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Feb 8, 2013 - *E-mail: [email protected], Tel. ... For the met-enkephalin pentapeptide at a water–graphite interface, we were able to obtai...
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Free Energy of Adsorption for a Peptide at a Liquid/Solid Interface via Nonequilibrium Molecular Dynamics Milan Mijajlovic, Matthew J. Penna, and Mark J. Biggs* School of Chemical Engineering, The University of Adelaide, Adelaide, South Australia, Australia 5005 S Supporting Information *

ABSTRACT: Protein adsorption is of wide interest including in many technological applications such as tissue engineering, nanotechnology, biosensors, drug delivery, and vaccine production among others. Understanding the fundamentals of such technologies and their design would be greatly aided by an ability to efficiently predict the conformation of an adsorbed protein and its free energy of adsorption. In the study reported here, we show that this is possible when data obtained from nonequilibrium thermodynamic integration (NETI) combined with steered molecular dynamics (SMD) is subject to bootstrapping. For the met-enkephalin pentapeptide at a water−graphite interface, we were able to obtain accurate predictions for the location of the adsorbed peptide and its free energy of adsorption from around 50 and 80 SMD simulations, respectively. It was also shown that adsorption in this system is both energetically and entropically driven. The free energy of adsorption was also decomposed into that associated with formation of the cavity in the water near the graphite surface sufficient to accommodate the adsorbed peptide and that associated with insertion of the peptide into this cavity. This decomposition reveals that the former is modestly energetically and entropically unfavorable, whereas the latter is the opposite in both regards to a much greater extent.

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INTRODUCTION Interaction of proteins and peptides with solid surfaces is a critical phenomenon in a wide range of natural and technological processes. Adsorption of blood-bound proteins is the first step in the immune response to medical implants.1,2 Nanoparticles introduced into the body are similarly coated by a protein layer3 that strongly influences their fate and effect − negative or otherwise − on the body. Learning from this, researchers are now functionalizing the surfaces of nanoparticles so as to better target vaccines and image-enhancing nanoparticles while eliminating their toxicity.4 Attachment of cells to tissue scaffolds in the production of artificial organs is also mediated through proteins.5,6 Many emerging bio- and nanotechnology applications also rely on interaction of peptides with inorganic surfaces including nanoparticle production via biomineralization,7,8 self-assembly of nanomachines,9 and biosensors.10,11 Identification of novel peptides, materials, and solvents for these and other applications in principle requires access to the free energy of protein adsorption. A small number of experimental methods exist for determining this free energy. Some (e.g., refs 12,13) have estimated the adsorption free energy of amino acids and peptides through Langmuir isotherm fits to experimental adsorption data. Others (e.g., refs 14,15) have used surface plasmon resonance (SPR) to derive the adsorption free energy. More recently, detachment of adsorbed proteins using atomic force microscopy (AFM) has also been utilized.15,16 These experimental approaches are, however, not without their problems. Analysis based on the Langmuir © 2013 American Chemical Society

isotherm and SPR is restricted to very weakly adsorbing systems because of the need for adsorption and desorption events to occur, whereas AFM is particularly challenging and time-consuming. In addition to these limitations, the experimental approach suffers from two major issues in the peptide, material, and solvent design contexts. The first is its limited ability to provide fundamental insight into the adsorption mechanism at a molecular level as indicated by the plethora of adsorption models and the debate that still surrounds them,2 whereas the second is the need for peptide/surface/solvent systems of interest to physically exist and be experimentally accessible − these issues combined limit the scope for innovation in the design process. Molecular simulation in principle opens up the possibility of addressing both these issues and the other limitations raised above for the experimental approach. The first molecular simulation-based efforts aimed at estimating the free energy of protein adsorption were either simplified (e.g., including only electrostatic interactions17) or semiempirical approaches based on combining computationally calculated adsorption enthalpies with entropy effects derived from experimental data for smaller molecules.18−20 More rigorous attempts to estimate the free energy of protein adsorption using molecular simulation was initiated by the application of the probability ratio (PR) method21 in molecular dynamics (MD) studies of the adsorption of peptides on SAMs22 and Received: December 4, 2012 Revised: January 17, 2013 Published: February 8, 2013 2919

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crystal surfaces.23−25 The PR method in its original incarnation was shown to suffer from insufficient sampling of peptide conformational space as well as unreliable estimates of the probability density distribution for regions not immediately adjacent to the surface.22 Latour et al.26−28 have addressed these problems using a combination of a biasing force and extended sampling with the replica-exchange molecular dynamics (REMD).29 Other techniques for the enhanced sampling of the peptide conformational space, such as the temperature-accelerated dynamics,30 have also been utilized in combination with the PR method.31 An alternative to the PR approach is thermodynamic integration (TI),32 in which the adsorption free energy is represented as the potential of mean force (PMF) that acts on the solute molecule. One of the most widespread techniques in evaluating the PMF of protein adsorption is the potential of mean constraint force method in which the center-of-mass (CoM) of the solute is restrained with a harmonic potential to a range of distances from the solid surface and the mean force on the peptide is assumed to be of the equal magnitude and opposite sign of the average restraining force obtained from an MD simulation. Whereas this approach can in principle be applied to any solute, it has so far been applied mostly to adsorption of amino acids or their side chain analogues.25,33−36 This is unsurprising considering the difficulties faced in sufficiently sampling the conformational space of proteins and peptides, especially in the vicinity of a solid surface where their conformational freedom is severely restricted. Another TI-based approach that has been used in calculating adsorption free energy profiles is the adaptive biasing force (ABF) method,37 which has been applied to a 12-mer peptide at the hydroxyapatite surface,38 although the relatively short simulation time of 500 ps means sampling is unlikely to be adequate and, consequently, the free energy estimate unreliable. The PR and TI methods are equilibrium MD methods that assume the rate of change of the reaction coordinate (peptidesurface distance) is low enough that the rest of the system is able to equilibrate with the slowly moving peptide, which is, in turn, able to fully explore its accessible conformational space. This requirement does, however, bring a computational cost. The alternative approach of combining nonequilibrium thermodynamic integration (NETI)39,40 with steered molecular dynamics (SMD)41 offers the potential to reduce the computational cost because it avoids the need for a lengthy equilibration process, which is a particularly challenging issue for proteins due to their complex conformational space. The NETI/SMD approach has been successfully applied to protein folding,42 protein−protein interactions43 and protein−ligand binding.44 Whereas it has also been used to estimate the free energy of adsorption of amino acids on inorganic surfaces,45,46 it has never been applied to peptide or protein adsorption. One objective of the study reported here is to demonstrate that the NETI/SMD approach can yield the free energy of adsorption of a peptide at a liquid/solid interface without resort to expensive enhanced conformational sampling methods such as REMD. A second, related, objective of the study reported here is to demonstrate that NETI/SMD provides a basis for elucidating entropic (and enthalpic) contributions to the peptide adsorption process.

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exp(− β ΔA12 ) = ⟨exp(− βW12)⟩

(1)

where β is the reciprocal of the product of the Boltzmann constant and temperature, W12 is the external work required to move the system between the two states, and the angle brackets represent an ensemble average from a number of independent simulations. When calculating the free energy of peptide adsorption using eq 1, the initial state of the system (state 1) is the one in which the peptide is adsorbed at the solid surface. SMD41 is then used to pull the peptide normally away from the surface toward and, finally, into the bulk, as shown in Figure 1.

Figure 1. Visual representation of the system studied here. The metenkephalin molecule and the topmost layer of the graphite surface are shown. The rest of the system (remaining planes of graphite and all water molecules) is omitted for clarity. The normal distance between the center of mass of the peptide and the graphite surface is the reaction coordinate. The insert represents a model free energy profile (i.e., the change in the free energy of the system as a function of the normal peptide−surface distance).

This allows the evaluation of the change in free energy along the normal to the solid surface (the reaction coordinate) as illustrated in the insert of Figure 1. The steps involved in this process are: (1) A number of configurations in which the peptide is adsorbed at the fluid/solid interface are created. (2) For each of these configurations: (a) The peptide is gradually pulled away from the surface using SMD, which involves the center of mass (CoM) of the peptide being restrained using a spring with a stiffness, k, to a coincident reference point that moves normal to the surface at a constant speed, vz. (b) At periodic intervals during the pulling procedure, δt, the work needed to pull the peptide from its initial adsorbed state to that point in time, nδt, is calculated using42

W (nδt ) = − kvz

∫0

t

dt ′[z CoM(t ′) − z CoM(0) − vzt ′]

(2) where zCoM(0) and zCoM(t′) are the position of the peptide CoM in the initial state and at time t′ ≤ nδt respectively. The set of n = 1,...,N pulling work values evaluated as the peptide moves from the adsorbed state along the reaction coordinate to the bulk phase constitutes the pulling work profile. (3) The pulling work profiles evaluated for all the configurations are used in eq 1 to yield the free energy change profile along the reaction coordinate.

METHODS

Theoretical Background. The basis of the NETI method of generating the change in free energy between two states, ΔA12, is the Jarzynski’s equality39,40 2920

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A−B−A configuration.52 The system consisted of a total of 16 468 atoms: 75 in the met-enkephalin molecule, 4180 carbon atoms in the graphite surface, and the remainder in 4071 water molecules. Simulation Details. All MD simulations required for this study were run using version 2.8 of NAMD.53 The simulations were conducted in the NVT ensemble at 300 K using a Langevin thermostat54 with the damping coefficient of 1 ps−1 applied to all heavy atoms. All bonds to hydrogen atoms in the peptide and water were made rigid using the Shake algorithm.55 A time step of 1 fs was used. To validate the choice of the NVT ensemble, water density in the bulk phase was measured in a 1 Å thick water layer at a distance of 20 Å from the solid surface and found to be 989 ± 2 kg/m3 comparing favorably with the value of 982 kg/m3 obtained from NPT ensemble simulations of the bulk phase at 25 °C and 1 atm using the same water model.49 Pulling work profiles (c.f., theoretical background of the Methods section) were obtained from 86 independent SMD simulations. The initial adsorbed states for these SMD simulations were obtained by running 100 unrestrained MD simulations, each of which lasted 15 ns, in the NVT ensemble at 300 K starting from the met-enkephalin molecule in the bulk phase and letting it spontaneously adsorb to the graphite surface. The peptide in these simulations was initially deemed to be adsorbed once the normal distance between its CoM and the solid surface remained below 5 Å for more than 5 ns and fluctuations in the root-mean-square deviation (RMSD) of the peptide Cα atoms were characterized by a standard deviation less than 1 Å. Ten of the initial simulations did not reach this state by the end of the 15 ns simulations and were hence discarded, whereas a further four of the initial adsorbed states were also later discarded when the subsequent SMD simulations showed the peptide was initially poorly adsorbed if at all. The SMD simulations were conducted by attaching the CoM of the adsorbed met-enkephalin molecule to a coincident reference point using a harmonic spring with a force constant of 100 kcal/(mol-Å2) and then pulling this reference point normally away from the surface toward the bulk phase with the velocity of 0.04 m/s. Simulations of

This approach has been validated here by applying it to an adsorbed water molecule and then comparing it to the free energy profile obtained from the probability ratio method. As Figure S1 of the Supporting Information shows, the comparison is excellent. Model Details. We have evaluated the free energy change profile for the adsorption of met-enkephalin at the water−graphite interface. Met-enkephalin is an opioid pentapeptide with the primary amino acid sequence Tyr-Gly-Gly-Phe-Met (YGGFM in single letter code). Because of its relatively small size, met-enkephalin has received significant attention in the molecular modeling community. Its high conformational flexibility due to the presence of two consecutive glycine residues in the middle of the sequence also makes it a good model system for so-called soft proteins47 (i.e., those that can undergo substantial structural change upon their adsorption at the solid surface). We have represented met-enkephalin in its physiologically relevant zwitterionic form, that is with NH3+ and COO− groups at N- and C-terms, respectively. The choice of graphite as the substrate was motivated primarily by the emerging importance of ordered carbonaceous surfaces, such as graphene and carbon-nanotubes, in a range of fields from nanoelectronics to biomedical applications. The Amber94 potential energy model48 was used to calculate the interatomic forces involving peptide atoms. Electrostatic and van der Waals 1−4 interactions are scaled down by a factor of 1.2 and 2 respectively as is the standard practice in Amber94.48 Water was represented using the TIP3P model.49 The interaction between the carbon atoms of the graphite and both the water and peptide atoms was modeled using a 12−6 Lennard-Jones (LJ) potential with the potential parameters of the aromatic carbon atoms in the Amber94 force field. Nonbonded interactions were cut off at 12 Å with a switching function applied between 10 and 12 Å for a smooth transition.50 Long-range electrostatic interactions beyond this cutoff distance were evaluated using the particle-mesh Ewald (PME) method.51 A rectangular volume of dimensions 46.73 × 46.86 × 73.4 Å3 with periodic boundary conditions was modeled. A rigid graphite basal plane surface was included at the base of this volume in the form of five parallel layers of hexagonally distributed carbon atoms in the

Figure 2. Representative snapshots of adsorbed (upper row) and bulk phase (lower row) met-enkephalin conformations in SMD pulling simulations (see text for details of how these representative conformations were selected). Adsorbed structures are shown in top-down and side (inset) views. Surrounding water molecules, as well as the graphite surface for bulk structures, are omitted for clarity. 2921

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35 ns were necessary to fully desorb the met-enkephalin molecule at this pulling velocity.

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RESULTS AND DISCUSSION Steered Molecular Dynamics. Exemplar snapshots of fully adsorbed and fully desorbed structures are shown in Figure 2. The three adsorbed structures are selected by first creating clusters of similar conformations (i.e., those conformations whose RMSD of Cα atoms was within 1 Å from a randomly selected reference structure) using an initial set of 86 adsorbed molecules and then taking the reference structure from each of the three most populated clusters. These three clusters account for 78% of all fully adsorbed molecules. For the representative structures in the bulk phase, a similar procedure was applied, but using the final snapshots of all 86 pulling simulations as the basis for clustering analysis. In this case, the three conformations shown in Figure 2 represent clusters that account for 73% of all bulk phase conformations. Unsurprisingly, a distinct difference between the two groups of structures is obvious from Figure 2. Adsorbed molecules are stabilized by favorable van der Waals interactions between hydrophobic parts of side chains and the hydrophobic graphite surface. Exposing the side chains to the surface is the driving force for flattening of the molecule observed in the figure. In the absence of the solid surface, hydrophobic interactions are promoted by intramolecular contacts, the consequence of which are more compact structures seen in the bulk phase conformations in Figure 2. Part a of Figure S2 of the Supporting Information demonstrates that, for a typical simulation, the variation of the distance between the peptide CoM and the graphite surface increases in a linear manner with time demonstrating that the CoM closely follows the moving reference point to which it is attached. This allows the use of the stiff spring approximation in calculation of the free energy profile.42 Experimentation with a smaller spring constant of 20 kcal/(mol-Å2) led to the peptide CoM lagging behind the reference point motion in the initial stage of the simulation due to the strong attractive force between the surface and the peptide (part b of Figure S2 of the Supporting Information) indicating this spring constant value is too low. The work profile (c.f. eq 2) derived from a typical SMD simulation is shown in Figure 3 with the fully desorbed phase, which is defined when the peptide CoM is beyond the point where the change in the pulling work becomes negligible, being used as the reference state; this reference state is used because it is common to all the SMD simulations, unlike the initial adsorbed state where the CoM position varies from between 3.8 to 4.9 Å (see Figure S3 of the Supporting Information for the distribution of these positions for the 86 simulations). This figure indicates that, in the case of the exemplar simulation, the peptide can be considered fully desorbed once its CoM is around 14 Å from the graphite surface. Free Energy Profile. Figure 4 shows the free energy profile obtained using the pulling work profiles of the 86 simulations in eq 1. The minimum in this profile, z(86) min = 4.3 ± 0.3 Å is an estimate of the distance at which the peptide CoM will sit from the surface when it is adsorbed, while the free energy associated with this minimum, ΔA(86) min = −26.3 ± 0.4 kcal/mol, is an estimate of the free energy of adsorption; the standard errors associated with these points have been evaluated using a bootstrapping technique,56 which we will return to in more detail below.

Figure 3. Pulling work profile for an exemplar SMD simulation with the desorbed peptide being the reference state (i.e., ΔA = 0).

Figure 4. Free energy profile (solid line), ΔA, average pulling work profile (dashed line), ⟨W⟩, fluctuations in the pulling work profile (dotted line), δW2, and energy dissipation profile (dash-dotted line), Wdiss, for met-enkephalin adsorption at the water−graphite interface. The position of the peptide CoM when adsorbed and the associated free energy of adsorption is indicated by the point ( × ) as determined from a bootstrap analysis.56.

The fluctuation in the pulling work, δW2 = ⟨(W − ⟨W⟩)2⟩, which is also shown in Figure 4, provides a basis for assessing the reliability of the free energy profile.42 For z ≥ z(86) min the work fluctuations are less than 5RT, which is within the acceptable range.39,42 For z ≥ z(86) min ; however, the work fluctuations rapidly increase beyond what is considered acceptable making the free energy estimates at these distances less reliable. This rapid increase in fluctuations close to the solid surface simply reflects the fact that few simulations started in this region (Figure S3 of the Supporting Information). If of interest, this problem could be addressed by undertaking SMD simulations that drag the peptide from the adsorbed state toward the surface. Fluctuations in the pulling work are a consequence of the energy dissipation.58 If the pulling was undertaken infinitely slowly, the process would be reversible and the required work equal in magnitude to the free energy. For finite pulling rates as occurs here, however, some energy is dissipated due to 2922

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hysteresis effects of barrier crossing under tension.58 For normally distributed pulling work values such as those in our simulations (Figure S4 of the Supporting Information), this dissipation can be estimated by Wdiss = ⟨W⟩ − ΔA, which is also shown in Figure 4. The small difference between this profile and that derived directly from the work fluctuations in the simulations, δW2, for z ≥ z(86) min confirms the goodness of the free energy profile down to the minimum. Free Energy of Peptide Adsorption and Location of Adsorbed Peptide above the Surface. Clearly the free energy profile derived from eq 1 will become more representative of the actual profile as the number of pulling work profiles used in the average increases. This is clearly indicated in Figure 5, which shows the variation of the minimum free

and standard deviation on the basis of limited data. Part a of Figure 5 shows that the estimated location of the minimum free energy above the surface decreases with increasing number of SMD simulations until it largely becomes invariant at around nS = 60 simulations, which can be equated to the predicted location of the CoM of met-enkephalin when adsorbed at the water−graphite interface, zads = 4.20 ± 0.03 Å.59 Use of results from more than this number of SMD simulations in conjunction with bootstrapping slowly reduces the standard error associated with the position of the free energy minimum, with it decreasing to ±0.02 Å at nS = 86, the maximum number of SMD simulations undertaken in the study reported here. Part b of Figure 5 indicates that the value of the free energy minimum obtained from application of bootstrapping to SMDderived data increases with the number of SMD simulations, nS, toward an upper limit, although this limit is not reached in the study reported here. This increasing trend is a consequence of the energy dissipation associated with nonequilibrium pulling being proportionately more dominant for low numbers of simulations. The asymptotic value could clearly be obtained by undertaking more simulations. However, it can also be derived by realizing that, for large numbers of SMD simulations (nS > 60 here), the bootstrapped free energy minimum values scale according to ΔAmin = ΔA(∞) min + k/nS (k = constant) as shown in part c of Figure 5. Extrapolating this plot to the vertical axis yields the nS → ∞ limit, ΔA(∞) min , which is equal to the predicted free energy of adsorption (i.e., ΔA(∞) min = ΔAads). Doing this here using the bootstrapped free energy minimum data points located in the range of 78 ≤ nS ≤ 86 gives a free energy of adsorption for met-enkephalin at the water−graphite interface of ΔAads = −24.99 ± 0.02 kcal/mol.59 Required Computational Effort to Estimate Free Energy of Adsorption and Peptide Location. The required accuracy of the predicted free energy of adsorption and adsorbed peptide location above the surface varies with intent. For example, rough estimates (e.g., ε = 0.5%) may be sufficient for initial screening of peptides (or surfaces or solvents) for a particular application, whereas refining results obtained from such screening will require a higher degree of accuracy (e.g., ε = 0.05%). Using the results in Figure 5, Table 1 shows Table 1. Estimates of the Computational Requirements for Prediction of the Position of the Adsorbed Peptide above the Surface and the Associated Free Energy of Adsorption Number of SMD Simulations (And Net Time) Required to Predict with the Indicated Relative Errora relative error, ε (%)

zads

ΔAads

0.5 0.1 0.05 0.01

26 (1.3 μs of time) 52 (2.6 μs of time) 57 (2.85 μs of time) 85 (4.25 μs of time)

64 (3.2 μs of time) 84 (4.2 μs of time) 85 (4.25 μs of time) b

The error is evaluated relative to the zads and ΔAads values obtained with ns = 86 SMD simulations. bInsufficient information to make a determination here. a

Figure 5. (a) Distance of peptide CoM above the graphite surface as a function of the number of SMD simulations used in the bootstrapping. (b) Free energy minimum as a function of the number of SMD simulations used in the bootstrapping. (c) Transformation of the data in (b) to obtain the infinite-simulation limit.

estimates of the number of simulations required to predict with varying degrees of accuracy the CoM position of a pentapeptide when adsorbed and its associated free energy of adsorption. This table shows, perhaps unsurprisingly, that more effort is required to evaluate the free energy of adsorption compared to the CoM of the adsorbed peptide, with the effort being

energy and its location above the surface as a function of the number of SMD simulations, nS, where the values and the associated standard errors are evaluated using bootstrapping,56,57 which is a statistical method for estimating a mean 2923

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arising in large part from the partial desolvation of the charged terminals of the zwitterionic peptide (the intrapeptide energy change is very modest at around −2.4 kcal/mol). The gain in entropy reflects the greater flexibility the peptide gains once the surface disrupts its native state,1 something that is not unexpected given met-enkephalin may be considered a soft peptide.47 This is consistent with Figure 2, which demonstrates that met-enkephalin molecules in the bulk phase are characterized with a tightly packed globular structure, whereas conformations of the adsorbed molecule appear to be considerably more disordered.

150−250% greater depending on the level of accuracy demanded. It also suggests that the computational effort required will be of the order of 1−10 μs of time depending on the purpose. Decomposition of the Free Energy of Adsorption. The free energy is, of course, composed of a potential energy component and an entropic component respectively (3)

ΔA = ΔU − T ΔS

As the change in potential energy in the adsorption process, ΔUads, is readily accessible from the molecular simulations undertaken in the process of evaluating the free energy of adsorption, ΔAads, the entropic contribution to the adsorption process, TΔSads, can also in principle be evaluated using eq 3. Although this in general leads to some uncertainty in the evaluated entropic contribution because it involves subtraction of two numbers of similar magnitude, we have done this here to build at least a semiquantitative understanding of the driving forces for the adsorption process. This analysis, the result of which is shown in the first row of Table 2, indicates that both

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CONCLUSIONS We have reported the first-ever use of nonequilibrium thermodynamic integration (NETI)39,40 combined with steered molecular dynamics (SMD)41 to determine the variation of the free energy of a peptide as it moves normally away from a liquid/solid interface into the bulk liquid phase. We have also shown that application of bootstrapping56 to this data is able to yield accurate estimates of the adsorption free energy and the position of the center-of-mass of the adsorbed peptide above the surface. For the system considered here, the 5-residue met-enkephalin peptide at the water−graphite interface, around 50 SMD simulations were required to obtain an estimate of the position of the adsorbed peptide above the interface within 0.1% relative error. Obtaining the free energy of adsorption to a similar level of accuracy required extrapolation of bootstrapped results obtained from around 80 SMD simulations using ΔAmin = ΔAads + k/nS (k = constant), which was observed to hold here for nS > 60 SMD simulations. Finally, we have demonstrated that the NETI/SMD approach allows elucidation of the changes in the overall entropy (positive here) as well as those associated with the main processes involved: formation of the water cavity adjacent to the surface (decrease in entropy) and the peptide insertion into that cavity (increase in entropy). This work indicates that the SMD/NETI approach is a viable tool for estimating with reasonable computational resource the free energy of adsorption for peptide adsorption at a liquid/solid interface and for elucidating the driving forces associated with this adsorption.

Table 2. Decomposition of the Free Energy of Adsorptiona process

ΔU (kcal/mol)

overall water cavity formation peptide insertion

−17.4 ± 0.3 5.5 ± 1.4 (#) −22.9 ± 1.1

ΔA (kcal/mol)

TΔS (kcal/mol)

−24.99 ± 0.02 7.6 ± 0.3 (*) 7.3 ± 0.1 −1.8 ± 1.5 (*) −32.3 ± 0.1 (#) 9.4 ± 1.2 (*)

a

The values calculated from use of eq 3 using input from the molecular simulations undertaken as part of the determination of the free energy of adsorption are indicated by (*). The values obtained from ΔUads = ΣΔUi and ΔAads = ΣΔAi are indicated by (#).

potential energy and entropy drive the adsorption process, with the former being slightly greater than twice as important as the latter. The molecular simulations undertaken here also allow elucidation of the changes in the potential and free energies and entropy for the two major processes involved in the peptide adsorption. The free energy change that accompanies the formation of the cavity in the water near the graphite surface into which the adsorbed peptide goes, which is shown in the second line of Table 2, can be obtained from the simulations by convoluting the free energy profile for water molecule sorption (part a of Figure S1 of the Supporting Information) with the number of water molecules displaced by the adsorbed peptide as a function of distance from the graphite surface (the water displacement profile, Figure S5 of the Supporting Information). The latter has been calculated as the difference in the number of water molecules as a function of the distance from the graphite surface when the peptide is in the bulk phase (i.e., when its CoM is above 15 Å) and when it is fully adsorbed (i.e., when its CoM is found below 4.9 Å). Unsurprisingly, this cavity formation process is somewhat unfavorable as the adsorbed water molecules lose the attractive potential energy arising from their interaction with the graphite surface as well as some entropy due to a small increase in the number of hydrogen bonds that the water molecules experience in the bulk phase (Figure S6 of the Supporting Information). Table 2 also shows that peptide adsorption occurs primarily because the peptide gains both potential energy and entropy when it adsorbs. The former primarily arises from the peptidesurface interaction (−51 kcal/mol) offset by a substantial reduction in the water−peptide interaction energy (+30.8 kcal/mol)

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ASSOCIATED CONTENT

S Supporting Information *

Validation of the NETI approach and water restructuring at the graphite interface during the peptide adsorption. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], Tel.: +61-8-8303-6317, Fax: +61-8-8303-4373. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest. 2924

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ACKNOWLEDGMENTS M.J.P. gratefully acknowledges receipt of an Australian Postgraduate Award (APA) from The University of Adelaide. M.M. is similarly grateful for the postdoctoral fellowship funding from The University of Adelaide. The supercomputing resources for this work were provided by eResearchSA and both the NCI National Facility at the Australian National University and the iVEC Facility at Murdoch University under the National Merit Allocation Scheme.

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of free energy profiles obtained by applying bootstrapping56,57 to work profiles akin to that in Figure 4 for nS = 2,...,86.

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