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Intrinsic viscosity of bovine serum albumin conformers
International Journal of Biological Macromolecules 42 (2008) 133–137
Intrinsic viscosity of bovine serum albumin conformers Rolando Curvale a,b,∗ , Martin Masuelli a , Antonio Perez Padilla b a
´ Area de F´ısico Qu´ımica, Facultad de Qu´ımica, Bioqu´ımica y Farmacia, Universidad Nacional de San Luis, San Luis, Argentina b Instituto de Investigaciones en Tecnolog´ıa Qu´ımica, CONICET, Chacabuco 917, 5700 San Luis, Argentina Received 19 December 2006; received in revised form 5 October 2007; accepted 5 October 2007 Available online 11 October 2007
Abstract Intrinsic viscosity of bovine serum albumin (BSA) at different pH values (2.7, 4.3, 7.4, 8 and 10) has been determined, as well as the Mark–Houwink constant and expansion factor. The traditional technique for data analysis using extrapolation to obtain intrinsic viscosity values shows an unusual behavior regarding concentration that can be observed in the values obtained for Huggins’ and Kraemer’s constants. © 2007 Elsevier B.V. All rights reserved. Keywords: Bovine serum albumin (BSA); Intrinsic viscosity; Conformers; Huggins’ constant; Kraemer’s constant; Mark–Houwink’s constant
1. Introduction Albumin is the most abundant protein in the mammal circulatory system. In blood, osmotic pressure receives an 80% contribution from albumin, which is also crucial in pH support. Its role is exerted through the transportation, metabolism and distribution of endogenous and exogenous ligands, extracellular antioxidant effect and in the free radicals protection. BSA is the most extensively studied protein [1] due to its availability, relatively low cost, stability and unusual capacity for binding to different ligands. In solution, BSA presents a versatile conformation modified by changes in pH, ionic strength, and cation presence, and that serves to characterize BSA structure, conditions and properties. Conformational change induced by pH is a reversible process [2]. Although there have been speculations on the possible function of each transition, its physiological meaning still remains in discussion. Foster [2] classified conformers as: “E” for expanded, “F” for fast migration, “N” for normal dominant form at neutral pH, “B” for basic form and “A” for aged at alkaline pH. The N–F transition implies the opening of the molecule by unfolding domain III [3,4]. The F form is characterized by increased viscosity, lower solubility and loss of ␣-Helix content
∗
Corresponding author. Tel.: +54 2652 426711; fax: +54 2652 426711. E-mail address: [email protected] (R. Curvale).
0141-8130/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ijbiomac.2007.10.007
[5] (Table 1). At pH <4, another BSA expansion generates loss of the helicoidal structure connecting domain I with domains II and III. This expanded form is known as E, and shows a new incre˚ increment in the axis ment in intrinsic viscosity and a 40–90 A of the axial hydrodynamic radium [6]. At pH 9, albumin changes conformation to B basic form. If the BSA solution is maintained at constant pH 9, low ionic strength and at 3 ◦ C during 3 or 4 days, another isomerization known as form A occurs. Viscosity of in-solution proteins depends on intrinsic protein characteristics (such as molecular mass, volume, size, shape, surface charge and deformation facility) and on ambiental factors (such as pH, temperature, ionic strength, etc.). The present work consisted on determination of intrinsic viscosity for different BSA conformers. The method of choice has been capillary viscosimetry because it is a simple and useful method that requires low cost equipment and yields useful information on soluble macromolecules. Although intrinsic viscosity is a molecular parameter that can be interpreted in terms of molecular conformation, it does not offer as high resolution on molecular structure as other methods do such as NMR, X-rays, etc. 2. Materials and methods BSA (lyophilized and deionized powder, purity grade >98%) was obtained from Fedesa S.A.-UNSL. Measurements were taken from fresh 2% BSA solutions. pH was adjusted with HCl or NaOH 1N. Solutions and dissolutions were prepared with
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R. Curvale et al. / International Journal of Biological Macromolecules 42 (2008) 133–137
Table 1 Conformational date of BSA Conformer
pH Name ␣-Helix (%)
E
F
N
B
A
2.7 Expanded 35
4.5 Fast 45
8 Normal 55
10 Basic 48
10 Aged 48
deionized water. Temperature was kept constant at 25 (±0.1) ◦ C using a LAUDA thermostatic bath. Determinations were done using an Ubbelohde “suspended level” viscosimeter (Schott Gerate), with a water draining time of 123.53 s. Even though this viscosimeter works in a solution volume independent fashion and allows dissolutions, it was here used performing at least three measurements for each concentration and was later washed until the solvent draining time was recovered. Six solutions with concentrations ranging from 0.125 to 2 g/dL BSA were measured at each pH. These solutions were previously prepared from a mother solution with a concentration determined by UV-absorbance at 278 nm with a Shimadzu UV-160A spectrophotometer. Density of each solution was measured using an Ant´on Paar DMA35N densitometer.
Fig. 1. Extraction methods for intrinsic viscosity of BSA at pH 2.71. Huggins’ method (); Kraemer’s method ().
3. Results In the literature, several mathematical equations that allow intrinsic viscosity determination by graphic extrapolation can be found. The most commonly used relations are as follows: • In Huggins’ method [7], intrinsic viscosity [η] is defined as the ratio of relative viscosity increment (ηi ) to concentration (C in g/mL) when it tends to zero: ηi (1) = [η] + KH [η]2 C C IUPAC recommends the term “increment of relative viscosity (ηi )”, instead of “specific viscosity”, because it has no attributions of specific quantity, meaning: ηi = ηr − 1 And let’s remember that: ηs ρ s ts = ηr = η0 ρ0 t0
(2)
Fig. 2. Extraction methods for intrinsic viscosity of BSA at pH 4.32. Huggins’ method (); Kraemer’s method ().
KH , KK and KSB represent Huggins’, Kraemer’s and Schulz– Blaschke’s constants, respectively, and [η] is the intrinsic viscosity with units inverted to concentration (mL/g). The obtained results are shown in Figs. 1–5. Table 2 shows the final values obtained through a numerical–computational procedure (VISFIT) that simultaneously adjusts both (Kraemer and Huggins) data series to a straight line with a common intersection [10].
(3)
where the subindex “s” indicates “solution” and “0” indicates “solvent”. • This method is equivalent to Kraemer’s [8] which relates the logarithm of relative viscosity to concentration when it tends to the limit value zero: 1 ln ηr = [η] − KK [η]2 C C
(4)
• While Schulz–Blaschke [9] relates the first term of Huggins’ equation to the increment in relative viscosity ηi (5) = [η] + KSB [η]ηi C
Fig. 3. Extraction methods for intrinsic viscosity of BSA at pH 7.4. Huggins’ method (); Kraemer’s method ().
R. Curvale et al. / International Journal of Biological Macromolecules 42 (2008) 133–137
135
Fig. 4. Extraction methods for intrinsic viscosity of BSA at pH 8.06. Huggins’ method (); Kraemer’s method (). Fig. 6. Logarithm form of Eq. (7) plotted using intrinsic viscosity data from plasmatic globular proteins [12]. BSA (Mw 66500 – [η] 4.2); -globulin (Mw 93000 – [η] 5.5); ␥-globulin (Mw 160000 – [η] 7.1); ␣-globulin (Mw 195000 – [η] 7.9) at pH 7.4 and 25 ◦ C.
globular proteins at pH 7.4 and 25 ◦ C [12] (Fig. 6). ln [η] = ln K∗ + a ln Mw
Fig. 5. Extraction methods for intrinsic viscosity of BSA at pH 9.97. Huggins’ method (); Kraemer’s method ().
The empirical Mark–Houwink equation relates intrinsic viscosity to relative molecular weight (Mw ) [11]. [η] = K∗ Mwa
(6)
where K* and a vary depending on macromolecule nature, used solvent and temperature. These are coefficients that are empirically calculated for each particular solute–solvent system using samples with known molecular weight. The logarithm form of Eq. (6) was plotted using intrinsic viscosity data from plasmatic
(7)
For these proteins, at 25 ◦ C, the calculated K* value (with [η] in mL/g) is 7.933 × 10−3 ; a = 0.58. Tanford et al. [13] inform K* = 7.16 × 10−3 and a = 0.66 for several proteins denaturalized in urea 8 M and -mercapto-ethanol 0.1 M, and which was calculated with the formula [η] = K* na being n the number of aminoacid residues. The K* coefficient is a function of solvent polarity and of intermolecular forces between the solute and the solvent [14]. The a exponent is an expansion factor that the molecule undertakes due to solvent presence. Calculated results for a are reported in Table 2. Globular proteins present lower intrinsic viscosity than do flexible polymers with comparable molecular weight. Also, intrinsic viscosity receives two molecular contributions: macromolecule volume and shape [15]: [η] = νVsp
(8)
Table 2 Physical chemistry data of BSA Conformer
pH [η] mL/g [10] [η] Eq. (5) [η] [23] KH KK KK + KH a Eq. (6) ν Eq. (10) Axial rate (a/b) ˚ [1] A ˚ 3 [1] Volume, A
E
F
Physiological
N
B
2.71 16.56 16.88 10.0 −0.148 0.517 0.37 0.69 14.87 11 Oblate 21 × 250 654500
4.32 5.72 5.99 3.93 −0.959 1.295 0.336 0.60 5.26 4.5 Prolate 40 × 129 97075
7.4 4.6 4.86 4.12 1.579 −0.935 0.644 0.58 4.27 3.5 Prolate 40 × 140 –
8.06 6.9 7.48 4.06 −1.741 2.012 0.271 0.61 6.37 5 Triangle 80 × 80 × 30 88250
9.97 6.27 6.56 4.3 −0.842 1.2 0.358 0.60 5.76 4.5 – –
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R. Curvale et al. / International Journal of Biological Macromolecules 42 (2008) 133–137
where ν, “universal function of form” [16], relates particle shape independently from volume. The ν factor is a function of the axial rate (a/b) of revolution ellipsoids; (the 2.5 minimum value corresponds to spherical particles); and Vsp is the specific volume of the macromolecule “swollen” with solvent molecules associated by H-bonds and other molecules trapped into the macromolecule’s interior (mL/g). Because Vsp is not measured experimentally, Eq. (8) converts into undetermined. In order to avoid this difficulty, partial specific volume V¯ for the anhydrate macromolecule is a common substitute for Vsp . [η] = νV¯ without solvatation
(9)
If it is assumed that hydration water and solvent water both present the same density, then in the case of hydration with δ grams of water per gram of dry protein Eq. (8) can approximate to: [η] = ν(V¯ + δV¯ 0 )
(10)
in which V¯ 0 is the partial specific volume for water. δ values ranging from 0.3 to 0.5 [17] have been obtained using NMR, IR and simulation techniques for globular proteins and without considering the influence of conformational changes. For BSA, it is accepted that δ = 0.4 g of water per protein gram and V¯ = 0.734 mL/g [18]. If Eq. (9) is rewritten in terms of volume per molecules, then: [η] =
νNVm Mw
(11)
where N is the Avogadro number and Vm is molecular volume. In addition to shape and hydratation, biomolecule electrostatic charge also affects intrinsic viscosity, which, in turn, is strongly dependent on solution pH and ionic strength. A rise in ionic strength will lower intrinsic viscosity. Early conceptions on BSA molecular shape converge to an ˚ axis [19] and an axial rate ∼3.5 oblate ellipsoid with 40 × 140 A [20]. Currently, evidence shows that the BSA molecule in solution, in a 4.5–8 pH range, is heart shaped. In solution and in crystalline state, BSA conformation is accepted as a triangular ˚ × 80 A ˚ equilateral prism with the following dimensions: 80 A ˚ and 30 A deep [20]. In acidic solution, the compact structure probably unfolds to a more expanded one that can be represented by an elongated ellipsoid. For ample and comprehensive study see Monkos [21]. The F form would have an 11% volume increase due to hydrodynamic radium change and its dimensions ˚ × 129 A ˚ [22]. The E form would undertake a new would be 40 A ˚ × 250 A ˚ approximate dimensions expansion resulting in 21 A [6]. Starting from BSA conformation N, all volume changes could be explained by ␣-Helix content loss, which would increase BSA-SH exposure to solvent. 4. Conclusions The use of the Huggins, Kraemer and Schulz–Blaschke methods for intrinsic viscosity determination (Eqs. (1), (4) and (5)) rendered results showing some difference. In particular, [η] is
an expression of the interference in-between the polymer and the solvent; and reflects the solvent’s ability to swell the macromolecule. Thus, we can see that BSA has a very low [η] value at pH 7.4 which explains the assigned globular shape. [η] triplicates its value at pH 2.7. This rise is due to hydration, shape change and charge, in addition to molecular aggregation. Williams and Foster [24] show that BSA has a strong tendency to dimerize at acid pH. The Huggins, Kraemer and Shulz–Blaschke coefficients (KH , KK and KSB , respectively) are non-dimensional and suitable for solvent quality assessment [25]. The Huggins coefficient is accepted as a parameter relating polymer–solvent interactions. It describes the resulting interaction from the point of view of existing differences between the chemical structures of solvent and macromolecule. Low KH values ranging from 0.25 to 0.5 are assigned to good solvatation, while higher values are due to poor solvents [26]. Similarly, negative KK values point to good solvents. The graphics show that, in our BSA–water system at different pH values, viscosity of dilute solutions exhibit an unusual dependence on concentration, which is reflected by negative or very high KH values and positive or negative KK values, as shows Table 2. Published literature has pointed out very few exceptional systems showing this behavior [27,28]. For example, ref. [29] shows this same behavior in a solution in which the solute is amphyphilic. The co-polymer is composed of flexible, non-polar polydimethylsyloxane blocks and polar polyurethane blocks. The relative block proportion, however, does not allow the authors to give a rational interpretation of the negative KH value. One type of protein classification is based on solubility and it is said that BSA is soluble although its water affinity is intermediate. It must be considered that solubility of general proteins is not comparable to that of polymers usually studied. BSA adopts a globular conformation with very strong internal interactions. Interaction with the solvent is through polar groups accessible at the molecular surface and that are modified by pH and salts. The high polar character in proteins generates a non-typical behavior with water; thus, in the case of BSA the dielectric constant of the solution increases 0.17 U/g. This increase is due to the rigid orientation of the bound water molecules [30]. The complexity of inter- and intra-molecular interactions present in the BSAwater system makes a simple interpretation for the KH and KK constant values rather impossible to elaborate. In theory, the sum of both constants equals to 0.5, which would indicate that the experiment renders adequate results. The results here displayed do not match this value but are similar to many other reported in the literature [25]. The Mark–Houwink Eq. (6) provides a practical and simplified method to calculate molecular weight through viscosity measurements. The K* coefficient is calculated at a determined temperature for a range of molecular weights and could be related to solvent and macromolecule polarity parameters [14]. As an approximation, we have considered that the K* value (7.933 × 10−3 ) stands constant during the runs at different pH and we have calculated the expansion factor value. Results in Table 2 show that at pH 7.4, BSA takes the shape of a random tightly coiled, proximal to the “theta” state, that untangles poorly
R. Curvale et al. / International Journal of Biological Macromolecules 42 (2008) 133–137
when pH changes. The random tightly coiled is an approximation to the shape BSA would adopt in the presence of a “good solvent” at pH 2.7. The intrinsic viscosity values here presented are higher than those obtained by Tanford and Bussell [23]. However, it must be considered that salt addition has been avoided, thus increasing electrostatic interactions among ionic groups; also, an increase in ionic strength decreases intrinsic viscosity. In the case of conformers F and E, our results better reflect the remarkable volume and shape changes that are endured by BSA. Acknowledgments We thank Fedesa S.A.-UNSL who kindly granted the bovine albumin needed for the present work and Project 2-9304. References [1] D.C. Carter, J.X. Ho, Adv. Protein Chem. 45 (1994) 153. [2] J.F. Foster, Albumin Structure. Function and Uses, Academic Press, 1977, pp. 53–84. [3] M.J. Geisow, G.H. Beaven, Biochem. J. 163 (1977) 477. [4] M.Y. Khan, Biochem. J. 236 (1986) 307. [5] J.F. Foster, J. Am. Chem. Soc. 82 (1960) 3741. [6] W.F. Harrington, P. Johnson, R.H. Ottewill, Biochem. J. 62 (1956) 569. [7] M.L. Huggins, J. Am. Chem. Soc. 64 (1942) 2716.
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[8] E.O. Kraemer, Ind. Eng. Chem. 30 (10) (1938) 1200. [9] G.V. Shulz, F.J. Blaschke, Praakt. Chem. 158 (1941) 130. [10] M.C. Lopez Martinez, F.G. D´ıaz Ba˜nos, A. Ortega Retuerta, J. Garcia de la Torre, J. Chem. Educ. 80 (2003) 1036–1038. [11] S.E. Harding, Prog. Biophys. Biol. 66 (1977) 207. [12] E.L. Hess, A. Cobure, J. Gen. Physiol. 33 (1950) 511. [13] C. Tanford, K. Kawahara, S. Lapanje, J. Am. Chem. Soc. 89 (1967) 729. [14] S. Qing, M. Di, Y. Li-Wei, C. Liang, J. Colloid Interface Sci. 30 (2004) 275. [15] J.T. Yang, Adv. Prote´ın Chem. 16 (1961) 323. [16] J. Garcia de la Torre, B. Carrasco, S.E. Harding, Eur. Biophys. J. 25 (1997) 361. [17] S.E. Harding, Biophys. Chem. 93 (2001) 87. [18] F.L. Gonzalez Flecha, V. Levi, BAMBED 31 (2003) 319–322. [19] V. Bloomfield, Biochemistry 5 (1966) 684. [20] M.L. Ferrer, R. Duchowicz, B. Carrasco, J. Garcia de la Torre, U. Acu˜na, Biophys. J. 80 (2001) 2422. [21] K. Monkos, Biochim. et Biophys. Acta 1748 (2005) 100–109. [22] G.I. Loeb, H.A. Scheraga, J. Phys. Chem. 60 (1956) 1633. [23] C. Tanford, J.G. Bussell, J. Phys. Chem. 60 (1956) 225. [24] E.J. Williams, J.F. Foster, J. Am. Chem. Soc. 82 (1960) 3741–3745. [25] M.C. Delpech, C.M. Oliveira, Polym. Test. 24 (3) (2005) 381. [26] F. Cilurzo, F. Selmin, P. Minguetti, L. Montanari, C. Lenardi, F. Orsini, G. Poletti, AAPS Pharm. Sci. Tech. (2005) E586. [27] J.Y. Olayemi, Makromol. Chem. 183 (1982) 2547. [28] M. Girolano, J. Urwin, R. Eur. Polym. J. 7 (1971) 693–698. [29] I. Yilgor, T.C. Ward, E. Yilgor, E.G. Atilla, Polymer 47 (4) (2006) 1179. [30] F. Haurowitz, The Chemistry and Function of Proteins, Academic Press, 1963.
Intrinsic viscosity of bovine serum albumin conformers Rolando Curvale a,b,∗ , Martin Masuelli a , Antonio Perez Padilla b a
´ Area de F´ısico Qu´ımica, Facultad de Qu´ımica, Bioqu´ımica y Farmacia, Universidad Nacional de San Luis, San Luis, Argentina b Instituto de Investigaciones en Tecnolog´ıa Qu´ımica, CONICET, Chacabuco 917, 5700 San Luis, Argentina Received 19 December 2006; received in revised form 5 October 2007; accepted 5 October 2007 Available online 11 October 2007
Abstract Intrinsic viscosity of bovine serum albumin (BSA) at different pH values (2.7, 4.3, 7.4, 8 and 10) has been determined, as well as the Mark–Houwink constant and expansion factor. The traditional technique for data analysis using extrapolation to obtain intrinsic viscosity values shows an unusual behavior regarding concentration that can be observed in the values obtained for Huggins’ and Kraemer’s constants. © 2007 Elsevier B.V. All rights reserved. Keywords: Bovine serum albumin (BSA); Intrinsic viscosity; Conformers; Huggins’ constant; Kraemer’s constant; Mark–Houwink’s constant
1. Introduction Albumin is the most abundant protein in the mammal circulatory system. In blood, osmotic pressure receives an 80% contribution from albumin, which is also crucial in pH support. Its role is exerted through the transportation, metabolism and distribution of endogenous and exogenous ligands, extracellular antioxidant effect and in the free radicals protection. BSA is the most extensively studied protein [1] due to its availability, relatively low cost, stability and unusual capacity for binding to different ligands. In solution, BSA presents a versatile conformation modified by changes in pH, ionic strength, and cation presence, and that serves to characterize BSA structure, conditions and properties. Conformational change induced by pH is a reversible process [2]. Although there have been speculations on the possible function of each transition, its physiological meaning still remains in discussion. Foster [2] classified conformers as: “E” for expanded, “F” for fast migration, “N” for normal dominant form at neutral pH, “B” for basic form and “A” for aged at alkaline pH. The N–F transition implies the opening of the molecule by unfolding domain III [3,4]. The F form is characterized by increased viscosity, lower solubility and loss of ␣-Helix content
∗
Corresponding author. Tel.: +54 2652 426711; fax: +54 2652 426711. E-mail address: [email protected] (R. Curvale).
0141-8130/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ijbiomac.2007.10.007
[5] (Table 1). At pH <4, another BSA expansion generates loss of the helicoidal structure connecting domain I with domains II and III. This expanded form is known as E, and shows a new incre˚ increment in the axis ment in intrinsic viscosity and a 40–90 A of the axial hydrodynamic radium [6]. At pH 9, albumin changes conformation to B basic form. If the BSA solution is maintained at constant pH 9, low ionic strength and at 3 ◦ C during 3 or 4 days, another isomerization known as form A occurs. Viscosity of in-solution proteins depends on intrinsic protein characteristics (such as molecular mass, volume, size, shape, surface charge and deformation facility) and on ambiental factors (such as pH, temperature, ionic strength, etc.). The present work consisted on determination of intrinsic viscosity for different BSA conformers. The method of choice has been capillary viscosimetry because it is a simple and useful method that requires low cost equipment and yields useful information on soluble macromolecules. Although intrinsic viscosity is a molecular parameter that can be interpreted in terms of molecular conformation, it does not offer as high resolution on molecular structure as other methods do such as NMR, X-rays, etc. 2. Materials and methods BSA (lyophilized and deionized powder, purity grade >98%) was obtained from Fedesa S.A.-UNSL. Measurements were taken from fresh 2% BSA solutions. pH was adjusted with HCl or NaOH 1N. Solutions and dissolutions were prepared with
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R. Curvale et al. / International Journal of Biological Macromolecules 42 (2008) 133–137
Table 1 Conformational date of BSA Conformer
pH Name ␣-Helix (%)
E
F
N
B
A
2.7 Expanded 35
4.5 Fast 45
8 Normal 55
10 Basic 48
10 Aged 48
deionized water. Temperature was kept constant at 25 (±0.1) ◦ C using a LAUDA thermostatic bath. Determinations were done using an Ubbelohde “suspended level” viscosimeter (Schott Gerate), with a water draining time of 123.53 s. Even though this viscosimeter works in a solution volume independent fashion and allows dissolutions, it was here used performing at least three measurements for each concentration and was later washed until the solvent draining time was recovered. Six solutions with concentrations ranging from 0.125 to 2 g/dL BSA were measured at each pH. These solutions were previously prepared from a mother solution with a concentration determined by UV-absorbance at 278 nm with a Shimadzu UV-160A spectrophotometer. Density of each solution was measured using an Ant´on Paar DMA35N densitometer.
Fig. 1. Extraction methods for intrinsic viscosity of BSA at pH 2.71. Huggins’ method (); Kraemer’s method ().
3. Results In the literature, several mathematical equations that allow intrinsic viscosity determination by graphic extrapolation can be found. The most commonly used relations are as follows: • In Huggins’ method [7], intrinsic viscosity [η] is defined as the ratio of relative viscosity increment (ηi ) to concentration (C in g/mL) when it tends to zero: ηi (1) = [η] + KH [η]2 C C IUPAC recommends the term “increment of relative viscosity (ηi )”, instead of “specific viscosity”, because it has no attributions of specific quantity, meaning: ηi = ηr − 1 And let’s remember that: ηs ρ s ts = ηr = η0 ρ0 t0
(2)
Fig. 2. Extraction methods for intrinsic viscosity of BSA at pH 4.32. Huggins’ method (); Kraemer’s method ().
KH , KK and KSB represent Huggins’, Kraemer’s and Schulz– Blaschke’s constants, respectively, and [η] is the intrinsic viscosity with units inverted to concentration (mL/g). The obtained results are shown in Figs. 1–5. Table 2 shows the final values obtained through a numerical–computational procedure (VISFIT) that simultaneously adjusts both (Kraemer and Huggins) data series to a straight line with a common intersection [10].
(3)
where the subindex “s” indicates “solution” and “0” indicates “solvent”. • This method is equivalent to Kraemer’s [8] which relates the logarithm of relative viscosity to concentration when it tends to the limit value zero: 1 ln ηr = [η] − KK [η]2 C C
(4)
• While Schulz–Blaschke [9] relates the first term of Huggins’ equation to the increment in relative viscosity ηi (5) = [η] + KSB [η]ηi C
Fig. 3. Extraction methods for intrinsic viscosity of BSA at pH 7.4. Huggins’ method (); Kraemer’s method ().
R. Curvale et al. / International Journal of Biological Macromolecules 42 (2008) 133–137
135
Fig. 4. Extraction methods for intrinsic viscosity of BSA at pH 8.06. Huggins’ method (); Kraemer’s method (). Fig. 6. Logarithm form of Eq. (7) plotted using intrinsic viscosity data from plasmatic globular proteins [12]. BSA (Mw 66500 – [η] 4.2); -globulin (Mw 93000 – [η] 5.5); ␥-globulin (Mw 160000 – [η] 7.1); ␣-globulin (Mw 195000 – [η] 7.9) at pH 7.4 and 25 ◦ C.
globular proteins at pH 7.4 and 25 ◦ C [12] (Fig. 6). ln [η] = ln K∗ + a ln Mw
Fig. 5. Extraction methods for intrinsic viscosity of BSA at pH 9.97. Huggins’ method (); Kraemer’s method ().
The empirical Mark–Houwink equation relates intrinsic viscosity to relative molecular weight (Mw ) [11]. [η] = K∗ Mwa
(6)
where K* and a vary depending on macromolecule nature, used solvent and temperature. These are coefficients that are empirically calculated for each particular solute–solvent system using samples with known molecular weight. The logarithm form of Eq. (6) was plotted using intrinsic viscosity data from plasmatic
(7)
For these proteins, at 25 ◦ C, the calculated K* value (with [η] in mL/g) is 7.933 × 10−3 ; a = 0.58. Tanford et al. [13] inform K* = 7.16 × 10−3 and a = 0.66 for several proteins denaturalized in urea 8 M and -mercapto-ethanol 0.1 M, and which was calculated with the formula [η] = K* na being n the number of aminoacid residues. The K* coefficient is a function of solvent polarity and of intermolecular forces between the solute and the solvent [14]. The a exponent is an expansion factor that the molecule undertakes due to solvent presence. Calculated results for a are reported in Table 2. Globular proteins present lower intrinsic viscosity than do flexible polymers with comparable molecular weight. Also, intrinsic viscosity receives two molecular contributions: macromolecule volume and shape [15]: [η] = νVsp
(8)
Table 2 Physical chemistry data of BSA Conformer
pH [η] mL/g [10] [η] Eq. (5) [η] [23] KH KK KK + KH a Eq. (6) ν Eq. (10) Axial rate (a/b) ˚ [1] A ˚ 3 [1] Volume, A
E
F
Physiological
N
B
2.71 16.56 16.88 10.0 −0.148 0.517 0.37 0.69 14.87 11 Oblate 21 × 250 654500
4.32 5.72 5.99 3.93 −0.959 1.295 0.336 0.60 5.26 4.5 Prolate 40 × 129 97075
7.4 4.6 4.86 4.12 1.579 −0.935 0.644 0.58 4.27 3.5 Prolate 40 × 140 –
8.06 6.9 7.48 4.06 −1.741 2.012 0.271 0.61 6.37 5 Triangle 80 × 80 × 30 88250
9.97 6.27 6.56 4.3 −0.842 1.2 0.358 0.60 5.76 4.5 – –
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R. Curvale et al. / International Journal of Biological Macromolecules 42 (2008) 133–137
where ν, “universal function of form” [16], relates particle shape independently from volume. The ν factor is a function of the axial rate (a/b) of revolution ellipsoids; (the 2.5 minimum value corresponds to spherical particles); and Vsp is the specific volume of the macromolecule “swollen” with solvent molecules associated by H-bonds and other molecules trapped into the macromolecule’s interior (mL/g). Because Vsp is not measured experimentally, Eq. (8) converts into undetermined. In order to avoid this difficulty, partial specific volume V¯ for the anhydrate macromolecule is a common substitute for Vsp . [η] = νV¯ without solvatation
(9)
If it is assumed that hydration water and solvent water both present the same density, then in the case of hydration with δ grams of water per gram of dry protein Eq. (8) can approximate to: [η] = ν(V¯ + δV¯ 0 )
(10)
in which V¯ 0 is the partial specific volume for water. δ values ranging from 0.3 to 0.5 [17] have been obtained using NMR, IR and simulation techniques for globular proteins and without considering the influence of conformational changes. For BSA, it is accepted that δ = 0.4 g of water per protein gram and V¯ = 0.734 mL/g [18]. If Eq. (9) is rewritten in terms of volume per molecules, then: [η] =
νNVm Mw
(11)
where N is the Avogadro number and Vm is molecular volume. In addition to shape and hydratation, biomolecule electrostatic charge also affects intrinsic viscosity, which, in turn, is strongly dependent on solution pH and ionic strength. A rise in ionic strength will lower intrinsic viscosity. Early conceptions on BSA molecular shape converge to an ˚ axis [19] and an axial rate ∼3.5 oblate ellipsoid with 40 × 140 A [20]. Currently, evidence shows that the BSA molecule in solution, in a 4.5–8 pH range, is heart shaped. In solution and in crystalline state, BSA conformation is accepted as a triangular ˚ × 80 A ˚ equilateral prism with the following dimensions: 80 A ˚ and 30 A deep [20]. In acidic solution, the compact structure probably unfolds to a more expanded one that can be represented by an elongated ellipsoid. For ample and comprehensive study see Monkos [21]. The F form would have an 11% volume increase due to hydrodynamic radium change and its dimensions ˚ × 129 A ˚ [22]. The E form would undertake a new would be 40 A ˚ × 250 A ˚ approximate dimensions expansion resulting in 21 A [6]. Starting from BSA conformation N, all volume changes could be explained by ␣-Helix content loss, which would increase BSA-SH exposure to solvent. 4. Conclusions The use of the Huggins, Kraemer and Schulz–Blaschke methods for intrinsic viscosity determination (Eqs. (1), (4) and (5)) rendered results showing some difference. In particular, [η] is
an expression of the interference in-between the polymer and the solvent; and reflects the solvent’s ability to swell the macromolecule. Thus, we can see that BSA has a very low [η] value at pH 7.4 which explains the assigned globular shape. [η] triplicates its value at pH 2.7. This rise is due to hydration, shape change and charge, in addition to molecular aggregation. Williams and Foster [24] show that BSA has a strong tendency to dimerize at acid pH. The Huggins, Kraemer and Shulz–Blaschke coefficients (KH , KK and KSB , respectively) are non-dimensional and suitable for solvent quality assessment [25]. The Huggins coefficient is accepted as a parameter relating polymer–solvent interactions. It describes the resulting interaction from the point of view of existing differences between the chemical structures of solvent and macromolecule. Low KH values ranging from 0.25 to 0.5 are assigned to good solvatation, while higher values are due to poor solvents [26]. Similarly, negative KK values point to good solvents. The graphics show that, in our BSA–water system at different pH values, viscosity of dilute solutions exhibit an unusual dependence on concentration, which is reflected by negative or very high KH values and positive or negative KK values, as shows Table 2. Published literature has pointed out very few exceptional systems showing this behavior [27,28]. For example, ref. [29] shows this same behavior in a solution in which the solute is amphyphilic. The co-polymer is composed of flexible, non-polar polydimethylsyloxane blocks and polar polyurethane blocks. The relative block proportion, however, does not allow the authors to give a rational interpretation of the negative KH value. One type of protein classification is based on solubility and it is said that BSA is soluble although its water affinity is intermediate. It must be considered that solubility of general proteins is not comparable to that of polymers usually studied. BSA adopts a globular conformation with very strong internal interactions. Interaction with the solvent is through polar groups accessible at the molecular surface and that are modified by pH and salts. The high polar character in proteins generates a non-typical behavior with water; thus, in the case of BSA the dielectric constant of the solution increases 0.17 U/g. This increase is due to the rigid orientation of the bound water molecules [30]. The complexity of inter- and intra-molecular interactions present in the BSAwater system makes a simple interpretation for the KH and KK constant values rather impossible to elaborate. In theory, the sum of both constants equals to 0.5, which would indicate that the experiment renders adequate results. The results here displayed do not match this value but are similar to many other reported in the literature [25]. The Mark–Houwink Eq. (6) provides a practical and simplified method to calculate molecular weight through viscosity measurements. The K* coefficient is calculated at a determined temperature for a range of molecular weights and could be related to solvent and macromolecule polarity parameters [14]. As an approximation, we have considered that the K* value (7.933 × 10−3 ) stands constant during the runs at different pH and we have calculated the expansion factor value. Results in Table 2 show that at pH 7.4, BSA takes the shape of a random tightly coiled, proximal to the “theta” state, that untangles poorly
R. Curvale et al. / International Journal of Biological Macromolecules 42 (2008) 133–137
when pH changes. The random tightly coiled is an approximation to the shape BSA would adopt in the presence of a “good solvent” at pH 2.7. The intrinsic viscosity values here presented are higher than those obtained by Tanford and Bussell [23]. However, it must be considered that salt addition has been avoided, thus increasing electrostatic interactions among ionic groups; also, an increase in ionic strength decreases intrinsic viscosity. In the case of conformers F and E, our results better reflect the remarkable volume and shape changes that are endured by BSA. Acknowledgments We thank Fedesa S.A.-UNSL who kindly granted the bovine albumin needed for the present work and Project 2-9304. References [1] D.C. Carter, J.X. Ho, Adv. Protein Chem. 45 (1994) 153. [2] J.F. Foster, Albumin Structure. Function and Uses, Academic Press, 1977, pp. 53–84. [3] M.J. Geisow, G.H. Beaven, Biochem. J. 163 (1977) 477. [4] M.Y. Khan, Biochem. J. 236 (1986) 307. [5] J.F. Foster, J. Am. Chem. Soc. 82 (1960) 3741. [6] W.F. Harrington, P. Johnson, R.H. Ottewill, Biochem. J. 62 (1956) 569. [7] M.L. Huggins, J. Am. Chem. Soc. 64 (1942) 2716.
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