‘RNATIONAL JOURNAL OF
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`{LTCTURE, FUNCTION AND INTERACTIONS
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`«
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`4V"!
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`* y 9
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`Q
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`3iological
`Aacromolecu es
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`MAR 13 1996
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`LIBRAR
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`Page 1 of 11
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`CSL EXHIBIT 1104
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`Page 1 of 11
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`CSL EXHIBIT 1104
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`Page 2 of 11
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`Page 2 of 11
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`

`

`Vol. 18. Nos. 1.2
`
`Biologicall
`-Ma——o——-S..§
`
`CONTENTS
`
`Fm I996
`
`This journal is abstracted/Inflated in Current Contents: Polymer Contents: Index Medias: Food Science and Techmlogy Abstracts:
`Excerpta Mm; EMBASE
`
`Ab initio tertiary-fold prediction of helical and non-helical protein chains using a genetic algorithm
`T. Dandekar. P. Argos (Germany) ..................................................................
`Mixed iota-kappa campenan gels
`MJ. Ridout. S. (hm, GJ. Brownsey. VJ. Morris (UK; Spain) .........................................
`Characterization and solution properties of a new esopolysaceharide excreted by the bacterium Annamaria: sp. strain
`I644
`L Bani. M. Milas. M. Rinaudo (France) ............................................................
`Chemical modification of silk fibroin with N-acetyI-chito-oligosnccharides
`Y. Gotoh. M. Tsukada. S. Aiha. N. Minoura (Japan) ..................................................
`Dielectric studies of proton transport in air—dried fully calcified and decalcified bone
`E Manet, L. Kubisr. F. .laroayk (Poland) ...........................................................
`Ell'ect of pressure on the deuterium exchange reaction of a-lactalbumin and B—lactoglobulin
`N. Tanaka. S. Kunugi (Japan) .......................................................................
`The interaction of sodium dodecyl sulfate and urea with cat-fish collagen solutions in acetate butler: hydrodynamic
`and thermodynamic studies
`C. Rose. A3. Mandal (India) .......................................................................
`Conformational transition of insulin induced by n-alkyltrimethylammonium bromides in aqueous solution
`C. Pombo. G. Prieto. J.M. del Rio. F. Sarmiento. M.N. Jones (Spain; UK) ...............................
`Viscosity of bovine serum albumin aqueous solutions as a function of temperature and couwutration
`K. Monkos (Poland) ...............................................................................
`Relations between move. viscoelastic and molecular properties in gluten from genetic variants of bread wheat
`.l. Hargreaves. Y. Popineau. M. Cornea. l. Lefebvre (France) ............................................
`Probing smivity relationship in diamine oxidase — reactivities of lysine and arginine residues
`MA. Shah. S. Tayyab, R. Ali (India) .................................................................
`Solution and gel rheology of a new polysaccharide excreted by the bacterium Alteration: rp. strain I6“
`L. Bout. M. Milan. M. Rinaudo (France) .............................................................
`Dependence of the content of unsubstituted (cellulosic) rep'ons in prehydrolysed xanthans on the rate of hydrolysis
`by hid-ohm mad endoglucanase
`B.E. Christensen, 0. Smidsrod (Norway) ..............................................................
`Molecular dynamics simulations of hybrid and complex type oliaosaccharides
`P.V. Balaji. P.K. Qasba. V.S.R. Rae (USA) ...........................................................
`Single crystals of V arnylose compleaed with glycerol
`SHD. Hulleman, W. Helbert. H. Chanzy (The Netherlands; France) .....................................
`Muscle contraction: the step-sine distance and the impulse-time per ATP
`CR. Worthington. G.F. Elliott (USA; UK) ...........................................................
`Rapid size distribution and purity analysis of gastric mucus flycoproteins by site exclusion chromatography/mum angle
`laser light scattering
`It. Jumel. l. Frebrig. S.E. Hardin; (UK; USA) .........................................................
`FGF protection and inhibition of human neutrophil elastase by carboxymethyl benzylamide sulfonate destrsn
`derivatives
`A. Meddahi. H. landhbar. J.~P. Camelle. D.:Barritnult, W. Homebeck (France) ..........................
`Lymphocyte activation etfect of (I—6)-2.5-anhydro.D-3lucitol and it derivatives with 3.44i-0-methyl and sulfate
`WP!
`T. Kakuchi. S. Umeda. T. Satoh. K. Yokota. T. Yuhta. A. Kikuchi. S. Murahayashi (Japan) ...............
`
`Short mun-nicotine
`Utilization of DNA as functional materials: preparation of filters containing DNA insoluhilind with alginic add pl
`K. lwata. T. Sawadaishi. S.~l. Nishimura. S. Tokura. N. Nishi (Japan) ...................................
`
`@ The paper used in this publication meets the requirements of ANSI/N150 23918-1992 (Permanence of Paper)
`
`
`
`0151-8130(199602)1B:1l2:1-8
`
`Page 3 of 11
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`l—e
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`5-8
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`9-”
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`19—26
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`27-3l
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`33-39
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`“-53
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`55-60
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`6l-68
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`69-75
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`77—8]
`
`83-9!
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`93—99
`
`IOI-IM
`
`llS-IZZ
`
`123-l3l
`
`03-139
`
`MI—MS
`
`M7448
`
`l49-l50
`
`0504.
`
`

`

`'l
`
`;'
`
`18 (I996) 61-68
`
`
`
`'3"."'l"“".“'“l"
`unannounced-m
`
`
`. lntemational Journal of Biological Macromolecules
`
`
`sity of bovine serum albumin aqueous solutions as a function of
`temperature and concentration
`
`K. Monkos
`
`Department of Biophysics. Silerlan Medical Academy. H. Jordana I9. “-008 Zabrze 8. Poland
`
`Received I0 March I995: revision received 30 May I995: accepted 2 June I995
`
`2m presents the results of viscosity determinations on aqueous solutions of bovine serum albumin (BSA) at a wide range
`_ .
`tions and at temperatures ranging from 5°C to 45°C. On the basis of these measurements a general formula connecting
`’
`viscosity :1, with temperature T and concentration e of the dissolved proteins was established:
`
` .rr. (—m-”
`
`
`' 1 this a. B, 3. l5 and A3 are described in the text below. A simple substantiation of the formula was also given. This rela-
`
`'—
`immediately the Mooney approximation and allows the prediction of the values of' the parameter S and a self-crowding
`this approximation. By applying an asymptotic form of the formula such rheological quantities as the intrinsic viscosity
`' ., coefficient were calculated
`
`Viscosity; Bovine serum albumin: Arrhenius formula; Huggins coefficient
`
`
`
`I. all
`
`'
`
`.
`
`
`'ty of liquidsl8 highly dependent on tempera-
`for simple liquids viscosity-temperature rela-
`are quite complex This has been evidenced by
`
`number of empirical expressions for this de-
`which have appeared in the literature [1..2]
`
`forming liquids the Williams-Landel—Ferry
`
`.- . I3] is widely used, which turns out to be ap~
`
`A
`in the range from glass transition temperature
`1.. t T‘+ I00°C. At higher temperatures the
`x3"
`ependent change of viscosity is usually
`according to an equation of the Arrhenius
`
`as
`—
`
`(1)
`
`JAE. R and Tare viscosity. activation energy of
`
`.
`
`author.
`
`—\.
`I50) © I996 Elsevier Science RV, All rights reserved
`» -
`4|30(95)0|057-2
`
`
`
`ar)
`
`
`
`Page 4 of 11
`
`viscous flow. gas constant and absolute temperature,
`respectively. The pre-exponential factor A is considered
`to be independent or approximately independent of tem-
`perature. Equation (1) is still widely used for different li-
`quids [4-7]. A very convenient way of data presentation
`in this case, consists of plotting the viscosity versus 7'"
`in a log-normal plot. in relatively narrow temperature
`ranges the dependence of In 1' on I" is then linear.
`However, viscosity data when taken at a sufficiently
`wide range of' temperatures, even for such a simple liq-
`uid as water, shows that this relationship is only approx-
`imately linear. Another empirical equation that is more
`accurate over wider
`ranges of temperature is
`the
`Vogel—Fulcher's expression (discussed in detail below).
`successfully established for many liquids [8,9].
`As far as is known, very little attention has been paid
`to the analysis of the viscosity—temperature relationship
`for protein solutions. In the present study. the results of
`viscosity detemiinations on aqueous solutions of bovine
`serum albumin (BSA) at a wide range of concentrations
`
`

`

`62
`
`K. Monkm/Inrermtlaml Journal of Biological Macrmlecule: I8 ( I995) 61-68
`
` 1|.
`
`1‘.
`
`are presented. 0n the basis of these measurements an
`analysis of applicability of the Vogel—Fulcher’s expres-
`sion is conducted. Because of some faults of such an
`
`analysis. an alternative treatment — based on an equa-
`tion of the Arrhenius fonn — is proposed. As a result,
`a generalized Arrhenius formula connecting the viscos-
`ity with temperature and concentration of the dissolved
`proteins is established. The obtained formula gives. in
`the natural way. the Mooney approximation [10]. At the
`same time it allows prediction of the coefficient S and
`the self-crowding factor K, as well. in Mooney‘s for~
`mula. At low concentrations. the intrinsic viscosity and
`the Huggins coefficient from the generalized Arrhenius.
`formula are determined.
`
`LExperhentnl
`
`2.1. Materials
`
`BSA (Cohn fraction V) was purchased from Sigma
`Chemical Company and was used without further puri-
`fication. From the crystalline form the material was
`dissolved in distilled water and then filtered by means of
`filter papers in order to remove possible undissolved
`fragments. The samples were stored at 4°C until just
`prior to viscometry measurements, when they were
`warmed from 5°C to 45°C. The pH values of such pre-
`pared samples were about 5.2. i.e. in the neighbourhood
`of the isoelectric point of BSA and changed only in-
`significantly during the dilution of the solutions.
`
`2.2. Vireomerry
`Capillary viscosity measurements were conducted
`using an Ubbelohde microviscometer placed in a water-
`bath controlled thermostatically at 5°C to 45°C g
`0.05°C. The same viscometer was used for all measure-
`
`ments and was mounted so that it always occupied the
`same position in the bath. Flow times were recorded to
`within 0.1 s. Solutions were temperature-equilibrated
`and passed once through the capillary viscometer before
`any measurements were made. For most concentrations
`the viscosity measurements were made from 5°C to 45°C
`in 5°C intervals. Such a range of temperatures was
`chosen because the secondary structure of BSA is rever-
`sible only below 45°C [ll]. Beyond this temperature.
`BSA loses the reversibility of secondary structure in the
`thermal denaturation. Therefore. we will call the tem-
`perature 45°C the high temperature limit.
`Solution densities and concentrations were measured
`by weighing as described previously [12]. The viscosities
`of the BSA solutions were measured for concentrations
`
`from 17.6 kg/m’ up to 363.4 kym’.
`
`lite-alumina”
`
`3.]. VogeI-Fulcher’s function
`As was mentioned above. the viscosity—temperature
`
`Page 5 of 11
`
`
`
`
`200
`,1 zoo
` mo
`
`thg/m‘
`
`
`Fig I. Plots of the parameters 2 (x) and To (0) in the V .
`Fulcher's function versus concentration; the curves show the fit
`‘
`cording to expressions (3) and (4). respectively.
`
`relationship over a broad temperature range can '
`described by the Vogel-Fulcher‘s expression:
`
`Z
`
`"
`
`=Wex
`
`”(T-T.)
`
`
`where W. Z and T0 are parameters. As it has ap-
`, «-
`
`the function may well lit the results of the vi
`- w
`measurements for BSA aqueous solutions in the w ..
`"
`
`range of concentrations. However. the adjustable - v
`
`ameters W. Z and To appeared to be dependent on w'
`centration and, for each fixed concentration. had to -
`calculated separately. The calculations were made
`..
`
`v
`applying a non-linear regression procedure in the
`-
`".-
`
`putational program STATGRAPHICS (version 5.0
`The results are shown in Figs.
`1 and 2. As we can .5
`each parameter depends on concentration in a diffe M ‘
`
`
`
`
`
`
`
`
`100
`
`:00
`
`100
`
`e‘aym’]
`
`Fig. 2. Plot of the parameter Win the Vogel-Fulcher's function
`concentration in a log-normal plot; a straight line shows the fit -
`ing to relation (5).
`
`

`

`
`
`K. Monitor/International Jana-nu! of Brblogital Macromolecules I8 (I995) 61-68
`
`63
`
`3.2. Generalization of the Arrhenius formula
`The results of the viscosity measurements for BSA
`aqueous solutions have shown that the plot of ln a) ver-
`sus I". for each fixed concentration. is not linear (see
`Fig. 3). This is especially seen in the case of higher con-
`centrations. To establish an exact relationship between
`’1 and T. for a fixed concentration, the viscosity for the
`concentration c = 291 kglm3 was measured at temp-
`eratures ranging from 5°C to 45°C in 2°C intervals.
`Then. it was assumed that: (i) relation of the type In
`1) = In F + GIT is fulfilled, and (ii) the quantities F and
`G are quasi-constant between temperature I and t + 2°C
`(i.e. between 5°C and 7°C, 7°C and 9°C and so on). The
`obtained values of In F and 6 were considered to be
`
`exact in the middle of each temperature range (i.e. for
`6°C. 8°C and so on). As has appeared, both in F and G
`are linear functions of temperature: -In F = 6. - le
`and G = 6; — 727‘, where 6,. 7., 62 and 71 are constants.
`Finally, the viscosity of a solution. for each fixed con-
`centration, could be written in the following way:
` AE
`RT)
`'
`
`n
`
`=
`
`exp(
`
`—B+DT+
`
`6
`
`()
`
`where B: 6. + 72. D = 'y. and A5, = R62.
`The above formula is identical to the Arrhenius rela-
`
`if the pre—exponential factor A = exp(-B 4»
`tion (1),
`OT). The calculation of numerical values of the coeffi-
`cients B, D and AE. by using the method described
`above is troublesome. This method was used only for
`the determination of the exact relation between viscosity
`and temperature (equation (6)). Numerical values of the
`coefficients B, D and A5, for all measured concentra-
`tions were calculated by applying a method described in
`the Appendix. The results are presented in Figs. 4 and
`5. As seen in Fig. 6 a curve obtained by using the rela-
`tion (6) gives a perfect fit to the experimental points over
`the whole range of temperatures. [t is also worth noting
`that the experimental values of water viscosity (when
`given in centipoise) agree very well with these calculated
`on the basis of relation (6) when 8 = B. = 25.94,
`D = D. = 0.02 K" and Ali} = A5. = 32.01 kJ/mol.
`Fig. 4 shows that the activation energy of viscous flow
`of solution AB, is a monotonically increasing function
`of concentration. How can one explain this fact? In a
`streamline flow of a solution molecules of both water
`and dissolved proteins take part. Therefore, the activa-
`tion energy AE, should be a superposition of the activa-
`tion energy of water AE,, and protein AE, molecules.
`80, it is quite natural to assume, that:
`
`as, = x,,n1:F + ma.
`
`(7)
`
`where XI: and X. are molar fractions of the dissolved
`proteins and water. respectively. The molar fractions are
`defined as follows:
`
`_‘
`.'
`
`: melons, which give the best fit to the data in
`.
`. 2 are as follows:
`
`,
`
`. + «302
`
`(3)
`
`‘ 558.9K, (1222.78 Km’kg" and a3 = 5.19 x
`.
`: 'h‘2
`
`
`
`
`
`L.
`139.9K, b2 = 0.48 Km’kg" and b, = 7.04
`
`1; in“ ks‘z-
`
`. ‘t + ‘12")
`
`-
`3.71 and d2 = 1.36 x 10'2 m3 kg“l and W
`" centipoise. It is obvious that the parameters
`
`d. define the viscosity of water.
`Fulcher’s expression (2) in conjunction
`
`my. .
`. (3). (4) and (5) gives a complete descrip—
`'-
`'
`viscosity as a function of temperature and
`
`-
`in for our samples. However,
`the sch-e
`. above has several faults: (i) none of the par-
`
`“ " Impression (2) has a clear physical meaning,
`tto explain the concentration dependence
`,
`m ers Z. To and Wand (iii) it is necessary
`
`[5;
`five numerical constants (a2, a3, b1. b3. d2)
`"7
`the viscosity as a function of temperature
`
`tration for a given protein. Taking this into
`u, an alternative treatment of the problem
`7 , proposed below.
`
`(4)
`
`(5)
`
`1.." $1“ — [1302
`
`v
`
`
`
`/
`
`,1x
`
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`
`(I
`
`/
`
`[I
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`I/
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`/
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`p/V’;
`
`si
`
`.-//I
`s:
`
`so
`I:
`r"-re’[x“]
`
`as
`
`as
`
`turedependenceofthevireosiiyofBSAsqueoussolu-
`_:- ..
`y commune c: 29! kg/m’ in a log—normal plot. (0)
`S
`points; straight lines show different slopes at dilferent
`
`
`
`Page 6 of 11
`
`

`

`
`
`
`
`K Monitor/International Journal of Biological Macromolecules 18 { I995) ("-68
`
`(up-Amman.
`
`c
`
`a-Bc
`
`AE,=
`
`8
`H
`
`N
`,":—L X =
`" prvw
`"
`
`
`N
`w
`1v,,+1vw
`
`where
`
`a3pwfl
`M,
`
`and
`
`fl=av-l
`
`The molecular weight of hydrated BSA is
`.‘
`a.m.u.
`[13]. So,
`in this case or = 3.667 x 106
`Relation (12) shows how the activation energy of a .~
`tion depends on concentration. In the relation the ‘-
`
`.
`
`.
`
`
`
`
`
`vation energy of dissolved proteins M, and _
`effective specific volume of a protein v must be
`
`‘
`into account as two adjustable parameters. As
`Fig. 4 relation (12) gives good approximation to
`
`= 5.374 x 105 kJ/mol
`experimental values for
`=1.417 x 10-3 m3/kg.
`In Fig. 5 the experimental values of the coeffi '
`«
`
`~
`and D from equation (6) are shown. As is seen,
`pend on concentration exactly in the same way as.
`
`it suggests that the reasoning presented above for
`
`can be repeated in this case, too. Therefore. one > _
`.
`tain the following relations:
`C
`”=a-ac"v‘”"”'
`and
`
`
`
`
`
`
`
`D:
`
`
`-
`c
`«1-3ch D.)+D.,
`
`where v, 8, and v, D, are adjustable parameters. ‘.
`above relations give a good fit
`to the expeno-g
`values when 39:3.891 x 105, D,=s43.s x" N
`
`
`
`Fig. 5. Plot: oftbeeoeflicientsfiflhnd D(x)versusconeen "
`Experimental points are obtained by using relations (A2) and
`respectively; the curves show the lit according to equation 0 .
`(l6). respectively.
`
`
`
`where N, and N. denotes mole numbers of the dissolv-
`ed proteins and water, respectively. The mole numbers
`N,= nip/Mp and N, = WM." where m, and m“, are
`masses of the dissolved proteins and water in a solution,
`respectively. and M, and M, denote their molecular
`masses. A simple calculation shows that the molar frac-
`tion of the dissolved proteins can be rewritten in the
`form:
`
`C
`
`Xp = ———
`c+(p—c)flp-
`Mw
`
`(9)
`
`where c and p denote the solute concentration and solu-
`tion density in kglmJ, respectively.
`The solution density can be expressed in the form:
`
`n = p. + d1 - Why)
`
`(‘0)
`
`where p., and v are the water density and the effective
`specific volume of a protein, respectively. The insertion
`of equation (l0) into equation (9) yields:
`C
`
`x,=~— (u)
`M
`M
`_L_
`——Lv—l
`
`"'Mw ‘(P' Mw
`
`)
`
`fraction of water X. = l — Xv
`Because the molar
`therefore the substitution of equation (1 1) into equation
`(7) gives the final form of the activation energy of a
`solution:
`
`150
`
` 0
`
`300
`
`I00
`
`$00
`
`300
`
`C[ltg;n’]
`
`Fig. 4. Plot of the solution activation energy AliI versus concentra-
`tion. (0) experimental points are obtained by using equation (M); the
`curve shows the m according to relation (:2) with a=3.667 x lo‘
`kglm’. v = Ml? x 10-3 mJlkg, A3,, = 32.01 U/mol and as,
`= 5.314 x :05 Ulmol.
`
`Page 7 of 11
`
`

`

`K. Mankos/ International Journal of Biological Macromolecules [8 (I995) 6I-68
`
`65
`
`a10”“ mslkg (Fig. 5). The insertion of equa-
`,' .. and (16) into formula (6) yields the follow-
`fisr relative viscosity of a solution:
`
`
`
`-,
`1"[a-Bc (-B+DT+ RT)]
`
`.
`
`_.B,+D,,T+ RT)
`
`
`3.3. Mooney's approximation
`Despite substantial efforts [15], a useful theory for the
`viscosity of moderately concentrated and concentrated
`solutions does not yet exist. Much effort has therefore
`been devoted to a search for empirical
`functional
`representations incorporating a wide concentration
`range ([l6] and references therein). However. as has
`been shown in our earlier work [l7]. in the ease of aque-
`ous solutions of globular proteins the most useful func-
`tional
`form describing the dependence of relative
`viscosity on concentration is that of Mooney [10].
`
`
`SQ
`
`n.=exp[ :- m]
`
`(I9)
`
`where Q 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 fraction I. = NAth/M where
`NA, V1, and M are Avogadro’s number,
`the hydro-
`dynamic volume of one dissolved particle and the mo-
`lecular weight, respectively. In his original work [IO],
`the author obtained equation (19) for hard spherical
`particles for which S = 2.5, so that. in the limit ¢~0, the
`equation yields the expression developed by Einstein:
`1;, = l + 2.56. In the ease of particles of arbitrary
`shape, S should exceed 2.5.
`Surprisingly enough, the Mooney relationship may be
`obtained in the natural way from the generalind Ar-
`rhenius formula (17). To do it, let us insert expressions
`(l3) and (14) into equation (17). Alter simple transfor-
`mations formula (17) can be rewritten in the form:
`
`
`
`M“
`
`(-§+15T+£)6RT
`
`Per-NA Vii
`n. = exp -—— (20)
`
`
`1- (v— M“ ) —ML0
`
`PWMP
`
`NAVh
`
`This relation is identical with Mooney's formula (19), if
`the parameter
`
`
`M
`
`PwNAVh (
`“
`
`S =
`
`-
`
`AE
`
`RT
`- B + 5T + —)
`
`and the self-crowding factor
`
`K: v-
`(
`
`
`M
`
`M
`
`" ) —L
`PuMp
`NAVh
`
`(
`
`2|)
`
`(22)
`
`As is seen, both coefficients can be calculated when
`the hydrodynamic volume of the dissolved proteins is
`known. BSA molecules in aqueous solutions can be
`treated as prolate ellipsoids of revolution with the main
`
`
`.
`
`-- a:
`
`‘- viscosity of water:
`
`—
`
`(17)
`
`(
`
`l8
`
`)
`
`
`
`»'
`
`}‘B,,,15=D,,-Dw and AE=AEp—AEW.
`'7) shows how relative viscosity of a solu-
`'-‘ on temperature and protein concentration.
`
`"
`---
`ers B D and A5,, are universal.
`
`,
`,
`. .. ity depends only on four parameters
`
`5' and v and these parameters have to be
`
`3
`. each type of dissolved protein At least
`
`'5 ' w »- parameters (AE and v) have some
`
`An activation energy AE can be inter-
`the frame of applications of the absolute
`
`,fie process offlow [I]. In this theory AE
`
`‘ the activation energy for the jump of a
`
`one equilibrium position in the liquid to
`
`-
`. u in the values of activation energy
`= 32.01 kJ/mol) and BSA (Al?p =
`ml) reflect the differences in molecular
`
`-u ions of these molecules. In the ab-
`guide to the appropriate choice of
`
`..
`'
`.
`size in solution, it is commonly
`
`L.‘ the effective molar volumeis proportional
`
`of a macrosolute; the constant of pro-
`
`i a
`- - to as the effective specific volume
`
`
`
`so
`
`‘5
`
`tl"c]
`
`ts
`
`
`'
`dependence of the viscosity of BSA aqueous solu-
`
`.
`-
`c = 335.6 Its/ml. (0) Experimental points;
`a: obtained by using equation (6) with a: 92.”.
`" ‘5. 8 ”4.23 Ulmol.
`
`
`
`Page 8 of 11
`
`

`

`66
`
`K. Monkm/lntemtloml Journal of Biological Macromoleades [8 (I995) 61-68
`
`
`
`
`
`curve, so that linear extrapolation gives a serious .;
`in [n] and k..
`
`The problem can he treated in another way
`
`to the second-order term. an expansion identical to 5'.
`in equation (23) can be obtained from:
`'
`
`[n]-— (5+15T+%)
`
`k|=%
`
`~ +1
`—§+D'T+A£-
`RT
`
`l
`k2=?
`
`6‘32
`
`Ag 2
`n)
`-§+IST+—
`
`(
`
`6H
`
`+
`
`A]?
`-§+DT+—
`RT
`
`«H
`
`5.!
`
`5]
`
`3.3
`
`L0
`
`15
`
`[PC]
`
`30
`
`‘5
`
`Fig 7. The parameter S. p'ven by equation (2| ), as a function of tern-
`penture.
`
`axes a = 14.1 nm and b =4.l am [13.18]. It gives the
`hydrodynamic volume of BSA Vh = 1.241 x 10-” m3.
`Takeda et al.
`[ll] have shown, on the basis of
`measurements of fluorescence anisotropy of labeled
`BSA. that the protein volume remains almost unchang-
`ed up to 45°C. In that case the expression (2]) indicates
`that the parameter S depends on temperature. in Fig. 7
`numerical values of the factor S, obtained from relation
`(21), are presented.
`The self-crowding factor K (equation (22)), in turn,
`appears to be independent of temperature. Substitution
`of the hydrodynamic volume Vb = 1.241 x 10'” in3
`in to relation (22) gives the numerical value K = 1.25. It
`is worth noting that in his original work [10] Mooney
`showed, on the basis of purely geometric arguments,
`that for rigid spherical particles values of K should lie
`between 1.35 and 1.91.
`
`3.4. Intrinsic viscosity and the Huggins coefficient
`At low concentrations, the relation between the solu-
`tion viscosity and the concentration may be expressed
`by the polynominal [l9]:
`
`1;; = in] + kilnl’c + kzlnl3cz + .
`where
`
`.
`
`.
`
`(23)
`
`[’l] = gig} tin/c
`
`is the intrinsic vimsity, 11,, = n, - l is the specific vis-
`cosity and the dimensionless parameter k. is the Hug-
`gins coefficient. The simplest procedure for treating
`viscosity data consists of plotting the inplc against con-
`centration, extrapolating it to the intercept (equal to [11])
`and obtaining the coefficient k, from the corresponding
`slope. However. as was pointed out [19] even if 11,, <
`0.7,
`the concentration dependence of rpm/c forms a
`
`Page 9 of 11
`
`So. both intrinsic viscosity and the coefficient of‘ v;
`pansion kl
`and k1 depend on temperature.
`numerical values of [n] and k. for BSA are presen ..
`Fig. 8. Itis interesting that the value of the Huggins"
`efficient k.
`in the high temperature limit (k,—- 0. ~>
`agrees very well with the precise result obtained 5
`Freed and Edwards [2!]. The authors calculated '.
`Huggins coefficient for the Gaussian random coil
`g.
`and obtained a value k. = 0.7574. There are no th
`ical estimations of the second coefficient k; in equa a
`
`'
`
`
`
`
`
`
`CI
`
`[4
`
`h].1o’[m’;trg]
`
`u-h
`
`ti'cl
`
`Fig. 8. The intrinsic viwosity [1p] and the Huggins coefficient In. L'
`by equations (24) and (25). respectively. as a function of tempera!
`
`
`
`
`
`

`

`K. Markos/International Journal of Blaloglcal Macromolecules 18 (1995) 61—68
`
`67
`
`, relations (25) and (26) show that k;
`‘ with the Huggins coefficient k. in a very
`
`
`
`12
`
`27
`()
`
`asymptotic form of the generalized Arrhenius formula
`for small concentrations, the intrinsic viscosity and the
`Huggins coefficient may be calculated. Both quantities
`depend on temperature and the Huggins coefficient, in
`the high temperature limit, agrees well with the theoreti-
`cal values obtained for the Gaussian random coil chain.
`The Huggins coefficient k. and the second coefficient of
`expansion k; are connected by relation (27), which
`seems to have quite a general form.
`
`Appendix
`
`To find the coefficients 8, D and A5, in equation (6),
`for a given concentration, we have minimized the square
`form:
`
`l
`
`_
`
`x— §(
`
`
`
`
`“I 2
`
`. RT)
`
`(An
`
`where z; = ln m, with respect to B. D and AL}. A simple
`calculation shows that:
`
`
`(“".>:3
`
`I' l
`
`7"
`
`E 2,)In
`
`I: I
`
`(A2)
`
`(A3)
`
`(A4)
`
`Putting the experimental values of 1" for a given con-
`centration, into relations (A2), (A3) and (A4) we have
`obtained numerical values of B, D and AB, which are
`presented in Figs. 4 and 5.
`
`
`f. . of temperature. Exactly the same relation
`M Mama and Remik [22] on the basis of
`
`with polystyrene and poly(methylmeth-
`'
`,‘md quite recently for some mammalian
`
`‘.. by Monkos [20]. This suggests that rela-
`
`‘
`quite a general character and is correct for
`
`r ofmolecules. Consequently, any property
`
`= which determines the magnitude of kl will
`
`.7 t the magnitude of k2. This conclusion is
`. u; it provides a test for any theoretical treat-
`=1:
`.
`solution viscosity.
`
`
`
`
`'ty of BSA solutions at temperatures up to
`‘3 a wide range of concentrations at pH values
`
`,, w 'c point may be quantitatively describ-
`. a <
`'zed Arrhenius formula (17). This for-
`
`
`
`
`i r, — n2)?
`
`
`:iifactor K. This transformation shows that K
`
`‘be transformed into Mooney‘s relation and
`calculation of the parameter S and a self—
`
`
`
`
`depend on temperature. On the basis of the
`
`’Page 10 of 11
`
`

`

`K. Mankaxflmemflml Journal of fialagi'ca!‘ Mac-mama's: J8 ( £995) 6J-68
`
`
`
`
`
`
`
`
`
`
`
`
`
`68
`
`
`Reta-ems
`
`
`
`
`
`[I] Fox. T.G.. Gralch. S. and Loshaek. S. In: Rheology. Vol. 1.
`
`
`
`
`
`
`
`
`
`
`
`(ER. Ein'ch. ed.). Academic Press. New York.
`I956. pp.
`
`
`
`
`
`
`
`
`AMT—45?.
`
`[2] Tanner, R.I. 111: Engineering Rheology, Clarendon Press. 0):-
`
`
`
`
`
`
`
`
`l‘ord. Revised edn. I988, pp. 348—352.
`
`
`
`
`
`
`[3] Perry. J.D. In: Viseoelastic properties of polymers. Wiley. New
`
`
`
`
`
`
`
`
`
`York. 1980.
`
`
`[4] Hayakawa, E.. Furuya. K.. Kuroda. T.. Moriyarna, M. and
`
`
`
`
`
`
`
`
`
`Rondo. A. Chm. Phil-m. MI. I99I; 39: 1282.
`
`
`
`
`
`
`
`
`[5} Fania. G.F.. Dimzis. F.R.. Bugle}. EB. and Christianson. D.D.
`
`
`
`
`
`
`
`
`
`Carbohyé. Palm. I992; I9: 253.
`
`
`
`
`
`[6] Bourrel. E... Ratsimbanfy. V.. Maury. L. and Brossani, C. J.
`
`
`
`
`
`
`
`
`
`
`PM. PM!. I994; 46: 53B.
`
`
`
`
`
`[7] Silva. LA.L.. Gonulves. MJ’. and Rao. MA. Carbohydr.
`
`
`
`
`
`
`
`
`
`Palm. 1994: 23: T7.
`
`
`
`
`[8] Chen. 11.5. In: Glass: Science and Technology (D.R. Uhlmann
`
`
`
`
`
`
`
`
`
`and NJ. Kreide. edsJ. Academic Press. New York. I936. PP.
`
`
`
`
`
`
`
`
`
`189.
`
`
`
`
`
`
`
`
`
`
`
`
`
`-
`
`:
`
`[9]
`
`
`[10]
`
`{Ill
`
`
`[12]
`
`
`113]
`
`{14]
`
`
`[15]
`
`[l6]
`
`[17]
`
`[18]
`
`
`119]
`
`
`[20]
`
`[21]
`
`[22]
`
`
`
`
`-
`
`--
`
`
`
`
`
`
`
`
`
`
`Bondi. A. In: Rheology. Vol. 4 (F.R. Ein'ch. ed.),
`
`
`
`
`
`
`
`
`
`Pleas. New York. 196?. pp. 56.
`
`
`
`
`
`
`Mooney. ”J. Colloid Sci. I951; 6: I62.
`
`
`
`
`
`
`
`Takeda, K.. Yoshidn, I. and Yamamoto. K. J. Prom» w;
`
`
`
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`
`
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`
`1991; I0:
`IT.
`
`
`
`Monkoe. K. and Turczynslti. B. Int. J. Biol. Mocmnwa'. 199];
`
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`
`.Ir. Adv. Prat. Chem. [985: 3?: I61.
`Peters, T.
`
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`aimed. Sim“. 1993: 22: 27.
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`:7
`Endre, 2.11. and Kmhel. P.W. Biophys. Chem. I986: 24:
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`
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`
`
`
`
`