Impact of pH on Fuzzy Interactions between Two Intrinsically Disordered Proteins

I.   INTRODUCTION

Intrinsically disordered proteins and protein regions (IDPs/IDRs) are prevalent in the eukaryotic proteome and play critical roles in a myriad of cellular functions [1, 2]. The inherent flexibility and lack of stable three-dimensional structures of IDPs/IDRs pose significant challenges in understanding their functions from the traditional structure-function paradigm. Although some IDPs/IDRs undergo a process known as ``folding upon binding"[3, 4] wherein they form stable structures upon interaction with their partners, many IDPs/IDRs form ``fuzzy complexes" maintaining their intrinsic disorder even when bound [5−7].

Historically, molecular recognition mechanisms have been explained using Fischer’s [8] ``lock-and-key" model and Koshland’s [9] ``induced fit" hypothesis. According to the “lock-and-key" model, the conformation of a free protein is essentially the same as its bound state, suggesting a rigid and preformed structure that perfectly complements its ligand. In contrast, the ``induced fit" hypothesis proposes that ligand binding induces conformational changes in the protein, leading to a new structure that is more complementary to the ligand. Both the ``lock-and-key" and ``induced fit" models, in their simplest forms, assume that proteins adopt a single, stable conformation under specific experimental conditions. However, this assumption does not hold true for intrinsically disordered proteins (IDPs), which are inherently dynamic and exist as a heterogeneous ensemble of conformations [10]. The dynamic nature of IDPs means that their functions cannot be fully explained by traditional models that consider only static structures. Therefore, there is a pressing need to explore new perspectives and develop hypotheses that can better capture the dynamic and multifaceted nature of IDP functions [11, 12]. Understanding these proteins requires approaches that consider the full spectrum of their conformational landscapes and their ability to adapt and respond to diverse cellular environments and interactions.

Protein 4.1G, as a membrane-associated cytoskeletal protein, plays a crucial role in maintaining normal cell morphology, regulating cell adhesion, migration, mitosis, and intercellular signal transduction [13−15]. It comprises five domains: the N-terminal headpiece region (Headpiece, HP domain), the FERM domain (four.one-ezrin-radixin-moesin domain), the FA domain (FERM adjacent domain), the SAB domain (spectrin-actin binding domain), and the CTD (C-terminal domain) [16]. Among these, the HP domain and the CTD region are intrinsically disordered protein domains. We previously reported the extremely fuzzy interaction between two disordered protein regions: protein 4.1G and a 26-residue motif at the C-terminal region of nuclear mitotic apparatus (NuMA), which binds specifically and plays a major role in the regulation of both symmetrical and asymmetrical cell divisions [15]. It turns out that the C-terminal domain of protein 4.1G (aa 939–1005) is the major region for binding to NuMA (aa 1800–1825) [17].

Our previous studies have identified the hydrophobic interaction sites within 4.1G CTD (aa 988–993: VTRVVV) and NuMA (aa 1814–1819: IINITM) as crucial for the binding of 4.1G CTD to NuMA [17, 18]. Additionally, we found that these hydrophobic segments maintain a relatively high secondary structure content under acidic conditions [19]. In our experiments, we discovered that 4.1G CTD and NuMA bind effectively under neutral and alkaline conditions, but their interaction is disrupted under acidic conditions. In our previous study [19], the binding free energies between 4.1G CTD and NuMA at neutral pH (see FIG. 1) and pH 3.6 under different salt concentrations were measured using isothermal titration calorimetry (ITC). At pH 3.6, the binding between 4.1G CTD and NuMA is completely abolished. At pH 7.0, as the salt ion concentration increases, the binding free energy between 4.1G CTD and NuMA decreases slightly. This suggests that electrostatic interactions also play a regulatory role in the binding of 4.1G CTD to NuMA. Therefore, we aim to investigate how pH regulates the interaction between 4.1G CTD and NuMA, beyond the influence of hydrophobic interactions.

Figure  1.  ITC measurements of the interaction between 4.1G CTD and NuMA under different salt concentrations.

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In this study, we performed molecular dynamics simulations of the 4.1G CTD-NuMA complex under different pH conditions and salt ion concentrations. Our analysis focused on the stability and binding free energy of the complex. The simulations revealed that the binding affinity between 4.1G CTD and NuMA significantly weakens under acidic conditions (pH 3.6) and high salt concentrations. Structural changes and dynamic variations of 4.1G CTD, observed in the simulation trajectories, elucidate the mechanisms behind the loss of interaction with NuMA at pH 3.6.

II.   METHODS

A   MD simulations of 4.1G CTD and NuMA complex at different pH and salt concentration

To elucidate the structure of the protein under acidic conditions (pH 3.6), we utilized propka3 [22] to predict the protonation states of 10 conformations [19]. The charged residues in 4.1G CTD and NuMA are unevenly distributed along their sequences. At neutral pH (7.0), 4.1G CTD possesses a net charge of −6, whereas NuMA exhibits a net charge of +7. When subjected to a low pH of 3.6, the net charge of 4.1G CTD alters to +6, and NuMA’s net charge adjusts to +8. Detailed information on the protonated residues under pH 3.6 conditions is provided in Table S1 (Supplementary materials, SM).

The system was neutralized by the addition of Na⁺ and Cl^– ions and solvated in a 7 nm periodic bounding octahedron box filled with TIP3P [23] water molecules. The salt ion concentrations were set to 0, 0.1, and 0.2 mol/L, respectively. The topology files for the system were generated using the CHARMM36m [24] force field.

The simulated system was first energy minimized using a 50,000-step typical ensemble (NVT) simulation with the V-rescale integrator [25]. This was followed by a 50000-step NPT simulation at 310 K to further equilibrate the system. Finally, the complex was released to minimize the entire simulation system after another 50,000 steps. The particle mesh Ewald (PME) algorithm [26] was used to calculate long-range electrostatic interactions. A cutoff of 1 nm was applied for direct space interactions, and the SHAKE algorithm [27] was utilized to constrain the lengths of all bonds involving hydrogen atoms. The simulation time step was set to 20 ps, followed by a 500 ns MD production run. All simulations were conducted using the Gromacs software package [28].

B   Gyrate calculation and clustering

The radius of gyration (R_g) for the trajectory was calculated using the Gromacs software package to assess the compactness of the protein complex over time. To categorize the trajectories based on their radii of gyration, we employed the K-means clustering algorithm. This method is computationally efficient for large datasets with both numeric and categorical attributes.

K-means [29, 30] clustering begins by randomly selecting K samples from the entire dataset to serve as initial cluster centroids. The algorithm then iteratively updates these centers until no further reassignments of data points to new cluster centers occur. In each iteration, samples are allocated to their nearest cluster center, and cluster centers are recalculated based on current cluster memberships. This process is repeated until convergence is achieved.

For our study, we set K=2, enabling the classification of trajectories into two categories: loose conformations and compact conformations. This approach effectively captures the dissociation behavior of the 4.1G CTD-NuMA complex under pH 3.6 conditions, providing valuable insights into its structural dynamics.

C   Binding free energy calculation by alanine scanning

Binding free energy calculations were performed using alanine scanning mutagenesis to identify key residues contributing to the binding affinity between 4.1G CTD and NuMA. Alanine scanning involves systematically mutating each residue in the interface to alanine and evaluating the impact on binding free energy. This method helps pinpoint critical residues essential for protein-protein interactions.

Molecular mechanics/Poisson-Boltzmann (generalized-Born) surface area (MM/PB(GB)SA) [31] is one of the most popular methods for estimating binding free energies. This method achieves a good balance between accuracy and computational efficiency. It is more accurate than most scoring functions, especially when dealing with protein-protein and protein-nucleic acid systems, and is less computationally demanding than alchemical free energy methods. The binding free energy for a complex can be estimated as follows:

where $E_{\rm{MM}}$ is the molecular mechanics energy, which includes bonded, electrostatic, and van der Waals interactions. $G_{\rm{solv}}$ is the solvation free energy, which can be further divided into polar (calculated using Poisson-Boltzmann or generalized-Born models) and nonpolar contributions. $T \Delta S$ is the entropy term, often estimated using normal mode analysis or other approximation methods.

Hot spot identification was performed by alanine scanning, where specific residues were mutated to alanine, and the free energy contribution was measured to determine their significance (typically a binding energy difference of 2 kcal/mol is used as the criterion for being a hot spot) [32]. The free energy contribution of an individual residue to 4.1G CTD and NuMA binding is typically measured by the binding free energy difference upon mutation to alanine, defined as:

where $\Delta G_{\rm{bind}}^{\rm{ala}}$ is the binding free energy of the mutant (mutated to alanine) complex. $\Delta G_{\rm{bind}}^{\rm{WT}}$ is the binding free energy of the wild-type complex.

The solvation free energy is calculated using the MM/PB(GB)SA approach, splitting it into electrostatic solvation energy and nonpolar solvation energy:

The nonpolar solvation energy is obtained using an empirical solvent-accessible surface area (SASA) formula:

where $\gamma_{\rm{SASA}}$ is the surface tension proportionality constant, and $\beta$ is a fitting parameter.

The gas phase free energy is composed of bonded, electrostatic, and van der Waals interactions. Typically, in MM/GBSA calculations, the entropic contribution to the binding free energy is often neglected [33]. However, in this study, we used a new approach based on interaction entropy (IE) [34, 35], for protein-ligand binding calculations. The “gas-phase" component of the binding free energy is given by:

where the interaction entropy $\Delta S_{\rm{IE}}$ is defined as:

where $P(x)$ is the Partition function of the system, and $k_{\rm{B}}$ is the Boltzmann constant. This can be computed by numerical integration over simulation time:

where $\beta=\dfrac{1}{k_{\rm{B}} T}$, $\Delta E_{\rm{MM}} =E_{\rm{MM}} - \left \langle E_{\rm{MM}} \right \rangle$ and $\left \langle E_{\rm{MM}} \right \rangle = \dfrac{1}{N} \displaystyle\sum^{N}_{i=1}E_{\rm{MM}}(t_i)$.

Different dielectric constants were used in computational alanine scanning (CAS) calculations, depending on the residue being mutated (nonpolar: $\epsilon$=1, polar: $\epsilon$=3, charged: $\epsilon$=5), the selection of $\epsilon$ adheres to the principles outlined in prior research [33]. Additionally, we explored alternative combinations of $\epsilon$ values, including uniform $\epsilon$ for all residues or combinations tailored to different residue types (nonpolar: $\epsilon$=1, polar: $\epsilon$=6, charged: $\epsilon$=10). Through comparative analysis, we determined that our chosen combination best aligns with experimental findings. This approach, combined with the interaction entropy method, provides a more accurate representation of the binding free energy changes due to mutations.

In summary, the binding free energy calculations using alanine scanning and the MM/PB(GB)SA method, with adjustments for different dielectric constants and inclusion of interaction entropy, allowed us to identify key residues that significantly contribute to the stability and binding affinity of the 4.1G CTD-NuMA complex under varying pH and salt concentration conditions.

D   Define secondary structure of proteins

To analyze the secondary structure of the protein throughout the molecular dynamics (MD) simulation trajectories, we utilized the define secondary structure of proteins (DSSP) program [36]. DSSP assigns secondary structure types to amino acid residues based on hydrogen bonding patterns and geometric criteria derived from the 3D atomic coordinates of the protein.

For each snapshot, the secondary structure of the protein was determined using the DSSP program. The atomic coordinates of the protein were provided as input to DSSP, which then computed the secondary structure elements, including alpha helices, beta sheets and random coils, for each residue. The output from DSSP included a sequence of secondary structure assignments for the entire protein. The secondary structure assignments from all snapshots of trajectories were compiled. The frequency of each secondary structure type for each residue was determined by counting the occurrences of each type across all snapshots. These profiles provided insights into the stability and dynamics of different secondary structural elements throughout the simulation, allowing us to understand the behavior of the protein under varying conditions.

III.   RESULTS AND DISCUSSION

A   Structural relaxation of the 4.1G CTD and NuMA complex under acidic conditions (pH 3.6)

To assess the influence of pH on the 4.1G-NuMA complex, we conducted molecular dynamics simulations across various salt ion concentrations at pH 3.6 (0, 0.1, 0.2 mol/L) and pH 7.0 (0, 0.1, 0.2 mol/L). While AlphaFold [20] and crystal structures [21] can provide a single stable conformation, these models are too rigid and do not allow for extensive exploration of the complex’s conformational space. To address this, the initial structures for pH 7.0 simulations were obtained from our previous replica-exchange molecular dynamics (REMD) simulations under neutral conditions [19], resulting in ten distinct conformations. For pH 3.6 simulations, the protonation states of these ten conformations were changed to reflect acidic conditions (see Methods for details). Each starting conformation was then subjected to a 500 ns MD simulation.

We calculated the changes in the radius of gyration (R_g) of the 4.1G-NuMA complex as the salt ion concentration increased from 0 to 0.2 mol/L under both pH 3.6 and pH 7.0 conditions. Using the K-means method, we clustered the simulation trajectories of each system into two groups based on R_g (see Table I). In all systems, there was a significant difference in R_g between the two clusters. Based on the centroid R_g values, we classified the trajectories into a compact state (Cluster 1) and a relaxed state (Cluster 2). When comparing the same salt ion concentrations, the centroid values of both Cluster 1 and Cluster 2 at pH 3.6 were higher than those at pH 7.0. Examination of the representative structures of the two clusters (see FIG. 2) revealed that in the Cluster 2 representative structures of the pH 3.6 and pH 3.6_0.1M systems, 4.1G CTD and NuMA were in a fully dissociated state. In contrast, under pH 7.0 conditions, the Cluster 2 representative structures of all three systems retained partial contacts between 4.1G CTD and NuMA. This observation aligns with our experimental results, showing that the binding between 4.1G CTD and NuMA is disrupted under pH 3.6 conditions. Under acidic conditions (pH 3.6), the 4.1G CTD-NuMA complex adopts a more relaxed and less compact structure, indicating a significant change in their interaction dynamics. This alteration suggests that the acidic environment disrupts the stability of the complex, leading to a more disordered and flexible configuration.

Table  I.  Clustering of simulation trajectories using K-means (concentration in mol/L, R_g in nm, population in %).

pH	Concentration	Cluster 1			Cluster 2
		Rg	Population		Rg	Population
3.0	0	1.61	84		2.40	16
	0.1	1.59	86		2.14	14
	0.2	1.57	76		1.87	24
7.0	0	1.42	49		1.81	51
	0.1	1.56	60		2.00	40
	0.2	1.53	75		1.81	25

 | Show Table

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Figure  2.  The representative structures for Cluster 1 and Cluster 2 are depicted, with NuMA shown in green and 4.1G CTD in blue. The representative structures have R_g values closest to the cluster center values.

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B   Residue contributions to binding free energy

To further investigate how interactions regulating the binding of 4.1G CTD and NuMA change under different pH conditions, we employed alanine scanning to calculate the binding free energy for various systems (see FIG. 3(a)). Our computational results were in complete agreement with experimental trends: the binding affinity at pH 3.6 was consistently lower than that at pH 7.0. Additionally, under pH 7.0 conditions, the binding affinity decreased as the salt ion concentration increased.

Figure  3.  Alanine scanning for binding free energy calculation. (a) Binding free energy calculated by alanine scanning for different systems. (b) Binding free energy contribution by nonpolar amino acids, polar amino acids, negatively charged amino acids, and positively charged amino acids. The combined contribution of negatively charged and positively charged amino acids is considered as the electrostatic contribution. (c) Change in binding free energy contribution by each residue in the pH 3.6 system compared to the pH 7.0 system.

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We calculated the contributions of different types of amino acids (nonpolar, polar, positively charged, and negatively charged) to the binding free energy (see FIG. 3(b)).

The contribution of nonpolar amino acids is primarily due to hydrophobic and van der Waals interactions, while the combined contributions of the positively charged and negatively charged amino acids are attributed to electrostatic interactions. At pH 7.0, electrostatic interactions have obvious contributions to the binding free energy. Increased ionic concentration reduced the binding affinity due to shielding of electrostatic interactions between the negatively charged 4.1G-CTD (net charge: −6) and positively charged NuMA (net charge: +8). Conversely, at pH 3.6, alterations in protonation states (see Table SI in SM) results in a net charge of +6 for 4.1G-CTD and +7 for NuMA. Thus, increased ionic concentration shields electrostatic repulsion, thereby facilitating binding. Among the four types of amino acids, positively charged amino acids exhibited the greatest difference between pH 3.6 and pH 7.0 conditions. Under pH 3.6 conditions, positively charged amino acids made a significantly negative contribution to the binding free energy. For negatively charged amino acids, their contribution at pH 7.0 was notably higher than at pH 3.6 under 0 and 0.1 mol/L salt ion concentrations, but this difference became negligible at higher salt ion concentrations. Interestingly, the trend observed for the contributions of nonpolar amino acids was contrary to our expectations; their contribution was smaller under pH 7.0 conditions compared to pH 3.6. In summary, the weakening of electrostatic interactions under pH 3.6 conditions disfavors the formation of the 4.1G CTD-NuMA complex.

We further compared the changes in the contributions of each residue to the binding free energy at pH 3.6 relative to pH 7.0, under the same salt ion concentration (see FIG. 3(c)). We identified residues that exhibited significant changes across different salt ion concentrations. The greater the change in binding free energy contribution, the more crucial the weakening of that residue under pH 3.6 conditions is to the disruption of the 4.1G CTD-NuMA interaction. Specifically, residues H940, H968, H983, H994, and E996 showed a significant reduction in their contributions to the binding free energy or exhibited a strong negative contribution under pH 3.6 conditions. This trend was consistent across all salt ion concentrations (0, 0.1, 0.2 mol/L). Notably, these residues are primarily histidines, aligning with the findings in FIG. 4(b). Under pH 3.6 conditions, the protonation of positively charged amino acids in 4.1G CTD (particularly C-terminal residues) is the main reason for the disruption of the 4.1G CTD-NuMA interaction.

Figure  4.  (a) The secondary structure probability of residues in different systems using the DSSP method. In the stacked plot, blue represents the probability of coil, green represents the probability of $\beta$-sheet, and orange represents the probability of $\alpha$-helix. (b) Changes in secondary structure probability for residues in the pH 3.6 system, using the pH 7.0 system as a reference.

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C   Changes in structure under pH 3.6

1   Secondary structure content

The secondary structure content provides insights into the structural stability and the extent of hydrophobic interactions within the protein. A higher $\alpha$-helix content signifies greater structural stability, while the $\beta$-sheet content, stabilized by interactions between 4.1G CTD and NuMA, reflects the strength of these hydrophobic interactions. We calculated the secondary structure probability of each residue in different systems using the DSSP method (see FIG. 4(a)). Our analysis identified three relatively stable secondary structure regions within 4.1G CTD, located at aa 969–981, 988–993, and 954–960. In all systems, the $\alpha$-helix in the 969–981 region remained highly stable, with a probability close to 100%. The $\beta$-sheet structures in the 988–993 and 954–960 regions also maintained relative stability, with probabilities around 40%. This indicates that under pH 3.6 conditions, the secondary structure of 4.1G CTD is not completely disrupted, thus retaining its ability to form hydrophobic interactions.

By further comparing the changes in the secondary structure probability of residues under pH 3.6 versus pH 7.0 conditions (see FIG. 4(b)), we found that the C-terminal region of 4.1G CTD (aa 990–1000) and the N-terminal region of NuMA (aa 1800–1810) exhibited the most significant reductions in secondary structure content. The probability decrease was observed over a continuous stretch of 10 residues and, in many positions, exceeded 20%. In the pH 3.6 systems, the secondary structure probability of these two segments dropped below 20%, with the secondary structure probability of the NuMA N-terminal almost reaching zero. Interestingly, the secondary structure content of the hydrophobic interaction segment 988–993 did not significantly decrease; instead, an increase in $\beta$-sheet content was observed in the 988–990 segment. This suggests that a significant number of residues in the C-terminal segments are protonated, leading to changes in charge distribution and, consequently, reduced secondary structure stability. Combining these findings with the results from the Section III.B, which showed a significant reduction in the binding free energy contribution of the C-terminal of 4.1G CTD under pH 3.6 conditions, we infer that the protonation of the C-terminal may lead to increased negative contributions from electrostatic interactions with NuMA. This indicates an enhancement of electrostatic repulsion.

2   Solvent-accessible surface areas

Solvent-accessible surface area (SASA) describes the surface area of a biomolecule that is accessible to solvent molecules, typically water. It represents the area where the solvent can physically contact the biomolecule. SASA is crucial for understanding the folding process of proteins, as hydrophobic residues tend to be buried inside the protein structure, while hydrophilic residues are more exposed to the solvent. Changes in SASA upon folding provide insights into the stability and folding dynamics of proteins.

We calculated the changes in SASA for 4.1G CTD and NuMA in both their complexed and isolated states from the molecular dynamics simulation trajectories to characterize the binding tightness between 4.1G CTD and NuMA (see FIG. S1 in SM). In the pH 7.0 system, the ΔSASA peak was the highest for the 988–1005 segment, followed by the 958–978 segment (see FIG. S1(a) in SM). This indicates that these two segments are more highly enclosed within the complex and have a larger contact area with NuMA. Compared to pH 7.0, the pH 3.6 system shows a significant decrease in ΔSASA for the C-terminal of 4.1G CTD (aa 990–1005) and the N-terminal of NuMA, indicating a reduced contact area between these segments under acidic conditions (see FIG. S1(b) in SM).

D   Changes in intermolecular contact probabilities

We calculated contact maps based on the residue-residue contact probabilities in the trajectories under both pH 3.6 and pH 7.0 conditions, where two residues within 0.3 nm were considered to be in contact. The contact maps successfully captured the interactions between 4.1G CTD ⁹⁸⁸VTRVVV⁹⁹³ and NuMA ¹⁸¹⁴IINITM¹⁸¹⁹ (see FIG. 5(a)), consistent with our previously published results. Additionally, under pH 3.6 conditions, there was no significant reduction in the contact probability at this binding site, which aligns with our hypothesis that the hydrophobic interaction site does not undergo significant changes with pH variation.

Figure  5.  (a) Residue contact probability between 4.1G CTD and NuMA in different systems. (b) Changes in contact map from pH 7.0 to pH 3.6 systems. In the heatmap, red represents enhancement, while blue represents attenuation.

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To further compare the effects of different salt ion concentrations at pH 3.6 and pH 7.0 (see FIG. 5(b)), we observed that the contact probability between the C-terminal of 4.1G CTD and the N-terminal of NuMA was significantly weakened under pH 3.6 conditions. Combining the residue contribution to binding free energy analysis in Section III.B and the secondary structure analysis in Section III.C.1, we conclude that the protonation of the C-terminal residues of 4.1G CTD under pH 3.6 conditions leads to increased electrostatic repulsion among positively charged amino acids. This results in weakened interactions between this segment and the N-terminal of NuMA, thereby reducing the binding free energy between 4.1G CTD and NuMA.

IV.   CONCLUSION

In this study, we investigated the interactions between 4.1G CTD and NuMA under varying pH and salt ion conditions to understand the regulatory mechanisms affecting their binding. Previous experimental results revealed that 4.1G CTD and NuMA bind effectively under neutral pH conditions, while this binding is disrupted under acidic conditions. MD simulation and free energy calculation showed that the protonation state changes of 4.1G CTD under pH 3.6 significantly weakened electrostatic attractions, leading to increased electrostatic repulsion and reduced binding free energy. Despite the contribution of hydrophobic interactions, as evidenced by consistent contact probabilities at key hydrophobic interaction sites, the overall interaction was compromised due to changes in electrostatic interactions.

Secondary structure analysis demonstrated that certain regions of 4.1G CTD, specifically aa 969–981, 988–993, and 954–960, remained relatively stable under both pH conditions. However, a significant reduction in secondary structure probability was observed at the C-terminal of 4.1G CTD (aa 990–1000) and the N-terminal of NuMA (aa 1800–1810) under acidic conditions. These findings indicate that the overall structural integrity and stability of the complex were significantly affected by pH variations. Additionally, our contact map analysis showed that, under pH 3.6 conditions, the contact probability between the C-terminal of 4.1G CTD and the N-terminal of NuMA was significantly weakened, further supporting our hypothesis.

These findings provide a comprehensive understanding of how pH and ionic strength regulate the binding dynamics of 4.1G CTD and NuMA, highlighting the critical role of electrostatic interactions in maintaining the stability of their complex. The impact of pH and the impact of ionic concentration are tightly related. The pH-induced changes in protonation states directly affect electrostatic interactions between the two proteins, which are modulated by ionic concentration. Additionally, protonation state changes affect protein conformation and structure, which are also important for binding. This study offers valuable insights into the molecular mechanisms underlying pH-dependent protein-protein interactions, which could have broader implications for understanding similar interactions in other biological systems.

Supplementary materials: Analysis for different systems and protonated residues under pH 3.6 conditions are shown.