Computational Prediction of Circular Dichroism Spectra and

Mar 14, 2014 - University of Bremen, D-28359 Bremen, Germany. •S Supporting Information. ABSTRACT: Circular dichroism (CD) spectroscopy is one of th...
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Computational Prediction of Circular Dichroism Spectra and Quantification of Helicity Loss upon Peptide Adsorption on Silica Robert H. Meißner,† Julian Schneider,‡ Peter Schiffels,† and Lucio Colombi Ciacchi*,§ †

Fraunhofer Institute for Manufacturing Technology and Advanced Materials IFAM, D-28359 Bremen, Germany Department Chemie, Technische Universität München, Lichtenbergstrasse 4, 85748 Garching, Germany § Hybrid Materials Interfaces Group, Faculty of Production Engineering and Bremen Center for Computational Materials Science, University of Bremen, D-28359 Bremen, Germany ‡

S Supporting Information *

ABSTRACT: Circular dichroism (CD) spectroscopy is one of the few experimental techniques sensitive to the structural changes that peptides undergo when they adsorb on inorganic material surfaces, a problem of deep significance in medicine, biotechnology, and materials science. Although the theoretical calculation of the CD spectrum of a molecule in a given conformation can be routinely performed, the inverse problem of extracting atomistic structural details from a measured spectrum is not uniquely determined. Especially complicated is the case of oligopeptides, whose folding/unfolding energy landscapes are often very broad and shallow. This means that the CD spectra measured for either dissolved or adsorbed peptides arise from a multitude of different structures, each present with a probability dictated by their relative free-energy variations, according to Boltzmann statistics. Here we present a modeling method based on replica exchange with solute tempering in combination with metadynamics, which allows us to predict both the helicity loss of a small peptide upon interaction with silica colloids in water and to compute the full CD spectra of the adsorbed and dissolved states, in quantitative agreement with experimental measurements. In our method, the CD ellipticity Θ for any given wavelength λ is calculated as an external collective variable by means of reweighting the biased trajectory obtained using the peptide−SiO2 surface distance and the structural helicity as two independent, internal collective variables. Our results also provide support for the often-employed hypothesis that the Θ intensity at λ = 222 nm is linearly correlated with the peptides’ fractional helicity.

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forces between polypeptides and materials.8 The free energy of adsorption can also be estimated via AFM force spectroscopy through the analysis of the adhesion force as a function of the loading rate9 or by means of other indirect methods such as quartz crystal microbalance with dissipation (QCM-D)10 and SPR spectroscopy.11 When the adsorption does not involve the formation or disruption of chemical bonds, classical molecular dynamics modeling has led to impressive results concerning the prediction of adhesion forces5 and free energies12 of adsorbed polypeptides. A large amount of progress toward consistency between simulation results and experiments has recently been achieved by developing and applying advanced simulation techniques, such as replica exchange methods, to explore the vast conformational space of polypeptides interacting with solid surfaces.12−14 Complementing the experimental results by providing atomistic resolution, these simulations have thus significantly advanced our understanding of biomolecular adsorption.15,16 More difficult to quantify, however, are the conformational changes associated with polypeptide adsorption. Circular dichroism (CD) spectroscopy is sensitive to changes in the secondary structure of polypeptides17 and can be applied

INTRODUCTION Proteins and oligopeptides are known to undergo a partial change in their conformations upon interaction with solid material surfaces, leading to either unfolding or folding of their native structures in solution. This phenomenon governs important biological processes such as blood clotting and amyloid fiber formation1 and determines the behavior of inorganic/organic interfaces during either biomineralization or, inversely, material recognition by short peptides.2 Preventing conformational changes in protein-based drugs (such as antibodies) induced by adsorption/desorption on the walls of storage containers, typically SiO2-coated glass vials, is of paramount importance for pharmaceutical industries,3 given the costs and risks associated with the lowered or modified activity of drug molecules in different folding states. Moreover, the tethering of active enzymes to solid supports, which has emerged as a promising route toward the biotechnological fabrication of environmentally sustainable catalysts, may lead to uncontrolled structural change and a reduction in enzymatic activity.4 There is thus a large amount of interest in understanding the interactions between polypeptides and inorganic surfaces at an atomistic level, a difficult task both for current experimental and modeling techniques.5,6 Experimentally, atomic force microscopy (AFM) methods have been used in rare cases for high-resolution imaging7 of adsorbed peptides and more often to measure the adhesion © 2014 American Chemical Society

Received: January 23, 2014 Revised: March 12, 2014 Published: March 14, 2014 3487

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to peptide/nanoparticle suspensions, at least in the case of colloids in the size range of a few tens of nanometers, for which light adsorption and scattering do not interfere with the CD signal of the biomolecules.18,19 Although modeling tools have been developed to compute the CD spectrum associated with a single biomolecular structure,20 knowledge of a measured spectrum is in most cases insufficient to determine the unknown biomolecule’s folding state uniquely. This is due to the fact that in a solution of polypeptides, either dissolved or adsorbed to a colloid surface, all possible structures (microscopic conformational states) are present at the same time, with individual probabilities determined by their relative variations of free energy through the Boltzmann distribution. In other words, particularly for small oligopeptides that exhibit broad and shallow folding/unfolding energy landscapes, one should consider two ensembles of structures in the macroscopic dissolved and adsorbed states, each associated with its distinct CD spectrum. In this work, we present a method to predict the structure and compute the CD spectra of oligopeptides either dissolved in water or adsorbed on material surfaces. It is based on molecular dynamics (MD) and exploits replica exchange with solute tempering (REST) combined with metadynamics (metaD) techniques.21 The method is applied to study an αhelical oligopeptide (4DAR5, as defined in refs 18 and 19) adsorbing on an anionic amorphous silica (SiO2) and produces results in quantitative agreement with experiments. Choosing the distance z between the peptide’s center of mass and the SiO2 surface and the peptide’s structural helicity H (as defined by the torsional angles of its backbone) as two independent internal collective variables, we perform a complete exploration of the energy landscape associated with the helical folding and unfolding during the adsorption process. Statistical analysis of the converged free-energy landscape provides average fractional helicities in the adsorbed and desorbed states, matching the experimental estimates previously obtained by 1H NMR and CD spectroscopy.18,19 Moreover, the CD ellipticity intensity Θ computed with the DichroCalc software20,22 for each microscopic state is treated as an external collective variable and is calculated by means of a reweighting procedure applied to the biased metadynamics trajectory in (z, H) space.23 This allows us to predict the full CD spectra associated with the adsorbed and desorbed states, in particular, the ellipticity value at a wavelength of 222 nm, Θ222. We show that Θ222 is linearly correlated with the peptide helicity, providing support for this often-employed hypothesis.24 Our results demonstrate how CD spectroscopy measurements can be put on equal footing with atomistic MD modeling, introducing a viable way to link experimental spectra with the number of secondary structure elements beyond the simple case of a single α-helix. In fact, we believe that discrepancies between measured and theoretically computed CD spectra24 arise not from limitations in the theoretical formalism (or its software implementation) underlying CD spectroscopy but from a lack of statistical averaging over the correct ensemble of biomolecular structures.

Figure 1. Snapshots from an unbiased equilibrium MD simulation of the 4DAR5 peptide adsorbing at an anionic SiO2 surface at pH 9.0 and 300 K. Left: t = 0 ns; right: t = 23 ns. The pictures were generated with VMD.44

18, the N and C termini were capped by an acetyl group (COCH3) and an amino cap (NH2), respectively. To model the colloidal SiO2 surface, the 22-Å-thick, hydroxylated amorphous silica slab obtained from ref 25 was used as a starting point. On each side of the slab, we deprotonated five OH groups, corresponding to a surface charge density of −0.087 C/m2 or to a Si−O− group density of 0.55 nm−2. This is very close to the value of 0.54 nm−2 estimated in ref 18 by means of titration experiments for SiO2 colloids dissolved at pH 9.0. Finally, Na+ counterions were added to the solvent to ensure charge neutrality of the combined silica, peptide, and water system. Although the periodicity of the SiO2 surface slab dictated the size of the simulation cell in the xy plane (60.5 × 60.5 Å2), its height was manually adjusted to 68.7 Å in order to reproduce the correct TIP3P water density (0.998 g/cm3) far away from the surface slab26 (Figure 2). Periodic boundary conditions were imposed in all directions.

Figure 2. Density profiles of the water, surface, and peptide in the interfacial system used as a starting configuration for further simulations (e.g., Figure 1).

Definition of the Force Field. The peptide−peptide, peptide−water, and water−water interactions were described with the all-atom AMBER03 force field27,28 combined with the TIP3P water model.29 For the interactions of the peptide and the water with the SiO2 surface, we employed the parameter set recently published in ref 30, which treats with particular care the point charges and the Lennard-Jones parameters of deprotonated silanol groups of the surface. Lorentz−Berthelot combination rules were employed to construct the LennardJones interaction potentials between the atomic species. The Si−Si and Si−O interactions within the surface slab were described by a modification of the Morse potential originally

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MODELS AND SIMULATION DETAILS Construction of the Model System. The 4DAR5 peptide model was constructed initially in an ideal α-helical conformation using the LEaP package of the Amber suite of programs and relaxed in bulk water in a 2 ns MD simulation at 300 K (Figure 1). According to the experimental protocol in ref 3488

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Figure 3. (a) Positions of the center of mass of arginine (ARG) and aspartic acid (ASP) residues of the 4DAR5 peptide during an unbiased MD simulation (Figure 1). (b) Evolution of the peptide’s position of the center of mass, zssd (green), and helicity, as defined in eq 3 (blue), during the same simulation.

Information Chapter S2). 105 theoretical CD ellipticities were calculated with the DichroCalc web interface20 augmented with the semiempirical parameter set as given by ref 22 on the basis of individual snapshots (microscopic conformational states) of the simulation trajectories. Calculation of the Gibbs Dividing Surface. The height zGDS of the Gibbs dividing surface (GDS) (which sets the zero of the collective variable corresponding to the position of the peptide center of mass in our RestMetaD simulations) was chosen so as to ensure that the surface excess of water molecules Γ is zero at this point.42 This corresponds to fulfilling the condition

introduced in ref 31. Although the original potential employs a charge equilibration scheme (Qeq32), we chose to employ fixed point charges with values as derived in ref 30 to ensure compatibility with the AMBER03 and TIP3P force fields and considerably reduce the computational effort. To account for the differences caused by the modified electrostatics with fixed charges, the Si−Si parameter needed to be retuned. The employed parameter set is reported in Supporting Information Table S1. Structural properties for bulk amorphous SiO2 computed with our modified potential are in good agreement both with experimental data and simulations employing the original force field (Supporting Information Chapter S1). Simulation Parameters. All of our MD simulations were carried out with the LAMMPS simulation software33 extended with the PLUMED metadynamics package34 to compute freeenergy landscapes. Additionally, we implemented in LAMMPS the Hamiltonian replica-exchange35 option, as required for replica exchange with solute tempering (REST).36 A time step of 2.0 fs was chosen in all simulations, constraining the bond lengths of all bonds involving hydrogen atoms to their equilibrium values via the SHAKE algorithm.37 A PPPM Ewald solver38,39 was used to calculate long-range Coulomb interactions. Pair interactions of the SiO2 Morse potential and the real-space part of the Coulomb interactions were truncated at 8.0 Å. As a consequence of the difficulties in applying a barostat to an interfacial system,40 all simulations were carried out within the NVT ensemble at 300 K by employing a Nosé− Hoover thermostat. To compute free-energy landscapes, adaptive bias potentials were added during the course of the MD runs according to the metadynamics scheme41 in the well-tempered ensemble23 using a bias factor of 10. Gaussian hills with a height of 0.7 kcal/mol were added every 0.5 ps. Values of the full width at halfmaximum of the Gaussians were chosen to be 0.1 and 0.3 Å for the helicity and distance collective variables, respectively. REST simulations were carried out as described in ref 12 using seven replicas of the system with potential energy rescaling factors corresponding to solute temperatures of 300, 325, 350, 375, 400, 425, and 450 K. Because of the artificial nature of the rescaled potential energy landscapes in the auxiliary hightemperature replicas, only the results of the system at 300 K were considered for the evaluation. Exchanges between neighboring replicas were attempted every 0.5 ps, which resulted in a uniform occupancies of all replicas (Supporting

Γ=

∫0

z GDS

ρwat (z) dz −

∫z

z max

bulk ρwat − ρwat (z) dz = 0

GDS

(1)

where ρwat(z) represents the water density at position z and 2 ρbulk wat = 0.998 g/cm is the TIP3P water density in liquid bulk. zmax was chosen to be one-third of the total length of the simulation box in the z direction to ensure that zGDS is not affected by the periodically repeated surface slab or by the density contribution of the peptide in the middle of the simulation box (Figure 2). Using this method, we obtain zGDL = 11.0 Å with respect to our arbitrary choice of the atomic coordinates in the simulation box. Reweighting a RESTmetaD Simulation. If convergence is achieved, the well-tempered metadynamics method allows us to obtain exact free-energy profiles associated with the biased collective variables s.23 However, the probability distributions of other degrees of freedom f are distorted if calculated directly from the simulation trajectory. Because the magnitude of the bias potential continuously increases with time in the welltempered metadynamics simulation, simple reweighting to recover the unbiased distributions of external collective variables is not possible in a straightforward manner. A suitable reweighting scheme for this situation has been devised in ref 43. The unbiased distribution Pu( f) can be calculated numerically from the temporal evolution of the biased histogram Nt(s, f) according to P u(f ) =

3489

∑s e βVbias(s , t )Nt(s , f ) ∑s , f e βVbias(s , t )Nt(s , f )

(2)

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Figure 4. (a) Free-energy surface G(H, zssd) of the 4DAR5 peptide in contact with an anionic silica surface. Temporal evolution of free-energy profiles (b) G(z), (c) G(Ha), and (d) G(Hs). Temporal convergence of (e) the free energy of adsorption ΔGads, (f) the mean adsorbed helicity ⟨Ha⟩, and (g) the mean dissolved helicity ⟨Hs⟩. The isolines in plot (a) are separated by 2.1 kcal/mol.

processes of adsorption and unfolding using RESTmetaD, as introduced in refs 12 and 21. RESTmetaD Simulations. We sample over all peptide conformations using two independent internal collective variables, namely, the distance of the peptide from the surface (or the solute−surface distance, zssd) and its structural helicity H. The structural helicity is defined as the number of residues i adopting a (partially) helical conformation on the basis of their backbone dihedral angles Φi and Ψi and the correlation with the values of the adjacent residues i ± 1:

To employ this algorithm for externally calculated collective variables, we included the CD ellipticity values, obtained via DichroCalc from the simulation snapshots, in the standard metadynamics output file, which subsequently could be postprocessed by the reweighting tool provided within the PLUMED package.

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RESULTS Unbiased MD Simulations. α-Helical peptide 4DAR5 (with sequence DDDDAAAAARRRR) has been the object of detailed experimental studies concerning its partial unfolding after adsorption on an anionic SiO2 colloidal surface using a combination of CD and 1H NMR spectroscopy.18,19 In the dissolved state, the folded α-helical structure is stabilized by the central poly-A sequence despite the net dipole arising from the positively charged arginine side and the negatively charged aspartic acid side. The helical loss caused by the adsorption on the negatively charged SiO2 surface at pH 9 has been quantified to amount to about 40%.18 We can reproduce this behavior qualitatively in unbiased molecular dynamics simulations. We start with the fully folded peptide dissolved in water placed 1.2 nm above a deprotonated amorphous silica surface model25 (Figure 1a) with a surface charge density corresponding to that determined experimentally. The height of the unit cell is adjusted to reproduce the correct TIP3P water density far away from the surface slab (Figure 2). Electrostatic interactions drive the spontaneous adsorption of the peptide through the poly-R side within a few nanoseconds in MD simulation at constant room temperature (Figures 1b and 3). After the initial adsorption, partial unfolding is observed until the simulation is stopped after 23 ns. In Figure 3, zssd is defined as the difference between the positions of the peptide’s (or residue’s) center of mass and the Gibbs’ dividing surface along the z direction normal to the surface: zssd = zcom − zGDS. We note that equilibrium unbiased MD simulations are able to capture only a few microstates of the dissolved and adsorbed states (unless performed over a time scale comparable to the experimental one, which is presently impossible). Therefore, from the unbiased MD trajectory we cannot quantify the adsorption behavior in terms of any experimental observable. To overcome this limitation, we carry out in the next section a thorough exploration of the phase space associated with the

N−1 i+1

H=

∑ ∏ i=2 j=i−1

1 [cos(Φj − Φ̅ i) + 1][cos(Ψj − Ψ̅i) + 1] 4 (3)

In this definition, Φ̅ i and Ψ̅ i represent the target values of residue i associated with an α-helical conformation (−68.75 and −45.0° for all residues, respectively). The (zssd, H) free-energy surface at 300 K calculated from a well-tempered RESTmetaD simulation using seven independent peptide replicas and lasting 1.5 μs per replica is shown in Figure 4a. At first glance, the free-energy landscape at large zssd reveals a shallow minimum in the region of helicity between 6 and 8. A major adsorption channel leads toward the surface, which retains the same helicity down to zssd = 7.5 Å, where a shallow local energy minimum is located. Further surface approach is possible only upon unfolding of the peptide (i.e., a decrease in helicity), eventually leading to a more stable minimum at zssd = 2.5 Å and H between 1 and 3. Along the adsorption channel, the energy barriers encountered are on the order of only 5 kcal/mol, which explains why in the unbiased MD simulation in Figure 1 adsorption and partial unfolding took place spontaneously at room temperature. Individual profiles of the free energy along either zssd or H are obtained upon integration of 2D surface G(H, zssd) over the other variable45 1 ⎡ G(q1) = − ln⎢ β ⎢⎣

∫q

q2,max

2,min

⎤ e−βG(q1, q2) dq2 ⎥ ⎥⎦

(4)

where q1,2 = (H, zssd). 3490

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The temporal evolution of G(zssd) during the RESTmetaD simulation is shown in Figure 4b, where the color code represents the simulation time (red to blue from 0 to 1500 ns). The shape of the free-energy profile at the end of the simulation allows us to define an adsorbed state (a) for distances shorter than zssd,0 = 16.5 Å and a dissolved state (s) for larger distances, where the free energy is flat, indicating that the peptide does not experience any surface interaction and behaves as in bulk solution. The average probability densities of finding the peptide in the adsorbed and dissolved states are ρa =

zssd,0

1 − zssd,min

1 ρs = zssd,max − zssd,0

∫z ∫z

zssd,0

e

−βG(zssd)

fH =

dz

e

−βG(zssd)

holds if N is sufficiently large (see below). Here, Θ∞ 222 = −40 000 deg cm2 dmol−1 is the theoretical ellipticity intensity of an infinitely long, ideal α-helix, and k = 2.5 is a constant that accounts for non-hydrogen-bonded amide carbonyl groups at the peptide termini.24 We have tested the validity of the empirical formula above by 20 calculating Θhel for ideally 222 using the DichroCalc software helical peptides with sequence (n−1)DARn (i.e., Dn−1AnRn−1) and comparing the results with the values predicted by eq 9. As shown in Figure 5a, the DichroCalc values start deviating from the empirical prediction for N < 7. Therefore, for the case of

ssd,0

dz (5)

(6)

We note that this definition of the free-energy difference refers to the molecular concentrations, in bulk solution as well as in close proximity to the surface, as the respective standard states. This differs from the commonly used experimental standard states of solution concentration and surface coverage. While the RESTmetaD simulation evolves, ΔGads varies as shown in Figure 4e. Note that even after 1.5 μs convergence is reached only within an error of about 2 kcal/mol at a value of 12 kcal/ mol. This indicates that the sampling orthogonal to the collective variables, though greatly enhanced by the REST technique, becomes a limiting factor here. A more detailed discussion of the convergence of the 2D free-energy surface G(H, zssd) can be found in Supporting Information Chapters S2 and S3. We can also compute profiles of the free energy as a function of H in both the adsorbed and dissolved states Ga(H) and Gs(H) (Figure 4c,d, respectively), using eq 4 with appropriate integral limits. At this point, we are able to calculate the expectation value of the peptide’s helicity in either state from Hmax min

(9)

47

⎛ρ⎞ ΔGads = −kBT ln⎜⎜ a ⎟⎟ ⎝ ρs ⎠

∫H

(8)

⎛ k⎞ hel ⎜ ⎟ + 100T Θ222 (N ) = Θ∞ 222 1 − ⎝ N⎠

The free energy of adsorption ΔGads can now be computed as13

⟨Ha,s⟩ = Za,s−1

hel Θ222 (N ) − Θcoil 222

where Θ222 is the CD ellipticity intensity measured at 222 nm, Θhel 222(N) is the intensity of an N-mer peptide with ideal αhelical structure, and Θcoil 222 is the intensity of a random-coil polypeptide. When Θ is expressed in the usual units of deg cm2 dmol−1, it can be assumed, following ref 46, that Θcoil 222 ≈ 250. It is also agreed that the empirical formula

ssd,min

zssd,max

Θ222 − Θcoil 222

e−βGa,s(H )·H dH

(7)

where Za and Zs represent the respective partition functions. The evolutions of ⟨Ha⟩ and ⟨Hs⟩ during the RESTmetaD simulation are shown in Figure 4f,g. The final values of 2.0 and 7.0 appear to be reasonably well converged, with an error of about 0.5 in both cases. To check the convergence in the dissolved state, we have performed an additional RESTmetaD simulation of the peptide in pure bulk water, obtaining a final value of ⟨Hs⟩ = 6.5, which is within the previously identified error (Supporting Information Figure S8). Calculation of Circular Dichroism Spectra. In this section, we exploit the knowledge of a vast number of conformational microstates in the (zssd, H) phase space together with their associated free energy gained through the RESTmetaD simulation to predict the experimentally measurable CD spectra of the 4DAR5 peptide in both the adsorbed and dissolved states. In the CD literature, the fractional helicity of a short peptide containing N amino acids is defined as

Figure 5. (a) CD ellipticities of ideally helical (n−1)DARn peptides containing N = 3n−2 amino acids computed either with DichroCalc (dashed line) or through the empirical formula in eq 9 (solid line). (b) Relationship between Θ222 and the fractional helicity f H = H/11.0. Each cross is calculated with DichroCalc from 105 snapshots of RESTmetaD trajectories for 4DAR5 in bulk water and adsorbed on SiO2. The straight line is drawn according to eq 8 with Θ∞ 222 = −40 000 2 −1 deg cm2 dmol−1 and Θcoil 222 = 250 deg cm dmol . (c) ⟨Θ222⟩ values computed from reweighted RESTmetaD trajectories plotted vs the corresponding theoretically predicted ⟨f H⟩ values (crosses) and compared to experimental estimates at various pH values18,19 (circles). Blue represents adsorbed; green, dissolved; red, random coil; and black, fully helical states. 3491

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the 4DAR5 peptide considered here, either the actual DichroCalc values or empirical eq 9 can be used without distinction to obtain the reference Θhel 222(N) value corresponding to a fully folded helical conformation. When the above assumptions are used, from a measurement of Θ222 for a peptide in solution it is possible to compute the fractional helicity f H from eq 8. It is commonly taken for granted that f H is directly related to the structural helicity of the peptide, as previously suggested from combined AFM and CD experiments.48 However, the contribution of the uncoiled part of the peptides to the CD signal is still debated,46 albeit theoretical CD spectra for fully helical peptides yield reliable results over the whole range of UV wavelengths.24 We can put this hypothesis on a firm basis by computing, for all of the microscopic states sampled during our RESTmetaD simulation of the 4DAR5 peptide in bulk water, their structural helicity H via eq 3 and their Θ222 intensity values via the DichroCalc software. Indeed, as shown in Figure 5b, the two values are to a very good extent linearly correlated. Note, however, the large spreading of the values of Θ222 at a given f H (on the order of 104 deg cm2 dmol−1) or by the values of f H at a given Θ222 (on the order of 0.4). This highlights the fact that evincing a molecular structure from a CD measurement is a nonuniquely defined problem, even for the simplest case of a partially helical and partially random-coiled peptide. The connection between molecular modeling and measured CD spectra should instead be made by taking into account the whole ensemble of structures defining a macroscopic state of the biomolecule, as we shall demonstrate in the following section. In the previous section we have obtained the 2D free-energy surface G(zssd, H) consisting of two ensembles of conformational microstates arbitrarily separated into adsorbed and dissolved from the plane at zssd,0 = 16.5 Å. The dependence of the free energy on any other unbiased collective variable (i.e., different from zssd or H) can be obtained by appropriately reweighting the biased RESTmetaD trajectory, as put forward in ref 43. In particular, we consider here as an additional collective variable the CD ellipticity at a given wavelength, Θλ, which can be calculated with the DichroCalc software for each microstate visited during the RESTmetaD simulation. As a result of the reweighting, we obtain a 2D free-energy profile G(Θλ, zssd) (Figure 6), out of which we can integrate 1D profiles Ga(Θλ) and Gs(Θλ) relative to the adsorbed and dissolved states, respectively (eq 4). The expectation value of Θλ in both states can be now computed from

−1 ⟨Θa,s λ ⟩ = Z

Θmax

∫Θ

min

e−βGa,s(Θλ)·Θλ dΘλ

(10)

In summary, for each macroscopic state a and s, we can predict computationally without empirical assumptions (other than the generic force field and DichroCalc parameter sets) both the average helicity ⟨Ha,s⟩ and the average ellipticity, for instance, at 222 nm, ⟨Θa,s 222⟩. This allows us to perform a comparison between the experimental results obtained by CD spectroscopy for the 4DAR5 peptide regarding both Θ222 and the fractional helicity, which we can compute as ⟨f H⟩ = ⟨H⟩/(N−2), where N is 13 in our case. In Figure 5c, we present with open circles the experimentally measured values18,19 of Θ222 versus the corresponding estimated experimental fractional helicities f H (eq 8) for the following cases: (i) an ideal random coil, for which it is assumed experimentally that Θ222 = 250 deg cm2 dmol−1 and f H = 0;47 (ii) an ideal α-helix ( f H = 1), for which eq 9 is assumed to hold; (iii) the dissolved peptide in solutions at pH 7.0 and 7.5; and (iv) the peptide adsorbed on the SiO2 colloid surface in solutions at pH 8.5 and 9.0. In the same figure, computational predictions of ⟨Θ222⟩ are indicated with crosses for the corresponding cases: (i and ii) the peptide in bulk water constraining H to either 0 or 11; (iii) the peptide dissolved in pure bulk water (thus formally at pH 7.0); and (iv) the peptide in the adsorbed state on a SiO2 surface with net charge roughly corresponding to the experimental charge density at pH 9.0. We note first that all values, both experimental and theoretical, lie on a straight line, again demonstrating the validity of the linear assumption in eq 8. Also notable is the strikingly good agreement between the experimental measurements and the computational predictions of Θ222 and f H for both the adsorbed and dissolved states of the 4DAR5 peptide. The slight deviation for the adsorbed case (which lies between the experimental values at pH 9.0 and 8.5) is most probably due to either the imprecise distribution of net charges on our surface model with respect to the experimental reality or the inaccuracy of our force field in the case of interfacial interactions. For an estimation of the error in the calculation of Θ resulting from sampling issues, see Supporting Information Chapter S4. Finally, in Figure 7 we report the full CD spectra in the range of wavelengths extending from 200 to 250 nm for the dissolved and adsorbed peptide (eq 7), along with available experimental data at 222 nm.18,19

Figure 7. Full CD spectra of the 4DAR5 peptide in solution and adsorbed on anionic SiO2 colloids predicted by our free-energy-based method in comparison to the corresponding experimental measurement.

Figure 6. Reweighted free-energy surface as a function of the unbiased Θ222 signal and zssd from a RESTmetaD simulation. The isolines are separated by 1.6 kcal/mol. 3492

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CONCLUSIONS

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ASSOCIATED CONTENT

S Supporting Information *

We have presented a computational method capable of predicting the changes in conformation of small peptides after adsorption to solid surfaces, in quantitative agreement with experimental studies. The method relies on the calculation of the free-energy landscape in the phase space defined by the peptide conformation and its distance from the surface using RESTmetaD simulations. In our case, to reach an acceptable convergence of the free-energy landscape, we have found it necessary to employ seven system replicas and carry out a biased molecular dynamics simulation lasting 1.5 μs, which represents a very heavy computational effort even for fixedcharge force fields. The application of the method is thus presently confined to short oligopeptides or possibly to small proteins with relatively rigid, globular structures. A main advantage of the method is that, after an appropriate reweighting procedure, it is possible to map the free-energy landscape using the CD ellipticity intensity as an external collective variable. As a direct result, the precise calculation of CD spectra for any macroscopic state of the peptide (here, dissolved in water solution or adsorbed on the SiO2 surface) becomes possible. The agreement between computational predictions and experimental measurements obtained here for the case of the 4DAR5 peptide in solution and adsorbed on SiO2 colloids is remarkably good (Figure 5c). As an interesting additional result, we have shown that the often-employed linear assumption between peptide helicity and CD ellipticity is correct, although precisely defined only in the case of macroscopic conformational states. In the case of single structures (i.e., of microscopic states), a linear correlation could also be found (Figure 5b), but it is not uniquely defined because of the large variances associated with the different contributions of various secondary structure elements. This means that a large number of individual structures with largely different structural helicities are associated with the same CD ellipticity value. Vice versa, different structures with the same structural helicity can lead to different CD ellipticities. In other words, the fractional helicity of a peptide in solution, inferred from CD measurements via eq 8, must be interpreted as an average value of a distribution of structures, each with its own, and different, structural helicity. Furthermore, deconvolution algorithms for CD spectra yielding information about the number of secondary structure elements are widely available.49 However, they do not allow precise insights into the conformational states in which the system lies. We believe that shifting the focus from individual secondary structure elements to ensembles (clusters) of structures giving rise to the same CD ellipticity may help in the interpretation of biomolecular CD spectra. The development of cluster-analysis methods based on similar CD spectral shapes over selected wavelength ranges rather than on similar (secondary) structural elements is conceivable. In particular, this may contribute to the development of empirical relationships between CD ellipticity and other (averaged) secondary structure elements, which is especially useful in understanding the complex atomic-scale conformational changes of biomolecules associated with the processes of surface adsorption and biomineralization.

Validation of the modified Demiralp potential for SiO2. Exchange probability in the RestMetaD simulations. Convergence of the free energy in the RestMetaD simulations. Error estimation for the computed CD ellipticity. 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]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are thankful to Carole Perry (Nottingham University, U.K.) and Tiffany Walsh (Deakin University, Australia) for fruitful discussions and suggestions. This work has been supported by EU-FP7-NMP grant 229205 ADGLASS and by the Deutsche Forschungsgemeinschaft through grant CI 144/2 (Emmy Noether Program).

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REFERENCES

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