Influence of the ionic strength on the heat-induced aggregation of the globular protein β-lactoglobulin at pH 7

International Journal of Biological Macromolecules 34 (2004) 21–28

Influence of the ionic strength on the heat-induced aggregation of the globular protein ␤-lactoglobulin at pH 7 Karine Baussay, Christel Le Bon, Taco Nicolai∗ , Dominique Durand, Jean-Pierre Busnel Polymères, Collo¨ıdes, Interfaces, UMR CNRS, Université du Maine, Av. Olivier Messiaen 72085 Le Mans Cedex 9, France Accepted 19 November 2003

Abstract The influence of the ionic strength on the structure of ␤-lactoglobulin aggregates formed after heating at pH 7 has been studied using static and dynamic light scattering. The native protein depletion has been monitored using size exclusion chromatography. Above a critical association concentration (CAC) well-defined clusters are formed containing about 100 monomers. The CAC increases with decreasing ionic strength. The so-called primary aggregates associate to form self similar semi-flexible aggregates with a large scale structure that is only weakly dependent on the ionic strength. The local density of the aggregates increases with increasing ionic strength. At a critical gel concentration, Cg , the size of the aggregates diverges. Cg decreases from 100 g/l without added salt to 1 g/l at 0.4 M NaCl. For C > Cg the system gels except at high ionic strength close to Cg where the gels collapse under gravity and a precipitate is formed. © 2003 Elsevier B.V. All rights reserved. Keywords: Globular protein; ␤-Lactoglobulin; Aggregation; Gel; Light scattering

1. Introduction Generally, heat-induced denaturation of globular proteins leads to aggregation of the proteins and above a characteristic concentration (Cg ) eventually a gel is formed [1]. The visual aspect of the gels and the value of Cg strongly depend on the strength of the electrostatic interactions [2]. At a pH far from the isoelectric point (pI) and at low ionic strength the gels are generally transparent and electron microscopy shows that linear aggregates are formed. At high ionic strength or close to pI the gels are turbid and more densely branched aggregates are observed. Cg is found to increase with increasing electrostatic interactions. Electron microscopy is well suited to show the rigidity and the degree of branching of linear aggregates formed under strong electrostatic interactions. But it cannot be used to quantitatively characterise the overall structure of the denser, more highly branched aggregates. Light scattering has proven to be a powerful technique for such a characterisation. It was shown with this technique that globular proteins such as bovum serum albumin (BSA) [3], ovalbumin ∗ Corresponding author. Tel.: +33-2-43-83-31-89; fax: +33-2-43-83-35-58. E-mail address: [email protected] (T. Nicolai).

0141-8130/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ijbiomac.2003.11.003

(OA) [4] and ␤-lactoglobulin (␤-lg) [5–7] form self similar aggregates characterised by a fractal dimension. Of these proteins ␤-lg is probably the best characterised, but even for this protein no systematic study was made of the structure of the aggregates as a function of the ionic strength. ␤-lg is the main whey protein and has molar mass 18 kg/mol and radius about 2 nm [8,9]. Here we will present the results of a systematic study of the structure of ␤-lg aggregates formed at pH 7 over a wide range of concentrations and ionic strengths.

2. Materials and methods 2.1. Materials The ␤-lactoglobulin used in this study was a gift from Lactalis (Laval, France) and contained about equal fractions of the variants A and B. We showed elsewhere that the aggregation rate is equal for the two variants in the mixture [10]. Solutions were extensively dialysed against salt free Mili-Q water at pH 7 with 200 ppm NaN3 added to avoid bacterial growth. After the dialysis the ionic strength was set by adding a concentrated solution of NaCl. For light scattering measurements the samples were filtered through

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K. Baussay et al. / International Journal of Biological Macromolecules 34 (2004) 21–28

0.2 ␮m pore size Anotope filters. The concentration was measured after filtration by UV absorption at 278 nm using extinction coefficient 0.96 l/g/cm [11]. Solutions in air tight light scattering cells were heated for 24 h in a thermostat bath at 80 ◦ C and subsequently rapidly cooled to 20 ◦ C.

(Rgz = R2g 0.5 ) and the second virial coefficient (A2 ) can be derived using the so-called Zimm approximation:   (qRgz )2 1 KC = 1+ (1 + 2Mw A2 C) qRgz < 1 (3) Ir Mw 3

2.2. Size exclusion chromatography

With the dynamic light scattering technique (DLS) the intensity autocorrelation function is measured: g2 (t) = I(0)I(t) / I [16]. g2 is related to the normalised electric field correlation function, g1 (t), by the Siegert relation [16]. g1 (t) was analysed in terms of a distribution of relaxation times:
  −t dτ (4) g1 (t) = A(τ)exp τ

SEC experiments were carried out at room temperature with TSK® PW 5000 + PW 6000 column set (30 cm + 60 cm) in series and a differential refractive index detector SHODEX RI 71. The columns were eluted with a 0.1 M NaNO3 solution at a flow rate of 1 ml/min, 200 ppm NaN3 was added as a bacteriostatic agent. The injected volume was 300 ␮l and the injected concentration was approximately 0.1%. The analysis lasted for 45 min. The refractive index increment dn/dC is taken as 0.189 ml/g [12]. 2.3. Light scattering Static and dynamic light scattering measurements were made using an ALV-5000 multi-bit multi-tau correlator and a Spectra Physics solid state laser operating with vertically polarized light with wave length λ = 532 nm. The range of scattering wave vectors covered was 3.0 × 10−3 < q < 3.5 × 10−2 nm−1 (q = 4πns sin(θ/2)/λ, with θ, the angle of observation and ns , the refractive index of the solution). The temperature was controlled by a thermostat bath to within ±0.1 ◦ C.

using the Laplace inversion routine REPES [17]. The apparent diffusion coefficient (D) was calculated from the average relaxation rate Γ = 1/τ as: D = Γ /q2 [16]. In highly dilute solutions when interactions are negligible D = D0 is related to the z-average hydrodynamic radius (Rhz = 1/Rh −1 z ) via the so-called Stokes–Einstein relation: kT D0 = for qRhz < 1 (5) 6πηRhz with k, the Boltzmann’s constant and η, the solvent viscosity. At larger values of qRhz rotation and internal dynamics of the particles influence D.

3. Results and discussion 2.4. Data analysis 3.1. Native β-lg The relative scattering intensity Ir was determined by subtracting the solvent scattering from the total scattering intensity and dividing by the scattering intensity of toluene. Ir is due to concentration fluctuations and is proportional to the osmotic compressibility (dπ/dC)−1 and the structure factor (S(q)) [13,14]: Ir = KC

RT S(q) dπ/dC

(1)

with R the gas constant and T the absolute temperature. S(q) expresses the scattering wave vector dependence of the scattering intensity and is unity for q → 0. K is a contrast factor:

 4π2 n2s ∂n 2 ntol 2 1 K= 4 (2) ns Rtol λ Na ∂C where Na is Avogadro’s number, ∂n/∂C is the refractive index increment, and Rtol is the Rayleigh ratio of toluene at 20 ◦ C (Rtol = 2.79 × 10−5 cm−1 at λ = 532 nm [15]). (ntol /ns )2 corrects for the difference in scattering volume of the solution and the toluene standard with refractive index ntol . In dilute solutions when interactions are weak, the weight average molar mass (Mw ), the z-average radius of gyration

We have studied the influence of the ionic strength on the interactions for native ␤-lg using static and dynamic light scattering. Native ␤-lg solutions contained aggregated proteins with a negligible weight fraction, but which nevertheless influence the light scattering intensity. We corrected for this influence using dynamic light scattering results as shown in ref. [18]. Fig. 1 shows the concentration dependence of KC/Ir at different ionic strengths (Cs ). For Cs ≥ 0.02 M NaCl the concentration dependence is independent of the ionic strength within the experimental error and is approximately linear for C < 60 g/l. We may calculate the molar mass and the second virial coefficient using Eq. (1). Mw = 38 kg/mol, i.e. about twice the molar mass of the monomer and A2 ≈ 1.6 × 10−7 mol/l/g2 independent of the ionic strength within the experimental error for Cs ≥ 0.02 M NaCl. At pH 7 ␤-lg is essentially present in the form of dimers except at very low ionic strength [19,20]. At lower ionic strength the effect of electrostatic repulsion becomes increasingly important. The equilibrium monomer–dimer is probably shifted more towards the monomer at low protein concentrations. The concentration dependence of the diffusion coefficient is almost negligible over the range of concentrations covered

K. Baussay et al. / International Journal of Biological Macromolecules 34 (2004) 21–28

23

10

0.003M 0.01M 0.02M 0.05M 0.1M 0.2M 0.4M

KC/Ir (10-5 mol/g)

8

6

4

2

0

20

40

60

80

100

C (g/L) Fig. 1. Concentration dependence of KC/Ir for native ␤-lg at different ionic strengths.

3.2. Native protein depletion We have measured the depletion of native ␤-lg as a function of the protein concentration at different ionic strengths. Unexpectedly, at low protein concentrations not all proteins aggregate and the fraction of unaggregated ␤-lg (F) decays to a plateau value, Fp . Fig. 2 shows examples of the dependence of F on heating time at 80 ◦ C. We do not claim that protein depletion stops entirely at Fp , but clearly it decreases relatively rapidly to a pseudo-plateau after which the decrease becomes logarithmically slow. Fp increases with decreasing protein concentration. We have made a systematic study of the concentration dependence of Fp over a range of ionic strengths. In order to assure that in all cases the plateau value was reached we have heated the samples for 24 h at 80 ◦ C. We checked for several samples that indeed the plateau value was obtained. For all ionic strengths Fp decreases with increasing protein concentration and stabilises at about 0.05 at high protein concentrations. Apparently 5% of the proteins in the sample do not aggregate under any circumstances. Of the remaining proteins an increasing fraction does not aggregate when the total protein concentration is decreased and this effect is stronger at lower ionic strength.

It appears that the proteins only aggregate above a critical association concentration, CAC. This is demonstrated in Fig. 3 where we have plotted Fp as a function of C/CAC. In this representation the results at different ionic strengths superimpose. For C > CAC we find that Fp = CAC/C +0.05, see solid line in Fig. 3. CAC decreases with increasing ionic strength, see Fig. 4. Apparently, the first step in the aggregation process requires a minimum concentration of proteins. The first step of the aggregation process of ␤-lg at pH 7 is the formation of so-called primary aggregates containing about 100 monomers [21]. The observed protein depletion 1.0

0.8

0.6 F

in the experiment for Cs > 0.02 M NaCl. At lower ionic strength D increases first due to repulsive electrostatic interaction. At high concentrations D decreases because screening by counterions decreases the electrostatic interactions while the friction between the proteins increases [18]. The q-dependence of D was negligible in all cases and the hydrodynamic radius calculated using Eq. (4) is 2.8 nm.

0.4

0.2

0.0 100

1g/L 0.05M 5g/L 0.003M

101

102

103

104

t (min) Fig. 2. Examples of the evolution of the fraction of unaggregated ␤-lg during heating at 80 ◦ C.

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1.0 1000

0.8

Fp

0.6

th (min)

0.003M 0.01M 0.02M 0.05M 0.1M 0.2M 0.4M

100

0.4 10 0.2

0.0 0.1

1 1

10

100

1

can be rationalised if we assume that the formation of the primary aggregates is controlled by an equilibrium reaction analogous to micelle formation of surfactants. However, contrary to micelles the primary aggregates are stable to dilution both at room temperature and at the original heating temperature. In fact, even if we dilute the samples without cooling, the primary aggregates remain intact. These observations imply that the bonds between the proteins in the primary aggregate become irreversible. In view of these considerations we propose that the initial step of the aggregation of ␤-lg is the formation of a well-defined cluster in equilibrium with monomers. The addition of salt screens electrostatic interactions and lowers the energy barrier for the formation of the clusters. The bonds in the cluster stabilise over time leading 10

CAC (g/L)

1

0.1

0.01 0.001

100

C (g/l)

C/CAC Fig. 3. Dependence of the fraction of unaggregated ␤-lg on C/CAC after heating 24 h at 80 ◦ C at different ionic strengths.

10

Fig. 5. Concentration dependence of the time needed at 73 ◦ C to deplete 50% of the fraction of native ␤-lg that will eventually aggregate. The dashed line represents the results obtained at 0.1 M NH3 COOH and the solid is a linear least squares fit through the data obtained without added salt.

to stable primary aggregates. We will show in the following that the size of the primary aggregates increases weakly with increasing ionic strength. Below the critical association concentration the probability to form a cluster is very small, but not zero which could explain that the fraction of aggregates continues to increases logarithmically. The rate at which native ␤-lg aggregates is a strong function of the heating temperature. Activation energies between 250 and 400 kJ/mol have been reported [22]. On the other hand, the concentration dependence of the aggregation rate is relatively weak. At pH 7 and 0.1 M NH3 COOH it was found that the time needed to aggregate half of the proteins (th ) decreases with the square root of the protein concentration independent of the temperature [22]. We have done a similar study at pH 7 without added salt so that the ionic strength is 0.003 M due to the presence of added azide. To characterise the aggregation rate we define th as the time needed to reach F = (1 + Fp )/2. The concentration dependence of th is compared in Fig. 5 with the results obtained at 0.1 M NH3 COOH indicated by the dashed line. The concentration dependence of the aggregation rate is much stronger at low ionic strength: th ∝ C1.5 . The reason for this strong concentration dependence is probably the increase of the effective ionic strength with increasing protein concentration caused by the contribution of counterions. In fact, at high protein concentrations the aggregation rate without added salt approaches that in 0.1 M NH3 COOH. 3.3. Aggregate structure

0.01

0.1

1

Cs (mol/L) Fig. 4. Ionic strength dependence of the critical association concentration.

In the second step of the aggregation process the primary aggregates associate into larger self similar structures, which leads above the critical concentration, Cg , to gelation.

K. Baussay et al. / International Journal of Biological Macromolecules 34 (2004) 21–28

which fits the data well over the whole q-range, implying that df = 2. Fig. 7 compares the structure factors obtained at different ionic strengths. The structure factors obtained at all salt concentrations is the same within the experimental error. We note, however, that recent small angle X-ray experiments have shown that the local structure of the aggregates varies with the ionic strength [23]. 3.4. Concentration dependence of the aggregate size Fig. 8 shows how Mw varies with the protein concentration at different ionic strengths between 3 mM and 0.4 M. For ionic strength up to 20 mM we observe a plateau at low concentrations. At these concentrations only the primary aggregates are formed. Chromatography shows that they are characterised by a rather narrow size distribution well separated from the residual unaggregated proteins [24]. There appears to be a small increase of the mass of the primary aggregates with increasing ionic strength. The formation of

Ir/KCa (kgmol-1)

106

1.8 g/L 4.6 g/L 9.3 g/L 18.4 g/L 26.9 g/L 30.7 g/L 32.2 g/L 36.5 g/L 37.4 g/L

105

104

103 0.001

0.01

0.1

q (nm-1) 1

0.1 S(q)

For C < Cg , however, the growth of the aggregates stagnates when most native proteins have aggregated [22]. The size of the aggregates at which their growth stagnates, increases with the protein concentration. This second aggregation step depends strongly on the ionic strength: the higher is the ionic strength the lower is the protein concentration where the primary aggregates start to associate as seen in the following. In order to characterise the size and the structure of ␤-lg aggregates formed as a function of the protein concentration at different ionic strengths we have heated ␤-lg solutions for 24 h at 80 ◦ C. We verified that the growth of aggregates had stagnated after this heating time. We note that the heating temperature strongly influences the aggregation rate, but not the structure of the aggregates [5]. Fig. 6a shows the dependence of Ir /KCa on the scattering wave vector for highly diluted solutions of aggregates formed at 0.05 M NaCl and different protein concentrations. Here Ca is the concentration of the aggregates corrected for the small fraction of residual unaggregated proteins. The molar mass and the size of the aggregates increase with increasing protein concentration. As was reported earlier for aggregates formed in 0.1 M NH3 COOH, all the curves can be superimposed by plotting S(q) = (Ir /KCa )/Mw as a function of q × Rgz , showing that the aggregates have a universal structure factor, see Fig. 6b. The advantage of this method is that it allows for the determination of Mw and Rgz even when the Zimm approximation (Eq. (3)) is no longer valid. However, for Rgz > 1000 nm the scattering intensity is no longer sensitive to Rgz over the range of q-values covered in the experiment and we only observe the self similar internal structure: S(q) ∝ q−df , with df the so-called fractal dimension. The solid line represents the following simple equation: 1 S(q) = (6) 1 + q2 R2gz /3

25

0.01

0.1

1

10 qRgz

Fig. 6. (a) Dependence of Ir /KCa on the scattering wave vector for ␤-lg aggregates formed at different protein concentrations after heating 24 h at 80 ◦ C at 0.05 M NaCl. (b) Same data as shown in (a) after normalizing Ir /KCa by Mw and q by Rgz .

such a well-defined primary aggregate was not observed for ovalbumin at similar conditions [4] nor were they observed for ␤-lg at pH 2 [25]. The association of the primary aggregates into larger self-similar aggregates leads to an increase of Mw with increasing concentration. The size of the aggregates increases with increasing protein concentration and diverges at Cg . The increase occurs at higher concentrations with decreasing ionic strength. For C > Cg we observe the formation of a homogeneous gel if Cs < 0.2 M. However, at higher ionic strengths we observe a precipitation of protein flocs between Cg and about 10 g/l. We interpret this precipitation as the formation of a gel that is not sufficiently strong to resist gravity.

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0.1

10

0.003M 0.01M 0.02M 0.05M 0.1M 0.2M 0.4M

0.01

0.001

Cg (g/L)

100

S(q)

1

0.1

1

0.001 1

0.1

1

Cs (mol/L)

10 qRgz

Fig. 7. Comparison of the structure factor of ␤-lg aggregates formed at different ionic strengths. The structure factors were obtained by superposition of the data obtained at different protein concentrations after heating 24 h at 80 ◦ C as shown in Fig. 6.

Fig. 9 shows the dependence of Cg on the ionic strength. The results are close to the critical gel concentrations of ␤-lg solutions heated for 1 h at 80 ◦ C reported in ref. [2] because gel times are short at 80 ◦ C except if C is very close to Cg . Cg increases strongly with decreasing ionic strength, but the relative variation weakens below 0.02 M. We speculate that the latter effect is caused by the contribution of counterions that becomes important at very low ionic strength where Cg is large. Cg also depends on the type of added salt since at 0.1 M NH3 COOH we observed Cg = 7 g/l while at 0.1 M NaCl we found Cg = 15 g/l. We note that in the presence of even a small amount of CaCl2 (1 mM) Cg is less that 1 g/l.

Fig. 9. Ionic strength dependence of the critical gelation concentration for ␤-lg after heating 24 h at 80 ◦ C.

Further information about the structure of the aggregates can be obtained from Fig. 10 where Mw is plotted versus d Rgz . For fractal objects Mw = aRgzf , where the prefactor a depends on the local structure of the aggregates and their size distribution [26]. The lower limit of Rgz and Mw is given by that of the primary aggregates and is independent of the ionic strength. Within the experimental error, the influence of the ionic strength on the dependence of Mw on Rgz can be interpreted in terms of a varying fractal dimension with the same local structure. In this interpretation df increases continuously with increasing ionic strength from 1.7 to 2.3. However, this result is inconsistent with the measured static structure factors that did not show such an important variation of df . An alternative interpretation is that the fractal dimension on large length scales does not vary strongly, but

107

0.003M 0.01M 0.02M 0.05M 0.1M 0.2M 0.4M

107

106 10

Mw (kgmol-1)

6

MW (kg/mol)

0.01

10

5

105

104 10

4

103 103 0.1

1

10

100

C (g/L) Fig. 8. Concentration dependence of Mw at different ionic strengths. The symbols are as in Fig. 7.

10

100

1000

Rgz (nm) Fig. 10. Dependence of Mw on Rgz for ␤-lg aggregates formed at different ionic strengths.

K. Baussay et al. / International Journal of Biological Macromolecules 34 (2004) 21–28

that the local structure varies with the ionic strength. In Fig. 10 the slopes of the solid lines through the data at the 3 highest ionic strengths are 2. For comparison a line with slope 1.7 is also drawn in Fig. 10. The implication of this interpretation is that the packing of the primary aggregates on short length scales is denser at higher ionic strength. Apparently, the large scale structure of the aggregates is not very dependent on the ionic strength, but the aggregates become significantly denser for ionic strengths higher than 0.05 M. The origin of this densification is probably the stronger branching of the aggregates at higher ionic strength. From Cryo-TEM and X-ray scattering experiments it appears that at low ionic strength the primary aggregates associate mainly head to tail, while at high ionic strength side ways association leading to branching becomes more common [23]. The hydrodynamic radius and the degree of flexibility of the aggregates can be probed by dynamic light scattering. The intensity autocorrelation functions were analysed in terms of a distribution of relation times (τ). The q-dependence of the apparent diffusion coefficient (D) was measured for highly diluted aggregates formed at different ionic strengths. For rigid spherical particles D does not depend on q even for qRh > 1. For rigid fractal aggregates D increases somewhat with increasing q due to the influence of rotational diffusion. Finally, for flexible particles one expects D ∝ q for qRh >> 1. As was shown earlier in ref. [5] master curves can be obtained by plotting the values of D/D0 obtained at different protein concentrations as a function of qRhz . Fig. 11 shows that master curves are obtained at all ionic strengths investigated. In all cases D increases with increasing q for qRhz > 1, but the increase is more im10

D/D0

0.003M 0.01M 0.02M 0.05M 0.1M 0.2M 0.4M

1

0.1

1

10 qR

hz

Fig. 11. Dependence of D/D0 on q × Rhz for highly diluted ␤-lg aggregates formed at different ionic strengths. The master curves were constructed by superposition of the data obtained from aggregates that were formed by heating protein solutions for 24 h at 80 ◦ C at different protein concentrations.

27

portant at lower ionic strength implying that the aggregate formed at lower ionic strength are more flexible. The lower flexibility at higher ionic strength is probably caused by the increasing degree of branching of the aggregates. The ratio Rhz /Rgz is about 0.7, independent of the ionic strength similar to that observed in 0.1 M NH3 COOH [5]. 3.5. Comparison with aggregation at pH 2 At pH 2 ␤-lg is strongly positively charged and heat-induced aggregation at pH 2 leads to the formation of linear aggregates with a diameter of about twice that of the monomers [25,27,28]. The rigidity of these fibrillar aggregates decreases with increasing ionic strength. At low ionic strength (0.01 M) the aggregates are very rigid and very large aggregates are formed even at very low conversion. This suggests that the aggregation occurs by a process of nucleation and growth. The monomer depletion is much slower at pH 2 than at pH 7. Although the effect has not been studied systematically, it appears that also at pH 2 not all proteins aggregate even after severe heat treatment and the concentration of unaggregated proteins increases with decreasing ionic strength. We speculate that a minimum protein concentration is needed to form stable nuclei. Fibrillar aggregates are also formed by OA and BSA [29,30]. Whereas the aggregates formed by ␤-lg and OA are irreversible, BSA forms reversible aggregates at pH 2 that disintegrate completely when diluted below a critical concentration, though aggregates formed at pH 7 are irreversible [29]. Again this critical concentration was found to increase with decreasing ionic strength. Probably in all these cases nuclei are initially formed via weak reversible bonds, but in the case of BSA at pH 2 the bonds are not stabilised in time. Also for fibrillar ␤-lg aggregates formed at pH 2 the critical gel concentration increases with decreasing ionic strength. At high ionic strength (0.1 and 0.2 M) flexible linear aggregates are formed with a size that increases with increasing protein concentration and diverges at Cg [25]. Similar linear flexible aggregates are formed by OA at pH 7 at all ionic strengths [4]. Cross-links are formed between the linear aggregates once they strongly overlap. The size of the aggregates diverges at lower concentrations when the ionic strength is increased and thus Cg decreases with increasing ionic strength. At pH 2 and lower ionic strength large rigid fibrils are formed even at low protein concentrations and it is not clear if and to what extent cross-links are formed. It is conceivable that the elasticity is caused by repulsive interactions, i.e. jamming of the rods. This is quite different from the situation at pH 7 and at higher ionic strength where the gelation is unambiguously caused by cross-linking. It has been suggested that the gelation of more rigid fibrillar protein aggregates is due to the formation of random binary contacts between semi-flexible rods [27,29,30]. Within this model the critical gel concentration corresponds to the percolation threshold of rods in contact. Semi-flexibility is taken into account by

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considering that the chains consist of L/P rigid sections of length P, where L is the contour length and P is the persistence length. At lower ionic strength the electrostatic repulsive interactions between the rods increase, which would lead to a lower jamming concentration as is observed for charged spheres. Instead it is found that Cg increases with decreasing ionic strength. The explanation has been sought in the fact that the effective thickness of the fibrils, Deff , decreases with increasing ionic strength and that Cg is approximately Deff /P [27,29,30]. An increase could also be caused by an increasing correlation between the orientation of nearest neighbouring rods because strong repulsive interactions drive neighbouring rods to align. Yet another possibility is that there is an attraction between the rods in contact without this necessarily leading to an irreversible bond. One might expect that such a net attraction increases with increasing ionic strength which would explain the decrease of Cg .

4. Conclusion Heat-induced denaturation of ␤-lg at pH 7 below a critical concentration, Cg , leads to the formation of stable self similar aggregates. The heating temperature influences the rate with which the aggregates are formed, but not their structure. The aggregate size increases with increasing protein concentration and diverges at the critical gel concentration Cg . Cg decreases with increasing ionic strength from 100 g/l in pure water to 1 g/l at 0.4 M NaCl. For C > Cg gels are formed, except at high ionic strength where Cg is small so that the gel is very fragile for C close to Cg . Consequently the gel collapses under gravity and a precipitate is formed. The initial step of the aggregation is the formation of primary aggregates containing about 100 monomers. The primary aggregates are only formed above a critical association concentration, CAC. Apparently smaller aggregates are not stable at pH 7. Larger aggregates are formed by association of the primary aggregates. The larger scale structure of the aggregates is little influenced by the ionic strength, but the density of the aggregates on small length scales increases with increasing ionic strength, probably caused by an increasing degree of branching. Increased branching causes the aggregates to be less flexible at higher ionic strength.

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