated
`from Eq. (6), Eq. (10) and Eq. (11), respectively
`
`t[C]
`
`s
`[ 11l X 103
`[m3/ kg]
`k l
`
`5
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`3.782
`4.070
`
`3.723
`4.007
`
`3.669
`3.949
`
`3.623
`3.899
`
`3.582
`3.855
`
`3.545
`3.816
`
`3.514
`3.782
`
`3.488
`3.754
`
`3.466
`3.730
`
`3.448
`3.712
`
`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- l)I.SOS
`
`(8)
`
`sion of Eq. (5) in the power series of concentra(cid:173)
`tion yields to the following polynomial:
`
`One can easily calculate from the above rela(cid:173)
`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(cid:173)
`ever, in
`this case,
`the calculations are very
`troublesome. For unhydrated ovalbumin iijb =
`1.56 and iijc = 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 S shows
`that hydrated ovalbumin is more elongated than
`the unhydrated form. This conclusion is consis(cid:173)
`tent with the recent results of Harding et al. [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 nm3 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(cid:173)
`lations, for rigid spherical particles by Mooney
`[28]. However,
`the measurements for bovine
`serum albumin [20] (K = 1.25) and for hen egg(cid:173)
`white lysozyme [19] (K = 2.91) showed that for
`aspherical particles, the values of K may lie out(cid:173)
`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(cid:173)
`trated solutions. At low concentrations, an expan-
`
`(9)
`
`is the intrinsic viscosity and
`lim Tlsp
`where [ 11l =
`c--> 0 C
`'llsp = 'llr- 1 is the specific viscosity. The intrinsic
`viscosity [ 11l and the Huggins coefficient k 1 can
`be calculated from the following expressions [20]:
`
`1
`[ 'lll = -a
`
`Er -Ew]
`[
`X -(Bp-Bw)+(Dp-Dw)T+ RT
`
`(10)
`
`(11)
`
`The higher coefficients of expansion k 2 , k3 and
`so on, are connected with the Huggins coefficient
`k 1 [19] and are omitted here. As shown earlier,
`the parameters a, BP, DP and EP are different
`for hydrated and unhydrated ovalbumin. How(cid:173)
`ever, as calculations showed, in both cases the
`values of [ 11l and k 1 are identical and they are
`presented in Table 1. It is worth noting that the
`numerical value of the intrinsic viscosity calcu(cid:173)
`lated from Eq. (10) at t = 25°C ([ 11l = 3.855 x 10- 3
`m3 /kg) agrees very well with the value given in
`
`Page 10 of 14
`
`

`

`K Monkos I Biophysical Chemislry 85 (2000) 7-16
`
`13
`
`Table 2
`Mark-Houvink-Kuhn- Sakurada exponent, critical concentrations, reduced critical concentrations and slopes of the regression
`lines log Tl,p vs. log[ 11k for ovalbumin, obtained from the fit of the curves in Figs. 4 and 5 and from Eq. (12)
`
`I[Cl
`
`5
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`so
`
`55
`
`0.323
`a
`c* [kgj m3l
`41.2
`c** [kgj m3l 349
`c* [ 11l
`0.168
`c** [ 11l
`1.42
`Slopes
`c < c*
`c > c**
`
`1.09
`8.41
`
`0.323
`41.8
`349
`0.168
`1.398
`
`0.322
`42
`350
`0.166
`1.382
`
`0.322
`42.6
`353
`0.166
`1.376
`
`0.323
`43.2
`352
`0.167
`1.357
`
`0.323
`43.5
`350
`0.166
`1.336
`
`0.325
`43.7
`349
`0.165
`1.32
`
`0.324
`44
`355
`0.165
`1.333
`
`0.321
`44.4
`345
`0.166
`1.287
`
`0.325
`44.4
`350
`0.165
`1.299
`
`0.323
`44.6
`350
`0.165
`1.294
`
`1.09
`8.17
`
`1.09
`7.90
`
`1.09
`7.75
`
`1.09
`7.58
`
`1.09
`7.38
`
`1.09
`7.28
`
`1.08
`7.14
`
`1.08
`7.04
`
`1.08
`7
`
`1.08
`7.06
`
`the literature at the same temperature ([ 'T)] = 3.9
`X 10- 3 m3 /kg) [7]. As pointed out by Tanford
`[25],
`the
`intrinsic viscosity of rigid macro(cid:173)
`molecules should be essentially independent of
`temperature. In our case, [ 'Y)] slowly decreases
`with increasing temperature and this indicates
`that ovalbumin is not a perfectly stiff molecule in
`
`the considered range of temperatures. The prob(cid:173)
`lem will be discussed below also.
`
`3.3. Three ranges of concentrations and
`determination of the MHKS exponent
`
`One of the commonly accepted method of ex-
`
`log T] 5p
`
`2,5
`
`2
`
`1,5
`
`0,5
`
`0
`
`-0,5
`
`-1
`
`-1,5
`
`• • • •
`•• ••
`•
`•
`
`-1,5
`
`-1
`
`-0,5
`
`0
`
`0,5
`
`log (TI]c
`Fig. 4. Specific viscosity as a function of c( 11l in a log- log plot for ovalbumin at I = 5°C; straight lines show different slopes in dilute
`(c < c*) and concentrated (c > c** ) regions. The arrows show the boundary concentrations c* (left arrow) and c** (right arrow).
`
`Page 11 of 14
`
`

`

`14
`
`K Monkos 1 Biophysical Chemistry 85 (2000) 7-16
`
`molecules. As is seen in Table 2, the values of c*
`slowly increase with increasing temperature and
`the product c*[ T)] is nearly the same over the
`whole range of temperatures. The slopes are
`nearly identical too. It is worth noting that the
`slopes in the dilute region, for quite different
`sorts of molecules, are in the range of 1.1-1.4
`[33,37-40].
`the semi-dilute domain (c* [ TJ] < c[ TJ] <
`In
`c**[ TJD, a non-linear dependence of log 'Tlsp -log
`[ TJlc, for randomly coiled globular proteins [7],
`citrus pectins [38] and mammalian hemoglobins
`[39] was observed. This is the case for ovalbumin
`over the whole range of temperatures also. As
`was proved by Lefebvre, in the semi-dilute region,
`the following equation for the relative viscosity is
`fulfilled [7]:
`
`) l j2a
`lnT), = 2a[ TJJc • C'
`
`C
`
`(
`
`- (2a- 1)[ TJJc •
`
`(12)
`
`where a is the MHKS exponent. In many cases,
`this quantity is used as a conformation indicator
`of molecules in solution. The values of the expo(cid:173)
`nent a are: 0 for bard spherical particles, 0.3-0.35
`for hard quasi-spherical mammalian hemoglobins
`[39], 0.5-1 for random coils [7,34,35,38,40-42] and
`
`•
`
`p