Electrostatic and Dispersion Interactions during Protein Adsorption on

ARTICLE pubs.acs.org/Langmuir

Electrostatic and Dispersion Interactions during Protein Adsorption on Topographic Nanostructures Patrick Elter,* Regina Lange, and Ulrich Beck Department of Interface Science, Institute for Electronic Appliances and Circuits, University of Rostock, Albert-Einstein-Strasse 2, 18059 Rostock, Germany ABSTRACT: Recently, biomaterials research has focused on developing functional implant surfaces with well-defined topographic nanostructures in order to influence protein adsorption and cellular behavior. To enhance our understanding of how proteins interact with such surfaces, we analyze the adsorption of lysozyme on an oppositely charged nanostructure using a computer simulation. We present an algorithm that combines simulated Brownian dynamics with numerical field calculation methods to predict the preferred adsorption sites for arbitrarily shaped substrates. Either proteins can be immobilized at their initial adsorption sites or surface diffusion can be considered. Interactions are analyzed on the basis of DerjaguinLandauVerwayOverbeek (DLVO) theory, including electrostatic and London dispersion forces, and numerical solutions are derived using the PoissonBoltzmann and Hamaker equations. Our calculations show that for a grooved nanostructure (i.e., groove and plateau width 8 nm, height 4 nm), proteins first contact the substrate primarily near convex edges because of better geometric accessibility and increased electric field strengths. Subsequently, molecules migrate by surface diffusion into grooves and concave corners, where short-range dispersion interactions are maximized. In equilibrium, this mechanism leads to an increased surface protein concentration in the grooves, demonstrating that the total amount of protein per surface area can be increased if substrates have concave nanostructures.

1. INTRODUCTION One of the first processes observed when an implant material comes into contact with a biological system is protein adsorption at the solidliquid interface. The resulting surface-bound protein layer mediates subsequent cellular adhesion and is therefore highly relevant to the design of biocompatible materials.1 Many studies have focused on the characterization and manipulation of adsorbed protein layers in order to improve implant properties for specific applications.24 Recent research focuses on the development of topographically nanostructured surfaces with characteristic dimensions between 1 and 100 nm, which are believed to influence protein adsorption and thus lead to an altered cellular response.511 This approach is supported by the observation that nanoscale surface topography has an intensified impact on cell adhesion in the presence of serum,9 suggesting a special role of serum proteins that have been previously adsorbed. Moreover, studies based on atomic force microscopy (AFM) have shown that on the molecular level some proteins preferentially adsorb in pits or grooves, suggesting that the creation of specific proteinsurface patterns may be possible. For example, human serum albumin was found to be primarily located inside pits with dimensions of 60 nm in diameter and about 1 nm in height on GaAs substrates.10 Furthermore, it has been demonstrated that for a number of proteins an increase in nanoscale roughness leads to a decrease in protein binding affinity and an increase in the number of adsorbed proteins in equilibrium beyond the corresponding increase in specific area.11 However, a comprehensive explanation of the physical mechanism that governs protein behavior in many studies remains elusive, and medical applications of nanostructured r 2011 American Chemical Society

surfaces are still based mainly on trial and error. As such, computer simulations can be particularly helpful in improving our understanding of the complex processes at the solidliquid interface. Adsorption under physiological conditions is usually strongly influenced by the electrical double layer and the London dispersion interactions between the proteins and the surface.1214 Consequently, any theoretical description must address important questions regarding how electrostatic and dispersion interactions are influenced by topography and how the interplay between these interactions controls protein adsorption. In addition, the interactions between neighboring adsorbates must be considered because they can substantially influence adhesion kinetics and equilibrium coverage.15 An efficient way to take these issues into account is through Brownian dynamics (BD) simulations1523 in which the proteins are displaced in small time steps according to their diffusion properties and the local forces acting on them. Typically, interactions are based on Derjaguin LandauVerwayOverbeek (DLVO) theory24,25 and can be derived from the relatively simple pair potentials of two particles or a particle and the substrate. However, for arbitrarily shaped substrates (e.g., surface structures with sharp edges, grooves, or pits), oftentimes there is no available analytical solution to the field equations. Therefore, we develop a special algorithm that combines BD simulations with numerical field calculation Received: April 13, 2011 Revised: May 28, 2011 Published: June 16, 2011 8767

dx.doi.org/10.1021/la201358c | Langmuir 2011, 27, 8767–8775

Langmuir

Figure 1. Schematic of (a) the simulation cell and (b) the substrate geometry. Proteins are modeled for simplicity as uniformly charged spheres and are allowed to diffuse in their respective force fields. The simulation cell consists of an interior region where space is discretized into small cubic elements. This region is where the nanostructured substrate is located. Note that the size of the elements shown is not drawn to scale and is in fact much smaller. The interior region is surrounded by an outer region with 3D periodic boundary conditions; this outer region is assumed to be far away from the substrate. The regions above and below the substrate serve as a protein basin and are maintained at a constant bulk concentration. The simulation starts with an empty substrate, which is gradually filled with proteins.

methods and enables an analysis of protein adsorption from aqueous electrolyte solutions onto nanostructured surfaces. Interestingly, preliminary studies that do not consider surface diffusion have shown that proteins have an increased probability of reaching positions near convex edges of oppositely charged substrates because of the better accessibility and increased electrical field strengths of these sites.26 Consequently, a comprehensive mechanism must explain why proteins in equilibrium are frequently observed in pits or concave corners of the substrate, even if the adsorption probability is lower for these positions. As such, we have simulated protein adsorption onto a grooved nanostructure while considering surface diffusion in order to analyze the local influence of electrostatic and dispersion interactions. We performed these simulations using the (almost) globular protein hen egg white lysozyme (N-acetylmuramidglycanohydrolase), which is characterized by well-defined physical parameters,2733 a high degree of comparability to other simulations12,16,23,26,28 and easy generalizability to other systems. On the basis of our computer simulations, we derive a simple mechanism for protein adsorption on topographically nanostructured substrates.

2. SIMULATION METHOD 2.1. Simulation Cell. A schematic of the simulation cell is shown in Figure 1a. It consists of an interior region, where space is discretized into small cubic elements, and an outer continuum region. Three-dimensional periodic boundary conditions were used under the standard minimal image convention.34 Each element of the interior region is either part of the substrate or

ARTICLE

part of the surrounding electrolyte solution, and local values such as the charge density or pair potentials can be assigned individually. Thus, an arbitrarily shaped nanostructure can be approximated by sufficiently combining many small elements. A partitioning of the interior region into cubic elements is particularly suitable for our simulations because the geometries investigated in this study have 90 edges. Moreover, the calculation of the force fields can be significantly accelerated by the high degree of symmetry. The free diffusion of proteins is allowed in both regions of the simulation cell, per Ermak and McCammon’s17,18 algorithm. Although the interior region is the location where adsorption takes place and where proteinsubstrate and protein protein interactions are considered, the outer region is assumed to be far enough away from the nanostructure such that only proteinprotein interactions are calculated there. The outer regions above and below the structure (Figure 1a) serve as a protein reservoir and are maintained at a constant bulk concentration. For simplicity, proteins are described as uniformly charged spheres,12 which allows the analytical calculation of proteinprotein interactions. The electrolyte molecules (i.e., Naþ and Cl) and the solvent (i.e., the water molecules) are not explicitly represented, but their influences on the potential distributions are considered. The simulation starts with an empty substrate, and all proteins are located in the reservoirs. The molecules are arranged so that no overlap occurs between the spheres or their periodic images in adjacent simulation cells. Subsequently, the system is relaxed and the substrate is gradually filled up with proteins until equilibrium is reached. 2.2. Brownian Dynamics. In a BD simulation, the displacement of each particle i is derived from the forces acting on it. The new particle position after a small time step Δt is considered to be the initial position for the following step. The gradual computation of many time steps results in the movement trajectory of a protein. A simple algorithm for updating the particle position is given by the following equation:17,18 ξi ðt þ ΔtÞ ¼ ξi ðtÞ þ

D0 Fi ðtÞΔt þ χ i ðΔtÞ kB T

ð1Þ

where ξi(t) is the position of particle i at time t, D0 is the diffusion coefficient for free diffusion, kB is the Boltzmann constant, and T is the system temperature. Protein movement is determined by a systematic net force Fi, which results from the interaction of the proteins with their environment (i.e., with the substrate and other proteins), and a stochastic displacement χi, which represents Brownian motion. The latter is generated from a set of random numbers by a BoxM€uller transformation;35 it has a Gaussian distribution with Æχiæ = 0, a variancecovariance ÆχRi χβj æ = 2D0ΔtδRβ δij (based on the diffusivity of the proteins), and no correlation with the systematic force.15 Indices R and β denote the coordinate directions (x, y, z) in space, and δ is the Kronecker delta function. All interactions and forces are assumed to be pairwise additive. We note that even though the latter simplification is widely used in BD simulations,15,36 this assumption does not consider three-way interactions and can thus lead to an overestimation of the electrostatic repulsion between two proteins near an edge of the substrate. For that reason, we neglect the electrostatic repulsion between two proteins when the substrate crosses the line of sight between two protein centers. After adsorption, proteins can either be fixed at the adsorption site or be allowed to diffuse further with a probability of desorption from the surface.15 Because it is generally expected 8768

dx.doi.org/10.1021/la201358c |Langmuir 2011, 27, 8767–8775

Langmuir

ARTICLE

that the diffusivity of a molecule will diminish by hydrodynamic friction and other forces when it nears a surface,37 the overall mobility of a protein is reduced by a factor of γ once it is in contact with the substrate. Interparticle hydrodynamic interactions are neglected in our model because of the high computational cost (as discussed later). 2.3. Interaction Potentials. Systematic net force Fi is derived from pair potentials based on DLVO theory,24,25 including electrostatic and London dispersion interactions. Protein protein interactions can be expressed analytically, whereas proteinsubstrate interactions must be calculated numerically and are assigned to the cubic mesh of the interior region so that the systematic force can be derived from elements that are adjacent to the center of the sphere. (See below.) Electrostatic proteinprotein interactions in an electrolyte solution can be expressed by the following screened Coulomb potential38 qprot 2 e20 expðkaÞ 2 expð krÞ ð2Þ Ui,ELj ðrÞ ¼ r 4πεr ε0 1 þ ka where k2 = (e02NA∑ν cνqν2)/(εrε0kBT) is the inverse Debye length, a is the radius of the protein sphere, r > 2a is the distance between two proteins, ε0 is the permittivity of free space, εr is the relative dielectric constant, e0 is the electron charge, and qprot is the net charge of a protein. Moreover, each ion species ν of the electrolyte is parametrized by its concentration cν and its charge qν. Proteinsubstrate interactions are derived from the nonlinear PoissonBoltzmann (PB) equation: rðε0 εr ðxÞrfðxÞÞ ¼ WðxÞ jðxÞ qν e0 fðxÞ ð1 WðxÞÞ qν e0 cν NA exp kB T ν

∑

ð3Þ

Here, ϕ(x) is the local electric potential in volts, j(x) is the local charge density of the substrate, and W(x) is a Boolean function, which is 1 for the solid side of the interface and 0 for the liquid side. Moreover, NA is Avogadro’s number, kB is the Boltzmann constant, and T is the system temperature. The electric potential is calculated by a nonlinear multigrid finite difference solver.35 The boundary conditions of the PB equation are set to a constant surface potential on the solid side of the interface and estimated using DebyeH€uckel theory for the outer grid points of the simulation cell.39 The net force between a protein sphere and the nanostructure is derived by a uniform weighting of the local electrostatic forces at the center of the sphere and weightings at six positions on the surface at particular Cartesian points. The vectors are precalculated for all positions ξ values centered in the sphere and are assigned to the respective cubic element ξ. Dispersion interactions are calculated using Hamaker’s approach.40 The nonretarded dispersion interaction between two arbitrarily shaped bodies is given by Z Z λq1 q2 U ¼ dv1 dv2 6 ð4Þ r V1 V2 where dv1 and dv2 designate the volume elements from the integrals over the total particle volumes V1 and V2, respectively, and r denotes the distance between dv1 and dv2. Moreover, q1 and q2 are the atom densities of the interacting bodies, and λ is the Londonvan der Waals constant. According to this

Figure 2. Numerical integration technique used for the calculation of the dispersion interactions. ξ denotes a vector to the cubic element where the protein sphere is centered, and η is a vector associated with the center of a cubic element that belongs to the substrate. A regular subgrid of integration points is distributed over the cubic elements, and Δ is the distance between the current integration point and the center of the sphere.

approach, the expression for two spheres of radius a is40 ( ) 2 2 2 2 r ð2aÞ A 2a 2a i, j Ui,DISP þ þ ln ð5Þ j ðrÞ ¼ 6 ri,2j ð2aÞ2 ri,2j ri,2j where A = π2λq1q2 is the Hamaker constant. Proteinsubstrate interactions are calculated from the numerical solution to eq 4. For this purpose, the interaction between an atom and a sphere with an atom density of q2 is first considered. An expression for the potential energy can be derived by integrating one of the volume integrals of eq 4 over a sphere of radius a40 Z Z λ1q2 UP ðRÞ ¼ dv1 dv2 6 r V1 ¼ atom V2 ¼ sphere Z Rþa r λ1q2 ¼ dr π fa2 ðR rÞ2 g 6 ð6Þ R r Ra which finally yields UP ðRÞ ¼

4πλq2 a3 3 ðR aÞ3 ðR þ aÞ3

ð7Þ

Here, R > a denotes the distance between the atom and the center of the sphere. Please note that atom density q1 is not required for a single atom and therefore does not appear in eqs 6 and 7. In the next step, UP is numerically integrated over the substrate volume with the atom density q1, as illustrated in Figure 2. Because of the rapidly decreasing slope of r6 in Hamaker’s equation, a fine subgrid with (2g þ 1)3 integration points is introduced for each cubic element of the substrate. Below, the protein sphere is centered at an arbitrary cubic element ξ of the interior region. The dispersion energy of the protein and the substrate is given by Z

Ui,DISP S ðξÞ ¼

g

g

V1 ¼ substr

g

∑η i ¼∑ g j ¼∑ g k ¼∑ g h3 wi, j, k

¼

4Ah3 3π

g

g

g

q1 UP dv1

4πλq1 q2 a3 3 ðΔ aÞ3 ðΔ þ aÞ3 a3

∑η i ¼∑ g j ¼∑ g k ¼∑ g wi, j, k ðΔ aÞ3 ðΔ þ aÞ3

ð8Þ

where the first sum is calculated over all cubic elements that belong to the substrate and η is the vector associated with the center of the element. The edge length of a cubic element is denoted by h. A cutoff radius of 10 nm was used to increase the calculation speed. The latter three sums run over the grid points 8769


Langmuir

ARTICLE

Figure 3. Interaction potentials and forces used in the simulation. (a) Lysozymelysozyme pair potential (without short-range repulsion) for a physiological salt concentration (0.137 mol/L NaCl; thick solid line) and at low ionic strength (0.01 mol/L NaCl; thick dashed line). The thin lines represent the individual contributions of the dispersion interactions (negative) and the electrostatic interactions (positive). (b) Orientation of the cross sections used in parts cg. (c) Cross section of the electric potential of the nanostructure in liquid at physiological salt concentrations. (d) Cross section of the local electric field strength. The electric field strength increases at convex edges and decreases in concave corners. (e) Magnitude of the electrostatic forces between a protein sphere and the nanostructure. The distribution of charge on the sphere leads to decreased forces directly at the convex edges and increased forces near convex edges and in the concave corners of the groove. (f) Cross section of the dispersion interaction pair potential between the protein sphere and the nanostructure. (g) Magnitude of the local dispersion forces. Dispersion forces dominate during contact with the substrate and are maximal in the concave corners of the groove. In c and d, the x and y axes denote the position in space. In eg, values are given with respect to the center of the sphere.

of the fine subgrid, and Δ = |η þ (h/(2g){i, j, k}) ξ| is the distance between the current integration point {i, j, k} of element η and the center of the sphere located at ξ. wi,j,k is the Gaussian weight.35 The computation time can be reduced significantly by symmetry analysis because the results of the latter three sums depend only on the relative position of the cubic element η with respect to the center of the sphere at ξ.

Finally, the calculation is repeated by gradually recentering the sphere at all elements that belong to the liquid (i.e., all discrete positions where the sphere does not overlap with the substrate), and the results are assigned to the corresponding cubic element of the interior region. The systematic net force vectors are precalculated for all positions ξ by numerical differentiation of the energy landscape using the finite differences estimation.35 8770


Langmuir Short-range Pauli repulsion is modeled indirectly by the BD algorithm; each time a particular displacement leads to a geometric overlap with another protein or with the substrate, the length of the displacement vector is reduced so that no overlap occurs. The order at which this is checked is modified at every time step to reduce possible correlation effects. Moreover, a steric exclusion height of 0.1 nm is introduced, which corresponds to the position of the potential minimum when Pauli repulsion is added to prevent dispersion forces from becoming singular. 2.4. Model Parameters. The interior region of the simulation box was discretized into 1283 cubic elements with edge lengths of 0.25 nm, which corresponds to a mesh size of 2.1 106 points. The entire simulation cell (i.e., the interior and outer regions) has a volume of (132 nm)3. A grooved nanostructure with plateau and groove widths of 8 nm and a groove depth of 4 nm was selected as the substrate (Figure 1b). The dimensions of the nanostructure were selected such that the groove width is significantly larger than the protein size, making possible comparisons between edges and planar areas. One groove is located on the top of the structure, and one is located on the bottom. An electric potential of ϕ0 = 0.1 V was assigned to the substrate, which is equivalent to the surface potential of mica.29 The electrical properties of mica are particularly suitable for modeling because many medically relevant materials also have a negative surface charge at pH 7. Moreover, mica has been established as a standard substrate for AFM experiments on protein adsorption. 27,33,41 Lysozyme was modeled as a uniformly charged sphere with a radius a of 1.5 nm,15 a molecular weight of 14 400 g/mol (i.e., a mass of m = 2.39 1023 kg/molecule), a net charge of þ8e at pH 7,30 and a diffusivity of D0 = 1.1 106 cm2/s.31 When the proteins are in contact with the substrate, the mobility of the proteins is reduced by a factor γ of 1.5 (i.e., 33% reduction) based on experimental observations adjacent to lysozyme (110) faces.32 For the calculation of the dispersion interactions, a fine subgrid of 729 points (g = 4) was used, extending the overall mesh size to 1.6 109 points. A Hamaker constant Ai,j of 2.0 1020 J was selected for proteinprotein interactions,15 and a Hamaker constant Ai,S of 1.4 1020 J, which corresponds to the dispersion interactions of lysozyme with mica,33 was selected for proteinsubstrate interactions. Protein concentrations of between 200 μg/mL and 4 mg/mL were examined in this study, leading to protein numbers of between 14 and 292 in the reservoirs at the beginning of the simulations. All simulations were carried out under physiological conditions (i.e., at a temperature of 37 C in a sodium chloride electrolyte with a concentration of 0.137 mol/L and a relative dielectric constant εr of 81). The time step Δt for the BD simulations was set to 4.1 ps so that the average displacements remained small as compared to the protein radius ((2DΔt)1/2 e 0.02a) and Δt was well above the lower limit for the time step in the algorithm of Ermak and McCammon18 (Δt > mD0/kBT ≈ 0.6 ps). Smaller time steps did not lead to appreciable improvements. The program code was developed entirely in Cþþ using GNU Cþþ version 4.3.1.

3. RESULTS AND DISCUSSION 3.1. Analysis of the Interaction Potentials. Figure 3a displays the pair potential of two lysozyme proteins as a function of distance both under physiological conditions (0.137 mol/L NaCl) and at low ionic strength (0.01 mol/L NaCl). The curves are composed of attractive dispersion interactions, which

ARTICLE

dominate at low distances and repulsive electrostatic interactions. The latter form a repulsive barrier with height and range depending on the number of ions available for the screening repulsion; the height and range decrease with higher ionic strength. Nevertheless, the range of electrostatic interactions at physiological salt concentrations is still significantly greater than that of the dispersion interactions. Our potential functions are consistent with previous studies on lysozyme adsorption at planar substrates, which demonstrate that the ionic-strengthrelated height of the repulsive barrier is a key factor in limiting equilibrium surface coverage.23 In contrast to proteinprotein interactions, both the dispersion and electrostatic components of the proteinsubstrate interactions are attractive because the proteins and the substrate are oppositely charged. Figure 3c shows the cross section of the electric potential through the substrate under a physiological salt concentration. The pixels in the diagram correspond to the cubic elements of the interior region in the simulation cell. The potential drops rapidly on the liquid side of the interface because of the high screening effect of the ions under physiological conditions, but it still extends noticeably into the groove. The potential distribution results in increased electric field strengths (Figure 3d) at convex edges because of greater field line densities but decreased field strengths near the concave corners of the groove. The higher electric field strengths near convex edges indicate a greater local attraction of charged groups, but their charge distribution over the protein sphere must be considered. Figure 3e displays the magnitude of the local electrostatic forces on the sphere. The forces shown have low magnitudes directly at the convex edges because the influence of the increased electric field strength is overcompensated for by an increased average distance of charge between the proteins and the substrate at these sites. Nevertheless, the net force is increased in the neighborhood of the convex edges, where both the average charge separation is smaller and parts of the sphere extend to regions with increased electric field strength. The electrostatic forces on the sphere are also increased in the concave corners of the groove because the sphere is simultaneously in contact with the sidewalls and the bottom of the groove. Hence, the average charge separation is small. It should be noted that the electrostatic force field may be more complex if the structural details of the proteins are included in the calculations. The pair potentials of the dispersion interactions and the resulting dispersion forces are shown in Figure 3f,g, respectively. The short-range dispersion interactions clearly predominate in contacts with the substrate by almost an entire order of magnitude, but they are rapidly outweighed by longer-range electrostatic interactions at larger proteinsubstrate distances. The greater separation of volume elements (i.e., dv1 and dv2 in eq 4) in combination with the rapidly decreasing slope of r6 from Hamaker’s approach led to a considerable drop in the dispersion energy and dispersion forces near convex edges. In contrast, the dispersion interactions are maximized in the concave corners because of simultaneous contact with the bottom and side walls of the groove. Consequently, the dispersion and electrostatic interactions are strong in the concave corners, but only electrostatic interactions have a large magnitude near convex edges. Because the concave corners have reduced accessibility, it is unclear which sites are ultimately favored by the proteins. Therefore, we analyze the local influence of both interaction types on the proteins during diffusion. 3.2. Preferred Adsorption Sites. Figure 4 shows the adsorption sites of the lysozyme molecules for various bulk 8771


Langmuir

ARTICLE

Figure 5. Adsorption isotherms (mean ( SD) of the model protein on the nanostructure under physiological conditions (i.e., at a NaCl concentration of 0.137 mol/L and a temperature of 37 C). The solid line denotes the total surface concentration on the nanostructure, the dashed line represents the surface concentration inside the grooves, and the dotted line denotes the surface concentration outside the grooves.

Figure 4. Adsorption sites of lysozyme on the nanostructure after 33, 50, and 100% equilibrium surface coverage is reached for different protein concentrations. The calculations were performed for physiological conditions (i.e., at a NaCl concentration of 0.137 mol/L and a temperature of 37 C), and surface diffusion was allowed. Note that the time step after which the respective surface coverage is reached strongly depends on the bulk concentration because of the higher probability of contact for a larger number of proteins during the simulation.

concentrations after 33, 50, and 100% equilibrium surface coverage is reached. The proteins were allowed to diffuse across the surface to derive the following results. Because lysozyme has a weak interaction with the substrate, equilibrium is determined by the balance between adsorption and desorption, hence it depends strongly on the bulk concentration. Previous studies on planar substrates obtained similar results and were able to show that the equilibrium surface coverage can be expected to depend on the bulk protein concentration, particularly at high salt concentrations.15 Interestingly, an increased number of proteins are found in the concave corners of the grooves. Clearly, the sites near the flanks of the grooves stabilize the adsorption of lysozyme because of increased interactions with the substrate and restricted degrees of freedom during diffusion. In addition, the strong proteinsubstrate interactions at these positions allow molecules to penetrate their electrostatic barrier, frequently leading to clustering at a single groove flank in the early states (see Figure 4 for 200, 500, and 1000 μg/mL). The interactions with the planar regions of the substrate, however, are lower and lead to a higher degree of desorption. The results indicate that although electrostatic interactions may influence the initial adsorption sites, the strong dispersion interactions in the concave corners are crucial to final protein stabilization. Only at higher lysozyme concentrations is the increased adsorption probability high enough to yield a steady state in which the planar regions outside the grooves also become noticeably occupied. The occupation ratio between planar faces and grooves is temporarily inverted for high lysozyme concentrations, and a higher coverage of the planar faces is observed in the beginning of the adsorption

process. (See Figure 4 for 33% equilibrium state at 2000 and 4000 μg/mL.) The concentration-dependent occurrence of the inverted occupation ratio reveals different adsorption kinetics in the grooves versus on the planar faces. An increased protein concentration obviously has a larger impact on the occupation rate of the planar region than on that of the groove. Figure 5 displays the surface concentration of adsorbed lysozyme at equilibrium for five different bulk concentrations. The curves were created by averaging 106 to 107 data points, depending on the bulk concentration and its corresponding rate to equilibrium. The total surface concentration exhibits a strong dependence on the bulk concentration and has a roughly Langmuir-like shape with smaller geometry-related deviations. Within the groove, the adsorbed surface concentration is almost constant because it is already fully populated at equilibrium at the lowest tested bulk concentration (200 μg/mL). In contrast, the curve for the planar regions outside the grooves shows a considerable dependence on the bulk concentration because desorption is compensated for at higher bulk concentrations, as described earlier. Although the absolute number of molecules in the planar regions is somewhat larger than in the grooves (Figure 4, 4000 μg/mL), the resulting surface concentration is always below the values obtained in the groove because the adsorption area is much larger. We also note that because of the small substrate dimensions and the large number of edges, the absolute value of the calculated surface concentrations outside the grooves cannot be compared to flat mica substrates with macroscopic dimensions, even if a strong concentration dependence is observed.42,43 Nevertheless, our simulations clearly imply that the total surface concentration (i.e., surface concentration considering both the planar areas and the grooves) is always greater than the concentration of planar regions alone. Hence, providing a substrate with a concave nanostructure leads to an increased amount of adsorbed proteins in equilibrium beyond the corresponding increase in surface area. However, the intensity of this effect depends on the roughness and the aspect ratio of the nanostructure in proportion to the protein size, and applications may require a fine tuning of the parameters for different protein types. Furthermore, we still must address how proteins reach the concave corners of the nanostructure. 8772


Langmuir

ARTICLE

Figure 7. Illustration of the protein adsorption mechanism. (a) Proteins are initially adsorbed near convex edges because of their better accessibility and the increased electrostatic forces near the edges. (b) Subsequently, proteins migrate by surface diffusion into concave corners, where they are stabilized by high dispersion interactions.

Figure 6. Adsorption sites of lysozyme on the nanostructure under physiological conditions (i.e., at a NaCl concentration of 0.137 mol/L and 37 C) when surface diffusion and desorption are prohibited. (a) The simulation after 2 107 time steps. The data identify the initial adsorption sites. (b) Surface coverage near equilibrium (after 6 108 time steps). The data demonstrate that even after a very large number of calculation steps the grooves are not completely filled with proteins.

3.3. Adsorption Mechanism. Figure 6 shows the adsorption sites of the proteins when surface diffusion is prohibited and the molecules are immobilized as soon as they come into contact with the surface. Part a displays occupancy shortly after the beginning of the adsorption process (after 2 107 time steps), and part b displays occupancy near equilibrium (after 6 108 time steps). Because desorption is not considered in this part of the study, the protein concentration plays only a minor role, and equilibrium is primarily determined by ionic strength.26 Nevertheless, the results allow us to identify the initial adsorption sites. The early time steps of these simulations reveal that proteins are preferably adsorbed near convex edges (Figure 6a) (i.e., exactly at those sites that are unfavorable if surface diffusion is taken into account). In contrast, the grooves were never completely filled with proteins within the investigated time frame (maximum of 6 108 time steps; see Figure 6b). The results are understandable given that the influence of the long-range electrostatic attraction is increased near convex sites and edges have a higher accessibility than planar faces or concave corners because of the greater surrounding liquid volume. Consequently, the initial adsorption sites are primarily determined by the synergy of long-range electrostatic interactions and the accessibility of the sites. Dispersion interactions, however, play a role only when the proteins are already very close to the substrate, in which case they no longer significantly influence the initial adsorption sites. The probability that a protein has its first contact with the substrate in the concave corners of the grooves in which dispersion interactions are maximal was found to be negligible as compared to the adsorption probability near the convex edges. Nevertheless, dispersion forces play an important role in stabilizing the adsorbed proteins in the long term, as they are an order of magnitude larger than the electrostatic forces when the molecule is in contact with the substrate. In summary, proteins preferentially adsorb near convex edges if surface diffusion and desorption are neglected and the proteins are immobilized at their initial adsorption site. In contrast, if

Figure 8. Protein surface concentration inside and outside the grooves as a function of time under physiological conditions (i.e., at a NaCl concentration of 0.137 mol/L and a temperature of 37 C). The protein bulk concentration was 2000 μg/mL, and surface diffusion was permitted. The solid line denotes the surface concentration outside the grooves, and the dotted line denotes the surface concentration inside the grooves.

surface diffusion is allowed, then concave corners are primarily occupied. Accordingly, we propose a two-step mechanism for protein adsorption on topographically nanostructured substrates, which is illustrated in Figure 7. In the first step, proteins preferentially adsorb in the neighborhood of convex edges because of the latter’s higher accessibility and the increased electrostatic forces there. However, once in contact with the substrate, dispersion forces mediate the long-term stability of adsorption, and these interactions are small at the initial adsorption sites (Figures 3e,g). Consequently, proteins desorb or randomly migrate over the surface in the second step until they reach positions that offer more stability. Therefore, in equilibrium, proteins are frequently found in concave corners where dispersion forces are strong. Finally, we must investigate more thoroughly whether proteins indeed reach the grooves via surface diffusion. Figure 8 shows the surface coverage inside and outside the grooves as a function of time at a bulk concentration of 2000 μg/mL. In these calculations, we allow surface diffusion of the proteins. The surface concentration in the grooves initially grows more slowly but finally reaches higher equilibrium values than in the planar 8773


Langmuir areas outside the groove. The sites outside the grooves are initially occupied faster because their adsorption probability is greater, and occupation is further accelerated by the high bulk concentration. Nevertheless, it is remarkable that the increase in the surface concentration inside the grooves is first delayed but then has approximately the same slope as observed for planar surfaces (Figure 8, black arrow). Such a strong increase cannot originate from nonadsorbed proteins in solution because the protein densities for the investigated concentrations are too low, and there are usually only a few proteins inside the small interior region of the simulation cell. Proteins coming into the interior region, however, have a greater chance of reaching the planar regions of the substrate. Hence, the increase does not result from the diffusion of nonadsorbed proteins reaching the grooves. That is, on the basis of the low direct adsorption probability for these sites, direct adsorption exclusively from the solution in the concave corners of the grooves would result in an increase in surface concentration with a low slope over simulation. Hence, the proteins reach the grooves primarily by surface diffusion, which provides a greater number of proteins. This interpretation is supported by experimental studies showing that lysozyme has considerable surface mobility on mica substrates.27 For the investigated nanostructure, the migration time into the grooves is short; therefore, a large number of proteins are found there even at early time steps (Figure 4, 33% equilibrium surface coverage). However, at high protein concentrations, the occupation rate of the planar areas is faster than the surface diffusion into the grooves, hence an inversion in the occupation ratio between planar faces and grooves is temporarily observed. Scopelliti et al.11 show in an experimental study that nanoroughness leads to both a decrease in protein affinity and an increase in the amount of adsorbed proteins in equilibrium. Our simulations provide a similar result and demonstrate that both effects can be understood if the different roles of electrostatic and dispersion interactions are considered, even if both the proteins and the nanostructures examined are smaller. Moreover, Bergman et al.10 observed that human serum albumin is preferentially adsorbed inside pits on GaAs substrates at pH 7.6 and the molecules appear to be packed closely together around the inner sides of rims that decorate the pits. Their results can also be understood in the context of our model; albumin has a negative net charge at pH 7.6,44 and the isoelectric point of GaAs is below pH 7.6.45 Consequently, the substrate has a negative net surface charge at pH 7.6 and only dispersion interactions are attractive. According to the presented mechanism, such a configuration promotes adsorption only near the concave corners of the rims in equilibrium and allows the proteins to penetrate their electrostatic barrier for clustering. Our simulations demonstrate that various experimental observations can be explained with the simple field approaches used in this study. This emphasizes the importance of the relationships among electrostatic interactions, surface diffusion, and dispersion interactions in the design of new nanomaterials. However, our simulation scheme has limits with respect to the influence of structural details of the proteins and hydrodynamic interactions. Although interparticle effects such as volume exclusion and electrostatic proteinprotein repulsion are basically considered in our algorithm, hydrodynamic interactions are neglected. Hydrodynamic interactions can influence the diffusion behavior of the proteins in a complex way because of their manybody character and long-range nature. For example, Ando and Skolnick46 have demonstrated in Brownian dynamics simulations that the reduced diffusivity of highly concentrated macromolecules

ARTICLE

in vivo can be explained only if hydrodynamic interactions are considered. Nevertheless, according to our model the greatest differences in surface concentration between the planar regions and the grooves occur at low protein concentrations, and the results are in qualitative agreement with experimental observations. Therefore, it seems reasonable to conclude that hydrodynamic interactions ultimately play a minor role in determining the equilibrium sites as long as protein concentrations are sufficiently low. Furthermore, a valuable improvement for future calculations would be a detailed consideration of the inhomogeneous charge distribution on the proteins and the orientation of the molecules in the local electric fields instead of using a uniformly charged sphere as a model protein. In this way, proteinprotein interactions could be described more realistically and may provide additional insight regarding effects such as macromolecular crowding and the development of protein multilayers. Finally, nanostructures may influence the conformation of adsorbed proteins, leading to an exposure or a concealment of cryptic sites and thus an alteration of the biological function of the protein. Hoda and Kumar have shown in BD simulations that both charge-patterned surfaces21 and topographically patterned surfaces22 can significantly influence the conformation of polyelectrolyte chains if molecules and patterns have dimensions of the same order of magnitude. The rigid protein shape used in the present study cannot provide information regarding protein conformation, but the derived mechanism may be a good starting point for combination with atomistic molecular dynamics simulations.

4. CONCLUSIONS We have presented a computer algorithm that combines Brownian dynamics simulations with numerical field calculation methods to predict protein adsorption sites on arbitrarily shaped nanostructures. Our simulations explain the different local roles of dispersion and electrostatic interactions in the adsorption process. While long-range electrostatic interactions and the accessibility of specific places primarily determine the initial adsorption sites, surface diffusion and short-range dispersion interactions determine the positions at equilibrium. We have shown that the interplay between these factors causes lysozyme molecules to adsorb initially near the convex edges of oppositely charged nanostructures with grooves. Subsequently, the proteins migrate by surface diffusion into the concave grooves. Our simulations demonstrate that substrates with concave nanostructures may lead to an equilibrium situation with an increased amount of adsorbed proteins beyond the corresponding increase in surface area. ’ AUTHOR INFORMATION Corresponding Author

*Tel: þ49 381/498-7242. Fax: þ49 381/498-118-7242. E-mail: [email protected].

’ ACKNOWLEDGMENT Funding from the Deutsche Forschungsgemeinschaft DFG (project BE 2362/2-2) is gratefully acknowledged. ’ REFERENCES (1) Andrade, J. D.; Hlady, V. Adv. Polym. Sci. 1986, 79, 1–63. (2) Wahlgren, M.; Arnebrant, T. Trends Biotechnol. 1991, 9, 201– 208. 8774


Langmuir (3) Hlady, V.; Buijs, J. Curr. Opin. Biotechnol. 1996, 7, 72–77. (4) Hook, A. L.; Thissen, H.; Voelcker, N. H. Trends Biotechnol. 2006, 24, 471–477. (5) Lord, M. S.; Foss, M.; Besenbacher, F. Nano Today 2010, 5, 66–78. (6) Song, W.; Chen, H. Chin. Sci. Bull. 2007, 52, 3169–3173. (7) Galli, C.; Coen, M. C.; Hauert, R.; Katanaev, V. L.; Wymann, M. P.; Gr€oning, P.; Schlapbach, L. Surf. Sci. 2001, 474, L180–L184. (8) Galli, C.; Coen, M. C.; Hauert, R.; Katanaev, V. L.; Gr€ oning, P.; Schlapbach, L. Colloids Surf., B 2002, 26, 255–267. (9) Lim, J. Y.; Hansen, J. C.; Siedlecki, C. A.; Runt, J.; Donahue, H. J. J. R. Soc., Interface 2005, 2, 97–108. (10) Bergman, A. A.; Buijs, J.; Herbig, J.; Mathes, D. T.; Demarest, J. J.; Wilson, C. D.; Reimann, C. T.; Baragiola, R. A.; Hull, R.; Oscarsson, S. O. Langmuir 1998, 14, 6785–6788. (11) Scopelliti, P. E.; Borgonovo, A.; Indrieri, M.; Giorgetti, L.; Bongiorno, G.; Carbone, R.; Podesta, A.; Milani, P. PLoS One 2010, 5, e11862. (12) Roth, C. M.; Lenhoff, A. M. Langmuir 1993, 9, 962–972. (13) Pasche, S.; V€or€os, J.; Griesser, H. J.; Spencer, N. D.; Textor, M. J. Phys. Chem. B 2005, 109, 17545–17552. (14) Roth, C. M.; Neal, B. L.; Lenhoff, A. M. Biophys. J. 1996, 70, 977–987. (15) Oberholzer, M. R.; Wagner, N. J.; Lenhoff, A. M. J. Chem. Phys. 1997, 107, 9157–9167. (16) Ravichandran, S.; Madura, J. D.; Talbot, J. J. Phys. Chem. B 2001, 105, 3610–3613. (17) Ermak, D. L. J. Chem. Phys. 1975, 62, 4189–4196. (18) Ermak, D. L.; McCammon, J. A. J. Chem. Phys. 1978, 69, 1352–1360. (19) Asthagiri, D.; Lenhoff, A. M. Langmuir 1997, 13, 6761–6768. (20) Brewer, D. D.; Tsapatsis, M; Kumar, S. J. Chem. Phys. 2010, 133, 034709. (21) Hoda, N.; Kumar, S. Langmuir 2007, 23, 1741–1751. (22) Hoda, N.; Kumar, S. Langmuir 2007, 23, 11747–11760. (23) Ravichandran, S.; Talbot, J. Biophys. J. 2000, 78, 110–120. (24) Derjaguin, B. V.; Landau, D. L. Acta Physicochim. URSS 1941, 14, 633–662. (25) Verwey, E. J.; Overbeek, J. T. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, Netherlands, 1948. (26) Elter, P.; Lange, R.; Thull, R.; Beck, U. Mater. Sci. Forum 2010, 638, 542–547. (27) Kim, D. T.; Blanch, H. W.; Radke, C. J. Langmuir 2002, 18, 5841–5850. (28) Wahlgren, M.; Arnebrant, T.; Lundstr€om, I. J. Colloid Interface Sci. 1995, 175, 506–514. (29) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans. 1 1978, 74, 975–1001. (30) Tanford, C.; Roxby, R. Biochemistry 1972, 11, 2192–2198. (31) Brune, D.; Kim, S. Proc. Natl. Acad. Sci. U.S.A. 1993, 90, 3835–3839. (32) Gorti, S.; Zuk, W. M.; Konnert, J.; Ward, K.; Tanaka, T.; Yang, H. J. Cryst. Growth 2001, 232, 256–261. (33) Leisten, F.; Wiechmann, M.; Enders, O.; Kolb, H.-A. J. Colloid Interface Sci. 2006, 298, 508–514. (34) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: New York, 1989. (35) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in C; Cambridge University Press: Cambridge, U.K., 2007. (36) Stankovich, J.; Garnie, S. L. Langmuir 1996, 12, 1453–1461. (37) Brenner, H. Chem. Eng. Sci. 1961, 16, 242–251. (38) Semmler, M.; Mann, E. K.; Ricka, J.; Borkovek, M. Langmuir 1998, 14, 5127–5132. (39) Nicholls, A.; Honig, B. J. Comput. Chem. 1991, 12, 435–445. (40) Hamaker, H. C. Physica 1937, 4, 1058–1072. (41) Rojas, O. J.; Ernstsson, M.; Neumann, R. D.; Claesson, P. M. Langmuir 2002, 18, 1604–1612. (42) Blomberg, E.; Claesson, P. M.; Fr€oberg, J. C.; Tilton, R. D. Langmuir 1994, 10, 2325–2334.

ARTICLE

(43) G€olander, C.-G.; Hlady, V.; Caldwell, K.; Andrade, J. D. Colloids Surf. 1990, 50, 113–130. (44) Fogh-Andersen, N.; Bjerrum, P. J.; Siggaard-Andersen, O. Clin. Chem. (Washington, DC, U. S.) 1993, 39, 48–52. (45) Kirovskaya, I. A.; Zemtsov, A. E. Russ. J. Phys. Chem. A 2007, 81, 96–101. (46) Ando, T.; Skolnick J. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 18457–18462.

8775


Electrostatic and Dispersion Interactions during Protein Adsorption on

Recommend Documents