Unraveling pH-dependent peptide conformational transitions via integration of main mechanical forces and side-chain interactions

The stability and flexibility of peptide structures are strongly influenced by environmental conditions, particularly pH. In this study, we investigate how changes in protonation states of pH-responsive residues modulate non-covalent interaction networks and drive conformational transitions. Using a β-hairpin peptide (PDB ID: 1K43) as a model system, we developed a tailored extension of the Main Mechanical Forces (MMFs) approach that explicitly accounts for side-chain protonation and its effects on non-covalent interaction patterns. Molecular dynamics (MD) simulations were performed to validate the MMFs-derived pH-related structural predictions and to provide complementary insights into pH-dependent conformational stability and flexibility of a peptide structure. The overall agreement between MMFs and MD results is an indication of the reliability of the proposed methodology. Overall, we present a refined MMFs-based methodological framework capable of predicting pH-dependent conformational transitions by systematically modelling changes in side-chain interaction patterns and non-covalent networks. This approach provides an effective calculation strategy for studying pH-responsive systems, which has potential to inform future simulation platforms focusing on peptide folding mechanisms.

Functional groups on peptide side chains provide a diverse array of reactive sites, enabling chemical modification and making peptides versatile platforms for the design of stimuli-responsive systems that, if appropriately designed as pH-responsive peptides, can respond to changes in pH and thereby support a wide range of applications (Hou and Liu, 2024). However, in addition to pH, other stimuli such as temperature, redox potential and light can also be exploited to induce selective structural changes (Hoffman, 2013; Mura et al., 2013). Due to the intrinsic properties of each specific amino acid composing a sequence, peptides can be readily engineered as stimulus-responsive materials, and the incorporation of non-natural amino acids or other small organic moieties can further extend both functionality and intended applications (Löwik et al., 2010). In this context, as an example of synergy between a natural amino acid sequence covalently bound to a small organic molecule, recent work has demonstrated the development of an efficient antibacterial peptide, which indeed leverages the synergistic combination of amphipathic helicity and metal-ion sequestration (Patamia et al., 2026).

To investigate the structural behaviour of peptides under varying pH conditions, we evaluated the applicability of the Main Mechanical Forces (MMFs) approach (Larocca et al., 2019; Larocca et al., 2021; Larocca et al., 2024b; a; 2025; Patamia et al., 2026), with the aim of extending the scope of this method of calculation to describe pH-dependent conformational transitions in well-defined peptide structures. In this framework, we have adapted the MMFs methodology to take into consideration that modulation of the pH modifies the protonation state of pH-responsive residues, leading to local conformational changes, with following variations of backbone dihedral angles, as well as alteration and remodelling of non-covalent interaction networks. The methodological extension carried out on the MMFs workflow explicitly accounts for the loss or modification of specific interactions resulting from protonation or deprotonation events in suitable functional groups, as determined by changes of the pH. To this end, after initial identification of the affected chemical interactions, we have considered the side chains pKa values of the pH-responsive residues (Miclotte et al., 2020) and adjusted the MMFs calculations, to reflect modifications of the corresponding contributions to the total dihedral angles. Namely, this implies to input a subtraction related to the partial contribution of the total dihedral angle values to be calculated (see details in Methods section and Supplementary Material). To set up our study, we selected a β-hairpin peptide (PDB code:1K43) (Pastor et al., 2002) containing a set of pH-responsive residues in the amino acidic sequence, thereby enabling investigation at pH 3, 7.4 and 11. Moreover, with this peptide we could perform a comparison between experimental and MMFs-derived structures (root-mean-square deviation, RMSD = 2.400 Å), with the latter used as reference to find out the specific non-covalent chemical interactions amongst the side chains of the residues, thus determining that the peptide 1K43 to adopt its actual β-hairpin structure. The comparison between experimental vs. calculated outputs demonstrated a robust agreement, supporting the use of the calculated structure as a reference for analysing the interaction network that drives folding. The results of this study, upon comparing the reference structure with the calculated structures at specific pH values, indicate that the studied β-hairpin peptide can retain its structural stability at acid pH (MMFs vs. experimental, RMSD = 2.486 Å), remains largely structured at physiological pH (RMSD = 3.922 Å), and becomes increasingly disordered at basic pH (RMSD = 6.761 Å). Following on the set-up of the pH-specific workflow and having modelled the structures of the peptide at a given pH value, molecular dynamics (MD) simulations were performed to enable the comparison of the outputs from MMFs and MD structural investigations at the corresponding pH conditions, thereby validating the MMFs predictions. In line with this, RMSD values were calculated by comparing MD-derived conformations with MMFs-predicted structures at 25 ns intervals, for each different pH value. The agreement observed through RMSD data supports the reliability and robustness of the MMFs-based structural predictions, even in the case that MD-derived conformational ensembles are used as benchmark.

Overall, building on the newly established framework, we have further extended the MMFs approach to the analysis of pH-dependent conformational changes. This enables the determination of structural insights into both peptide folding mechanisms and the influence of environmental factors, such as the pH, which can induce changes to the molecular flexibility. In this regard, a key challenge in peptide design for drug discovery applications is to develop methods that allow the rapid identification of amino acidic sequences with well-defined structures, in order not to compromise the binding to such a biological target, as the result of a high and uncontrolled conformational flexibility (Pastor et al., 2002). Additionally, this approach provides insight into the pH range in which a peptide remains structurally stable or, in contrast, becomes increasingly disordered, thereby further supporting the development of so-called conformational switches (Anderson and Andersen, 2017), given their wide applications as biosensors (Vallée-Bélisle and Plaxco, 2010), chelators for metal ions (Ambroggio and Kuhlman, 2006) and drug delivery systems (Langlet-Bertin et al., 2010; Iacobucci et al., 2012).

The calculation of the backbone dihedral angles φ and ψ of the β-hairpin peptide 1K43 (Pastor et al., 2002) selected for this study was carried out using the MMFs approach, as set out in methods recently reported in the literature (Larocca et al., 2024b; Larocca et al., 2024a). Briefly, the MMFs calculations initially focus on the determination of the starting threshold distances (r i) established between the side chains of the interacting residues. Once each r i is obtained, the Coulombian force acting through the interacting atoms of the side chains can be calculated. In turn, this enables to define the equation that reports the respective potential energy (U) which contains the partial dihedral angle (δφ°) of interest. As calculated partial dihedral angle, the MMFs method considers the rotation obtained as the result of each single interaction of the side chains in residues with their neighbour interacting residues. Subsequently, knowing r i, it is possible to define the equation of the torque moment, which also contains the partial dihedral (δφ°) angle to be determined (Larocca et al., 2024b; Larocca et al., 2024a). Therefore, equalizing potential energy (U) and torque moment (τ), the value of the partial dihedral angle of interest for a specific interaction can be obtained using the arctangent of the angle. By adding up all the partial dihedral angles, it is possible to obtain the total dihedral angle of a given residue into a peptide structure. Following on this approach, the MMFs method has been adopted to calculate the backbone dihedral angles φ and ψ of the amino acidic sequence of the β-hairpin peptide 1K43 (Pastor et al., 2002), using a dedicated PDB file of the fully unfolded peptide (with the backbone dihedral angles φ = ψ = 180°) processed with Molefacture plug-in in VMD (Humphrey et al., 1996; Mayne et al., 2013).

In this work, to further assess the conformational changes associated with pH variation, the MMFs approach was also adopted. However, it was implemented within a revised calculation methodology specifically designed to account for the influence of pH-dependent protonation/deprotonation effects on the structural variations of pH-responsive residues. This enabled the development of a modified MMFs calculation protocol suitable for describing pH-dependent conformational changes. More in detail, MMFs calculations were performed at different pH values, taking into account the amino acid residues and the pKa values of their corresponding side chains, to further investigate the effects of protonation/deprotonation equilibria of the ionizable functional groups present in pH-responsive side chains and their role in driving conformational changes upon pH variation. Initially, the MMFs approach was employed to calculate the backbone dihedral angles φ and ψ of the β-hairpin peptide sequence (PDB code: 1K43 (Pastor et al., 2002)), and the obtained results were compared with the structure reported in the literature (Mayne et al., 2013). Subsequently, based on the amino acid sequence of the peptide and after estimating the possible structural changes induced by pH variation in relation to the pKa values of the pH-responsive residues (ARG1, LYS3, TYR6, GLU12, and ARG14), the MMFs calculations were performed using the modified methodology described below. This modification was necessary to investigate the conformational changes at pH 3, 5 (Pastor et al., 2002), 7.4, and 11 (details of the calculations are provided in the Supplementary Material).

MMFs calculation for the reference structure

Dihedral angle φ. The β-hairpin peptide sequence was used to generate a.pdb file of the fully unfolded peptide, with backbone dihedral angles set to φ = ψ = 180°, using the Molefacture plug-in implemented in VMD (Humphrey et al., 1996; Mayne et al., 2013). Subsequently, MMFs calculations were performed based on the most recent developments of the methodology (Larocca et al., 2024b; a) and using, as reference values for the partial charges, those reported in the literature (Cornell et al., 1995). The calculations of the backbone dihedral angles φ were carried out by introducing specific modifications concerning the glycine residues and the involvement of intramolecular non-covalent interactions affecting the two terminal residues. At pH values below neutrality, namely, pH five for the reference structure, in agreement with the experimental data (Pastor et al., 2002), and pH 3 according to our investigation, calculations for the glycine residues (GLY2, GLY8, and GLY13) considered the electrostatic interaction (attraction) between the terminal charges (EITC). A good agreement between the calculated and experimental dihedral angle values was obtained by setting the EITC folding factor to 0 Å and multiplying the EITC-related partial dihedral angle contribution (δφ EITC) by a factor of 2. Furthermore, for the two terminal residues (ARG1 and ARG14), the possibility of additional intramolecular interactions was considered. For ARG1, an intramolecular electrostatic repulsion between the positively charged ammonium group and the guanidinium group was taken into account, whereas for ARG14 an electrostatic attraction between the negatively charged carboxylate group and the positively charged guanidinium group was considered. In both cases, the corresponding folding factor was set to 0 Å. The introduction of these two additional intramolecular interactions enabled a better agreement between the experimental dihedral angle values and those obtained from the calculations, including comparison with the dihedral angles derived from the MD-generated conformers at varying pH values. A further important aspect concerns ASN7, the residue located at the centre of the sequence. For the calculation of its φ dihedral angle, in addition to the conventional non-covalent interactions considered within the MMFs framework, the steric repulsion (i.e., van der Waals steric repulsion (Larocca et al., 2019)) of the proton bound to the Cα atom with neighbouring residues at positions 7 ± 1 (TYR6 and GLY8) and 7 ± 2 (THR5 and ILE9) was also taken into account. This steric repulsion effect was modelled as an electrostatic monopole–monopole repulsive interaction between the involved protons, with the folding factor set to 0 Å. The inclusion of this additional interaction resulted in improved agreement between the experimental dihedral angle values and those obtained from both the original MMFs calculations and the MD-derived conformers.

Dihedral angle ψ. For the calculation of the dihedral angles ψ, the procedures recently described in the literature were also adopted (Larocca et al., 2024b; a). As reported in our previous studies, the calculation of ψ requires the use of specific equations that account for the corresponding φ dihedral angle values associated with the secondary structure of the residue under investigation. Because not all possible combinations of secondary-structure-related φ values were observed in our earlier studies, a complete set of equations could not be established (Larocca et al., 2024b; Larocca et al., 2024a). Therefore, in the present work, we introduce additional equations for the calculation of ψ angles that incorporate previously unobserved combinations of φ secondary structure values. The updated equations are reported in Table 1.

MMFs calculation at pH 3

At acidic pH (3), the calculations were performed by considering the conformational changes associated with the protonation of ionizable functional groups. In the present study, the residues affected at pH 3 are GLU12 and ARG14, respectively involving the side-chain functional group of GLU12 and the C-terminal carboxyl group of ARG14. Furthermore, neighbouring residues engaged in polar interactions, including hydrogen bonding and electrostatic attraction/repulsion, were also found to undergo conformational changes, which in turn led to variations in the corresponding backbone dihedral angles.

Dihedral angle φ (pH = 3). For the calculation of the dihedral angles φ at pH 3, protonation of the terminal carboxylate group of the last residue (ARG14) was taken into account. Consequently, the folding factor associated with the EITC was set to 0 Å for both ARG14 and ARG1. Since protonation neutralizes the charge of the terminal carboxylate group, the EITC-related partial dihedral angle contribution was subtracted for both terminal residues. In addition, the folding factor was set to 0 Å for all neighbouring residues involved in polar interactions with the protonated terminal carboxyl group of ARG14 and the terminal ammonium group of ARG1, and the corresponding affected partial dihedral angle contributions were consequently subtracted. Specifically, the following modifications were applied to the residues: - LYS3: subtraction of the partial dihedral angle contributions associated with EITC, electrostatic repulsion, and hydrogen-bond interactions, with the corresponding folding factors set to 0 Å;

TYR11: subtraction of the partial dihedral angle contributions associated with EITC and hydrogen-bond interactions, with the corresponding folding factors set to 0 Å;

GLU12: subtraction of the partial dihedral angle contributions associated with EITC, electrostatic repulsion, and hydrogen-bond interactions, with the corresponding folding factors set to 0 Å;

ARG14: subtraction of the partial dihedral angle contributions associated with EITC, hydrogen-bond interactions, and intramolecular electrostatic attraction, with the corresponding folding factors set to 0 Å.

Furthermore, at acidic pH, the dihedral angles of the glycine residues (GLY2, GLY8 and GLY13) were calculated using the same approach adopted for the reference structure, as described above, including the methodological updates that enabled improved agreement with the experimental data.

Dihedral angle ψ (pH = 3). For the calculation of the dihedral angles ψ at pH 3, the equations adopted were those previously reported in the literature (Larocca et al., 2024b; Larocca et al., 2024a), including the newly updated formulae reported in Table 1. Differently, for the calculation of ψ1, an additional modification was introduced, as follows: - ARG1 (ψ1): subtraction of the partial dihedral angle contributions associated with EITC, electrostatic repulsion, and intramolecular electrostatic repulsion, with the folding factor set to 0 Å.

MMFs calculation at pH 7.4

Dihedral angle φ (pH = 7.4). At physiological pH (7.4), i.e., slightly basic conditions, the MMFs calculation approach enabled the study of conformational changes in the β-hairpin peptide of interest by introducing modifications consistent with the possible deprotonation of functional groups bearing acidic protons, according to their pKa values. Specifically, we have adopted the following updates to the MMFs reference method previously reported in the literature (Larocca et al., 2024b; Larocca et al., 2024a): - GLY (in positions 2, 8, and 13): calculations were performed as previously reported (Larocca et al., 2024b; Larocca et al., 2024a);

• Residues containing polar functional groups (that may be affected by pH-induced changes, in turn altering non-covalent polar interactions) – i.e., LYS3, TRP4, THR5, TYR6, ASN7, THR10, TYR11, GLU12 and ARG14: the folding factor associated with the EITC contribution (δφ EITC) was set to 0 Å;

LYS3: partial dihedral angle contributions associated with EITC (folding factor = 0 Å), electrostatic repulsion, and hydrogen bonding were subtracted;

ARG14: the hydrophobic interaction contribution was subtracted, whereas the partial dihedral angle contributions for EITC (folding factor = 0 Å) were retained.

Dihedral angle ψ (pH = 7.4). For the calculation of the dihedral angles ψ at pH 7.4, the equations adopted were those previously reported in the literature (Larocca et al., 2024b; Larocca et al., 2024a), including the newly updated formulae reported in Table 1. Differently, for the calculation of ψ1, the following modification was introduced: - ARG1 (ψ 1): partial dihedral angle contributions associated with EITC (folding factor = 0 Å) were subtracted, along with the hydrophobic interaction contribution, while retaining its associated folding factor.

MMFs calculation at pH 11

Dihedral angle φ (pH = 11). At pH 11, the MMFs calculation approach was applied by introducing specific modifications to account for the deprotonation of functional groups bearing acidic protons, according to their corresponding pKa values (LYS3, TYR6, and TYR11). In this context, the following measures, including updates, were introduced to the reference MMFs methodology previously reported in the literature (Larocca et al., 2024b; Larocca et al., 2024a): - GLY2, GLY8, and GLY13: calculations were performed according to the procedures previously described in the literature (Larocca et al., 2024b; Larocca et al., 2024a);

• Residues containing polar functional groups (that may be affected by pH-induced changes, in turn altering non-covalent interactions–i.e., LYS3, TRP4, THR5, TYR6, ASN7, THR10, TYR11, GLU12, and ARG14: the folding factor associated with EITC contribution (δφ EITC) was set to 0 Å;

• LYS3: subtraction of the partial dihedral angle contributions associated with EITC, electrostatic repulsion, and hydrogen-bond interactions, with the corresponding folding factors set to 0 Å;

THR5 and TYR6: for these two residues, the THR5–TYR6 interaction was treated differently depending on the residue under consideration. For THR5, the THR5–TYR6 interaction providing the largest contribution to the total dihedral angle calculation was identified as a hydrophobic interaction, whereas for TYR6, the TYR6–THR5 interaction contributing most significantly to the total dihedral angle was identified as a hydrogen-bond interaction. This approach takes into account the latest developments set out for MMFs-based calculations (Larocca et al., 2024a), following the modification of the non-covalent interactions resulting from deprotonation of the TYR6 side-chain phenolic group. Furthermore, the partial dihedral angle contributions associated with EITC (with the folding factor set to 0 Å) and hydrogen-bond interactions involving TYR6 were subtracted to account for the effects of deprotonation;

ASN7: the EITC folding factor was set to a value different from 0 Å, consistent with the calculations performed at pH values other than the physiological value. Therefore, the same assumptions adopted for pH 3 and pH five were applied;

TYR11: similarly to TYR6, deprotonation of the TYR11 side chain affected the conformational behaviour of the entire structure. Consequently, an additional interaction was introduced, namely, the electrostatic attraction between the deprotonated TYR11 side chain and the ARG14 side chain, hereafter referred to as ‘electrostatic attraction after deprotonation’. In addition, the partial dihedral angle contributions associated with EITC (with the folding factor set to 0 Å), hydrogen-bond interactions, and electrostatic attraction after deprotonation were subtracted;

ARG14: subtraction of the partial dihedral angle contributions associated with hydrogen-bond interactions, electrostatic attraction after deprotonation, and EITC (with the folding factor set to 0 Å).

Dihedral angle ψ (pH = 11). For the calculation of the dihedral angles ψ at pH 11, the equations adopted were those previously reported in the literature (Larocca et al., 2024b; Larocca et al., 2024a), including the updated formulations listed in Table 1. For ψ 1 (ARG1), the deprotonation-induced modification of the polar interactions was taken into account by considering only hydrophobic interactions as determinant for the calculation of ψ 1. The total ψ 1 value was then obtained by multiplying each hydrophobic interaction contribution by −1 and summing the resulting terms.

MD simulations

The MD simulations of the complexes were performed with YASARA after the structure (PDB code:1K43) was retrieved from the Protein Data Bank (RCSB PDB, https://www.rcsb.org/). A periodic simulation cell extending 10 Å from the protein surfaces was employed. The cell was filled with water, with a maximum sum of all water bumps of 1.0 Å and a density of 0.997 g/mL. The setup included optimizing the hydrogen bonding network (Krieger et al., 2006) to increase the solute stability and a pKa prediction to fine-tune the protonation states of protein residues at the chosen pH of 3, 7.4 and 11 (Krieger et al., 2006). To assess the robustness of the protonation-state assignment, the pKa values predicted by YASARA were additionally compared with independent predictions obtained using the H++, PypKa, and KaML servers as explained below. With an excess of either Na or Cl to neutralize the cell, NaCl ions were supplied at a physiological concentration of 0.9%. The cutoff was 10 Å for Van der Waals forces (the default used by AMBER) (Hornak et al., 2006), and no cutoff was applied to electrostatic forces (using the Particle Mesh Ewald algorithm) (Essmann et al., 1995). The equations of motions were integrated with multiple time steps of 2.5 fs for bonded interactions and 5.0 fs for nonbonded interactions at a temperature of 298 K and a pressure of 1 atm. Initially, a short MD simulation was run on the solvent only to remove clashes. The entire system was then energy minimized using a steepest descent minimization to remove conformational stress, followed by a simulated annealing minimization until convergence (<0.01 kcal/mol Å). Finally, 250 ns MD simulation without any restrictions and a stable pH (3, 7.4 and 11) was conducted and the conformations were recorded every 200 ps. We have subsequently compared the MMFs calculated structures with structures retrieved from the MD calculations and saved at every 25ns. Molecular Dynamics Trajectory Analysis are reported in the following repository: https://zenodo.org/records/21930424?token=eyJhbGciOiJIUzUxMiJ9.eyJpZCI6ImQwYmFhYjNkLTk2Y2QtNGQwNi04ZGI4LTMwY2FjZTg4ZDIwNiIsImRhdGEiOnt9LCJyYW5kb20iOiI2ZGQ4YzliNjgxMzIzYzk1MjlhMDIwZDcwZGRhNjlmYiJ9.Ew8vTPuBIxoU1oQr53p2maFStmjht4H6vJDbN_hmnOk16XKJbpi4mfmGi_jTiLK3C_buYX-G72XAzaaOcVDjvw). We have performed additional pKa calculations using the H++, PypKa, and KaML servers and compared these predictions with those obtained using YASARA. Overall, the independent calculations show a high degree of consistency, particularly for the residues most relevant to the protonation state at the simulation pH. For Glu12, the three methods predict pKa values of 4.27 (YASARA), 4.20 (H++), 4.26 (PypKa), and 4.27 (KaML). For Lys3, the corresponding values are 10.61, 10.60, 10.77, and 10.30. The two Tyr residues also show consistent predictions, with values ranging from 9.65 to 10.80. These results provide independent support for the protonation states assigned in the simulations. Importantly, these results support the protonation-state assignments used for all three simulation conditions. At pH 3.0, Lys3 and both Arg residues are protonated, Tyr6 and Tyr11 are predominantly neutral, while Glu12 is predominantly protonated. At pH 7.4, Lys3 and both Arg residues remain protonated, Glu12 is deprotonated, and the Tyr residues remain predominantly neutral. At pH 11.0, Glu12 is deprotonated and Lys3 is predominantly deprotonated, whereas the Arg residues remain predominantly protonated; the Tyr residues are expected to be substantially deprotonated at this pH. The data for the pKa calculation is included in the Zenodo repository.

This study was conducted to investigate the possibility of employing the MMFs calculation methodology (Larocca et al., 2019; Larocca et al., 2021; Larocca et al., 2024b; Larocca et al., 2024a; Larocca et al., 2025; Patamia et al., 2026) as a theoretical tool useful also for describing how specific pH variations may induce conformational changes in peptide structures. In particular, the primary aim was to determine whether, and to what extent, pH-responsive residues contribute to conformational changes following protonation/deprotonation events at specific pH values. Accordingly, the MMFs approach was used to investigate variations in the backbone dihedral angles associated with pH-responsive residues and to elucidate the underlying mechanisms related to non-covalent interactions among their side chains, as well as the effects of protonation/deprotonation equilibria on the establishment and disruption of specific non-covalent chemical interactions. The β-hairpin peptide 1K43 (Pastor et al., 2002) was selected as a model system because it contains several pH-responsive residues, namely, ARG1, ARG14, LYS3, TYR6, TYR11, and GLU12, which were expected to provide significant insights into the structural effects of pH variation. Initially, the 1K43 structure was modelled using the MMFs methodology, and the resulting calculated structure was compared with the experimental one. The calculated structure was then used as the starting point for subsequent investigations of pH-induced structural changes at pH 3, 7.4, and 11.

To further validate the theoretical findings, molecular dynamics (MD) simulations were performed at the same pH values and the resulting conformational features were compared with those predicted by the MMFs approach. Based on the amino acid sequence of 1K43 (Pastor et al., 2002), MMFs calculations were carried out to determine the backbone dihedral angles φ and ψ, starting from a dedicated PDB structure of the fully unfolded peptide in which all initial backbone dihedral angles were set to φ = ψ = 180°. By applying the MMFs methodology as set up in its most recent developments (Larocca et al., 2024b; Larocca et al., 2024a), a structural model of the 1K43 peptide was obtained which, upon comparison with NMR conformer 6 (the most representative conformer of the experimental ensemble (Pastor et al., 2002)), showed high agreement with the experimental structure, yielding an RMSD value of 2.400 Å (Figure 1). The RMSD value, although slightly higher than 2.000 Å, can be mainly attributed to the limited accuracy in the calculation of the dihedral angles associated with the terminal residues ARG1 and ARG14. This observation is consistent with our previous studies (Larocca et al., 2024b; a; Patamia et al., 2026), in which this feature was identified as a limitation of the MMFs approach.

However, in this case, only a modest yet acceptable agreement was observed for the φ dihedral angle of GLY2. Nevertheless, we found that glycine residues require a different calculation approach under acidic conditions, as observed for both the reference structure (experimentally determined at pH 5 (Pastor et al., 2002)) and the pH 3 conditions investigated in this study. In contrast, at physiological pH (7.4) and under strongly basic conditions (pH 11), the calculation of glycine dihedral angles was satisfactorily described using the MMFs methodology according to the previously reported calculations methods (Larocca et al., 2024b; Larocca et al., 2024a). This behaviour represents one of the main findings of the present study, indicating that glycine residues require different calculation approaches depending on the pH of the medium. Specifically, under acidic conditions, the calculation of the φ dihedral angle requires consideration of all possible non-covalent interactions involving the neighbouring residues. On the contrary, under basic conditions, the agreement obtained using the previously reported methodology confirms that the φ angle of a glycine residue at generic position “n” is primarily governed by its coplanarity with the flanking residue at position “n – 1”. Based on these observations, we propose that acidic conditions may induce greater local conformational flexibility in glycine residues. Owing to the achiral nature of the Cα atom, such flexibility may facilitate additional interactions between glycine and its neighbouring residues, thereby influencing the corresponding backbone dihedral angles. To investigate the peptide structure under acidic conditions (pH 3), the backbone dihedral angles were first calculated using the MMFs approach, in order to generate a structural model at this pH value. Subsequently, MD simulations of the peptide were performed under the same conditions. As described in the Methods section, the calculations were carried out by considering protonation of both the terminal carboxylate group of ARG14 and the side-chain carboxyl group of GLU12, which were expected to induce significant local conformational changes. The peptide structure obtained from the MMFs calculations at pH 3 was compared both with the experimental structure and with the ensemble of conformers generated by the MD simulations performed at the same pH value. Comparison between the MMFs-derived and experimental structures at pH 3 yielded an RMSD value of 2.486 Å (Figure 2A). Furthermore, comparison of the MMFs-derived structure with the MD conformational ensemble at pH 3 resulted in an RMSD value as low as 2.69 Å (Table 2), indicating a substantial degree of structural stability of the peptide under acidic conditions.

Subsequently, by combining the MMFs and MD approaches and adopting the same methodological framework, we investigated the conformational changes occurring at pH 7.4. Comparison of the MMFs-derived structural model with the experimental structure yielded an RMSD value of 3.922 Å (Figure 2B), suggesting partial preservation of the native structural arrangement. Furthermore, comparison of the MMFs-derived structure at pH 7.4 with the corresponding MD conformational ensemble resulted in an RMSD value as low as 3.31 Å (Table 3). These findings indicate an increase in the structural flexibility of the peptide at slightly basic pH and further support the efficiency of the MMFs calculation approach to predict conformational transitions induced by pH variation. Indeed, the robust agreement observed between the MMFs-derived structure and the MD conformational ensemble confirms the suitability of this methodology for describing pH-dependent structural changes in peptide systems.

Finally, we extended our investigation to the structural behaviour of the peptide at pH 11, adopting the same combined MMFs/MD approach. Comparison between the MMFs-derived structure and the experimental structure yielded an RMSD value of 6.761 Å (Figure 2C), suggesting a substantial loss of the native structural organization and indicating that the peptide adopts a largely unstructured conformation under strongly basic conditions. This observation was further supported by comparison of the MMFs-derived structure with the MD conformational ensemble generated at pH 11, which resulted in an RMSD value as low as 2.88 Å (Table 4). This result confirms that the MMFs calculation approach correctly predicts the structural consequences associated with a significant increase in pH. Additional evidence supporting the MMFs prediction was obtained by comparing the calculated structure with the final conformer extracted from the MD trajectory (250 ns conformer). The superposition of these two structures yielded an RMSD value of 2.88 Å (Figure 3), further confirming the consistency between the MMFs predictions and the MD-derived conformational behaviour at pH 11.

Peptides exposed to pH variations can undergo local conformational changes when pH-responsive residues are present within their sequence. In such cases, protonation and deprotonation events (determined by pH changes) alter the values of the backbone dihedral angles, which in turn produce local conformational transitions. Namely, this results in modified patterns of non-covalent interactions involving the affected side chains. This behaviour is of particular interest in the design of stimuli-responsive peptide-based materials (Hou and Liu, 2024; Hoffman, 2013; Mura et al., 2013; Löwik et al., 2010), where a detailed understanding of structural stability and flexibility under different environmental conditions is essential. In the present study, we employed the MMFs approach (Larocca et al., 2019; Larocca et al., 2021; Larocca et al., 2024b; a; 2025; Patamia et al., 2026) to investigate how pH variations may induce conformational changes, by focusing on pH-responsive residues and the corresponding non-covalent interactions affected by protonation/deprotonation equilibria. As a model system, we selected the β-hairpin peptide 1K43 (PDB code: 1K43) (Pastor et al., 2002), whose amino acid sequence contains several pH-responsive residues, making it suitable for evaluating the effects of different pH conditions (3, 7.4, and 11) on conformational stability. The study was initially validated through comparison between the experimental structure and the MMFs-derived structural model, which yielded an RMSD value of 2.400 Å (Figure 1). To perform this investigation, the MMFs methodology was appropriately extended to account for side-chain modifications associated with protonation and deprotonation processes, as well as the resulting changes in the pattern of non-covalent interactions. This enabled a detailed analysis of the conformational stability and flexibility of the peptide at each pH value considered. Molecular dynamics (MD) simulations were subsequently performed to assess the reliability of the pH-dependent structural predictions generated through MMFs. The results obtained using the newly refined MMFs methodology developed in this work indicate that the β-hairpin peptide remains structurally stable under acidic conditions (pH 3 and 5), exhibits increased conformational flexibility at physiological pH (7.4), and adopts a largely unstructured conformation under strongly basic conditions (pH 11). These findings were further supported by the MD simulations, which showed a consistent pH-dependent conformational trend.

In conclusion, we present an enhanced MMFs-based methodology capable of predicting pH-dependent conformational transitions by explicitly accounting for protonation/deprotonation-induced changes of side chains and resulting variations in the non-covalent interaction network. Accordingly, this study highlights how the fine-tuning of media properties can be used for the modulation of supramolecular properties in peptides. The proposed approach provides a useful theoretical framework for investigating the structural response of peptides to variations in pH and may contribute to the rational design and characterization of pH-responsive peptide systems.