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`CSL EXHIBIT 1098
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`Page 1 of 11
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`CSL EXHIBIT 1098
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`BIOCHIMICA ET BIOPHYSICA ACTA
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`//
`—_______—_________—__J ,n 7,
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`0167-483511997/“7
`Copyright © 1997 Elsevier Science B.V. All rights reserved
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`Printed in The Netherlands
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`(9 The paper used in this publication meets the requirements of ANSI/N180 Z39.48-l992 (Permanence of Paper).
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`Page 2 of 11
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`Page 2 of 11
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`BKXTNIMK'A ET BIOPHYSIC.‘ AL‘I'A
`
`MM '5 vital m: (ll/Tr!" Ctmlettts Lift Silent-n - Blulugu'tll Abilrucls - ChemicalAbxlrml.r - [ruler Chtml't-ui - Index Mrdicu: - ("SA Abstracts -
`Eu (rpm Medial (EMBASE) - ercrrnre Update - Cllrrcnl Awurrltris trt Blnlngica/ Silence: (CABS)
`
`Glutathione alters the mode of calcium-mediated
`regulation of adenylyl cyclase in membranes from
`mouse brain
`J. Nakamura and S. Bannai (Japan)
`Structure of membrane glutamate carboxypeptidase
`MD. Rowlings and AJ. Barrett (UK)
`Acetylcholinesterases from Elapidae snake venoms:
`biochemical. immunological and enzymatic char-
`acterization
`
`239
`
`247
`
`Y. Frobert. C. Crétninon, X. Cousin, M.-H. Rémy.
`J.-M. Chatel. S. Bon, C. Bon and J. Grassi
`
`253
`
`268
`
`277
`
`(France)
`Purification and characterization of two new cy-
`tochrome P"_‘50 relatedto CYPZC subfamily from
`rabbit small intestine microsomes
`Y. Shimizu, E. Kusunose, Y. Kikuta. T. Arakawa.
`K- ’ehr'hm and M-IKusurwse Hare")
`.
`.
`High salt concentrations
`induce dissocration of
`dimeric rabbit muscle creatine kinase. Phys'c‘)‘
`chemical
`characterization of
`the monomeric
`'
`spCCIes
`F. Couthon, E. Clones and C. Wu! (France)
`Characterisation of a xylanolytic amyloglucosidase
`or Termitomyces clypeatus
`'
`A.K. Ghosh. AK. Naskar and S. Serigupta (India) 289
`Kinetic study of the suicide inactivation of latent
`polyphenoloxidase from iceberg lettuce (Lacruca
`saliva)
`induced by 4-tert-butylcatechol
`in the
`presence Of 505
`.
`5- Citazarra.
`J- Cabanes. 1- Escr'ba’m and F-
`Garcta-Cannona (Spam)
`.
`Concentration and temperature dependence of vrs-
`cosity in lysozyme aqueous solutions
`K- M"""05 (Poland)
`
`297
`
`304
`
`continued
`
`Information for Contributors
`
`I'll
`
`rt se uence- a er
`q
`5110
`P P
`Cloning and characterization of a protein phos-
`phatase type l-binding subunit from smooth mus-
`cle similar to the glycogen-binding subunit of
`liver
`K. Hirano. M. Hirano and DJ. Hartshorrle (USA)
`
`Regular papers
`
`Characterization and mutational studies of equine
`infectious anemia virus dUTPase
`H. Shun. M. D. Robek, D. s. Threadgill, L. 5‘
`Marikowski, CE. Cameron, F.J. Fuller and 5.1..
`Payne (USA)
`Characterization of the affinity of the GW activator
`protein for glycolipids by a fluorescence de-
`quenching assay
`N. Smiljanic-Georgljell. B. Rigat, B. X59. w. Wang
`and D. J. Mahurari (Canada)
`Identification of flz-glycoprotein l as a membrane—
`associated protein in kidney: purification by
`calmodulin affinity chromatography
`on. Kllzrke. R. Rojkjtzr. L Christensen and l.
`St‘housbae (Denmark)
`Characterization of the interaction between Bl-gly-
`coproteinland calmodulin. and identification ofa
`binding sequence in Bz-glycoprotein I
`R. Rajkjar. DA. Khzrke and l. Schousboe (Den—
`mark)
`Site-specific modification of rabbit muscle creatine
`kinase with sulfhydryl-specific fluorescence probe
`by use of hydrostatic pressure
`N. Tanaka. T. Tonal and S. Kunugi (Japan)
`Target size analysis of an avermectin binding site
`from Drosophila melanogaster
`A. Pomes, E. Kempner and S. Rohrer (USA)
`
`[77
`
`l8l
`
`I92
`
`203
`
`217
`
`226
`
`233
`
`Page 3 of 11
`
`i l
`
`l
`
`i
`'
`
`n-“_—_—.—n——
`“aw-“n“
`
`
`
`Protein Structure & Molecular Enzymology
`
`Vol. 1339. No. 2: 23 May 1997
`
`B B
`
`A
`
`
`Contents
`
`

`

`331
`
`
`34]
`
`344
`
`
`
`
`
`
`
`
`Effects of profilin—annexin I association on some
`
`
`
`
`
`
`properties of both profilin and annexin I: modifi-
`
`
`
`
`
`
`
`cation of the inhibitory activity of profilin on
`
`
`
`
`
`
`
`
`actin polymerization and inhibition of the self-as-
`
`
`
`
`
`
`sociation of annexin l and its interactions with
`
`
`
`
`
`
`
`liposomes
`
`M.-T. Alvarez—Martinez, F. Porte, J.P. Liautard
`
`
`
`
`
`and J. Sri Widada (France)
`
`
`
`
`
`Cumulative Contents, Vol, 1339
`
`
`
`Author Index
`
`
`
`
`
`Efficient purification. characterization and partial
`
`
`
`
`
`amino acid sequencing of two a-1,4-g1ucan lyases
`
`
`
`
`
`
`
`from fungi
`
`
`KM. ngh,
`S. Yu,
`T.M.I.E. Christensen,
`
`
`
`
`
`
`K. Bojsen and J. Marcussen (Denmark)
`
`
`
`
`
`
`Photoaffinity labeling of peroxisome proliferator
`
`
`
`
`proteins
`rat hepatocytes;
`in
`binding
`dehy-
`
`
`
`
`
`drocpiandrosterone sulfate— and bezafibrate-bind-
`
`
`ing proteins
`
`
`H. Sugiyama, J. Yamada, H. Takumu, Y. Kadama,
`
`
`
`
`
`
`
`
`T. Wazanabe, T. Taguchi and T. Saga (Japan)
`
`
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`
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`
`
`
`
`311
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`321
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`Page 4 of 11
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`Page 4 of 11
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`

`

` Biochimica et Biophysica Acta 1339 (1997) 304—310
`
`——K
`
`
`HIUCIHMIK'A I'I‘ BIUPNV‘JI'A ”c”
`
`BBB__“
`
`
`
`Concentration and temperature dependence of viscosity in lysozyme
`aqueous solutions
`
`Karol Monkos ‘
`
`Department of Biophysics, Silesian Medical Academy. H. Jordana I9. 4I-808 Zabrze 8, Poland
`
`Received 25 September 1996; revised 2 January 1997; accepted 9 January 1997
`
`
`
`Abstract
`
`The paper presents the results of viscosity determinations on aqueous solutions of hen egg-white lysozyme at a wide
`range of concentrations and at temperatures ranging from 5°C to 55°C. It has been proved that. at each fixed concentration.
`the viscosity-temperature dependence may be quantitatively described by the modified Arrhenius formula. On the basis of
`the generalized Arrhenius formula, the parameters of the Mooney approximation were calculated. It has been concluded that
`lysozyme molecules in aqueous solution behave as hard quasi-spherical particles. By applying an asymptotic form of the
`generalized Arrhenius formula. such rheological quantities as the intrinsic viscosity and Huggins coefficient were
`calculated.
`
`Keywords: Lysozyme: Viscosity; Arrhenius formula; Activation energy; Huggins coefficient
`
`1. Introduction
`
`Hen egg-white lysozyme is a well-known enzyme
`that acts as a glycoside hydrolase. This small globular
`protein consists of two functional domains located on
`each side of the active site cleft and contains both
`
`helices and regions of 3 sheet, together with loop
`regions, turns and disulfide bridges [1]. Its structure,
`dynamics and hydration have recently been studied
`extensively by a wide range of experimental
`tech-
`niques including 1H, 13C and l5N-NMR spectroscopy
`[1—6], dielectric spectroscopy [7—9]. Fourier trans-
`form infrared spectroscopy [10.11] and X-ray crystal-
`lography [12]. Some sophisticated theoretical meth-
`ods have also been applied to those problems in the
`
`
`
`‘ Corresponding author.
`
`'
`
`lysozyme
`solution the
`in a
`[13—15].
`literature
`molecules are surrounded by water. It participates in
`stabilizing the protein structure and stimulating the
`activity of active site. Comparison of solution NMR
`parameters with those predicted by the crystal struc-
`tures of the protein has shown the very close similar-
`ity of the structure of lysozyme in solution and in
`crystals. Although recent X-ray diffraction studies of
`dehydrated lysozyme crystals have revealed numer-
`ous small displacements in the positions of individual
`atoms, the overall conformation does not differ greatly
`from that of the fully hydrated protein [16].
`As is known, size and shape of proteins have 'an
`important influence on their hydrodynamic properties
`in solution. Such properties have not been sufficiently
`studied for lysozyme solutions. This is especially lhc
`case for the viscosity of lysozyme solutions. III-(he
`present study, the results of viscosity determinations
`
`0l67-4838/97/$I7.00 Copyright © 1997 Elsevier Science B.V. All rights reserved.
`PII 80167-4838(97)00013-7
`
`Page 5 of 11
`
`

`

`K. Monkos / Biochimr'ca er Biophysical Acra I339 ( I997) 304-310
`
`305
`
`on aqueous solutions of hen egg-white lysozyme at a
`wide range of concentrations and at
`temperatures
`ranging from 5°C to 55°C are presented. On the basis
`l of these measurements, a generalized Arrhenius for-
`l mula [l7] connecting the viscosity with temperature
`' and concentration of the dissolved proteins is dis-
`? cussed. At a fixed temperature the generalized Arrhe-
`l nius formula gives the Mooney approximation [18],
`i.e., the viscosity—concentration relationship. and al-
`-1ows calculation of the coefficient 8 and the self-
`, crowding factor K, as well. in Mooney’s formula. At
`] 10w concentrations. an asymptotic form of the gener-
`‘ alized Arrhenius formula is presented.
`
`2. Materials and methods
`
`2.1. Materials
`
`Hen egg-white lysozyme was purchased from
`Sigma Chemical Company and was used without
`further purification. From the crystalline form the
`material was dissolved in distilled water and the
`
`, solution was treated to remove dust particles with
`filter papers. The samples were stored at 4°C until
`ijust prior to viscometry measurements. when they
`were warmed from 5°C to 55°C. The pH values of
`' such prepared samples were about 7.0 and varied
`slightly with different protein concentrations.
`
`2.2. Viscomerry
`
`The viscosity of lysozyme solutions was previ-
`ously investigated by Lefebvre [19]. The author has
`_ reported results mainly for lysozyme in fully dena-
`tured state, i.e., in the random coil conformation. For
`the solutions of lysozyme in the native state,
`the
`author has shown that the flow behaviour was New—
`tonian for shear rates from 0 to at least 128.5 s"I and
`up to a concentration of at least 370 kg / m3. This is
`important information because it justifies the use of a
`y
`' viscometer, which is a simple and convenient experi-
`mental tool, for viscosity measurements of lysozyme
`solutions.
`
`Viscosity was measured with an Ubbelohde-type
`capillary microviscometer with a flow time for water
`of 28.5 s at 25°C. The microviscometer was placed in
`a waterbath controlled thermostatically at 5°C to
`
`55°C 1 0.05°C. The same viscometer was used for all
`
`it always
`measurements and was mounted so that
`occupied the same position in the bath. Flow times
`were recorded to within 0.1 3. Solutions were temper-
`ature-equilibrated and passed once through the capil-
`lary viscometer before any measurements were made.
`For most concentrations the viscosity measurements
`were made from 5°C to 55°C in 5°C intervals. Such a
`
`range of temperatures was chosen because above
`55°C the thermal denaturation of lysozyme occurs.
`Solutions densities were measured by weighing
`and protein concentrations were detemiined by a dry
`weight method in which samples were dried at high
`temperature for several hours. This method was re-
`cently successfully applied to other globular proteins
`too [20,21]. The viscosities of the lysozyme solutions
`were measured for concentrations from 24.9 kg/m3
`up to 342.6 kg/m".
`
`3. Results and discussion
`
`3.1. Generalized Arrhenius formula
`
`For glass-forming liquids the temperature-depen-
`dent change of viscosity is analysed according to the
`Williams-Landel’Feny equation, which turns out to
`be applicable in the range from glass transition tem-
`perature 7;; to about Ts + 100°C [22]. At higher tem-
`peratures an equation of the Arrhenius form is widely
`used:
`
`n=ACXP(;F;)
`
`(I)
`
`where, E, R and T are viscosity, activation energy of
`viscous flow, gas constant and absolute temperature.
`respectively. However. it gives a good approximation
`to the experimental values only in relatively narrow
`temperature ranges. Viscosity data, when taken at a
`sufficiently wide range of temperatures, show that the
`dependence of 1n n on T" is not linear, i.e., Eq. (1)
`is not a good one. Very recently we have proved, on
`the basis of the results of viscosity determinations on
`aqueous solutions of bovine serum albumin, that the
`most useful relation connecting the viscosity with
`temperature is a somewhat modified Arrhenius for-
`mula.
`It describes the viscosity-temperature depen-
`
`Page 6 of 11
`
`

`

`
`
`
`
`.._.__..__.s.___......s.
`
`306
`
`K. Monkos / Binrhimica e! Biophysim Arm I339 ( l 997) 304—310
`
`
`
`
`
`Activationenergy[LI/mot]
`
`:siii
`
`O
`
`50
`
`1“
`
`150
`
`M
`
`150
`
`”I
`
`350
`
`c lkg/rn‘J]
`
`Fig. 2. Plot of the solution activation energy If> versus concentra-
`tion. (0) experimental points are obtained by using the least
`squares method; the curve shows the fit according to Eq. (3) with
`a = 7.956~ 10’ kg/m“.
`u = 2.592. to" m-‘/kg. E“. = 32.0:
`kJ/mol and El, = 3.97-10‘ kJ/mol.
`
`influence of its neighbouring molecules [24]. Fig. 2
`shows that E5 is a monotonically increasing function
`of concentration. One can easily explain this fact. In
`a streamline flow of a solution molecules of both
`
`water and dissolved proteins take part. Therefore. the
`activation energy Es should be a superposition of the
`activation energy of water
`EW and protein Er
`molecules. As has been shown in our earlier work
`
`[17]. this leads to the following relation:
`
`ES=E€E(Ep—E“.)+E“,
`
`where
`
`
`a = p M”
`w M“
`
`and
`
`fl = av - l
`
`(3)
`
`(4)
`
`(5)
`
`The quantities c. pw. v, M" and Mw denote the
`solute concentration and water density in kg/ m“. the
`effective specific volume of a protein and the molec-
`ular masses of the dissolved proteins and water.
`respectively. The effective specific volume is the
`constant of proportionality between the effective m0-.
`lar volume and the molar mass of a macrosolute [25]-
`The molecular weight of hydrated hen egg-white
`lysozyme is 14320 Da [26]. So,
`in this case 01=
`7.956 X 105 kg/m". In Eq. (3) the activation energy
`of dissolved particles Ep and the effective specific
`volume of a particle u must be taken into account as
`two adjustable parameters. The parameters were cal-
`
`dence from the neighbourhood of solution freezing-
`point up to the vicinity of the temperature where the
`protein’s thermal denaturation occurs and has the
`form [17]:
`
` E3
`n=exp(—B+DT+ RT)
`
`(2)
`
`where B and D are parameters and Es is the activa-
`tion energy of viscous flow of solution. The above
`formula is identical to the Arrhenius relation in Eq.
`(1), if the pre-exponential factor A = exp (-B + DT).
`Fig.
`1 shows the results of lysozyme solution viscos-
`ity measurements at
`the highest concentration we
`studied here. As seen. a curve obtained by using the
`relation from Eq. (2) gives a very good fit to the
`experimental points over the whole range of tempera-
`titres. For the smaller concentrations a situation is the
`
`same. For all concentrations the parameters B, D and
`135 were calculated by using the least squares method.
`It
`is worth noting that
`the experimental values of
`water viscosity (when given in centipoise) agree very
`well with those calculated on the basis of Eq. (2)
`when B = Bw = 25.94, D = Dw = 0.02 K" and E3
`= E.“~ = 32.01 kJ/mol.
`An activation energy of viscous flow E can be
`interpreted within the frame of applications of the
`absolute rate theory to the process of flow [23].
`In
`this theory E is identified as the activation energy for
`the jump of a molecule from one equilibrium position
`in the liquid to the next or as a minimum energy
`required for a molecule of the solution to escape the
`
`VlscosltyltP]IIttI3a
`
`ao
`
`10
`
`20
`
`so
`‘lCl
`
`u
`
`a
`
`no
`
`Fig. 1. Temperature dependence of the viscosity of hen egg-white
`lysozyme aqueous
`solution for
`the concentration c = 342.6
`kg/m". (O) Experimental points; the curve shows the fit ob-
`tained by using Eq. (2) with B = 122.94. I) = 0.|69 K" and
`E‘ = 169.39 kJ/mol.
`
`Page 7 of 11
`
`

`

`K. Mon/(ox / Biochimir'u et Biophysica Acta I 339 f I 997) 304—3I0
`
`307
`
`culated by using the least squares method too. The
`. obtained values are as
`follows:
`Ep = 3.97 X 104
`l u/mol and 1!=2.592X10‘3 m3/kg. As seen in
`i Fig. 2, Eq.
`(3) gives good approximation to the
`i experimental values then. Differences in the values of
`; activation energy of water (Ew=32.01 kJ/mol).
`1
`lysozyme (E,J = 3.97 X 10“ kJ/mol) 'and bovine
`l serum albumin (15'p = 5.374 X 105 kJ/mol) [17] show
`' that
`this quantity depends strongly on molecular
`weights and dimensions of the molecules. To estab-
`lish the exact dependence between those quantities.
`the experimental values of ED for more proteins are
`needed.
`
`.'
`J
`
`The coefficients 3 and D from Eq. (2) depend on
`‘
`. concentration exactly in the same way as ES. Both 8
`and D increase monotonically with increasing con-
`centration. Therefore, one can write the same rela-
`
`1
`
`tions as for Es:
`C
`B=a_,,c(8.,—B..)+Bw
`and
`
`C
`
`(7)
`D=a_Bc(Dp-Dw)+Dw
`l where V, BF and V. DP are adjustable parameters.
`' The above relations give a good fit to the experimen-
`tal values for v= 2.615 X 10" kag, Bp= 2.642
`X 104 and for v= 2.6x 10'3 kag, DP=41.97
`K ". The three values of the effective specific vol—
`ume obtained above differ each other only slightly
`and give the average value (v) = 2.602><10‘3
`m5/kg. By substituting Eq. (3). (6) and (7) into Eq.
`(2), one can obtain the following relation for relative
`viscosity of a solution:
`”=1
`I
`710
`
`<6)
`
`8
`t)
`
`9
`
`()
`
`C
`
`
`=exp{a_BC[—(Bp—Bw)+(Dp—DW)T
`
`EP—Ew
`+ R,
`1}
`
`where n“ denotes viscosity of water:
`EW
`—B +D T+—
`
`11..
`
`=
`
`exp(
`
`w
`
`w
`
`RT)
`
`At a fixed temperature, Eq. (8) describes the viscos-
`ity-concentration dependence of a solution. On the
`other hand. as has been shown in our earlier work
`
`Page 8 of 11
`
`in the case of aqueous solutions of globular
`[27].
`proteins, the most useful functional form describing
`the dependence of relative viscosity on concentration
`is that of Mooney [18]:
`
`
`n.
`
`expl 1 _ m
`a]
`
`(10)
`
`where (I)
`
`is the volume fraction of the dissolved
`
`particles, K is a self—crowding factor and S denotes
`the parameter which.
`in general. depends on the
`shape of the dissolved particles and on hydrodynamic
`interactions of proteins in solution. The volume frac-
`tion <D=NAVc/M where NA. V and M are Avo-
`gadro’s number,
`the hydrodynamic volume of one
`dissolved particle and the molecular weight, respec-
`tively. One can easily show that Mooney’s relation,
`given in the above form, is identical with Eq. (8). if
`the parameter
`
`MW
`
`S =
`
`pw NAV
`
`>< —(Bp— 3w) + (Dp— Dw)T+
`
`
`
`
`Ep — Ew
`
`and the self—crowding factor
`
`Mw
`Mp
`
`
`
`prp NAV
`
`K = V -
`
`(11)
`
`(12)
`
`Both coefficients can be calculated when the hydro-
`dynamic volume of the dissolved proteins is known.
`Hen egg-white lysozyme molecules can be treated as
`prolate ellipsoids of revolution with the main axes
`a = 4.5 nm and b = 3 nm [26]. It gives the hydrody-
`namic volume of hen egg-white lysozyme V: 2.12
`X 10‘26 In}. Fig. 3 shows the numerical values of
`the parameter S obtained from Eq. (11). As is seen
`this parameter decreases monotonically with increas-
`ing temperature from S = 3.425 (at r= 5°C) up to
`S = 2.697 (at t= 55°C).
`
`The Mooney formula describes the viscosity-con-
`centration dependence from dilute up to concentrated
`solutions and the parameters S and K do not depend
`on concentration. For dilute solutions.
`i.e.,
`in the
`
`limit (D—> 0, one can transform the Eq. (10) into the
`form: 1),: l + Sd’. This is the well-known relation
`developed by Einstein. who has proved that for hard
`spherical particles immersed in a solution, S = 2.5.
`
`

`

`308
`
`K. Man/(05 / Biochimica e! Biophysir'a Am: 1339 (I997) 304—310
`
`to
`
`o
`
`10
`
`a
`
`to
`
`so
`
`so
`‘[CI
`
`M 3
`
`.3
`
`1.1
`
`2.0
`
`2.7
`
`2.5
`
`Fig. 3. The parameter S, given by Eq. (11). as a function of
`temperature.
`
`Simha [28] has extended the technique employed by
`Einstein for a suspension of nonspherical particles.
`The viscosity contribution caused by a suspension of
`nonspherical particles depends on their orientation
`with respect to the direction of flow of the fluid. This
`orientation is modified by two effects: (1) the orienta-
`tion of the principal axis of the particles to the flow
`direction by the flow and (2) the rotational Brownian
`motion produced as a reaction of the particles to the
`random heat motions of the solvent. The latter effect
`
`acts against the first one. Simha showed that in the
`case when the Brownian motion prevails and the
`orientation of particles is completely at random, the
`factor S depends, in a very complicated way, on the
`axial ratio [2 = a/b of the dissolved particles. How-
`ever, for ellipsoids of revolution for which 1 < p <
`15, the asymptotic formula can be used [29]:
`
`S=2.5+0.4075(p-l)1508
`
`(13)
`
`Hen egg-white lysozyme has the axial ratio p = 1.5
`and the above formula gives S = 2.643 then. This
`value agrees well with the experimental one in the
`high temperature limit (r= 55°C). as could be ex-
`pected. At the same time, it indicates that the hen
`egg-white lysozyme molecules in aqueous solution
`behave as hard quasi-spherical particles.
`in turn,
`The self—crowding factor K (Eq. (12)),
`does not depend on temperature. Substitution of the
`volume V= 2.12 X 10‘26 in3 into Eq. (12) gives the
`numerical value K = 2.91. It is worth noting that in
`his original work [18], Mooney showed, on the basis
`of purely geometric arguments. that for rigid spheri-
`cal particles. values of K should lie between 1.35
`and 1.91. There are no theoretical estimations of the
`
`In
`self-crowding factor for ellipsoids of revolution.
`this case the values of the factor K should, undoubt-
`
`edly, lie in a wider range than for spherical particles.
`Therefore. all experimental values of K are valuable.
`It is not possible to obtain the exact value of the
`parameters S and K when the hydrodynamic volume
`of the dissolved proteins is not known. In this case,
`one can obtain only the ratio of K/S by the method
`proposed by Ross and Minton [30]. The authors
`transformed Mooney‘s formula (Eq. (10)) into the
`form with only one parameter K/S, but then it
`is
`necessary to know the intrinsic viscosity. The ratio
`K/S was obtained by the authors for two sets of data
`for human hemoglobin. However, as has appeared,
`
`Page 9 of 11
`
`(16)
`
`the fit of the modified Mooney’s formula to the
`experimental points was not the best one, especially
`in the moderately concentrated region. The problem
`was discussed in detail in our previous paper [21] and
`an alternative treatment of the problem has been
`proposed there.
`
`3.2. Low concentration limit
`
`At
`
`low concentrations,
`
`the relation between the
`
`solution viscosity and the concentration may be ex-
`pressed by the polynominal [31]:
`7’s
`2
`,
`1
`Tp=l711+krl7ll c+k2[n]3c‘+k3[n]4c3+...
`('4)
`
`where
`
`_ . 22
`P31 .-
`["1
`is the specific
`is the intrinsic viscosity, 7;”, = n, — 1
`viscosity, the dimensionless parameter kl
`is the Hug-
`gins coefficient and k3. k3 are the higher coefficients
`of the expansion. In our case the generalized Arrhe-
`nius Eq. (8) can be expanded in the power series of
`concentration. too. An expansion identical to that in
`Eq. (14) can be obtained from:
`1
`[111:3 —(Bp—Bw)+(Dp—DW)T+
`
`
`Ep-—E,,
`RT
`
`(15)
`
`kl
`
`1
`:5
`
`
`23
`Ep—E, +1
`
`RT
`
`—(BI,—B“.)+(D,,—DW)T+
`
`

`

`K. Mmtkns / Bf(}(‘llfllli(‘ll el Binpltysica Arm I if 9 ( I997) 304—3 I 0
`
`309
`
`' Table I
`1} The numerical values of the intrinsic viscosity [1]] and the Huggins coefficient kI for hen egg—white lysozyme calculated from Eq. (15)
`
`y and Eq. (16)
`dc]
`
`5
`
`I0
`
`IS
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`2.41
`2.42
`2.45
`2.49
`2.54
`2.59
`2.66
`2.74
`2.83
`2.94
`3.05
`3 ["1x 103[m3/kgl
`
`kl 1.58 l.35 L39 L42 1.45 [.48 1.50 1.53 LS4 l.56 l.57
`
`
`
`
`
`
`
`
`
`
`
`are connected with the Huggins coefficient kl
`following way:
`
`in the
`
`1
`k =k2-—
`2
`.
`12
`
`k_
`
`=
`
`k,3
`
`lk+1
`4
`24
`
`l
`l
`1
`k =k"——k2+ _k1——
`4
`l
`2
`l
`6
`80
`
`(17)
`
`('8)
`
`([9)
`
`independently of temperature. The above relation-
`ships show that any property of a solution which
`determines the value of kI will also determine the
`value of k2, k3 and so on. In other words, the Eqs.
`( l7)—( 19) provide a test for any theoretical treatment
`Iv
`of dilute solution viscosity.
`
`4. Conclusions
`
`The viscosity of hen egg-white lysozyme solutions
`at temperatures up to 55°C and in a wide range of
`concentrations at neutral pH may be quantitatively
`described by the generalized Arrhenius formula (8).
`This formula enables the calculation of parameters in
`Mooney’s approximation. The value of the parameter
`S at high temperature limit indicates that lysozyme
`molecules in aqueous solution behave as hard quasi-
`spherical particles. The asymptotic form of the gener-
`alized Arrhenius formula for small concentrations
`enables the calculation of the intrinsic viscosity and
`the Huggins coefficient. Both quantities depend on
`temperature. The higher coefficients of expansion in
`the power series of concentration k2, k3 and so on,
`are connected with the Huggins coefficient and the
`Eqs. (l7)—(l9) provide a test for any theory of dilute
`solution viscosity.
`
`The higher coefficients of expansion have a more
`complicated form and are omitted here. As seen both
`intrinsic viscosity and the Hutygins coefficient depend
`on temperature. ThisIS the case for the higher coeffi-
`cients of expansion, too. The numerical values of [1;]
`fl and k1 for hen egg-white lysozyme are presented in
`Fig. 4 and in Table 1.
`It
`is worth noting that
`the
`numerical value of the intrinsic viscosity calculated
`from Eq. (15) at t= 25°C ([n]—-— 2.66 X10 m/kg)
`agrees very well with the value given in the literature
`at the same temperature ([n]= 27 10' kag)
`
`A lot of numerical values of k1 have been pub-
`'
`llished in the literature ([31] and refs.
`therein) The
`lack of agreement for different liquids and solutions
`ensues from the fact that the intermolecular hydrody-
`; namic interactions can be different and, in each case.
`kl should be studied in detail separately. Thus, the
`experimental values of kl are desirable. There are no
`theoretical estimations of the higher coefficients of
`expansion in Eq. (14). However, on the basis of the
`'generalized Arrhenius formula (8), expansion in the
`power series of concentration. the coefficients k3. k 3
`and so on can be calculated. As has appeared, they
`
`
`
`
`
`TheIntrinsicvisually
`
`.. o
`
`"x:
`
`a-:
`
`
`
`TheHugginscoefficient
`
`[MN/I‘ll
`
`t [(71
`
`Fig. 4. The intrinsic viscosity [1)] (—) and the Huggins coeffi—
`cient
`Itl
`(
`), given by Eq. (l5) and Eq. (l6), respec-
`‘Iively. as a function of temperature.
`‘
`
`Page 10 of 11
`
`

`

`
`
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`(1979) Arch. Biochem.
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`[16] Kachalowa, G.S., Morozov. V.N., Morozowa, T.Ya., My-
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`Page 11 of 11
`
`Page 11 of 11
`
`