Energetics of an n→π^* Interaction that Impacts Protein Structure

Abstract

The trans/cis ratio of the amide bond in N-formylproline phenylesters correlates with electron-withdrawal by a para substituent. The slope of the Hammett plot (ρ = 0.26) is indicative of a substantial effect. This effect arises from a favorable n→π^* interaction between the amide oxygen and ester carbonyl. In a polypeptide chain, an analogous interaction can stabilize the conformation of trans peptide bonds, α-helices, and polyproline type-II helices.

Certain non-covalent interactions are known to direct a polypeptide chain to assume a folded structure. Those interactions include the hydrophobic effect, hydrogen bonding, Coloumbic forces, van der Waals forces, and cation–π interactions.¹ Recently, we suggested that n→π^* interactions should be added to this list.^2,3 In an n→π^* interaction (which is not to be confused with an n→π^* electronic transition) the oxygen of a peptide bond (O_i−1) donates electron density from one of its lone pairs into the antibonding orbital of the carbon in the subsequent peptide bond (C_i^′=O_i). This O_i−1···C_i^′=O_i interaction, which mimics the approach of a nucleophile to the electrophilic carbon of an acyl group, is strongest when O_i−1 is positioned proximally and along the Bürgi–Dunitz trajectory to C_i^′=O_i. In polypeptides, this geometry occurs in the α-helix and polyproline type-II (PPII) helix,^2c which is the structure assumed by the strands of the prevalent collagen triple helix.^3,4

The n→π^* interaction can occur only if the peptide bond containing O_i−1 is trans (i.e., Z), as opposed to cis (E). Accordingly, the trans/cis ratio of an Xaa_i−1–Pro_i peptide bond can report on the strength of an n→π^* interaction. We had demonstrated previously that the n→π^* interaction contributes to the endogenous preference for trans peptide bonds.^2c Here, we present a simple model system that uses the trans/cis ratio of a peptide bond to report on the energetics of an n→π^* interaction.

We reasoned that the strength of an n→π^* interaction could be altered by using p-substituted phenyl esters of N-formyl-l-proline to modulate the electrophilicity of the carbonyl (C_i^′=O_i). Our expectation was that the trans/cis ratio would correlate with that electrophilicity. We chose N-formylproline because its trans/cis ratio is close to unity and can thus serve as the basis for a highly sensitive assay.^2c The esters were synthesized by condensation of N-formylproline with the corresponding phenol using PyBOP activation, and were purified by flash chromatography.

We used ¹H NMR spectroscopy to measure the trans/cis ratio of each ester (90−170 mM) in CDCl₃. We chose chloroform as the solvent to minimize effects from differential solvation of the trans and cis isomers. Because the isomerization of the peptide bond is slow on the NMR timescale, two sets of signals were observed in the spectrum of each ester. Though most of the resonances exist as multiplets and overlap with those from their isomer, the resonance of the formyl proton appears as two singlets—one for each iso mer. The larger, upfield resonance arises from the trans isomer. Integration of the two signals provides the trans/cis ratio at the amide bond.

We find that more electron-withdrawing p-substituents correlate strongly with larger trans/cis ratios (Table 1). Moreover, a linear relationship exists between the log of the trans/cis ratio and the Hammett parameter (σ_p) of the substituent (Figure 1A), which is indicative of an electronic effect.⁵ The values of K_trans/cis and σ_p are related by ρ = ∂log(K_X/K_H)/∂σ_p = 0.26. This ρ-value signifies that the electronic effect of X on K_trans/cis is substantial, especially given that the interconversion of the cis and trans isomers of Fm–Pro–OC₆H₄-p-X does not involve a change in covalent bonding.

Table 1.

Trans/Cis Ratios (CDCl₃) and σ_p Values of X in Fm–Pro–OC₆H₄-p-X at 25 °C.

X	σpa	Ktrans/cis	ΔG (kcal/mol)b
NO2	0.78	4.13 ± 0.05	−0.84
CN	0.66	3.95 ± 0.03	−0.81
H	0.00	2.120 ± 0.005	−0.45
OMe	−0.27	2.01 ± 0.04	−0.41
NMe2	−0.83	1.67 ± 0.02	−0.30

^aFrom ref. 6.

^bΔG = –RTlnK_trans/cis.

Figure 1.

Relationship between the trans/cis ratio and electron-withdrawing ability of X in Fm–Pro–OC₆H₄-p-X. (A) Values of K_X are from experimental data (Table 1) and give ρ = 0.26. (B) Values of K_X are from density functional theory calculations on the trans isomer with C^γ-exo pyrrolidine ring pucker (Table 2) and give ρ = 0.60.

Density functional theory (DFT) calculations predicted a similar correlation between K_trans/cis and σ_p (Table 2; Figure 1B), and enabled a detailed analysis. Electron-withdrawing substituents on a phenyl ring are known to increase the electrophilicity⁷ (and reactivity⁵) of aryl esters. The electronics of an ester can be described by three major resonance forms: A–C (Scheme 1). As the phenyl substituent becomes more electron-withdrawing, forms B and C become disfavored⁸ due to π-polarization.⁹ The diminished delocalization increases the energy of the C_i′=O_i π orbital and decreases the energy of the C_i′=O_i π^* orbital, making C_i′=O_i more electrophilic. The decreased delocalization is also manifested in the increased contribution from resonance form A, which results in greater double-bond character and higher C_i′=O_i vibrational frequency.⁸ These effects are observed theoretically in the cis isomer, which represents the ester electronics in a state unperturbed by the n→π^* interaction. In the cis isomer, the calculated vibrational frequency ( v_Ci^′=O_i ) of the carbonyl increases with the electron-withdrawing ability of the p-substituent (Table 2). Moreover, natural bond order (NBO¹⁰) analysis of the cis isomer demonstrates a decrease in the ester π^* orbital energy ( E_π^*C_i^′=O_i ) with increasing electron withdrawal (Table 2). These two effects are indicative of the increased electrophilicity of C_i^′=O_i that results from electron-withdrawing groups.

Table 2.

Results of Density Functional Theory Calculations (B3LYP/6−31+G^*) and Natural Bond Order Analysis on the trans and cis Isomers of Fm–Pro–OC₆H₄-p-X with C^γ-exo Pyrrolidine Ring Pucker.

X	ΔE (kcal/mol)a	νC′i=Oi (cm−1)b,c	Eπ*,C′i=Oi (Hartrees)c	En→π* (kcal/mol)d	rOi-1···C′i (Å)d
NO2	2.22	1837	−0.43033	1.45	2.88
CN	2.08	1835	−0.42692	1.39	2.89
H	1.27	1829	−0.41043	0.86	2.98
OMe	1.22	1826	−0.40713	0.83	2.99
NMe2	0.94	1824	−0.40115	0.68	3.02

^aΔE = –RTlnK_trans/cis.

^bUnscaled.

^ccis Isomer.

^dtrans isomer.

Scheme 1.

The strength of the n→π^* interaction in the trans isomer was examined directly with NBO analysis. Second-order perturbation theory indicates that as the trans/cis ratio increases, so does the energy ( E_n→π^*) of the interaction between the lone pair on the amide carbonyl oxygen and the π^* orbital of the ester (Table 2). The increasing strength of the n→π^* interaction is reflected in the decreasing distance ( r_Oi−1···C_i^′ ) between the amide oxygen and ester carbon (Table 2). The value of ρ = 0.60 for the theoretical data (Figure 1B) is greater than that for the experimental data (Figure 1A). The pyrrolidine ring was held in the C^γ-exo conformation during the theoretical analyses, as this ring pucker allows for much greater n→π^* interaction than does the C^γ-endo conformation.^2b,11 The pyrrolidine ring has, however, a slight preference for the C^γ-endo pucker.¹² Hence, the effect of the p-substituent on the trans/cis ratio is amplified in the calculations.

The link between the electron-withdrawing ability of the remote p-substituent and the trans/cis ratio support the role of an electronic n→π^* interaction in the conformational preference of the amide bond. This effect cannot be steric. Located in the para position, the aryl substituent is remote from the amide bond. Moreover, if the effect were steric, then the trans/cis ratios would fall in line with the steric bulk of the substituent. Such a correlation was not observed, as the K_trans/cis value of the smallest substituent, a proton, is between those of the largest substituents, dimethylamino and nitro.¹³

We conclude that an n→π^* interaction occurs between the amide and ester groups in this model system. In addition, we propose that this interaction has important ramifications for protein structure. An n→π^* interaction could stabilize not only a trans peptide bond, but also an α-helix and PPII helix.^2c The α-helix,¹⁴ like the β-sheet,¹⁵ is stabilized by C_i^′=O_i···H–N hydrogen bonds between main-chain atoms.^1b,16 The C_i^′=O_i bonds in α-helices are, however, demonstrably longer than those in β-sheets.¹⁷ This greater bond length is consistent with the manifestation of an n→π^* interaction in an α-helix. In contrast to the α-helix and β-sheet, the PPII helix does not contain any hydrogen bonds between its main-chain atoms. Yet, recent data indicates a notable prevalence of the PPII helix in both folded proteins and unfolded polypeptide chains.¹⁸ We propose that the n→π^* interaction stabilizes the PPII helix, contributing significantly to its prevalence. Accordingly, the n→π^* interaction is a non-covalent interaction, like the hydrophobic effect, hydrogen bonding, Coloumbic forces, van der Waals forces, and cation–π interactions,¹ that directs a polypeptide chain to assume a folded structure.