mm 16 Number 1 1994
`
`N'TERNATIONAL JOURNAL OF
`
`$TRUCTURE, FUNCTION AND INTERACTIONS
`
`Biological
`Macromolecules
`
`
`
`utterworth—l—l cin cman n
`
`Page 1 of 7
`
`CSL EXHIBIT 1049
`
`Page 1 of 7
`
`CSL EXHIBIT 1049
`
`

`

`February 1994
`Volume 16 Number 1
`lJBMDR 16(1)
`1—56 (1994)
`ISSN 0141—8130
`
`INTERNATIONAL JOURNAL OF
`
`Biological
`Macromolecules
`
`
`
`STRUCTURE, FUNCTION AND INTERACTIONS
`
`Close mutual contacts of the amino groups in DNA
`J. Spaner and J. Kypr
`Onset of the fully extended conformation in (mMe)Leu derivatives and
`short peptides
`C. Tonia/a. M. Pantano. F. Formaggio, M. Crisma, G. M. Banora, A. Aubry,
`D. Bayou], A. Dautant. W. H. J. Baesten, H. E. Schoemaker andJ. Kamphuis
`
`A study of enzymic degradation of a macromolecular substrate, poly[llP-(2-
`hydroxyethyl)-L-glutamine], by gel permeation chromatography and kinetic
`modelling
`J. Pyle/a, J. Jakes‘ and F. Rypadek
`
`Heparin binding to monodispersa plasma fibronectin induces aggregation
`without large-scale changes in conformation in solution
`L. Vui/Iard, D. J. S. Hu/mes, I. F. Purdom and A. Miller
`
`3 7
`
`3
`
`Collagen organization in an oriented fibrous capsule
`B. Bradsky and J. A. M. Ramshaw
`
`Viscometric study of human, bovine, equine and ovine haemoglobin in
`aqueous solution
`K. Mon/res
`
`Limited proteolysis of [Hactoglobulin using thermolysin. Effects of calcium
`on the outcome of proteolysis
`E. Dufour, M. Dalga/arrando and T. Haert/é
`
`Enzymatic degradation of chitins and partially deacetylated chitins
`Y. Shigemasa, K. Saita, H. Sashiwa and H. Saimota
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`Int. J. Biol Macromol. 1994 Volume 16 Number 1
`
`l
`
`Page 2 of 7
`
`Page 2 of 7
`
`

`

`Viscometric study of human, bovine,
`equine and ovine haemoglobin in
`aqueous solution
`
`K. Monkos
`Department of Biophysics, Silesian Medical Academy, H. Jordana 1.9, 47-808 Zebrze 8,
`Poland
`
`Received 28 June 7993: revised 28 September 1993
`
`This paper presents the results of viscosity determinations on aqueous solutions of several
`mammalian haemoglobins at an extremely wide range of concentrations. Rheological
`quantities such as the intrinsic viscosity and Huggins coefficient were calculated on the
`basis of the modified Mooney's formula. Using the dimensionless parameter c[i1], the
`existence of three characteristic ranges of concentrations was shown. By applying Lefebvre's
`iormula for the relative viscosity in the semi~dilute regime, the Mark—Houvink exponent was
`evaluated.
`
`Keywords: viscosity; Huggins coefficient; Mark-Houvink exponent
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`‘
`
`
`
`- 'c measurements. as a convenient experimental
`,
`still extensively used in many investigations of
`
`'
`ctic polymers and biological macromolecules
`
`fin n'n"". In biological systems. proteins (when
`l as solutions) are found in most cases at rather
`
`wcentrations. This is especially the case for
`
`, ”bin (Hb). which is present in erythrocytes at
`- —nely high concentration of 5.4 mmol 1‘1
`IL. Our knowledge of the properties of proteins in
`
`ted solutions is still
`limited. and one of the
`for this is that the choice of methods available
`
`' allows the study of molecular sizes and shapes
`
`',
`‘ asinteractions of proteins in concentrated media.
`‘
`i
`' measurements alone, or in conjunction with
`
`hods such as dielectric or electron paramagnetic
`.
`- spectroscopy, have been used in investigations
`
`,
`z
`. haemoglobin in solutions°' ”. However. as far
`
`'.. know, very little attention has been paid to the
`. 'c study of other mammalian haemoglobins.
`
`' "present work. we report results on the viscosity
`1‘
`tions of human. bovine. equine and ovine
`bin over a large range of concentrations
`
`.
`1 from the dilute regime to concentrations higher
`,
`physiological conditions. The dependence of
`
`7_ v on concentration in terms of the modified
`7 '5 equation is discussed. The Huggins coefficient
`exponent of the Mark— Houvink equation were
`
`
`
`. . blood was obtained from healthy, haemato-
`
`
`
`
`
`. } [94/010031—05
`'
`I
`4— orth-Heinemann Limited
`
`Page 3 of 7
`
`logically normal adult volunteers via venepuncture into
`heparin. Bovine. equine and ovine blood samples
`were taken in the same way. The fresh erythrocytes
`were washed several
`times with 0.9% NaCl solution.
`Membrane-free Hb solutions were prepared by haemolysis
`with water, followed by high-speed centrifugation. The
`pH values of such prepared samples were as follows:
`human Hb, pH 7; bovine Hb, pH 7.3; ovine Hb, pH 7.4;
`equine Hb, pH 7.7. These values changed insignificantly
`during the dilution of the solutions. The samples were
`stored at 4°C until just prior to viscometry measurements,
`when they were warmed to 25“C.
`
`Viscometry
`Capillary viscosity measurements were conducted
`using an Ubbelohde microviscometer placed in a
`waterbath controlled thermostatically at 25 j: 0. l “C. The
`same viscometer was used for all measurements and was
`mounted so that it always occupied precisely the same
`position in the bath. Flow times were recorded to within
`in 5. Solutions were temperature-equilibrated and passed
`once through the capillary viscometer before any
`measurements were made. Five to ten flow-time
`measurements were made on each concentration. The
`relative viscosity '1, was measured, where r], = "Mo and
`i1 and no are the viscosities of the solution and the solvent,
`respectively.
`Solution densities and haemoglobin concentrations
`were measured by weighing, as described previously7.
`The relative viscosities of the haemoglobin solutions were
`measured for concentrations from several gl'l up to
`~525gl'1 for human Hb. ~500gl'l for equine Hb
`and ovine Hb, and «490 g l'1 for bovine Hb. The results
`are shown in Figure I.
`
`Int J. Biol. MacromoL. 1994 Volume 16 Number I
`
`31
`
`

`

`Viscomem‘c study of mammalian haemoglobins: K. Monkos
`
`'70
`
`60
`
`50
`
`10
`
`4o
`
`30
`
`20
`
`100
`
`200
`
`300
`cEg/l]
`Plot of the relative viscosity :1, versus concentration c for
`Fig-c l
`human (at. ovine (n). equine t.) and bovine haemoglobin (A); the
`curves show the lit obtained by using equation (3) with parameters .4
`and B from Table I
`
`4 00
`
`$00
`
`Results and discussion
`
`Mconey's approximation
`Despite substantial efforts”, a useful theory for the
`viscosity of moderately concentrated and concentrated
`solutions does not yet exist. Much efl'ort has therefore
`been devoted to a search for empirical
`functional
`representations
`incorporating a wide concentration
`range”“°. However. as has been shown in our earlier
`work“. in the case of aqueous solutions of globular
`proteins. the most useful functional form describing the
`dependence of relative viscosity on concentration is that
`of Mooney":
`
`S
`
`n,=exp[l_4;<¢]
`
`(H
`
`where o is the volume fraction of the dissolved particles.
`S denotes the shape parameter and K is a self-crowding
`factor. The volume fraction d) = NA Vc/M where NA, V
`and M are Avogadro's number.
`the volume of one
`dissolved particle and the molecular weight. respectively.
`The solute concentration c is in gl". In his original
`work”. Mooney obtained equation (I) for spherical
`particles for which 8 = 2.5. so that, in the limit tit—00.
`the equation yields the expression developed by Einstein:
`7', = l + 25¢. In the case of particles of arbitrary shape.
`S should exceed 2.5.
`
`It is known that the volume of hydrodynamic particles
`may include a shell of water of hydration. Because the
`shell may change with concentration, it is difficult to
`evaluate accurately the value of d) as a function of protein
`concentration. This problem was circumvented by Ross
`and Minton’. They generalized Mooney‘s equation to
`the form:
`
`n, = exp %—
`l - E [nlc
`
`(2)
`
`32
`
`Int. J. Biol. MacromoL I994 Volume to Number I
`
`Page 4 of 7
`
`is the intrinsic viscosity and a”, = q, — l is the speci
`viscosity. There is only one adjustable parameter (K/ V‘-
`in equation (2). For
`two sets of data for hu .: .‘
`haemoglobin. the best fit of the above formula to .:_
`experimental points was obtained for K/S = 0.4 and 0.41
`However, as seen in Figure I in Ref. 9. the fit is not t .»
`best one, especially in the moderately concentrat"
`region.
`.1
`The problem can be treated in another way.
`volume fraction 4) can be rewritten as 43 = ac. whe _
`at = NAV/M, and then equation (1) takes the form:
`
`
`,=ex
`
`"
`
`AC
`p[l-Bc
`
`:|
`
`(3
`
`.
`
`where A = as and B = 01K are two adjustable parame
`and the ratio B/A = K/S. Mooney’s relation given in t
`above form has two merits: (i) it is not necessary to kno
`the intrinsic viscosity. and (ii) by fitting of the two
`parameters A and B. the equation gives good approximati - .7:
`to experimental values over the whole range ofconcent -
`tions and the ratio K/S can be obtained as we ;
`Mooney‘s equation has been fitted in this way to t .r
`experimental values
`for all haemoglobin soluti w
`investigated. As seen in Figure l, a good fit over t
`whole range of concentrations was obtained.
`'
`adjustable parameters for all samples are shown in Table
`The value of K/S = 0.432 obtained for human haemr-
`globin is in good agreement with that of Ross ean"
`Minion. However. the most interesting parameters =
`»-
`the absolute values of S and K in equation (I). So.
`.-
`indications about these parameters can be obtained '1
`the following way. As is known from crystallograp '
`studies. human haemoglobin is a spheroid with main ax ...
`64 x 55 x 50A‘9 and molecular weight 68 000. Let
`—.
`suppose that
`there is no hydration shell around I
`haemoglobin molecules. In this case. the volume fraction
`4: can be calculated for all concentrations. and equation (1 ‘7
`can be fitted to the experimental points with tw-'._
`parameters S and K. Such a procedure gives S = 3.
`"'
`and K = 1.491 for our experimental data. Tanfordz" h»
`calculated that the value of S for human haemoglobins
`should lie between 2.5 and 4.8. This allows indirect.
`calculation of the self-crowding factor K. using t ‘
`experimental values of K/S. The value of K/S =0
`-
`obtained by Ross and Minton" gives. in this case. a val
`of K in the range between 1 and 1.92. For our value of
`K/S = 0.432. K is in the range of 1.08 to 2.07. Our value!
`
`Table 1 Parameters of the haemoglobin samples obtained from I"
`fit of Mooney‘s relation to the experimental points (Figure I) and f
`‘
`equations (6) and t7)
`
`"
`
`Haemoglobin
`
`Human
`
`Bovine
`
`Equine
`
`.4 (ml 3 ' ')
`Btmlg")
`Q = §
`t.
`k,
`wt:
`
`2.77
`l.2
`0.432
`0.932
`0.786
`0.904
`
`4.37
`1.03
`0.236
`0.736
`0.458
`0.846
`
`4.22
`0.96
`0.228
`0.728
`0.447
`0343
`
`OM
`
`3.4
`1.06
`0311'
`0111'
`0.576-'
`0.374
`
`

`

`Viscomen'ic study of mammalian haemoglobins: K. Mon/ms
`
`A/
`
`k
`
`a
`
`0.7
`
`0.6
`
`i
`
`0.5 /
`
`”A
`
`[(4
`0. 8
`0.7
`0.6
`Figure 2 Correlation of coefficients k. and k2. Experimental data:
`human ‘9’” ovine t- ). equine (o) and bovine haemoglobin (A): the
`straight line is plotted according to equation (8)
`
`are given in Table I. For all investigated haemoglobins,
`kz/kf 76 1. However, as is shown in Figure 2. the plot of
`k2 versus kf is linear and the following analytical relation
`is fulfilled (with correlation coefficient 0.999):
`
`k, = k: — 0.0834
`
`(8)
`
`is worth noting that Maron and Reznik“. on
`It
`the basis of experiments with polystyrene and poly-
`(methylmethacrylate). obtained a similar relation with a
`numerical value of 0.09. This suggests that equation (8)
`has quite a general character and is correct for different
`sorts of molecules.
`
`Three ranges of concentrations and determination of the
`Mark-Houivink exponent
`The usual method of generalization of experimental
`results for different polymer systems consists of using
`reduced variables In the ease of the viscosity-concentration
`relation,
`this parameter is a dimensionless quantity
`[n]c“‘. The dependence of the specific viscosity on [n]c
`in a log—log plot exhibits classical behaviour for all our
`samples. with transitions from dilute to semi-dilute
`solution at concentration c", and from semi-dilute
`to concentrated solution at concentration c“. Such
`behaviour has been observed for cellulose derivatives“,
`citrus pectinsm and some globular proteins in random
`coil conformation". In Figure 3. the master curve for
`bovine haemoglobin is shown. The master curves have
`the same form for the other haernoglobins. The parameters
`describing the curves are shown in Table 2. The boundary
`concentrations 0‘ and c“ are nearly superimposed,
`especially for equine. bovine and ovine haemoglobins.
`In the dilute region (c[n] < c’[n]),
`the molecular
`dimension is not perturbed by the other molecules and
`the average hydrodynamic volume of the molecule is the
`same as for infinite dilution. As is seen in Table 1. the
`slopes for all investigated samples are nearly identical in
`this range. It is worth noting that the slopes in the dilute
`domain are in the range of 1.1—1.4 for quite different
`sorts of moleculesm'“z .
`As was shown by Lefebvre". in the semi-dilute region.
`the following equation for the relative viscosity is fulfilled:
`llln
`
`)
`
`— (2a - lit“[n]
`
`(9)
`
`C C
`
`“
`
`ln n, = Za[n]c'(
`
`Int. J. Biol Macromol. I994 Volume 16 Number I 3
`
`‘K lie nearly in the middle of these ranges and
`‘
`bly are very close to true values for human
`
`bin. However, such evaluation is only possible
`ofmolecules of known sizes. It is worth noting
`
`.ord", using independent measures of the
`
`-
`‘ of water of hydration. has also estimated that
`
`probable value of S in this case lies between 3.7
`4.: ..... use the ratio of K/S should not depend on the
`_‘u- water of hydration, one can use it to calculate
`
`-
`.4715 I: 0.4, it gives K in the range of 1.48 to 1.56,
`'7}. [S = 0.432. K is in the range of 1.598 to [.68.
`
`f
`.
`..
`from Table I. substantial differences exist
`.vfi ues of K/S for the investigated samples. This
`
`. :1 first difl'erent mammalian haemoglobins do not
`
`2 same shape in solution and/or that they interact
`“solvent in a somewhat difl‘erent manner.
`
`
`
`I sity and the Huggins coefficient
`concentrations,
`the relation between the
`..~ . » ity and the concentration may be expressed
`
`. ominal“:
`
`‘ ‘an + Hare + kzDIJ’C’ +
`
`(4)
`
`
`
`is the Huggins
`’x dimensionless parameter k,
`”
`The simplest procedure for treating viscosity
`'
`-: of plotting the "WI: against concentration,
`
`“
`.1
`it
`to the intercept
`(equal
`to [n]) and
`"
`_ the coefficient kl from the corresponding slope.
`
`' ms was pointed out in Ref. 16. even if 11,, < 0.7.
`tration dependence of n,,,/c is curved. so that
`
`- lation gives a serious error in [n] and k..
`- .. can be solved for solutions for which the
`
`:- of Mooney's formula are fulfilled. Mooney‘s
`
`*(l) or (3) can be expanded in the power series
`
`.
`s tion. Limiting to the second-order term. an
`, » expansion to that in equation (4) can be obtained
`
`t' K25+!)
`
`‘uS=A
`_'
`
`(5)
`
`(6)
`
`.r
`
`31
`
`K
`K2
`6— — l
`
`3( sz+6s+ )
`
`(7)
`
`.','_.¢ viscosity and the Huggins coefficient
`
`on the basis of equations (5) and (6), for all our
`
`f -
`r in samples, are shown in Table I. The results
`flx-r " ‘ calculations for rigid, non-interpenetrating
`
`.
`.
`t-Ve given a range of numerical values of k 1'
`that our
`results for equine. bovine and
`
`.
`, mi : obin are quite consistent with results of
`”no" (It, =0.76) and with the precise results
`
`2
`.v For the Gaussian random coil chain by Freed
`.- : us" (it, = 0.7574). Surprisingly enough, the
`l; Meient value for human haemoglobin is close
`
`Willie, k; = 0.894 obtained by Peterson and
`
`f
`-
`'in a model of penetrable spheres.
`.1‘ are no theoretical estimations of the second
`
`_’
`k; in equation (4). However,
`the theory“
`_, dbl. for rigid. non-interpenetrating spheres, the
`
`‘. , It} should equal 1. The values of k1 calculated
`'l- A“ of equation (7). as well as the ratios kl/k’.
`
`
`
`Page 5 of 7
`
`

`

`Viscometric study of mammalian haemoglobins: K. Mon/to:
`
`
`
`—‘l
`
`—0.
`
`5 log [11c
`Figure 3 Specific viscosity as a function of dry] in a log-log plot for
`bovute haemoglobin; straight
`lines show different slopes in dilute
`(r: < c’) and concentrated (r > c") regions
`
`O
`
`0.5
`
`where a is the Mark-Houvink exponent. Figure 4 shows
`the experimental points for bovine haemoglobin and the
`curve resulting from the fit,
`taking c‘ and a as
`adjustable parameters. The values of c‘ obtained by this
`procedure are in good agreement with the values
`determined from the master curve of Figure 3. The values
`of a (Table 2) are nearly the same, except for human
`haemoglobin. The Mark-Houvink exponent for flexible
`polymers is in the range of 0.5—l (Ref. 30). However,
`a = 0 in the case of hard spherical particles, and a = 1.7
`for hard long rods. The Mark—Houvink exponent values
`listed in Table 2 indicate that all haemoglobins studied
`here behave as hard quasi-spherical particles, in agreement
`with the model proposed for human haemoglobin by Ross
`and Minton"”'3'.
`It
`is important
`to add that
`the
`Lelebvre equation was originally applied to zero shear
`rate data In our case, for concentrations close to c“,
`
`
`
`100
`
`200
`
`300
`
`clg/ll
`
`Flgm 4 Plot of the relative viscosity versus concentration in a
`log—normal plot in a semi-dilute region. (0) experimental points for
`bovine haemoglobin; the curves show the lit obtained by using equation
`(9)
`
`34 Int. J. Biol MacromoL 1994 Volume l6 Number 1
`
`Page 6 of 7
`
`Table 2 Parameters of the haemoglobin samples obtained from ,
`fit of the curves in Figures 3 and 4 and from equation (9)
`
`Haemoglobin
`
`Human
`
`0.3
`763
`394
`0.21
`1.09
`
`1.!
`7.57
`
`Bovine
`
`0.338
`66.5
`375
`0.29
`L64
`
`I.”
`7.02
`
`Equine
`
`0.348
`64.9
`376
`0.27
`LS9
`
`l.l2
`6.47
`
`O a...
`
`0 _.‘.
`67.2
`J75
`I l:
`l
`.1:
`
`H
`6.0}
`
`a
`c‘ (g l ‘ 'l
`c“ (g l ' ‘l
`c’ [a]
`r" ['1]
`Slopes
`c<r‘
`t‘ > c“
`
`.-
`
`the shear rate was about 1005”. However. as was q '
`recently shown by Miiller et al.” for shear rates ran
`from I to 200 s‘ ', human haemoglobin solutions exhi :
`Newtonian behaviour up to a concentration of at
`w.
`.,
`450 g l‘ ‘. This indicates that application of the Lefeb ,3
`equation in our case is justified and that the Mar
`Houvink exponent has its usual meaning.
`In the concentrated region (c[n] > c”[n]), the e .... ;
`of entanglements become important. As was shown ..
`Axelos et al.’8 for citrus pectins, which are relativ .
`flexible polymers, the slope in this region is 3.4. A hi in t'
`value (about 5) was obtained by Castelain et al." for
`,
`non-rigid molecule of hydroxyethylcellulose. The val 7‘
`listed in Table 2 suggest that the highest value of slo_ ;
`in this region occurs for stiff molecules. This is
`..
`agreement with the results of Ref. 32, where the author!
`showed that the slope should be approximately 8 for s --
`I
`chained molecules. It
`is interesting to note that
`.
`second critical concentration c” for all
`investigated
`haemoglobins is only slightly higher than the concen - ..
`ol' the haemoglobin in erythrocytes, which is an
`5.4 mmoll‘l or 367gl". This may explain why
`concentration of haemoglobin in erythrocytes is not‘
`higher, i.e. the haemoglobin concentration achieves t
`highest value at which entanglements are not yet presenttv
`In other words. haemoglobin molecules in erythrocyta
`achieve the highest concentration at which they can move
`relatively freely with minimal frictional interaction.
`
`Conclusions
`
`The viscosity of mammalian haemoglobin solutions 0V6!“-
`a wide range of concentrations at pH values near tMv
`isoelectric point may be quantitatively described by th
`modified Mooney's equation (equation (3)). 0n the basil
`of Mooney's asymptotic form for small concentrations.
`the intrinsic viscosity and the Huggins coefficient may
`be calculated. The Huggins coeflicient Itl and the second
`coefiicient of expansion [(2 are connected by equation (3b
`which seems to have quite a general form. The values for
`the Mark-Houvink exponent confirm that all investigated
`haemoglobins behave as hard quasi-spherical particles-
`The values for the second critical concentration c’"
`suggest that mammalian haemoglobin concentration In
`erythrocytes achieves the optimum value. Despite the:
`similarities, substantial differences exist between specific
`especially for K/S and k1 values. This indicates that each
`mammalian haemoglobin in solution should be studifll
`in detail separately.
`
`

`

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`Page 7 of 7
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`Int. J. Biol. Macromol, 1994 Volume 16 Number 1
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`35
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`Page 7 of 7
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