16962
J. Phys. Chem. C 2007, 111, 16962-16973
RAD16II β-Sheet Filaments onto Titanium Dioxide: Dynamics and Adsorption Properties Susanna Monti* Istituto per i Processi Chimico-Fisici (IPCF-CNR), Area della Ricerca, Via G. Moruzzi 1, I-56124 Pisa, Italy ReceiVed: July 3, 2007; In Final Form: August 29, 2007
The adsorption and dynamics of a β-sheet filament made of RAD16II self-assembled peptides onto the TiO2 rutile (110) surface in aqueous solution have been studied through classical molecular dynamics simulations. Different arrangements of the filament on the surface have been considered and analyzed in order to identify preferential binding modes. The simulations results suggest that RAD16II filaments can strongly adsorb onto titanium dioxide surfaces through direct and indirect interactions of their charged side chains with both titanium and oxygen atoms of the these interfaces, in agreement with experimental data. The strength of adsorption, which is strictly connected with the number and type of peptide-surface contacts, governs the filament mobility. However, side chain interactions have little influence on the flexibility of the supramolecular aggregate. Indeed, the integrity of the filament is maintained by backbone hydrogen-bonding interactions, which are preserved during the whole simulation time.
1. Introduction In recent years, the research activity in the field of biomaterials is increasingly directed toward the creation of biomimetic surfaces through the incorporation of peptides, proteins, and DNA/RNA strands for a variety of technological and medical applications (biosensors, bioreactors, chromatographic supports, prosthetic materials, etc.). Due to its advantageous bulk and surface properties, titanium is extensively used.1 Its biocompatibility, low modulus of elasticity, high strength-to-weight ratio, excellent resistance to corrosion, and the strongly adherent surface oxide film which passivates the metal in biological systems make it the best candidate to be modified for the design of new improved materials. Among the various surface engineering techniques aimed at further enhancing titanium biocompatibility, biochemical methods that control surface characteristics by immobilization and/ or delivery of proteins, enzymes, or peptides are of definite interest. These methodologies can be used to substitute or supplement physicochemical or morphological techniques and, as confirmed by several interesting examples reported in the literature,2-6 are very promising approaches. However, for successful applications, some important factors should be taken into account when complex molecular species are assembled on material surfaces. First, the functional structure or the active site of the adsorbed biomolecule as well as their threedimensional arrangement and activity should not be influenced by the surface during or following the attachment. Second, the attachment should be stable and be able to bind the molecule to the surface through strong interactions not susceptible to disruption by hydrolysis or other environmental perturbations. Among the molecules of direct relevance to the biochemical modification of titanium oxide surfaces, spontaneously selfassembling oligopeptides represent a very interesting novel class of biomaterials.7-15 The members of this family are selfcomplementary amphiphilic oligopeptides that have regular repeating units of positively charged residues, such as lysine * To whom correspondence should be addressed. E-mail: s.monti@ ipcf.cnr.it. Phone: +39-050-3152520. Fax: +39-050-3152442.
(Lys ) K) or arginine (Arg ) R), and negatively charged residues, such as aspartic acid (Asp ) D) or glutamic acid (Glu ) E), separated by hydrophobic amino acids such as alanine (Ala ) A) or leucine (Leu ) L). They exhibit remarkable secondary structure plasticity and multifaceted behavior and spontaneously assemble to form macroscopic structures that can be fabricated into various geometric shapes. Some of them are organized as strong β-sheets in aqueous solutions, and some other have the ability to undergo secondary structure transition from β-sheet to R-helix in response to changes in temperature, pH, and salt concentration. Amphiphilic peptides, such as RAD16 and EAK16, are soluble at low millimolar concentrations in salt-free aqueous solutions, but when exposed to physiological media or salt solutions, they form hydrogel-like matrices with a high water content (>99%). Several selfassembling peptide scaffolds support cell attachment, proliferation, and differentiation, and those containing the motif ArgAla-Asp (RAD), which has high specificity for integrin receptors, can be used as ligands for attaching cells to surfaces. The sequence RARADADARARADADA (RAD16II) with N- and C-termini blocked by acetylation and amidation, to prevent rapid degradation, is of particular interest.16-18 Besides its similarity to the RGD (Arg-Gly-Asp) sequence, that is characteristic of some integrin receptors, it robustly supports the attachment and growth of many types of non-neural primary and transformed cells. In a recent study, Hwang and co-workers used atomistic simulations to investigate the structure and elastic properties of filaments comprised of RAD16II peptides.19 They were the first ones to determine possible supramolecular structures in agreement with experimental observations. Among all possible combinations of β-sheet filaments, generated through a series of molecular dynamics simulations, they identified the most stable ones and succeeded in characterizing their elastic properties using three different methodologies. Despite the fact that extensive studies of RAD16II filaments have resulted in elucidation of many aspects of their structure, elasticity, and in vivo behavior, important issues concerning, for example, their adsorption onto titanium-based materials and thus their possible use as surface coating bioadhesive motifs,
10.1021/jp075154g CCC: $37.00 © 2007 American Chemical Society Published on Web 10/12/2007
RAD16II β-Sheet Filaments onto Titanium Dioxide remain to be resolved. Therefore, it is of great interest to investigate the behavior of peptide β-sheet assemblies when in contact with TiO2 surfaces in order to understand the mechanisms which determine the formation of stable coated surfaces for efficient cell-matrix interactions. In this paper, atomistic molecular dynamics simulations are used to investigate the RAD16II-TiO2 system in aqueous solution, focusing the study on structural effects that the rutile (110) surface and explicit water molecules might have on the peptide matrix in an attempt to characterize the binding of RAD16II filaments to titanium-based materials. The ideal approach to simulate the dynamics of the adsorption process on TiO2 interfaces would be to use the detailed surface protonation behavior, that is, the reaction of association and dissociation occurring at the metal oxide layer. However, such methodologies have not been applied to large molecular ensembles due to the formidable complexity behind the atomistic description of the surface chemistry. Nevertheless, results from different experimental studies indicate that water can adsorb both molecularly and dissociatively on a perfect TiO2 rutile (110) surface.20 Moreover, while most of the experimental results agree that water does not dissociate on rutile (110) except at defect sites, theoretical studies predict both dissociative and nondissociative adsorption.21,22 However, as stated in ref 23, water dissociation on TiO2 rutile (110) remains controversial. The current investigation is limited to a neutral nonhydroxylated surface since this effort is part of a coordinated experimental and computational study, which to date has focused primarily on the stability of TiO2-peptide complexes in aqueous solution. This is accomplished by choosing conditions similar to those found after the adsorption process and by X-ray photoelectron spectroscopy (XPS) and near-edge X-ray absorption fine structure (NEXAFS) measurements,24 that is, when the new material, made of TiO2 and peptide layers, is already assembled. Recent experimental studies have shown that selfassembling peptides strongly adsorb onto TiO2 surfaces, forming ordered arrangements.24 The computational approach chosen is a reasonable compromise between the realism of a quantum dynamics description, only possible on smaller systems, and the practicality of classical simulation methods based on force field parameters derived from ab initio calculations.25-27 The ability of classical techniques to describe realistically the adsorption processes on TiO2 has been demonstrated in a number of papers.27-32 Recently, Langel and co-workers through detailed theoretical studies have succeeded in simulating the interface of the rutile (100) surface in aqueous solution in contact with Na+, Cl- ions,31 and flexible collagen I triple helices by classical molecular dynamics.32 2. Materials and Methods 2.1. Construction of a Reduced RAD16II Fiber Model. The coordinates of four RAD16II filaments (β-sheet bilayers), that differed only in the backbone hydrogen-bonding register and found to be similarly stable through molecular dynamics by Hwang and co-workers, were kindly provided by Professor W. Hwang. As reported in ref 19, the constructed β-sheet tapes were compatible with the filament dimensions obtained from AFM33 measurements. The filaments were 1 molecule in width and 52 peptides in size and were arranged as β-sheet bilayers. The 2 sheets, forming the bilayer, were made of 26 peptide chains, each arranged in antiparallel orientation, and due to the alternating location of hydrophobic and hydrophilic side chains the Ala side chains were placed inside the bilayer.10 The models were classified by Hwang et al. according to hydrogen-bonding patterns of the backbone atoms (S1, S2, S3,
J. Phys. Chem. C, Vol. 111, No. 45, 2007 16963
Figure 1. Original S1313 structure of the RAD16II β-sheet filament and the reduced model employed in these MD simulations. β strands are highlighted by solid arrows. Perspective view of the reduced filament model onto rutile (110) with its β-sheet planes in parallel orientation with the respect to TiO2 layer. Color codes: carbon, yellow; oxygen, red; nitrogen, blue; and titanium, gray.
Figure 2. Schematic representation of the 16-peptide filament together with its parallel (para) and perpendicular (perp) arrangements with respect to the TiO2 surface. The various strands are named according to the position of para peptides on the surface (L ) plane in contact with the surface). Residue numbers are reported. Backbone hydrogen bond are represented by dashed lines.
and S4) and were combined to give antiparallel β-sheets (S13, S14, S23, and S24). Bilayers composed of β-sheets were named according to the constituting units (S1313 ) S13 + S13, S1324 ) S13 + S24, S1423 ) S14 + S23, and S2424 ) S24 + S24). As stated by the authors, there was no distinct lowest energy state and the S1313, S1324, S1423, and S2424 had all probable configurations. Moreover, the exact register of the hydrogen bonds did not seem to be important in determining the single filament mechanics. Taking into account their results, one of the provided structure (S1313) was chosen for our calculations (Figure 1). The backbone hydrogen-bonding pattern and the arrangement of the various strands are schematized in Figure 2. A 10 ns simulation of the whole filament with water molecules and the TiO2 surface, whose size depends on the peptide matrix dimension, was prohibitive for our computational resources, thus a smaller model was defined. The stability of a number of fibers of different lengths was checked through short molecular dynamics simulations performed with the GB/SA approach,34,35 which efficiently describes the electrostatics of
16964 J. Phys. Chem. C, Vol. 111, No. 45, 2007 peptide in water environment, representing the solvent implicity as a continuum, and includes the charge screening effects of salt. The aim of this preliminary test was to define an appropriate reduced bilayer segment having characteristics similar to the ones displayed by the original structure and a molecular packing, in the region far from the boundaries, relatively uniform and stable in solution. A segment made of 16 peptide chains (8 for each sheet) revealed to be an appropriate choice (Figures 1 and 2). In fact, when subjected to short MD runs (about 150 ps) at T ) 300 K, the core of the structure, formed by the 8 peptide chains in the center of the matrix (4 chains for each β-sheet plane), was not affected by border effects, and the structure was stable and tightly packed with small deviation of the backbone atoms from the starting conformation (RMSD < 0.2 Å). The stability of the complex was further checked by calculating its association energy (Ebind), defined as the sum of the intermolecular interaction energy (Eint) and the deformation energies (∆Ei) of the constituting molecules, that is, the gain in energy due to conformational rearrangements of the aggregated molecules with respect to the isolated condition.36,37 The interaction energy in the selected model overcame the increase in energy produced by the deformation process, implying a highly stable ensemble (average association energy -1766 ( 6 kcal/mol). The comparison with smaller stable aggregates of different sizes also revealed that the chosen dimensions could quite well represent the existing filaments. The binding energy of various models was compared by calculating the energy of the complex per atom EAbind ) Ebind/N, where N is the total number of atoms present in the aggregate.38 In the case of a dimer EAbind was around -0.28 kcal/mol, for a tetramer it was about -0.39 kcal/ mol, and for a octamer, a dodecamer, and a tetradecamer, the EAbind values were around -0.48, -0.56, and -0.59 kcal/mol, respectively, whereas for the selected esadecamer, EAbind had a lower negative value (-0.62 kcal/mol), confirming the strong character of this association. Besides, the reported values suggest that the aggregation of additional units is favored. 2.2. Molecular Dynamics Simulation Set Up. The model of the TiO2 surface, including force field and other simulation details, was described in a previous article,27 where it was also validated and proved to be a reliable representation of the hydrated rutile (110) layer, giving possible pictures of the adsorption mode of amino acids, peptides, and macromolecules (such as collagen segments)27-29 and producing results in satisfactory agreement with experimental observations and measurements.39 The rutile (110) layer in contact with peptide and water molecules contained 297 accessible Ti atoms and 891 O atoms (594 bridging and 297 terminal oxygens) and was about 70 and 77 Å in the x and y dimensions, respectively. The filament, a rectangular ribbon with a cross-sectional width of w ≈ 60 Å, height h ≈ 23 Å, and length l ≈ 40 Å (measured as end-to-end distance), 16 peptides in size, extracted from the original S1313 structure of Hwang and co-workers, and optimized after short MD simulations using the GB/SA approach, was positioned close to the TiO2 surface, avoiding bad steric and electrostatic interactions, in two different orientations. In the first one, hereafter called para, the filament model was oriented with its β-sheet planes parallel to the titanium dioxide surface, choosing a reciprocal position that allowed the formation of hydrogen bonds between the charged peptide side chains (Arg and Asp) and the surface oxygen atoms (bridging and outof-plane oxygens) and/or coordination of the carboxyl groups of the Asp residues with accessible titanium atoms. Instead, in the second orientation, hereafter called perp, the ribbon β-sheet
Monti planes were almost perpendicular to the TiO2 layer with a major side (l) in contact with the surface. Considering that preferential interactions between charged peptides and TiO2 interfaces involve mainly amino acid side chains20,40,41 and that peptide termini are blocked with NH2 and COCH3 groups, the other less probable arrangement (i.e., with the terminal regions close to the TiO2 layer (w)) was not examined in the present investigation. The systems were inserted in rectangular parallelepiped boxes with dimensions of about 77 × 85 × 91 Å3 and were solvated with TIP3P water molecules42, removing the water falling within a 2 Å radius from both the TiO2 surface and the filament. All simulations were performed by use of the AMBER9 suite of programs with the ff03ua force field43 and developed parameters for TiO2 atoms.27 The systems, consisting of the TiO2 surface, the peptide filament, and about 14 000 water molecules, were minimized and subjected to MD for 100 ps at constant temperature, T ) 600 K, and volume with fixed filament and surface, in order to randomize water positions. Then, pre-equilibration at constant temperature (T ) 310 K) and volume followed by constant pressure MD runs, to adjust the system density, were performed. Andersen temperature coupling scheme44,45 was used to control the temperature, and bond lengths were constrained using the SHAKE algorithm.46 The time step was set to 2 fs. Periodic boundary conditions were applied in x, y, and z directions, and the particle mesh Ewald method was used for computation of electrostatic forces. Surface atoms were frozen during all the simulations, which were conducted for 11 ns in the NVT ensemble, with the first nanosecond considered equilibration and the last 10 ns used for analysis. The system configurations were saved every 10 ps. 2.3. Structural and Dynamical Characterizations. The stability of the filament was analyzed by inspecting the overall measure of the drift from the initial structure, via the backbone root-mean-square deviation (RMSD) as a function of the simulation time, the fluctuations of the individual residues, expressed by CR root-mean-square fluctuations (RMSF) averaged over time, and the behavior of secondary structure elements, calculated with the program DSSP.47 Pattern of hydrogen bonds were identified, considering H-donor-acceptor angles lower than 60 degrees and donoracceptor distances lower than 3.5 Å, and classified according to their type and persistence. The percentage of time each residue spent forming a hydrogen bond (pHb) was calculated as the ratio of the total number of time steps during which the residue was hydrogen bonded (nHb) and the product of the total number of time steps (ntot) and the number of H-bond types observed for that residue during the simulation (ntype).48 According to this definition the percentage pHb ) 100nHb/ntotntype was equal to 100% if a given residue made a single type of H-bond throughout the whole simulation time, whereas if two different H-bond types were observed the percentage reduced to 50%. Local and global motions of the filament were determined by calculation of the distances of peptide centers of mass from the TiO2 surface and variation of the orientation of the β-sheet planes with respect to each other and with respect to the surface. Principal component analysis (PCA)49-53 was used to identify the nature and relative importance of the essential deformation modes of the filaments from the MD samplings and to describe their motion with respect to the surface. The method is based on the diagonalization of the positional covariance matrix C of selected atoms, whose elements are given by
RAD16II β-Sheet Filaments onto Titanium Dioxide
cij )
() 1
M
J. Phys. Chem. C, Vol. 111, No. 45, 2007 16965
M
∑{xi(k) - 〈xi〉}{xj(k) - 〈xj〉} k)1
(1)
where M is the total number of configurations and xi are the atomic coordinates. The resulting eigenvectors describe a direction in the high-dimensional configurational space, that is the nature of deformation movements, whereas eigenvalues represent the mean-square fluctuation of the total displacement along the eigenvectors, that is the amount of variance explained by each movement. In essence, the eigenvectors describe, vectorially, each mode of the structural deformation and the eigenvalue for a mode indicates its relative importance in the motion within the trajectory. This last quantity can be expressed as the percentage of total variance explained by each essential movement as
%var ) 100
λi
∑i λi
(2)
Backbone atoms were chosen to characterize the flexibility of the structures, and the relevant motions of the systems were studied by projecting the trajectory onto the major individual eigenvectors. The projections were analyzed for their timedependent behavior. The central hypothesis of this analysis is that only the directions indicated by eigenvectors with sufficiently high eigenvalues are important for the description of the system dynamics.54,55 Motions along the selected eigenvectors are mainly anharmonic fluctuations, slower correlated modes of motion that are more likely to be relevant to biological functions. The lowest eigenvalues and corresponding eigenvectors represent, instead, the directions for which the data has the smallest variance (harmonic thermal fluctuations). Earlier studies have shown that, when reduced to the essential space, the first few eigenvectors are sufficient to describe most of the macromolecule correlated motions.55 To quantify internal flexibility, the mean structure was computed by aligning all the sampled conformations to the starting structure, minimizing the coordinate RMSD between their corresponding backbone atoms, and averaging the position of each backbone atom over all the aligned structures. Instead, to evaluate the motion on the surface, translations and rotations were not removed and the alignment was performed considering the atoms of the TiO2 layer which were frozen during the whole simulation time. 3. Results and Discussion 3.1. Internal Deformations and Stability of the Models. 3.1.1. RMSD. During the first 5.5 ns of the simulations the RMSD of the backbone atoms from the initial conformation, displayed in Figure 3, shows a steady but small increase (∆RMSD ≈ 0.7 Å) in both parallel and perpendicular arrangements, which might suggest that the structures, in both cases, undergo minor conformational readjustments with respect to the equilibrated starting conformations. After this period, the RMSD stabilizes around values in the range 1.3-1.4 Å. Close inspection of the trajectories reveals that there is greater conservation of the geometries in the central region of the β-strands whereas greater structural variations take place at the extremities of the peptide chains, where the residues adopt more curved conformations than those in the initial models due to interactions with solvent molecules, as might be expected. However, stabilization after 5.5 ns indicates that the whole configuration remains intact, substantial conformational changes have not occurred, and the
Figure 3. (a) Root-mean-square deviation of the backbone atoms from the initial conformation for para and perp, and (b) RMSD of the backbone atoms of the eight strands in the central region of the β-sheet bilayer for para and perp.
secondary structure is maintained. During the simulations, the eight strands in the central region of the β-sheet bilayers stay packed together and maintain a well ordered antiparallel β-strand alignment, very close to the starting orientation, in both para and perp simulations till the end of the production runs. This can be noticed through the examination of the RMSDs of the central section shown in Figure 3, which fluctuate around average values of 0.62 ( 0.11 Å and 0.54 ( 0.08 Å for para and perp, respectively. 3.1.2. RMSFs and Secondary Structure Analysis. Fluctuations of individual residues, measured as CR root-mean-square fluctuations averaged over time, which reflect the mobility of the peptide β-strands, are compared in Figure 4 for the two cases. The shapes of the curves are very similar to each other displaying remarkable oscillations and thus a high degree of flexibility in the portions of the peptide chains near both Nand C-termini. Greater variations are found in the C-terminal segments of each strand, where no hydrogen bonds between the Ala residue, terminated with a NH2 group, and the COCH3terminus group belonging to the neighboring β-strand are present to stabilize the structures, whereas the N-terminus segments show reduced mobility (RMSF < 1 Å) because of the conserved hydrogen-bonding patterns between the Arg and Asp residues on adjacent chains (Figure 2). The overall level of fluctuation in the secondary structure is a little lower for perp than that for para; however, the differences between the two models are not striking. As expected, the strands L1, U1, L7, and U8 at the edges of the filaments exhibit greater fluctuations due to the increased number of possible interactions with water molecules and, interestingly, these oscillations seem to be most
16966 J. Phys. Chem. C, Vol. 111, No. 45, 2007
Monti
Figure 4. Fluctuations of individual residues, measured as CR rootmean-square fluctuations averaged over time for para and perp.
Figure 6. Time evolution of the backbone trajectory projections along the first four eigenvectors of the covariance matrix of para (a) and perp(b), representing internal motion, with the corresponding probability distributions (right side curves). The corresponding percentages of total variance explained by each essential movement are: 38%, 6%, 4%, and 3% for para and 27%, 8%, 7%, and 4% for perp.
Figure 5. Analysis of the secondary structure elements for para (a) and perp (b).
marked for the para simulation, where also strands U7 and L8 should be included. However, the greatest fluctuation is observed for the perp case, where the Ala 3815 residue, located at the end of the U8 strand, moves far away from its initial position (closer to L8) and stretches into the solvent. The CR displacement is about 12.5 Å and is greater than that observed for the other marked fluctuations, where it is always lower than 7.5 Å. It might be speculated that the interaction with the surface adds a perturbation, which contributes to destabilization and loss of secondary structure in the border regions. However, the values of RMSF for the core residues are predominantly less than 0.5 Å, indicating highly conserved β-sheet arrangements and general stability of both models. In agreement with RMSD results, the central section of the bilayers is less mobile and quite rigid, implying that the largest RMSDs found are not caused by unfolding of the whole configuration. The secondary structure analysis shown in Figure 5, performed with the DSSP program,
confirms this picture. In fact, as it can be noticed, each peptide remains largely β-strand throughout the duration of the simulation. 3.1.3. Principal Component Analysis (PCA). PCA has been employed to probe the above findings in a systematic and simple way and has allowed the identification of relevant peptide backbone folding motions from small-amplitude vibrations via projecting the deviations of the MD trajectories from the average structures onto selected eigenvectors. Ideally, for uncorrelated small-amplitude vibrations, the corresponding projections will simply fluctuate around an average value yielding approximately a Gaussian distribution function. Strong deviations from such a unimodal behavior would single out interesting modes that can be associated to collective changes involving many atoms. Figure 6 shows the variation in the coefficient of each of the four major principal components as a function of the simulation time with their probability distributions. The coefficients of modes 2, 3, and 4, which contribute approximately 6, 4, and 3%, respectively, for para and approximately 8, 7, and 4%, respectively, for perp to the overall variance of the peptide backbone, oscillate around zero. They are characterized by fairly symmetric, narrow, and unimodal distributions, and thus the deformation of the structures along each of these major eigenvectors can be classified as peptide backbone vibrational motions, which include small twisting and bending movements of the terminal amino acids. As far as the interpretation of the behavior of folding transitions is concerned, it is possible to neglect all backbone vibrational motions and consider only the first principal components, which are responsible, instead for 38% and 27% of the entire internal change of the filaments in para and perp, respectively. In contrast to modes 2-4, the lowest order projections vary broadly, exploring two different flat regions corresponding to two conformation clusters. These zones are clearly visible in Figure 7, where the three-dimensional PCA curve is displayed. Indeed, mode 1 is strongly anharmonic
RAD16II β-Sheet Filaments onto Titanium Dioxide
Figure 7. Three-dimensional PCA curves for para (black line) and perp (red line), showing that the conformations in the trajectory can be grouped into a few clusters.
Figure 8. First essential mode of para and perp from PC analysis, representing internal deformations. This image is generated by projecting the entire MD trajectory onto the first eigenvector. Minimum, maximum, and intermediate structures are visualized to evidence the movements of the different sections of the strands. Only backbone atoms have been considered. Upper plane sheets are in gray and lower plane sheets are in black. The coordinates can be found in the Supporting Information section.
and is likely to be a conformational transition, which begins at about 2.2 ns and persists until about 4.8 ns in the para case, whereas in the case of perp the conformational change is faster (it lasts a few ps) and takes place at about 5.6 ns. In both simulations, when the time goes up to about 6 ns, the first principal component reaches a stable state, which can also be validated in the RMSD curve where some features of the first principal component can be identified. These findings imply that the first principal component plays a more important role than the other three principal components. Moreover, from the examination of probability distributions of the displacements along corresponding eigenvectors (right side of Figure 6), it is clear that the projection process yields for mode 1 a bimodal distribution function, suggesting again a conformational change which might include movements of the subunits with respect to each other. The nature of the motion of both para and perp is illustrated in Figures 8-10, where the greatest variations of the backbone atoms with respect to the average structure are represented using the maximum, minimum, and intermediate projected structures
J. Phys. Chem. C, Vol. 111, No. 45, 2007 16967 of the first essential mode. The structures are superimposed to highlight the extrema of each essential motion. The large anharmonic fluctuations in para appear to originate from the two conformational transitions of L7- and L8-ending segments. The first one is a significant spatial readjustment of the terminal portion of L7 between residues Ala 3831 and Ala 3833; the three-peptide chain moves away from the surface, breaking the initial contact of Ala 3833 with the TiO2 layer, and aligns its backbone with the L5 strand. The second one is a marked conformational change of the C-ending segment of L8 between residues Ala 3849 and Ala 3851; the three-peptide chain bends toward the upper plane forming a sort of turn. The motion of this segment induces the opening up of the gap between the two β-sheet planes in proximity to the corner of the bilayer, thus, allowing the insertion of a few water molecules (four in all) as can be noticed in Figure 11, where the first and final structures of para are displayed. However, the movements of these water molecules appear to be confined to this sort of cavity, whose entrance, in the final conformation, seems to be obstructed by the bent L8 tail. More interestingly, in addition to these water molecules grouped in the right-hand corner of the filament (Figure 11), two other water molecules, evidenced through the CPK representation, are detected inside the bilayer. The one located on the left-hand side of the structure, near Asp 3608 between L1 and L2, is present in both the starting and the final configurations suggesting that it was absorbed during the equilibration phase and remained trapped in the gap between the two planes. This water is confined in that specific location till the end of the simulation due to the tight packing of the structure. Observing the position of this water in the initial configuration (Figure 11a), that is its closeness to the lower (L) β-sheet plane, and the dynamics of the water molecules located between the peptides and the TiO2 surface, it can be deduced that the absorbed water was in contact with the TiO2 surface during the early steps of the equilibration phase. Then, due to the reduced motion of Asp and Arg side chains of the L plane, which can be engaged in direct interactions with the surface atoms, the aforementioned water is detached from the TiO2 layer and is translocated inside the peptide bilayer. The movement involved probably simultaneous exchange of the peptide-water hydrogen bonds, as a consequence of the narrow size of the temporary channels that were formed. The almost central position (near Ala 3773 between U5 and U6) of the other water molecule, visible in Figure 11b, also suggests that this water was absorbed in a similar way. From the examination of the structure of L near its terminal strands, it can be noticed that the conspicuous deformation of the L8 chain in the C-terminus region influences the motion of the nearby residues belonging to the U7 and U8 strands, which as a result have a wider wagging motion than that observed for the terminal portions of the other β-strands. However, the movement involves only two amino acids and the deformation does not extend to the central section of the filament, which remains compact and stable. As far as the perpendicular arrangement is concerned, the dominant motion is a bend of the terminal portion of the U8 strand (between residues Ala 3813 and Ala 3815), which is located far from the TiO2 surface, whereas minor twisting movements, involving the terminus parts of the strands, are noticed in the chains closer to the surface (L1 and U1). Contrarily to para, the inside of perp bilayer is inaccessible to water molecules for the entirety of the simulation and no structure disruption is observed. In both para and perp simulations, the filaments are not affected by independent
16968 J. Phys. Chem. C, Vol. 111, No. 45, 2007
Monti
Figure 9. First essential mode of para from PC analysis, representing internal deformations. This image is generated by projecting the entire MD trajectory onto the first eigenvector. Minimum, maximum, and intermediate structures are visualized to evidence the movements of the different sections of the strands. Only backbone atoms have been considered. Color codes: titanium, gray; oxygen, red; carbon, green; nitrogen, blue. The coordinates can be found in the Supporting Information section.
Figure 11. Starting (a) and final (b) configurations of para. All peptide atoms are shown in stick mode. All of the water molecules are not shown for clarity. Water molecules in the bilayer are rendered in CPK representation in red and white. Hydrogen bonds are displayed as dashed gray lines. Color codes: titanium, gray; oxygen, red; carbon, green; nitrogen, blue; hydrogen, white.
Figure 10. First essential mode of perp from PC analysis, representing internal deformations. This image is generated by projecting the entire MD trajectory onto the first eigenvector. Minimum, maximum, and intermediate structures are visualized to evidence the movements of the different sections of the strands. Only backbone atoms have been considered. Color codes: titanium, gray; oxygen, red; carbon, green; nitrogen, blue. The coordinates can be found in the Supporting Information section.
motions of the central β-strands, indicating that external perturbations have no systematic effects on the relative positions of the strands in the two bilayers. 3.1.4. Hydrogen Bonds. To further illustrate how the local microenvironment can affect bilayer structures, the intra- and interpeptide hydrogen bonds are also analyzed. According to the hydrogen-bonding criterion chosen, a single donor could theoretically form more than one hydrogen bond at any given
time if there were a sufficient number of acceptor sites in its neighborhood. As already discussed in the beginning of this subsection, the backbone-backbone hydrogen bonds are well conserved in both models and the supramolecular organization of the RAD16II peptides in parallel β-sheet planes is maintained till the end of the simulation. Detailed analysis of the hydrogen-bonding networks formed in the two planes (L and U) and classification of the hydrogen bonds according to their types, namely, backbone-backbone (bb), backbone-side chain (bs), and side chain-side chain (ss), reveal that the ss interactions are decidedly preferred and the ratio between the total number of H bonds found in the upper plane (U) and those in the lower plane (L) is equal to 1.4 and 1.0 for para and perp, respectively. A deeper inspection of the two simulations shows that the U and L planes of perp and the U plane of para have ≈88% of ss and ≈8% of bs hydrogen bonds, with an average pHb of about ≈15 and ≈3%, respectively, while in the L plane of para, the number of bs interactions (≈15%) is greater than the value found for the other planes,
RAD16II β-Sheet Filaments onto Titanium Dioxide and their average pHb is longer (≈10%). Even though s-s interactions are preferred, their population (≈78%) and duration (average pHb ≈ 2%) are lower than the values found for the other plane (U), confirming once again the limited mobility of the side chain groups close to the TiO2 layer, which remained in the confined regions for quite a long time being engaged in direct interactions with the surface atoms or with the adsorbed water molecules. Indeed, the reduction of ss H bonds can be explained considering the smaller number of free side chains, which can intermittently break and re-form the hydrogenbonding contacts with the other free neighboring side chains and backbone atoms. 3.2. Adsorption Characteristics and Global Dynamics of the Filaments. In agreement with previous simulations,27-29 water is almost uniformly distributed onto the TiO2 surface and water molecules far form the peptide chains are truly adsorbed, being almost immobile above Ti atoms or by forming strong hydrogen bonds with the surface oxygen atoms. No restrictions have been imposed on the dynamics of water molecules, which are free to move around and explore all the accessible regions of the simulation box. However, the surface is not totally covered with water because of the presence of the peptide filaments, which engage in favorable and stable interactions with different portions of the surface. The number of contacts strictly depends on the arrangement of the molecules with respect to the TiO2 layer and on the affinity of the involved groups. At the very beginning of the simulations, that is before equilibration, no water molecules were present in the region between the filament and the surface and thus, especially in the case of para where all the side chains of the L sheet pointed toward the TiO2 layer, a large area of the TiO2 interface was, in principle, available for direct interaction with the peptide groups. However, after equilibration, only a few titanium sites (10 for para and 3 for perp) (Figure 12c,a) were in contact with Arg and Asp amino acids, whereas all the other Ti atoms were covered with water. At the end of both of the simulations, the number of Ti sites involved in the peptide binding is further reduced, as can be seen in Figure 12d,b. Instead, several surface oxygens interact directly with the amino groups of the side chains from the beginning to the end of the simulations. The number of water molecules that populates the regions between the filaments and the TiO2 surface during the course of the simulation is shown in Figure 13. In the case of perp, the number of water molecules adsorbed onto the portion of the surface under the filament oscillate constantly around 195, with a standard deviation of about 4. Peptide-surface contacts are only a few, and the fluctuations in the amount of water appear to be a result of the motion of the strand side chains. Instead, in the case of para during the first 4 ns, a remarkable increase of hydration of about 12% can be observed. Then, in the subsequent 4 ns, the number of water molecules grows more slowly and at the end of this period stabilizes, fluctuating around 270 till the end of the simulation. Even though a greater number of contacts between the L plane side chains and the surface atoms are established, the permeation of water molecules into the space between this β-sheet plane and the TiO2 interface suggests that the filament is not rigidly adsorbed but moves moderately onto the surface. The trend displayed in Figure 13 for para also suggests that the slower rearrangement of water (8 ns) is correlated with the surface area “occupied” by the molecule and with the motion of the peptide side chains close to the surface. 3.2.1. Specific Interactions. Contacts between the filaments and the surface are identified on the basis of atom-surface
J. Phys. Chem. C, Vol. 111, No. 45, 2007 16969
Figure 12. Para (c,d) and perp (a,b) surface coverage after equilibration (a,c) and at the end of the simulations (b,d). Only water oxygens are displayed and are colored in red. Surface oxygens are colored in gray, and titanium atoms are colored in yellow. RAD16II filaments have been removed to evidence the solvation of the surface atoms in the region occupied by the peptide macrostructures.
Figure 13. Diagram showing the number of water molecules in the region between the filament and the TiO2 surface as a function of the simulation time.
distances, considering values in the range 1.8-4.2 Å to be acceptable. The initial contacts of para involve 21 residues distributed almost equally among all of the strands. The highest number of contacts, which is equal to four, is found for L6, L7, and L8; L1, L2, L3 ,and L5 have two contacts, whereas only one direct interaction is observed for the L4 strand. Ninetyfive percent of these interactions involve Arg residues, and the
16970 J. Phys. Chem. C, Vol. 111, No. 45, 2007 average distance is equal to 2.8 ( 0.2 Å. Only one bidentate attachment (Asp 3848) is noticed, and the distance between carboxyl oxygens and titanium atoms is equal to 2.03 Å, in agreement with earlier results.27-29 During the course of the simulations direct contacts are broken and re-formed, but due to strong competition with the water molecules, which enter the region between the peptides and the surface, the number of these interactions decreases (reduction ≈ 38%). Although some direct contacts with the TiO2 layer are lost, a network of hydrogen bonds between the charged side-chain groups and the water molecules adsorbed onto the surface or hydrogen bonded to the surface oxygen atoms is established. However, this pattern of H bonding fluctuates dynamically, as expected, given the fluctuating nature of the environment. Further examination of the sampled conformations reveals that 13 persistent H bonds (pjHb ≈ 92%) from the -NH2 of the side chains of Arg to surface oxygens and a strong bidentate coordination of Asp 3848 are maintained unaltered during the whole run. As far as perp is concerned, its four initial direct contacts with the surface are not distributed uniformly throughout the length of the L1 chain. Three of them involve residues close to each other near the C-terminus region of the strand (Arg 3612, Asp 3614, and Asp 3616), whereas the N-terminus portion of L1 interacts with the surface through the Arg 3604 side chain. Average distances of the -NH2 groups of Arg and the carboxyl oxygens of Asp 3614 from the surface are equal to 3.3 ( 0.2 and 3.7 ( 0.1 Å, respectively, while Asp 3616 is nearer to the layer, having one of its carboxyl oxygens at about 1.98 Å form the TiO2 interface. During the simulation all of the initial contacts except one (Asp 3616) are lost. However, examination of the trajectory reveals that the filament is persistently bound to the surface through the monodentate coordination of Asp 3616, which is located at the extremity of L1, and the interactions between the filament and the surface are mediated by the adsorbed water molecules. Fluctuating H bonds from Arg and Asp side chains with adsorbed water molecules are also observed. 3.2.2. Motion of the Bilayers. The main collective degrees of freedom necessary to describe the dynamics of the filaments on the surface has been derived from the eigenvectors of the diagonalized C-matrix (defined in section 2.3), which has been constructed without removal of overall rotational and translational motions of the filaments. Figure 14 shows projections of the backbone trajectory on the first four eigenvectors of the covariance matrix, for para and perp, ordered by the size of the corresponding eigenvalues. The trends of the curves, the percentage of total variance explained by each essential movement and the visual inspection of system animations along each selected vectors, suggest that the first mode can effectively represent the most relevant movements of the filaments with respect to the surface (low-frequency modes), being responsible for 53% and 56% of the overall motion of para and perp, respectively. The plots also suggest that the translational and rotational motions of the two systems are quite different and span different time scales. For para, the first principal component exhibits a slow decrease and reaches a stable state when time goes up to ≈9 ns. Motion along this mode has a long relaxation time, which is comparable to the sampling window of 10 ns. On the contrary, a faster relaxation is observed for perp, where mode 1 displays damped oscillations around zero. However, to have a clearer picture of the motion, the projected structures of the first essential mode, for each model, are superimposed and displayed in Figures 15 and 16.
Monti
Figure 14. Time evolution of the backbone trajectory projections along the first four eigenvectors of the covariance matrix of para (a) and perp (b) representing motion with respect to the surface. The corresponding percentages of total variance explained by each essential movement are: 53%, 12%, 5%, and 3% for para and 56%, 18%, 5%, and 4% for perp.
As expected, in the case of perp, the first two modes are observed to contribute the most to a rigid rotation of the bilayer with respect to the surface. Interestingly, mode 1 (Figure 16) is a combined rotation of the filament about the basal strand adsorbed onto the surface and about the in-plane axis passing through Asp 3606 perpendicular to the strand orientation. Mode 2 contributes almost totally to the rotation of the filament about the in-plane axis passing through Asp 3606 perpendicular to the strand orientation, and it accounts for 18% of the overall motion. Modes 3, 4, and 5 have been examined, but none contributes more than 5% to the overall motion in both para and perp simulations, and thus they are not reported. In the case of para, mode 1 (Figure 15) has contributions in rotations about the three different axes. The first one seems to be located along the backbone of the L8 chain, the second one appears to be positioned in the L plane and perpendicular to the strands’ orientation, and the third one seems to be almost perpendicular to the TiO2 surface and appears to pass through one of the residues in the range Ala 3803-Ala 3805. Visual inspection of the motion suggests that the rotation of the bilayer about the L8 strand is the prevailing movement and is responsible for the detachment of strands L1-L4 from the surface thus resulting in the loss of four anchoring points. Mode 2 contributes most to the rotation about the axis perpendicular to the TiO2 surface, and it accounts for 12% of the overall motion. However, due to the presence of the greater number of contacts, between the amino acid side chains and the surface atoms with respect to perp, all of the movements of para have smaller amplitudes.
RAD16II β-Sheet Filaments onto Titanium Dioxide
J. Phys. Chem. C, Vol. 111, No. 45, 2007 16971
Figure 15. Two different views of the first essential mode of para, representing the motion with respect to the surface. Internal deformations have not been filtered. Structures were generated by projecting the entire MD trajectory onto the first eigenvector. Minimum, maximum, and intermediate structures are visualized to evidence the movements of the strands. Only backbone atoms have been considered. Color codes: titanium, gray; oxygen, red; carbon, green; nitrogen, blue. The coordinates can be found in the Supporting Information section.
Figure 16. First essential mode of perp, representing the motion with respect to the surface. Structures were generated by projecting the entire MD trajectory onto the first eigenvector. Minimum (cyan), maximum (orange), and intermediate (black) structures are visualized to evidence the movements of the strands. Only backbone atoms have been considered. Color codes: titanium, gray; oxygen, red; carbon, green; nitrogen, blue. The coordinates can be found in the Supporting Information section.
The major differences observed are in the filament flexibility and water orientational dynamics. These differences are probably due to the enhanced rigidity of the filament when placed onto the TiO2 surface in parallel orientation and to the presence of the layer interface potential influencing the side chain motion and perhaps increasing border effects. Despite the dissimilar behavior of the two systems, some important features are well preserved, such as the filament geometry in the central region, β-sheet secondary structure, and the bilayer packing. Combining all of the above results, it appears that the filament motion and
solvation are highly sensitive to the local microenvironment. For example, the presence of water inside the bilayer may, to a large degree, relies on the dynamic fluctuations of the local microenvironment, which perturbs the stability of the macrostructure in the border regions of the filament. Results suggest that the adsorption strength and the structure preservation are also highly sensitive to the hydration state. It is expected that the introduction of further strands would strongly influence the interaction of the peptide with the surface and possibly act to stabilize the peptide filament on the TiO2 layer.
16972 J. Phys. Chem. C, Vol. 111, No. 45, 2007 4. Conclusions These MD simulations have provided some insights into the conformational dynamics of a model of RAD16II self-assembled β-sheet filament when in contact with a TiO2 layer on a 10 ns time scale. These results suggest that bilayers made of eight-strand β-sheets are sufficient to provide stable template for further elongation of the fibrillar ordered peptide aggregate and addition of new strands could stabilize highly ordered configurations, in agreement with both experimental and theoretical observations. The comparison between two different arrangements on the surface has allowed to pay particular attention to the motion and conformational flexibility of the structures. In particular, the stability of both adsorbed configurations has provided further evidence that this small model may be a reasonable approximation to the true structure of RAD16II filaments, and consistent with experimental data, the simulations have indicated clearly that peptide matrices containing alternating positively and negatively charged residues can strongly adsorb onto titanium-based materials, engaging direct and indirect interactions with the surface atoms through their amino acid side chains. According to MD results, the strength of adsorption is strictly connected with the number and type of peptide-surface contacts, which is maximum when the filament lay flat on the TiO2 layer. The tendency to adopt such an arrangement has been evidenced, analyzing the filaments motion on the surface. Indeed, the higher mobility of perp with respect to para and its propensity to rotate and orientate its more hydrophilic faces toward the TiO2 layer suggest that the adhesion pattern on hydrophilic surfaces is determined by the increase of favorable driving electrostatic interactions involving side chain groups. These findings are in agreement with AFM observations and surface tension measurements reported by Chen. et al.11 on EAK16II fibrillar assemblies, where they evidenced the key role played by the charge distribution in determining the nanostructure characteristics and the surface adhesion properties. However, these simulations remain an approximation to the true properties of the bilayer systems, and 10 ns is still a relatively short period of time. It would be very interesting to extend both the simulation time and the filament size to explore in more detail the stability of adsorbed RAD16II bilayers, to give a more realistic description of the border effects and water penetration, and to understand how these perturbations influence the filament conformation and its adsorption onto TiO2 surfaces. Acknowledgment. The author thanks Professor Wonmuk Hwang for generously providing the coordinates of four similarly stable RAD16II β-sheet filaments. The author is grateful to David A. Case for granting permission to use the AMBER 9 package. Most of the calculations reported in this paper were carried out on the resources of the CINECA Supercomputer Center (Progetti Supercalcolo 2007). Supporting Information Available: Animations of para and perp systems along the first eigenvector. This material is available free of charge via the Internet at http://pubs. acs.org. References and Notes (1) Diebold, U. Surf. Sci. Rep. 2003, 48, 53-229. (2) Puleo, D. A.; Nanci, A. Biomaterials 1999, 20, 2311-2321. (3) Puleo, D. A.; Kissling, R. A.; Sheu, M. S. Biomaterials 2002, 23, 2079-2087.
Monti (4) Matsumura, K.; Hyon, S. H.; Nakajima, N.; Peng, C. Y.; Iwata, H.; Tsutsumi, S. J. Biomed. Mat. Res. 2002, 60, 309-315. (5) Schliephake, H.; Scharnweber, D.; Dard, M.; Rossler, S.; Sewing, A.; Meyer, J.; Hoogestraat, D. Clin. Oral Impl. Res. 2002, 13, 312-319. (6) Goransson, A.; Jansson, E.; Tengvall, P.; Wennerberg, A. Biomaterials 2003, 24, 197-205. (7) Holmes, T. C. Trends Biotechnol. 2002, 20, 16-21. (8) Zhang, S.; Altman, M. React. Funct. Polym. 1999, 41, 91102. (9) Zhang, S.; Holmes, T. C.; DiPersio, C. M.; Hynes, R. O.; Su, X.; Rich, A. Biomaterials 1995, 16, 1385-1393. (10) Zhang, S. Nat. Biotechnol. 2003, 21, 1171-1178. (11) Hong, Y. S.; Legge, R. L.; Zhang, S. G.; Chen, P. Biomacromolecules 2003, 4, 1433-1442. (12) Fung, S. Y.; Keyes, C.; Duhamel, J.; Chen, P. Biophys. J. 2003, 85, 537-548. (13) Jun, S.; Hong, Y.; Imamura, H.; Ha, B. Y.; Bechhoefer, J.; Chen, P. Biophys. J. 2004, 87, 1249-1259. (14) Keyes-Baig, C.; Duhamel, J.; Fung, S. Y.; Bezaire, J.; Chen, P. J. Am. Chem. Soc. 2004, 126, 7522-7532. (15) Davis, M. E.; Motion, J. P. M.; Narmoneva, D. A.; Takahashi, T.; Hakuno, D.; Kamm, R. D.; Zhang, S. G.; Lee, R. T. Circulation 2005, 111, 442-450. (16) Holmes, T. C.; de Lacalle, S.; Su, X.; Liu, G. S.; Rich, A.; Zhang, S. G. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 6728-6733. (17) Yokoi, H.; Kinoshita, T.; Zhang, S. G. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 8414-8419. (18) Ellis-Behnke, R. G.; Liang, Y. X.; You, S. W.; Tay, D. K. C.; Zhang, S. G.; So, K. F.; Schneider, G. E. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 5054-5059. (19) Park, J.; Kahng, B.; Kamm, R. D.; Hwang, W. Biophys. J. 2006, 90, 2510-2524. (20) Schmidt, M. Arch. Orthop. Trauma. Surg. 2001, 121, 403410. (21) Bandura, V.; Sykes, D. J.; Shapovalov, V.; Truong, T. N.; Kubicki, J. D.; Evarestov, R. A. J. Phys. Chem. B. 2004, 108, 7844-7853. (22) Barnard, A. S.; Zapol, P.; Curtiss, L. A. Surf. Sci. 2005, 582, 173188. (23) Henderson, M. A. Surf. Sci. Rep. 2002, 46, 1-308. (24) Polzonetti, G.; Battocchio, C.; Iucci, G.; Dettin, M.; Gambaretto, R.; Di Bello, C.; Carravetta, V. Mater. Sci. Eng., C 2006, 26, 929934. (25) Bandura, A. V.; Kubicki, J. D. J. Phys. Chem. B 2003, 107, 1107211081. (26) Predota, M.; Bandura, A. V.; Cummings, P. T.; Kubicki, J. D.; Wesolowski, D. J.; Chialvo, A. A.; Machesky, M. L. J. Phys. Chem. B 2004, 108, 12049-12060. (27) Carravetta, V.; Monti, S. J. Phys. Chem. B 2006, 110, 61606169. (28) Monti, S. J. Phys. Chem. C 2007, 111, 6086-6094. (29) Monti, S.; Carravetta, V.; Zhang, W.; Yang, J. J. Phys. Chem. C 2007, 111, 7765-7771. (30) Koppen, S.; Langel, W. Surf. Sci. 2006, 600, 2040-2050. (31) Koppen, S.; Langel, W. Surf. Sci. 2006, 600, 2040-2050. (32) Koppen, S.; Ohler, B.; Langel, W. Z. Phys. Chem. 2007, 221, 320. (33) Hwang, W.; Marini, D. M.; Kamm, R. D.; Zhang, S. J. Chem. Phys. 2003, 118, 389-397. (34) Tsui, V.; Case, D. A. Biopolimers 2001, 56, 275-291. (35) Onufriev, A.; Bashford, D.; Case, D. A. Proteins 2004, 55, 383394. (36) Brooks III, C. L. B.; Karplus, M.; Pettitt, B. M. Proteins: A Theoretical PerspectiVe of Dynamics, Structure, and Thermodynamics; John Wiley: New York, 1988. (37) Catlow, C. R. A. In Computer Modelling of Fluids, Polymers, and Solids; Catlow, C. R. A., Parker, S. C., Allen, M. P., Eds.; NATO ASI Series, Mathematical and Physical Sciences 293; Kluwer Academic: Dordrecht, 1990. (38) Murgich, J.; Rodriguez, J. M.; Aray, Y. Energy Fuels 1996, 10, 68-76. (39) Polzonetti, G.; Battocchio, C.; Dettin, M.; Gambaretto, R.; Di Bello, C.; Carravetta, V.; Monti, S.; Iucci, G. Mater. Sci. Eng., C, in press. (40) Roddick-Lanzillotta, A. D.; McQuillan, A. J. J. Colloid Interface Sci. 1999, 217, 194-202. (41) Roddick-Lanzillotta, A. D.; McQuillan, A. J. J. Colloid Interface Sci. 2000, 227, 48-54. (42) Jorgensen, W. L. J. Am. Chem. Soc. 1981, 103, 335-350. (43) Case, D. A. et al. AMBER 9; University of California: San Francisco, 2006. (44) Andrea, T. A.; Swope, C. W.; Andersen, H. C. J. Chem. Phys. 1983, 79, 4576-4584.
RAD16II β-Sheet Filaments onto Titanium Dioxide (45) Andersen, H. C. J. Chem. Phys. 1980, 72, 2384-2393. (46) Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. J. Comput. Phys. 1977, 23, 327-341. (47) Kabsch, W.; Sander, C. Biopolymers 1983, 22, 2577-2637. (48) Forrest, L. R.; Tieleman, D. P.; Sansom, M. S. P. Biophys. J. 1999, 76, 1886-1896. (49) Amadei, A.; Linssen, A. B. M.; Berendsen, H. J. C. Proteins 1993, 17, 412-425. (50) de Groot, B. L.; Hayward, S.; van Aalten, D. M. F.; Amadei, A.; Berendsen, H. J. C. Proteins 1998, 31, 116-127.
J. Phys. Chem. C, Vol. 111, No. 45, 2007 16973 (51) Wlodek, S. T.; Clark, T. W.; Scott, L. R.; McCammon, J. A. J. Am. Chem. Soc. 1997, 119, 9513-9522. (52) Orozco, M.; Perez, A.; Noy, A.; Luque, F. J. Chem. Soc. ReV. 2003, 32, 350-364. (53) Meyer, T.; Ferrer-Costa, C.; Perez, A.; Rueda, M.; Bidon-Chanal, A.; Luque, F. J.; Laughton, C. A.; Orozco, M. J. Chem. Theory Comput. 2006, 2, 251-258. (54) Creveld, L. D.; Amadei, A.; van Schaik, R. C.; Pepermans, H. A. M.; de Vlieg, J.; Berendsen, H. J. C. Proteins 1998, 33, 253-264. (55) de Groot, B. L.; van Aalten, D. M. F.; Amadei, A.; Berendsen, H. J. C. Biophys. J. 1996, 71, 1707-1713.
