Conformational Dependence of the Circular Dichroism Spectra of

Article pubs.acs.org/JPCB

Conformational Dependence of the Circular Dichroism Spectra of Single Amino Acids from Plane-Waves-Based Density Functional Theory Calculations E. Molteni,† G. Onida,† and G. Tiana*,†,‡ †

Department of Physics, Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy INFN, sezione di Milano, via Celoria 16, 20133 Milano, Italy

‡

S Supporting Information *

ABSTRACT: We study the conformational dependence of circular dichroism (CD) spectra of amino acid molecules by means of an efficient ab initio DFT approach which is free from the typical gauge invariance issues arising with the use of localized basis sets and/or real-space grids. We analyze the dependence of the chiroptical spectra on the backbone dihedrals in the specific case of alanine and consider the role of side chain degrees of freedom at the examples of leucine, phenylalanine, and serine, whose side chains have different physicochemical properties. The results allow one to identify the most diagnostic regions of the CD spectra and to critically compare the conformations which match the experimental CD data with conformations extracted from the rotamer library. The inclusion of a solvation shell of explicit water molecules and its effect on the CD spectrum are analyzed at the example of alanine.

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INTRODUCTION A detailed knowledge of the conformational properties of single amino acids is the starting point to understand the kinetic and thermodynamic behavior of proteins. For instance, the determination of the numerical parameters of most force fields used in the simulation of protein folding, protein−protein association, and in silico drug design is based on experimental data for the constituent amino acids.1 The use of discrete rotamers to describe the side chain of amino acids is another way of employing single-amino-acid properties to understand those of the whole protein molecule.2 This reductionist approach arises straightforwardly from the fact that the finegrained properties of small molecules, like amino acids, are easier to investigate than those of complex proteins. Besides their importance as building blocks of the living matter, amino acids can be also used in the synthesis of nanomaterials.3 Amino acids in solution, noncovalently bound to other molecules, can behave as self-assembling units4 and can be used to functionalize other nanoparticles5,6 or to construct multifunctional hydrogelators.7 In spite of their small size, amino acids and amino-acid-based small molecules display a remarkable conformational freedom, which in turn contributes to determine the mesoscopic properties of the assembly.3 One of the techniques widely employed to study the conformational properties of proteins and other aminoacidic molecules is circular dichroism (CD), which relies on the optical activity of amino acids arising from their molecular chirality and is rather simple to apply experimentally. Typically, they are studied in the far-UV range, between 190 nm, below which the absorption of the water solvent typically obscures the dichroism, and 260 nm. While in the case of proteins and large © 2015 American Chemical Society

peptides the mapping between conformational properties of the molecule and experimental circular dichroism spectrum, although essentially based on phenomenology, is quite well established,8 this is not the case for smaller molecules. Amino acids, although much smaller than proteins, display a rich conformational variability: for instance, even a simple amino acid such as alanine has been shown to display a high number of low-energy conformers in the gas phase,9,10,13 but these were experimentally characterized only in terms of rotational spectra.13 Therefore, it would be useful to develop an efficient strategy to obtain conformational information from the CD spectrum of small systems, ranging from small peptides down to single amino acids. The first step in such a strategy is to be able to assess to which extent the CD spectrum of amino acids depends on their conformational properties. In the past decade the calculation of chiroptical properties of amino acids within a quantum-mechanical approach has been the subject of several works.14−26 The more general framework of chiroptical calculations for small molecules27−29 has been recently reviewed, e.g., in refs 30 and 31. Both CD and optical rotatory dispersion (ORD) spectra can be obtained from the electronic magneto-optical response function, with CD and ORD being related to its imaginary and real parts, respectively. Although it would be in principle possible to compute ORD from CD and vice versa via a Kramers−Kroenig transform, the latter is of scarce usefulness in Received: November 27, 2014 Revised: March 3, 2015 Published: March 20, 2015 4803

DOI: 10.1021/jp5118568 J. Phys. Chem. B 2015, 119, 4803−4811

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The Journal of Physical Chemistry B

magnetically induced dichroism in solids (such as Kerr rotation).

practice, since the knowledge of the spectra on the entire frequency axis is needed to compute the integral transform.30 In the case of amino acids, ORD is usually studied off-resonance in the visible light region (which falls well below the optical absorption onset). CD, instead, requires to work in the absorbing (resonant) region, i.e., in the UV and vacuum-UV ranges. Most of the existing works on amino acids mainly focus on calculating the optical rotation at the wavelength of the sodium D line (589.3 nm)18−20,22,25,26 or rotational strength values for one26 or a few electronic excitations;24 only some of them compute full ORD curves21,22 or full CD spectra.14−17,19,23 Full frequency-dependent spectra potentially contain more information than the bare value of optical rotation at a fixed wavelength and are hence more reliable to assign the absolute configuration, as pointed out, e.g., by Kundrat et al.22 On the other hand, the rich conformational variability of amino acids and the influence of the solvent on the measured spectra increase the complexity of the problem. The importance of taking into account a correct Boltzmann averaging of all possible conformers, in order to reliably reproduce the experimentally observed specific rotation values, and the problems related to the description of the solvent have been discussed by several authors.14,20,21 In particular, Kundrat and co-workers calculated the specific rotation at 589.3 nm and ORD in the 200−600 nm range for some amino acids,21 including aromatic ones,22 considering zwitterionic, cationic, and anionic forms in water solution at different pH values within a continuum solvent model. In ref 19 the same authors focused on the pH dependence of the specific rotation of solvated amino acids at a fixed frequency, at the aim of rationalizing empirical rules thereof,18,20 considering amino acids in water using an explicit solvent approach and molecular dynamics. Pecul and co-workers computed the optical rotation of some amino acids in gas phase25,26 and in water solution,25 while other authors14,16,17 calculated full CD spectra of few amino acids in their neutral gas phase form as well as in the solvated zwitterionic one. Most of the above-mentioned works also investigated the conformational dependence of the computed chiroptical properties. Single geometries have instead been considered by Jansik et al.15 in their calculation of the gas phase two-photon absorption, CD, and two-photon CD spectra for all amino acids. In this work we address the issue of conformational dependence of the chiroptical response by performing ab initio calculations, via density functional theory (DFT), of the CD spectra of several conformers of alanine, leucine, phenylalanine, and serine. In the case of alanine, we also investigate the effects of solvation by including a surrounding shell of explicit water molecules. We obtain CD spectra of freely rotating molecules, corresponding to the trace of the CD tensor, within linear response theory, making use of Kohn−Sham excitation energies and complex momentum matrix elements computed within the velocity gauge. The implementation is free from gauge invariance problems and benefits of all the advantages of a pure plane-waves basis in terms of convergence checks and in terms of of easy integration with existing large-scale DFT codes such as ABINIT39 and QUANTUM ESPRESSO.40 The present work extends to natural dichroism the plane-wave approach which has recently become available41 for the calculation of the

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METHODS Circular dichroism, being defined as the difference in absorption coefficients for right (R) and left (L) circularly polarized light, can be expressed in terms of the imaginary part of the difference between polarization-resolved refraction indexes nR and nL. For randomly oriented chiral molecules, the difference Δn = nR − nL is given by 8πNω Δn(ω) = Tr(βμν ) (1) 3c where N is the molecular density, c the speed of light, and βμν(ω) is the tensor expressing the linear dependence of the induced electric and magnetic dipole moments ω μμ (ω) = αμν(ω)Eν(ω) − i βμν (ω)Bν (ω) (2) c ω mμ(ω) = χμν (ω)Bν (ω) + i βμν (ω)Eν(ω) (3) c on the time derivative of the perturbing magnetic and electric fields.32−35 Here α(ω) and χ(ω) are the electric polarizability and magnetic susceptibility tensors, respectively (throughout this work we will use Greek letters for coordinates and Latin letters for states). Within standard linear response, βμν(ω) can be expressed in terms of the tensor Gμν(ω) =

1 ℏ

⎧ ⟨0|μμ̂ |n⟩⟨n|m̂ ν |0⟩ ⎪

∑⎨

ωn0 − ω − iγ n≠0 ⎩ ⎪

+

⟨0|m̂ ν |n⟩⟨n|μμ̂ |0⟩ ⎫ ⎬ ωn0 + ω + iγ ⎭ ⎪

⎪

(4)

in the form βμν (ω) = −

iℏme ωqe 2

Gμν(ω) (5)

In eq 4, μ̂ = qr̂ and m̂ = (q/2m)r̂ × p̂ are the electric and magnetic dipole operators, respectively, |0⟩ and |n⟩ are ground and excited states of the system, and ωn0 = (En − E0)/ℏ. Equation 4 should ideally be evaluated in the limit of vanishing imaginary shifts iγ; however, a finite (and small) value of γ is often used in order to mimick experimental broadening effects. By inserting the resolution of the identity, one can rewrite r̂ × p̂ matrix elements in terms of those of r̂ and p̂, assuming completeness of the basis set. Moreover, ⟨r̂⟩ and ⟨p̂⟩ matrix elements can in principle be transformed into each other by exploiting the commutator rule iℏ [r,̂ Ĥ ] = p̂ + [r,̂ Vnl] m

(6)

where Vnl(r,r′) is a possible nonlocal contribution to the potential, such as the one which arises when pseudopotentials are used to describe the effect of core electrons. In this way, the numerators in eq 4 can be evaluated in terms of momentum matrix elements only, possibly corrected for the nonlocal pseudopotential contribution. The above approach is currently used for CD calculations both in quantum chemistry and in the electronic structure physics communities,28,31,36−38,42 although somewhat different approaches have been proposed in the literature, such as those implementing real-time wave function propagation or Stern4804


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× 10−3 eV/Å. Finally, Kohn−Sham electronic wave functions and eigenvalues, computed for both occupied and empty states, were used as an input in the calculations of chiroptical spectra. In order to correct for the gap underestimation arising from neglection of self-energy and many-body effects, a scissor operator correction is applied. Since only the linear part of the optical response enters in the calculation of CD spectra, the correction can be implemented as a rigid shift of the spectrum along the energy axis (not the wavelength one), keeping the line shape intact,56,57 while additional terms would appear in the nonlinear response.57 The applied shifts are 1.4, 1.6, and 1.5 eV for phenylalanine, serine, and methyloxirane, respectively, and 0.9 eV for hydrophobic molecules (alanine and leucine). We carefully checked the convergence of our results with the volume of the supercell and with the energy cutoff of the PW expansion. All final calculations were carried out in a cubic supercell of size 20 × 20 × 20 Å, which proved to be large enough for all the systems considered. The kinetic energy cutoff was set to 20 Ha, in both the self-consistent and non-selfconsistent calculations. To generate the initial ionic configurations, classical molecular dynamics simulations of zwitterionic alanine in water, and of water-only systems, were performed with the Gromacs code,58 using the Amber03 force field,59 the TIP3P water model,60 and periodic boundary conditions. The total simulation time was of 50 ns for zwitterionic alanine in water, and of 23 ns for the water-only system, and snapshots were saved every nanosecond. From each snapshot of the alanine + water system we extracted a small cluster containing the zwitterionic alanine surrounded by the 20 closest water molecules. Three snapshots displaying similar conformation of the alanine molecule were chosen, far enough from each other in order to avoid correlations in water positions. Similarly, we extracted five independent clusters of 20 water molecules from the water-only simulation.

heimer-like linear response schemes.29 In practical implementations, however, difficulties in preserving the gauge invariance and the independence of the results from rigid translation and rotation of the system with respect to the simulation cell have been shown to arise.29 In fact, although the length and velocity gauges are in principle equivalent to each other, the several (and often unavoidable) approximations entering actual calculations may break the gauge invariance. As a consequence, a spurious dependence of the calculated spectra on the origin of the reference system may arise.31,44 The most widely known example of these problems is associated with the use of incomplete localized basis sets within the length gauge. In this case, the origin dependence can be cured (for methods based on variationally optimized wave function) by introducing suitable magnetic-field-dependent phase factors, such as in the GIAOs45 or IGLO46,47 approaches. However, other issues besides the basis incompleteness one may arise, as discussed by several authors.29,43,48,49 In particular, in pseudopotential (PP)based calculations the nonlocal part of the PP must be adequately coupled to the external electromagnetic field in order to preserve gauge invariance (although in the linear response case only first-order corrections are needed.48,49) Moreover, problems can arise when differential operators are represented on discrete real-space grids, such as in the approach of Varsano et al.,29 since such representations are inherently not gauge invariant. In fact, the expectation value of the angular momentum operator itself may change when atoms are displaced with respect to the grid points (even working within the velocity gauge), requiring suitable filtering techniques to avoid spurious structures in the calculated spectra.29 Our plane-waves-based approach is free from all the abovementioned problems, since (i) we adopt the velocity representation and (ii) we evaluate all spatial derivatives in the reciprocal space, avoiding any discrete operator representation. Gradient (momentum) matrix elements are evaluated including the nonlocal pseudopotential contribution to eq 6. As an explicit check of translational and rotational invariance, we performed a series of CD calculations for simple benchmark systems, namely a methane molecule with modified CH bond lengths or with modified hydrogen substituents. Calculated spectra show the correct features, i.e., opposite CD for two enantiomeric species and independence of CD spectra on the position and orientation of the molecule. The latter are satisfied to an excellent degree (see panels A, B, and C of Figure S1 in the Supporting Information). The straightforward analysis of numerical convergence with respect to the basis set is exemplified in panel D of the same figure, for the case of an alanine molecule in vacuo. In Figure S2 in the Supporting Information we show that the contributions stemming from the nonlocal part of the pseudopotential have a visible, although not dramatic, effect on the calculated CD, slightly improving the agreement with the experimental spectrum. Computational Details. Self-consistent electronic structure calculations were carried out within density functional theory (DFT)50,51 in the local density approximation (LDA) for the exchange-correlation functional, using the Ceperley and Alder results52 as parametrized by Teter and Pade.53 The ion− electron interaction was treated using norm-conserving pseudopotentials of the Troullier−Martins type,54 as available on the Abinit39 Web site. Structural optimizations were performed with the Broyden−Fletcher−Goldfarb−Shanno (BFGS) method,55 until forces were below a threshold of 5

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RESULTS Validation of the Computational Scheme. We tested the validity of our numerical implementation on (R)methyloxirane (see inset in Figure 1), a small chiral molecule which does not display conformational flexibility and is often used as a benchmark for optical activity calculations.27,29

Figure 1. Experimental (black crosses and line) and calculated (red line) CD spectra of (R)-methyloxirane in vacuo. In the inset, our DFToptimized molecular structure is shown using yellow, cyan, and red to represent carbon, hydrogen, and oxygen, respectively. 4805


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+60°, −60° and ψ = −120°, −60°, 0°, +60°, +120°, +180°). Starting from each of them, we performed an energy minimization in vacuo within DFT, optimizing ionic positions with the Broyden−Fletcher−Goldfarb−Shanno (BFGS) method.55 To recapitulate the main features of the potential energy surface, we display our minimization trajectories in the central panel of Figure 2, where the color code indicates the change in

The resulting CD spectrum for an energy-minimized structure is displayed in Figure 1, where it is compared with the experimental spectrum obtained in vacuo.27 The two most evident features of the experimental spectrum, that is, a large positive peak at ∼160 nm and a negative one at ∼175 nm, are correctly predicted by our calculation. A similar agreement holds in the case of the absorption spectrum, which displays two low-energy peaks in the same range of energies (shown in Figure S3 of the Supporting Information). The above benchmark comparison between theoretical and experimental spectra exemplifies the achievable accuracy in computed CD spectra of small molecules as obtained by the present DFT-based ab initio approach. In particular, although the agreement with respect to peak intensities remains somehow qualitative due to the approximate treatment of self-energy and many-body effects, the position and sign of the main CD peaks are well reproduced. The agreement is of the same quality of that reported in previous computational works,29 including the worsening of the correspondence with the measured spectra in the high-energy part of the spectra. This may be due to the typical approximations of the theory, such as the limited number of final (excited) states included in the calculation of eq 4 or the neglection of vibrational effects.61 Dependence of the CD Spectrum on the “Backbone” Degrees of Freedom: The Case of Alanine in Vacuo. Amino acids display two main degrees of freedom, namely the torsions along the backbone (−N−C−C−) and the torsions of the side chain dihedrals, which are specific for each kind of amino acid. Alanine, whose side chain is a rigid methyl group bearing no relevant degrees of freedom, allows one to focus only on the backbone conformational effects. On the experimental side, amino acid absorption and CD spectra are routinely measured in solution62 or by deposing solid thin films on transparent substrates.11,12 Gas phase experimental studies of amino acids are rare due to their relatively low thermal stability associated with usually high melting points and low vapor pressures. Moreover, these few gas phase studies are usually devoted to molecular rotational spectra,13 while we are not aware of CD measurements of amino acids in true gas phase. Consequently, CD spectra measured on amino acid amorphous thin films will be taken as the best approximation against which to compare calculated spectra of isolated amino acid molecules. An additional complexity stems from the fact that while amino acids in a neutral solution are stable in their zwitterionic state, in the gas phase they assume their neutral form, with COO− and NH3+ replaced by COOH and NH2 groups, respectively, due to the lack of stabilization and charge-screening effects arising from neighboring solvent molecules. Solvation effects in the case of Alanine will be explicitly addressed in a specific section below. In peptides, the two backbone dihedrals of the ith amino acid are usually labeled ϕ, defined by the atoms Ci−1−Ni−Ci−Ci, and ψ, defined by the atoms Ni−Ci−Ci−Ni+1. In the present case we are considering a single alanine that is amidated and carboxylated, respectively, at the ends. Consequently, we define ϕ here as the dihedral H−N−C−C, so that it displays a period of π due to the fact that the two hydrogens of the amide group are undistinguishable; we then define ψ as N−C−C−OH, hence displaying a 2π periodicity. The goal is to study the CD spectra as a function of ϕ and ψ. For this purpose, we generated 18 initial conformations varying ϕ and ψ according to a 3 × 6 grid of values (ϕ = 0°,

Figure 2. Geometry optimization of neutral alanine in vacuo, starting from 18 initial conformations, plotted as a function of ϕ and ψ. Contiguous colored dots indicate the optimization trajectory, the color code indicating the energy in kT units, with T = 290 K corresponding to room temperature. The parameters of obtained low-energy conformers are highlighted with small colored circles, and the corresponding structures are shown, with the same colors, around the central panel. Color codes for the ball-and-stick models are the same as in Figure 1, with the nitrogen atom shown in gray.

energy along each trajectory in units of kT at room temperature. The minimization trajectories highlight three main basins of attraction, at ϕ ∼ −30° and ψ ∼ −180°, at ϕ ∼ +60° and ψ ∼ 150°, at ϕ ∼ −60° and ψ spanning from −60° to +60°. The absolute energy minimum was found at ϕ = 54.2° and ψ = 163.3°, but several conformations were found displaying energies of the order of kT (black to purple points in the central panel of Figure 2) and thus being thermodynamically relevant at room temperature. These conformations are indicated with colored circles, and the corresponding molecular geometries are shown by arrows, around the central panel. In panel A of Figure 3 we display the CD spectra calculated for the nine low-energy conformations shown in Figure 2. The spectra display overall a strong conformational dependence. The dependence is more pronounced with respect to ψ, something not unexpected because of the motion of the electronegative oxygen; a similar trend was found in previous works for the optical rotation at 589.3 nm of zwitterionic alanine in solution18 and of neutral gas phase alanine.26 Most structures with similar CD spectra have the COOH and NH2 groups oriented on the same side, as shown in the panels B and C of Figure 3; in panel D, instead, we show the spectra of two conformations which only differ in the carboxyl group orientation: interestingly, changing the sign of ψ (i.e., the orientation of the carboxyl group) in an otherwise unmodified structure results in a change of sign of all CD peaks, thus mimicking the effect of switching to the opposite enantiomer. 4806


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and to differences in experimental conditions (e.g., thin film samples). For example, the low-energy feature appearing in the calculated spectra at about 240 nm corresponds to a low-energy excitation from an occupied state localized on the amino group to an empty π* orbital on the carboxylic group, as reported by several authors.63,64 Its energy is underestimated in our LDA calculation as well as in Bechstedt et al.64 with respect to more exact CCSD(T) results63 due to the limitation of the rigid scissor approach, and its intensity may be biased due to the partial charge-transfer character of the excitation. Although this conformer is not the global energy minimum according to our DFT calculation and to other conformational studies of alanine in vacuo (see e.g. refs 9, 10, and 13), it has an energy only slightly above (of the order of kT) that of our DFT ground state. Since we have no direct information on the conformer population in the thin film at the experimental conditions, we cannot exclude that a large contribution to the measured CD spectra can indeed be ascribed to the presence of this conformer. Dependence of the CD Spectrum on the Side Chain Conformation: Leucine, Phenylalanine, and Serine. To investigate the dependence of the CD spectrum on the dihedrals defining the side chain conformations (rotamers), we focused our attention on three amino acids with different chemical properties and whose experimental spectra on thin film samples are available. Leucine displays a nonpolar, rather long side chain; serine has a polar one, while that of phenylalanine is a benzyl group. Side chain dihedrals are labeled χ1 and χ2 for leucine and phenylalanine and χ1 for serine. To select an initial set of possible conformations for CD spectra calculations, we use the rotamer library of ref 2, which lists the most probable conformations of the side chains extracted from structured proteins. One should however keep in mind that the relative energy ordering obtained from such a knowledge-based library might differ from that of isolated amino acids due to the fact that the preferred rotamers observed in proteins can be influenced by long-range interactions within the protein65 (see also refs 66−69). In the case of leucine, there are two significant rotamers, called MT (χ1 = −65°, χ2 = 175°), corresponding to a probability of 59%, and TP (χ1 = −177°, χ2 = 65°), observed with probability 29%. All other rotamers correspond to probabilities lower than 2%. We hence consider MT and TP as our initial candidates for CD spectra calculations. A geometry optimization performed within DFT for such conformations in vacuo ends up in essentially unchanged values of the dihedrals. The optimized dihedral values are χ1 = −63°, χ2 = 170° for the MT conformer and χ1 = −178°, χ2 = 61° for the TP conformer (see insets in Figure 5A), confirming that MT and TP are indeed structural local minima for an isolated leucine molecule. As shown in Figure 5A, the computed CD spectra of MT and TP leucine are extremely similar, despite the structural difference between the two rotamers. In this case, hence, the chiroptical properties of the molecule are not affected significantly by the orientation of the nonpolar side chain. The gross features of this spectrum, in particular the main positive peak at ∼180 nm, match indeed the experimental data. In the case of phenylalanine, the two main rotamers are T80 (χ1 = −177°, χ2 = 80°, probability 33%) and M-85 (χ1 = −65°, χ2 = −85°, probability 44%). Again, a DFT structural optimization confirmed them as stable minima for the isolated

Figure 3. Panel A: calculated CD spectra for the 9 conformers of alanine in vacuo displayed in Figure 2, using the same color code. Panels B and C compare the spectra of conformations with similar ϕ and ψ values; panel D shows the comparison of the spectra of two conformers with opposite orientation of the carboxyl group.

The spectral region that undergoes the largest change with respect to conformation changes of alanine is the one around 180 nm (see also the standard deviation plotted in Figure S4 of the Supporting Information). Such region can hence be considered as the most diagnostic one to identify the conformation itself. To study the sensitivity of the CD spectrum with respect to other molecular degrees of freedom besides the conformational dihedrals ψ and ϕ (i.e., bond lengths and angles), one can consider the minimization trajectory leading to the structure (ϕ ≃ −60°, ψ ≃ −60°), encircled in black in Figure 2, whose backbone orientation does not change appreciably. Although the energy decreases by 14 kT due to the optimization of such nonconformational degrees of freedom, the spectrum remains essentially unchanged (see Figure S5 in the Supporting Information). The conformer (ϕ ≃ −60, ψ ≃ −60) circled in black in Figure 2 is the one which, among those we studied, produces the spectrum most similar to the one experimentally measured in thin alanine films, dominated by a sharp positive peak at about 180 nm,11,12 as shown in Figure 4. The discrepancies in secondary peaks may be ascribed both to the limitation of the theory (e.g., the rigid scissor correction)

Figure 4. Experimental CD spectrum of alanine11 (black crosses and curve), compared with the calculated spectrum for conformer (ϕ = ≈−58 ψ = ≈−65) which structure is displayed in the inset (red curve). 4807


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values of χ1, starting with 12 conformations with χ1 = n × 30° with n = 0, ..., 11, and then refining the scan around the minima (see Figure S6 in the Supporting Information). The three lowest energy conformations we found (at χ1 = 40°, −40°, and 180°) correspond closely, although not exactly, to the rotamers P, M, and T reported in ref 2. Noticeably, also their relative energies ordering matches the ordering of probabilities found in structured proteins, although the probabilities values do not match quantitatively. The associated CD spectra are displayed in Figure 5D. They are qualitatively similar to the spectra of the corresponding rotamers, but their fine-grained structure is more similar to each other than those displayed in Figure 5C. This calculation suggests that for serine the difference in the CD spectrum of its rotameric states lies essentially in an energy shift of its peaks, and the sensitivity of these spectra to the orientation of the polar side chain is intermediate between those found for a nonpolar (leucine) or an aromatic (phenylalanine) side chain. Solvation Effects. We consider now the effects of water, restricting to the paradigmatic case of alanine. In the present ab initio approach, solvation is mimicked by adding a shell of explicit water molecules around the amino acid. Compatibly with the required numerical effort, we choose to use 20 water molecules which are enough to fill the nearest-neighbor shell of alanine. We first verified that the zwitterion is the stable form in water solution, i.e., that neutral alanine spontaneously converts to its zwitterionic form upon DFT geometry optimization in water. This conversion is associated with a substantial change in the CD spectrum (see Figure S7 in the Supporting Information), despite the relatively small conformational change in terms of ϕ and ψ dihedrals (Δϕ ∼ 22°, Δψ ∼ 13°). We then performed a classical molecular dynamics simulation58 of zwitterionic alanine, after solvating it with 339 explicit TIP3P water molecules60 at 300 K. After equilibration (10 ns) we extracted three equilibrium conformations of the amino acid and of the 20 closest water molecules. These conformations were chosen among those that had different arrangements of the above-mentioned water shell, while the alanine molecule only displayed small conformational changes (with a maximum variation of ∼19° for ϕ and of ∼13° for ψ). On these three conformations of the system, we performed an ab initio DFT geometry optimization and calculated absorption and CD spectra on the resulting optimized structures. The average CD of these three conformations is displayed in black in Figure 6, together with its standard deviation. Individual spectra are reported in Figure S8 of the Supporting Information. At variance with the spectra computed for alanine in vacuo, no CD signal appears at wavelength larger than 210 nm. Moreover, due to the presence of water, the experimentally accessible spectral window is limited to wavelengths above 180 nm (where water starts to absorb). In this 180−210 nm region the computed CD spectrum displays a single positive peak, with a mild amount of variability with respect to the alanine conformation in water. This variability is indeed larger than that observed for neutral alanine in vacuo (see e.g. panels B and C in Figure 3). In our calculation, however, the high variability of CD spectra arises both because of the changes in the molecular electronic structure and because of the presence of a small number of water molecules. Despite the fact that in the limit of a large number of molecules the chirality (hence the CD) of a water-

Figure 5. Calculated CD spectra (and corresponding structures) of different rotamers of gas phase amino acids (colored curves), compared to experimental spectra (black crosses and curves). Specifically, for the case of leucine (panel A): MT rotamer (red curve), TP rotamer (blue curve); for phenylalanine (panel B): T80 rotamer (red), M-85 rotamer (blue); for serine (panel C): P rotamer (red), M rotamer (blue), T rotamer (magenta). Panel D shows CD spectra of the three conformational minima found for serine through a geometry scan on the χ1 dihedral: χ1 = 40 (red curve), χ1 = −40 (blue), χ1 = 180 (magenta). Experimental data are reproduced from ref 11 (LEU and SER) and from ref 12 (PHE).

molecule. The corresponding calculated CD spectra are displayed in Figure 5B, and in this case, they are remarkably different from each other. A marked dependence of chiroptical properties of aromatic amino acids on their conformation has been previously reported e.g. by Kundrat and Autschbach.22 In particular, at wavelengths larger than 180 nm the CD features of T80 and M-85 are almost opposite. Consequently, unlike the case of leucine, the orientation of the aromatic side chain is clearly determinant in the chiroptical properties of this molecule. The experimental data are well matched by the CD spectrum computed for the T80 rotamer. In the case of serine, the rotamer library displays three relevant conformers, labeled P (χ1 = 62°, probability 48%), T (χ1 = −177°, probability 22%), and M (χ1 = −65°, probability 29%). Energy minimizations starting from these dihedrals do not change appreciably their values, indicating that they are local minima in vacuo. The CD spectra obtained from the corresponding optimized conformations are displayed in Figure 5C. They are neither identical to each other, as in the case of leucine, nor completely different, as in the case of phenylalanine. The three spectra share a common pattern, with a negative part, a positive peak, and a further negative one. The main positive peaks displayed by all the rotamers match qualitatively the experimental spectrum (cf. black curve in Figure 5C). To better elucidate the role of the chosen conformations in the non-clear-cut case of serine, we extended our analysis by carrying out a systematic geometry scan over the side chain conformations, characterized by the single dihedral χ1. As a byproduct, we may investigate whether the theoretical rotamer populations, based on their computed total energy, are consistent with those extracted from a rotamer library based on amino acids conformations within protein sequences. We hence computed and plotted the DFT total energy versus the 4808


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backbone. Confirming the results of previous studies,18,26 the spectrum displays a marked dependence on ψ, which controls the position of the carboxyl oxygen. Moreover, it depends less strongly on ϕ and negligibly on bond lengths and angles. The most diagnostic region is in the vacuum-UV, around 180 nm. When alanine is solvated by water, the region of the spectrum below 180 nm is strongly affected by the absorption of water, and anyway is affected by large statistical fluctuations in our calculations, due to the limited number of water molecules we can account. The part of the spectrum above 210 nm disappears, and the CD signal between these two wavelengths displays a stronger conformation dependence than in vacuo, as expected because of the zwitterionic state of the termini of the amino acids, which rotate when changing ϕ and ψ. The comparison of the CD spectra of several conformations of the side chains of different amino acids indicates a different degree of sensitivity with respect to their physicochemical properties. Leucine, whose side chain is nonpolar and hydrophobic, displays a negligible dependence of the CD spectrum on the relative position of its side chain. The position of the benzyl side chain of phenylalanine, which is still nonpolar, but larger than that of leucine (and with a different electronic structure), has a very strong impact on its CD spectrum. Also in the case of serine, the CD spectrum has a marked dependence on the position of its polar, hydrophilic side chain, although not as strong as for phenylalanine. For all the studied amino acids we could identify conformations whose calculated CD spectra are similar to the experimental one. In the case of alanine in vacuo it corresponds to a local energy minimum, set approximately kT above the global DFT-LDA minimum. Both rotamers of leucine are compatible with the experimental data. In the case of phenylalanine, the rotamer which is slightly less populated in the rotamer library is the more similar to the experimental CD spectrum. However, one should remember that the rotamer library is obtained from the analysis of amino acids in structured proteins, and consequently rotamers are expected to be also affected by the protein tertiary structures. This is particularly evident in the case of serine, in which case an energy scan of the degrees of freedom of the side chain allows a better agreement with the experimental data than using the bare structures from the rotamer library. Summing up, we showed that the strength of the dependence of the CD spectrum of amino acids on their conformational properties depends on the chemical properties of the amino acids and on the detailed spectral region. This can be predicted by DFT calculations and thus used as diagnostic of the main conformation populated by the amino acid. Our computational approach is suitable for larger and more complex biomolecules, within the range of 102−103 Da, for which the mapping between conformational properties and experimental CD spectra is still unclarified.

Figure 6. Average and standard deviation of the calculated CD spectra for three structures of zwitterionic ALA sorrounded by 20 water molecules, differing in the arrangement of the latter (solid black lines and error bars). The 10 red thin curves correspond to averages over three conformations of a 20 H2O cluster with no alanine. All combinations of three out of the five calculated spectra are used.

only system averages to zero, in the present case, due to the small number of molecules, statistical fluctuations in the chirality of the system result in spurious non-null CD contributions. A similar effect has been noticed by Kundrat et al. in the case of glycine.20 To investigate this point we have calculated reference CD spectra for five water-only systems, representing the solvation shell without the alanine. The individual spectra (both optical absorption and CD) are reported in Figure S9 of the Supporting Information. All the average CD spectra of water, averaged on the same number (three) of replicates, that can be obtained by combinations of the five calculations are also displayed in Figure 6. Above 190 nm the CD spectrum of solvated alanine is certainly more intense than solvent fluctuations. The same is not true below 190 nm, where water displays its main absorption and CD signals (cf. lower panels of Figures S7 and S8 in the Supporting Information).

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DISCUSSION While the conformational dependence of the CD spectra of large peptides and proteins is largely well characterized, at least empirically, that of their amino acidic constituents is less well established. A better detailed understanding would be useful now, in view of the role of amino acids not just regarded as building blocks of biomolecules but also as constituent of nanoparticles with tailor-made properties. Computational simulations appear as an ideal tool to study how the CD spectrum of amino acids depends on their conformational properties because they allow a complete control on the conformation of the molecule, something that no experimental technique can give, and at the same time they are not excessively challenging in terms of computational cost. In particular, the specific choice we made of performing DFT calculations within the velocity gauge in a plane-waves basis and avoiding any real grid representation of differential operators is free from origin-dependence issues. Moreover, our implementation allows a ready check of numerical convergence and is easily integrated with existing large-scale, plane-waves DFT codes.39,40 We made use of alanine in vacuo, whose side chain is particularly simple and rigid, to study the dependence of the CD spectrum on the dihedrals defined by the amino acid

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ASSOCIATED CONTENT

S Supporting Information *

Figures concerning robustness of the results. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone +39 02503 17221; Fax +39 02503 17487; e-mail guido. [email protected] (G.T.). 4809


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The Journal of Physical Chemistry B Notes

(19) Kundrat, M. D.; Autschbach, J. Computational Modeling of the Optical Rotation of AminoAcids: A New Look at an Old Rule for pH Dependence of Optical Rotation. J. Am. Chem. Soc. 2008, 130, 4404− 4414. (20) Kundrat, M. D.; Autschbach, J. Ab Initio and Density Functional Theory Modeling of theChiroptical Response of Glycine and Alanine in Solution Using Explicit Solvation and Molecular Dynamics. J. Chem. Theory Comput. 2008, 4, 1902−1914. (21) Kundrat, M. D.; Autschbach, J. Time Dependent Density Functional Theory Modeling of Chiroptical Properties of Small Amino Acids in Solution. J. Phys. Chem. A 2006, 110, 4115−4123. (22) Kundrat, M. D.; Autschbach, J. Time Dependent Density Functional Theory Modeling of Specific Rotation and Optical Rotatory Dispersion of the Aromatic Amino Acids in Solution. J. Phys. Chem. A 2006, 110, 12908−12917. (23) Krykunov, M.; Kundrat, M. D.; Autschbach, J. Calculation of Circular Dichroism Spectra from Optical Rotatory Dispersion, and Vice Versa, as Complementary Tools for Theoretical Studiesof Optical Activity Using Time-Dependent Density Functional Theory. J. Chem. Phys. 2006, 125, 194110. (24) Skomorowski, W.; Pecul, M.; Sałek, P.; Helgaker, T. Electronic Circular Dichroism of Disulphide Bridge: Ab Initio QuantumChemical Calculations. J. Chem. Phys. 2007, 127, 085102. (25) Pecul, M. Conformational Structures and Optical Rotation of Serine and Cysteine. Chem. Phys. Lett. 2006, 418, 1−10. (26) Pecul, M.; Ruud, K.; Rizzo, A.; Helgaker, T. Conformational Effects on the Optical Rotation of Alanine and Proline. J. Phys. Chem. A 2004, 108, 4269−4276. (27) Carnell, M.; Peyerimhoff, S. D.; Breest, A.; Gödderz, K. H.; Ochmann, P.; Hormes, J. Experimental and Quantum-Theoretical Investigation of the Circular Dichroism Spectrum of R-Methyloxirane. Chem. Phys. Lett. 1991, 180, 477−481. (28) Yabana, K.; Bertsch, G. F. Application of the Time-Dependent Local Density Approximation to Optical Activity. Phys. Rev. A 1999, 60, 1271−1279. (29) Varsano, D.; Espinosa-Leal, L. A.; Andrade, X.; Marques, M. A. L.; di Felice, R.; Rubio, A. Towards a Gauge Invariant Method for Molecular Chiroptical Properties in TDDFT. Phys. Chem. Chem. Phys. 2009, 11, 4481−4489. (30) Polavarapu, P. L. Renaissance in Chiroptical Spectroscopic Methods for Molecular Structure Determination. Chem. Rec. 2007, 7, 125−136. (31) Crawford, T. D.; Tam, M. C.; Abrams, M. L. The Current State of Ab Initio Calculations of Optical Rotation and Electronic Circular Dichroism Spectra. J. Phys. Chem. A 2007, 111, 12057−12068. (32) Rosenfeld, L. Quantenmechanische Theorie der Natürlichen Optischen Aktivität von Flüssigkeiten und Gasen. Z. Phys. 1929, 52, 161−174. (33) Caldwell, D. J.; Eyring, H. The Theory of Optical Activity; WileyInterscience: New York, 1971. (34) Condon, E. U. Theories of Optical Rotatory Power. Rev. Mod. Phys. 1937, 9, 432−457. (35) Barron, L. Molecular Light Scattering and Optical Activity, 2nd ed.; Cambridge University Press: Cambridge, 2004. (36) Diedrich, C.; Grimme, S. Systematic Investigation of Modern Quantum Chemical Methods to Predict Electronic Circular Dichroism Spectra. J. Phys. Chem. A 2003, 107, 2524−2539. (37) Furche, F.; Ahlrichs, R.; Hättig, C.; Klopper, W.; Sierka, M.; Weigend, F. Turbomole. WIREs Comput. Mol. Sci. 2014, 4, 91−100. (38) Hidalgo, F.; Sànchez-Castillo, A.; Noguez, C. Efficient FirstPrinciples Method for Calculating the Circular Dichroism of Nanostructures. Phys. Rev. B 2009, 79, 075438. (39) Gonze, X.; Amadon, B.; Anglade, P.-M.; Beuken, J.-M.; Bottin, F.; Boulanger, P.; Bruneval, F.; Caliste, D.; Caracas, R.; Cote, M.; et al. ABINIT: First-Principles Approach to Material and Nanosystem Properties. Comput. Phys. Commun. 2009, 180, 2582−2615. (40) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.; et al. QUANTUM ESPRESSO: a Modular and Open-Source Software

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the CINECA award under the ISCRA initiative, for the availability of high performance computing resources and support. This work is part of the ETSF user project no. 547.70

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