Impact of Structural Flexibility on Tunneling Contribution to the Reaction Mechanism of Spontaneous Succinimide Formation in Asn-Gly-Containing Peptides

Abstract

Spontaneous deamidation and isomerization of asparagine (Asn) residues is a major pathway of nonenzymatic protein aging, where Asn-Gly-containing peptides (NG motifs) represent the most reactive sequence. In this context, the first step of isomerization is succinimide formation, which is initiated by a concerted proton-transfer and nucleophilic activation step. Although the overall mechanism is established, the detailed nature of the rate-determining succinimide formation step and the possible role of nuclear quantum effects remain unclear. Here, we combine density functional theory (DFT), intrinsic reaction coordinate (IRC) analysis, and quantitative NMR kinetics to investigate hydrogen/deuterium (H/D) substitution effects on NG isomerization in different model peptides, which represent both conformationally flexible and restricted systems. Deuteration preserves the reaction pathway and structural evolution, indicating an invariant classical reaction coordinate. However, kinetic isotope effects in the flexible peptide system reveal a mixed classical–tunneling mechanism in the rate-determining step with observable deviations from classical over-the-barrier behavior. In contrast, the conformationally restricted peptide shows suppressed tunneling contributions. These findings demonstrate that conformational accessibility modulates proton tunneling in spontaneous peptide rearrangements and extends nuclear quantum effects beyond enzymatic systems to nonenzymatic processes associated with protein aging.

1. Introduction

Spontaneous deamidation and isomerization of asparagine (Asn) residues represents one of the most widespread nonenzymatic post-translational modifications in proteins, playing a central role in long-term protein aging and structural degradation [1,2,3,4,5,6]. This transformation is particularly relevant in long-lived proteins such as crystallins, hemoglobin, and other slow-turnover structural proteins, where cumulative chemical damage contributes to functional decline over timescales of months to years [7,8,9,10,11]. In addition, NG-mediated (asparagine-glycine, Asn-Gly) deamidation has been implicated in pathological processes associated with protein instability, and has been explored in the context of prodrug activation and chemotherapeutic strategies [12].

At the molecular level, NG motifs constitute the most reactive sequence context for deamidation [13]. The reaction proceeds via intramolecular nucleophilic attack of the Gly backbone amide nitrogen on the Asn side chain carbonyl carbon, followed by cyclization to a five-membered succinimide intermediate, deamidation and subsequent hydrolysis to yield both β- and α-aspartic acid products (Figure 1) [14].

Figure 1.

Schematic pathway of NG sequence deamidation, isomerization and rearrangement. The reaction proceeds via intramolecular nucleophilic attack of the Gly backbone amide nitrogen on the Asn side chain carbonyl carbon, followed by cyclization to a five-membered succinimide intermediate, deamidation and subsequent hydrolysis to yield both β- and α-aspartic acid products. The β-Asp isomer corresponds to a backbone-elongated isoaspartic acid residue containing an additional methylene insertion within the peptide backbone, whereas the α-Asp form retains the canonical backbone connectivity. The succinimide-forming cyclization represents the rate-determining and isotope-sensitive step of the overall isomerization pathway, making it suitable for mechanistic investigation.

The overall transformation is commonly described by a multistep kinetic scheme, where succinimide formation from Asn constitutes the rate-determining step characterized by the reaction rate coefficient k₁ [14]:

$$\mathrm{A}\mathrm{s}\mathrm{n}\stackrel{k_1}{\to }\mathrm{S}\mathrm{u}\mathrm{c}$$ (1)

$$\mathrm{S}\mathrm{u}\mathrm{c}\begin{array}{c}{k}_2\\ \begin{array}{c}\to \\ \leftarrow \end{array}\\ k_{-2}\end{array}\mathsf{\beta }-\mathrm{A}\mathrm{s}\mathrm{p}$$ (2)

$$\mathrm{S}\mathrm{u}\mathrm{c}\begin{array}{c}{k}_3\\ \begin{array}{c}\to \\ \leftarrow \end{array}\\ k_{-3}\end{array}\mathsf{\alpha }-\mathrm{A}\mathrm{s}\mathrm{p}$$ (3)

Although this kinetic framework is well established, the detailed nature of the proton-transfer events associated with succinimide formation remains incompletely understood. In particular, increasing evidence from proton-transfer and proton-coupled electron transfer (PCET) reactions suggests that nuclear quantum effects, including proton tunneling, can contribute to reaction rates. While the occurrence of tunneling in enzymatic reactions is not disputed, its mechanistic importance for enzymatic rate enhancement has been the goal of several investigations. In particular, there is ongoing debate as to whether protein dynamics directly facilitate tunneling or whether the dominant catalytic effect arises from electrostatic preorganization of the active site [15,16,17,18,19,20]. While such effects have been extensively investigated in enzymatic systems, their role in spontaneous peptide backbone rearrangements remains largely unexplored.

Hydrogen/deuterium (H/D) substitution in experiments leads to measurable changes in reaction rates and can be used to obtain data about kinetic isotope effect (KIE) value, as well as impact on activation energy (E_a) and Arrhenius pre-exponential factor (A). These values provide a sensitive probe for distinguishing classical over-the-barrier processes from mechanisms involving quantum mechanical contributions to proton transfer, if the investigated system is close to classical limits, as is the case for the reaction observed herein. However, for calculations beyond the harmonic approximation, path integration with inclusion of thermal averaging would be the appropriate method [21,22,23]. The KIE can be calculated as the ratio of the two reaction rate coefficients:

$$KIE={\displaystyle \frac{k_1\left(\mathrm{H}\right)}{k_1\left(\mathrm{D}\right)}}$$ (4)

where k₁(H) and k₁(D) are the rate coefficients of the molecules containing the proton (protium) or deuterium isotope, respectively [24]. As Equation (1) can be considered as an elementary unimolecular reaction, it is reasonable to use the Arrhenius formula to describe its temperature dependence. Substituting the Arrhenius expressions for the rate coefficients into Equation (4) yields an expression from which the activation energy difference (ΔE_a) and the pre-exponential factor ratio $\mathrm{l}\mathrm{n}{\displaystyle \frac{A\left(\mathrm{H}\right)}{A\left(\mathrm{D}\right)}}$ can be determined. Plotting the ln(KIE) against the ${\displaystyle \frac{1}{T}}$ values, a straight line can be obtained, the slope of which represents ΔE_a ($E_{\mathrm{a}}\left(\mathrm{D}\right)-E_{\mathrm{a}}\left(\mathrm{H}\right)$), and the intercept represents the $\mathrm{l}\mathrm{n}{\displaystyle \frac{A\left(\mathrm{H}\right)}{A\left(\mathrm{D}\right)}}$ value [21].

Importantly, isotope substitution is employed here as a mechanistic perturbation rather than a biological mimic, allowing direct insight into the underlying potential energy surface. The propensity for proton tunneling is strongly influenced by conformational dynamics that modulate donor–acceptor distances, a factor known to vary significantly across peptide sequence and local structure [25]. Here, we investigate the rate-determining succinimide formation step in NG isomerization using a combined computational and experimental approach. Density functional theory (DFT) and intrinsic reaction coordinate (IRC) calculations and analysis were performed on a deuterated Ac-Asn-NH-CH₃ + H₂O model system and compared with previously reported protonated pathways. In parallel, NG isomerization was examined experimentally under deuterated conditions and reduced temperatures using quantitative NMR spectroscopy, enabling determination of rate constants, half-lives, activation energies, kinetic isotope effects and impact on Arrhenius pre-exponential factors. By combining structural, energetic, and kinetic analyses across conformationally flexible (Ac-NGAA-NH₂) and conformationally restricted (Ac-NGEA-NH₂) model peptides, we aim to elucidate how local structural constraints modulate proton-transfer dynamics and to assess whether nuclear quantum effects contribute to spontaneous peptide backbone rearrangements relevant to protein aging processes.

2. Materials and Methods

2.1. QM Calculations

To investigate the effect of proton–deuterium exchange on the reaction mechanism of Ac-Asn-NH-CH₃ + H₂O, IRC path and calculations were completed at the B3LYP/6-31+G(d,p) level of theory in a vacuum at 298.15 K. We performed deuteration at every proton position that can get substituted when dissolved in D₂O for laboratory experiments. The endpoint and the transition state optimizations, frequency and DFT calculations were completed at the B3LYP/6-311++G(d,p) level of theory in a vacuum (Note S1 and Tables S1–S8 within Supplementary Data S2). All were completed with the Gaussian 09 B01 and the Gaussian 16 C01 software packages. The protonated calculations were described in our previous article [14]. QM structures were visualized with the open-source Jmol 3D chemical structure viewer (http://www.jmol.org/).

2.2. Peptide Synthesis and Purification

The preparation of Ac-NGEA-NH₂ was carried out by solid-phase peptide synthesis; for this, the Fmoc/tert-butyl strategy was used with Rink-amide MBHA resin, as in previous articles [13,14]. Peptide acetylation, and purification with a reversed-phase HPLC was also performed in a similar manner as previously described [13,14]. After the purification, the peptide was identified by ESI-MS and NMR spectroscopy. The Ac-NGAA-NH₂ peptide was obtained from Gábor Mező and Kata Enyedi.

2.3. NMR Experiments

Time-dependent 1D ¹H-NMR measurements (zgesgp) were carried out with a Bruker AVANCE-III 700 MHz instrument (Bruker, Billerica, MA, USA) (at Eötvös Loránd University) to follow the isomerization as we described in the Note S1 within Supplementary File S1 and previously [14]. Before the sample preparation, the peptides and the sodium phosphate buffer were twice lyophilized and resolved in D₂O for the deuterated samples. The experiments were carried out at 28, 37 and 55 °C for protonated and deuterated Ac-NGAA-NH₂ samples, and at 37 and 55 °C for protonated and deuterated Ac-NGEA-NH₂ samples. The pH was adjusted to 7.4 for the protonated samples and to 7.0 for the deuterated samples, taking into account the effect of proton–deuterium exchange [14,26].

Only the deuterated measurements were performed in the current study, the protonated results were reported in our previous article [14]. The assignment of the deuterated measurements (Note S1–S3 and Figure S1–S6 within Supplementary Data S1) shows a high correspondence (Δδ_max < 2 Hz) for both the Ac-NGAA-NH₂ and Ac-NGEA-NH₂ samples compared to their protonated counterparts [14,27,28].

2.4. Determination of Kinetic Parameters

Based on the integral values of the relevant NMR signals, kinetic parameters were determined using the COPASI software application, version 4.27 (http://copasi.org/). The estimated parameters together with their standard deviations were the rate coefficients k₁, k₂, and k₃, and the equilibrium constants K₂ and K₃. The rate coefficients k–₂ and k–₃ were calculated from $K_2={\displaystyle \frac{k_2}{k_{-2}}}$ and $K_3={\displaystyle \frac{k_3}{k_{-3}}}$ using the error propagation formula including the estimated covariances to calculate their standard deviations. All errors reported are half-widths of 95% confidence intervals based on the Student distribution of the estimated values.

The half-lives (t_1/2) of the overall isomerization reactions were determined from k₁ values using the following relation:

$$t_{1/2}={\displaystyle \frac{\mathrm{l}\mathrm{n}2}{k_1}}$$ (5)

Furthermore, the KIE values were calculated using the above-mentioned equation (Equation (4)). From the temperature dependence of the obtained KIE values, the ratio of Arrhenius pre-exponential factors and difference in activation energies (ΔE_a) can be obtained using the following equations:

$$\ln \left(KIE\right)=\mathrm{l}\mathrm{n}{\displaystyle \frac{A\left(\mathrm{H}\right)}{A\left(\mathrm{D}\right)}}+{\displaystyle \frac{E_{\mathrm{a}}\left(\mathrm{D}\right)-E_{\mathrm{a}}\left(\mathrm{H}\right)}{R}}·{\displaystyle \frac{1}{T}}$$ (6)

$$∆E_{\mathrm{a}}=E_{\mathrm{a}}\left(\mathrm{D}\right)-E_{\mathrm{a}}\left(\mathrm{H}\right)$$ (7)

For comparison, ΔE_a values were determined from QM calculations with the following equations:

$$∆H^{‡}=H_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{e}}-H_{\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t} \mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\mathrm{x}}$$ (8)

$$E_{\mathrm{a}}=∆H^{‡}+2RT$$ (9)

where H is the sum of electronic and thermal enthalpies (from Gaussian frequency calculation and energy optimalization output files).

3. Results and Discussion

3.1. QM Computational Results

We have previously examined the first major step of NG isomerization in detail in terms of changes in structural parameters, charge distribution and natural bond orbitals, in order to make conclusions regarding the driving force of the reaction. Based on our previous results, the first step of the NG isomerization reaction—which is also the rate-determining step for the overall isomerization, i.e., the formation of the succinimide ring—involves the transfer of protons, the transition state formation, the ring closure and the irreversible NH₃ release microsteps [14]. To identify any potential differences or similarities with the previously identified reaction pathway and structural rearrangement, we performed deuteration of the Ac-Asn-NH-CH₃ + H₂O molecules at every proton position that can get substituted when dissolved in D₂O for laboratory experiments. This H-D exchange involved the four protons bonded to the three nitrogen atoms and the two protons of the water molecule. The endpoint and the transition state optimizations, frequency and DFT calculations were completed at the B3LYP/6-311++G(d,p) level of theory in a vacuum at 298.15 K.

For the structural comparison (Figure 2 and Table 1, and Tables S4, S6 and S8 within Supplementary Data S2), we used 4 + 1 angle values and 1 distance value, namely the ϕ, ψ, χ₁, and χ₂ dihedral angles as well as the Bürgi–Dunitz angle (N_Gly-C^γ_Asn-O^δ_Asn, θ(BD)) and distance (N_Gly-C^γ_Asn, d(BD)), which are indicators of the successful nucleophilic attack of the Gly nitrogen on the carbonyl carbon atom in the Asn side chain [29,30].

Figure 2.

Structural comparison of the protonated [14] (green carbon atoms) and deuterated (purple carbon atoms) molecular structures. Comparative illustration of (a) the optimized open forms, (b) the transition states, and (c) the optimized succinimide structures calculated at the B3LYP/6-311++G(d,p) level of theory in a vacuum. All three pairs show a high degree of structural similarity.

Table 1.

Structural parameters of the open, transition state and succinimide ring structures. Comparison of the structural parameters of protonated [14] and deuterated QM systems (shown in Figure 2 and Tables S4, S6 and S8 within Supplementary Data S2), namely dihedral angles (ϕ, ψ, χ₁, and χ₂) as well as the Bürgi–Dunitz angle (N_Gly-C^γ_Asn-O^δ_Asn, θ(BD)) and distance (N_Gly-C^γ_Asn, d(BD)).

	Protonated Open	Deuterated Open	Protonated Transition State	Deuterated Transition State	Protonated Succinimide	Deuterated Succinimide
ϕ/°	−166.45	−167.07	−171.61	−171.61	−128.64	−128.70
ψ/°	162.92	−178.48	−140.95	−140.95	−141.97	−141.94
χ1/°	−165.63	−134.65	−176.45	−176.45	140.71	140.68
χ2/°	−165.98	93.44	−134.04	−134.04	−59.61	−59.60
θ(BD)/°	66.50	67.45	109.78	109.78	124.20	124.20
d(BD)/Å	3.21	3.38	2.64	2.64	1.40	1.40

The structural comparison of the deuterated and the protonated molecules shows high similarity. Comparing the dihedral angles, we found deviations of less than 0.5% in all cases except for three. In these three cases, greater deviations are found between the open forms for the dihedral angles ψ, χ₁, and χ₂, which means an 18.6°, 30.98° and 100.58° difference. This suggests that there is a different orientation in the side chains, but the backbones still show a great similarity. The Bürgi–Dunitz angle in the deuterated molecule changes from an initial 67.45° to 109.78° as the molecule reaches a transition state and settles at 124.20° in the succinimide form, which is almost equal to the protonated case, where these values are 66.50°, 109.78° and 124.20°, respectively. The Bürgi–Dunitz distance decreases from an initial value of 3.38 Å to 2.64 Å in the transition state, and finally to 1.40 Å upon reaching the succinimide structure, which is again similar to the protonated case, where these values are 3.21 Å, 2.64 Å and 1.40 Å, respectively. The 109.78° Bürgi–Dunitz angle and the 2.64 Å bond length observed in the transition state also fulfill the conditions necessary for ring closure, as they are close to the ideal bond angle (109.5°) and bond length (3.25 Å) for a nucleophilic attack on the carbonyl group [29,30].

For further comparison, we calculated activation energies (E_a) and the difference in activation energies (ΔE_a) from the optimized open forms and the transition states (Table 2 and Tables S4, S6 and S8 within Supplementary Data S2).

Table 2.

Energy values of the protonated [14] and deuterated QM systems calculated at the B3LYP/6-311++G(d,p) level of theory in a vacuum at 298.15 K. H values are the sum of electronic and thermal enthalpies (from Gaussian frequency calculation and energy optimalization output files) for open, transition state (TS) and succinimide forms. From these values, the activation energies (E_a) and the difference of activation energies (ΔE_a) were calculated.

	Protonated	Deuterated
H (open)/Hartree	−740.977393	−741.000365
H (TS)/Hartree	−740.905707	−740.924692
H (succinimide)/Hartree	−740.988360	−741.007298
ΔH‡ (open-TS)/kJ mol−1	188.21	198.68
Ea (open-TS)/kJ mol−1	193.17	203.64
ΔEa (open-TS)/kJ mol−1	10.47

The activation energies of the protonated and deuterated QM systems were found to be 193.17 and 203.64 kJ mol⁻¹, respectively, which yields a difference of 10.47 kJ mol⁻¹.

In addition to the Bürgi–Dunitz distance described above, we were also able to compare the distances between other atoms in the reaction center of the deuterated system (Figure 3) as we did previously with the protonated one.

Figure 3.

Changes in the interatomic distances between the atoms involved in the succinimide ring formation from the open form along the reaction coordinate. Changes in atomic distances (a) when they were present as protons (this case was already discussed in great detail in our previous article [14]) and (b) when the protons were replaced by deuterium atoms at every proton position that can get substituted when dissolved in D₂O for laboratory experiments. All changes in interatomic distances show a high degree of similarity between the protonated and deuterated QM systems.

The two diagrams showing distance pairs also suggest, in agreement with the above findings, that there is no significant difference between the deuterated and protonated classical reaction pathways. The same pairs of atoms that change together are present, demonstrating how the N_Gly-D_Gly, O_D2O-D_D2O and C^γ_Asn-N^δ_Asn (Figure 3a—green, black and light blue) bonds present in the initial phase of the reaction decompose as the reaction progresses, and how bonds O_D2O-D_Gly, N^δ_Asn-D_D2O and C^γ_Asn-N_Gly (Figure 3a—blue, light pink and purple) form between other pairs of atoms.

3.2. Kinetic Analysis Based on NMR Experiments

In our experiments, we followed the NG isomerization of both Ac-NGAA-NH₂ and Ac-NGEA-NH₂ peptides in their deuterated form, performed a detailed kinetic analysis and compared the obtained parameters to our previous results on protonated samples [14]. As mentioned above, NG isomerization can be described by five reaction rate coefficients (Equations (1)–(3); k₁, k₂, k₋₂, k₃ and k₋₃). The comparison of the k₁, k₂ and k₃ reaction rate coefficients (Table 3) of the deuterated experiments shows that the rate-determining step is the deamidation and succinimide ring closure, as the k₁ values are smaller than the k₂ and k₃ values also under deuterated conditions, similarly to the protonated experiments [14]. This alignment, alongside the QM computational results for the rate-determining step, further strengthens the idea that the isomerization proceeds via a similar overall reaction pathway for both the protonated and the deuterated samples, if the classical reaction mechanism is considered. Furthermore, the k₁ reaction rate coefficient values, in agreement with previous literature results [13,14], show in both protonated and deuterated experiments that lowering the temperature decelerates the reaction (Table 3).

Table 3.

Reaction rate coefficients and half-life values of protonated and deuterated peptides and their corresponding kinetic isotope effect (KIE) values. For protonated [14] and deuterated Ac-NGAA-NH₂ and Ac-NGEA-NH₂ peptides, the isomerization reaction was observed by NMR at different temperatures and reaction rate coefficients (Equations (1)–(3); k₁, k₂, k₋₂, k₃ and k₋₃), and half-life values (Equation (5); t_1/2) were determined. At each temperature, kinetic isotope effect (KIE) values were calculated according to Equation (4). Error values refer to the half-widths of their 95% confidence intervals. The abbreviation ‘n. d.’ stands for ‘not determined’.

Peptide	T, °C		k1, h−1	k2, h−1	k−2, h−1	k3, h−1	k−3, h−1	t1/2, h	KIE
Protonated -NGAA-	55	value	0.2192	5.211	0.0938	0.68	0.0346	3.2	5.02
		error	0.0039	0.163	0.0044	0.08	0.0088
Deuterated -NGAA-	55	value	0.0436	1.356	0.012	0.4106	0.0126	15.9
		error	0.00041	0.019	0.00044	0.0073	0.00073
Protonated -NGAA-	37	value	0.027	0.714	n. d.	n. d.	n. d.	25.7	6.25
		error	0.008	0.32	n. d.	n. d.	n. d.
Deuterated -NGAA-	37	value	0.0043	0.1835	0.0009	0.0585	0.00147	160.5
		error	0.00011	0.0052	0.00011	0.0022	0.00016
Protonated -NGAA-	28	value	0.0047	0.120	n. d.	0.055	0.017	147.5	6.88
		error	0.00047	0.023	n. d.	0.033	0.011
Deuterated -NGAA-	28	value	0.00068	0.0194	0.00001	0.01003	0.0007	1014.0
		error	0.000026	0.0068	n. d.	0.0052	n. d.
Protonated -NGEA-	55	value	0.057	2.03	0.043	0.385	n. d.	12.2	2.37
		error	0.007	0.44	0.044	0.24	n. d.
Deuterated -NGEA-	55	value	0.024	1.0239	0.0041	0.2373	0.0039	28.8
		error	0.0016	0.0821	0.00081	0.0186	0.00105
Protonated -NGEA-	37	value	0.0075	0.327	0.0052	0.058	n. d.	92.4	2.64
		error	0.0003	0.022	0.0023	0.005	n. d.
Deuterated -NGEA-	37	value	0.00284	0.1987	0.0046	0.0342	0.0028	244.1
		error	0.000021	0.0025	0.00021	0.0008	0.00038

After the irreversible rate-determining step, the isomerization becomes complete with two equilibrated processes (Equations (2) and (3)); therefore, we can establish k₋₂ and k₋₃ values for the conversion back to succinimide alongside the k₂ and k₃ values. A comparison of the equilibrium constants $K_2={\displaystyle \frac{k_2}{k_{-2}}}$ and $K_3={\displaystyle \frac{k_3}{k_{-3}}}$ suggests that, under the experimental conditions examined in this article, K₂ is generally higher, with the β-Asp product being formed in greater proportions than the α-Asp product under all circumstances, even in the deuterated case, just as we observed with the protonated version, further supporting the similarity in the reaction outcomes.

In addition to the tetrapeptide containing alanine with a neutral side chain at the third amino acid position, we also performed deuterated experiments with a peptide containing glutamic acid with a negatively charged side chain at the same amino acid position. As we have previously established [14], the reaction rate of the Ac-NGEA-NH₂ peptide containing glutamic acid is significantly lower than that of the Ac-NGAA-NH₂ peptide containing neutral alanine under all experimental conditions we have tested. Furthermore, within the temperature range we examined, it is true that the reaction rate of the glutamic-acid-containing peptide decreases as the temperature decreases. According to these, the previous [14] and current experimental results support the fact that proton–deuterium exchange has no effect on the trends observed in such experimental outcomes. However, deuteration leads to slower reactions with higher half-life values (t_1/2) in all cases.

From the k₁ values of the reactions, we obtained KIE values for each peptide and temperature. In the case of the Ac-NGAA-NH₂ peptide, the calculated KIE values show that at 55 °C, where the molecules are more likely to have sufficient energy to overcome the potential energy barrier, a value of 5.02 is obtained. As the temperature, and therefore the energy, decreases, the experiments result in higher KIE values over the investigated temperature range: 6.25 at 37 °C and 6.88 at 28 °C. Reactions whose primary KIE value exceeds 6–10 can no longer be explained solely by the difference in zero-point energies between lighter and heavier isotopes—and thus by a classical reaction mechanism—but instead indicate the presence of the tunneling effect [21,31]. Comparing this with the observed KIE values, which show an increasing trend as the temperature decreases, it can be concluded that the reaction shifts toward the tunneling mechanism within the 55–28 C° range. In contrast, for the Ac-NGEA-NH₂ peptide, we observed much lower KIE values with almost no temperature dependence, which are 2.37 at 55 °C and 2.64 at 37 °C.

The temperature dependence of KIE values can be evaluated through plotting ln(KIE) against 1/T (Figure 4). The fitted line is expected to be linear, where the slope gives the difference in activation energies (ΔE_a) between protonated and deuterated forms, and the intercept gives $\mathrm{l}\mathrm{n}{\displaystyle \frac{A\left(\mathrm{H}\right)}{A\left(\mathrm{D}\right)}}$, the ratio of Arrhenius pre-exponential factors, both being sensitive indicators of tunneling. In this sense, a ΔE_a value greater than 5.86 kJ mol⁻¹ (1.4 kcal mol⁻¹) and an $\mathrm{l}\mathrm{n}{\displaystyle \frac{A\left(\mathrm{H}\right)}{A\left(\mathrm{D}\right)}}$ value of less than −0.7 are both evaluated as being traditional markers of tunneling effects [21].

Figure 4.

Temperature dependence of KIE values. The ln(KIE) values obtained for (a) Ac-NGAA-NH₂ and (b) Ac-NGEA-NH₂ peptides are shown as a function of 1/T. Numerical values of the difference in activation energies (ΔE_a) between protonated and deuterated forms (slope) and the intercept $\mathrm{l}\mathrm{n}{\displaystyle \frac{A\left(\mathrm{H}\right)}{A\left(\mathrm{D}\right)}}$, the ratio of Arrhenius pre-exponential factors, are annotated in the figure. Both values are sensitive indicators of tunneling.

In the case of the Ac-NGEA-NH₂ peptide, the ΔE_a value is 5.07 kJ mol⁻¹, which is less than the tunneling limit, indicating a classical mechanism. The low KIE values reported above (Table 3) support the same mechanism, while the $\mathrm{l}\mathrm{n}{\displaystyle \frac{A\left(\mathrm{H}\right)}{A\left(\mathrm{D}\right)}}$ value of −1.0 exceeds the tunneling limit, but only slightly. In contrast, the Ac-NGAA-NH₂ peptide shows a ΔE_a value of 9.67 kJ mol⁻¹, clearly indicating tunneling contributions to the mechanism, as well as the $\mathrm{l}\mathrm{n}{\displaystyle \frac{A\left(\mathrm{H}\right)}{A\left(\mathrm{D}\right)}}$ value of −1.9. As mentioned above, the KIE values of Ac-NGAA-NH₂ (Table 3) also approached the tunneling limits, indicating a mixed classical–tunneling mechanism, especially at lower temperatures, where the classical over-the-barrier mechanism is less likely to occur.

The main difference between the Ac-NGEA-NH₂ and Ac-NGAA-NH₂ peptides lies in their structural flexibility. As we previously proposed, the structure of the Ac-NGEA-NH₂ peptide is more constrained, as it may adopt a β-turn-like conformer. This conformer disfavors succinimide formation as the Bürgi–Dunitz distance and angle are far from the ideal [14]. This explains our observation about the absence of tunneling contribution to the reaction mechanism in the case of Ac-NGEA-NH₂, since quantum tunneling requires close spatial proximity. In contrast, Ac-NGAA-NH₂ and Ac-Asn-NH-CH₃ peptides are flexible enough to sample multiple conformational states, thereby providing opportunity for being in spatial proximity, needed for succinimide formation, and enabling both classical mechanism and tunneling contribution. This is consistent with the fact that the experimentally obtained ΔE_a value of 9.67 kJ mol⁻¹ (Ac-NGAA-NH₂) is very close to the computational value of 10.47 kJ mol⁻¹ (Ac-Asn-NH-CH₃ + H₂O), indicating that the experimental and computational results are in good agreement for the two investigated flexible systems. It can be concluded that the nature of the succinimide formation is a mixed classical–tunneling mechanism, if the system is structurally not constrained.

4. Conclusions

Combined quantum chemical calculations and quantitative NMR kinetic analyses demonstrate that proton–deuterium exchange does not alter the fundamental classical reaction pathway of NG isomerization. Structural comparisons of the protonated and deuterated QM systems revealed highly similar conformational evolution along the reaction coordinate, including comparable Bürgi–Dunitz geometries, transition-state arrangements, and reaction-center distance changes associated with succinimide ring formation. Consistent with these observations, the experimentally determined kinetic profiles retained the same overall topology under both protonated and deuterated conditions. According to this, succinimide formation remains the rate-determining step of the isomerization process after H/D isotope exchange.

Despite the preservation of the classical pathway, deuteration produced substantial kinetic effects. Importantly, the computational results indicate that the observed kinetic isotope effects originate primarily from differences in proton-transfer energetics rather than from major structural alteration of the reaction pathway, which enables the evaluation of kinetic isotope effects (KIE). Based on the results derived from NMR experiments of the Ac-NGAA-NH₂ peptide, the determined KIE, ΔE_a and $\mathrm{l}\mathrm{n}{\displaystyle \frac{A\left(\mathrm{H}\right)}{A\left(\mathrm{D}\right)}}$ values together support the presence of a significant tunneling contribution during the rate-determining succinimide-forming step. In particular, the progressive increase in the KIE from 5.02 at 55 °C to 6.88 at 28 °C is consistent with a mixed classical–tunneling mechanism, in which the contribution of tunneling becomes more probable at lower temperatures. It is noteworthy that this temperature-dependent change in KIE is reflected in the ΔE_a value of 9.67 kJ mol⁻¹, which is also indicative of tunneling and in close agreement with the computational ΔE_a value of 10.47 kJ mol⁻¹.

Another notable outcome of this study is the strong contrast between the experimentally investigated Ac-NGAA-NH₂ and Ac-NGEA-NH₂ peptides, which represents conformationally more flexible and restricted systems, respectively. While the Ac-NGAA-NH₂ system displayed a mixed classical–tunneling mechanism, for the Ac-NGEA-NH₂ peptide, the determined KIE, ΔE_a and $\mathrm{l}\mathrm{n}{\displaystyle \frac{A\left(\mathrm{H}\right)}{A\left(\mathrm{D}\right)}}$ values together suggest that there is no relevant tunneling contribution in the succinimide-forming step. These findings suggest that conformational accessibility may play a critical role in regulating tunneling probability in spontaneous peptide isomerization reactions.

The present results therefore extend the relevance of tunneling phenomena beyond well-studied enzyme-catalyzed proton-transfer reactions to spontaneous peptide backbone rearrangements. Since NG motifs are widespread in long-lived proteins susceptible to deamidation and isomerization, these findings raise the possibility that tunneling may contribute to nonenzymatic protein aging pathways under physiologically relevant conditions. Further investigation of larger peptide and protein systems may provide valuable insight into the role of quantum mechanical effects in spontaneous post-translational modifications and long-term protein stability.

Abbreviations

BD	Bürgi–Dunitz
DFT	Density functional theory
ESI-MS	Electrospray ionization mass spectrometry
H/D	Hydrogen/deuterium
HPLC	High-performance liquid chromatography
IRC	Intrinsic reaction coordinate
KIE	Kinetic isotope effect
NG	Asn-Gly, asparagine-glycine
NMR	Nuclear magnetic resonance
PCET	Proton-coupled electron transfer
QM	Quantum mechanical
TS	Transition state

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/biom16091266/s1, Supplementary File S1. Note S1: 1H-NMR spectra recording, processing, and analysis procedures. Figure S1: An example of 1D ¹H-NMR spectrum of deuterated Ac-NGEA-NH₂ peptide. Note S2: Figures S2–S6: Diagrams of the measured and fitted relative concentrations determined by the parameter estimation process, measured at 55, 37 and 28°C for Ac-NGAA-NH₂ peptide and at 55 and 37°C for Ac-NGEA-NH₂ peptide. Supplementary Data S1. ¹H-NMR resonance assignment, coupling patterns and coupling constants. Note S1: Technical details of NMR measurements. Note S2: Signal assignment and coupling constants of deuterated Ac-NGAA-NH₂ peptide and the products of its isomerization reaction (Ac-αDGAA-NH₂ and Ac-βDGAA-NH₂). Figure S1: 1D ¹H-NMR spectrum of deuterated Ac-NGAA-NH₂ peptide. Figure S2: 1D ¹H-NMR spectrum of the products of the isomerization reaction of deuterated Ac NGAA-NH₂ (Ac-αDGAA-NH₂ and Ac-βDGAA-NH₂). Figure S3: Enlargements of 1D ¹H-NMR spectra of deuterated Ac-NGAA-NH₂, and the products of its isomerization reaction (Ac-αDGAA-NH₂ and Ac-βDGAA-NH₂). Note S3: Signal assignment and coupling constants of deuterated Ac-NGEA-NH₂ peptide and the products of its isomerization reaction (Ac-αDGEA-NH₂ and Ac-βDGEA-NH₂). Figure S4: 1D ¹H-NMR spectrum of deuterated Ac-NGEA-NH₂ peptide. Figure S5: 1D ¹H-NMR spectrum of deuterated Ac NGEA-NH₂ and the products of its isomerization reaction (Ac-αDGEA-NH₂ and Ac-βDGEA-NH₂). Figure S6: Enlargements of 1D ¹H-NMR spectra of deuterated Ac-NGEA-NH₂, and the products of its isomerization reaction (Ac-αDGEA-NH₂ and Ac-βDGEA-NH₂). Supplementary Data S2. Input parameters, coordinates and absolute energies of the structures used in IRC path calculations, structure optimizations and analysis. Note S1: Input parameters for IRC path calculations. Table S1: Cartesian coordinates and input parameters of open form of the deuterated system. Table S2: Cartesian coordinates and energy value of iteration step 43 of the open form of the deuterated system. Table S3: Cartesian coordinates and input parameters of iteration step 43 of the open form of the deuterated system. Table S4: Cartesian coordinates and energy values of the optimized open form of the deuterated system. Table S5: Cartesian coordinates and input parameters of transition state of the deuterated system. Table S6: Cartesian coordinates and energy values of the transition state of the deuterated system. Table S7: Cartesian coordinates and input parameters of succinimide of the deuterated system. Table S8: Cartesian coordinates and energy values of the optimized succinimide of the deuterated system.

Author Contributions

Manuscript writing: F.P. and A.P.; paper preparation: F.P., A.P., B.S.Á., I.J. and E.K.; Supplementary Files preparation: F.P. and B.S.Á.; theoretical calculations: F.P. and I.J.; analysis of the theoretical calculations: F.P.; peptide synthesis: F.P.; NMR measurements and analysis: F.P.; kinetic model establishment: E.K.; kinetic data analysis: E.K., F.P. and B.S.Á.; kinetic and theoretical data visualization: I.J. and F.P.; general supervision: A.P.; manuscript conceptual elaboration: A.P.; provided financial support and instrumentation for the research: A.P. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary File S1, Supplementary Data S1–S2 files. All other relevant data are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

Funding Statement

HUN-REN–ELTE Protein Modelling Research Group. This work was completed in the ELTE Thematic Excellence Programme (Szint+), supported by the Hungarian Ministry for Innovation and Technology, and the ELTE Institutional Excellence Program (1783-3/2018/FEKUTSTRAT), supported by the Hungarian Ministry of Human Capacities and grants from the European Union and the State of Hungary, co-financed by the European Regional Development Fund (VEKOP-2.3.3-15-2017-00020, VEKOP-2.3.2-16-2017-00014). Project no. 2018-1.2.1-NKP-2018-00005 has been implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the 2018-1.2.1-NKP funding scheme. Project no. RRF-2.3.1-21-2022-00015 has been implemented with the support provided by the European Union, supported by the Ministry for Innovation and Technology from the Hungarian NRDI Fund (2020-1.1.6-JÖVŐ-2021-00010). Project no. 2025-3.1.1-ED-2025-00013 has been implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the 2025-3.1.1-ED-NKP funding scheme. This work was supported by the Hungarian National Research, Development and Innovation Fund (STARTING 2024/150597; and Adv_25 153035). Further support was provided by the SNN 148580 project implemented with the support provided by the Ministry of Innovation and Technology of Hungary from the National Research, Development and Innovation Fund, financed under the SNN_24 funding scheme, and by the Slovenian Research and Innovation Agency.