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Diffusion and Partitioning of Macromolecules in Casein Microgels: Evidence for Size-Dependent Attractive Interactions in a Dense Protein System Paulo D. S. Peixoto,*,†,‡ Antoine Bouchoux,*,†,‡,@ Sébastien Huet,∥,⊥ Marie-Noel̈ le Madec,†,‡ Daniel Thomas,§ Juliane Floury,†,‡ and Geneviève Gésan-Guiziou*,†,‡ †

INRA, UMR1253 Science et Technologie du Lait et de l’Œuf, 65 rue de Saint Brieuc, 35000 Rennes, France AGROCAMPUS OUEST, UMR1253, 65 rue de Saint Brieuc, 35000 Rennes, France § Team Translation and Folding, Université de Rennes 1, UMR CNRS 6290 IGDR, Campus de Beaulieu, 35000 Rennes, France ∥ CNRS, UMR 6290, Institut de Génétique et Développement de Rennes, 35000 Rennes, France ⊥ Université de Rennes 1, Structure Fédérative de Recherche Biosit, Faculté de Médecine, 35000 Rennes, France ‡

S Supporting Information *

ABSTRACT: Understanding the mechanisms that determine the diffusion and interaction of macromolecules (such as proteins and polysaccharides) that disperse through dense media is an important fundamental issue in the development of innovative technological and medical applications. In the current work, the partitioning and diffusion of macromolecules of different sizes (from 4 to 10 nm in diameter) and shapes (linear or spherical) within dispersions of casein micelles (a protein microgel) is studied. The coefficients for diffusion and partition are measured using FRAP (fluorescence recovery after photobleaching) and analyzed with respect to the structural characteristics of the microgel determined by the use of TEM (transmission electron microscopy) tomography. The results show that the casein microgel displays a nonspecific attractive interaction for all macromolecules studied. When the macromolecular probes are spherical, this affinity is clearly size-dependent, with stronger attraction for the larger probes. The current data show that electrostatic effects cannot account for such an attraction. Rather, nonspecific hydration molecular forces appear to explain these results. These findings show how weak nonspecific forces affect the diffusion and partitioning of proteins and polysaccharides in a dense protein environment. These results could be useful to better understand the mechanisms of diffusion and partitioning in other media such as cells and tissues. Furthermore, there arises the possibility of using the casein micelle as a size-selective molecular device.

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INTRODUCTION

macromolecular interactions and diffusion in different systems.12−15 The focus of the current work is macromolecular diffusion and molecular interaction within one specific medium, the casein micelle, which is a dense protein assembly of colloidal size. For this purpose, the diffusion and partitioning behavior of a group of macromolecules (proteins and dextrans) with a range of characteristics (size and shape) was investigated in casein micelle dispersions of different concentrations. The casein micelle is the major protein constituent of milk. It is natural, biodegradable, and has the form of a biocompatible microgel,16,17 which contains ∼70% of water and ∼30% dry matter (minerals and the proteins, α1, α2 and β-caseins). It is a spongelike structure with many water-filled cavities.18 It

The fundamental understanding of the physical interactions between proteins and protein−polysaccharides in dense media is a fundamental issue in biology,1 medicine,2 and biotechnology.3 Recent understanding of these interactions has contributed to the development of a range of “smart” nanostructured materials used in biochemical analyses,4 in biomedical implants as catalyzers,5 in molecular severance devices,6 and in molecular carriers.7−11 The development of molecular vehicles that are able to deliver macromolecules (most often proteins) can, for instance, be used to create vaccines against diseases as AIDS or hepatitis C, or to enable oral delivery of medicines for cancer therapy.8−10 Furthermore, the study of the interactions that influence the diffusion of macromolecules in dense media is a key factor in the better understanding of cell biology.12 For this reason, many recent and established publications have investigated the physics of © 2015 American Chemical Society

Received: September 12, 2014 Revised: January 19, 2015 Published: January 20, 2015 1755

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structure of casein microgels close to their original state in the aqueous solution, samples were submitted to high pressure freezing followed by freeze substitution. Casein samples were frozen in a Leica EM PACT2 high-pressure freezer then immediately transferred to an automatic freeze substitution system (Leica EM AFS2) equipped with an automatic reagent handling system (Leica EM FSP). In order to increase the contrast, the samples were freeze-substituted in acetone containing 0.1% uranyl acetate at −90 °C for 60 h. The temperature was then raised at a rate of 3 °C/h to −50 °C, after which the samples were kept at this temperature for a further 24 h. At the end of this period, samples were washed once with acetone and then three times with 100% ethanol at −50 °C and then infiltrated with resin/100% ethanol mixtures by raising the volume-to-volume proportion of Lowicryl HM20 (25% for 2 h, 50% for 2 h, 75% overnight, and 100% four times for 1 h). Finally, polymerization was carried out at −50 °C for 48 h and at 20 °C for 48 h. To completely avoid the nucleation of ice, a dense (210 g/L) dispersion was used where the micelle particles are close to each other.32,33 The correlation between the casein concentration (C) (in g/ L) and the volume fraction (ϕ) of micelles in the dispersion (upper and lower axis in Figure 2) is given by the native voluminosity of the microgel [v = 4.4 mL/g and ϕ = 4.4 × 10−3 × C(g/L)].33 ϕ is the ratio of the volume occupied by the micelle particles divided by the total volume of the dispersion. For microgels that are soft and deformable such as the casein micelle, it may be noted that it is possible to concentrate the solution so that ϕ has a value higher than 1. In such cases, the micelle particles are fully touching and have compressed to a lower volume, thus leading to a true voluminosity that is lower than the native one. Because volume fractions can exceed unity, they are better referred to as “effective” volume fractions. The TEM analyses were conducted using a Tecnai G2 Sphera electron microscope (FEI Company, Eindhoven, The Netherlands) operating at 200 kV. A tilt series of uranyl-stained 200 nm thick sections were recorded at a nominal magnification of 25000. Digital images were automatically recorded on a Gatan Ultrascan CCD camera over a tilt range from −60 to +60 with an angular increment of 1°. The eTomo graphical user interface of the IMOD Tomography package was used to perform the 3D reconstruction. Images were preprocessed and aligned. The 3D reconstructions were performed by weighted back-projection. The 3D volumes were imported into the 3D visualization software CHIMERA37 for visualization. A Gaussian smoothing filter (width 0.37 nm) was applied. The radius, rf of the internal elements (called here fibers) forming casein microgels and the mean distance between next neighbors fibers (ξ) were extracted from 5 nm in-depth tomogram 2D slices. The Figure SI-1 of the Supporting Information explains the procedure. The repeatability of the measurement was evaluated using data from five different casein microgels. Preparation of the Macromolecular Probes. Dextrans (Dex) and proteins were used as the diffusing species. All macromolecules were fluorescently labeled with either fluorescein isocyanate (FITC, in the case of the FRAP experiments) or rhodaminisothiocyanate (RITC, in the case of FCS experiments). Proteins. The proteins used in the experiments were αlactalbumin, β-lactoglobulin, and bovine serum albumin. All are globular proteins which can be reliably considered as rigid spherical particles for the diffusion experiments.12,14 Note-

displays a diameter of around 100 nm and a surface comprising a so-called “hairy” layer composed of a brush of κ-casein.19 Both the hairy layer and the internal spongy casein core of the micelle are negatively charged at a neutral pH.19 The casein micelle is an interesting particle as it can readily be used as a drug carrier, notably in an oral delivery system.16 Some studies have demonstrated the potential of the casein micelle to deliver molecules with anticancer properties such as curcumin20 or other polyphenols.21,22 Other studies have reported on the strong attractive interactions between casein microgels and lysozyme23 or lactoferrin.23,24 In these last examples, the attraction between the micelle and the transported molecule is expected since casein, as already mentioned, is mainly negatively charged at neutral pH, while the two studied proteins have a surface that is positively charged and show a natural propensity to aggregation.25−29 Nonetheless, a broader study on the diffusion of proteins or polysaccharides through the casein micelle and the subsequent interactions is still very much lacking. Thus, in this study, the diffusion of a selection of macromolecular probes of various charges (neutral and negative) and shapes (linear and spherical) in a dispersion of casein microgel is investigated using an experimental approach based on the FRAP technique (fluorescence recovery after photobleaching). The measured diffusivities are used to calculate the partition coefficients that in turn reveal the interactions of the probes with the casein. The magnitude and the possible nature of these interactions are discussed in the context of the structural and physicochemical characteristics of the macromolecular probes and the casein microgel.

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EXPERIMENTAL SECTION Preparation and Structural Characterization of the Casein Media. Preparation of Casein Microgel Dispersions. Dispersions with casein concentrations ranging from 20 to 100 g/L were prepared by the direct rehydration of casein powder prepared in-house.29,30 The powder had a composition of 91% w/w of total solids (TS), 85.6% of caseins, 8.5% of minerals, and 4.6% of noncasein protein matter.30 The solution used to rehydrate the powder was the permeate obtained from the ultrafiltration (UF) of skimmed milk; this is the aqueous phase most often used for reconstitution because it maintains the main properties of the native casein micelles.31 The average ionic composition of the permeate was ∼20 mM Na+, ∼40 mM K+, ∼10 mM Ca++, ∼30 mM Cl−, ∼10 mM phosphate, and ∼10 mM citrate.30 For the experiments performed with a higher ionic strength, a previously rehydrated solution of 60 g/L of casein was mixed with a permeate solution containing 340 mM of NaCl 2 h prior to the FRAP measurement. The final concentration of casein in this case was 30 g/L, and the final concentration of Na+ and Cl− were raised to 190 and 180 mM, respectively. Concentrated samples of casein micelles (150 to 250 g/L) were obtained by using the osmotic pressure technique as previously described.30 Samples were kept in dialysis bags, at 20 °C, for 1 week in a UF-polyethylene glycol (35 kDa, SigmaAldrich, St. Louis, MO) solution containing 0.02% thimerosal and 0.1% sodium azide (Sigma-Aldrich). The dried weight of a small sample of each prepared medium was measured to obtain the final casein concentration in the bag. In all the cases, the pH of the casein micelle dispersion was found to be 6.8. Characterization of the Microgel Structure Using Electron Tomography and 3D Reconstruction. In order to keep the 1756

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Table 1. Partition Coefficients (K) and Internal Diffusion Coefficients of Proteins and Dextrans Determined by Using Different Methods (FRAP, FCS, and Dialysis) diffusion coefficients (μm2 s−1)

partition coefficients (K) a

FCS

dialysis

probes Dex4 Dex10 Dex20 Dex40 Dex70 α-LA β-LG BSA

3.3 − − − 1.1 − 7.5 −

− − − − − − 8.0 −

a

D250g/L

D1

setting D1 = D250g/Lb

using D1 as fitting parameterc

experimental

deduced from a data fit to the Cell model

2.0 2.0 1.5 1.5 1.5 4.5 6.5 27.0

2.0 1.5 1.5 1.5 2.5 4.0 6.0 26.5

42.0 22.1 9.6 4.0 1.3 5.3 2.7 1.4

40.4 18.1 11.3 5.3 2.5 2.4 1.2 1.2

FRAP (Cell model)

a

Description of FCS and dialysis can be found in the Supporting Information. bD250g/L is the diffusion coefficient measured experimentally at a casein concentration of 250 g/L, which corresponds to the diffusion of the probe inside the microgel. cD1 is the diffusion coefficient of the probes within the microgel as given by the data fit of the Cell model using both D1 and K as variable parameters (eq 1).

measurements and applying the Cell model of Jönsson et al.36 The accuracy of this method was then validated for some probes by the use of fluorescence spectroscopy correlation and direct measurements of probe concentrations within the casein microgel by the use of chromatography. FRAP Measurements. The FRAP technique was used for measuring the diffusion coefficients, D, of the probes. It was carried out using an inverted confocal laser scanning microscope (Nikon, Champigny-sur-Marne, France). The samples were observed using a 40× objective lens (oil immersion) with a numerical aperture of 1.30. The sample was placed between glass slides, and the measurements were directly recorded at a constant distance of 35 μm from the coverslip. The FITClabeled molecules were excited using a 50 mW sapphire laser system at a wavelength of 488 nm and detected on a 500 to 530 nm spectral bandwidth. All experiments were performed at 20 °C in an air-conditioned room. Image size was fixed to 256 × 256 pixels with a pixel of 1.24 μm. It was verified that the bleaching effect was homogeneous in the different Z planes. The bleached spot was around 10 μm in diameter. Data were analyzed using the methodology described in a previous work.37 The observation that the area of the bleach spot did not decrease over time (see the Figure SI-3 of the Supporting Information) showed that the fluorescence recovery curves were limited by diffusion. Thus, the diffusion coefficient measured in this work (applying the findings of Braga et al.37) represents the effective diffusion coefficient (Deff) or effective diffusivity.38 Analyses of the recorded images were carried out using the EZ-C1 Free Viewer 300, Gold version 3.2, (Nikon Corporation, Tokyo, Japan). A typical example of data is illustrated by Figure SI-3 of the Supporting Information. Estimation of the Partition Coefficients by Use of Jö nsson’s Cell Model.41 The Cell model developed by Jönsson et al. is suitable for describing the diffusion behavior of a probe in a heterogeneous medium such as a colloidal or microgel dispersion. This model is based on the principle that before the point where particles are touching each other (close-packing), the increase in their concentration does not change their structure but merely brings them closer together. Thus, in the concentration range below that of close-packing, the diffusion coefficient of the probe inside the microgel (D1) is independent of the number of microgel particles in the solution. On the basis of these assumptions, the Cell model represents the dispersion of casein microgels as being composed of two phases, the continuous aqueous medium (0) and the microgel

worthy, their overall net charge is negative at pH 6.8, as is the case for the casein microgel (see Table SI-1 of the Supporting Information). The α-lactalbumin, α-LA (≈ 95% purity) was sourced from a confidential origin. The β-lactoglobulin, β-LG (≈ 95% purity) was purified by STLO-INRA (Rennes, France) and is a dimeric protein when under the operating conditions of this study.34 The α-LA and β-LG labeling was carried out inhouse using a previously described protocol.35 The efficiencies of the cross-linking reaction between the FITC or RITC labels and the proteins (when the cross-linking experiment was done by the authors) were determined by mass spectroscopy (QSTAR XL-Applied Biosystems, Ontario, Canada). About 37% of the proteins were monolabeled and about 5% were dilabeled. FITC-bovine serum albumin protein BSA (∼96% of purity) was purchased directly from Sigma-Aldrich. Table SI-1 of the Supporting Information summarizes the physicochemical characteristics of all three proteins. Dextrans. Dextran molecules of different sizes were used as examples of nonsticky linear polysaccharides probes1 (Table SI2 of the Supporting Information). Fluorescently-labeled sextrans (FITC and RITC for the FRAP and FCS experiments, respectively) were purchased from Sigma-Aldrich and referred to here as Dex4, Dex10, Dex20, Dex 40, and Dex70, according to their nominal molecular weight in kD. All labeled molecules (dextrans and proteins) were diluted down to 20 g/L using distilled water. The prepared solutions were stored at −18 °C and protected from light prior to fluorescence measurements. Sample Preparation for the Diffusion Experiments. To determine the diffusion coefficient of the macromolecular probes in the casein dispersions and gels, the labeled probes were mixed with the prepared casein dispersions with concentrations below 210 g/L. In the case of the two concentrated dispersions (>210 g/L), a small drop of the probe solution was put in contact with the casein gel for 1 h, which was an adequate time to ensure a homogeneous fluorescence background throughout the casein gel. In all cases, the final concentration of the probes was 0.5 g/L. It was verified that the concentration of the probes (0.5 or 5.0 g/L) had little effect on their diffusion coefficient (Figure SI-2 of the Supporting Information). Measurement of the Partition Coefficients. The partition coefficients between the micelle phase and the surrounding liquid phase of the media were estimated by using the diffusion coefficients obtained from the FRAP 1757

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Langmuir (1). Within each phase, a probe i has different diffusion coefficients (D0 and D1) and different concentrations (in the aqueous phase, CiS and in the microgel, CiCM). Using these parameters, the model establishes the relation between the effective diffusivity Deff of the probe that is experimentally measured and the particle volume fraction (ϕ) in the medium (i.e., the relative volume occupied by the micelles in the medium): 1 − βφ

1

Deff = D0

(

1− 1−

displaying either low diffusion (diffusion inside the microgels) or fast diffusion (diffusion in the surrounding aqueous phase) (Experimental details are given in the Supporting Information). The FCS experiments were carried out with three different probes (β-LG, Dex4, or Dex70 labeled with RITC) and in casein dispersions of 30 g/L. Dialysis Experiments. The partition coefficient was also directly evaluated using a dialysis procedure. The nonlabeled protein (β-LG) was put into a 100 kDa cutoff rigid compartment containing 100 g/L of casein (see the Supporting Information for experimental details). The compartment was put in contact with a bath of solvent having the same concentration of β-LG. β-LG was then able to diffuse through both compartments. After 3 days which enabled equilibrium under gentle stirring, the relative concentration of β-LG were quantified in each compartment using chromatography (see the Supporting Information for details) and used to calculate the partition coefficient (K).

CiCM Ci

S

)φ 1 +

βφ 2

(1)

where β is defined as β=

D0Ci S − D1CiCM D0Ci S +

D1Ci CM 2

(2)

■

and the partition coefficient (K) of probe i is K=

RESULTS Internal Structure of the Microgel: Correlation Length (ξ) and Average Fiber Radius (rf). The radius of the internal elements of the microgel (referred to as fibers), rf, and the correlation length ξ of the microgel material (the average distance between the fibers) were determined from the 3D tomograms obtained with cryo-frozen and cryo-substituted casein samples. This analysis (Figure 1 and Figure SI-1 of the Supporting Information) gives an average internal fiber radius (rf) of 0.75 ± 0.25 nm and a half correlation length (ξ/2) of 2.3 ± 0.3 nm. These quantitative measurements are in the range of those previously reported in studies using microscopy. In a cryomicroscopy study carried out with frozen samples of diluted casein dispersions (without any staining), Trejo et al.18 reported values of pore radii ranging roughly from 2.5 to 15 nm. Since a pore radius is always statistically larger (from about

Ci CM Ci

S

(3)

In this work, the diffusion coefficient D0 of the probe in the aqueous phase (UF) was measured experimentally using FRAP in the absence of casein micelles (see values presented in Table SI-1 of the Supporting Information). Knowing the values of D0 and the Deff at different volume fractions (ϕ), it is then possible to deduce K and D1 for each probe by fitting the experimental data to the Cell model represented by eqs 1 to 3. In this study, it was possible in all cases to fit the experimental data to the Cell model, and the closeness of fit proved to be satisfactory for each migrating molecule studied (see Table 1 and Figure 2). Of relevance is that the Cell model being always applicable indicates that the chosen probes are able to penetrate and diffuse through the microgels, as opposed to probes that would be adsorbed to the microgel surface for instance. Indeed, if such a surface adsorption phenomenon were predominant, D1 would relate somehow to the diffusion of the microgel particles in the dispersion. In this case, and noting that the microgel diffusion necessarily depends on the concentration of casein (falling to zero as ϕ approaches 1), it would not be possible to fit the data with the Cell model having a unique value for D1; as opposed to what was obtained in this work (Table 1, Figure 2). Furthermore, the fact that surface binding phenomena are absent or do not have a strong influence on the measured diffusivities (hence on the D1 values obtained from the fits) is also supported by the diffusion results obtained just after closepacking of the casein micelles (ϕ ≈ 1.1, C = 250 g/L, Figure 2). In this situation, the micelles indeed occupy all the volume in the dispersion and are slightly compressed against each other. So if the probes were predominantly bound to the surface of the micelles (without diffusing through them), the steric confinement induced by the close-packing of the micelles would dramatically decrease their overall diffusion at this concentration (i.e., D250g/L). This is clearly not what is observed (Figure 2), as the measured diffusivities at ϕ ≈ 1.1 can be fitted in the continuity of those obtained at lower concentration. So in conclusion, these data are only compatible to the case of probes that diffuse within the casein microgels. Fluorescence Correlation Spectroscopy (FCS). The measurement of fluorescence fluctuations as a function of time enables the quantification of the proportion of migrating molecules (β-LG, Dex4, or Dex70 labeled with RITC),

Figure 1. Analysis of a 3D tomogram of casein microgel sample at a casein concentration of 210 g/L. (A) Overall view of the gel. The dotted line is the approximate contour line of the object, and the red square indicates the center of the region of the magnified view. (B) Magnified view of a thin slice (5 nm thick) in the center of the microgel (negative view). The applied software replaces the electron dense elements by ellipses. The fiber radius (rf) is defined as the smallest radius of each ellipse. (C) Image B after modification. The correlation length (ξ) is obtained from the distances between one fiber and its closest neighbors (red arrows). See the Supporting Information for details. 1758

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Figure 2. Relative diffusivity Deff/D0 as a function of the casein concentration in the microgel dispersion for rigid (proteins, A) and deformable (dextrans, B) probes. The lines are the fits using the Cell model36 to the experimental data.

3 to 5 times) than ξ,39,40 one can estimate their values of ξ/2 ranging from around 0.5 to 5.0 nm. Thus, the values of ξ/2 obtained by Trejo et al.19 are seen to be of the same order of magnitude as those obtained from the present work. However, since the authors quote only the range of porous variation (and not a quantitative distribution of pore radius), no average value can be extracted from their work that could be directly compared to those from the current study. The data reported here are also consistent with the work of MacMahon et al.41 and Dalgleish et al.,42 which reports a pore size between 1.5 and 10 nm (ξ/2 = 0.3 to 3.3 nm) for negativestained fast dried samples. The maximum pore size reported by this work is also in the range of the intermediate characteristic lengths obtained in previous SAXS studies of the casein micelle and that were attributed to ∼10 nm voids or soft regions distributed within the microgel.43 Diffusion and Partition Coefficients in the Casein Microgels. Figure 2 (panels A and B) shows the relative diffusivity (Deff/D0) of rigid (proteins) and deformable (dextrans) probes in dispersions of casein microgels with casein concentrations ranging from 20 to 250 g/L, which corresponds to a volume fraction of the dispersion from ∼0.1 to 1.1, respectively. Both figures show a continuous decrease of Deff/D0 as a function of a rising casein concentration. Moreover, the nature of the probe strongly influences the rate of fall of the relative diffusivity: for a similar radius, Deff/D0 decreases much faster for rigid than for deformable probes as the casein concentration in the dispersion increases. No simple power law or exponential decrease can fit these diffusion data as it would be the case for particles diffusing through continuous media.40 However, the Cell model proposed by Jönsson et al., which considers the medium as a discontinuous two-phase system where a diffusing molecule displays two different diffusion coefficients (eq 1), enables a good fit with this data (Figure 2, panels A and B). The data fit displayed by these figures were achieved by varying both K (the partition coefficient) and D1, the diffusivity of the probes in the microgel. The obtained values of K and D1 are given in Table 1. Another way of fitting the data is to first set D1 at the value of diffusivity obtained experimentally at C = 250 g/L. This approximation seems quite reasonable since, at this concentration, the micelles occupy all the available space without being

excessively compressed (ϕ = 1.1). As a consequence, all the probes diffuse through the casein matrix that makes up the medium. The data fit then consists in varying K to best describe the data for the whole range of concentrations at ϕ < 1. With no surprise, the obtained K values are again close to those obtained from the first method. The K values obtained from both fit procedures are considered as good estimates of the “real” K value. For the probes β-LG, Dex4, and Dex70, the K values determined by FRAP are also very close to the ones obtained using FCS (Table 1, see the Supporting Information for details). Furthermore, the direct measurement of K for β-LG, without labeling, and using a method based on dialysis and HPLC, also gives a value that is close to the one measured by FRAP (Table 1, see the Supporting Information for details about the method used), thus further validating the results. Table 1 shows that for all protein probes, the partition coefficients are greater than 1; the implication is that the probe concentration is always greater (from 1.5 to 27 times) in the microgel than in the surrounding aqueous phase. More important, K increases as a function of the size of the protein molecule. In contrast, in the case of dextrans, K is slightly greater than 1 but does not show any clear increase as a function of the size of the dextran molecule. As a consequence, proteins systematically have higher K values than the corresponding dextran molecule of comparable molecular weight. In all cases, if the probe-microgel interaction between the migrating molecule and the surrounding medium was only repulsive, K would have been inferior to 1.13 Thus, because all K values are in fact greater than 1, the presence of some attractive interactions between the probes and the microgel medium is demonstrated. Effect of Ionic Concentration on the Partition Coefficients. All the proteins used in this work (i.e., both the protein probes and the casein proteins), have net electrostatic charges that are negative at pH 6.8. This suggests that any electrostatic interactions between the probes and caseins are predominantly repulsive. However, it is noted that the indicated proteins are composed of both negative and positive amino acid residues (with more negative than positive ones). Thus, it is still theoretically possible that some local 1759

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volume effects. Two models can be used to estimate the partition coefficient K in such a case. The first model was developed by Ogston et al.13 based on the probability of placing a spherical molecule of radius rh within a static array of rigid fibers of infinite length. Using this model, K can be expressed as follows:

attracting interactions may exist in certain regions of the protein(s) that are locally positive. In order to check whether or not these effects exist, the influence of an increase in ionic strength was investigated (by addition of 170 mM NaCl). Figure 3 shows that there is no detectable difference in Deff/D0

2⎤ ⎡ ⎛ rh ⎞ ⎥ ⎢ K = exp −φ⎜⎜1 + ⎟⎟ ⎢ ⎝ r f ⎠ ⎥⎦ ⎣

(4)

where rf is the radius of the fibers and ϕ is the volume fraction they occupied in the medium. Even if this model was originally derived for the partitioning of particles in fibrous media, Ogston’s expression is known to be reliable in predicting the partition coefficients of proteins in agarose and dextran gels.46 It therefore seems reasonable to use it to predict results obtained with dispersions of casein micelles. In casein microgel, ϕ is estimated as 0.736/4.4 = 0.17 where 0.736 mL/g is the specific volume of the casein microgel,32 and 4.4 mL/g is the so-called voluminosity of the microgel, expressed as volume per gram of casein.33 A second model proposed by Button et al.15 was developed for molecules that diffuse within meshlike structures made of flexible polymers. In this case, the model attributes a freeenergy penalty (F) to molecules entering the polymer matrix. This penalty is in the order of F ≈ (rh/ξ)υ. The exponent υ is a constant that depends on the nature of the probes and on the quality of the solvent: υ = 2 for a randomly branched polymer such as dextran and υ = 3 for a solid spherical probe diffusing through a good solvent.15 Following this approach, the partitioning coefficient K can be written as

Figure 3. Effect of NaCl concentration on the relative diffusivity of protein probes (α-LA, β-LG, and BSA) in a microgel dispersion of 30 g/L of casein. κ−1 is an estimate of the Debye screening length (calculated as in ref 44 see the Supporting Information and discussion for further details on calculation).

(which is directly related to K), at the two ionic concentrations examined, thus indicating that electrostatic forces do not appear to play a role in the observed attractive interaction between the diffusing molecule and the casein microgel.

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DISCUSSION The principal results of FRAP measurements are the diffusion coefficients set out in Figure 2, which reflect the diffusional behavior of probes of various sizes and characteristics in dispersions of dense casein microgels. The following discussion is, however, not directly focused on the numerical values of these diffusion coefficients but rather concentrates on the partition coefficients that were deduced from these same diffusion data. In fact, these partition coefficients are always greater than 1, indicating that a positive attraction necessarily exists between the diffusing probes and the material that constitutes the microgel. The discussion starts by a qualitative estimation of the strength of this attractive force between the probes and the casein microgel. This is done by comparing the experimental results with the situation where probe partitioning is only attributed to excluded volume effects. Such effects are estimated from theoretical models by using the internal characteristic dimensions of the casein micelle obtained through the use of TEM. A more quantitative estimation of the attraction then follows in the second part of the discussion. This is presented by quantifying the attractive interactions using a thermodynamic model where both excluded volume effects and probemicrogel attraction forces contribute to the partitioning of the diffusing element between the two phases. The section concludes with the discussion of the possible origins of such attractive molecular forces. Only the Presence of Attractive Interactions Can Explain the K Values. In absence of any positive attractive molecular force, the energetic barrier that a diffusing molecule must overcome to enter a gel structure is only due to excluded

⎡ ⎛ 2r ⎞υ⎤ ⎡ F ⎤ K = exp⎢ − ⎥ ≈ exp⎢ −⎜ h ⎟ ⎥ ⎢⎣ ⎝ ξ ⎠ ⎥⎦ ⎣ kBT ⎦

(5)

where kB is the Boltzmann constant and T the temperature in Kelvin. Figure 4 (panels A and B) show the variation of K as a function of probe radius according to the two models described above (eqs 4 and 5). Both of these models clearly predict that most of the diffusing molecules used in the current study should be largely excluded from the microgel noting that the predicted K values are generally lower than 0.6 in most cases. On the other hand, Figure 4C compares the maximum values obtained from those predictions to the actual K values measured in the current work and also to those that have been estimated from the recent work of Salami et al.45 on the diffusion of linear and spherical PEG probes into dispersions of casein microgels (this being the same casein system and physicochemical conditions as in the present work). The difference between the predicted and measured values is even more accentuated here, with measured K values that can be two orders of magnitude higher than what is expected when molecule-medium interactions are considered to be purely steric. In contrast to the expected rapid fall in the partition coefficient, K (in the case of absence of attractive interactions), Figure 4C in fact shows a nontrivial behavior of K as a function of the probe size. These findings clearly indicate that, even for the smallest probes studied, an attractive interaction exists between the probe and the microgel. At this point, one approach would be to directly model the K values of Figure 4C using theories that take into account the 1760

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attractive forces based on suitable theories in conjunction with the experimental values of Figure 4C. Attractive Interactions: Size-Dependent Behavior for Spherical Probes. The aim of this section is to estimate, for all probes studied, the strength of their attractive interaction with the casein microgel medium. To do so, the K values of the probes, which are linked to their activity coefficients outside and within the microgel, were considered to be dictated by two additive factors: an attractive interaction and a repulsive one, as proposed by Jiao et al.1 These authors have used this approach for a diffusing system similar to that reported here where a net protein−polysaccharide or protein−protein attractive interaction was also observed experimentally. It is noteworthy that such a description was also used in some recent numerical simulations.12 At thermodynamic equilibrium, the chemical activity of a probe i is identical inside the micelle (superscript CM) to that outside (aqueous medium, superscript S), so that

μCM = μiS i

(6)

which can also be written as

γiCMXiCM = γiSXiS

(7)

where γi is the activity coefficient and Xi the mole fraction of probe i in both of the defined phases. In the current case, the probe concentration in each phase is sufficiently low to consider that Xi = CiVs, where Vs is the molar volume of the solvent. It is also reasonable to assume that the probe follows closely ideal behavior in the solvent (i.e., γsi ≈ 1), as the concentration of probes in the solvent or in the micelles is always very low (between 0.01 up to 0.1 mM at the most). Equation 7 then gives γiCMCiCM ≈ CiS , meaning γiCM ≈ K −1

Following Jiao’s work, decomposed into

1

(8)

the activity coefficient is then

ln γiCM = ln γiCM(exvol) + ln γiCM(attract) = ln K −1

γCM(exvol) i

(9)

γCM(attract) i

where and are the contributions to the activity coefficient of the excluded volume effects and the attractive interactions, respectively. The contribution γCM(exvol) can be estimated following the i work of Button et al.15

Figure 4. Variation of the partition coefficient K as a function of the radius rh of the probe. Graphs A and B: theoretical values predicted by the Ogston and Button models based on TEM data. Calculations are performed with values rf and ξ/2 that correspond to the average “fiber” radius (rf ≈ 0.75 ± 0.25 nm) and correlation length (ξ /2 ≈ 2.3 ± 0.3 nm). The blue square region in the figures gives the size range of the molecules used in the present study. In the case of graph B, the theoretical variations of K are given for both spherical objects (υ = 3) and polymers (υ = 2). Graph C: experimental values compared with values predicted by the two models. The theoretical values of K are estimated from eqs 4 and 5 using ξ /2 = 2.6 nm and rf = 1.00 nm. The values of K estimated from the work of Salami et al.45 (using the same conditions of pH, ionic strength, and casein composition as in the current study) are also displayed for comparison.

⎛ 2r ⎞υ ln γiCM(exvol) = ⎜ h ⎟ ⎝ ξ ⎠

(10)

while the contribution γCM(attract) can simply be expressed as a i function of the increment of Gibbs free energy (δGiMC(attract)), characterizing the attractive molecular forces between the probe and the microgel: ln γiCM(attract) =

δGiCM(attract) si RT

(11)

The Gibbs energy of attraction, Gi, is given in Joules per mol of probes per unit surface area of the molecule. si corresponds to the surface area of probe i, and R is the universal gas constant. Equations 9, 10, and 11 lead to the following expression, which allows the estimation of the strength of the attraction

existence of attraction forces between the probes and the casein medium. However, it is not possible to do that without knowing more information about the system as, for example, the strength and nature of the attractive interactions. The second approach, which is followed in the next sections, consists in determining and discussing the characteristics of the 1761

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δGMC(attract) with the shape of the molecule than with its chemical nature. This behavior is typical of a nonspecific interaction between the probe and the medium.1 (It is noteworthy that a nonspecific interaction occurs when the surface of the probe and the medium display many equivalent attractive sites.) Since the trends observed do not appear to depend on the chemical composition of the probes, one is tempted to qualitatively explain the results on purely entropic arguments. In this context, the strength of binding (∝δGMC(attract)) between two similar particles is related to two principal factors: (i) the associated contact surface area, (ii) the local dynamics of each particle and the associated reduction in its mobility induced by the formation of the complex.48−51 In the case of spherical probes, an increase in δGMC(attract)/ nm2 is observed with increasing size or molecular weight (Figure 5). This can hardly be considered as the result of a simple increase in the contact surface area between the probes and the caseins [factor (i)]. Indeed, all the protein probes have sizes (rh ≈ 2.1−3.9 nm) that are higher than the size of the microgel structures (ξ/2 ≈ 2.3 nm); so the increase of the size of the probe may not increase the contact surface area. On the other hand, the second argument based on the local dynamics of the probes and the casein chains greatly applies here. The entropic cost for stopping a probe and then forming a complex is indeed directly related to the size and mobility of the probe, with higher costs for small and mobile probes than for the large and less mobile ones. This is in direct agreement with the presented data showing that the affinity for the casein medium increases with the size of the spherical probes (Figure 5). It is considered that this entropic argument can also explain the results obtained with linear polymers. In this case, it is necessary to understand that a polymer displays a fast segmental motion at the scale of the monomer (which over long timescales is responsible for the effective translational diffusion of the whole polymer).39,48 Moreover, the polymer adopts an unfolded form when it is in a confined system such as the casein matrix.39,48 As a consequence, the binding strength between the polymer and the casein segments is in some way related to the entropic cost that is necessary to suppress the segmental motions of the polymer, as the rate of the local segmental motion is influenced only by the nature of the polymer and not by its overall size.39,48 It is not surprising that the binding energy per surface unit area is virtually independent of the polymer molecular weight. Returning now to the unprocessed results of the reported experimental work (i.e., the diffusion coefficients given in Figure 2), one could ask if it is possible to quantitatively describe the diffusion of the probes based on some theory of diffusion in a dense and “attractive” medium. However, answering this question is quite difficult since current theories already show that there is a nontrivial relation between diffusion coefficients at short and long timescales in a “simple” dense medium that is predominantly repulsive.52 In the case of an attractive medium, the situation is further complicated by the binding events that occur simultaneously to diffusion.52 However, even though it is not possible to explain quantitatively the presented diffusion results, the work of Ando et al.12 shows that one can qualitatively discriminate between pure repulsive regimes and attractive ones using probe diffusion coefficients of spherical probes. Ando et al. used computer simulations to predict the diffusion of a spherical particle in a system formed by highly concentrated polydisperse

force knowing the partitioning coefficient K and the size characteristics of the probe and microgel structure: δGiCM(attract)

⎛ 2rh ⎞υ⎤ RT ⎡ −1 ⎢ = ln K − ⎜ ⎟ ⎥ ⎝ ξ ⎠ ⎥⎦ si ⎢⎣

(12)

Figure 5 presents the values of −δG , which is the energy per mol per unit surface area of the molecule, as a CM (attract)

Figure 5. Calculated Gibbs attractive free energy increment (−δGMC(attract)) per unit surface area of the probe as a function of probe molecular weight (MW). The data for PEG and PEGdendrimers was taken from Salami et al.45

function of its molecular weight for the different diffusing species: these values are either determined from the current work or extracted from the data of Salami et al.45 For the proteins and PEG-dendrimers, the surface area used to calculate δGMC(attract) is based on a sphere. On the other hand, and since almost all the deformable probes (dextrans and PEG) have a radius rh larger than ξ/2, these molecules are expected to diffuse through the medium as unfolded linear chains. This phenomenon was predicted theoretically and further supported by experimental data.48,49 Thus, the surface area of the dextrans and PEG are then considered as long linear rods, with a radius of 0.5 and 0.3 nm and a length of each monomer of 0.6 and 0.5 nm, respectively (based in the steric surface of these molecules, see the Figure SI-5 of the Supporting Information). For the three different proteins and the PEG-dendrimers, the evolution of the attraction per unit surface area of the molecule with its MW displays a similar trend (Figure 5): that is a linear increase of −δGMC(attract) is observed as a function of the MW of the probe. It is noteworthy, since molecules (dendrimers, linear PEGs, dextrans, and spherical proteins) of different densities (as a function of MW) and surface characteristics are being compared; the trends observed are more meaningful than the magnitude of the energy. Nevertheless, these data show that the order of magnitude of these interactions is never very high (5− 30 kT/nm2). The observed behavior for these spherical probes is quite different from that of the dextrans and the linear PEGs, which adopt a rodlike form when diffusing through dense environments:46,47 the attractive energy per surface area of the molecule is seen to be independent of their MW. It can be clearly seen that globular PEG (dendrimers covered by PEG) and linear PEG show very different tendencies even though these probes have surfaces with a near identical chemical composition. The implication is a stronger correlation of 1762

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configuration.57−60 In the triple-stranded collagen molecule, most of the amide protons and CO groups from the polypeptide backbone are too far apart to form a direct hydrogen bond. Thus, water molecules can act as bridges between the H donors and acceptors.58 Since there is an energetic cost to maintain these water bridges, their partial replacement by neighboring hydrophilic and less mobile groups (such as the ones widely present on the surface of the different probes used in this work) is energetically favorable.58 This phenomenon generates a nonspecific affinity by any hydrophilic probe and consequently these original properties. It is noteworthy that the magnitude of the attractive component measured in the present work (0.1 to 1 kT/nm2) is very consistent with attraction forces of hydrophilic origin. In the collagen case, Leikin et al. indeed estimate that about 2 H bonds (considering, 5 kT per H bond) are involved in the attraction between two collagen molecules.58 In our case, about the same number of H bonds is obtained with the different probes. As an example, it is estimated that about 1 H bond is involved in the interaction between one α-LA (surface area ≈ 55 nm2, δGMC(attract) ≈ 0.15 kT/nm2) and the casein.

spheres (∼300 g/L). They simulated two scenarios: one without any attractive interactions between the probe and the spheres, the other with nonspecific attractive interactions between the probe and the spheres. In the latter case, the diffusion coefficient D was found to be much lower than without attractive interactions. Furthermore, the decrease of D with the size of the probe was found to be much faster in the case where attractions exist between the probes and the medium. This behavior is found for different types of nonspecific attractive forces (electrostatics, van der Waals), indicating that the shape of the attractive/repulsive potential does not induce an important impact in long time diffusions. The trend observed by Ando et al., along with the magnitude of the decrease in relative diffusivity as a function of probe size, is similar to the one observed in the current work (for probes of similar size, Figure 2). As an illustration of that, the three proteins used in this work (α-LA, β-LG, and BSA) display a Deff/D0 of ∼0.07, 0.05, and 0.02, respectively, at the maximum casein concentration, while the Deff/D0 values obtained by Ando through computer simulations for sticky particles of the same size and in a medium of similar concentration are ∼0.07, 0.04, 0.02, respectively. In contrast, particles displaying only hard sphere repulsions show Deff/D0 values that are significantly different (i.e., ∼0.1, 0.08, 0.06, respectively). Hydration Forces: Casein Molecular Conformation Explains the Attractive Interaction. Different forces at the molecular level including electrostatic, hydrophobic, van der Waals/London, and hydration interactions may be considered responsible for a net attraction between protein molecules or between polysaccharides and proteins. In the current study, electrostatic effects are unlikely to be responsible for the observed molecular attraction. The obvious reason for this is that the probes for which this attraction was observed were either neutral (PEG) or, on average, negatively charged (i.e., as is the casein microgel). However, in the case of protein probes, and as briefly touched on in Results, it may still be suggested that some electrostatic effects exist in parts of the molecule at the level of one or more amino acid groups, thus leading to local attraction forces between parts of caseins and protein molecules that have opposing electrostatic charges. However, if such effect were to exist, it is likely that the change in the aqueous ionic strength from 80 to 170 mM [i.e., a decrease in Debye length (κ−1) from ∼6 to ∼3 Å, see the Supporting Information for the exact calculation] would have produced some changes in K, which was not the case (Figure 3). In the same way, the presence of a hydrophobic force is not a satisfactory answer since the degree of hydrophobicity of β-LG is lower than that of α-LA.53 Furthermore, PEG and dextrans are largely hydrophilic molecules.54 Also it is unlikely that other type of forces such as van der Waals/London forces are involved in the intermolecular attraction. These forces are indeed very short-range and are more likely to happen between partners that are mostly hydrophobic and poorly covered by water molecules (in contrast to the caseins and the majority of the probes).55 On the other hand, hydrophilic interactions, facilitated by water bridges, could better explain the presented data. Such interactions, also called hydration forces, are present in those proteins with a rather extended secondary structure such as caseins56,57 or collagen.58,59 Collagen, that takes its name from the latin “glue” and interacts with a wide variety of molecules, is one example of a protein with a completely extended

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CONCLUSIONS Experimental measurements of the diffusion of various macromolecular probes (proteins and dextrans) in dispersions of casein micelles, a natural microgel constituted of interlaced chains of caseins, are presented. On the basis of the diffusion coefficients obtained, it is deduced that the probes are in all cases more concentrated inside than outside the casein micelle. On the basis of some structural characterization of the casein micelle interior, it is shown that such a behavior can only be explained through the presence of an attraction forces between the probes and the casein material that make the microgel. This was unexpected because there was nothing in the properties of the probes and the microgel that could a priori lead to this behavior: it could only be explained through the presence of hydration forces between the probe surfaces and the interior of the casein microgel. Moreover, it was found that the strength of the molecular attraction is related to the size and shape of the probes. A reasoned explanation for the phenomenon is proposed: this is mostly based on the effect of the size of a probe on its mobility at local scale. The findings from this work concerning the casein micelle may be applied to enable the understanding of the link between molecular diffusion and partitioning in other dense biological media, for example, cells or tissues. The findings from this work also suggest that the casein micelle (or other close-related protein assembly) may have a use as a size-selective molecular device.

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ASSOCIATED CONTENT

S Supporting Information *

Characterization of the casein gel structure using transmission electron microscopy and tomogram construction; properties of the studied diffusing molecules; effect of molecular concentration; data from the FRAP procedure; fluorescence correlation microscopy; dialysis experiments; calculation of the Debye screening length in different solvents; and steric surface of PEG and dextran molecules. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. 1763

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Langmuir *E-mail: [email protected]. *E-mail: [email protected].

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Present Address @ Laboratoire d’Ingénierie des Systémes Biologiques et des Procédés/LISBP, UMR 5504/792 INRA-CNRS-INSA, 135 avenue de Rangueil, 31077 Toulouse cedex 04, France.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors wish to acknowledge with thanks the financial support received form INRA (Institut Nationale de Recherche Agronomique) and from BBA (Bretagne Biotechnologie Alimentaire). They are also grateful to the members of the Microscopy Rennes Imaging Center for their technical assistance with the microscopy used in this study.

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