Intermolecular Forces in Bovine Serum Albumin Solutions Exhibiting

Oct 4, 2000 - Dietler, G.; Aubert, C.; Cannell, D. S.; Wiltzius, P. Phys. ...... Roger Parker , Timothy R. Noel , Geoffrey J. Brownsey , Katrin Laos ,...
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Biomacromolecules 2000, 1, 757-763

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Intermolecular Forces in Bovine Serum Albumin Solutions Exhibiting Solidlike Mechanical Behaviors Shinya Ikeda* and Katsuyoshi Nishinari Department of Food and Nutrition, Osaka City University, Osaka 558-8585, Japan Received July 19, 2000; Revised Manuscript Received August 28, 2000

Mechanical properties of bovine serum albumin (BSA) solutions were analyzed to gain information on intermolecular forces that stabilize the system under normal physiological conditions. BSA solutions showed unexpectedly large zero shear viscosity values under steady shear flows but responded like solids to sinusoidal linear strains: the storage shear moduli were always larger than the loss shear moduli in the frequency range 1-100 rad/s. These results suggest that BSA solutions are so-called colloidal crystals in which colloidal particles are ordered in an array due to strong repulsive forces among particles. However, the pair potential between BSA molecules predicted based on the conventional Derjaguin-Landau-Verwey-Overbeek theory failed to explain these remarkable mechanical properties of BSA solutions. Additional repulsive forces other than electrostatic must be introduced to explain stability of BSA aqueous dispersions. Introduction Soluble proteins are generally stable under normal physiological conditions. Intramolecular noncovalent interactions and covalent disulfide bonds hold compact three-dimensional protein structures in solutions. The reactive nonpolar amino acids are maintained in the hydrophobic core of the protein, and the polar side chains are placed on the exterior. Environmental changes can cause denaturation and destabilization, however: that is, unfolding of the proteins resulting in exposure of interior reactive regions and sulfydryl groups.1,2 Denatured proteins thus can aggregate through intermolecular interactions such as hydrophobic interactions, disulfide bonding, hydrogen bonding, and electrostatic interactions. While forced or artificial denaturation/aggregation processes such as heat or acid/base treatments are utilized in foods, cosmetics, and the pharmaceutical industries for structuring product systems, self-assembly of proteins in vivo can lead to serious pathological consequences. Recent studies show that losing control and regulation of cellular environments can cause formation of fibrous amyloid deposits, like those seen in Alzheimer’s or Creutzfeldt-Jakob disease, and that the vast majority of normally soluble proteins having no obvious sequence or structural similarities are likely to form these insoluble amyloid fibrils.3-5 The only requirement for amyloid fibril formation, regardless of protein structure, seems to be a partial denaturation causing slow aggregation.3-5 Therefore, not only examination of protein structure but also understanding of the fundamental intermolecular forces regulating stability of native proteins, and destabilization/ aggregation of denatured proteins, are crucial for finding the way to prevent such protein aggregate formation. Protein aggregation is usually accompanied by a loss of R-helical structure and formation of an intermolecular β-sheet6-8 while structures of resultant aggregates are believed to be controlled by intermolecular force balances.9-14 If protein molecules are highly charged in a low ionic strength medium, aggregation proceeds relatively slowly due

to electrostatic repulsive forces among protein molecules. Proteins thus show a tendency toward forming linear aggregates, with a low degree of branching, composed of fine strands with a diameter of several nanometers.9 In contrast, absence of strong repulsive forces among proteins leads to more random and coarse particulate aggregates as a result of fast aggregation.9,13 Experiments and computer simulations on particle aggregation processes in general have shown that structures of aggregates are determined by the cross-linking reaction probability at contact of two particles.15-20 Two limiting regimes for such aggregation processes are reaction- and diffusion-limited aggregation, corresponding, respectively, to situations where the reaction probability is sufficiently lower than unity, and large and close to unity. In the case of reaction-limited aggregation, the aggregation rate is slow and the resultant aggregates are more compact, with fractal dimensions of 2.0-2.2,15,17-19 and a linear strandlike structure can be seen locally. The diffusion-limited aggregation proceeds much faster than this and forms coarse randomly aggregated structures, with lower fractal dimensions of 1.7-1.8.15,17-19 All these results seem to be in line with the hypothesis that various proteins with no structural similarities can form fibrous aggregates in the case that these proteins are partially unfolded, and their aggregates develop slowly. Even in a physiological environment in vitro, a protein solution can possess an ordered structure. It has been known for some time that colloidal particles, with sufficiently strong repulsive forces, order into a crystalline lattice in a medium, which is called a colloid crystal.21-23 Matsumoto and coworkers have reported that aqueous colloids of globular proteins, such as ovalbumin and bovine and rat serum albumin, are capable of forming colloid crystals that exhibit typical solidlike mechanical behaviors with elasticity under small-strain, and yield stress against flow.24-27 However, protein colloids have shown some unique behaviors in comparison with well-defined particle dispersions like la-

10.1021/bm005587o CCC: $19.00 © 2000 American Chemical Society Published on Web 10/04/2000

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tex: these are (1) elasticity was almost independent of protein concentration in a certain concentration range and (2) adding ions in order to reduce repulsive forces among protein molecules by shielding surface charges turned out to increase elasticity. Although the concentration independence of elasticity was described as occurring by an auto-controlled mechanism,24 these results revealed that even intermolecular events among native proteins are poorly understood. A scattering experiment would be an easy, yet powerful, way to investigate the crystalline ordered structures of proteins. However, light, neutron, or X-ray scattering measurements failed to detect a definite solidlike structure: only a broad peak was observed, even for a system that showed elasticity and yield stress,24,28,29 although the peak position appeared to be consistent with the interparticle distance when a uniform distribution of the particles is assumed.29 Mechanical properties of protein dispersions not only have significant influence on mass-transport events in biological systems30 but also provide information on intermolecular forces determining thermodynamic properties of the system.31,32 Therefore, mechanical analyses are suitable for investigating mechanisms causing stabilization, destabilization, and aggregation of proteins. In this study, we have analyzed aqueous solutions of native bovine serum albumin (BSA) since BSA has been well characterized, and used as a model protein, by many researchers. The goal is to shed light on intermolecular forces among proteins creating stable states under physiological conditions. This should be paralleled with self-assembling behavior among partially denatured proteins due to environmental changes. Theoretical Background DLVO Pair Potential in a Colloid Crystal. A colloid crystal is a three-dimensionally ordered structure in a solution formed by colloidal particles with repulsive interactions such as charged latex spheres.21,23,33,34 It is known that a bodycentered-cubic (bcc) array is formed at a low volume fraction φ up to ca. 0.03 and this turns into a face-centered-cubic (fcc) array at a higher volume fraction.21 As a result, colloidal crystals exhibit solidlike viscoelastic behaviors under sufficiently small oscillating strains.23 However, a colloid crystal is considered less well-defined than a complete crystal array because, even for an albumin dispersion with a solidlike dynamic viscoelasticity, only a broad scattering peak has been observed.24 While the intermolecular distance estimated from the peak position seems consistent with theoretical values based on the uniform distribution assumption,29 albumin colloids appear to possess a liquidlike nature in terms of neutron or X-ray scattering.25,28 Therefore, vacant sites should exist in the crystal-like array into which adjacent particles can diffuse via an activated process. If there are sufficient vacant sites for particles to move into in all planes simultaneously, the entire system can flow. Interactions between two colloidal particles are represented through the pair potential UT that is the total interaction energies from various origins. The conventional DerjaguinLandau-Verwey-Overbeek (DLVO) theory sums the re-

Ikeda and Nishinari

pulsive electrostatic Ur and attractive van der Waals Ua forces as a function of separation distance. For two spheres35,36 4πψ02a(R - a) a Ur ) ln 1 + exp[-κ(R - 2a)] R R-a

(

Ua ) -

(

[

1 A 1 x2 + 2x + + 2 ln 12 x2 + 2x x2 + 2x + 1 x2 + 2x + 1

)

(1)

)]

(2)

where  is the dielectric constant of the medium, ψ0 is the surface potential of the particles, a is the particle radius, R is the center-to-center distance between particles, κ-1 is the Debye length, A is the Hamaker constant, and x ) (R 2a)/2a. The Debye length, characteristic of the diffusive electric double layer, is κ-1 ) (kBT/2e2CNA)1/2, where kB is the Boltzmann constant, T is the absolute temperature, e is the elementary electric charge, C is the ionic concentration, and NA is the Avogadro number. The total potential energy of interaction is taken as the pairwise sum of contributions involving nearest neighbors, pairwise additivity of interactions being assumed as a first approximation.34,37 Shear Modulus. The shear modulus of a colloid crystal is identical to that of a unit cubic array provided that a local deformation is proportional to that of the entire system. In an fcc array, each particle has 12 adjacent neighbors and is sitting around the local minimum of the potential created by the other particles. The center-to-center particle distance at rest, Rm, is related to the volume fraction of particles φ by Rm ) 2a (φmax/φ)1/3, where φmax is the maximum volume fraction ()0.74 for an fcc array). Applying a small deformation to such an array causes a stress since distortion of the particle array increases the potential energy of the particles by displacing the positions of neighboring particles with respect to the central particle. The shear modulus G0 of this unit crystal is deduced from a stress tensor expression which takes into account the pair potential UT.23,34,37 G0 )

(

)

12φmax ∂2 4 ∂ U (R ) + U (R ) 5πRm ∂R2 T m Rm ∂R T m

(3)

Here, relaxation was not considered: G0 is the static or the high-frequency limit of the dynamic shear modulus. The validity of this equation has been confirmed already for wellcharacterized particle dispersions like latex sphere dispersions stabilized by strong electrostatic repulsive forces.23 Zero Shear Viscosity. The steady shear viscosity of colloidal crystals has been shown to decrease markedly with increasing shear rate due to destruction of the ordered structure. However, a value for the low shear-rate-limiting viscosity, i.e. zero shear viscosity η0, can be observed. Values of η0 for a colloid crystal are determined by both hydrodynamic effects of particles, ηHS, and contributions from intermolecular forces among colloidal particles in a crystal array, ηCF (η0 ) ηHS + ηCF). The purely hydrodynamic contribution can be represented by the Krieger-Dougherty equation38

(

ηHS ) ηS 1 -

φ φmax

)

-(5/2)φmax

(4)

where ηS is the viscosity of the continuous phase (solvent).

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The colloidal force contribution ηCF has been formulated by Ogawa et al.39 based on Eyring’s transitional state theory40

( )

ηCF ) ηSφ exp

E kBT

(5)

where E is the activation energy when a particle changes its position to an adjacent vacant site through an activation process. The activation potential barrier E is related to the summation of pair potentials among particles. When a particle transfers to an adjacent vacant site in a unit fcc array, the interparticle distance becomes the shortest at the midpoint (R* ) x3Rm/2), which is the activated state. Since there are four adjacent particles at the distance R*,37 the activation energy E can be approximated as E ) 4UT(R*)

(6)

Materials and Methods Cold alcohol precipitated BSA was purchased from Sigma Chemicals (St. Louis, MO) and used without further purification. Other chemicals were of reagent grade quality. BSA solutions were prepared by dissolving in distilled water, with/ without 0.1 mol/dm3 alkali metal salts, under moderate stirring for 90 min. Solutions containing 1-10% w/w BSA showed pH values of ca. 7.0. Some solutions were titrated with 0.1 mol/dm3 HCl, or acetic acid, to be pH ) 4.5. The volume fraction φ, of BSA, was determined spectrophotometrically at 279 nm (UV-2500PC, Shimadzu, Kyoto, Japan) using the extinction coefficient 279 ) 0.667 cm2mg-1,41 and the partial specific volume υ j ) 0.734.42 BSA is an R-helix43 rich protein and is an elongated ellipsoid, in shape, with semiaxes of ca. 7 and 2 nm,44 while Stoke’s radius has been determined to be 3.48 nm.45 Thus, the BSA molecule was assumed here to be a sphere with radius a ) 3.48 nm. The Hamaker constant A for a globular protein should be ca. 1kBT.32,46 The mean surface potential ψ0 was evaluated based on ψ0 ) ze/[4πa(1+κa)], where z is the mean number of net charges on the protein surface.36 The value of z in a pH 7.0 solution should be approximately -10 based on the proton titration curve.47 In the presence of 0.1 mol/dm3 chloride ion, z would be as low as -20 due to chloride ion binding.48 Steady shear viscosity and dynamic viscoelasticity measurements were made using a Rheometrics Fluids spectrometer (RFSII, Rheometrics, Inc., NJ) equipped with a cone and plate geometry test fixture (5 cm in diameter and 0.04 rad in angle). Initial strain sweep measurements of the storage modulus G′, loss modulus G′′, and dynamic viscosity η* allowed linear viscoelastic regions to be established. Since typical linear viscoelastic strain regions extended up to 0.05, a strain of 0.03 was applied in most measurements. Frequency sweep measurements were performed in the angular frequency range of 1-100 rad/s. The steady shear viscosity η was then measured at shear rates dγ/dt from 0.001 to 800 s-1. Results and Discussion Some albumin colloids such as BSA, rat serum albumin, and ovalbumin have been shown to possess an apparent yield

Figure 1. (a) Steady shear rate dependence of viscosity (b) and stress (O) and angular frequency dependence of dynamic viscosity (2) and complex dynamic modulus (4) of 10% w/w BSA aqueous solution at 20 °C. (b) Angular frequency dependence of storage (9) and loss shear modulus (0) of 10% w/w BSA aqueous solution at 20 °C.

stress to flow due to certain ordered arrangements of molecules, even at very low concentrations such as 0.01% w/w.27 However, the existence of a Newtonian flow region at lower flow rates, as will be demonstrated below, seems to raise an overlooked question about the stability of protein colloids. Steady shear flow properties of a BSA solution are compared with dynamic viscoelastic properties in Figure 1. Under steady shear flows, two Newtonian flow regions were observed at both the high and low limiting shear rates, and a strong shear thinning in the intermediate shear rate region. The shear stress was less dependent on the shear rate on decreasing the rate to 0.01 s-1, indicating that an apparent yield stress might exist, as has been observed in some colloidal systems. However, by further decreasing the shear rate, another Newtonian region appeared, with a large value of the low limiting shear viscosity (zero shear viscosity), suggesting that this system was capable of flowing while still maintaining its overall structure at the very low rate. Values of the dynamic viscosity η*, or the complex dynamic shear modulus G*, were much larger than those of the steady shear viscosity η or the steady shear stress σ at the comparable angular frequency and the shear rate. Coincidence of η* with η (or G* and σ) at a comparable time scale

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Figure 2. Flow (a) and dynamic (b) mechanical behaviors of 10% w/w BSA aqueous solution at 20 °C at pH 7.0 in the presence of 0.1 mol/dm3 LiCl (9), NaCl (b), KCl (0), CsCl (O), or RbCl (1) or at pH 4.5 adjusted by acetic acid (4) or hydrochloric acid (2).

of observation is known as the Cox-Merz rule,49 which is valid only for systems for which a large strain under steady flow does not destroy the structure determining mechanical properties. Therefore, not only the typical solidlike behavior (G ′ > G′′) observed in the frequency dependence of the dynamic shear modulus, but also the invalidity of the CoxMerz rule shown in Figure 1, supports the concept of a solidlike structure in a BSA solution. Such structures appeared to be able to flow very slowly, e.g., at 0.001 s-1, but gradually break up with increasing shear rate. These results were repeatable: the second-run steady shear viscosity measurements attempted after a few minutes interval produced identical results to the first measurements (data not shown), suggesting that the solidlike structures disturbed by shearing recovered almost immediately. Figure 2 shows effects of adding various alkali metal salts, or acids, on steady shear and dynamic properties of BSA solutions. In the presence of 0.1 mol/dm3 monovalent salt, the characteristic Debye length κ-1 is only ca. 1 nm, which is much shorter than the interparticle distance (ca. 15 nm) in these experimental conditions. Nevertheless, large zero shear viscosity values, and solidlike behaviors, were observed regardless of salt species. Adding hydrochloric or acetic acids to reach pH 4.5 only slightly decreased zero shear viscosity and shear modulus values compared to the solutions with added salts. Since the isoelectric point of BSA is ca. 5.5,46

Ikeda and Nishinari

Figure 3. Concentration dependence of flow (a) and dynamic (b) mechanical behaviors of BSA aqueous solution at 20 °C. Solid and open symbols in part a represent viscosity and stress, respectively, and in part b represent storage and loss modulus, respectively. Concentrations: 0.01 (b, O), 0.1 (2, 4), 1 (9, 0), and 10% w/w (1, 3).

the molecule is negatively or positively charged at pH 7.0 or 4.5, respectively. Therefore, neither the absence of the strong electrostatic repulsive forces among protein molecules, nor the sign of the mean protein surface charges, appeared critical for exhibiting solidlike mechanical properties. Figure 3 shows the concentration dependence of the steady shear flow and dynamic viscoelastic properties of BSA solutions. The 0.01% w/w BSA system showed an almost Newtonian flow, while its dynamic modulus was not detected, due to a very small mechanical response. The systems with BSA concentrations of 0.1% w/w, or higher, were non-Newtonian. Increasing BSA concentration from 0.1 to 10% w/w increased both the zero shear viscosity, and the dynamic shear moduli, but by less than an order of magnitude. An abrupt exhibition of solidlike structures with increasing concentration followed by little concentration dependence of η, σ, G ′, or G′′ has been observed generally for globular proteins.27 Suppressing an increase in the shear moduli as with increasing concentration has been designated as an “auto-controlled mechanism”24 although its actual mechanism is not yet proposed. Because of insufficient electrostatic repulsions, loose aggregates of native protein molecules may be expected. However, the little concentration dependence of mechanical responses in the concentration

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Intermolecular Forces in Bovine Serum Albumin

Table 1. Temperature Dependence of Steady Shear Flow Characteristics for a 10% w/w BSA Solution temperature (°C)

η0 (Pa‚s)

τ (s)

E/kBT

10 20 30 40

24.2 14.0 5.6 4.2

159 148 110 42

12.5 12.2 11.6 11.5

BSA did not denature, at least below 40 °C. Figure 4b shows the temperature dependence of the dynamic viscoelastic behavior. Both the storage and the loss moduli increased with decreasing temperature, so that values of G ′, G′′, and tan δ were shifted along the abscissa to form smooth curves, which is called time-temperature superposition. The storage modulus was always larger than the loss modulus (tan δ was always less than unity) over the four decades of frequency range, confirming that changes in temperature below the denaturation temperature did not significantly change the solidlike structures in BSA solutions, and that such solidlike behavior was not due to the limited frequency range available. On the basis of the zero shear viscosity values obtained (Table 1), the activation energy was evaluated using eq 8, E ) kBT ln

Figure 4. (a) Reduced steady shear viscosity of 10% w/w BSA solutions plotted against dimensionless shear rate determined at 10 (b), 20 (2), 30 (9), and 40 °C (1). The solid line represents the Cross equation (eq 7) with m ) 0.9. The inset shows DSC heating curve of 10% w/w BSA solution at the heating rate of 1 °C/min. (b) Timetemperature superposition master curves of G ′, G′′, and tan δ measured at 10 (b, O; aT ) 1), 20 (2, 4; aT ) 0.333), 30 (9, 0; aT ) 0.0250), and 40 °C (1, 3; aT ) 0.00333) for 10% w/w BSA solutions.

range from 0.1 to 10% w/w cannot be explained if the solidlike mechanical behavior is simply due to protein aggregation. The temperature dependence of steady shear flow behaviors is summarized in Figure 4a in the form of reduced viscosity (η - η∞)/(η0 - η∞) as a function of the dimensionless shear rate τ(dγ/dt), where τ is the characteristic time of the shear thinning behavior. Values of the zero shear viscosity were evaluated based on the equation of Cross50 η - η∞ ) η0 - η ∞

1 dγ m dt

( )

1+ τ

(7)

where the constant m is a measure of the severity of shear thinning. The observed slight decreases in η0 and τ with rising temperature (Table 1) were in line with expectation, since a shear thinning flow is considered as a consequence of competing Brownian motion and shear distortion. The inset in the Figure shows the differential scanning calorimetry heating curve for a 10% w/w BSA solution, confirming that

(

)

η0 - ηHS ηSφ

(8)

derived from eq 5, and the resulting values of E are summarized also in Table 1. Because of the high zero shear viscosity values measured, relatively large values (>10kBT) were obtained. However, the activation energy for the 10% w/w BSA solution at 20 °C was estimated to be less than 0.01kBT using eq 6 together with eqs 1 and 2 (UT ) Ur + Ua). Such negligibly small values of E, based on the DLVO potential, arise because of the high salt concentration which is sufficient enough to eliminate electrostatic repulsive forces between protein molecules. Therefore, electrostatic repulsive and van der Waals attractive forces alone do not suffice to explain the stability of BSA solutions against aggregate formation under normal conditions. A non-DLVO repulsive potential must be introduced to explain the extremely large values of E found for BSA solutions. The existence of physical forces other than those included in the DLVO theory has long been discussed in colloid science since, for example, stable particle dispersions in the absence of sufficient electrostatic repulsions have been recognized.51,52 In cases where an additional repulsive force is believed to exist, it is often referred to as a hydration pressure. The attractive counterpart is generally designated the hydrophobic interaction. The origin of these forces is believed to be electron acceptor-electron donor interactions, often referred to as polar interactions.51 Strong polar interactions orient water molecules adsorbed on the surface of colloidal particles, and thus the stability of the colloidal system is conferred by those hydrated water molecules that force the two particles apart at contact. Additionally, the influence of the orientation of hydration water molecules would be long-range, compared to the size of the single water molecule, through hydrogen bonding: i.e., the first hydrated layer could orient the second layer, the second layer would

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Ikeda and Nishinari

Figure 5. Pair potential in 10% w/w BSA solution containing 0.1 mol/ dm3 NaCl at 20 °C. ∆Gh ) 1.47 mJ/m2 and l ) 3.87 nm were evaluated based on a ) 3.48 nm, φ ) 0.0671, η0 ) 14.0 Pa‚s, G0 ) 5.0 Pa, κ-1 ) 0.96 nm, ψ0 ) 22.4 mV, and A ) 1kBT.

likewise influence the third layer orientation, and so on. Such polar forces, especially in aqueous media, could be up to 100 times greater than either the van der Waals attractive, or electrostatic repulsive, energies at close range (1-5 nm).51,53 Intermolecular or intersurface forces have been categorized based on direct mechanical measurements.54 If two molecularly smooth rigid surfaces are hydrated, intersurface repulsive forces arise at a very close separation (less than a few nanometers) due to structural hindrance and restructuring of water molecules hydrated on, and located near, the surfaces. These forces show oscillatory behaviors in a cycle of ca. 0.25 nm, corresponding to the size of the single water molecule, and this is strong evidence that these forces are primarily due to structural hindrance of ordered water layers.55 However, such an oscillatory hydration force has been observed only between molecularly smooth rigid surfaces. For rough surfaces such as lipid bilayers, perhaps because oscillatory repulsions are smeared out by thermal fluctuations at surfaces, only exponentially decaying repulsions have been observed.56-58 The formulation of the pair potential generating an exponential hydration force between two spherical particles has been given as53-59 Uh ) ∆Ghπal exp[-(R - 2a)/l]

(9)

where ∆Gh (J/m2) is the free energy of hydration between the corresponding parallel flat plates and l (nm) is the decay length. In this study, values of ∆Gh and l were calculated by solving two simultaneous equations: one for the relationship between the total pair potential UT () Ur + Ua +Uh) and the static shear modulus G0 (eq 3), and the other for that between UT and η0 (eqs 6 and 8). Values of ∆Gh ) 1.47 mJ/m2 and l ) 3.87 nm were thus obtained. The order of the magnitude of the hydration energy is comparable with those reported for mica surfaces.54 The value of l might supposedly be about the size of a single water molecule if only directly hydrated water molecules are involved. However, the so-called hydration repulsive forces are known to extend up to tens of nanometers in range.51,58 Figure 5

presents estimated pair potentials between two BSA molecules for a 10% w/w BSA solution containing 0.1 mol/dm3 NaCl at 20 °C. These have been normalized by the Brownian thermal energy kBT and are expressed as a function of the interparticle distance. Because of the sufficiently high ionic strength, the electrostatic term is relatively small, while the van der Waals attractive potential becomes pronounced only at a very short distance. Thus, the solidlike mechanical behaviors and the stabilities of BSA solutions seem to be rationalized by introducing an intersurface repulsive force decaying exponentially with distance, which dominates the overall pair potential. It should be noted, however, that any repulsive forces that are determined by the surface area and decay exponentially with distance would have the same mathematical form as eq 9. Additionally, little concentration dependence of mechanical behaviors shown in Figure 3 implies that the dominant potential Uh adopts appropriate values of ∆Gh and l automatically, depending on the concentration. The hydration force is only a possible candidate for the origin of repulsive forces between BSA molecules and much further exploration is needed. It may sound reasonable that values of moduli of charged particle dispersions should decrease with increasing ionic concentration, since increasing ionic concentration should weaken electrostatic repulsive forces among particles. However, this was not the case for some albumin colloids: values of the complex dynamic modulus, and the apparent yield stress, increased with increasing ionic concentration.26 To explain those results, the Debye length κ-1 was treated as a fitting parameter for calculating values of the modulus using an essentially the same equation as eq 1 in this study. Increasing modulus values with increasing ionic concentration could thus be well fitted by the calculated results even though the physical meaning of such a procedure seemed rather unclear. For example, the estimated Debye length values differed by 2 orders of magnitude from those predicted based on the ionic concentration in the system.26 Additionally, the extraordinary large values of zero shear viscosity for BSA solutions found in this study appeared impossible only by adjusting the value of κ, because changes in the latter would change the value of the second term in the right-hand of eq 1 by only less than one, and thus the value of the activation energy E in eq 5 would remain almost constant. Therefore, introducing an additional force rather than a parametrized fitting seems inevitable. Extraordinary mechanical behaviors are not unique to proteins. Xanthan is a microbial exopolysaccharide produced by Xanthomonas campestris with a linear sequence of pentasaccharides. Aqueous solutions of xanthan are also known to exhibit peculiar flow and viscoelastic properties similar to BSA solutions; that is, pronounced shear thinning behavior under steady shear flow, solidlike responses to dynamic small strains, and violation of the Cox-Merz rule.60,61 The existence of a yield stress is often reported but a low limiting Newtonian flow region appears if the accessible shear flow rate is lowered,60 just as is the case with the BSA solutions included in this study. Because of these unique mechanical properties, xanthan solutions are called “weak gels,” and find practical applications in many

Intermolecular Forces in Bovine Serum Albumin

industries. However, the solidlike character of xanthan solutions stems from totally different origins. The xanthan molecule is an essentially linearly bonded sugar-ring chain, with branching short side chains. Under normal conditions, a xanthan chain adopts a helical conformation, which is highly stiff, and extended like a rod (Kuhn length ∼240 nm).62 Thus, solidlike character arises from topological entanglements of such extended rigid molecular chains. If the lifetime or the relaxation time of entanglements is sufficiently longer than the time scale of observation, the system behaves as a solid, which is the case for xanthan. However, due to the absence of permanent cross-links, such a system will never rupture under steady shear flow and will recover given sufficient time.62 In conclusion, BSA aqueous dispersions appear to have a colloidal crystallike structure stabilized by strong repulsive interactions among the globular protein molecules, and show solidlike rheological behaviors under normal physiological conditions. The repulsive forces are believed to be dominated by a molecular surface related force such as a hydration force, and would be lost on denaturation which leads to exposure of the hydrophobic core of the protein. Direct measurements of intermolecular forces between two protein molecules is unlikely to be at the present time, although there are currently some promising attempts to directly measure forces between protein layers absorbed on mica surfaces.63,64 Further developments of experimental techniques are required to clarify the origin of the stability of proteins. Acknowledgment. Part of this work was financially supported by the Nestle Science Promotion Committee, Japan. S.I. is indebted to Professor E. Allen Foegeding of North Carolina State University for stimulating discussions on protein stabilities, which initiated this study. References and Notes (1) Griffin, W. G.; Griffin, M. C. A.; Martin, S. R.; Price, J. J. Chem. Soc., Faraday Trans. 1993, 89, 3395-3406. (2) Qi, X. L.; Holt, C.; McNulty, D.; Clarke, D. T.; Brownlow, S.; Jones, G. R. Biochem. J. 1997, 324, 341-346. (3) Guijarro, J. I.; Sunde, M.; Jones, J. A.; Campbell, I. D.; Dobson, C. M. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 4224-4228. (4) Chiti, F.; Webster, P.; Taddei, N.; Clark, A.; Stefani, M.; Ramponi, G.; Dobson, C. M. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 35903594. (5) Kowalewski, T.; Holtzman, D. M. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 3688-3693. (6) Belloque, J.; Smith, G. M. J. Agric. Food Chem. 1998, 46, 18051813. (7) Clark, A. H. Gelation of globular proteins. In Functional Properties of Food Macromolecules, 2nd ed.; Hill, S. E., Ledward, D. A., Mitchell, J. R., Eds.; Aspen Publishers: Gaithersburg, MD, 1998; pp 77-142. (8) Ikeda, S.; Foegeding, E. A.; Hardin, C. C. J. Agric. Food Chem. 2000, 48, 605-610. (9) Clark, A. H.; Judge, F. J.; Richards, J. B.; Stubbs, J. M.; Suggett, A. Int. J. Pept. Protein Res. 1981, 17, 380-392. (10) Langton, M.; Hermansson, A.-M. Food Hydrocolloids 1992, 5, 523539. (11) Vreeker, R.; Hoekstra, L. L.; den Boer, D. C.; Agterof, W. G. M. Food Hydrocolloids 1992, 6, 423-435. (12) Dickinson, E. J. Chem. Soc., Faraday Trans. 1994, 90, 173-180. (13) Hagiwara, T.; Kumagai, H.; Nakamura, K. Biosci. Biotech. Biochem. 1996, 60, 1757-1763. (14) Ikeda, S.; Foegeding, E. A.; Hagiwara, T. Langmuir 1999, 15, 85848589. (15) Weitz, D. A.; Huang, J. S.; Lin, M. Y.; Sung, J. Phys. ReV. Lett. 1985, 54, 1416-1419.

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