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Journal of Colloid and Interface Science 398 (2013) 255–261
Contents lists available at SciVerse ScienceDirect
Journal of Colloid and Interface Science
www.elsevier.com/locate/jcis
Coacervates of lysozyme and b-casein
Skelte G. Anema a, C.G. (Kees) de Kruif b,⇑
a
b
Fonterra Research Centre, Private Bag 11029, Dairy Farm Road, Palmerston North, New Zealand
Van‘t Hoff Laboratory for Physical and Colloid Chemistry, Padualaan 8, Utrecht University, The Netherlands
a r t i c l e
i n f o
Article history:
Received 1 December 2012
Accepted 7 February 2013
Available online 27 February 2013
Keywords:
Complex coacervation
Proteins
Lysozyme
Casein
b-Casein
a b s t r a c t
Complexes are formed when positively charged lysozyme (LYZ) is mixed with negatively charged caseins.
Adding b-casein (BCN) to LYZ leads to flocculation even at low addition levels. Titrating LYZ into BCN
shows that complexes are formed up to a critical composition (x = [LYZ]/([LYZ] + [BCN]). The formation
of these complex coacervates increases asymptotically toward the molar charge equivalent ratio (xcrit),
where the size of the complexes also seems to grow asymptotically. At xcrit, insoluble precipitates of
charge-neutral complexes are formed. The precipitates can be re-dispersed by adding NaCl. The value
of xcrit shifts to higher values on the LYZ side with increasing salt concentration and pH. Increasing the
pH, de-protonates the BCN and protonates the LYZ, and therefore, charge neutrality will shift toward
the LYZ side. xcrit increases linearly from 0.2 at no salt to 0.5 at 0.5 M NaCl. It ends abruptly at a salt concentration of 0.5 M after which a clear mixed solution remains. Away from the charge equivalent ratio, it
seems that the buildup of charges limits the complex size. A simple scaling law to predict the size of the
complex is proposed. By assuming that surface charge density is constant or can reach only a maximum
value, it follows that scattering intensity is proportional to |(1 x/xcrit)|3 where x is the mole fraction of
one protein and xcrit the value of the mole fraction at the charge equivalent ratio. Both scattering intensity
and particle size seem to obey this simple assumption. For BCN–LYZ, the buildup occurs only at the LYZside in contrast to lactoferrin which forms stable complexes on either side of xcrit. The reason that the
complexes are formed at the BCN side only may be due to the small size of LYZ, which induces a bending
energy in the BCN on adsorption.
Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction
Recently, we investigated the interaction of lactoferrin (LF) and
lysozyme (LYZ) with both native casein micelles as found in skim
(bovine) milk [1] and with the individual caseins [2]. LF has a
pI 8.0. The pI of LYZ is calculated as 9.32 and experimentally
found at 10.9. Thus, a LYZ may carry up to net 10 positive charges
(from arginine and lysine) at neutral pH, which is quite high taking
into account that it is a relatively small protein with a molar mass
of 14.3 kDa. Adding LF to bovine skim milk induced a disintegration of the casein micelles [1]. This was a surprising phenomenon
which had not been reported before. Both LF and LYZ bound
strongly to the individual caseins and sodium caseinate, which is
a mixture of the caseins as found in milk [2]. The binding has all
the characteristics of a complex coacervation which is defined by
IUPAC [3] as:
‘‘(complex) coacervation caused by the interaction of two oppositely charged colloids’’.
⇑ Corresponding author.
E-mail address: [email protected] (C.G. (Kees) de Kruif).
0021-9797/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.jcis.2013.02.013
While coacervation is defined by IUPAC [3] as:
‘‘The separation into two liquid phases in colloidal systems. The
phase more concentrated in colloid component is the coacervate,
and the other phase is the equilibrium solution’’.
In actual fact, the interaction of LF (and LYZ) with the caseins
does not readily lead to a new phase, but it has a clear signature
of the interaction of oppositely charged colloids. The interaction
can be reversible and can be disrupted on addition of salt, which
are also characteristics for complex coacervates of polysaccharides
and proteins [4,5]. On the other hand, if the proteins were mixed at
such a ratio that charge neutrality was achieved, the formation of
large complexes increased exponentially. Thus, at charge neutrality
of the complexes, they grew asymptotically. In that sense, we may
say that a new phase was formed. This ‘‘new phase’’ (a precipitate
and in the strict sense of the IUPAC definition not a coacervate) disappeared when the composition was away from charge neutrality.
The binding of LF and LYZ to other proteins is of scientific interest but has also practical aspects as for instance LF is added to infant formula because of its immuno-regulatory and bacteriostatic
properties. LYZ is applied in cheese making as a bacteriostatic for
Clostridium tyrobutyricum, a spore forming microorganism that
may spoil cheese ripening. Exactly for these reasons, the binding
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of LYZ to caseins has been investigated previously by Thapon and
Brule [6] and de Roos et al. [7]. Pan et al. [8] made nanoparticles
by heating mixtures of b-casein (BCN) and LYZ. Lindhoud et al.
[9] studied the salt dependent interaction of LYZ and polyelectrolyte (PE) complex micelles, showing that at salt levels above
0.3 mol/L the interaction is absent. LF binds particularly strong
(at neutral pH) to osteopontin (OPN; bone sialoprotein I) a largely
unstructured phosphorylated and sialated protein present in
cheese whey [10]. OPN resembles and is genetically related to
caseins present in casein micelles in mammalian milk and responsible for calcium transport to the neonate. From all these studies, it
is clear that LF and LYZ do bind to caseins under certain conditions.
Basically, the pH must be between the respective iso-electric points
and salt levels must be low because on addition of salt the complexes are destroyed.
The interaction of oppositely charged proteins has been sparsely studied. For instance, there is not a review paper, as far as
we know, while there are several on the interaction between oppositely charged proteins and polysaccharides [4,5]. There is a very
extensive and detailed review on the interaction of oppositely
charged polymers by Voets et al. [11], where they state that the
interaction between oppositely charged polymers is complex coacervation, although again strictly speaking, a new phase is not always formed. As said, literature on protein–protein complex
coacervation is scarce. The reason being that complex coacervation
is usually strongest in polyelectrolyte (polysaccharide) systems in
comparison with often more globular proteins. Gelatin (a polyelectrolytic protein) coacervates were studied extensively and were
the system used by Overbeek and Voorn [12] to develop the first
theoretical model on complex coacervation. The complexation of
gelatin and gum Arabic is well described. Burgess [13] and Tiwari
et al. [14] used oppositely charged gelatins to form coacervates
as a vehicle for drug delivery, which in fact motivated much work
on complex coacervation.
An extremely interesting example of protein–protein complex
formation is in the adhesive glue of sand-castle worm, the caddisfly larvae, and mussels [15]. The glue consists of highly acidic and
highly basic proteins. Although the precise mechanism is yet not
fully clear, it is evident that the opposite charges of the proteins
plays a key role. Synthetic polymers with properties mimicked
from the proteins indeed serve as underwater glue.
LYZ is a small cationic protein and studied in combination with
milk proteins, b-lactoglobulin [16], a-lactalbumin [16–20], and
casein [8,21]. Using native LYZ and a succinilated LYZ, Biesheuvel
et al. [22] studied the complexation of these proteins. Phase separation was observed under suitable conditions: pH between the pI,
high protein concentration, low salt and, surprisingly, low temperature. It is surprising, since complex coacervates are usually a –
thermal [5]. In addition, Biesheuvel et al. [22] developed a theoretical model incorporating both electrostatic and nonelectrostatic
interactions.
The behavior of the system used by Biesheuvel does not compare with the LYZ/a-lactalbumin system. LYZ and a-lactalbumin
are homologous molecules of nearly equal molar mass. Obviously,
the succinilation changes essential properties of the anionic protein. Salvatore et al. [17] also point out that they find different
behavior. They do not find a thermodynamic equilibrium behavior
and no temperature dependence. Therefore, it seems that small
subtleties of each system may lead to a different behavior. The
interaction of LYZ with casein was focused on the formation of
(permanent) complexes after heating [8,21].
LF, a relatively large cationic protein, forms large(r) complexes
with milk proteins but it is not always clear whether a real liquid
coacervates phase is formed. Lampreave et al. [23] used blactoglobulin which formed complexes but a-lactalbumin did
not. Maybe the charge distribution of b-lactoglobulin which is
known to be ‘‘patchy’’, that is, nonhomogeneous [24], affects the
interaction behavior. Recently, we studied the interaction of LF
with caseins [1,2] and found a clear equilibrium complexation
depending on mixing ratios and moderate salt concentrations.
Finally, protein–protein interaction is of primordial importance
in living organisms. Protein–protein recognition controls many of
the biophysical and biochemical processes. Also the interaction of
enzymes and proteins is a clear example of recognition of structures. Although there is a clear interaction, these systems do not
form complex coacervates. They may form (temporal) oligomeric
structures [25]. In summary, it seems that the complexes formed
by LYZ and other globular proteins are somewhere between protein recognition/docking and a macroscopic complex coacervate liquid, which make them possibly a good candidate to study these
interesting phenomena.
The interaction of proteins with DNA and RNA has been studied
extensively as well. Record et al. [26] proposed that the binding of
a positive ligand, for example, a protein or oligo-lysine to a linear
nucleic acid would neutralize an equivalent amount of phosphates
resulting in the release of the counterions that had been associated
with the phosphates [27]. The interaction depends on the charge
state of the protein and thus on pH. Arcesi et al. [28] developed a
generalized electrostatic model for the wrapping of DNA around
histones. Their model contains three terms of an electrostatic origin, and a fourth term takes into account the elastic energy to bend
a DNA around the histone complex.
Experiments have revealed that the pH is a parameter of secondary importance as discussed by Wittemann and Ballauf [29].
The reason for this is that complexes may spontaneously overcharge because there is a competition between maximizing the
electrostatic interaction, which favors electro neutrality (and
would add a Van de Waals energy), and the release of (condensed)
counter ions upon overcharging [30]. The overcharging occurs if a
flexible macro-ion binds to spherical or cylindrical macro-ions
[30]. It is for this reason that pH is an important factor but not
the decisive one [29].
Thus, free energy gain derives from the liberation of counter
ions as nicely illustrated by Wittemann and Ballauf [29]. Also
Yamniuk et al. [10] and others [5,31,32] argue that complex
coacervation is driven by the release of counter ions, and therefore,
it is entropy driven. Voorn [33] and Voorn and Overbeek [12] were
the first to develop a theoretical framework for complex coacervation (based on the experiments of Bungenberg-de-Jong and Kruyt
[34–36]), and they also pointed out that the entropy contribution
was a driving force for the complex coacervation of gum Arabic
and gelatin. Later, extensions were developed of the Voorn-Overbeek theory, and just recently, a very extensive and detailed study
was presented in the thesis of Spruijt [37], which applies, refines,
and extends the original theoretical concepts of Voorn [33].
Spruijt’s theoretical modeling contains an entropical and electrical
field energy contribution, which leads to a less prominent role of
the counterion release.
Carlsson et al. [38] present extensive Monte Carlo computer
simulations of the interaction of a negatively charged polyelectrolyte with ‘‘LYZ’’. The results indicate that a patchy distribution of
the charges leads to stronger complex even if the overall charge
of the protein is still negative. A stiffer polymer (due to charge
repulsion and or bond angle energy) leads to less complexation.
Low salt concentration is advantageous as well. Too low salt stiffens the polyelectrolyte. Carlson et al. show that the addition of a
short range attraction (Lennard–Jones type) gave a better agreement with experimental results.
The interaction of LYZ with the caseins was distinctly different
from that of LF with the caseins. LF formed stable (overcharged)
complexes with the caseins at all mixing ratios, which near charge
neutrality of the system asymptotically grew in size because, as we
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suggested, the overcharging limits the size of the complexes. A
simple scaling law could be used to describe the various systems
at low salt content [2]. LYZ however seemed to overcharge only
with an excess of BCN so only with negatively charged complexes.
Adding BCN to LYZ even at very minute quantities led to flocs and
precipitates. We therefore decided to undertake a separate study of
the interaction of LYZ with the caseins. In addition, we will investigate the salt sensitivity of the system by adding NaCl.
In this study, we will report on the interaction of LYZ with the
individual caseins and particularly BCN. The LYZ-casein interaction
appeared to be different from LF-casein in that only in a limited regime, stable complexes could be formed. We think that this is
caused by the small size of the LYZ protein which induces bending
energy in the BCN polymer on binding to LYZ. As a result, over or
undercharging is severely limited and therefore the complexes
aggregate as a result of Van der Waals attractions between the
neutral complexes.
2. Experimental
2.1. Protein samples and solutions
The j-casein (KCN) and LYZ (from chicken egg white, >90% purity) were obtained from Sigma Aldrich (Sigma–Aldrich, St. Louis,
Mo, USA). The BCN was obtained from EURIAL (Rennes, France).
LF (>90% purity) and sodium caseinate (NaCN) were obtained from
the Fonterra Cooperative Group, (Auckland, New Zealand). All
proteins were used as supplied. Stock solutions of LF, LYZ, and
the caseins were prepared at about 10 mg/mL (w/w). Exact concentrations were determined using UV absorption at 280 nm and
using reported extinction coefficients [39,40]. Sodium azide
(Sigma–Aldrich, St. Louis, Mo, USA) was added to the protein solutions at 0.02% (w/w) as a preservative. The ionic strength of protein
dispersions was low (less than 10 mM) as based on conductivity
measurements.
2.2. Dynamic light scattering and turbidity/transmission
measurements
Dynamic light scattering (DLS) was performed using a Malvern
Zetasizer Nano ZS instrument (Malvern Instruments, Malvern,
Worcestershire, UK) using the techniques described previously
[41]. Turbidity/transmission measurements were performed using
257
a Jasco V580 spectrophotometer (Japan Spectroscopic Co., Hachioji
City, Japan) using the techniques described previously [42].
2.3. pH measurements
The pH of solutions was measured using a N61 Schott-Gerate
combination pH electrode (Schott-Gerate, Hofheim, Germany)
associated with a Radiometer PHM 92 Lab pH meter (Radiometer
Analytical, Bronshoj, Denmark).
3. Results and discussion
3.1. pH on mixing the protein solutions
Electrostatic complexes will be formed on titrating one PE solution into another. The PE’s must be oppositely charged and at the
same pH about halfway between the respective pKa’s. The relevant
quantity is the mixing mole fraction, x, which equals [LYZ]/
([LYZ] + [CN]) (where CN refers to the BCN, KCN or NaCN). In
Fig. 1A, we present the titration of BCN into LYZ and vice versa at
a starting pH of 6.56. The variation in pH is typical for such an
experiment. At the LYZ side, pH goes down due to the release of
protons. Charge neutrality is achieved at the inflection point, at
about x = 0.5 (mg/mg). The sample gets rather turbid after only
50 lL of BCN has been added to LYZ, and the solution appeared
clearly flocculated. On titration of LYZ into BCN, the system gets
turbid but only flocculated after x = 0.2. The experimental data
starting from either side nicely join. This is remarkable because
for x > 0.2, the system is completely flocculated, but that does
not seem to influence the exchange of protons. Even adding
25 lL of BCN to LYZ results in flocculation. By adding salt, the system becomes clear again (at x = 0.4 and at [NaCl] P 0.3 mol/L).
Similar experiments were made for KCN (Fig. 1B) and NaCN
(Fig. 1C) with LYZ. Both the KCN and NaCN flocculated strongly
on mixing with LYZ. Only on the casein side, in a very small region,
could soluble complexes be formed. It is remarkable that on titration of LYZ into the casein solutions, the intensity and apparent
particle size diverge at x < 0.2, whereas the inflection point in the
pH curve is at x = 0.5. If LYZ is replaced by LF, the divergence always
coincides with the inflection point, which indicates the charge
neutrality of the complexes formed [2]. For BCN–LYZ, the formed
complexes at x = 0.2 must be charge neutral; otherwise, their
growth would be limited. The composition of the complexes must
be about 0.5 because they are charge neutral. The LYZ fraction is
Fig. 1. pH as a function of mixing ratio. (A) BCN (14.9 mg/mL) and LYZ (13.6 mg/mL) at pH = 6.56. (B) KCN (8 mg/mL) and LYZ (13.6 mg/mL) (C) NaCN (10 mg/mL) with LYZ
(13.6 mg/mL) solution. Titrations were started from either side (r, ).
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only 0.2 instead of 0.5 as would follow from the pH curve. Therefore, the complexes are stabilized up to x = 0.2 by the negative
repulsive charge of the BCN. On further lowering the relative
BCN concentration (by adding LYZ), the complexes become unstable because no overcharging occurs. Even the first drop of BCN into
LYZ leads to flocculation. On increasing the salt concentration, the
flocculated systems become clear again.
3.2. Scattering intensity and size of the complexes
Fig. 2. Scattering intensity (r) and apparent particle size ( ) of LYZ–BCN mixtures
as a function of mass fraction. [NaCl] = 0.01 mol/L.
Similar to the pH measurements, we recorded the scattering
intensity and the apparent particle size from a cumulant fit of
the intensity autocorrelation function. In Fig. 2, we present the
data for titrating LYZ into BCN. On titration of BCN into LYZ, scattering intensity diverges at xcrit = 0.2 (note x is still in mg/mg).
Since molar mass of LYZ is 14.3 kDa and BCN molar mass
24 kDa, xcrit is about 0.3 mol/mol or about three BCN molecules
per LYZ molecule. Complexes consist of at least 1000 molecules
as the size increases by a factor of 10 or more.
Titration from the LYZ side is not meaningful because flocculation occurs on the first addition of BCN–LYZ. This is in contrast to
the casein-LF systems, which are symmetrical and can be titrated
Fig. 3. Titration of BCN with LYZ at different salt concentrations. Scattering intensity (r) and size (s). (A) [NaCl] = 0.13 mol/L at the asymptote, xcrit = 0.34. (B)
[NaCl] = 0.21 mol/L, xcrit = 0.42. (C) [NaCl] = 0.26 mol/L at the asymptote, xcrit = 0.5. (D) [NaCl] = 0.5 mol/L.
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past xcrit [2]. After titration of BCN with LYZ beyond xcrit, the flocs
could be redispersed by adding NaCl.
Since NaCl seemed to ‘‘soften’’ the interactions, we used BCN
with salt levels of 0.2 mol/L and 0.5 mol/L NaCl, respectively; the
LYZ did not contain added salt (Fig. 3A and C). Therefore, the salt
concentrations at the asymptote were 0.13 mol/L and 0.26 mol/L
for Fig. 3A and C, respectively. We also did an experiment where
we added 0.21 mol/L NaCl to both the BCN and LYZ solutions
(Fig. 3B). Scattering intensity diverges at xcrit where the systems
become very turbid. But after the critical point, the system is flocculated and does not re-disperse.
We continued to add another 400 lL LYZ, but the system remained flocculated. This contrasts with using LF, which was stable
on each side of xcrit[2]. On adding NaCl up to 0.5 mol/L gives a clear
solution again. Therefore, we did a titration of LYZ into BCN where
each protein dispersion contained 0.5 mol/L salt (Fig. 3D). From
Fig. 3D, it is clear that around x = 0.5, there is a weak sign of complexation. Particle size goes up slightly while intensity seems to
come down a bit; however, visibly nothing happened. In order to
see the stability of the complexes, we titrated LYZ (with no salt
added) into BCN (with 0.5 mol/L NaCl). This gave stable complexes
with an xcrit = 0.5. At the endpoint, the effective [NaCl] was
0.27 mol/L. We also titrated BCN (no salt added) into LYZ (in
0.5 mol/L NaCl) and xcrit = 0.5 (Fig. 4). This was, in fact, the same
as for the titration of BCN into LYZ (Fig. 3C). So it seems that below
[NaCl] = 0.5 mol/L, complexes may be formed.
We gathered the data from the above figures and plotted xcrit vs.
[NaCl] at xcrit (Fig. 5). It is interesting to see that xcrit seems to go to
xcrit = 0.5 at high salt, the same value as found for the inflection
point in the pH titration curve of Fig. 1. It also means that even
at lower salt concentrations, insoluble complexes are formed before overall charge neutralization. Also the results shown in
Fig. 5 suggest that complexes may be formed up to x = 0.2 (at the
BCN side), but then, flocculation will occur in the no salt limit.
3.3. Complexation as a function of pH
In order to investigate the (weak?) pH dependence of the complexation, we increased the pH to approximately halfway between
the pI of BCN (pI 4.6) and LYZ (pI 10.9). We thought that the
interactions may become ‘‘softer’’ and more symmetrical. With
softer, we mean that the complexes may become more liquid like
rather than a precipitate. We raised the pH of both dispersions to
7.66 by adding 1 mol/L NaOH. Initial trials showed that either
adding BCN–LYZ or vice versa immediately gave flocculation when
no salt was present.
We then tried titrating LYZ into BCN at pH = 7.66 with 0.21 mol/L
NaCl in both solutions (Fig. 6). The critical composition is at x = 0.5,
[NaCl] = 0.21 mol/L. In the case where the pH of the stock solutions
was 6.55 and at [NaCl] = 0.26 mol/L, the critical composition was at
x = 0.4. So the higher pH shifts xcrit to the LYZ side. This is expected
as BCN will be more de-protonated and LYZ more protonated.
Therefore, complex composition will shift toward LYZ in order to
reach charge neutrality.
In a further experiment, we adjusted the pH of both protein
solutions to pH = 9.01, so much closer to the pI of LYZ. Adding 10
or 20 lL of BCN to 1 mL of LYZ (at pH = 9.01, no salt) immediately
gives floculation, and the flocs formed can swirl around in the cuvette and do not re-disperse even when adding salt up to 0.6 M.
Adding 20 lL LYZ to 1 mL of BCN also gives flocculation; however,
adding 50 lL of 3 M NaCl disperses the flocs ([NaCl] = 0.15 mol/L).
This dispersion is further titrated with LYZ including 0.15 mol/L
NaCl in the LYZ (Fig. 6B). The particle size analysis shows small
particles that are even smaller than the BCN dispersion. We
titrated this dispersion with LYZ to which NaCl was added to the
same level of 0.15 M. After 700 lL, LYZ (x = 0.4) size goes up but
does not stabilize as observed at previous additions as both size
and scattering intensity go up. We measured the changes as a function of time, and it seems that the particles are marginally stable
and now flocculate by a growth process.
It was noted that on adding LYZ to BCN small flocs may appear,
and these flocs do not redissolve. This is caused by the local overconcentration of LYZ. We carefully added the LYZ while stirring but
could not prevent the formation of a few flocs that sedimented.
These flocs occasionally disturb the correlation function during
the particle size analysis, although this was not considered too
serious.
Overall, it seems that LYZ behaves as a multivalent microion as
it has effects similar to those when, for example, calcium is added
to casein suspensions. The addition of calcium gives turbid casein
suspensions or can actually flocculate the casein from solution.
As with LYZ, these effects are also dependent on the salt concentration of the systems.
3.4. Modeling of the experimental results
The mixing (mole) fraction x = [LYZ]/([LYZ] + [CN]) (where CN
stands for BCN, KCN, or NaCN) is the relevant quantity as it
0.8
xcrit (mg/mg)
0.6
flocculated
solution
0.4
0.2
complexes
0.0
0.0
0.2
0.4
0.6
0.8
[NaCl] (mol/L)
Fig. 4. LYZ (in 0.5 mol/L NaCl) titrated with BCN (no salt) xcrit = 0.5. [NaCl] = 0.27 mol/L at the xcrit. Scattering intensity (r) and size (s).
Fig. 5. Critical flocculation concentration against salt concentration.
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Fig. 6. (A) pH = 7.66. LYZ titrated into BCN. xcrit = 0.5, [NaCl] = 0.21 mol/L at xcrit. (B) pH = 9.01. LYZ titrated into BCN. xcrit = 0.4, [NaCl] = 0.15 mol/L at xcrit = 0.4. Scattering
intensity (r) and size (s).
determines the number of (positively) charged proteins over the
total number of protein particles present. Voets et al. [11] define
a charge fraction f+ (and f = 1 f+) which is the number of chargeable groups in the polymers with respect to the total, independent
of the actual dissociation state. Here, we have proteins with both
positive and negative chargeable groups with varying pK. We
therefore use the unambiguously defined mass fraction (or mole
fraction) x = [LYZ]/([LYZ] + [CN]), where [LYZ] and [CN] maybe
either in mol/L or in g/L (=mg/mL).
At a critical fraction, xcrit, the number of positive and negative
charges is just equal. In a separate paper [2], we argued that outside xcrit the buildup of charge in the complex limits its growth.
As a result for a complex of size r, the surface charge is:
jð1 x=xcrit Þjr3 =r 2 ¼ constant or r 3 1=jð1 x=xcrit Þj3
ð1Þ
We used this reasoning intuitively, but it was shown by Park
et al. [30] that oppositely charged macro-ion complexes can overcharge spontaneously. Also in the bending of DNA around histones,
there is an energy penalty depending on the size of the protein
complex [28].
Since we titrate one PE into the other, the mass concentration
(i.e., mg/mL) is about constant as the two PE’s have a similar concentration. For scattering particles that change their association
behavior at a constant total concentration, the scattering intensity
is proportional to u r3, where u is volume fraction and is approximately constant in our experiments. Thus, scattering intensity is
determined by:
Iscat jð1 x=xcrit Þj3 þ constant
ð2Þ
It is clear that salt concentration has an influence as well, because on adding salt the complexation diminishes (Figs. 3 and 6)
and the release of counter ions contributes less to the free energy
gain. In the case of LF-casein, overcharging occurred on either side
of xcrit [2]. Here, charge build up is present only at the casein side,
but the mechanism seems to be the same. The drawn lines in
Figs. 1–4 and 6 represent the fit determined using Eq. (2).
In dynamic light scattering, a weighted average particle size is
measured: rhydr = <r6>/<r5>. Hence larger particles, if present, are
heavily weighted. Also the presence of initial clusters, as in the case
of KCN will cause irregularities. The particle size would, in the
present situation, scale as the cube root of the intensity or
r3hydr =Iscat ¼ constant. Indeed, this ratio appears to be constant and
particularly in the critical complex region (results not shown).
Deviations occur only at x-values close to the pure components
as a result of clusters in the stock samples. Thus, regardless of
how simple the model may be, it is self-consistent.
4. General discussion
The LYZ–BCN system seems to behave somewhat differently
from the LF-casein systems. For ‘‘equilibrium’’ systems such as LF
plus casein [2] or b-lactoglobulin with gum Arabic [32] or oppositely charged synthetic polymers [11], complexation is strongest
at the charge neutral situation, thus at the inflection point in the
pH curve, xneutr. In the case of LYZ and BCN, complexation occurs
only at the BCN side and if [NaCl] concentration is between 0.3
and 0.5 mol/L. At lower salt levels, the system flocculates even at
lower mass fractions than xneutr.
The stability of complexes outside xneutr is explained and shown
by Park et al. [30] to be a consequence of the overcharging of the
complexes, which allows the release of extra counter ions with
the accompanying entropy gain. This scenario applies for a PE
binding to a spherical or cylindrical colloid, for example the binding of DNA to a histone octamer to form a complex known as a
nucleosome [43,44]. Thus, the complex will have the same charge
as the PE. However, if the bending energy of the PE is taken into
account, the complex may be under charged, overcharged or
(coincidentally) neutral, which then will lead to Van der Waals
flocculation. It therefore seems that the small size of the LYZ
protein prevents an effective binding of BCN and as a result only
limited or no overcharging occurs. This then leads to flocculation.
The computer simulations of Carlsson et al. [38] are fully consistent
with this picture.
It was observed that adding LYZ to BCN under stirring produced
stable complexes, although some small flocs may appear due to local overconcentration. These flocs do not re-disperse. Adding low
levels of BCN to the LYZ immediately leads to flocs and these also
do not redisperse. The fact that stable complexes are only found at
the BCN side indicates that BCN must ‘‘decorate’’ LYZ, and if a relative excess of LYZ is present, the BCN serves as glue. On adding
salt, the PE binding will be diminished and the electro-neutral
point will go to higher x-values until the electro-neutral point of
the system is reached at x = 0.5. The reason that the complexes
are stable on the BCN side only may derive from the small size of
the LYZ protein. At x = 0.2 mg/mg, the mole fraction is about 0.31
and thus about 3 BCN per LYZ. Charge neutrality occurs at
Author's personal copy
S.G. Anema, C.G. (Kees) de Kruif / Journal of Colloid and Interface Science 398 (2013) 255–261
x = 0.5 mg/mg which corresponds with x = 0.63 mol/mol or about 3
BCN per 2 LYZ. So at x = 0.2 mg/mg, LYZ can bind 1.5 BCN only
instead of 3 which would lead to overcharging and stability up to
x = 0.5 mg/mg. Adding salt shifts stability to higher x-values. This
can be understood because now there are fewer condensed
(Manning) ions and therefore a lesser penalty on the binding of
several BCN. At any salt concentration (<0.5 mol/L), charge
neutrality will occur at about the same x-value. In other words,
the bending energy of BCN decreases with salt concentration and
whether that is due to entropic or enthalpic energy remains to
be established.
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