Peptide secondary structure folding reaction coordinate: Correlation between uv raman amide iii frequency, psi ramachandran angle, and hydrogen bonding

We used UV resonance Raman (UVRR) spectroscopy to quantitatively correlate the peptide bond AmIII 3 frequency to its Ψ Ramachandran angle and to the number and types of amide hydrogen bonds at different temperatures. This information allows us to develop a family of relationships to directly estimate the Ψ Ramachandran angle from measured UVRR AmIII 3 frequencies for peptide bonds (PBs) with known hydrogen bonding (HB). These relationships ignore the more modest Φ Ramachandran angle dependence and allow determination of the Ψ angle with a standard error of (8°, if the HB state of a PB is known. This is normally the case if a known secondary structure motif is studied. Further, if the HB state of a PB in water is unknown, the extreme alterations in such a state could additionally bias the Ψ angle by (6°. The resulting ability to measure Ψ spectroscopically will enable new incisive protein conformational studies, especially in the field of protein folding. This is because any attempt to understand reaction mechanisms requires elucidation of the relevant reaction coordinate(s). The Ψ angle is precisely the reaction coordinate that determines secondary structure changes. As shown elsewhere (Mikhonin et al. J. Am. Chem. Soc. 2005, 127, 7712), this correlation can be used to determine portions of the energy landscape along the Ψ reaction coordinate. Introduction The various techniques of molecular spectroscopy constitute the toolset used by scientists for investigating molecular conformations and reaction mechanisms. These various spectroscopic techniques require quantitative correlations between the spectral parameters measured and the molecular conformational parameters. NMR and especially multidimensional NMR techniques are certainly the most powerful spectroscopic methods for solution studies. 1928 J. Phys. Chem. B 2006, 110, 1928-1943 10 by C R -D. We are optimistic that these relationships will be very useful for protein conformational studies, especially in the field of protein folding. This is because any attempt to understand reaction mechanisms, such as, for example, protein folding, requires elucidation of the relevant reaction coordinate(s). The Ψ angle is precisely the reaction coordinate that determines secondary structure changes. As shown elsewhere 60 the correlation we propose can be used to experimentally determine features of the energy landscape along this Ψ reaction coordinate. Such an experimental insight into a protein conformation and energy landscape is crucially needed, since there are still a lot of unresolved questions regarding the theoretical modeling of protein folding despite remarkable recent achievments. As described elsewhere, 43 the 21-residue alanine-based peptide AAAAA(AAARA) 3 A (AP) was prepared (HPLC pure) at the Pittsburgh Peptide Facility by using the solid-state peptide synthesis method. The AP solutions in water contained 1 mg/ mL concentrations of AP, and 0.2 M concentrations of sodium perchlorate, which was used as an internal intensity and frequency standard. UV Resonance Raman Instrumentation. The Raman instrumentation has been described in detail elsewhere. Results and Discussion Dependence of AmIII 3 Frequency on Ramachandran Angles and Hydrogen Bonding. The amide III (AmIII) band region is complex. We recently examined this spectral region in detail and identified a band, which we call AmIII 3 and which is most sensitive to the peptide bond conformation. Peptide Secondary Structure Folding Reaction Coordinate J. Phys. Chem. B, Vol. 110, No. 4, 2006 1929 gives rise to strong N-H to C R -H bend coupling. In contrast, for R-helix-like Ψ and Φ Ramachandran angles the N-H and C R -H bonds are approximately trans The physical origin of this Ψ angle AmIII 3 frequency dependence is that the hydrogen van der Waals radii in the C R -H and N-H bonds are in contact for positive Ψ angles Relative Impact of the Ψ and Φ Ramachandran Angles on the AmIII 3 Frequency. Although the projections of the N-H and C R -H bending motions on each other (and as a result the degree of coupling between them) depend on both the Ψ and Φ Ramachandran angles, an examination of a model of a peptide bond Asher et al. Mirkin and Krimm 73 theoretically examined the Ψ and Φ frequency dependence of the AmIII band of "alanine dipeptide" (N-acetyl-L-alanine-N-methylamide). They concentrated on peptide bond 2, whose frequencies were close to those measured experimentally. Although Mirkin and Krimm claim in their conclusions, that AmIII frequency shows strong dependence on both Ψ and Φ Ramachandran angles, we note that the impact of changes in the Φ angle is relatively modest if we only include the allowed regions of the Ramachandran plot In the allowed regions of Ramachandran plot, Mirkin and Krimm 73 calculated a 25-40 cm -1 AmIII frequency span over the allowed Ψ angles for fixed Φ angles In addition, the largest 16 cm -1 span in the AmIII frequency with Φ angle occurs in an almost forbidden region of the Ramachandran plot between the -sheet and R-helical regions (at Φ angles of -134°and -90°and Ψ angle of 60°, Figures 47 for details). Black line (s): Fit of calculated points using the eq 3 (see text for detail). Note: Grey regions show the forbidden and/or nearly forbidden Ψ Ramachandran angles based on recent Ramachandran plots. 1930 J. Phys. Chem. B, Vol. 110, No. 4, 2006 Mikhonin et al. 3 and 4). In contrast, in the R-helical region of the Ramachandran plot the AmIII frequency of alanine dipeptide shows no more than 8 cm -1 Φ angular span, while in the -strand region of the Ramachandran plot the AmIII frequency shows no more than 6 cm -1 Φ dependence Ianoul et al.'s 59 combined experimental and theoretical studies of Ac-X-OCH 3 (X ) Val, Ile, Leu, Lys, Ala) revealed a 9 cm -1 AmIII 3 frequency shift upon an 18°increase of the Φ Ramachandran angle from -96 to -78°. In addition, Ianoul et al. also performed theoretical calculations for Ala-Ala at a fixed R-helix-like Ψ angle of -21°and calculated only a 3 cm -1 AmIII 3 frequency upshift upon the 20°increase of Φ angle from -95°to -75°. Thus, Ianoul et al. never observed more than a 9 cm -1 shift of AmIII 3 frequency due to variation of the Φ Ramachandran angle. In addition, we recently 60 measured the UVRR AmIII 3 frequencies of two different secondary structure conformations in aqueous solutions with very similar Φ angles, but very different Ψ angles. Specifically, an equimolar mixture of PLL and PGA forms an antiparallel -sheet 60 (Ψ ≈ 135°, Φ ≈ -139°), which shows an AmIII 3 frequency at 1227 cm -1 . In contrast individual PLL and PGA samples form extended 2.5 1 -helices 60 (Ψ ≈ 170°, Φ ≈ -130°), which show AmIII 3 frequencies at ∼1271 cm -1 . To summarize, the total Φ angular span of the AmIII 3 frequencies appears experimentally 59 to be no more than 9 cm -1 and no more than 16 cm -1 in the allowed regions of the Ramachandran plot from theoretical calculations. Thus, we conclude that Ψ Ramachandran angular dependence of the AmIII 3 frequency dominates the Φ angular dependence in the allowed regions of Ramachandran plot. If we totally neglect the Φ angular dependence of AmIII 3 frequency, this could enable an error in the Ψ-dependent AmIII 3 frequency of no more than (8 cm -1 (since the total Φ angular span of AmIII 3 frequencies no higher than 16 cm -1 , Formation of PB-water and PB-PB HBs upshift the AmIII 3 frequency, in part, due to the resulting increased C(O)dN double ν III3 (ψ,φ,HB P-P ,HB P-W ,T) = ν III3 (ψ,HB P-P ,HB P-W ,T) (2) ν III3 (ψ,HB P-P ,HB P-W ,T) = {ν 0 -A sin(ψ -R 0 )} + Δν III3 (HB P-P ,HB P-W ,T) (4) Peptide Secondary Structure Folding Reaction Coordinate J. Phys. Chem. B, Vol. 110, No. 4, 2006 1931 bond character. 75, The relationships given below by eqs 5 (for non-HB PB in a vacuum), 6A-D (PB in aqueous solutions), and 7A-C (PB in the absence of water) are shown in Correlation between AmIII 3 Frequency and Ψ Ramachandran Angle in the Absence of HB. We measured the UVR AmIII 3 frequencies for the AP R-helix 42,89 (∼1263 cm -1 , 0°C), XAO PPII 42,43 (1247 cm -1 , 0°C), PLL and PGA 2.5 1 -helix 60 (∼1271 cm -1 , 0°C), and PLL-PGA mixture antiparallel -sheet 60 (∼1227 cm -1 , 0°C) conformations of different polypeptides in aqueous solutions. Each of these conformations has known Ramachandran angles We can calculate the AmIII 3 frequencies that would result from the above peptide conformations in the fictitious case where the PB did not partake in any HB at all. This would be done by subtracting the HB-induced AmIII 3 frequency shifts By fitting the above four "non-HB" data points to eq 3, we obtain the following semiempirical relationship, which relates 1932 J. Phys. Chem. B, Vol. 110, No. 4, 2006 Mikhonin et al. the AmIII 3 frequency to the Ψ Ramachandran angle dependent coupling between N-H and C R -H bending motions The blue curve in Correlation of AmIII 3 Frequency and Ψ Ramachandran Angle for Two-End-On PB-PB HBs: Infinite r-Helix, Interior Strands of -Sheet in Water. Each PB in infinitely long R-helices and in interior strands of multistranded -sheets in aqueous solutions (Appendix, The green curve in The magenta curve in Peptide Secondary Structure Folding Reaction Coordinate J. Phys. Chem. B, Vol. 110, No. 4, 2006 1933 cm -1 HB-induced upshift as well as the temperature-dependent term to eq 5 and write The black curve in Correlation of AmIII 3 Frequency and Ψ Angle for a PB in Water If Its HB State Is Unknown. If the HB state of a PB in aqueous solution is unknown, we suggest the use of eq 6E, which is the "average" of eqs 6A-D. This will minimize the error in determination of the Ψ Ramachandran angle and will allow the estimation of the Ψ angle with the error bounds discussed below. Correlation between AmIII 3 Frequency and Ψ Ramachandran Angle in Peptide Crystals. Figures 6 and 7 show that the crystal data appear to roughly follow the sinusoidal relationship between the AmIII 3 frequency and the Ψ Ramachandran angle (see red dashed curve in Anhydrous r-Helical and -Sheet Conformations. If we dehydrate a two-end-on PB-PB HB R-helical conformation, we will see a 5 cm -1 AmIII 3 frequency downshift due to the loss of hydrogen bonding to the normally present sheath of water. The In the case of a PB where only the CdO group is involved in PB-PB HB, we estimate that the AmIII 3 frequency is 12 cm -1 upshifted with respect to non-HB PB (Appendix, The In the case of PB, where only the NH group is PB-PB HB, we estimate the AmIII 3 frequency to be 35 cm -1 upshifted with respect to non-HB PB (Appendix, The black curve in Thus, the families of eqs 6A-D and 7A-C predict the correlation between the AmIII 3 frequency and the Ψ angle for the common conformations of peptides and proteins. If the HB is known for a particular PB, the appropriate equation can be used to determine its Ψ angle from the observed AmIII 3 frequency. In the case where the HB state of a PB in aqueous solution is unknown, one can use eq 6E. These relationships will become less accurate if the PB has an unusual Φ angle or unusual HB pattern (see below). Prediction of UVRR AmIII 3 Frequencies of Other Secondary Structures. On the basis of the known Ψ Ramachandran angle and HB patterns, we can predict the AmIII 3 frequencies of other secondary structures such as the π-helix, 3 10 -helix UVRR spectra of HEWL amyloid fibrils, 100 which are dominated by -sheet conformations contain three spectroscopic features in the AmIII 3 region: ∼1210, ∼1230, and ∼1255 cm -1 . The dominating ∼1230 cm -1 feature certainly derives from antiparallel -sheet, though a minor contribution of several turn conformations is also possible The error associated with neglecting the Φ angle also gives rise to the uncertainty in the Ψ angle determination. Ianoul et al. Additional bias can occur if we do not know the HB state of a PB in water. This could give rise to a bias of the AmIII 3 frequency of (6 cm -1 , which would lead to a Ψ angle bias of (6°in eq 6E. Thus, a typical UV Raman measurement of a typical sample would find a random error of e(8°in the Ψ angle, assuming a known HB state. However, extreme alterations in the unknown HB state of a PB in water could additionally bias the Ψ angle by (6°. Conclusions We used UV resonance Raman spectroscopy to investigate the dependence of the AmIII 3 frequency on the Ψ Ramachandran angle and on the nature of PB HBs. These results allow us to formulate relationships that allow us to estimate the Ψ Ramachandran angles from observed AmIII 3 frequencies for both aqueous solutions of peptides and proteins as well as for the anhydrous states of peptides and proteins. A typical Raman measurement of a typical sample would find a random error of e(8°in the Ψ angle, assuming a known HB state. However, if the HB state of a PB in water is unknown, extreme alterations in such a state could additionally bias the Ψ angle by (6°. We are optimistic that these relationships will be very useful for protein conformational studies, especially in the field of protein folding. This is because any attempt to understand reaction mechanisms, such as protein folding, requires elucidation of the relevant reaction coordinate(s). The Ψ angle is precisely the reaction coordinate that determines secondary structure changes. As shown elsewhere, 60 the correlation we propose can be used to determine features of the energy landscape along this Ψ reaction coordinate

Quantum transport and utilization of free energy in protein α\alpha-helices

The essential biological processes that sustain life are catalyzed by protein nano-engines, which maintain living systems in far-from-equilibrium ordered states. To investigate energetic processes in proteins, we have analyzed the system of generalized Davydov equations that govern the quantum dynamics of multiple amide I exciton quanta propagating along the hydrogen-bonded peptide groups in $\alpha$-helices. Computational simulations have confirmed the generation of moving Davydov solitons by applied pulses of amide I energy for protein $\alpha$-helices of varying length. The stability and mobility of these solitons depended on the uniformity of dipole-dipole coupling between amide I oscillators, and the isotropy of the exciton-phonon interaction. Davydov solitons were also able to quantum tunnel through massive barriers, or to quantum interfere at collision sites. The results presented here support a nontrivial role of quantum effects in biological systems that lies beyond the mechanistic support of covalent bonds as binding agents of macromolecular structures. Quantum tunneling and interference of Davydov solitons provide catalytically active macromolecular protein complexes with a physical mechanism allowing highly efficient transport, delivery, and utilization of free energy, besides the evolutionary mandate of biological order that supports the existence of such genuine quantum phenomena, and may indeed demarcate the quantum boundaries of life.Comment: 40 pages, 20 figure

Quantum transport and utilization of free energy in protein α-helices

The essential biological processes that sustain life are catalyzed by protein nano-engines, which maintain living systems in far-from-equilibrium ordered states. To investigate energetic processes in proteins, we have analyzed the system of generalized Davydov equations that govern the quantum dynamics of multiple amide I exciton quanta propagating along the hydrogen-bonded peptide groups in α-helices. Computational simulations have confirmed the generation of moving Davydov solitons by applied pulses of amide I energy for protein α-helices of varying length. The stability and mobility of these solitons depended on the uniformity of dipole-dipole coupling between amide I oscillators, and the isotropy of the exciton-phonon interaction. Davydov solitons were also able to quantum tunnel through massive barriers, or to quantum interfere at collision sites. The results presented here support a nontrivial role of quantum effects in biological systems that lies beyond the mechanistic support of covalent bonds as binding agents of macromolecular structures. Quantum tunneling and interference of Davydov solitons provide catalytically active macromolecular protein complexes with a physical mechanism allowing highly efficient transport, delivery, and utilization of free energy, besides the evolutionary mandate of biological order that supports the existence of such genuine quantum phenomena, and may indeed demarcate the quantum boundaries of life

Peptide bond vibrational coupling

Neutral trialanine (Ala3), which is geometrically constrained to have its peptide bond at Φ and Ψ angles of α-helix and PPII-like conformers, are studied at the B3LYP/6-31+G(d,p) level of theory to examine vibrational interactions between adjacent peptide units. Delocalization of the amide I, amide II, and amide III3 vibrations are analyzed by calculating their potential energy distributions (FED). The vibrational coupling strengths are estimated from the frequency shifts between the amide vibrations of Ala3 and the local amide bond vibrations of isotopically substituted Ala3 derivatives. Our calculations show the absence of vibrational coupling of the amide I and amide II bands in the PPII conformations. In contrast, the α-helical conformation shows strong coupling between the amide I vibrations due to the favorable orientation of the C=O bonds and the strong transitional dipole coupling. The amide III3 vibration shows weak coupling in both the α-helix and PPII conformations; this band can be treated as a local independent vibration. Our calculated results in general agree with our previous experimental UV Raman studies of a 21-residue mainly alanine-based peptide (AP). © 2007 American Chemical Society

Dependence of the AmII'p proline Raman band on peptide conformation

We utilized UV resonance Raman (UVRR) measurements and density functional theory (DFT) calculations to relate the AmII'p frequency to the Ψ angle. The AmII'p frequency shifts by ∼ 25 cm-1 as the Ψ angle is varied over allowed angles of the Pro peptide bond. The AmII'p frequency does not show any significant dependence on the Ψ dihedral angle. The conformation sensitivity of the AmII'p frequency derives from conformation-induced changes in the planarity of the Pro peptide bond; Ψ angle changes push the amide nitrogen out of the peptide bond plane. We use this AmII'p frequency dependence on the Ψ angle to track temperature-induced conformation changes in a polyproline peptide. The temperature-induced 7 cm -1 downshift in the AmII'p frequency of the polyproline peptide results from an ∼45° rotation of the Ψ dihedral angle from Ψ = 145° (ideal PPII conformation) to Ψ = 100° (collapsed PPII conformation). © 2009 American Chemical Society

Dependence of amide vibrations on hydrogen bonding

The effect of hydrogen bonding on the amide group vibrational spectra has traditionally been rationalized by invoking a resonance model where hydrogen bonding impacts the amide functional group by stabilizing its [ -O-C=NH+] structure over the [O=C-NH] structure. However, Triggs and Valentini's UV-Raman study of solvation and hydrogen bonding effects on e-caprolactum, N,N-dimethylacetamide (DMA), and N-methylacetamide (NMA) (Triggs, N. E.; Valentini, J. J. J. Phys. Chem. 1992, 96, 6922-6931) casts doubt on the validity of this model by demonstrating that, contrary to the resonance model prediction, carbonyl hydrogen bonding does not impact the AmII′ frequency of DMA. In this study, we utilize density functional theory (DFT) calculations to examine the impact of hydrogen bonding on the C=O and N-H functional groups of NMA, which is typically used as a simple model of the peptide bond. Our calculations indicate that, as expected, the hydrogen bonding frequency dependence of the AmI vibration predominantly derives from the C=O group, whereas the hydrogen bonding frequency dependence of the AmII vibration primarily derives from N-H hydrogen bonding. In contrast, the hydrogen bonding dependence of the conformation-sensitive AmIII band derives equally from both C=O and N-H groups and thus, is equally responsive to hydrogen bonding at the C=O or N-H site. Our work shows that a clear understanding of the normal mode composition of the amide vibrations is crucial for an accurate interpretation of the hydrogen bonding dependence of amide vibrational frequencies. © 2008 American Chemical Society

Dependence of glycine CH<inf>2</inf> stretching frequencies on conformation, ionization state, and hydrogen bonding

We experimentally and theoretically examined the conformation, pH, and temperature dependence of the CH2 stretching frequencies of glycine (gly) in solution and in the crystalline state. To separate the effects of the amine and carboxyl groups on the CH2 stretching frequencies we examined the Raman spectra of 2,2,2-d3-ethylamine (CD 3-CH2-NH2) and 3,3,3-d3-propionic acid (CD3-CH2-COOH) in D2O. The symmetric (vsCH2) and asymmetric (vasCH2) stretching frequencies show a significant dependence on gly conformation. We quantified the relation between the frequency splitting (Δ = v asCH2 -vsCH2) and the ξ angle which determines the gly conformational geometry. This relation allows us to determine the conformation of gly directly from the Raman spectral frequencies. We observe a large dependence of the vsCH2 and v asCH2 frequencies on the ionization state of the amine group, which we demonstrate theoretically results from a negative hyperconjugation between the nitrogen lone pair and the C-H antibonding orbitais. The magnitude of this effect is maximized for C-H bonds trans to the nitrogen lone pair. In contrast, a small dependence of the CH2 stretching frequencies on the carboxyl group ionization state arises from derealization of electron density from carboxyl oxygen to C-H bonding orbitals. According to our experimental observations and theoretical calculations the temperature dependence of the vsCH2 and v asCH2 of gly is due to the change in the hydrogen-bonding strength of the amine/carboxyl groups to water. © 2008 American Chemical Society

UV resonance Raman determination of polyproline II, extended 2.5 <inf>1</inf>-helix, and β-sheet ψ angle energy landscape in poly-L-lysine and poly-L-glutamic acid

UV resonance Raman (UVR) spectroscopy was used to examine the solution conformation of poly-L-lysine (PLL) and poly-L-glutamic acid (PGA) in their non-α-helical states. UVR measurements indicate that PLL (at pH = 2) and PGA (at pH = 9) exist mainly in a mixture of polyproline II (PPII) and a novel left-handed 2.51-helical conformation, which is an extended β-strand-like conformation with Ψ ≈ 1170° and Φ ≈ 130°. Both of these conformations are highly exposed to water. The energies of these conformations are very similar. We see no evidence of any disordered "random coil" states. In addition, we find that a PLL and PGA mixture at neutral pH is ∼60% β-sheet and contains PPII and extended 2.5 1-helix conformations. The β-sheet conformation shows little evidence of amide backbone hydrogen bonding to water. We also developed a method to estimate the distribution of Ψ Ramachandran angles for these conformations, which we used to estimate a Ψ Ramachandran angle energy landscape. We believe that these are the first experimental studies to give direct information on protein and peptide energy landscapes. © 2005 American Chemical Society

Peptide secondary structure folding reaction coordinate: Correlation between UV Raman amide III frequency, ψ Ramachandran angle, and hydrogen bonding

We used UV resonance Raman (UVRR) spectroscopy to quantitatively correlate the peptide bond AmIII3 frequency to its ψ Ramachandran angle and to the number and types of amide hydrogen bonds at different temperatures. This information allows us to develop a family of relationships to directly estimate the ψ Ramachandran angle from measured UVRR AmIII3 frequencies for peptide bonds (PBs) with known hydrogen bonding (HB). These relationships ignore the more modest Φ Ramachandran angle dependence and allow determination of the ψ angle with a standard error of ±8°, if the HB state of a PB is known. This is normally the case if a known secondary structure motif is studied. Further, if the HB state of a PB in water is unknown, the extreme alterations in such a state could additionally bias the ψ angle by ±6°. The resulting ability to measure ψ spectroscopically will enable new incisive protein conformational studies, especially in the field of protein folding. This is because any attempt to understand reaction mechanisms requires elucidation of the relevant reaction coordinate(s). The ψ angle is precisely the reaction coordinate that determines secondary structure changes. As shown elsewhere (Mikhonin et al. J. Am. Chem. Soc. 2005, 727, 7712), this correlation can be used to determine portions of the energy landscape along the ψ reaction coordinate. © 2006 American Chemical Society

UV Resonance Raman Investigation of the Aqueous Solvation Dependence of Primary Amide Vibrations

We investigated the normal mode composition and the aqueous solvation dependence of the primary amide vibrations of propanamide. Infrared, normal Raman, and UV resonance Raman (UVRR) spectroscopy were applied in conjunction with density functional theory (DFT) to assign the vibrations of crystalline propanamide. We examined the aqueous solvation dependence of the primary amide UVRR bands by measuring spectra in different acetonitrile/water mixtures. As previously observed in the UVRR spectra of <i>N</i>-methylacetamide, all of the resonance enhanced primary amide bands, except for the Amide I (AmI), show increased UVRR cross sections as the solvent becomes water-rich. These spectral trends are rationalized by a model wherein the hydrogen bonding and the high dielectric constant of water stabilizes the <i>ground state</i> dipolar ^–OCNH₂⁺ resonance structure over the neutral OCNH₂ resonance structure. Thus, vibrations with large CN stretching show increased UVRR cross sections because the CN displacement between the electronic ground and excited state increases along the CN bond. In contrast, vibrations dominated by CO stretching, such as the AmI, show a decreased displacement between the electronic ground and excited state, which result in a decreased UVRR cross section upon aqueous solvation. The UVRR primary amide vibrations can be used as sensitive spectroscopic markers to study the local dielectric constant and hydrogen bonding environments of the primary amide side chains of glutamine (Gln) and asparagine (Asn)