Glutamine and Asparagine Side Chain Hyperconjugation-Induced Structurally Sensitive Vibrations

Abstract

We identified vibrational spectral marker bands that sensitively report on the side chain structures of glutamine (Gln) and asparagine (Asn). Density functional theory (DFT) calculations indicate that the Amide III^P (AmIII^P) vibrations of Gln and Asn depend cosinusoidally on their side chain OCCC dihedral angles (the χ₃ and χ₂ angles of Gln and Asn, respectively). We use UV resonance Raman (UVRR) and visible Raman spectroscopy to experimentally correlate the AmIII^P Raman band frequency to the primary amide OCCC dihedral angle. The AmIII^P structural sensitivity derives from the Gln (Asn) C_β–C_γ (C_α–C_β) stretching component of the vibration. The C_β–C_γ (C_α–C_β) bond length inversely correlates with the AmIII^P band frequency. As the C_β–C_γ (C_α–C_β) bond length decreases, its stretching force constant increases, which results in an upshift in the AmIII^P frequency. The C_β–C_γ (C_α–C_β) bond length dependence on the χ₃ (χ₂) dihedral angle results from hyperconjugation between the C_δ=O_ε (C_γ=O_δ) π* and C_β–C_γ (C_α–C_β) σ orbitals. Using a Protein Data Bank library, we show that the χ₃ and χ₂ dihedral angles of Gln and Asn depend on the peptide backbone Ramachandran angles. We demonstrate that the inhomogeneously broadened AmIII^P band line shapes can be used to calculate the χ₃ and χ₂ angle distributions of peptides. The spectral correlations determined in this study enable important new insights into protein structure in solution, and in Gln- and Asn-rich amyloid-like fibrils and prions.

Graphical abstract

Introduction

Amyloid-like fibril protein aggregates and prion proteins often contain stretches of glutamine (Gln) and asparagine (Asn) residues. For example, polyglutamine (polyGln)-rich fibrils are the pathological hallmarks of several “CAG” codon repeat diseases.^1–9 Similarly, Sup35p and Ure2p prions contain Gln-and Asn-rich regions that drive their aggregation and cause loss-of-function of these normally soluble proteins.¹⁰

Because Gln and Asn side chains can hydrogen bond to water, the peptide backbone, or other side chains, they serve unique roles in protein structure and conformational transitions. Unfortunately, there is relatively little known about the mechanisms by which the primary amide groups of Gln and Asn interact with other protein constituents or what role they play in the aggregation of prions and fibrils. Consequently, it is important to find spectroscopic markers that can be used to monitor the conformations and hydrogen bonding environments of Asn and Gln side chains in order to develop a deeper understanding of the roles that these residues play in protein aggregation.

There are few methods to quantitatively examine the conformations of Gln and Asn side chains in prion and fibril aggregates. Recent solid-state NMR studies^11–13 suggest that there are at least two different populations of Gln side chain conformers in polyGln fibrils. Sharma et al.¹⁴ claim on the basis of low-resolution X-ray fiber and powder diffraction data that the side chains in polyGln fibrils adopt an unusual bent conformation; however, these highly uncommon side chain structures have not been substantiated by other studies.

High resolution X-ray diffraction studies^15,16 on small peptide microcrystals that contain amyloidogenic sequences have revealed important, atomic-resolution details regarding the steric zipper interactions that could occur in Gln- and Asn-rich prions and fibrils. These studies indicate, for example, that differences in the structures and hydrogen bonding interactions of amino acid side chains give rise to different fibril polymorphs. However, the conformations observed in the small peptide crystals may not reflect the side chain structures and hydrogen bonding interactions that occur in bona fide prion and fibril aggregates.

UV resonance Raman (UVRR) is a powerful, emerging tool for studying the conformations of proteins, as well as the structure, local hydrogen bonding, and dielectric environments of amino acid side chains.^17–28 Deep UV excitation (∼200 nm) selectively resonance enhances secondary and primary amide vibrations.^29,30 Previous investigations of secondary amide vibrations have developed a detailed understanding of the UVRR spectral dependence on the peptide bond structure and its hydrogen bonding.^31–34 For example, Asher and co-workers^35–37 quantitatively correlated the Amide III₃ (AmIII₃) frequency to the peptide bond Ramachandran Ψ dihedral angle. They determined that the structural sensitivity of the AmIII₃ vibration derives from coupling between the peptide backbone amide N–H and C_α–H bending motions.³⁵ This fundamental insight enabled incisive investigations that elucidated, in detail, the mechanism of α-helix (un)folding in a wide range of solution environments.^38–43

We seek to develop a similar deep understanding of the UVRR spectral dependence of primary amide vibrations on the structure of Gln and Asn side chains. In this work, we discover the structural sensitivity of the Amide III^P (AmIII^P) vibration on the primary amide OCCC dihedral angle (the χ₃ and χ₂ angles of the side chains Gln and Asn, respectively). The potential energy distribution (PED) of this vibration in Gln (Asn) contains significant contributions of C_β–C_γ (C_α–C_β) stretching, N_εH₂ (N_δH₂) rocking, and C_δ–N_ε (C_γ–N_δ) stretching motions. We find that the structural sensitivity of the AmIII^P mode originates mainly from the C_β–C_γ (C_α–C_β) bond length dependence on the χ₃ (χ₂) dihedral angle. We demonstrate that the C_β–C_γ (C_α–C_β) bond length correlation on the χ₃ (χ₂) dihedral angle derives from hyperconjugation between the C_β–C_γ (C_α–C_β) σ orbital and the C_δ=O_ε (C_γ= O_δ) π* orbital.

We compare our results with the Gln and Asn entries of the Shapovalov and Dunbrack side chain rotamer library⁴⁴ and examine the dependence of Gln (Asn) χ₃ (χ₂) dihedral angles on the peptide backbone Ramachandran (Φ, Ψ) angles. We observe distinct χ₃ and χ₂ dihedral angle preferences for Gln and Asn residues that adopt PPII, β-sheet and α-helix Ramachandran angles. Applying this new insight and the dependence of the χ₃ dihedral angle on the AmIII^P vibrational frequency, we determine the χ₃ angle distribution of Gln₃ and Asp₂-Gln₁₀-Lys₂ peptides in aqueous solution. We find that Gln₃ and Asp₂-Gln₁₀-Lys₂ favor χ₃ dihedral angles similar to those of Gln in solution. This result is consistent with Gln₃ and Asp₂-Gln₁₀-Lys₂ containing side chains that are completely solvated.

Our work here develops a novel spectral marker for experimentally probing the structures of Asn and Gln side chains in fibrils and prion aggregates. Our methodology does not require extensive isotopic labeling or crystallization and allows us to monitor the side chain structural changes that occur during protein aggregation. This enables crucial, molecular-level insights into the role that Gln and Asn side chains play in stabilizing fibril and prion aggregates. We are developing new insights into why Gln- and Asn-rich sequences have strong propensities to aggregate into amyloid-like fibrils and prions.

Experimental Details

Materials

l-Glutamine (l-Gln, ≥99% purity), l-glutamine t-butyl ester hydrochloride (Gln-TBE, ≥98% purity), and glycyl-l-glutamine (Gly-Gln, ≥97% purity) were purchased from Sigma-Aldrich. d-Glutamine (d-Gln, 98% purity) was purchased from Acros Organics, and N-Acetyl-l-glutamine (NAcGln, 97% purity) was purchased from Spectrum Chemical Mfg. Corp. l-seryl-l-asparagine (Ser-Asn, ≥99% purity) was purchased from Bachem. Optima-grade H₂O was purchased from Fisher Scientific, and D₂O (99.9% atom D purity) was purchased from Cambridge Isotope Laboratories, Inc. Gln₃ was purchased from Pierce Biotechnology at 95% purity.

Sample Preparation

Gly-Gln and Ser-Asn were obtained as crystalline powders and used without further purification or recrystallization. d-Gln, NAcGln, l-Asn, and GlnTBE crystals were prepared by drying saturated solutions in water. l-Gln crystals were obtained by drying a saturated solution in the presence of 0.1 M NaCl. N-deuterated crystals were prepared via multiple rounds of recrystallization in D₂O. Samples of Gln₃ were prepared at 0.5 mg·mL⁻¹ in HPLC-grade water containing 0.05 M sodium perchlorate (Sigma-Aldrich, ≥98% purity). The sodium perchlorate was used as an internal intensity standard to allow us to subtract the contribution of water.

X-ray Diffraction

X-ray diffraction of crystals was performed using a Bruker X8 Prospector Ultra equipped with a copper microfocus tube (λ = 1.54178 Å). The crystals were mounted and placed in a cold stream of N₂ gas (230 K) for data collection. The frames collected on each crystal specimen were integrated with the Bruker SAINT software package using the narrow-frame algorithm. The Supporting Information discusses, in detail, the methods used to determine the unit cells and crystal structures of the compounds examined.

Visible Raman Spectroscopy

Visible excitation Raman spectra of crystals were collected using a Renishaw inVia spectrometer equipped with a research-grade Leica microscope. Spectra were collected using the 633 nm excitation line from a HeNe laser and a 5× objective lens. The spectrometer resolution was ∼2 cm⁻¹. The 918 and 1376 cm⁻¹ bands of acetonitrile⁴⁵ were used to calibrate the spectral frequencies.

UV Resonance Raman Spectroscopy

UV resonance Raman (UVRR) spectra of crystals were collected using CW 229 nm light generated by an Innova 300C FreD frequency doubled Ar⁺ laser.⁴⁶ The crystalline specimens were spun in a cylindrical brass cell to prevent the accumulation of thermal or photodegradation products. A SPEX triplemate spectrograph, modified for use in the deep UV, was utilized to disperse the Raman scattered light. A Spec-10 CCD camera (Princeton Instruments, model 735-0001) with a Lumagen-E coating was used to detect the Raman light. The power of UV light illuminating the sample ranged from ∼1.5 to 2 mW. The 801, 1028, 2852, and the 2938 cm⁻¹ bands of cyclohexane were used to calibrate the 229 nm excitation UVRR spectral frequencies.

UVRR solution-state measurements were made using ∼204 nm excitation. The UV light was generated by Raman shifting the third harmonic of a Nd:YAG laser (Coherent, Inc.) with H₂ gas (∼30 psi) and selecting the fifth anti-Stokes line. A thermostated (20°) flow cell was employed to circulate solutions in order to prevent the contribution of photo-degradation products. The scattered light was dispersed and imaged using a double monochromator, modified for use in the UV in a subtractive configuration⁴⁷ and detected with a Spec-10 CCD camera.

Computational Details

Density Functional Theory (DFT) Calculations

The DFT calculations⁴⁸ were carried out using the GAUSSIAN 09 package.⁴⁹ The geometry optimizations and frequency calculations were performed using the M06-2X functional⁵⁰ and the 6-311++g** basis set. The presence of water was simulated implicitly by employing a polarizable continuum dielectric model (PCM). Vibrational frequencies were calculated using the harmonic approximation. The calculated frequencies were not scaled. The potential energy distribution (PED) of each vibration was obtained from the Gaussian output files by employing a MATLAB program that we wrote (see Supporting Information). Figure 1 shows the DFT calculated minimum energy structure of l-Gln and the atomic labeling scheme. To study the conformational dependence of the Raman bands, we fixed the χ₃ dihedral angle of l-Gln, reoptimized the geometry, and calculated the harmonic vibrational frequencies for a series of conformers with χ₃ angles of −16°, 0°, 4°, ±30°, ±60°, ±90°, ±120°, ±150°, and ±180°.

Figure 1.

Geometry of optimized structure and atomic labeling scheme of l-Gln used in DFT calculations and band assignments.

Results and Discussion

Assignment of l-Gln UVRR Bands in H₂O and D₂O

Figure 2 shows the band-resolved ∼204 nm excitation UVRR spectra of l-Gln in H₂O and D₂O. Visible Raman and infrared spectra band assignments of l-Gln were reported previously by Ramirez and co-workers for both solid-state crystalline samples⁵¹ and in the solution state.⁵² Ramirez and co-workers made assignments without performing normal mode calculations in their study of crystalline l-Gln. In their solution-state study, they employed DFT calculations to aid in band assignments. We found that their reported frequencies did not match those in our solution-state UVRR spectra and that their band assignments were inconsistent with our intensity expectations of the resonance enhanced bands.

Figure 2.

UVRR spectra excited at ∼204 nm of l-Gln in (a) H₂O and (b) D₂O. The spectral contributions of the solvents have been subtracted. The reduced ${\chi }^2({\chi }_{\text{red}}^2)$ statistics for the spectral fits shown in (a) and (b) are 0.55 and 1.8, respectively.

In the work here, we perform a new normal mode analysis of l-Gln in order to assign our UVRR spectra. We employ DFT calculations that use a more modern functional (M06-2X) than that of Ramirez and co-workers. These assignments build off of our previous, detailed assignment of propanamide,²⁸ a model for the side chains of Gln and Asn. Our assignments of l-Gln in H₂O and D₂O are shown in Tables 1 and 2, respectively.

Table 1. UVRR Frequencies (cm⁻¹) and Assignments of l-Gln in H₂O.

expt	calcd	potential energy distributiona (≥5% contribution)
1679	1745	νCδOε (75), −νCδNε (8), βNεCδCγ (7)
1652	1666	δas′NH3 (48), −δasNH3 (44), −ρNH3 (5)
1620	1623	−σNεH2 (86), −νCδNε (10)
	1621	δasNH3 (40), δas′NH3 (48), δsNH3 (10)
1585	1715	−νCO (53), νCO (33), ρCαC (7)
1464	1494	σCβH2 (88)
	1466	−δsNH3 (33), σCγH2 (30), ωCγH2 (7), −ωCβH2 (5), νCβCγ (5)
1447	1460	−σCγH2 (44), −δsNH3 (36)
1427	1445	−ωCγH2 (17), νCγCδ (13), σCγH2 (13), ωCβH2 (13), −νCδNε(9), −νCβCγ (5), −δsNH3 (5), ρCδO (5)
1411	1419	−νCO (26), ρCαH (12), νCαC(11), ωCγH2 (8), βCOO (7), νCδNε (7), −νCO (7), −νCγCδ (6)
1365	1388	ρCαH (25), ωCβH2 (13), νCO (10), −ρ′CαH (9), νCαCβ (8), −τCβH2 (6), −νCαC (5)
1351	1358	−ρCαH (30), ωCβH2 (16), −τCβH2 (15), τCγH2 (9), νCδNε (6)
1328	1348	−τCβH2 (26), −ωCβH2 (18), −ρ′CαH (13), −νCδNε (11)
1293	1309	−τCγH2 (35), −ρ′CαH (26), ρCβH2 (8), −ρCαH (6)
1264	1272	−ωCγH2 (43), −ωCβH2 (20), νCδNε (13)
1206	1215	−τCβH2 (21), −νCαCβ (18), −τCγH2 (16), −ρ′NH3 (13), δNCαC(OO) (5)
1158	1153	−ρ′CαH (20), τCγH2 (17), −ρ′NH3 (13), τCβH2 (12), −νCαCβ (8), ρCγH2 (6)
1130	1122	νCβCγ (34), ρNεH2 (17), −νCαCβ (7), νCαN (6), −βNεCδCγ (5)
	1109	ρNH3 (27), −ρ′CαH (10), −ρNεH2 (10), −δ′NCC(OO) (9), −ρCαH (7), νCαN (7)
1110	1097	νCβCγ (26), −ρNεH2 (26), −νCδNε (13), −ρNH3 (8)
	1038	νCαN (36), −νCβCγ (9), ρCβH2 (8), ρ′NH3 (6), ρCγH2 (5), ρ′CαH (5)
1078	1003	ρNH3 (25), −νCαN (19), ρCγH2 (14), ρCβH2 (14), νCαCβ (7), −τCβH2 (5)
1006	974	−ρ′NH3 (38), νCαCβ (25), −νCαC (8), −σCCαCβ (7), νCαN (6)

^aν, stretch; δ_as, asymmetric deformation; δ_s, symmetric deformation; δ, deformation; σ, scissoring; ρ, rocking; ω, wagging; β, in-plane bending; τ, twisting.

Table 2. UVRR Frequencies (cm⁻¹) and Assignments of l-Gln in D₂O.

expt	calcd	potential energy distributiona (≥5% contribution)
1650	1739	νCδOε (78), −νCδNε (7), βNεCδCγ (7)
1637	1708	νCO (55), −νCO (34), −ρCαC (7)
1465	1494	σCβH2 (88)
1453	1465	−σCγH2 (48), −ωCγH2 (15), −νCβCγ (8), −νCδNε (7), ωCβH2 (6)
1440	1454	−σCγH2 (35), νCδNε (19), −νCγCδ (14), ωCγH2 (9), −ρCδOε (5)
1412	1424	−νCO (29), νCαC (12), −νCO (10), ωCβH2 (10), βCOO (9), νCδNε (9), ρCαH (8)
1368	1393	ωCβH2 (21), ρCαH (15), νCO (11), νCαCβ(8), −ρ′CαH (6), νCO (6), −νCαC (5), νCδNε (5)
1344	1362	−ρCαH (37), −ωCγH2 (13), νCδNε (12), ωCβH2 (11), ρ′CαH (7), σNεD2 (5)
	1349	−τCβH2 (44), τCγH2 (20), −ρCαH (15), −ρ′CαH (6)
	1304	−ρ′CαH (32), −τCγH2 (29), ρCβH2 (8), −ρCαH (7)
	1282	−ωCγH2 (37), −ωCβH2 (33), σNεD2 (8), ρCαH (7), νCδNε (6)
	1202	−δasND3 (23), δas′ND3 (20), τCβH2 (17), τCγH2 (12), νCαCβ (8)
	1198	δasND3 (27), τCβH2 (12), τCγH2 (11), −ρ′CαH (9), νCαCβ(8), δsND3 (7), −δas′ND3 (7)
	1186	−δas′ND3 (52), −δsND3 (27), −νCαN (8), −δasND3 (6)
1161	1150	σNεD2 (56), ρ′CδOε (11), νCγCδ (9), ωCγH2 (8)
	1131	νCαCβ(21), −δsND3 (16), −νCαN (14), δasND3 (13), −τCγH2 (5)
	1119	−νCβCγ (17), δasND3 (10), δNCαC(OO) (9), −νCαCβ(8), −δsND3 (8), σCγCβCα (7), −νCαN (6), δas′ND3 (5)
	1105	νCβCγ (44), −δsND3 (15), δasND3 (8), δas′ND3 (6), −νCαCβ (5)
	1058	ρCβH2 (21), ρ′CαH (16), ρCγH2 (12), δ′NCαC(OO) (9), −νCαC (6), δC′CαCβ(6), νCαCβ(5), −ρND3 (5)
992	998	νCαN (29), δsND3 (15), −δ′NCαC(OO) (10), −ρCαC (7), −νCβCγ (5), −σCCαCβ (5)
960	959	ρNεD2 (22), νCδNε (14), νCγCδ (10), −σNεD2 (9), −νCαN (9), −βNεCδCγ (8), νCαC (6), νCδOε (6)
929	920	νCαC (17), ρCγH2 (16), ρND3 (16), −τCβH2 (8), βCOO (8), −δ′NCαC(OO) (7), ΠNεCδCγ (6)

^aν, stretch; δ_as, asymmetric deformation; δ_s, symmetric deformation; δ, deformation; σ, scissoring; ρ, rocking; ω, wagging; β, in-plane bending; τ, twisting; Π, out-of-plane deformation.

The UVRR spectra are dominated by bands that derive from vibrations of the primary amide group. This is because these resonance enhanced vibrations couple to the strong ∼180 nm NV₁ electronic transition. These resonance enhanced amide bands contain significant contributions of C_δ–N_ε stretching because the electronic excited state is expanded along this coordinate.⁵³

The spectral region between 1600 and 1700 cm⁻¹ is dominated by two primary amide vibrations, the Amide I^P (AmI^P) and Amide II^P (AmII^P) bands. The superscript ^P denotes the primary amide to distinguish these vibrations from the widely known vibrations of secondary amides found in proteins. The AmI^P band is located at ∼1680 cm⁻¹ and derives mainly from C_δ=O_ε stretching. In D₂O, the AmI^P band (called the AmI'^P) downshifts to ∼1650 cm⁻¹. The AmII^P band at ∼1620 cm⁻¹ derives from a vibration whose PED contains mostly N_εH₂ scissoring (∼86%) and C_δ–N_ε stretching (∼10%). Upon N-deuteration, the C_δ–N_ε stretching and ND₂ scissoring motions decouple. This causes the AmII^P band to disappear, and a new band, which derives from N_εD₂ scissoring, appears at ∼1160 cm⁻¹.

The most intense features of the Gln spectra in Figure 2 occur in the region between 1400 and 1500 cm⁻¹. Most of the bands found in this region derive from CH₂ scissoring or wagging modes. However, we assign the most intense band, located at ∼1430 cm⁻¹, to a vibration that contains significant contributions of CH₂ wagging, C_γ–C_δ stretching, CH₂ scissoring, and C_δ–N_ε stretching in its PED. This assignment is based on our previous work with propanamide,²⁸ which shows a similar intense band at ∼1430 cm⁻¹.

The region between 1200 and 1400 cm⁻¹ contains bands that derive mostly from C_αH rocking, CH₂ wagging, and CH₂ twisting modes. We assign the ∼1365 and ∼1350 cm⁻¹ bands in the Figure 2a spectrum to C_αH rocking modes. We assign the strong bands located at ∼1330 cm⁻¹, ∼1290 cm⁻¹, and the very weak ∼1205 cm⁻¹ bands to CH₂ twisting modes. The ∼1265 cm⁻¹ feature is assigned to a CH₂ wagging vibration. Only two bands, at ∼1370 and ∼1345 cm⁻¹, appear in D₂O. We assign the ∼1370 cm⁻¹ band to a CH₂ wagging mode and the ∼1345 cm⁻¹ band to a C_αH rocking mode. We conclude that these vibrations appear strongly in the UVRR spectrum in Figure 2b because they contain significant C_δ–N_ε stretching.

The region between 1000 and 1200 cm⁻¹ contains bands that derive from vibrations with large C–C stretching, N_εH₂ rocking, or NH₃ rocking contributions. Most of the vibrations in this region are complex. We assign the ∼1160 cm⁻¹ band to a coupled C_αH rocking/CH₂ twisting mode. The PED of this vibration contains a significant contribution of NH₃ rocking, which likely accounts for the disappearance of this band upon N-deuteration. We assign the ∼1080 and ∼1005 cm⁻¹ bands to NH₃ rocking vibrations.

The remaining two bands in the 1000–1200 cm⁻¹ region are located at ∼1130 and ∼1110 cm⁻¹. The observed frequency difference between these two vibrations is ∼20 cm⁻¹, which is close to the calculated ∼25 cm⁻¹ difference of our DFT calculations. We assign the 1130 cm⁻¹ band to a vibration that is mainly an in-phase combination of C_β–C_γ stretching and N_εH₂ rocking. The ∼1110 cm⁻¹ band is assigned to a vibration that consists of an out-of-phase combination of C_β–C_γ stretching and N_εH₂ rocking. This vibration also contains a significant C_δ–N_ε stretching component (∼13%), which is in phase with N_εH₂ rocking.

The in-phase combination of N_εH₂ rocking and C_δ–N_ε stretching of the ∼1110 cm⁻¹ vibration is reminiscent of the AmIII mode of secondary amides. While complex, the AmIII vibration contains significant contributions of in-phase C–N stretching and N–H in-plane bending motions of the secondary amide group. We propose to call the ∼1110 cm⁻¹ mode the Amide III^P (AmIII^P) because the eigenvector composition of this vibration is analogous to that of the canonical AmIII of secondary amides. As discussed in detail below, the AmIII^P vibration is sensitive to the χ₃ and χ₂ dihedral angles of Gln and Asn.

Conformational Dependence of the AmIII^P Band

We performed DFT calculations on l-Gln molecules with χ₃ dihedral angles fixed at different values (see Computational section for details) in order to identify spectroscopic markers that are diagnostic of the side chain χ₃ and χ₂ dihedral angles of Gln and Asn, respectively. We examined the frequency dependence of different primary amide vibrations and found that the AmIII^P vibrational frequency and normal mode depends strongly on the OCCC dihedral angle.

Figure 3a shows the calculated cosinusoidal dependence of the AmIII^P vibrational frequency on the χ₃ dihedral angle. The maximum frequency of the vibration occurs at χ₃ ∼ 0°, while minima occur near χ₃∼ ± 90°. The Gln AmIII^P band frequency dependence on the χ₃ angle follows a cosinusoidal relationship:

Figure 3.

Calculated AmIII^P frequency and bond length dependence on the χ₃ dihedral angle of the Gln side chain. (a) AmIII^P frequency dependence, (b) C_β–C_γ bond length, (c) C_δ–N_ε bond length, (d) C_α–C_β bond length, and (e) the dependence of the AmIII^P frequency on the C_β–C_γ bond length.

$$\nu ({\chi }_3)={\nu }_0+Acos(2{\chi }_3)+Bcos({\chi }_3-C)$$ (1)

where ν₀ = 1084 cm⁻¹, A = 10 cm⁻¹, B = 3 cm⁻¹, and C = −31°. These parameters were calculated from a least-squares fit of eq 1 to the frequency dependence on the χ₃ angle in Figure 3a.

Figure 3a shows that the AmIII^P frequency dependence on the χ₃ dihedral angle is asymmetric about χ₃ ∼ 0°. This asymmetry is due to the chirality of l-Gln and l-Asn and leads to the requirement of two cosine terms to express the χ₃ frequency dependence of eq 1. This is evident when we compare the l-Gln χ₃ dependence on the AmIII^P frequency with that of butyramide (shown in Supporting Information Figure S1). In the case of butyramide, which is achiral, there is no asymmetry about 0°. As a result, the AmIII^P frequency dependence on the OCCC dihedral angle of butyramide can be satisfactorily modeled with just one cosine term (Supporting Information eq S1).

Origin of the OCCC Dihedral Angle Dependence of the AmIII^P Vibration

Understanding the conformational dependence of the AmIII^P frequency on the primary amide OCCC dihedral angle requires a detailed knowledge of the atomic motions that give rise to the vibration. On the basis of our normal mode calculations of Gln, butyramide (Supporting Information Table S14), and propanamide,²⁸ we conclude that N_εH₂ rocking, C_δ–N_ε stretching, and C_β–C_γ stretching define the AmIII^P vibration. However, depending on the OCCC dihedral angle, other motions such as C_βH₂ twisting and C_α–C_β stretching can contribute to this vibration.

Therefore, we examined how the Gln C_δ–N_ε, C_β–C_γ, and C_α–C_β bond lengths change as a function of the χ₃ dihedral angle in order to understand the origin of the conformational sensitivity of the AmIII^P vibration. Changes in these bond lengths impact the AmIII^P frequency by affecting the vibrational mode bond force constants. As seen in Figure 3b–d, all the bond lengths show a dependence on the χ₃ dihedral angle. However, as seen in Figure 3b, the C_β–C_γ bond length shows the largest dependence on the χ₃ dihedral angle. The AmIII^P vibrational frequency has a strong correlation with the C_β–C_γ bond length, as shown in Figure 3e. The AmIII^P vibrational frequency increases as the C_β–C_γ bond length decreases and vice versa.

The C_β–C_γ bond length dependence on the χ₃ dihedral angle appears to be due to hyperconjugation between the C_β–C_γ σ and the C_δ=O_ε π* orbitals (Figure 4). This interaction is strongest when these orbitals maximally overlap in the absence of significant phase cancellation due to the π* orbital antisymmetry. When hyperconjugation occurs, the σ orbital donates electron density to the π* orbital, which decreases the C_β–C_γ bond order and increases its bond length. This decreases the C_β–C_γ stretching force constant, which downshifts the AmIII^P frequency.

Figure 4.

Hyperconjugation results in the C_β–C_γ bond length sensitivity to the χ₃ dihedral angle. Overlap of C_β–C_γ σ and C_δ=O_ε π* NBO molecular orbitals when the χ₃ dihedral angle is (a) 0°, (b) +90°, and (c) ±180°.

We tested this hypothesis with natural bond orbital (NBO) analysis, which allows the DFT calculated electron densities to be displayed in terms of approximate σ and π* molecular orbitals. According to our hypothesis, the C_β–C_γ bond length should be largest when hyperconjugation is maximized and smallest when there is no hyperconjugation. Indeed, as seen in Figure 4b, there is significant overlap of the C_β–C_γ σ and C_δ=O_ε π* NBO molecular orbitals at ±90°, where the C_β–C_γ bond length is largest. In contrast, at χ₃ ∼ 0°, where the C_β–C_γ bond length is shortest, the orbital overlap cancels due to the antisymmetry of the π* orbital. Figure 5 shows the NBO charge on the C_β atom. As expected from our hyperconjugation hypothesis, the NBO C_β atom charge is less negative at χ₃ ∼ ±90° compared to χ₃ ∼ 0°. The NBO C_β atom charge becomes even more negative at χ₃ ∼ ±150° and χ₃ ∼ ±180°, even without additional hyperconjugation of the C_β–C_γ σ and C_δ=O_ε π* orbitals. This result is likely an artifact because these extreme χ₃ dihedral angles are associated with physically impossible high energy structures that will be subject to other electron density alterations.

Figure 5.

NBO charge of C_β in l-Gln as a function of the χ₃ dihedral angle.

Our model accounts for the AmIII^P frequency downshift as the dihedral angles approach χ₃ ∼ ±90°, where hyperconjugation is strongest. This behavior is the reverse of the Bohlmann effect,^54–57 where a “negative” hyperconjugation transfers electron density from a lone pair orbital to an optimally positioned C–H σ* orbital. This decreases the C–H bond order and substantially downshifts the C–H stretching frequencies.

Experimental Dependence of AmIII^P Band Frequency on OCCC Dihedral Angle

We experimentally examined the dependence of the AmIII^P band frequency on the primary amide OCCC dihedral angle by measuring the UVRR and visible Raman spectra of different Gln and Asn derivatives in the solid-state. We determined the structures of each of the different Gln and Asn derivative crystals with X-ray diffraction and assigned the AmIII^P band by performing DFT calculations and examining band shifts upon N-deuteration. Our X-ray diffraction methods and the band assignments of the crystals are discussed, in detail, in the Supporting Information.

Dependence of AmIII^P Band Frequency in Crystals

Figure 6 shows the AmIII^P frequency dependence on the experimentally determined primary amide OCCC dihedral angles. We fit the experimental data to a function of the same form as eq 1, obtaining the following relationship:

Figure 6.

Experimental correlation of the AmIII^P frequency to the χ₃ dihedral angle. The average frequency (from the 633 and 229 nm Raman spectra) of the AmIII^P band was plotted as a function of the OCCC dihedral angle: 1 = l-Gln, 2 = Gly-Gln, 3 = d-Gln, 4 = GlnTBE, 5 = NAcGln, and 6 = Ser-Asn. The data were fit with eq 2 (black line, $r_{\text{adj}}^2=0.83$). The blue curve corresponds to eq 3. The red curve corresponds to eq 4. The yellow curve corresponds to eq 5 and is an average of the red and blue curves.

$$\nu ({\chi }_3)=1066({\text{cm}}^{-1})+29({\text{cm}}^{-1})cos(2{\chi }_3)+9({\text{cm}}^{-1})cos({\chi }_3+99°)$$ (2)

which is shown in the Figure 6 black curve. To obtain the eq 2 parameters, we fixed the A/B ratio to ∼3 as found in eq 1 and performed a least-squares minimization of the experimental data. Equation 2 provides an excellent fit of the experimental data and captures the chiral asymmetry that occurs near χ₃∼ ±90°.

Dependence of AmIII^P Band Frequency for Fully Hydrated Primary Amides

The AmIII^P band frequency also depends on the local hydrogen bonding and dielectric environment of the primary amide group.²⁸ In water, the AmIII^P band of l-Gln is located at ∼1110 cm⁻¹, as compared with ∼1097 cm⁻¹ in the solid-state. On the basis of Rhys et al.'s neutron diffraction study,⁵⁸ the solution-state equilibrium structure of l-Gln in water does not appear to differ significantly from the single known l-Gln crystal structure.⁵⁹ From their solution-state structure, we determine that the equilibrium χ₃ dihedral angle of l-Gln in water is ∼ −12.8°. This differs by less than a degree (−13.54°) from the l-Gln crystal examined in this study. Thus, by setting the AmIII^P frequency to 1110 cm⁻¹, χ₃ to −13.54°, and solving for ν₀, we obtain eq 3:

$$\nu ({\chi }_3)=1083({\text{cm}}^{-1})+29({\text{cm}}^{-1})cos(2{\chi }_3)+9({\text{cm}}^{-1})cos({\chi }_3+99°)$$ (3)

which is shown by the Figure 6 blue curve. This equation correlates the AmIII^P band frequency to OCCC dihedral angles for situations in which the primary amide group is fully exposed to water, such as in polyproline II-like (PPII-like) structures, 2.5₁-helices,⁶⁰ and extended β-strand-like peptide conformations dissolved in water.

Dependence of AmIII^P Band Frequency for Low Dielectric Constant and Weak Hydrogen Bonding Environments

The AmIII^P frequency downshifts ∼15 cm⁻¹ in the low dielectric and hydrogen bonding environment of acetonitrile compared to that in water (see Supporting Information and Figure S6). This downshift derives from the different water versus acetonitrile stabilizations of the ground state O_ε=C_δN_εH₂ and ⁻O_εC_δ=N_εH₂⁺ resonance structures of the primary amide group.²⁸ In both solvents, the O_ε=C_δN_εH₂ resonance structure dominates; however, in acetonitrile, the ⁻O_εC_δ=N_εH₂⁺ resonance structure contributes less than in water. Thus, the C_δ–N_ε bond length is larger in acetonitrile compared to water due to the lesser favorability of the ⁻O_εC_δ=N_εH₂⁺ resonance structure. Consequently, there is a smaller C_δ–N_ε stretching force constant in acetonitrile compared to water, which results in a downshift of the AmIII^P frequency.

Equation 3 can be modified in order to account for situations where the primary amide group is not engaged in significant hydrogen bonding interactions or when located in a low dielectric environment. We apply a 15 cm⁻¹ downshift in ν₀ from eq 3 to determine eq 4:

$$\nu ({\chi }_3)=1068({\text{cm}}^{-1})+29({\text{cm}}^{-1})cos(2{\chi }_3)+9({\text{cm}}^{-1})cos({\chi }_3+99°)$$ (4)

which is shown in red in Figure 6.

Dependence of AmIII^P Band Frequency for Unknown Dielectric and Hydrogen Bonding Environments

We suggest the use of eq 5, which is the average of eqs 3 and 4, for cases where the hydrogen bonding and dielectric environment of the primary amide group is unknown:

$$\nu ({\chi }_3)=1076({\text{cm}}^{-1})+29({\text{cm}}^{-1})cos(2{\chi }_3)+9({\text{cm}}^{-1})cos({\chi }_3+99°)$$ (5)

It can be applied, for example, to determine the side chain χ₃ and χ₂ dihedral angles of Gln and Asn residues located in turn structures of proteins. For these residues, it may not be clear if the side chains are hydrogen bonded to water, to other side chains, or the peptide backbone. Equation 5 is shown by the yellow curve in Figure 6.

Predicting Side Chain χ₃ and χ₂ Dihedral Angles in Gln and Asn as a Function of Ramachandran (Φ, Ψ) Angles

Shapovalov and Dunbrack⁴⁴ recently developed a new peptide backbone dependent rotamer library, which includes the nonrotameric Gln and Asn side chain χ₃ and χ₂ dihedral angles. Their database was compiled by analyzing high resolution crystal structures from the Protein Data Bank (PDB) and consists of ∼30000 entries for Asn and ∼20000 entries for Gln. Parts a and b of Figure 7 show Ramachandran plots of all of the Gln and Asn entries in the Shapovalov and Dunbrack database. The Gln and Asn side chains populate similar regions of the Ramachandran plot, and both show a preference for α-helical region (Φ, Ψ) angles. Asn populates a much broader range of (Φ, Ψ) angles, especially in the nearly forbidden “bridge” region between β-sheet and α-helical regions of the Ramachandran plot.

Figure 7.

Gln and Asn side chain χ₃ and χ₂ dihedral angle dependence on secondary structure. Plots showing Ramachandran angles for PDB entries from the Shapovalov and Dunbrack database of (a) Gln and (b) Asn. The colored boxes correspond to canonical PPII (Φ = −65°, Ψ = 145°) angles (red), β-sheet (Φ = −115°, Ψ = 130°) angles (blue), and α-helix (Φ = −63°, Ψ = −43°) angles (yellow). Distributions of χ₃ and χ₂ dihedral angles for Gln and Asn residues that have (Φ, Ψ) angles close to canonical: (c,d) PPII-like, (e,f) β-sheet, and (g,h) α-helical structures.

We used the Shapovalov and Dunbrack database to examine the side chain χ₃ and χ₂ dihedral angle preferences of Gln and Asn residues that possess canonical PPII, β-sheet, or α-helix Ramachandran angle values. On the basis of work by Richardson⁶¹ and Karplus,⁶² we assume (Φ, Ψ) angles centered around (−65°, 145°) for canonical PPII structures, (−115°, 130°) for canonical β-sheets and (−63°, −43°) for canonical α-helices. Parts c–h of Figure 7 depict histograms of the χ₃ and χ₂ dihedral angles observed for the population of Gln and Asn residues with canonical PPII, β-sheet or α-helical Ramachandran angles.

The Gln and Asn side chain χ₃ and χ₂ dihedral angles clearly depend upon the peptide bond Φ and Ψ angles. This correlation could result from a preference for particular χ₃ or χ₂ dihedral angles for stretches of consecutive peptide bonds with (Φ, Ψ) angles that result in PPII, β-sheet, or α-helical secondary structures. Alternatively, it could result from a preference for χ₃ or χ₂ dihedral angles for the (Φ, Ψ) angle values of their individual peptide bonds.

The χ₃ and χ₂ dihedral angle histograms of Gln and Asn residues that populate the canonical PPII region of the Ramachandran plot are shown in Figure 7c,d. The distribution of χ₃ angles adopted by Gln is broader than that of the χ₂ angles of Asn. Both histograms are centered about negative dihedral angles, with Gln showing a peak at around χ₃ ∼ −8° and Asn showing a peak near χ₂ ∼ −36°. It should be noted that the bias due to the l-amino acid chirality gives rise to a clear preference for negative χ₂ dihedral angles for the shorter side chain Asn residues.

The χ₃ and χ₂ dihedral angle histograms of Gln and Asn with β-sheet (Φ, Ψ) angles in Figure 7e,f differ dramatically from one another. The population of Gln χ₃ dihedral angles (Figure 7e) is nearly symmetric about χ₃ ∼ 0°. The histogram is bimodal, with two peaks located near χ₃ angles of ∼ −44° and ∼41°. In contrast, the population of Asn residues (Figure 7f) predominately adopts negative dihedral angles and is peaked around χ₂ ∼ −61°. A minor peak also occurs around χ₂ ∼ 56°.

Parts g and h of Figure 7 show histograms of the χ₃ and χ₂ dihedral angles of Gln and Asn residues that adopt canonical α-helical Ramachandran angles. As in Figure 7e, the Figure 7g Gln χ₃ dihedral angle population is roughly bimodal and nearly symmetric about χ₃ ∼ 0°. It is peaked at χ₃ angles of ∼ −34° and ∼45°. In contrast, in Figure 7h, the population of Asn χ₂ dihedral angles is narrow and sharply peaked at χ₂ ∼ −19° with two minor peaks at χ₂ ∼ −49° and ∼62°.

The χ₃ and χ₂ dihedral angle dependencies on the peptide bond Ramachandran angles, shown by the Shapovalov and Dunbrack database, enable us to predict the most probable AmIII^P frequencies of Gln and Asn residues that adopt canonical PPII, β-sheet, and α-helix (Φ, Ψ) angles (shown in Table 3). For example, using eq 3, we calculate that Gln and Asn side chains with PPII (Φ, Ψ) angles will have a maximum probability of showing AmIII^P bands centered at ∼1111 cm⁻¹ and ∼1096 cm⁻¹, respectively. Similarly, we calculate that the AmIII^P bands of Gln residues with β-sheet Ramachandran angles will have the greatest probability of being located at ∼1080 cm⁻¹ and/or ∼1089 cm⁻¹. In contrast, the AmIII^P bands for Asn residues with β-sheet (Φ, Ψ) angles will have the largest probability of being located at ∼1064 cm⁻¹ and/or ∼1075 cm⁻¹. For α-helical Ramachandran angles, we calculate that the probability maxima for AmIII^P bands will be at ∼1076 cm⁻¹ and/or ∼1098 cm⁻¹ for Gln and ∼1058, ∼1085, and/or ∼1107 cm⁻¹ for Asn residues.

Table 3. Predicted AmIII^P Frequencies and OCCC Dihedral Angles for Gln and Asn Residues with Different Ramachandran Angles.

	Φ (deg)	Ψ (deg)	Gln		Asn
			χ3 (deg)	AmIIIP freq (cm−1)	χ2 (deg)	AmIIIP freq (cm−1)
PPII	−65	145	−8 (−22, −32)a	1111 (1106, 1099)a	−36	1096
β-sheet	115	130	−44, 41	1089, 1080	−6, 56	1075, 1064
α-helix	−63	−43	−34, 45	1098, 1076	−49, −19, 62	1085, 1107, 1058

^aValues in parentheses were measured experimentally for Gln₃ and Asp₂-Gln₁₀-Lys₂.

We can calculate the expected Raman spectral AmIII^P band shapes from the Gln χ₃ and Asn χ₂ dihedral angle histograms in Figure 7 using the AmIII^P Raman band frequency dependencies of eqs 2–5. These calculated band shapes (not shown) are unphysically broad (>100 cm⁻¹). This clearly indicates that these histograms derive from the inhomogeneous distribution of χ₃ and χ₂ angles of individual Gln and Asn residues within the proteins found in the Shapovalov and Dunbrack database. This distribution of Raman frequencies from the calculated AmIII^P band is much broader than the homogeneous line width of an AmIII^P band expected for a single Gln and Asn residue in a typical PPII, β-sheet, or α-helix conformation in proteins. The large widths of the Gln χ₃ and Asn χ₂ dihedral angle histograms result because the residues in the Shapovalov and Dunbrack database exist in a larger distribution of conformations, hydrogen bonding states, and chemical environments than we have so far encountered in our UVRR investigations.

Experimentally Determined Gln PPII-like Structure Peptide χ₃ Dihedral Angles

UVRR Spectra of Gln Peptides in PPII-like Structures

We examined the UVRR spectra of two peptides, Gln₃ and Asp₂-Gln₁₀-Lys₂, in order to determine their solution-state χ₃ angles. Xiong et al.³⁰ previously showed that Asp₂-Gln₁₀-Lys₂ exists in predominately PPII-like and 2.5₁-helix-like conformations when prepared using a “disaggregation” protocol developed by Wetzel and co-workers.⁶³ In this protocol, the Asp₂-Gln₁₀-Lys₂ peptide is initially dissolved in a mixture of trifluoroacetic acid and hexafluoroisopropanol. These solvents are subsequently evaporated under dry N₂ gas, and the peptide is redissolved in pure water.

The UVRR spectra indicate that Gln₃ has predominately PPII-like peptide bond conformations. Figure 8a shows the peak fitted ∼204 nm excitation UVRR spectrum of Gln₃ in the region between 1050 and 1500 cm⁻¹. The AmIII₃ region, between ∼1200 and 1280 cm⁻¹, is most sensitive to the secondary structure of the peptide because its frequency depends on the Ramachandran Ψ angle.^35,37 This region is well fit by two Gaussian bands located at ∼1210 and ∼1260 cm⁻¹. Using the methodology of Mikhonin et al.,³⁷ we correlated the band peak positions to their Ψ angles. We used their eq 6A to correlate the 1210 cm⁻¹ frequency of the AmIII₃ band to a Ψ angle of 103° ± 3° and the 1260 cm⁻¹ frequency to a Ψ angle of 157° ± 2°. The Ψ angle of ∼157° derives from peptide bonds situated in PPII-like conformations, while the Ψ angle of ∼103° derives from peptide bond situated in β-strand-like conformations. Assuming identical Raman cross sections for these two different species, we find that the peptide bonds are dominated by PPII-like Ψ angles (∼87 ± 2%), while a small fraction adopt β-strand-like Ψ angles (∼13 ± 2%). This is supported by the circular dichroism spectra of Gln₃ shown in Supporting Information Figure S7, which show a predominantly PPII spectral signature.

Figure 8.

Deconvolution of the UVRR spectra of Gln₃ and Asp₂-Gln₁₀-Lys₂. (a) Fitting the 204 nm excitation UVRR spectrum of Gln₃. (b) The 198–204 nm difference spectrum of Asp₂-Gln₁₀-Lys₂ taken from Xiong et al.³⁰ The inset shows the AmIII^P region of Asp₂-Gln₁₀-Lys₂. The ${\chi }_{\text{red}}^2$ statistics for the spectral fits shown in (a) and (b) are 1.1 and 0.74, respectively.

χ₃ Dihedral Angle Determination of Side Chains in Gln Peptides

The AmIII^P bands of Gln₃ and Asp₂-Gln₁₀-Lys₂ are found in the region between ∼1050 and 1150 cm⁻¹. On the basis of our normal mode analysis of Gln, we fit this region for Gln₃ with four bands that derive from C_αH rocking/C_γH₂ twisting, C_β–C_γ stretching/N_εH₂ rocking, NH₃ rocking/C_α–N stretching, and the AmIII^P vibrations. For Gln₃, these bands are located within a broad asymmetric spectral feature at ∼1080, ∼1106, ∼1130, and ∼1160 cm⁻¹.

We assign these Gln₃ bands based on our analysis of Gln. We assign the ∼1160 cm⁻¹ band to a C_αH rocking/C_γH₂ twisting mode, the ∼1130 cm⁻¹ band to a C_β–C_γ stretching/N_εH₂ rocking vibration, and the ∼1080 cm⁻¹ band to a NH₃ rocking/C_α–N stretching mode. The ∼1106 cm⁻¹ band appears as a low-frequency shoulder feature and is assigned to the AmIII^P vibration. This is very close to the predicted AmIII^P vibrational frequency band center from the Gaussian fit of PPII-like structures in Figure 7c, as listed in Table 3. In fact, the AmIII^P frequency band center of Gln₃ differs by only ∼5 cm⁻¹ from the predicted frequency band center (∼1111 cm⁻¹) for PPII Ramachandran angles.

Figure 8b shows the 198–204 nm difference spectrum of disaggregated Asp₂-Gln₁₀-Lys₂ published by Xiong et al.³⁰ Xiong et al. showed that excitation at 198 nm enhances the primary amide UVRR bands more than does excitation at 204 nm. Thus, the Figure 8b Asp₂-Gln₁₀-Lys₂ difference spectrum is dominated by the primary amide Gln side chain bands with little interference from the secondary amide peptide bond UVRR bands.

The inset in Figure 8b shows the region where the AmIII^P band of Asp₂-Gln₁₀-Lys₂ is located. We parsimoniously peak fit this region to three Gaussian bands located at ∼1099, ∼1118, and ∼1140 cm⁻¹. Using prior knowledge from our analysis of Gln, we assign the bands at ∼1118 and ∼1140 cm⁻¹ to the C_β–C_γ stretching/N_εH₂ rocking and C_αH rocking/C_γH₂ twisting vibrations, respectively. The ∼1099 cm⁻¹ band is assigned to the AmIII^P band.

The AmIII^P bandwidths of Gln₃ and Asp₂-Gln₁₀-Lys₂ are ∼30 cm⁻¹, which is similar to that of Gln in H₂O (Figure 2a). These bandwidths are roughly twice as large as those found in the Raman spectra of the different Gln and Asn derivative crystals, which we measure to be on average ∼13.3 ± 5.0 cm⁻¹. This bandwidth is significantly larger than our spectrometer resolution of ∼4.5 cm⁻¹. Thus, if we assume a Lorentzian band shape, we estimate that the AmIII^P band homogeneous line width for a Gln compound with a well-defined χ₃ angle is ∼6.6 cm⁻¹. The fact that the AmIII^P bandwidths of solution-state Gln, Gln₃, and Asp₂-Gln₁₀-Lys₂ are much broader than those measured in our crystals suggests that there is a distribution of hydrogen bonding states and χ₃ angles in these compounds.

Given the estimated homogeneous line width, we can roughly calculate the distribution of χ₃ angles of Gln, Gln₃, and Asp₂-Gln₁₀-Lys₂ by using a methodology that is similar to that of Asher et al.³⁶ To do this, we assume that the inhomogeneously broadened AmIII^P bands derive from a distribution of different χ₃ dihedral angles, which can be represented as the sum of M Lorentzian bands:

$$A(\nu )=\frac{1}{\pi }\sum _{i=1}^M{I}_i\frac{{\mathrm{\Gamma }}^2}{{\mathrm{\Gamma }}^2+{(\nu -{\nu }_i)}^2}$$ (6)

where I_i is the intensity of a Lorentzian band that occurs at a given center frequency, ν_i, and Γ is the homogeneous line width.

We can apply eq 3 to correlate the ν_i AmIII^P frequencies of the M Lorentzian bands to their corresponding χ₃ dihedral angles. As shown in Figure 6, a single AmIII^P frequency can correspond to as many as four possible χ₃ dihedral angles. However, the Shapovalov and Dunbrack database show that χ₃ dihedral angles that are greater than +90° and less than −90° are nearly forbidden (Figure 7). Thus, we consider only the two χ₃ dihedral angle solutions that are found in the region between −90° and +90°, as shown in Figure 9.

Figure 9.

χ₃ dihedral angle historgrams calculated by decomposing AmIII^P bands into a sum of Lorentzians for (a) Gln, (b) Gln₃, and (c) Asp₂-Gln₁₀-Lys₂ in water. Because the solution to eq 3 is double valued between ±90°, the histograms show two peaks. The histograms were fit to two identical Gaussians that differed only in center χ₃ dihedral angles (shown in dashed lines). The sum of the Gaussians is shown in the solid red lines.

To determine which of the two remaining χ₃ dihedral angle solutions is occurring in our peptides, we first fit the histograms to the sum of two Gaussians with identical amplitudes, A, and widths, w, but different center χ₃ angles, χ̄_3,1 and χ̄_3,2:

$$I({\chi }_3)=A{e}^{-{\left(\frac{{\chi }_3-{\overline{\chi }}_{3,1}}{w}\right)}^2}+A{e}^{-{\left(\frac{{\chi }_3-{\overline{\chi }}_{3,2}}{w}\right)}^2}$$ (7)

The Gln, Gln₃, and Asp₂-Gln₁₀-Lys₂ results all show one Gaussian centered at negative χ₃ angles and another Gaussian centered at positive χ₃ angles (Figure 9). For Gln, we assume that the Gaussian centered at χ₃ ∼ −13° is the physically relevant solution based on the neutron diffraction study of Rhys et al.⁵⁸ For Gln₃ and Asp₂-Gln₁₀-Lys₂, we conclude that the Gaussians centered at negative χ₃ angles correspond to the physically relevant solutions to eq 3 because they fall within the range of χ₃ dihedral angles most commonly adopted by Gln residues that populate PPII (Φ, Ψ) angles (Figure 7c).

Figure 10 shows the resulting χ₃ dihedral angle distributions for Gln, Gln₃, and Asp₂-Gln₁₀-Lys₂ by assuming the physically relevant solutions to eq 3. The distributions of Gln₃ and Asp₂-Gln₁₀-Lys₂ populate χ₃ angles similar to that of Gln. This suggests that primary amides of Gln₃ and Asp₂-Gln₁₀-Lys₂ are fully solvated like that of monomeric Gln in water. Thus, the Gln side chains are not engaged in side chain–backbone peptide bond hydrogen bonding as previously hypothesized.⁶⁴

Figure 10.

Comparison of χ₃ dihedral angle distributions between (a) Gln, (b) Gln₃ in a predominately PPII-like conformation, and (c) Asp₂-Gln₁₀-Lys₂ in a PPII/2.5₁-helix equilibrium. (d) χ₃ angle distribution of Gln residues with PPII-like Ramachandran angles from the Shapovalov and Dunbrack database.

Determination of the Gibbs Free Energy Landscape for Gln and Gln Peptides along the χ₃ Dihedral Angle Reaction Coordinate

The structure sensitivity of the AmIII^P band enables us to determine the Gibbs free energy landscape of the Gln side chains along the χ₃ dihedral angle structure coordinate. To do this, we assume that the probability of each χ_3,i angle in the χ₃ dihedral angle distributions of Gln, Gln₃, and Asp₂-Gln₁₀-Lys₂ shown in Figure 10a–c is given by a Boltzmann distribution:

$$\frac{p({\chi }_{3,i})}{p({\chi }_{3,0})}=e^{-(\mathrm{\Delta }G({\chi }_{3,i})/RT)}$$ (8)

where p(χ_3,i)/p(χ_3,0) is the ratio of populations with χ₃ angles χ_3,i and χ_3,0. The angle, χ_3,0, is the minimum energy χ₃ angle, R is the molar gas constant, T is the experimental temperature (293 K), and ΔG(χ_3,i) = G(χ_3,i) − G(χ_3,0). We assume in eq 8 that each χ₃,_i dihedral angle state has a degeneracy of one.

To calculate the free energy difference, ΔG(χ_3,i), between a particular χ_3,i angle and the equilibrium χ_3,0 angle, we rearrange eq 8:

$$\mathrm{\Delta }G({\chi }_{3,i})=-RTln\left[\frac{p({\chi }_{3,i})}{p({\chi }_{3,0})}\right]$$ (9)

Figure 11 shows the calculated Gibbs free energy landscapes of Gln, Gln₃, and Asp₂-Gln₁₀-Lys₂ along the χ₃ dihedral angle structure coordinate. We model the side chain free energies about the equilibrium χ_3,0 angles in terms of a simple Hooke's Law torsional model:

Figure 11.

Gibbs free energy landscapes of (a) Gln, (b) Gln₃, and (c) Asp₂-Gln₁₀-Lys₂. The energy wells can be modeled by assuming a harmonic oscillator model torsional spring: ΔG(χ_3,i) = (τ/2)(χ_3,i − χ_3,0)², where τ is the torsional spring force constant and (χ_3,i − χ_3,0) is the displacement from the equilibrium position.

$$\mathrm{\Delta }G({\chi }_{3,i})=\frac{\tau }{2}{({\chi }_{3,i}-{\chi }_{3,0})}^2$$ (10)

where τ is the torsional force constant. We can fit the free energy landscapes in Figure 11 to eq 10 to determine the torsional force constants along the χ₃ dihedral angle coordinate of Gln, Gln₃, and Asp₂-Gln₁₀-Lys₂. We find that τ ∼ 12 J·mol⁻¹·deg⁻² for Gln, ∼ 16 J·mol⁻¹·deg⁻² for Gln₃, and ∼ 13 J·mol⁻¹·deg⁻² for Asp₂-Gln₁₀-Lys₂. The similarity of the Gln₃ and Asp₂-Gln₁₀-Lys₂ χ₃ angle torsional force constants of Gln most likely results from the similar side chain constraints and solvation states of these compounds.

Conclusions

We determined the dependence of the AmIII^P band frequency on the χ₃ and χ₂ dihedral angles of Gln and Asn side chains. The AmIII^P vibration is complex and consists of C_δ–N_ε (C_γ–N_δ) stretching and N_εH₂ (N_δH₂) rocking motions that are out-of-phase with C_β–C_γ (C_α–C_β) stretching in Gln (Asn). The frequency of the AmIII^P vibration shows a cosinusoidal dependence on the χ₃ and χ₂ dihedral angles of the Gln and Asn side chains. The structural sensitivity of the AmIII^P vibration derives from hyperconjugation between the C_β–C_γ (C_α–C_β) σ and the C_δ=O_ε (C_γ=O_δ) π* orbitals. Hyperconjugation between these two orbitals increases the C_β–C_γ (C_α–C_β) bond length, which decreases the C_β–C_γ (C_α–C_β) stretching force constant and causes a downshift in the AmIII^P frequency. In this case, hyperconjugation gives rise to spectroscopic markers diagnostic of local dihedral angles. This suggests that future studies of conformationally dependent hyperconjugation interactions will enable the discovery of new, structurally sensitive spectroscopic makers.

The correlations between the AmIII^P frequency and the χ₃ and χ₂ dihedral angles of Gln and Asn side chains will be useful for protein conformational investigations, particularly for amyloid-like fibril and prion aggregates. In general, fibril and prion aggregates are insoluble and cannot be crystallized. Therefore, there are few approaches to obtain molecular-level structural information. As a result, little is known about the structure of Gln and Asn side chains in fibrils. The AmIII^P spectroscopic marker band enables us to experimentally probe conformations of the Gln side chains of polyGln fibrils in order to obtain new, molecular-level insights into fibril structures.