Proteins and Peptides at Gold Surfaces: Insights from Atomistic

Chapter 10

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Proteins and Peptides at Gold Surfaces: Insights from Atomistic Simulations L. Bellucci, G. Brancolini, A. Calzolari, O. Carrillo Parramon, S. Corni,* and R. Di Felice* Centro S3 Istituto Nanoscienze - CNR, via Campi 213/A, 41125 Modena, Italy *E-mails: [email protected]; [email protected]

Computer simulations at the atomistic level, jointly with experiments, can provide the microscopic picture behind protein-surface interactions. The complexity of the inherent phenomena, that span several time and length scales, call for a hierarchical strategy, from electronic structure approaches (limited in the accessible sizes and times) to classical methods, able to treat larger systems and longer time scales, but involving more assumptions and providing less details. Here we introduce the atomistic simulation methods that we have developed and applied to treat the interaction of peptides and proteins with the Au(111) surface in water. We succinctly describe principles, assumptions and limitations of ab initio, classical atomistic molecular dynamics and Brownian dynamics docking methods as applied to the protein-surface problem, with specific focus on the work of our group. The possible extension to coarse-grained method is also discussed.

Introduction There is a wide consensus in considering the interaction between proteins and inorganic surfaces as the key to understand the biological response to inorganic materials. In fact, any inorganic materials that come into contact with a biosystem (being an extended surface or a nanoparticle) is readily covered with the proteins expressed by the biosystem. The subsequent biological fate of the inorganic materials (e.g., being recognized as an extraneous body or activate specific © 2012 American Chemical Society In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


biological pathways) is determined by which proteins adsorb on the surface, their orientation, their possible conformational changes and the associated disclosure of cryptic epitopes (1–4). This has been verified in biological and biomedical applications such as cell-adhesion and proliferation on artificial scaffolds, study of the biocompatibility of surgical implants, prevention of bacteria adhesion to surface. Moreover, understanding adsorption processes of bio-molecules to the inorganic surfaces constitute the first step to rationalize the behavior of the new generation of nanoscale-based systems, which are of great importance in many emerging disciplines spanning from nanotechnology to nanomedicine (5–9). The importance of unraveling the microscopic determinants of protein-surface interaction is thus clear, but this task is still a challenge. From an experimental point of view, in fact, interrogating the interface requires to get rid of the preponderant signal from the bulk. Moreover, proteins are intrinsically complicate systems, and measurements are often challenging already in bulk solution, even more so at interfaces. While various experimental methods have been used to explore protein-surface interfaces (10–14) these are by no means routine experiments (15, 16). In this context, computational simulations can provide an important contribution to the understanding of protein surface interaction. In particular, simulations that take into account the chemical nature of the system, possibly at the atomistic level of detail, can provide the most intimate level of knowledge. Unfortunately, simulations of protein-surface interactions are also very challenging. Firstly, protein-surface systems are large from an atomistic point of view, as they easily comprise (including solvent water molecules) tens or hundreds of thousands of atoms. In addition, biomolecular adsorption on solid surfaces is a complex process that involves many dynamical steps, from the initial recognition of the molecule by the surface to the equilibrium conformational rearrangement of the adsorbed molecule. Therefore, to analyze the adsorption phenomenon, it is necessary to investigate the dynamical behavior of the system, that, in many cases is hard to be directly sorted out (16, 17). The rationalization of such aspects represents one of the major challenges for both experimental and theoretical investigation methodologies . Finally, computational approaches that have been developed during the years to treat proteins and to treat inorganic surfaces separately are not always straightforward to integrate, since the underlying approximations may be different; often these approaches are implemented in different codes. In the last few years, together with our coworkers, we have developed and applied various levels of computational description for investigating protein-surface interactions. In particular, we have identified the surface(s) of gold as an important system, and our activity has been mainly focused on this material. In fact, gold is important in practical applications (it enables optical and electrochemical detection (18), has been used in nanobioelectronics (19, 20), and is relevant for plasmonics (21). Gold easily exposes a clean and relatively defectiveless surface in the experiments, which limits the uncertainties in the comparison with theoretical, defect-free, models. Moreover, adsorption of simple molecules on Au in controlled conditions (e.g. ultra-high vacuum) has been studied extensively (22–24). While these studies do not have an immediate relevance for protein-surface interaction (where the role of the aqueous solution 230 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


cannot be neglected), they are important as an intermediate step to compare with calculations. Our development has followed a sequential multiscale strategy (25, 26), improved by including information from experiments whenever possible. Multiscale refers to the use of different levels of computational description, apt to the investigation of the system properties at different length and time scales. Sequential indicates that the different levels of computational description are not applied to different portions of the system within a given calculation (as in a parallel or concurrent multiscale approach), but that they are applied one after the other to the entire system (e.g., the output of one calculation is the starting point of another at a different level). For example, ab initio simulations provide a picture of the system detailed up to the electronic structure, but they are currently limited to few hundreds or mostly thousand of atoms, and to phenomena taking place in the hundreds of ps domain (27). Classical atomistic molecular dynamics (MD), in the bio-oriented flavor encoded in force fields such as AMBER (28), CHARMM (29) and OPLS (30) and software packages such as GROMACS (31) and NAMD (32), are neglecting electronic structure details as well as a faithful description of the fastest vibrational motions in the systems, but can explore hundreds of thousands of atoms over a time span up to the μs (ms with specialized supercomputers (33)). Clearly, each technique can address only a subset of the open issues on protein-surface interactions; therefore, building a comprehensive microscopic picture of proteinsurface interaction requires more than a single technique. Our group has tackled the problem of investigating protein-gold interactions using (i) first-principle simulations at the density functional theory (DFT) level (34–37), (ii) classical atomistic MD with a force field derived by DFT calculations and experimental data (GolP) (38), (iii) Brownian dynamics (BD) simulations of the protein-surface docking, guided by an implicit water force field (ProMetCS) developed from GolP (39). In this chapter we introduce all these techniques, focusing on the specific flavors used by us. Moreover, we discuss some selected examples of the applications of these techniques to show their potentialities and the current limitations. Finally, we also dedicate the last section to discuss coarsegrained models for proteins (40). In such models the atomistic structural and/or dynamical details are partially lost (several atoms are grouped in single interaction sites, some motions are projected out) in favor of faster simulations (routinely μs) of larger systems (e.g., entire virus capsides). In perspective, the extension of these simplified methods to protein-gold systems may help unraveling large protein rearrangements (or even unfolding) of proteins interacting with surfaces.

Ab Initio Studies The power of ab initio computational methods lies in their high theoretical level and their practical accuracy in reproducing and interpreting experimental data, without the inclusion of ad-hoc empirical parameters. Ab initio methods allow access to the electronic structure of the system, which is ultimately responsible for the interaction mechanisms of matter in any phase. (e.g. 231 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


polarization effects, bond formation/breaking, screening, etc). All the ab initio results we present in the following are based on density functional theory (DFT), which provides the ground-state energy of an interacting system of electrons in an external potential in terms of a functional of the ground-state electronic density. This kind of calculations have the significant advantage of being able to predict in an unbiased manner the electronic structure, the equilibrium geometry and the time evolution of complex systems that are a priori unknown, but the disadvantage of requiring large computational efforts. The current trend away from wavefunction-based methods toward the use of DFT is justified by the profitable compromise for the latter between the resulting accuracy and the scale of the systems that can be tackled. It is to be remarked that the most commonly used DFT approaches (i.e., those based on Generalized Gradient Approximation, GGA, exchange-correlation functionals such as PBE and PW91 mentioned below) do not catch the effects of dispersion interactions, which is dominant for most of the amino acids on gold (38). Recently, various approaches have been proposed to overcome this limitation (we refer to a recent review addressing specifically dispersion for molecules on surfaces (41)). In the context of protein/inorganic interfaces, the huge size of the system prevents the application of ab initio approaches to the whole target system. Yet, they are doable and they have an important role to understand protein/surface interactions in model systems: (i) Structural and electronic DFT (42) ground state characterizations of entire or partial amino acids adsorbed at inorganic substrates, which unravel a degree of adsorbate/substrate coupling beyond the level of pure physisorption and are a basis for the development of classical force fields (34–37, 43); (ii) Car-Parrinello (CP) molecular dynamics (MD) simulations (44), which reveal electronic coupling also for a peptide on Au(111) in water (37). CP is one of the most popular examples of ab initio molecular dynamics (AIMD). CP implements - in a unified Lagrangian framework - the classical Newton’s dynamics of the nuclei under the effect of the forces due to the corresponding electronic structure, evaluated ab initio at the DFT level. Thus, CP conjugates the statistical time evolution, typical of molecular dynamics, with the description of the electronic structure of the interface, typical of the ab initio techniques. Cysteine/Au(111) by DFT Cysteine is an example of molecules with a reactive group that functions as anchor for attaching to metal surfaces. It has, in fact, a thiol functionality and behaves similarly to methanethiols on gold (34, 35, 45). The adsorption of cysteine on Au(111) involves S(thiolate)-Au bonds, with the S headgroups sitting preferentially at bridge sites. DFT-PW91 calculations were carried out for both atomic optimization and single-point electronic structure calculations (hydration effects were not investigated): details of the methodology are reported in the original works (34, 35). The computed dissociative adsorption energy gain of ~20 kcal/mol indicates the formation of a covalent bond, which is reinforced by the analysis of the electronic structure. The investigation of the electronic density of states (DOS) for the most stable adsorption configuration shows peaks due to the hybridization between the S p orbitals and the Au d band: in particular, a bonding 232 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


peak is located at 5 eV below the Fermi level and an antibonding peak is located at 1 eV below the Fermi level. Figure 1 illustrates the DOS and representative bonding and antibonding orbitals formed by the cysteine highest occupied molecular orbital (HOMO) with the Au d orbitals. It was also shown that the amino functional group of cysteine can participate in the molecule/surface bonding, by increasing the interaction energy and forming other hybrid orbitals (34, 35). The adsorption mechanism of cysteine on Au(111) complies with the Newns-Anderson model of atomic and molecular chemisorption (46): this essentially states that interaction of a localized orbital on the adsorbate with the narrow d band of the metal produces hybrid orbitals of both bonding and antibonding type, below and above the edges of the metal d band.

Figure 1. Left bottom: Density of states (DOS) of the cysteine/Au(111) system (solid line) and of the clean unreconstructed Au(111) surface (dotted line). The solid (dotted) vertical lines identify the energy positions of the selected hybrid bonding (antibonding) S-Au orbitals on the right side. The Fermi level has been set as the origin of the energy scale. The insets show charge density plots of the S-localized orbitals of the isolated cysteine radical and the corresponding energy levels are indicated (on the same energy scale used for the DOS). Left top: s and p S-projected DOS of cysteine adsorbed in the thiolate geometry on Au(111) with the S at the bridge lattice site (gray areas) and total DOS of the interface. Right: bonding (bottom) and antibonding (top) representative orbitals formed by the cysteine HOMO with the Au d bands. Adapted from ref. (35) with permission. Copyright 2003 American Chemical Society. Histidine/Au(111) and GolP by DFT Within the working hypothesis that the interaction of proteins with inorganic surfaces occurs mainly through the amino acid side chains, the investigation of the coupling of the histidine side chain with a gold surface may yield significant insights on the interaction mechanisms in more complex situations. This system is inherently different from the case of cysteine: in fact, imidazole does not have an obvious functional group that protrudes from the molecule but the reactive N 233 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


atoms are part of the hetero-ring (we can broadly speak of an aromatic as opposed to alkylic adsorbate). DFT-PBE calculations (excluding hydration effects) reveal that, irrespectively of the initial condition for atomic relaxation (molecular orientation and registry with the substrate lattice), the optimal adsorption geometry is with the imidazole plane almost perpendicular to the surface plane and the unprotonated N1 atom on top of a Au atom of the (111) lattice (Figure 2) (36).

Figure 2. (a) Top view of the Au surface top (111) plane with highlights of the three typical low-energy adsorption sites in the hexagonal lattice. (b) Structure of imidazole with atomic labeling. (c) Side view of the most energetically favorable optimized geometry (d) Top view of a starting configuration in which the N1 atom is located above a top Au site (N1 is one-fold coordinated with Au) and the imidazole plane lays parallel to the (111) substrate planes. (e-f) Top views of other starting configurations that were taken into account, with also N2 towards the surface. Adapted from ref. (36) with permission. Copyright 2008 Americal Chemical Society.

The adsorption energy gain of ~10 kcal/mol is half of that for cysteine on Au(111). This value is definitely larger than the typical values for physisorption of the order of a few kcal/mol (47), yet smaller than those indicative of strong chemical bonds (such as those formed by thiols with gold). Despite the fact that imidazole does not have an obvious functional group for anchoring to surfaces and correspondingly adsorbs less strongly than thiols on Au(111), actually the N1 lone pair behaves as such. Consequently, the Newns-Anderson adsorption picture is found also in this case: examples of bonding and antibonding orbitals are illustrated in Figure 3. A thorough inspection of the hybrid orbitals, presented in the original work (36), shows the formations of both π and σ N1-Au “bonds”. 234 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Figure 3. Isosurfaces plots of relevant hybrid orbitals formed at the imidazole/Au(111) interface. (a) Bonding orbital with π-like shape with energy 5.18 eV below the Fermi level. (b) Antibonding orbital with σ-like shape with energy 0.75 eV above the Fermi level. Adapted from ref. (36) with permission. Copyright 2008 American Chemical Society.

Similar DFT calculations were performed for several amino acid side chains on Au(111) in vacuo and the results were used to parameterize novel interaction terms for the classical force fields to simulate protein interaction with the Au(111) surface. The OPLS force field was originally chosen (38), but the procedure is also compatible with other force fields such as AMBER and GROMACS. The OPLS GolP force field was employed to simulate β-sheet folds on Au(111) (48). Polyserine/Au(111) by Car-Parrinello MD To our knowledge, only one ab initio MD simulation of a whole peptide on an inorganic surface (including liquid water, Figure 4) has been reported so far (37), which was feasible thanks to a huge international supercomputing effort, namely the DEISA consortium (www.deisa.eu). The results of the simulation indicate that weak chemical interactions of dative-bond character confer to a prototype secondary structure (an antiparallel β-sheet made of hydroxyl amino acids) and its hydration layer the capability of discriminating among gold surface sites in a cooperative manner. The first-principle character of the simulation allows direct access to the electronic structure of the system (composed of approx. 600 atoms) at every instant along the trajectory of 20 ps. Although no covalent bond between the β-sheet (or water) and the surface is detected, a weak but not negligible electronic interaction exists, beyond the simple physisorption picture. This weak-interaction regime can be described as an incipient oxygen-to-gold dative bond, and it is not related to nonbonding interactions (e.g., van der Waals forces). Figure 4(b-d) shows the distribution of Löwdin net atomic charges during the simulation for the gold atoms, as well as for the oxygen atoms of water (Owat) and of Ser side chains (Oser). The Löwdin population analysis reveals a small, but evident, electron donation from the Ser hydroxyl groups and water molecules to the gold 235 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


surface. Gold atoms of the inner zone (Figure 4b) maintain an average neutral behavior (i.e., q ~ 0e-), whereas those of the two external layers present a net electron accumulation. The opposite is true for water molecules close to the surface (Figure 4c) and for the Oser belonging to interface 1 (Figure 4d), which roughly donate an average charge amount of ~0.05e- per oxygen atom. Water molecules that are distant >3-4 Å from the surface and the Oser of the interface 2 are instead hardly affected by the presence of the metal. Concisely, a weak surface/side-chain interaction is active, but no strong chemisorption exists for the polyserine on Au(111). This notable interaction is due to the collective action of many adsorption sites: although each of them contributes quite weakly, the concerted process makes adhesion effective.

Figure 4. (a) Side view of the system in the simulated unit cell (dashed line), with definition of interfaces 1 and 2. (b-d) Distribution of the atomic Löwdin charges over the entire simulation span for: the 4 Au layers in panel (b); interstitial (green) and liquid (blue) water oxygens in panel (c); the oxygens of Ser side chains (Oser) at interface 1 (red dots) and 2 (black triangles) and the backbone oxygens (OBB, gray). Adapted from ref. (37) with permission. Copyright 2010 American Chemical Society. By an analysis of correlation maps (37), it is also shown that the hydration layer plays an active role in surface-site discrimination by the peptide, via its own adsorption site preferences. This evidence supports the concept of the hydrated protein as a single entity, where both the protein and the hydration layer contribute to the recognition process, competing with the rest of the solvent for the gold surface. Similar recognition water capability has been further detected in H2O/Au interface at room temperature (49). Ab initio molecular dynamics simulations are powerful tools to investigate the structure and interaction mechanisms of small peptides on metal surfaces. However, they are not doable in any desirable case. The feasibility conditions are: (i) the preparation of a model system of contained size, which plays a role in larger realistic systems (such as serine side chains in gold-binding peptides); (ii) the availability of huge supercomputing resources. The backdrop is the short simulation length, in the range of tens of picoseconds, during which complex plastic motions are not accessible. The advantage is that, for all the motions that 236 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.

are indeed accessible, one gets automatically the electronic structure of the system, which is the basic ingredient that allows for a deep insight into the mechanisms for coupling, recognition and selectivity.


Classical Atomistic MD On a general ground, MD simulations (50–52) propagate an initial molecular conformation forward in time, providing a detailed information on the atomic motions of the system. Therefore, MD is the “natural” tool of choice to study the dynamical evolution of the adsorption processes. Hence, it is not surprising that most of the atomistic simulations of protein-surface interactions are currently performed at this level. The heart of MD simulation method is the availability of a suitable potentialenergy function to solve the equation of motion for the nuclei. In the already introduced ab-initio CP method (44, 51), the energy function is obtained resolving the electronic structure of the molecular system “on the fly” during the simulation. As noted above, the CP method requires considerable computational resources (because of the cost of propagating DFT quantities at each step) that limit the possible system size and the time length of the simulation. The description of the time evolution of the nuclei of the system (i.e. nuclear motion) is penalized by the necessity to integrate the equation of motion of the fast fluctuations of the electronic degrees of freedom (adiabatic condition). The latter requires the use of time steps smaller than those needed to integrate the motion of the nuclei alone, thus limiting the exploration of the phase space at the atomic scale. The drawback of this approach is, therefore, the huge computational load and, consequently, the short accessible simulation times that do not currently allow the description of processes of a large-atomic-scale object that occur on long time scales as the adsorption processes or conformational rearrangements of biomolecules at metal surface in solution. On the contrary, classical MD relies on the possibility to parameterize predefined potential energy-functions for either the intramolecular and intermolecular interactions of the system by using empirical/experimental data and/or independent electronic structure calculations. In this way, the explicit description of the electronic structure is abandoned, the system is modeled fully at the classical level and the time evolution of the system is obtained by numerically integrating the Newton’s equations of motion at the atomic time scale. The classical MD simulation method introduces further approximations with respect to ab initio MD. However, since it requires less computational resources and operates at the atomic time scale, it can be efficiently used to investigate dynamical atomistic conformational processes that occur in the time regime of hundred of nanoseconds/ a few microseconds (53) or even, with special programs and dedicated machines, in the regime of milliseconds (33). Classical MD simulations have been widely adopted in the study of biological systems (54, 55), however, its applicability is subordinated to the availability of a suitable potential-energy function and the related parameters. The potential-energy functions and the parameter set define the so called classical 237 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


force fields (FFs): AMBER (28), CHARMM (29) and OPLS (30) are, for example, biomolecular FFs routinely used to perform MD simulations by using specific bio-oriented MD codes such as GROMACS (31) and NAMD (32). The functional form of these biomolecular FFs is essentially the same and consist of several discrete terms that describe the different interactions (the so called “bonding” and “non-bonding” interactions) among the atoms of the system: harmonic terms are used to describe atom bond lengths and angles, Fourier series terms are used to describe torsions, whereas Lennard-Jones and Coulomb functions are used to describe intermolecular interactions (52). The set of parameters are typically determined by quantum chemical calculations possibly corrected to reproduce desired experimental data. The mentioned biomolecular FFs share very similar potential-energy functions, however, the protocols used in the FF parameterization differ from each other and, therefore, the parameters are not interchangeable among different FFs. Although the FFs to describe protein in water have been developed for a long time and are still being improved, FFs purposely designed to treat biomoleculessurfaces interaction are still elusive (56, 57). For protein-gold interfaces a new FF was produced and described by our group (38). It is an extension of the OPLS/AA FF where specific parameters to describe the interaction of biomolecules with the Au(111) surface are added. This classical gold-protein FF, termed GolP, is based on an atomistic (although rigid) description of the gold substrate. It is defined with the same potential-energy functions of the OPLS FF, therefore it is compatible with bio-oriented MD codes mentioned above. Last but not least, it includes gold polarization effects (image charges induced by the adsorbed charge density (58)). The FF parameters are based on a careful mixing of quantum mechanical calculations (DFT and MP2 level of theory) and experimental data of adsorption energies of various organic molecules from the gas phase to Au(111) (see the original paper for details (38)). GolP FF has been applied to determine the adsorption free energy of amino acids on the gold surface (59, 60). Using MD simulations and thermodynamic integration techniques (61, 62) Hoefling et al (63) computed the potential of mean force for all proteogenic amino acids as a function of the distance between the center of mass of each amino acid and the gold layer. From the adsorption free energy profile the authors were able to describe the adsorption of the amino acids with the gold surface has a triphasic behavior. In an initial diffusive phase, the potential of the gold is hardly influencing the amino acid. At a distance of 5 Å from the bound state, the slope of the energy potential increases significantly, and the amino acid associates with the gold. In the final binding phase, the potential becomes even steeper. They observed that the adsorption free energies of the amino acids are dependent on their chemical character, and they determined an order of affinity based on the nature of the amino acids. In particular, aromatic amino acids have the highest affinity followed, in the order, by sulfur-containing, positive, polar and, sharing the lowest affinity aliphatic and negative amino acids. An important finding of this computational study was a correlation of the β-sheet propensity of amino acids with the adsorption to gold, highlighting the tendency of the gold surface to induce amino acid internal conformations suitable for β-sheet formation. 238 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


In a more recent work, Hoefling et al (48) studied the interaction between the gold surface and polypeptides with β-sheet folding by using standard MD simulation and GolP FF. The authors observed that the substrate adsorption occurred quickly, but the adsorption of the substrate to the gold surface is not specific. Furthermore, extending the length of the simulation to 100 ns, no desorption or major rearrangements of the protein have been observed, once the substrate adsorption occurred. The mentioned studies answered some important basic questions about the protein/gold interaction; however, increasing the biomolecule complexity, other issues related to the sampling of large-scale conformational changes appear. To exemplify these kinds of phenomena a preliminary MD simulation was performed on a complex system composed by the Amyloid β (Aβ) peptide (63) (PDB code 1IYT), gold surface and water (see Figure 5). Aβ is the building block of the amyloid plaques characteristic of Alzheimer’s disease. The system was modeled with GolP FF in explicit SPC water using periodic boundary condition (50, 64). The simulation was performed at constant temperature (300 K) with the GROMACS software package. In Figure 5 three sets of initial conformations of the hybrid system are reported. Gold surface spans the XY plane of a rectangular box of size 90×90×75 Å. The first system (S1) is depicted in the top left of Figure 5. It was obtained by positioning the center of mass of the Aβ peptide at center of the rectangular box, and aligning the molecule so that the major principal axes of inertia corresponds to the X axis. The second and the third systems (S2 and S3) were obtained by consecutive rotation of the S1 structure around the X axis, and are depicted respectively in the top center, and in the top right of Figure 5. In all the systems the protein heavy atoms were initially held at a distance greater than 16 Å from gold surface, ensuring that the protein was not interacting with the surface at the beginning of the simulations. Following the scheme shown in Figure 5, the system S1 and S2 system were used as starting point of a MD simulation each, whereas the S3 system was used as the starting point for two independent simulations. In the bottom of Figure 5 are shown the final conformations (i.e. E1, E2, E3_A and E3_B) for all the systems after 16 ns of classical MD simulation. From the analysis of the MD trajectories, we observed that Aβ quickly approached the gold surface in the first few nanoseconds of the MD simulations. In all cases the adsorbed peptides remained trapped to the gold surface and during the rest of the simulation, large conformational rearrangements of the peptide were not observed. Comparing the final structures reported in the bottom of Figure 5, it was not possible to identify a preferential “binding mode” or “adsorption mode” of the (Aβ) peptide to the gold surface. In particular, the large difference between the conformation E3_A and E3_B shows that the adsorption conformation is not merely determined by the starting conformation. The description of the adsorption process, however, is restricted to the observation of an unique adsorption event for each simulation. Moreover, the adsorption process is unspecific and it depends on how the substrate (randomly) approaches the surface. The observation of these few events are not enough to describe the complex dynamical behavior of the peptide on gold, and enhanced sampling techniques are necessary to explore the possible adsorption modes and conformations of the biomolecules at the gold/water interface. 239 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Figure 5. The Aβ peptide is shown in cartoon representation. C-terminus and N-terminus are depicted in purple and orange respectively. The other residues are encoded by color: red for negative residues, blue for the positive residues, green for the polar residues, and white for the hydrophobic residues. Gold slab is in yellow. Water molecules, which fill the whole box of simulation, are not shown. In the top, the initial structures used as starting point for the MD simulations are shown (i.e S1, S2 and S3). In the bottom, we depict the final structures from the MD simulations (i.e. E1, E2, E3_A and E3B).

Among the various methods used to enhance the sampling of MD simulations (52), we mention the temperature-replica exchange MD (65) (T-REMD), the temperature intervals with global exchange of replicas (TIGER & TIGER2) (66) and non-Markovian metadynamics (67), which have been applied to protein-surface systems. Ensuring an adequate sampling of the conformation of the adsorbed substrate, these techniques begin to be widely used in the study of the heterogeneous systems, where the interactions differ in type and in the intensity and the sampling can be particularly difficult (54, 55). In the very recent work of Schneider and Colombi Ciacchi (68), for example, the adhesion force between a small peptide and oxide surfaces has been studied by using metadynamics and steered molecular dynamics (69) techniques. With the aid of these advanced techniques to improve the sampling, the Classical MD simulations provide one of the most powerful methods of investigation for the study of the adsorption process and biomolecules/inorganic interface in solution, which however require large amounts of high performance computing (HPC) resources. A major challenge remains the extension and the parameterization of the new force fields designed to describe the protein/inorganic-surface interactions.

Rigid-Body Docking: Predicting Protein-Surface Encounter Complexes Brownian Dynamics (BD) and Langevin Dynamics (LD) computational methods are usually employed for the study of the motion and the interactions 240 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


of biological macromolecules in solvent. These methods offer the possibility of accessing phenomena whose time- and length-scale is much greater than that normally achievable in atomistic MD simulations. BD strategies are based on physical approximations to reduce the complexity of the system simulated. In rigid-body docking the macromolecules are treated as rigid bodies, neglecting their internal degrees of freedom which are not always fundamental for the description of the processes under investigation. This approximation which greatly reduces the complexity, allow the atomic details of the macromolecules to be conserved. A range of methodological developments have been implemented in a number of software packages. Atomically detailed rigid-body BD simulations have been implemented for example in UHBD (70), SDA (71) and Macrodox (72), which are routinely used to evaluate electrostatic properties of biomolecular systems as well as to perform Brownian Dynamics simulations for a wide range of length scales enabling the investigation of molecules with tens to millions of atoms. In order to describe the diffusion and association of proteins to metal surfaces, a BD methodology developed for the computation of protein-protein encounter complexes (73) has been recently adapted to the protein-surface problem and implemented in SDA6.00 (74). In protein-surface docking with SDA, the protein is modeled as a particle diffusing in a solvent that is treated as a continuum exercising frictional and random, stochastic forces on the protein; while the metal surface is described as a large multi-layers cluster placed in the XY-plane (Figure 6). For the description of the protein-surface association processes with BD methods, the implicit solvent model must be designed specifically for the surface considered. It has been shown that existing implicit solvent models can be successfully used for hydrophobic surfaces, where there is no water between the surface and the protein (75, 76). On the contrary, some MD simulations with explicit water have shown that for strong polar surfaces, protein binding is not occurring to the surface but rather to a structured water layer (77, 78). Even when the protein binds directly to the surface, the structuring of water close to hydrophilic surface modifies water properties w.r.t the bulk, and standard continuum model cannot be applied (79). To properly describe the adsorption of proteins to metal surfaces with a continuum solvent in BD, specific properties of the hydration shell on metal surfaces should be accounted for by including additional, semi-empirically parameterized terms in the protein-surface forces (17, 39). In protein-surface docking with BD, the starting position and orientation of the protein is generated randomly at a given distance from the surface, which defines the limit where the protein-surface interaction energy becomes negligible. At each BD step a protein-surface interaction energy and the force acting on the protein are computed using the implicit-solvent ProMetCS force field, developed and parameterized for protein-gold surface interaction (39). The ProMetCS energy includes the following terms: (i) a sum of pair-wise interatomic Lennard-Jones terms that describes van der Waals and weak chemical interactions between the biomolecule and the gold surface (based on the fully atomistic force field GolP, see above (38)); (ii) the electrostatic interaction free energy in the 241 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


water environment, which includes an “image-charge” interaction energy of the protein effective charges with a flat infinite, overall uncharged, metal surface along with the direct Coulomb interaction of protein effective charges with the charges placed at each Au atom, mimicking a gold surface non-zero potential. Electrostatic energy also includes a desolvation correction term (80, 81) which takes into account the change of the electrostatic interaction energy due to polarization and distortion of the hydration shell at small protein – Au surface distance; (iii) a protein hydrophobic desolvation and (iv) a surface desolvation free energy term arising from the partial replacement of the metal hydration shell by the protein. Millions of putative protein-docking complexes can be generated in a few hours on a commodity cluster by this BD. The low-energy protein-surface complexes resulting from the docking must therefore be clustered according to their conformational similarity to reduce this overwhelming number of structures. Data-mining techniques, like clustering of structures by similarity, are efficient tools to sort out representative information from either most stable or populated docking poses (82). Various applications of this method are presently on-going in our group. As an example, we report in Figure 6 one of the structure obtained by docking ubiquitine, a small protein, on Au(111) (83). This system has been chosen since there are experimental NMR data that identify the ubiquitine patch interacting with Au nanoparticles (13), making a comparison with docking results possible.

Figure 6. Example of a protein-surface association complex obtained by BD rigid docking. The protein is ubiquitin, docked on a neutral Au(111) surface in water.

Finally, we remark that rigid body docking, when used alone, is useful only if the protein conformation is not drastically altered by adsorption. Alternatively, it can be combined with classical MD simulations, which are in principle able to describe conformational changes: rigid body docking provides initial structures for the protein-surface encounter complex, then MD simulations can be started to investigate conformational rearrangements due to the interaction with the surface. In practice, the time-scales accessible to MD are currently too short, in general, 242 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.

to study extensive changes of secondary and tertiary structural elements, such as partial or complete unfolding. Expensive enhanced sampling techniques could be used in selected cases to investigate the problem. Alternatively, models describing the protein to a coarser level than atomistic MD may reach the required time scales. These models are introduced in the next section.


Extending Coarse-Grained Protein Models to Protein-Surface Systems When we simplify the structure of a protein by considering only those atoms or sets of atoms that are supposed to be fundamental in the behavior of the system, we say that we are dealing with a coarse-grained model. Different coarse-grained models of proteins could be set depending on the properties and the phenomena under study (40). Figure 7 shows different examples and their applications.

Figure 7. Different coarse-grained models, with a description of the cases in which they are normally used depending on the level of accuracy needed and on the complexity of the problem under study. This is illustrated in a two axes graph indicating the complexity of the representation (that is the number of beads per aminoacid) and the complexity of the parametrization (number of parameters used to analize the problem). Reprinted with permission from ref. (40). Copyright 2005 Elsevier.

The reduced number of atoms is not the only feature of a coarse-grained model: in addition to the simplification of the structure the corresponding potentials and nonbonded interactions have to be modified accordingly. This can be seen as follows: suppose that the atomistic structure of the protein can be described by a set of N variables {Q1,...,QN} and their momenta. These variables 243 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


can be for example the usual Cartesian coordinates or, more likely, proper internal coordinates (e.g., bond lengths, angles and dihedrals). Coarse graining a protein means to reduce this set of variables to a smaller one, {Q1,...,QR} with R < N. The basic function from which we can get a proper theoretical description of the physical system is the probability density of finding the system in a given state, P{Q1,...,QN}. In our coarse-grained model, we have a new probability density which comes from integrating out N − R variables. In terms of the potential energy of the protein V{Q1,...,QN} and after integrating out momenta, the new probability density reads

Therefore, if we reduce the number of degrees of freedom of a protein, we have to use a new potential energy VCG(Q1,....QR) that reproduces the probability density in eq. 1. How to find this new potential energy is not an easy task, and some assumptions and approximations have to be considered. Some authors use the so-called Boltzmann Inversion method (BI (84)), where the potential energy is written as:

This is a strong assumption but it generally leads to coherent results. The probability density Pi(Qi) of each reduced variable Qi becomes independent from the others and it is straightforward to show that

The probability Pi(Qi) can be extracted from a standard atomistic MD, which makes the use of this potential for coarse-grained simulations possible. Alternative approaches can be used in order to find a theoretical potential for the coarse grained model. If the model consists only of the Cα, one of them is the so-called Kovacs potential (85). It is a harmonic potential between each pairs of Cα and reads

with

244 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


The general form eq. 4 is often used to retain the topology of the protein unchanged. K(rij) is called Kirchhoff function and has to do with the type of interaction between the atoms. rij is the distance between Cα atoms (or beads) i and j and rij0 is the initial equilibrium position of the bead pair. The distance dependence of the Kirchhoff function in eq. 5 comes from the study of the mean forces that Cα atoms feel in atomistic molecular dynamics. The fitted values a and d are respectively 40 kcal mol-1Å-2 and 3.8 Å. This potential leads to good coarsegrained dynamics, which accurately conserves the main dynamical properties of the protein (86). Another approach is to build a potential from the principal component analysis (PCA) of a fully atomistic MD. This is done with the set of eigenvectors and eigenvalues found with essential dynamics (87) as:

where M is the number of essential modes retained in the model, and is the equilibrium position vector ( and are 3N vectors collecting the Cartesian coordinates of all the N atoms in the system). The potential V in eq. 6 is a second order approximation to the total potential that depends on the results of essential dynamics. V replaces the entire force field considered in a standard molecular dynamics, i.e., it accounts for bound, unbound and solvation interactions. Using this potential in a Langevin or Brownian dynamics for the coarse-grained protein, one gets an equivalent trajectory of the protein with the same flexibility (B-factors, RMSD, correlation patterns, Lindemann coefficients, etc) of the original MD. One can take advantage of this second order potential energy to study systems with higher complexity. That could be the case, for example, of a protein on a metallic surface where the interaction with the metal can be added to V in eq. 6 giving rise to a hybrid potential. We are currently testing this method by including in such hybrid potential a term accounting for the direct interaction with gold based on GolP, and another term taking into account protein and metal desolvation, as in ProMetCS (39). We are also testing an even simpler coarse-grained model for protein-surface interactions, based only on the backbone atoms, which uses only a Lennard-Jones 12-6 potential. We use effective interaction parameters obtained by assuming that all the atoms of an aminoacid side chain are concentrated on its corresponding Cα. This is a really simplistic assumption that will be improved in the future. The interaction with gold is again introduced by protein-Au Lennard-Jones terms obtained from GolP. Preliminary results are encouraging. As an example, in Figure 8 we show a comparison of the B-factors obtained by an atomistic GolP MD (10 ns long) and the corresponding LD using the simple coarse-grained potential for ubiquitine on an Au(111) surface in water. As it can be seen, both lines describe qualitatively the same behavior, which means that even such simple potential and backbone based coarse-grained model is providing reasonable results. 245 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Figure 8. B factors describing the mean dispersion of backbone atoms for ubiquitine docked on a gold surface. Black line refers to the atomistic MD results. Red line refers to the results of the LD with the hybrid potential described in the text. MD and LD simulations are both 10ns long. As it can be seen, both qualitatively represent the same overall behavior, although minor deviations are present.

Conclusions In this chapter we have succinctly introduced the various computational approaches that our group has been developing and applying to the study of the interaction between proteins and inorganic (gold) surfaces. Our approach comprises a sequential multiscale strategy that can be applied to materials other than gold and that can provide an answer to many of the open questions in the field. The development and use of these tools evolve in parallel with experiments, as the picture provided by combining experiments and computations is broader and more solid than that coming from one of the two sources alone. We have also put particular care in making our development freely and openly available to the scientific community (http://web.fisica.unimo.it/prosurf/toolbox.html), with the hope of triggering further improvements and allowing applications by other groups. Finally, we have also sketched some of the lines of ongoing developments, which include the testing of enhanced sampling methods and the use of coarse-grained models. We note that a similar approach can be extended to DNA interaction with inorganic solid surfaces and nanoparticles. 246 In Proteins at Interfaces III State of the Art; Horbett, T., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2012.


Acknowledgments We are grateful to Elisa Molinari for continuous stimulating discussions. The work presented here is mostly the result of a joint effort of our group at the Center S3 CNR-NANO and the groups of Rebecca Wade, Gideon Schreiber, Israel Rubinstein, Alexander Vaskevic and Kay Gottschalk, who are most gratefully acknowledge here. Our work is funded by the European Commission through projects PROSURF (contract FP6-028331) and DNA-NANODEVICES (contract FP6-029192), by the Italian Institute of Technology, Platform Computational, through Seed project MOPROSURF (2010-2013) and by MIUR under the FIRB project ITALNANONET. The computational facilities and staff at CINECA (Bologna, Italy) are acknowledged. The EU FP6 DEISA infrastructure network (DECI project Psi-Wat) provided the supercomputing time for the CP simulation, carried out at BSC in Spain, while the EU FP7 PRACE infrastructure network (Preparatory project 2010PA0412) provide the time for preliminary simulations of Amyloid β peptide on gold, carried out at TGCC in France.

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Proteins and Peptides at Gold Surfaces: Insights from Atomistic

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