Albumin adsorption onto pyrolytic carbon: A molecular mechanics approach

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1 Albumin adsorption onto pyrolytic carbon: A molecular mechanics approach Sara Mantero, 1 Daniela Piuri, 1 Franco M. Montevecchi, 1 Simone Vesentini, 1 Fabio Ganazzoli, 2 Giuseppina Raffaini 2 1 Dipartimento di Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano, Italy 2 Dipartimento di Chimica, Politecnico di Milano, Via Mancinelli 7, Milano, Italy Received 3 August 2000; revised 7 June 2001; accepted 11 June 2001 Abstract: A number of implants of cardiac valve prosthesis, vascular prosthesis, and coronary stents present a pyrolytic carbon interface to blood. Plasma protein adsorption is essential for the hemocompatibility of the implanted devices. This work quantitatively evaluates the molecular interaction force between a biomaterial surface (pyrolytic carbon) and plasma protein (albumin) binding sites through a simplified molecular model of the interface consisting of (i) multioriented graphite microcrystallites; (ii) selected fragments of albumin; and (iii) a water environment. A number of simplifying assumptions were made in the calculation: the albumin molecule was divided into hydrophobic and hydrophilic subunits (helices); an idealized clean, nonoxidized polycrystalline graphite surface was assumed to approximate the surface of pyrolytic carbon. The interaction forces between albumin helices and pyrolytic carbon surfaces are evaluated from potential energy data. These forces are decomposed into a normal and a tangential component. The first one is calculated using a docking procedure (F tot MAX = N). The second one (F ), calculated by mean of geometric models estimating the energy variation associated with the protein sliding on the material surface, varies within the range ± N. The molecular simulations were performed using the commercial software package Hyperchem 5.0 (Hyperchem, Hypercube, Canada) John Wiley & Sons, Inc. J Biomed Mater Res 59: , 2002 Key words: molecular modeling; protein adsorption; albumin; pyrolytic carbon; molecular mechanics INTRODUCTION Correspondence to: S. Mantero; mantero@biomed. polimi.it Contract grant sponsor: Politecnico di Milano Large Scale Computing (LSC) program for the Molecular Level Instrumentation for Biomaterial Interface Design (BID) project John Wiley & Sons, Inc. Pyrolytic carbon is a biomaterial used in cardiac valve prosthesis, vascular prosthesis, and coronary stents. Once immersed in the hematic flow, the biomaterial interacts with plasma proteins, which form a monolayer adsorbed onto the surface through hydrophobic interactions. The nature of these plasma proteins and their adsorption strength affect the implanted devices hemocompatibility. 1,2 Experimental works found that the adsorbed protein monolayer is mainly composed by albumin, which is held so tenaciously that it cannot be easily removed, 3 7 and devised experimental ways to measure these adhesion forces. 8,9 Because of chemical and physical surface characteristics, pyrolytic carbon shows excellent hemocompatibility. In biomedical devices it is found in a graphite microcrystalline state with multioriented crystallites and large boundary area. 10,11 Albumin coats the biomaterial with a stable monolayer, inhibiting the initiation of the coagulation response. Spatial orientation and movements of proteins are also influenced directly by the biomaterial topography and mechanical force computation associated with protein-surface interactions can provide a qualitative method to identify these interactions. It is now widely recognized that molecular modeling can play an important role in biomaterial design and in protein adsorption phenomena onto surfaces analysis. Many aspects of protein adsorption at solidliquid interface have been studied, 12,13 and a unified theory of intermolecular and surface force has been well established. 14 The approach based on classical mechanics assumes that the total interaction potential energy for protein adsorption can be explicated as the sum of the electrostatic interaction, the dipolar attraction, the dispersive attraction and the overlap repulsion (van der Waals contributions). Park calculated and compared the interaction potential energy between all possible

2 330 MANTERO ET AL. orientation of four proteins (lysozyme, trypsin, immunoglobulin Fab, and hemoglobin) and five neutral polymer surfaces. The results show that among all these contributions, the dispersion interaction is the major force holding the protein on the polymer surface. 12,13,15 The aim of the present work is to propose a methodology to quantitatively evaluate the interaction force between a biomaterial surface and an adsorbed protein in water. As an example, albumin adsorption on pyrolytic carbon is analyzed through an elementary molecular model of the biointerface. The adsorption is studied by computer simulation at the atomistic level and through a multiscale mechanical analysis. Three constituents make up the molecular model adopted in the present exploratory study. The first one is an ideal atomic model of a small fragment of pyrolytic carbon consisting of a few parallel planes of carbon atoms. Note that a clean graphite surface has the great advantage that electrostatic interactions due to either free charges or to permanent dipoles are missing. Therefore, the interaction is predominantly due to van der Waal s interactions. This fact, which has an obvious computational appeal in this preliminary, methodological study, is clearly an oversimplification in simulating real pyrolytic carbon. The second constituent, the albumin molecule, 16 is divided into hydrophilic and hydrophobic units (helices) in the computer simulations. We consider that two such helices separately approach the carbon atoms in two different orientations, either from above, with their axis parallel to the planes, or from one side, with their axis perpendicular to the planes. The third and final constituent is made up of water molecules for simplicity. Any other solute is ignored in this preliminary study, in particular, the possible presence of ions. This choice is obviously related to the difficult problem of dealing with long-range electrostatic interactions in computer simulations with periodic boundary conditions. 17 These simulations permit us to obtain quantitatively the interaction forces between representative hydrophobic and hydrophilic helices and the carbon planes in water. The results are used to estimate the interaction force of the whole albumin through a simplified representation of the protein adsorption and a mechanical analysis to elucidate the adsorption phenomenon. It has to be expected that the interaction force of albumin with a real pyrolytic carbon surface would be larger than the one estimated by our procedure, because we neglected electrostatic, and in particular dipolar interactions with the partially oxidized surface. The comparison between the different interaction energies calculated in the present computer simulations showed a more favorable value for adhesion when the hydrophobic helix interacts with the surface. Therefore, the normal component of the interaction force was estimated using two simple biointerface models composed by the hydrophobic helix in water and a differently oriented ideal pyrolytic carbon surface. Such force was evaluated from the interaction energy as a function of the distance between the center of mass of the helix and the planes. From the same simulation results, the tangential component of the interaction force between albumin and the surface of ideal pyrolytic carbon was also derived through two geometric models that account for molecular translation. The results allow quantifying the total interaction force between an albumin molecule and the carbon surface in terms of the interaction of the hydrophobic helix. According to the proposed procedure, normal and tangential forces between the albumin molecule and the surface of ideal pyrolytic carbon were calculated using a multiscale approach, based on atomistic computer simulations and continuum mechanics methods. MATERIALS AND METHODS The biointerface model The biointerface model includes three elements: Model of ideal pyrolytic carbon as a random aggregation of domains measuring Å. 4 The generation of the model proceeds from the atomic level to microcontinuum. The domains are made of two or six small graphite parallel planes measuring about Å. 2 This optimal geometrical conformation was found using a molecular mechanics (MM + forcefield), running the conjugate gradient algorithm up to a gradient better than 10 3 (kcal/mol Å). Figure 1 shows two atomic models of ideal pyrolytic carbon domains. Two parallel carbon planes compose the first domain, and six carbon planes form the second one. The figure shows also the domain s surface facing albumin. Albumin protein model. The molecular structure of crystalline albumin was obtained from the Protein Data Bank ( Data include structural details, the amino acid sequence, the subdivision into helices, and the Cartesian coordinates of the nonhydrogen atoms. 7 Figure 2 shows the albumin molecule as obtained from the Protein Data Bank. Simplified physiologic environment model. A box of water was assumed to represent the plasmatic component in which the helices are diluted. Figure 3 shows the water molecules optimized in a local energy minimum by running molecular mechanics (Amber forcefield) using the conjugate gradient algorithm up to a gradient better than 10 3 (kcal/mol Å). Afterwards, we selected two subunits (helices), namely a hydrophobic (A5C) and a hydrophilic (A1A) helix in zwitterion form shown in Figure 4. Further studies were carried

3 ALBUMIN ADSORPTION AND MOLECULAR MECHANICS 331 Figure 1. Domain of two graphite parallel planes (a) and domain of six graphite parallel planes (b) measuring about Å. 2 They are characterized by real interatomic and interplanar distances. Carbon-carbon bond distance is 1.41 Å if the two carbons belong to the same hexagon, and 2.46 Å if the two carbons belong to different hexagons on the same plane, 3.5 Å being the distance between two different planes of the same domain. out on these helices interacting with the carbon planes in different orientations. Figure 5 shows the four molecular models of the investigated biointerface: (a) hydrophilic helix with its axis parallel to the carbon planes in water; (b) hydrophobic helix with its axis parallel to the carbon planes in water; Figure 2. The albumin protein molecule imported from Protein Data Bank, the international repository for the processing and distribution of 3-D macromolecular structure data. Figure 3. The 1200 water molecules box.

4 332 MANTERO ET AL. was performed with the Amber forcefield using periodic boundary conditions. Energy minimization was carried out with the conjugate gradient algorithm, up to a gradient >10 3 (kcal/mol Å). The normal component of the interaction force Figure 4. The atomic structure of the hydrophobic helix A5C: LEU-LYS-GLU-CYS-CYS-GLU (a) and of the hydrophilic helix A1A: SER-GLU-VAL-ALA-HIS-ARG-PHE-LYSASP (b). (c) hydrophilic helix with its axis perpendicular to the carbon planes in water; and (d) hydrophobic helix with its axis perpendicular to the carbon planes in water. The biointerfaces composed by helices parallel and perpendicular to the carbon planes are designated as BC1 and BC2, respectively (see Fig. 5). The energy optimization in water, which allows calculating the interaction potential energy, In order to quantify the normal component of the interaction force between albumin and the carbon surfaces, we calculated the interaction potential energy as a function of the distance between the center of mass of the helix and the surface in BC1 and BC2 biointerfaces. The helix center of mass was shifted vertically from 0.5 to 0.9 nm, with respect to the plane, with increments <0.02 nm. For each position of the center of mass an equilibrium optimization was performed, and the interaction potential energy value was calculated. The interaction potential energy as a function of the distance between the center of mass of the helix and the carbon plane was subsequently fitted to an analytical equation. Two different equations for BC1 and BC2 biointerfaces were adopted, both forms having a theoretical justification. We interpolated the BC1 potential energy with a function Figure 5. Visualization of the four biointerfaces after a molecular static energy optimization. Hydrophilic helix with its axis parallel to the carbon planes (a); hydrophobic helix with its axis parallel to the carbon planes (b); hydrophilic helix with its axis perpendicular to the carbon planes (c); hydrophobic helix with its axis perpendicular to the carbon planes (d).

5 ALBUMIN ADSORPTION AND MOLECULAR MECHANICS 333 which is a sum of two terms: (1) the overall attraction energy between a nondeformable sphere (the modeled helix, in our case) and a plane and (2) the repulsive component of the Lennard-Jones potential energy. 18 E VdW = H 6 a d + a 2a + d + ln d 2a + d + 4 d 0 12 d where H is Hamaker constant, a is sphere radius, d is sphereplane distance, d 0 is sphere-plane reference distance, and is equilibrium energy. Since electrostatic and/or dipolar interactions with the ideal pyrolytic carbon surface are missing, we interpolated the BC2 potential energy with the Lennard-Jones potential energy: 6 (2) E VdW = 4 d 12 0 d d 0 d where d is sphere-plane distance, d 0 is sphere-plane reference distance, and is equilibrium energy. Afterwards, we calculated the interaction force for BC1 and BC2 biointerfaces, respectively: E VdW = F d VdW d = 6 H 4a d 12 0 d 2 2a + d (1) d 13 (3) 7 E VdW = F d VdW d = 4 12 d 0 12 d + 6 d 6 0 (4) 13 d The tangential component of the interaction force The tangential component of the interaction force between an albumin helix and the ideal pyrolytic carbon surface was obtained using two monodimensional geometric models (M1 and M2) to represent the tangential movement of the helix on the material surface. Models M1 and M2 take in account the characteristics of the different carbon surfaces represented in BC1 and BC2 biointerfaces: The carbon surface of the BC1 biointerface shows almost perfect isotropic characteristics: during every translation on the surface, the helix faces similar material structure s properties, as shown in Figure 6. The carbon surface of the BC2 biointerface shows orthotropic characteristics. In fact, during a translation parallel to the planes the protein faces the same structural properties of the material [Fig. 7(a)]. Conversely, during a translation perpendicular to the planes the protein faces different structural properties of the material, because adjacent planes are shifted by a half hexagon [Fig. 7(b)]. The geometric model M1 defines all possible molecular translations in BC1 biointerfaces and the molecular translations parallel to the planes in BC2 biointerface. All carbon atoms pairs (A i,b i ) can be represented by pseudo-atoms (C i ) halfway located between them, as shown in Figure 8. During translation the helix interacts with all pseudo-atoms of the material surface. Figure 6. Some possible helix translations on the graphite domain surface of BC1 interface (a) and the pseudo-atoms spatial position used to describe the material surface in interface BC1 (b). The geometric model M2 defines the helix translation perpendicular to the planes in BC2 biointerfaces. Each plane can be represented by a carbon pseudo-atom (A i ). The shifted plane distribution (each plane is translated by a half hexagon compared with the adjacent ones) is described by a sequence of alternating pseudo-atoms, as shown in Figure 9. The helix interacts with all carbon pseudo-atoms during its translation. In both models the helix is treated as a particle concentrated in its center of mass. For M1 and M2 models we simulated three mechanical states: Stable equilibrium state, where the sum of all normal and tangential components of the interaction force between the particle and the pseudo-atoms is zero. Instable equilibrium state, where again the sum of all normal and tangential components of the interaction force between the particle and the pseudo-atoms is zero, but any perturbation moves the molecular system toward the stable equilibrium state. Nonequilibrium state, where only the sum of all normal component of interaction force between the particle and the pseudo-atoms is zero. The particle needs application of an external tangential force to be kept in firm position onto the material surface. All mechanical states were described by simple trigonometric equations as a function of the distance between the particle and the surface plane. Figure 7. Some possible helix translations on the graphite domain surface of BC2 interface (a) and the carbon atoms spatial position used to describe the material surface in interface BC2 (b).

6 334 MANTERO ET AL. Figure 8. The geometric model and the trigonometric equations used to describe the interaction force in nonequilibrium state for model M1. In order to calculate the tangential force in the nonequilibrium state for both M1 and M2 we used, for each point to point interaction, the analytic Equations (3) and (4), respectively. Finally, we calibrated the calculation of the tangential component with two coefficient K 1 and K 2 : K 1 = d equilibrium d simulation where d equilibrium is the distance between the particle and the plane at equilibrium, calculated using M1 and M2 models, whereas d simulation is the distance between the particle and the plane at equilibrium calculated by molecular simulation; and K 2 = F equilibrium 60% F simulation 60% where F equilibrium60% is the force calculated for a 60% normal displacement from equilibrium state calculated using M1 and M2 models and F simulation60% is the force calculated for a 60% normal movement from equilibrium state calculated by Equation (3) for BC1 biointerface and Equation (4) for BC2 biointerface. The albumin interaction force In order to calculate the total interaction force between the ideal pyrolytic carbon surface and the whole albumin, we determined a weight for its helices as a function of their amino acid polarity and identified the helices with the same polarity as those used in simulating the BC1 and BC2 biointerfaces. Because simulation results confirm that, as expected, the albumin adsorption on the carbon planes is governed by the hydrophobic interactions, we report in Table I the hydrophobic adhesion domains for albumin and the amino acid sequence of the hydrophobic helices that compose the four interacting domains for one of the two identical asymmetrical submolecules (1E, 2E, 3E, and 4E). Figure 10 shows a different perspective of the adsorption of albumin onto ideal pyrolytic carbon, of the orientation of the graphitic domains and of the related geometrical models M1 and M2. The normal force for each adhesion site (F i ) calculated for BC1 and BC2 was averaged to take into account the random orientation of the ideal pyrolytic carbon domains F i = F BC1 + F BC2 2 (5) Figure 9. The geometric model and the trigonometric equations used to describe the interaction force in nonequilibrium state for model M2.

7 ALBUMIN ADSORPTION AND MOLECULAR MECHANICS 335 Domain Helixes Helixes Amino Acid Number TABLE I Hydrophobic Domains (1E, 2E, 3E, and 4E) Helixes Amino Acid Sequence 1E 1E.1 11 GLU-PRO-GLU-ARG-ASN-GLU-CYS-PHE-LEU-GLN-HIS 2E 2E.1 19 LEU-LEU-GLU-CYS-ALA-ASP-ASP-ARG-ALA-ASP-LEU-ALA-LYS-TYR-ILE-CYS-GLI-ASN- GLN 2E.2 6 LEU-LYS-GLU-CYS-CYS-GLU 2E.3 10 LEU-LEU-GLU-LYS-SER-HIS-CYS-ILE-ALA-GLU 3E 3E.1 15 PRO-GLN-ASN-LEU-ILE-LYS-GLN-ASN-CYS-GLU-LEU-PHE-GLU-GLN-LEU 4E 4E.1 24 LYS-ARG-MET-PRO-CYS-ALA-GLU-ASP-TYR-LEU-SER-VAL-VAL-LEU-ASN-GLN-LEU- CYS-VAL-LEU-HIS-GLU-LYS-THR Boldface = reference helix. Hence, the total normal component of force in the configuration of best adhesion of albumin on the ideal pyrolytic carbon surface (assuming all domains to interact with the surface) is F tot = k F i (6) where k is the number of adhesion sites. In order to calculate the tangential component of the interaction force (F tot ) between albumin and ideal pyrolytic carbon, we assumed that one half of the helices interacts in the same way as in BC1 biointerface and the other half in the same way as in BC2 biointerface. In the first case the force is always calculated using model M1, and in the second case the force is the weighted average of that calculated for M1 and M2. RESULTS AND DISCUSSION The energy optimization performed on hydrophilic and hydrophobic helices interacting with ideal pyrolytic carbon planes both in a parallel and in a perpendicular orientation shows that the energy of the hydrophobic helix is much more affected by the interaction than the hydrophilic helix. For this reason we were able to simplify the further analysis by taking into account only one reference hydrophobic helix A5C (LEU-LYS-GLU-CYS-CYS-GLU) interacting with the carbon planes to describe the BC1 and the BC2 biointerface. Figure 11 shows the calculated potential energy for the BC1 and BC2 biointerfaces as a function of the distance between the center of mass of the hydrophobic helix and the planes. The BC1 potential energy was fitted to Equation (1), with the values of the parameters as follows: H = J; a = 0.15 nm; d 0 = 0.41 nm; and = J, whereas the BC2 potential energy was fitted to Equation (2), with the final parameters: d 0 = 0.51 nm Figure 10. A perspective of albumin molecule s adhesion on a volumetric element of pyrolitic carbon (a) and the geometrical model related to the pyrolitic carbon domain orientations (b). Figure 11. Equilibrium potential energy as a function of the distance between helix center of mass and planes for BC1 and BC2 biointerfaces.

8 336 MANTERO ET AL. Figure 12. Normal component of interaction forces for BC1 and BC2 as a function of the distance of the helix center of mass from the reference plane. and = J. The normal components of the interaction force for BC1 and BC2 biointerfaces are described by Equations (3) and (4), respectively, with these parameters values. Figure 12 shows the normal component of the interaction forces as a function of the distance between the helix center of mass and the planes for BC1 and BC2 biointerfaces. The tangential component of interaction force was calculated considering the helix as a particle as described in Materials and Methods. For the tangential displacement of the helices with respect to the carbon planes, we calculated the point to point interaction force (between the particle and a single pseudo-atom of the material) using Equation (3) with the parameters calculated for model M1 and using Equation (4) with the parameters calculated for model M2. Tables II and III report the normal and tangential components of the interaction force calculated in normal equilibrium state between the particle and 16 materials pseudo-atoms for model M1 and between the particle and 28 materials pseudo-atoms for model M2. The total tangential component of the interaction force was calculated by the vector sum among the point to point force described in Table II and calibrated by K 2 coefficient (5.39) for model M1 and by the vector sum among the point to point force described in Table III calibrated by K 2 coefficient (10.1) for model M2 (the final values are shown in the last column of Table II and Table III). Figures 13 and 14 show the total tangential component of the interaction force for models M1 and M2 as a function of the distance between the particle and the plane passing through the pseudo-atoms of the mate- TABLE II Normal and Tangential Component of Point-to-Point Interaction Force Calculated by Eq. (3) for Model M1 a d [nm] i d i [nm] i F i [N] F i [N] F [N] a d, vertical equilibrium distance between the particle and the plane passing through the material s pseudo-atoms calibrated by coefficient K 1 = 0.92; d i, distance between the pseudo-atom i and the particle i, i are described in Figure 8.

9 ALBUMIN ADSORPTION AND MOLECULAR MECHANICS 337 TABLE III Normal and Tangential Component of Point-to-Point Interaction Force Calculated by Eq. (4) for Model M2 a d [nm] i j d i,j [nm] i,j F i,j [N] F i,j [N] F [N] a d, vertical equilibrium distance between the particle and the plane passing through the material s pseudo-atoms calibrated by coefficient K 1 = 1.02; d i,j, distance between the pseudo-atom i,j and the particle i,j, i,j are described in Figure 9. rial. The tangential stress on an albumin molecule interacting with the ideal pyrolytic carbon surface was finally obtained by taking the ratio between the total tangential force and the adhesion molecular area: = F A mol where A mol 50 nm 2 is the assumed interacting molecule surface roughly inferred from the overall molecular size (see Fig. 2). Figure 15 shows the tangential surface stress of model M1 as a function of the particle position. We remark that the tangential stress values in stable and instable equilibrium state is zero for all particlereference plane distance and the tangential stress values of nonequilibrium state decrease with increasing distance between the particle and the reference plane. The normal component of the interaction force in best adhesion configuration of an albumin molecule on the ideal pyrolytic carbon surface were calculated using Equations (5) and (6), with the forces calculated for biointerfaces BC1, BC2 and models M1, M2. Figures 16 and 17 show the normal the tangential component of the total interaction force as a function of the distance between the center of mass of the hydrophobic sites of albumin and the ideal pyrolytic carbon surface. The periodic pattern of tangential component of the total interaction force corresponds to the alternation of the potential energy surface of albumin tangential equilibrium state and nontangential equilibrium state. Figure 13. Tangential component of interaction force for model M1 as a function of the distance of the particle from the reference plane. Figure 14. Tangential component of interaction force for model M2 as a function of the distance of the particle from the reference plane.

10 338 MANTERO ET AL. Figure 15. Shear stress surface for model M1 as a function of the distance between the particle and the reference plane. Tangential component of total albumin interac- Figure 17. tion force. CONCLUSIONS Figure 16. force. Normal component of total albumin interaction The adsorption of albumin in water onto an ideal pyrolytic carbon surface was investigated through a multiscale approach based on atomistic computer simulations and multiscale mechanics procedures. In this preliminary study, for practical reasons, basically related to computer and code limitations, we adopted a simplified model of the biointerface. First, in the simulations we only considered a few subunits of albumin, consisting of a hydrophilic and of a hydrophobic helix. Second, the biomaterial surface was taken as formed by a random orientation of nonoxidized and smooth graphite crystallites, simulating in turn an idealized, defect-free pyrolytic carbon surface. The individual graphite crystallites were simply described by a small number of carbon planes (2 to 6). This number was shown to be adequate to describe a graphite surface, 19 although it should be pointed out that the surface (in-plane) polarizability of graphite is not accounted for in current force fields. On the other hand, the use of such a model for the biomaterial is necessarily a simplified picture of pyrolytic carbon, which is made of a large distribution of graphite microdomains in random orientation with a hierarchy of grain structures. Moreover, surface modifications due to oxidation may be relevant in real samples, but are not easily included in atomistic simulations. Third, the physiological environment was considered as made up of water molecules only, neglecting the presence of ions. This assumption is obviously related to the difficult problem of dealing with long-range electrostatic (Coulomb) interactions in computer simulations when periodic boundary conditions are used. In this case, more advanced (and time-consuming) methods must be adopted, such as for instance the Ewald sums technique. 17 Fourth, we do not include any electrostatic interactions between the helices and the carbon planes. In this preliminary work a multiscale approach (hydrophobic site hydrophobic helix albumin) was developed into a hierarchical set of models to estimate the interaction force at the interface between albumin and pyrolytic carbon. Standard simulation tools (molecular mechanics, in particular) provide the basis for a mechanical analysis. The force values we obtain have the correct order of magnitude, whereas the fitted parameters in Equations (1) and (2) roughly show the expected values. A number of simplifying assumptions have been introduced to ease the calculation, many of them ask for future refinements. We know that unfolding appears once the albumin molecule approaches the interface surface in order to expose the hydrophobic sites to the interface; a detailed model for unfolding will affect the medium/long range force evaluation, in particular in the presence of ions that modify the ionic strength of the solution, as previously pointed out. On the other hand, the real carbon surface offers a far less regular shape than we assumed, which clearly affects the short-range force evaluation. Despite these shortcomings, the approach proposed here offers a frame capable of incorporating future more realistic assumptions. This capability depends mostly on specific experimental data and on computer power large enough to model larger protein portions.

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