Adsorption of Unstructured Protein β-Casein to Hydrophobic and

Article pubs.acs.org/Langmuir

Adsorption of Unstructured Protein β‑Casein to Hydrophobic and Charged Surfaces Chris H.J. Evers,†,¶ Thorbjörn Andersson,‡ Mikael Lund,*,† and Marie Skepö*,† †

Division of Theoretical Chemistry, Lund University, Lund, Sweden Material Design, Tetra Pak Packaging Solutions AB, Lund, Sweden

‡

S Supporting Information *

ABSTRACT: In this Monte Carlo simulation study we use mesoscopic modeling to show that β-casein, an unstructured milk protein, adsorbs to surfaces not only due to direct electrostatic and hydrophobic interactions but also due to structural rearrangement and charge regulation due to proton uptake and release. β-casein acts as an amphiphilic chameleon, changing properties according to the chemical environment, and binding is observed to both positively and negatively charged surfaces. The binding mechanisms, however, are fundamentally different. A detailed, per-residue-level analysis shows that the adsorption process is controlled by a few very specific regions of the protein and that these change dramatically with pH. Caseins, being the most abundant proteins in milk, are crucial for the properties of fermented dairy products, such as nutrition, texture, and viscosity, but may also influence adhesion to packaging materials. The latter leads to product losses of about 10%, leading to economical and environmental problems.

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INTRODUCTION Dairy products, with their complex colloidal composition, adsorb readily on a variety of surfaces. One example is yogurt and other fermented milk products where 10% remains in the package after attempting to pour out the product.1 Obviously, this has economical as well as environmental consequences, and one might prevent this effect either by changing the properties of the dairy product or, more likely, by using a packaging material with less adhesive properties. Milk proteins adsorb to a variety of surfaces and the adsorption process between proteins and surfaces in general is driven by intermolecular forces that depend on charge density, hydrophobicity, ionic strength, pH, etc.2−7 β-Casein is one of the most abundant constituents in milk,8 and numerous studies have been devoted to its adsorption to hydrophobic surfaces. At neutral pH, β-casein adsorbs with the hydrophobic C-terminal anchored to hydrophobic surfaces, while the hydrophilic N-terminus protrudes into the solution and forms a brushlike structure.9−14 Theoretical studies using self-consistent field theory qualitatively confirm this structure, and significant effects of ionic strength and pH are found15,16 in line with experimental results.17,18 For negatively charged surfaces, such as silica, the few available studies show that adsorption can be both strengthened19 and weakened by increasing ionic strength.7 The influence of ionic strength indicates the importance of electrostatic interactions, which are screened at high salt concentrations. Further, theoretical studies of unstructured saliva protein20 show that adsorption to charged surfaces may occur due to conformational rearrangements.21,22 © 2012 American Chemical Society

Electrostatic interactions are crucial when studying protein− surface interactions, and a commonly applied model is to treat the protein with a charge distribution corresponding to that found in bulk solution. Such approaches do not take into account that acidic and basic groups can be titrated when exposed to other charged objects. In reality, the protein charge is not constant but depends on the chemical environment. The description of the charge regulation mechanismcaused by proton fluctuationscan be traced back to the Carlsberg laboratories in the 1920s23 and can be formalized using statistical mechanical perturbation theory.24,25 In a number of studies on protein adsorption to surfaces, proton equilibria are discussed, and it is generally found that charge regulation may contribute significantly to the interaction free energy and that this contribution is strongly dependent on the solution conditions.26−31 In this theoretical study we focus on bovine β-casein (βCN) adsorption to hydrophobic as well as charged surfaces under different solution conditions, including situations corresponding to milk and fermented milk. The intrinsically unstructured proteins are described in mesoscopic detail, where each amino acid is represented by a bead. Using Monte Carlo simulations, we investigate the importance of structural rearrangements when approaching surfaces, and quantify the effect of pH and charge regulation. Received: March 1, 2012 Revised: May 1, 2012 Published: July 11, 2012 11843

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fitting the energy function to the inter-residue distance, rij, distribution in five crystal structures34−38 (Supporting Information). The Pauli repulsion parameter, εrep, was set to 0.2 kBT.39 For the interaction between hydrophobic residues (Ala, Ile, Leu, Met, Phe, Pro, Trp, Val), the attraction strength, εh, was 0.5 kBT and the interaction range, rh, was the size of a water molecule, 0.3 nm. This particular choice of hydrophobic parameters is motivated by the weighted average hydrophobicity of βCN according to Eisenberg’s hydrophobicity scale,40 as well as by results from atomistic computer simulations between small, hydrophobic molecules.41 Unless otherwise stated, the hydrophobic interaction parameter between hydrophobic residues and the surface, εh,s, was zero. For electrostatics, zi and zj are the charge numbers of each residue, λB = 0.71 nm is the Bjerrum length in water at 298 K, κ−1 = 1.08 nm is the Debye screening length in milk with ionic strength, I = 80 mM,42,43 rz,i is the perpendicular (z-direction) distance between the particle i and the Gouy−Chapman surface with charge number density, ρ. Further, charge regulation is captured by titrating acidic and basic amino acids according to the microscopic environment. The titration free energy depends on electrostatics, pH, and the intrinsic acid dissociation constants: pKa,i = 3.6 (Ctr), 3.9 (Asp), 4.1 (Glu), 6.5 (His), 8.5 (Cys), 8.6 (Ntr), 10.1 (Tyr), 10.8 (Lys), 12.5 (Arg).44 In this work, we assume that all five phosphorylated serines are saturated with calcium, rendering these net-neutral. Method. The equilibrium properties of the model system described above were obtained using Metropolis Monte Carlo (MC) simulations45 in the canonical ensemble (NVT). For simulations in bulk solution, we used a cubic simulation container with the minimum image convention and periodic boundaries in all three directions. For simulations near a surface, periodicity was applied only in the xydirections. Configurational space was sampled using six different Monte Carlo moves: (1) monomer translation, (2) protein translation, (3) protein rotation around a random axis, (4) crankshaft where a random number of connected monomers were rotated around the axis connecting the first and the last monomer, (5) branch rotation where a random number of monomers at a protein end were rotated around the axis between the last and a random monomer, and (6) proton titration where acidic or basic amino acids were (de)protonated. New configurations were accepted with probability,

MODEL AND THEORY

Model. We use a coarse-grained model to examine properties of βCN in solution and adsorption to surfaces. The flexible chain-like protein is represented by a freely-jointed chain of soft beads connected by harmonic bonds. Counterions and salt are implicitly described, and the solvent, water, is treated as a dielectric continuumsee Figure 1.

Figure 1. Monte Carlo simulation model of βCN near a Gouy− Chapman surface of charge density, ρ. Solvent and salt are implicitly incorporated via the Bjerrum length, λB, and the inverse Debye length, κ, respectively. The disordered protein is described as a bead model with neutral (white), cationic (blue), and anionic (red) amino acid residues. Amino acid sequences were obtained from UniProtKB32 (Supporting Information), and each amino acid i and the N- and C-terminus are represented by spheres with radii, Ri = ((3/4π)(mi/ρprot))1/3, where mi is the residue mass, and ρprot is the protein density, 1.4 g/L.33 The system energy, U, was calculated by summing the contributions listed in Table 1. For the harmonic bonds the force constant, kb = 76 kBT/nm2, and equilibrium distance, req = 0.49 nm, were obtained by

Table 1. Energy Contributions to the System Energy Hamiltonian (see text for details) energy

pacc (k → l) = min{1, exp(− β ΔUk → l)}

expression

Pair Interactions bonds

where β = kBT = 2.5 kJ/mol is the thermal energy at 298 K and ΔUk→l the total energy difference between states k and l. The equilibrium phase of the simulations was performed using at least 105 and 106 steps for bulk and protein−surface simulations respectively, while production runs involved at least 106 and 107 steps. All simulations were performed using the Faunus framework for molecular simulations,46 subversion revision 666. Analysis. As a function of the mass center position, rcm, we have sampled statistical mechanical averages of (1) residue charge numbers, zi, (2) root-mean-square end-to-end distance, Ree, and (3) radius of gyration, Rg = ⟨(Σimi|ri,cm|2/(Σimi)⟩0.5 where |ri,cm| is the residue distance from the mass center. Since acidic and basic groups can be either protonated or deprotonated, the average net charge, ⟨Z⟩ = ⟨Σizi⟩, has a variance which defines an important property, the protein charge capacitance,25,47

b

∑ k b(rij − req)2 ij

Pauli repulsion

⎛ R i + R j ⎞12 ⎟⎟ ε 4 ∑ rep⎜⎜ ⎝ rij ⎠ ij all

hydrophobic

h

∑ εh ,

for rij ≤ rh

ij

electrostatic

el

∑ ij

Surface Interactions hydrophobic

zizjkBTλB rij

e−κrij

h

∑ −εh,s ,

for rz , i ≤ rh

C ≡ ⟨Z2⟩ − ⟨Z⟩2 = −

i

electrostatic

el

⎧ 1 + Γ0 exp(− κrz , i) ⎫ ⎬ , with ⎩ 1 − Γ0 exp(− κrz , i) ⎭ ⎪

⎪

⎪

⎪

∑ 2zikBT ln⎨ i

tit

∑ kBT(pH − pKa,i) ln 10,

∂⟨Z⟩ 1 ∂⟨Z⟩ =− ln 10 ∂pH βe∂φ

(2)

where φ is an external electric potential. Hence, C is simply the derivative of the pH titration curve, and an external potential will cause a change in protein net charge, ΔZ ≈ −βeCΔφ. The latter is the essence of charge regulation that can be estimated by a single parameter, C. The capacitance is an intrinsic protein property, and depends on pH and salt concentration, and on protein sequence and structure. When pH is close to pKa of a titratable site, the degree of protonation is close to one-half and is easily perturbed by an external

⎛1 ⎛ πλ ⎞⎞ B ⎟ ⎟ Γ0 = tanh⎜⎜ sinh−1⎜ρ 2 2I ⎠⎟⎠ ⎝ ⎝ titration

(1)

−1

for i protonated

i

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potential.47 Thus, for most proteins, the capacitance peaks at around 4 and 10, due to an abundance of acidic and basic residues. The Helmholtz free energy of interaction between the protein and surface was calculated from the mass center distribution, g(rz,cm):

βΔA(rz ,cm) = − ln g (rz ,cm)

(3)

The effective free energy per residue i, βΔA′i, was obtained by replacing rz,cm in eq 3 with rz,i.

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RESULTS AND DISCUSSION Protein in Bulk Solution. The amino acid sequence alternations and other properties for four variants of βCN and one mutant are listed in Table 2. βCN A1 is one of the two most common variants and is used as a reference protein in the following discussion.

Figure 3. βCN A1 radius of gyration, Rg, as a function of pH, and semitransparent histograms at pH 4.5 (red) and 14 (blue).

nm and rs ≈ 9.5. The latter is in the middle of the two extremes rs = 6 (random coil) and rs = 12 (rod). Figure 4 provides a closer look at the fermentation process where pH is lowered from approximately 6.7 to 4.5. In normal

Table 2. Amino Acid (AA) Sequence Alternations and Number of Acidic, na, Basic, nb, and Hydrophobic, nh, Residues for Four Bovine βCN Variants and One Mutant32,48,49,a AA position

a

variant

67

106

122

na

nb

nh

A1 A2 A3 B A1 H106Q

His Pro Pro His His

His His Gln His Gln

Ser Ser Ser Arg Ser

28 28 28 28 28

22 21 20 23 21

106 107 107 106 106

Figure 4. Ten-residue average of the βCN A1 residue charge number, ⟨zi⟩, at pH 6.7 (− −, (magenta)) and 4.5 (, (blue)) and of the residue hydrophobicity, ⟨εh⟩.

See Supporting Information for full sequences.

Figure 2 gives the net mean charge number, ⟨Z⟩, and charge capacitance, C, for independent bulk simulations of βCN at

Figure 2. βCN A1 total net charge number, ⟨Z⟩, and capacitance, C, as a function of pH. The dashed lines correspond to milk (pH 6.7) and fermented milk (pH 4.5).

milk (pH 6.7), the N-terminus contains two negatively charged regions, while the remaining tail is more hydrophobic and net neutral. Hence, at this pH, the protein resembles an amphiphile with a charged hydrophilic head and a hydrophobic tail. In fermented milk (pH 4.5), however, the amphiphilic character is reduced since the negative charge of the headgroup is decreased, and the tail is net positively charged. A reduction of the amphiphilic nature and of the headgroup charge agrees well with the experimental observation that casein micelles coagulate and partly disintegrate during the fermentation process.51,52 Protein Adsorption to Surfaces. Effect of Surface Type. We now examine how surface properties influence the adsorption free energy and charge of βCN A1see Figure 5. When a flexible protein approaches a surface, the number of

different pH values. The isoionic point where ⟨Z⟩ = 0 is at pH 5.1, close to the experimentally found value of 5.2.50 The protein charge capacitance shows two main peaks, with one maximum at pH 4 and another at around pH 11, corresponding to acidic and basic residues that give large contributions to C when pH is close to their pKa values. Thus, in fermented milk (pH 4.5) βCN is close to a capacitance peak, while for milk (pH 6.7) the capacitance is closer to a minimum. Hence, charge regulation is more important in the former case. Next, we examine the radius of gyration, Rg, and as shown in Figure 3, we observe a minimum near the isoionic point due to minimal electrostatic repulsion within the chain. The histogram, however, shows a large variance in Rg, and the frequencies, f(Rg), shift only slightly to the right upon increasing pH from 4.5 to 14. The perturbations of Ree and the shape ratio, rs = R2ee/ R2g, by pH are also smaller than the fluctuations, and Ree ≈ 17

Figure 5. Free energy, βΔA, and net charge number, Z, at pH 4.5 as a function of the distance between the βCN A1 mass center and a surface with ρ = 0 (− −, red), ρ = −0.5 nm−2 (, blue), ρ = 0, εh,s = 0.5 kBT (− •, green), and ρ = −0.5 nm−2, εh,s = 0.5 kBT (, yellow). The black dotted lines indicate bulk values. 11845

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4.5 nm which leads to an increase in Rg, while Rg,x and Rg,y remain constant (data not shown). The difference in adsorption mechanism between the positively and negatively charged surface is thus a stretching of the protein toward the positively charged surface, while the protein configuration remains unaffected until rz,i ≈ Rg near the negatively charged surface. The effective free energy per residue near a negatively charged surface (Figure 7, top left) shows a deep minimum

possible configurations decreases along with the chain entropy. This results in repulsion from a neutral surface and even from a hydrophobic surface. That is, the attractive hydrophobic interactions are negligible compared to the entropic repulsion. For a negatively charged surface, a free energy minimum is observed due to attractive electrostatic interactions with the positively charged protein. As the protein is able to charge regulatei.e. protons can come and gothe positive charge of the protein increases when approaching the surface. This mechanism is active only at low pH where the protein has a high capacitance (Figure 2) as already discussed through eq 2. When adding hydrophobicity to the negatively charged surface (with ρ = −0.5 nm2)or any short-range interaction the electrostatic and hydrophobic interactions cooperate in a nonadditive manner, and give rise to a −4kBT free energy minimum. Effect of Surface Charge Density. The effect of surface charge density as well as charge regulation is shown in Figure 6.

Figure 7. Contour plot of the effective free energy, βΔA′i, per βCN A1 residue, i, as a function of the residue distance, rz,i, from a ρ = −0.5 nm−2 (top left) and a 0.5 nm−2 (top right) surface at pH 4.5, and typical MC snapshots for each case (bottom). The dotted line is a fit of eq 4 for the position of the free energy minimum as a function of i.

near residue 109 and several other minima throughout the protein. Near a positively charged surface (Figure 7, top right), several minima are seen near the N-terminus, while the tail is repelled if rz,i ≲ κ−1 ≈ 0.2Rg. Close inspection of the contour plots reveals that parts which show the deepest energy minima at close contact in one case are repelled in the other case. Comparison with Figure 4 shows that negatively charged regions are adsorbing on the positively charged surfaces, and vice versa. Hence, when adsorbing to a negatively charged surface, the region around residue 109 gives the largest attractive contribution, while other positively charged groups adsorb as well, although not with the same strength nor range (Figure 7, bottom left). Figure 7, right, shows a different behavior for adsorption to a positively charged surface. At pH 4.5, the negative charges are located mainly near the N-terminus, while the overall charge is net positive. Attraction is observed only for high surface charge densities and when charge regulation is considered. In the most preferable adsorbed conformation, the negatively charged part stretches toward the surface while the positively charged tail remains in solution (Figure 7, bottom right). Thus, the protein behaves as a grafted polymer where approximately 43 amino acids in the N-terminus are in contact with the surface; the remaining residues are distributed as a surface perturbed random walk. For a diffusion-like process of N steps of size Δx, the root-mean-square average position is

Figure 6. βCN A1 properties at pH 4.5 as a function of the mass center distance from a charged surface with ρ/nm−2 = −0.6 (− •, light blue), −0.5 (, dark blue), −0.3 (− −, red), 0.3 (− •, green), 0.5 (, yellow) and 0.6 (− −, magenta). (Top) Free energy, βΔA, with (left) and without (right) charge regulation. (Bottom) Net protein charge number, Z, radius of gyration, Rg (solid lines) and its z-component, Rg,z (dashed lines).

For both negatively and positively charged surfaces, the strength of electrostatic surface−protein interactions increases with an increase in absolute charge density, and the free energy minimum becomes steeper and deeper. Despite being positively charged in bulk solution at pH 4.5, βCN A1 is attracted to the positively charged, nonhydrophobic surface. Here, charge regulation has a striking effect: Without it, the protein is repelled from the surface; if included, there is a distinct free energy gain of several kBT. Due to the high capacitance of the protein, it adapts its charge to the environment, and the deviation from the bulk charge increases with absolute charge density (Figure 6, bottom left). The radius of gyration is dependent on the mass center distance from the surface and reveals that the adsorption mechanism changes dramatically with the sign of the surface charge. Upon approaching a negatively charged wall, the zcomponent of Rg retains its bulk value until rz,cm < Rg, when Rg,z decreases linearly to zero at rz,cm = 0. Due to the constraints in the z-direction, it is forced to stretch in the x- and y-directions instead, which leads to an overall increase in Rg. Similar behavior is seen at close contact with a positively charged wall. At intermediate distances, however, Rg,z increases from 3.7 to

⟨x 2(N )⟩1/2 = N αΔx

(4)

with α = 0.59 for an unperturbed self-avoiding random walk.53 Substituting x(N) with the position of the absolute free energy minimum, min(βΔA′i), as a function of the number of residues from the last grafted monomer, rz,min(βΔA′i)(i − i0), and fitting for the results near a positively charged surface with i0 = 43 gives α = 0.4 and Δx = 1.3 nm. The dotted line in Figure 7 shows that the tail is indeed well described by eq 4. 11846

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strongly decreases (Figure 2). Hence, the free energy minimum near the negatively charged surface gradually disappears as pH is raised−see Figure 9. The effect of charge regulation is

This mechanism also explains the shape difference of the free energy and net charge curves (Figure 6). Near a positively charged surface, the protein stretches to the surface, leading to a decrease in free energy at rz,cm > Rg, and a sharp decrease in Z as the acidic residues in the headgroup are deprotonated. Near a negatively charged surface, the adsorbing amino acids are distributed along the protein sequence, albeit a strong attraction is observed for the middle part of the chain. The protein does not stretch upon approaching the surface, and the charge increases gradually, while the free energy minimum is steeper and at rz,cm ≲ Rg. Variants and Mutant. Figure 8 gives the protein−surface free energies and net charges for four βCN variants and one

Figure 9. Free energy, βΔA, and net charge number, Z, as a function of the distance between the βCN A1 mass center and a ρ = −0.5 nm−2 surface at pH 4.5 (, dark blue), 5.0 (− −, red) and 5.5 (− •, green), 6.0 (, yellow), and 6.7 (− −, magenta).

strongest in the fermented milk system where the capacitance is at its maximum; this effect gradually decreases as pH increases to 5.5. In the pH range 5.5−6.7, the capacitance is almost constant (Figure 2), but the charge deviation increases as the protein becomes more negatively charged. Note that calcium binding equilibria to phosphoserines may also contribute to the capacitance if the calcium activity is close to the Ca2+−Ser dissociation constant. While we here assume full binding and thus neglect this contribution, the current theoretical framework could be expanded to include this effect.

Figure 8. Free energy, βΔA, and net charge number, Z, as a function of the distance from a ρ = −0.5 nm−2 surface at pH 4.5 for βCN A1 (, dark blue), A2 (− −, red), A3 (− •, green), A1 H106Q (, yellow), and B (− −, magenta).

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mutant. The free energy behavior for the two most common variants, A1 and A2, is almost identical, even though the net charge is reduced by one elementary charge as the basic His69 in A1 is substituted with neutral proline in A2. Variant B is less common and has a higher charge due to a mutation of neutral Ser122 to basic arginine, and hence, the energy minimum is slightly deeper. The rarely found variant A3 has an even lower charge than A2 due to an additional point mutation at 106 from basic histidine to neutral glutamine. The decrease in adsorption by 1−1.5 kBT is almost completely due to the His106 mutation, as becomes clear by comparing with A1 H106Q, which is point mutated only at 106 and notas A3also at 69. His106 is in the strongest adsorbing region around residue 109. Hence, replacing a histidine in this region has a much stronger effect than at position 69 as in A2. Even though the charge dependence on the protein−surface distance is identical for A2 and A1 H106Q, the resulting free energy minimum is decreased by 50% for the latter protein, showing that, apart from the net charge, the location of charges in the protein also has a major influence on adsorption. The protein−surface dependence of the charge deviation from the bulk value ΔZ is identical for all five variants, implying that they have similar protein charge capacitances, cf. eq 2. Milk vs Fermented Milk. The results given above focus on adsorption of βCN at pH values corresponding to fermented milk systems. For pH corresponding to normal milk, the protein has a net negative charge, and the charge capacitance

CONCLUSION We have studied the interaction between unstructured β-casein and hydrophobic and/or charged surfaces using a mesoscopic protein model where the amino acid sequence is represented by a bead model with fluctuating charges. Our results show that the protein−surface free energy is highly dependent on surface properties, pH, protein sequence, and charge capacitance. The latter quantifies charge regulation and at low pHas found in fermented milk productsthis gives rise to significant attractive protein−surface interactions ignored by static charge models. For a negatively charged surface at low pH, βCN is attracted via positively charged residues, centrally located in the chain. This attraction is enhanced in a nonlinear fashion by hydrophobic interactions. For a positively charged surface, the negative end of βCN can stretch and reach the surface, while the rest of the chain is repelled. This closely resembles a grafted polymer. This study shows that due to amphiphilic properties and high charge capacitance, βCN acts as a molecular chameleon, changing its properties according to the surface, and hence, adsorption is possible on many surface types. Lastly, while we focus here on single proteins, we expect the above mechanisms to echo also in crowded environments. To fully account for many-body effects, the presented coarsegrained model may provide the foundation for additional studies of multiple casein molecules in the presence of adsorbing surfaces. 11847

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(13) Aktinson, P. J.; Dickinson, E.; Horne, D. S.; Richardson, R. M. Neutron Reflectivity of Adsorbed β-Casein and β-Lactoglobulin at the Air/Water Interface. J. Chem. Soc., Faraday Trans. 1995, 91, 2847− 2854. (14) Fragneto, G.; Su, T. J.; Lu, J. R.; Thomas, R. K.; Rennie, A. R. Adsorption of Proteins from Aqueous Solutions on Hydrophobic Surfaces Studied by Neutron Reflection. Phys. Chem. Chem. Phys. 2000, 2, 5214−5221. (15) Leermakers, F. A. M.; Aktinson, P. J.; Dickinson, E.; Horne, D. S. Self-Consistent-Field Modelling of Adsorbed β-Casein: Effects of pH and Ionic Strength on Surface Coverage and Density Profile. J. Colloid Interface Sci. 1996, 178, 681−693. (16) Dickinson, E.; Pinfield, V. J.; Horne, D. S.; Leermakers, F. A. M. Self-Consistent-Field Modelling of Adsorbed Casein Interaction between Two Protein-Coated Surfaces. J. Chem. Soc., Faraday Trans. 1997, 93, 1785−1790. (17) Kull, T.; Nylander, T.; Tiberg, F.; Wahlgren, N. M. Effect of Surface Properties and Added Electrolyte on the Structure of β-Casein Layers Adsorbed at the Solid/Aqueous Interface. Langmuir 1997, 13, 5141−5147. (18) Velev, O. D.; Campbell, B. E.; Borwankar, R. P. Effect of Calcium Ions and Environmental Conditions on the Properties of βCasein Stabilized Films and Emulsions. Langmuir 1998, 14, 4122− 4130. (19) Nylander, T.; Tiberg, F.; Wahlgren, N. M. Evaluation of the Structure of Adsorbed Layers of β-Casein from Ellipsometry and Surface Force Measurements. Int. Dairy J. 1999, 9, 313−317. (20) Dunker, A. K.; et al. Intrinsically Disordered Protein. J. Mol. Graphics Modell. 2001, 19, 26−59. (21) Skepö, M.; Linse, P.; Arnebrant, T. Coarse-Grained Modelling of Proline Rich Protein 1 (PRP-1) in Bulk Solution and Adsorbed to a Negatively Charged Surface. J. Phys. Chem. B 2006, 110, 12141− 12148. (22) Skepö, M. Model Simulations of the Adsorption of Statherin to Solid Surfaces. Effects of Surface Charge and Hydrophobicity. J. Chem. Phys. 2008, 129, 185101. (23) Linderstrøm-Lang, K. Om Proteinstoffernes Ionisation. C. R. Trav. Lab. Carlsberg 1924, 15, 1−29. (24) Kirkwood, J. G.; Shumaker, J. B. Forces between Protein Molecules in Solution Arising from Fluctuations in Proton Charge and Configuration. Proc. Natl. Acad. Sci. U.S.A 1952, 38, 863−871. (25) Lund, M.; Jönsson, B. On the Charge Regulation of Proteins. Biochemistry 2005, 44, 5722−5727. (26) Ståhlberg, J.; Jönsson, B. Influence of Charge Regulation in Electrostatic Interaction Chromatography of Proteins. Anal. Chem. 1996, 68, 1536−1544. (27) Menon, M. K.; Zydney, A. L. Determination of Effective Protein Charge by Capillary Electrophoresis: Effects of Charge Regulation in the Analysis of Charge Ladders. Anal. Chem. 2000, 72, 5714−5717. (28) Biesheuvel, P. M.; van der Veen, M.; Norde, W. A Modified Poisson-Boltzmann Model Including Charge Regulation for the Adsorption of Ionizable Polyelectrolytes to Charged Interfaces, Applied to Lysozyme Adsorption on Silica. J. Phys. Chem. B 2005, 109, 4172−4180. (29) Biesheuvel, P. M.; Wittemann, A. A Modified Box Model Including Charge Regulation for Protein Adsorption in a Spherical Polyelectrolyte Brush. J. Phys. Chem. B 2005, 109, 4209−4214. (30) Lund, M.; Åkesson, T.; Jö nsson, B. Enhanced Protein Adsorption Due to Charge Regulation. Langmuir 2005, 21, 8385− 8388. (31) Hartvig, R. A.; van de Weert, M.; Østergaard, J.; Jorgensen, L.; Jensen, H. Protein Adsorption at Charged Surfaces: The Role of Electrostatic Interactions and Interfacial Charge Regulation. Langmuir 2011, 2634−2643. (32) Magrane, M.; The UniProt Consortium, UniProt Knowledgebase: a Hub of Integrated Protein Data. Database 2011, bar009. (33) Fischer, H.; Polikarpov, I.; Craievich, A. F. Average Protein Density Is a Molecular-Weight-Dependent Function. Protein Sci. 2004, 13, 2825−2828.

ASSOCIATED CONTENT

S Supporting Information *

Amino acid sequences, method for harmonic bond parameter fitting from crystal structures, and a simulation movie. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*[email protected] (M.L.); [email protected] (M.S.). Present Address ¶

Van ’t Hoff Laboratory for Physical and Colloid Chemistry, Utrecht University, Utrecht, The Netherlands Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the Vinnova supported VINN Excellence Centre SuMo Biomaterials for making this collaboration possible, Lunarc for providing computer time, and Olof Svensson for useful discussion. Vinnova, Vinnmer Program, eSSENCE@LU, as well as the Linneaus Center of Excellence “Organizing Molecular Matter”, Lund, Sweden, are thanked for financial support.

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