Quantum chemical studies on nucleophilic sites in calcium ion bound zwitterionic calmodulin loops

Abstract

We perform quantum chemical (QC) calculations based on the density functional theory (DFT) approach for biologically relevant zwitterionic polypeptides, comprising of isolated calcium (Ca²⁺) ion bound EF-hand loops of calmodulin (CaM). The HOMO and the LUMO levels are observed to be dominated by terminal capping contributions which fall off exponentially in neighboring energy levels. These levels with negligible capping contributions are considered as HOMO⁻ and LUMO⁺. In loop 1 and loop 2 of CaM, HOMO⁻ and LUMO⁺ are dominated by acidic aspartates and polar residues whereas only polar side chains contribute in the energy levels of loop 3 and loop 4. We find that the HOMO⁻ of loop 3 shows strong localized electron density on the side chain phenyl ring of tyrosine. This is an indication of potential nucleophilic sites for tyrosine phosphorylation in CaM. Our calculation provides a systematic way of interpreting the functionality of zwitterionic polypeptides at physiological conditions from the electronic energy spectra. Moreover, the capping levels indicate possible device applications.

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Introduction

Protein function is governed by its amino acid sequence, three dimensional conformation and the solvent conditions. One such function in proteins is post-translational modification,¹ where polar amino acids play important role via phosphorylation involving a reversible process of addition of a phosphate group from ATP in presence of kinases.² The side chain hydroxyl groups in polar amino acids like serine, threonine and tyrosine easily loose a proton leaving the oxygen atom as a nucleophilic centre. This nucleophile then attacks the phosphorous (P_γ) of ATP and gets phosphorylated.^2–4 Calmodulin, CaM^5,6 is an EF-hand protein with four calcium binding loops, which undergoes phosphorylation both in vitro and in vivo. The phosphorylated CaM plays crucial role in regulation of signal transduction and other cellular activities.^7,8 Recently, EF-hand peptides have been designed to undergo phosphorylation and serve as phosphorylation dependent sensors near neutral pH conditions.^9,10 There are polar amino acids in CaM loops, like T26, T28 and T29 in loop 1, T62 in loop 2 and S101 in loop 3 which show very little phosphorylation in vitro.¹¹ Mass spectrometry results show that tyrosines, Y99 from loop 3 and Y138 from loop 4 of Ca²⁺ bound CaM are potential phosphorylation sites involving their phenyl ring O_h atom.⁸ Apart from experiments, theoretical investigations on phosphorylation of tyrosine including the identification of transition state have been carried out through quantum chemical (QC) methods.^2–4,12 However, it is not understood why different polar residues in CaM show difference in phosphorylation.

An understanding of chemical reactivity of a system can provide insight into nucleophilic or electrophilic character. The chemical reactivity is interpreted from the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the electronic ground state,¹³ calculated by QC methods. These methods are computationally expensive and typically limited to systems of 200–300 atoms. In the context of large bio-molecules like proteins (>1000 atoms) one needs to truncate the system to an optimal one, depending on the properties to be explored through QC calculations.^14–17 Such truncations lead to unsatisfied valencies at the terminals, which are capped by appropriate groups. However, the truncations and terminal cappings affect the HOMO–LUMO levels non-trivially.^17–20 In our earlier QC study¹² based on polarizable continuum model (PCM), we have used neutral capping^16,21–23 with acetyl group at the N-terminus and N-methylamide group at the C-terminus of calcium (Ca²⁺) ion bound isolated loops of CaM. We find that HOMO of loop 3 has localized electron density on the phenyl ring O_h of Y99, which can participate in a nucleophilic attack to undergo phosphorylation.

In an aqueous solution at neutral pH, any protein, peptide or amino acid acquires zwitterionic character with protonated amide group at the N-terminus and de-protonated carboxyl group at C-terminus.²⁴ The electrostatic interaction between such charged terminals gets screened in presence of counterions.²⁵ Debye screening length²⁶ is a measure of length scale of screened electrostatic interaction. For isolated CaM loops, the Debye screening length (∼8 Å) of charged terminals at physiological salt concentrations (∼150 mM) is large compared to end-to-end distance (∼5 Å), indicating that the charge–charge electrostatic interaction between truncated ends is not completely screened. This leads us to cap terminals of the isolated CaM loops with charged groups resembling the zwitterionic state as done in other QC studies.^27–29 In this work, we ask: how does the nucleophilic centre for phosphorylation at tyrosine sites behave in presence of charged terminal capping? This is non-trivial for polar residues experiencing long range electrostatic interaction with charged sites. The functional aspects of zwitterionic peptides have not been looked into in the earlier QC studies.

We perform density functional theory (DFT) based QC calculations of the four isolated Ca²⁺ bound zwitterionic CaM loops with polarizable continuum model (PCM)³⁰ using the Gaussian03 package in order to elucidate stability and functionality of different loop residues. The chemical reactivity of a system is measured through the Fukui index calculation. For a fixed molecular geometry it is defined as the change in electronic density upon removal of an electron from the HOMO or upon addition of an electron to the LUMO. The nucleophilicity index, f_k⁻ = q_k^N − q_k^N−1 measures the capacity of atom k to provide a nucleophilic attack. Similarly the electrophilicity index, f_k⁺ = q_k^N+1 − q_k^N denotes the tendency of an atom to act as an electrophile.¹² Our DFT calculations indicate that such charged groups at the terminals introduce localized energy levels in the vicinity of HOMO and LUMO. The presence of such levels indicates that the loops may have device applications. The terminal capping contribution falls off exponentially near HOMO–LUMO levels so that one can define HOMO⁻ and LUMO⁺ levels with negligible capping effect. Further, we show that Y99 contributing to HOMO⁻ of CaM loop 3 can act as a nucleophile even in zwitterionic state and pose as a potential site to undergo phosphorylation consistent with experimental evidence.⁸

Methods

We use the X-ray crystal structure of Ca²⁺ bound (holo) CaM (PDB ID: 1CLL)⁶ in our study. All atom molecular dynamics (MD) simulations of holo-CaM in explicit water with counter-ions is performed with NAMD³¹ program at 300 K and 1 atm pressure in isothermal–isobaric (NPT) ensemble using periodic boundary conditions and 1 femtosecond time-step.³² The CHARMM27 (ref. 33) force field and the TIP3P water model have been used in the MD simulation. We perform an energy minimization of 1000 steps and then run 100 nanoseconds (ns) long simulations. The four Ca²⁺ binding EF-hand loops (1, 2, 3, 4) of CaM are isolated from the 100 ns structure, retaining the coordinated water molecule. The truncated loop ends are capped with amino (NH₃⁺) and carboxylate (C_γO1O2⁻) groups at the N- and the C-terminals respectively, resembling the zwitterionic state. The resulting structures are optimized in NAMD using the conjugate gradient algorithm followed by 5 ns of MD simulation, in presence of explicit water and counterions. The parameters for simulation of these loops are same as for the whole CaM. The QC calculations are done for both force-field optimized and simulated conformations.

The QC DFT calculations are done by variationally minimizing the Hamiltonian of an interacting many-electron system for fixed nuclear coordinates, the electronic correlations being approximated through general functionals of the electron density.¹² We use the Gaussian03 package³⁴ with B3LYP functional and 6-31G(d,p) basis set in combination with polarizable continuum model (PCM)³⁰ for implicit solvent effect as used in previous studies.^{3,12,29,35,36} The total ground state energy is estimated by the self consistent field method and the molecular orbitals (MOs) are computed followed by natural population analysis (NPA) to determine the partial atomic charges.

Results

The terminal capping contribution, taken as sum of squares of MO coefficients of the constituent atoms, is shown for C-terminal carboxylate (C_γO1O2⁻) capping, C⁽²⁾_C-ter and N-terminal amino (NH₃⁺) capping, C⁽²⁾_N-ter of the Ca²⁺ bound loops in Fig. 1. C⁽²⁾_C-ter (Fig. 1a) of Ca²⁺–loop 1 shows maximum at the HOMO with decreasing amplitude towards lower energy levels (−5 eV to −20 eV). C⁽²⁾_C-ter is non-zero at −24.1 eV and −26.8 eV, the electron density being solely localized over the capping carboxylate oxygen atoms. Fig. 1b shows that the contribution, C⁽²⁾_C-ter decreases exponentially from the HOMO towards the lower energy levels (ΔE = |E_i − E_HOMO|) with a decay constant, ξ^(L1)_C-ter = 0.4 eV of loop 1. Similarly, C⁽²⁾_N-ter (Fig. 1c) is predominant at the LUMO but decreases in amplitude at higher energies (0 eV to 4 eV). Fig. 1d shows the amino capping contribution C⁽²⁾_N-ter to the LUMO and higher energy levels (ΔE = |E_i − E_LUMO|), exhibiting an exponential decay with ξ^(L1)_N-ter = 0.03 eV in loop 1. Similar exponential decay of terminal capping contributions is observed for the other Ca²⁺ ion bound loops (see ESI, Fig. S1†) with respective decay constants given in Table 1. We designate the levels with negligible capping effect closest to HOMO as HOMO⁻ (E⁻) and LUMO as LUMO⁺ (E⁺) of the Ca²⁺ bound loops of CaM. The values of E⁻, E⁺ and the corresponding energy gap Δ = E⁺ − E⁻ of these loops are given in Table 2.

Fig. 1 The contribution of terminal capping of Ca²⁺–loop 1 complex. (a) C-terminal C_γO1O2⁻ capping contribution and (b) its exponential decay from HOMO to lower energy states (in eV). (c) N-terminal NH₃⁺ group capping contribution and (d) its decay from LUMO to higher energy states (in eV).

Table 1 The decay constants (in eV) of terminal capping groups of CaM loops

Loop	ξ^loopC-ter (eV)	ξ^loopN-ter (eV)
1	0.4	0.03
2	0.3	0.01
3	0.5	0.01
4	0.01	0.03

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Table 2 HOMO⁻ (E⁻), LUMO⁺ (E⁺) and corresponding energy gap Δ (in eV) of the Ca²⁺ bound loops of CaM

Loop	E^− (eV)	E^+ (eV)	Δ (eV)
1	−6.01	0.53	6.54
2	−6.00	0.50	6.50
3	−5.81	0.41	6.22
4	−5.60	0.43	6.03

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Let us consider the N-terminal loops 1 and 2. The HOMO⁻ of Ca²⁺–loop 1 complex (Fig. 2a) show delocalized electron density contributed from side chain carboxylate O1 and O2 atoms of acidic D22 and from backbone carbonyl O of polar G23. The LUMO⁺ (Fig. 2b) finds predominant contribution from backbone carbonyl group of polar T26. A similar delocalized electron density at HOMO⁻ (Fig. 2c) of loop 2 exists, where side chain carboxylate oxygen atoms of acidic D58 and backbone atoms of polar G59 contribute. On other hand, the LUMO⁺ (Fig. 2d) electronic density of loop 2 is localized on side chain carboxamide group of polar N60. The HOMO⁻ and LUMO⁺ of both these loops reflect very similar electronic structures with aspartates contributing at HOMO⁻ and polar residues contributing at LUMO⁺. The aspartates, D22 and D58 share equivalent positions (position III) in respective loops.

Fig. 2 (a) HOMO⁻ and (b) LUMO⁺ of Ca²⁺–loop 1 complex. (c) HOMO⁻ and (d) LUMO⁺ of Ca²⁺–loop 2 complex.

The individual atomic (α) contributions of D22 from position III (C⁽²⁾_III,D22,α), to HOMO⁻ of Ca²⁺–loop 1 complex shown in Fig. 3a, indicates that the carboxylate oxygen atoms, O1 and O2 show large contributions to HOMO⁻ compared to any other atoms. Similarly, the individual atomic contributions of T26 from VII^th position (C⁽²⁾_VII,T26,α) to LUMO⁺ of Ca²⁺–loop 1 is shown (Fig. 3b). The contribution to LUMO⁺ predominantly comes from the constituent atoms of its backbone carbonyl group. We show orbital (2s, 2p_x, 2p_y and 2p_z) specific contributions (C⁽²⁾_III,D22,O1) of the O1 atom of D22 to HOMO⁻ and that of the carbonyl O (C⁽²⁾_VII,T26,O) of T26 to LUMO⁺ (Fig. 3c). The nature of hybridization predominantly shows a p-character at both HOMO⁻ and LUMO⁺ with huge contribution from the respective 2p_y orbitals of D22, O1 and T26, O. The orbital specific contribution of the other carboxylate O2 atom of D22 to HOMO⁻ (see ESI, Table S1†) indicates major participation of its 2p_z electrons. A similar hybridization pattern at HOMO⁻ of Ca²⁺–loop 2 complex is observed (see ESI, Table S1†) for carboxylate oxygen atoms of D58, showing major contributions through their 2p orbitals. On the other hand, LUMO⁺ of Ca²⁺–loop 2 complex being characterized by N60, exhibits similar hybridization pattern involving 2p electrons of its side chain carboxamide group atoms (see ESI, Table S2†).

Fig. 3 Individual atomic (α) contribution, (a) C⁽²⁾_III,D22,α of D22 towards HOMO⁻ and (b) C⁽²⁾_VII,T26,α of T26 towards LUMO⁺ of Ca²⁺–loop 1 complex. (c) Orbital specific contribution, C⁽²⁾_III,D22,O1 of D22, O1 towards HOMO⁻ and C⁽²⁾_VII,T26,O of T26 O towards LUMO⁺ showing the nature of hybridization.

The HOMO⁻ and the LUMO⁺ levels are significantly different in the C-terminal domain loops 3 and 4 compared to that of N-domain. HOMO⁻ of Ca²⁺–loop 3 complex (Fig. 4a) shows strong localized electron density on polar Y99 side chain, while LUMO⁺ (Fig. 4b) electron density is contributed by polar side chains of S101 and Y99. Similar to loop 3, the side chain of Y138 in Ca²⁺–loop 4 complex contributes predominantly to HOMO⁻ (Fig. 4c), while LUMO⁺ (Fig. 4d) has again contributions from two polar residues, N137 and Y138 involving their side chains.

Fig. 4 (a) HOMO⁻ and (b) LUMO⁺ of Ca²⁺–loop 3 complex. (c) HOMO⁻ and (d) LUMO⁺ of Ca²⁺–loop 4 complex.

We show atom-specific contributions of Y99 at position VII (C⁽²⁾_VII,Y99,α) and Y138 at position X (C⁽²⁾_X,Y138,α) corresponding to HOMO⁻ and LUMO⁺ of loops 3 and 4 (Fig. 5a and b) respectively. Fig. 5a shows that backbone atoms including the coordinating carbonyl O atom of Y99 neither contributes to HOMO⁻ nor LUMO⁺ of loop 3. The phenyl ring carbon atoms C_γ, C_ζ and hydroxyl O_h contribute predominantly to HOMO⁻, while the other ring carbon atoms, namely C_δ1, C_ε1, C_δ2 and C_ε2 contribute to LUMO⁺. A similar picture evolves from C⁽²⁾_X,Y138,α (Fig. 5b), with the ring carbon atoms C_γ, C_ζ contributing to both HOMO⁻ and LUMO⁺ and the O_h predominantly participating in HOMO⁻. The orbital specific contributions of the side chain O_h atom of Y99 and Y138 to HOMO⁻ reflect strong hybridization of 2p electrons (see ESI, Table S1†). The other polar residues contributing to LUMO⁺ electron density, S101 (loop 3) and N137 (loop 4) at loop position IX also show hybridization with dominating 2p character (see ESI, Table S2†). Thus the HOMO⁻ and the LUMO⁺ of the C-terminal domain loops share similar electronic structure but strikingly different from that of N-terminal domain loops.

Fig. 5 Atom specific contribution (a) C⁽²⁾_VII,Y99,α of Y99 towards HOMO⁻ (black) and LUMO⁺ (grey) of Ca²⁺–loop 3. (b) C⁽²⁾_X,Y138,α of Y138 towards HOMO⁻ (black) and LUMO⁺ (grey) of Ca²⁺–loop 4. (c) The nucleophilicity index, f_k⁻ of the atoms of Y99.

We perform the Fukui index calculation for all the loops. Both f_k⁻ and f_k⁺ of all the zwitterionic CaM loops are dominated by capping atoms. The C-terminal capping C_γO1O2⁻ group oxygen atoms show maximum nucleophilicity (∼0.5), while the N-terminal capping atoms of NH₃⁺ group exhibit maximum electrophilicity (∼0.5). We find significant values of f_k⁻ and f_k⁺ corresponding to Y99 atoms contributing to both HOMO⁻ and LUMO⁺ of Ca²⁺–loop 3. The f_k⁻ for all the non-hydrogen atoms of Y99 is shown in Fig. 5c. We find that the phenyl ring O_h atom shows maximum nucleophilicity followed by the ring carbon atom, C_γ. Comparing f_k⁻ and f_k⁺ of the O_h atom, clearly indicates that it can be suitable for nucleophilic attack to ATP in order to get phosphorylated. On the other hand, f_k⁻ of O_h atom of Y138 (see ESI, Table S3†) do not reflect its nucleophilic character in contrast to the in vitro experiments.⁸ The nucleophilicity index of the contributing atoms to HOMO⁻ and the electrophilicity index of the contributing atoms to LUMO⁺ are much lower than the capping atoms (see ESI, Tables S3 and S4†).

Discussion

Our calculations on the zwitterionic state of the isolated CaM loops indicate dominant contributions of terminal capping localized around the HOMO–LUMO levels. Such behavior is quite unlike the earlier study with neutral terminal capping,¹² where the HOMO–LUMO levels are free from capping effects. This behavior of charged terminals is similar to the effect of impurities on ground state energy spectrum.^37,38 Within the decay profile of C_γO1O2⁻ capping (for instance, ξ^(L1)_C-ter = 0.4 eV), there are a number of pure capping levels which are isolated and show no contribution from the loop atoms. The maximum of C_γO1O2⁻ capping contributions is separated from the adjacent pure capping level by 0.1 eV, which corresponds to approximately 12 000 nm. HOMO⁻ energy level corresponds to 3000 nm with respect to the maximum capping level. Although both wavelengths belong to infra-red (IR) range, the huge difference in wavelength should be measurable by IR spectroscopic techniques. On the other hand, the NH₃⁺ capping levels (for instance, ξ^(L1)_N-ter = 0.03 eV) are not so well separated from the loop atoms.

We also compare the contribution of zwitterionic charged capping with respect to that of neutral capping at the HOMO–LUMO levels. The maximum contribution of C_γO1O2⁻ capping of loops 1 and 2 occur at energies similar to the HOMO level in corresponding neutral capped systems. However, for both the zwitterionic capped Ca²⁺–loop 3 and Ca²⁺–loop 4 complexes, the maximum contribution of C_γO1O2⁻ capping is observed at about 0.5 eV higher than the corresponding HOMO level in the neutral capped cases (see ESI, Fig. S2†). The HOMO of zwitterionic Ca²⁺–loop 3 is at −5.14 eV compared to −5.71 eV in neutral case. Similarly, the HOMO of Ca²⁺–loop 4 in zwitterionic state occurs at −4.79 eV compared to −5.18 eV in neutral system.

The negatively charged C-terminal capping, C_γO1O2⁻ with an excess electron induces an additional electronic state within the HOMO–LUMO gap of the neutral capped peptides leading to bridging of the gap. The N-terminal NH₃⁺ capping contributes very close to the LUMO of the neutral capped CaM peptides. Thus the gap decreases from 5.71 eV to 4.98 eV in Ca²⁺ bound loop 3 and from 5.19 eV to 4.62 eV in Ca²⁺ bound loop 4 upon introducing zwitterionic charged states at the terminals. Since, the C_γO1O2⁻ capping contributions are not mixed with other residue contributions; they may act like sensors in the IR range.

The redefined HOMO⁻ and LUMO⁺ bear qualitative similarities with the HOMO–LUMO levels of neutral capped CaM loops. In case of the neutral capped N-domain loop 1, the HOMO finds participation from acidic aspartates, D22, D24 and polar G23, while other polar residues, T28 and T29 contribute to the LUMO. The nature of residues contributing to HOMO⁻ and LUMO⁺ levels of loop 1 is similar in both studies. The HOMO and the LUMO levels of loop 2 with neutral capping show contribution of acidic D64 and hydrophobic F65, respectively. The nature of contributing residues to HOMO⁻ with zwitterionic caps is similar; however the difference lies in the LUMO⁺, being governed by a polar residue. The HOMO and the LUMO levels of neutral capped C-domain Ca²⁺ bound loop 3 exhibits strong localized charge density on the polar side chain of Y99 similar to the present study. Moreover, the nucleophilic character of Y99 remains preserved with either capping, albeit a quantitative comparison of f_k⁻ of O_h atom reveals a more potential nucleophile (f_k⁻ ∼ −0.1) with neutral capping. We find localized electron density on acidic E139 at the HOMO and on the phenyl ring of Y138 at the LUMO of neutral capped loop 4. But with zwitterionic capping both HOMO⁻ and LUMO⁺ are predominated by Y138. However, the role of Y138 as a potential nucleophile remains obscured with either of the cappings.

We also consider a different conformation of Ca²⁺ bound loop 3 and loop 4 generated from MD simulation. The simulated conformation shows root mean squared deviation (RMSD) of 0.3 Å and 0.2 Å for Ca²⁺ bound loop 3 (see Fig. 6a) and loop 4 (see Fig. 6b) complexes with respect to their force-field optimized geometries. We perform single point energy calculation on the simulated conformation. The contributions of N-terminal capping, C⁽²⁾_N-ter (Fig. 6c) and C-terminal capping, C⁽²⁾_C-ter (Fig. 6d) of the simulated conformation of Ca²⁺–loop 3 complex is similar to that of the optimized conformation. The capping contributions of the Ca²⁺–loop 4 complex in both simulated and optimized conformations are also similar (Fig. 6e and f). We define the HOMO⁻ and the LUMO⁺ levels as earlier. The residue contributions to the HOMO⁻ and the LUMO⁺ levels in the MD generated conformation also reflect qualitative similarity. Y99 contributes predominantly to both these levels in Ca²⁺–loop 3 along with minor contribution from I100 and S101 to the LUMO⁺ level. In the simulated conformation of Ca²⁺ bound loop 4, the HOMO⁻ and the LUMO⁺ levels find predominant contribution from Y138 along with minor contributions from E139 to HOMO⁻ and N137 to LUMO⁺ level.

Fig. 6 Force-field optimized (yellow) and MD simulated (green) conformations of (a) Ca²⁺–loop 3 and (b) Ca²⁺–loop 4. The contribution of terminal capping, (c) C⁽²⁾_N-ter and (d) C⁽²⁾_C-ter of Ca²⁺–loop 3 complex for optimized (red) and simulated (black) conformations. The contribution of terminal capping, (e) C⁽²⁾_N-ter and (f) C⁽²⁾_C-ter of Ca²⁺–loop 4 complex for optimized (red) and simulated (black) conformations.

Conclusion

In conclusion, we perform implicit solvent QC calculations based on DFT approach for the isolated Ca²⁺ coordinated CaM loops³⁹ in zwitterionic state. We show that terminal capping contributions are localized near HOMO and LUMO levels which decay exponentially in the neighboring levels, so that one can define HOMO⁻ and LUMO⁺ levels with negligible terminal effects. The HOMO⁻ and LUMO⁺ show significant differences between the N- and the C-domain loops. HOMO⁻ of N-domain loops 1 and 2 are comprised of contributions from acidic aspartates, whereas LUMO⁺ by polar residues. However, HOMO⁻ and LUMO⁺ of C-domain loops 3 and 4 exhibit strong localized electron density on the phenyl rings of tyrosines. We show from the Fukui index that the terminal charges do not interfere with the nucleophilic character of Y99. Our prediction on exponential decay of C_γO1O2⁻ capping effects within the neighborhood of HOMO–LUMO levels can be experimentally verified through IR spectroscopy. Finally, we show a novel method of interpreting the electronic structure with charged terminal capping on an overall neutral polypeptide which forms a more realistic model of biologically active molecule like protein. The capping levels may have significance in device applications in the nanometer length scale.

Acknowledgements

S. S. thanks UGC, INDIA for fellowship; M. G. and J. C. thank DST for funding and MDR thanks the Associateship program of the SNBNCBS.

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Footnotes

† Electronic supplementary information (ESI) available: Five tables showing nature of hybridization, nucleophilic and electrophilic indices of atoms contributing to HOMO⁻ and LUMO⁺ and two figures illustrating exponential decay of terminal capping in different loops, comparison of zwitterionic and neutral capping contributions. See DOI: 10.1039/c6ra10846f

‡ Also at Unit of Nanoscience and Technology-II and The Thematic Unit of Excellence on Computational Materials Science, S. N. Bose National Centre for Basic Sciences, Sector III, Block JD, Salt Lake, Kolkata 700098, India.

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