Effects of pH and Salt Concentration on Stability of a Protein G Variant Using Coarse-Grained Models

Abstract

The importance of charge-charge interactions in the thermal stability of proteins is widely known. pH and ionic strength play a crucial role in these electrostatic interactions, as well as in the arrangement of ionizable residues in each protein-folding stage. In this study, two coarse-grained models were used to evaluate the effect of pH and salt concentration on the thermal stability of a protein G variant (1PGB-QDD), which was chosen due to the quantity of experimental data exploring these effects on its stability. One of these coarse-grained models, the TKSA, calculates the electrostatic free energy of the protein in the native state via the Tanford-Kirkwood approach for each residue. The other one, CpHMD-SBM, uses a Coulomb screening potential in addition to the structure-based model C_α. Both models simulate the system in constant pH. The comparison between the experimental stability analysis and the computational results obtained by these simple models showed a good agreement. Through the TKSA method, the role of each charged residue in the protein’s thermal stability was inferred. Using CpHMD-SBM, it was possible to evaluate salt and pH effects throughout the folding process. Finally, the computational pK_a values were calculated by both methods and presented a good level of agreement with the experiments. This study provides, to our knowledge, new information and a comprehensive description of the electrostatic contribution to protein G stability.

Introduction

A knowledge of the factors that affect the thermal stability of proteins is of fundamental importance in understanding the basic principles that govern the behavior of these macromolecules as well as in the rational development of biotechnological applications (1, 2, 3). It is widely known that a variation in pH and salt concentration can affect the thermal stability of proteins (4, 5, 6), indicating the importance of electrostatic interactions. Indeed, studies have shown the thermal stability of proteins can be enhanced by optimizing charge–charge interactions (7, 8, 9). Establishing a relationship between the distribution of ionizable residues and the features of folding and thermal stability can therefore provide valuable information for protein engineering.

Several levels of approximation have been proposed for protein models and for evaluating the electrostatic contributions of unfolding free energy (10, 11, 12, 13). In several of these studies, versions of structure-based models that include a fixed charge have been adopted to study the contribution of the electrostatic interaction in the unfolded state and the interaction between proteins and charged macromolecules (7, 14, 15, 16, 17, 18). Recently, to study pH effects on the folding dynamics of the N-terminal domain of ribosomal protein L9 (19), the constant-pH molecular dynamics (MD) method (CpHMD) (19, 20, 21) was implemented and the results showed a good level of agreement with the experiments. Another alternative to evaluate the charge-charge contribution to protein stability is the Tanford-Kirkwood model (TK) (22), which enables the individual electrostatic interaction of each ionizable residue to be calculated (23). Makhatadze and colleagues (24, 25, 26, 27) have managed to optimize proteins by the mutation of specific residues, which are predicted by the TK approach with a solvent accessibility modification, the Tanford-Kirkwood Solvent Accessibility (TKSA) method. In this study, both methods, CpHMD and TKSA, are used to study the importance of pH and salt concentration in 1PGB-QDD stability.

1PGB-QDD is a variant of the B1 domain of protein G with mutations T2Q, N8D, and N37D (Fig. 1 A). Protein G is a multidomain protein present in the cell wall of G streptococcus containing the immunoglobulin G binding domains denoted as B1 and B2 (28, 29, 30, 31, 32). These proteins differ by six amino acids and do not have disulfide bonds (33, 34). Also, experimental data showed that the protein folds/unfolds as a two-state model without kinetic intermediates (34). However, Sikosek et al. (35) have shown that a set of mutations may lead to new folds and as consequence, the protein folds/unfolds passing through an intermediate state. PGB1-QDD has 56 amino acids (including the NH₂-terminal Met) and a regular α/β structure. The fold consists of a four-β-sheet and one α-helix bundled against the sheet. The charged residues are almost entirely surface exposed (36) and display distinct pH-dependence protein stability (33). Another important factor is that PGB1-QDD displays the highest stability at low salt concentrations (37). Due to its dependence on salt concentration and pH, this protein becomes an excellent target for studying electrostatic interactions using coarse-grained models. There are more rigorous and sophisticated ways to conduct constant pH simulations than using coarse-grained models (38, 39, 40). Nevertheless, these simplified models have a low computational cost, have been able to reproduce some experimental results, and allow an insightful overall view of the dominant folding mechanisms and effects (19).

Figure 1.

(A) Structure of PGB1-QDD is built from wild-type protein with PDB:1PGB. The side chains are shown for residues that have major contributions to protein stability. (B) Shown here is the primary sequence of PGB1-QDD with highlighted acidic residues, which have the highest charge variations in the studied pH range. To see this figure in color, go online.

Salt concentration and pH dependence in 1PGB-QDD stability were tested using the TKSA and CpHMD-SBM methods, and the results are in qualitative agreement with the experiments. The contribution of each ionizable residue to this protein stability was also calculated using the TKSA. From CpHMD simulations, it was possible to evaluate the dependence of the free energy unfolding barrier and thermal denaturation on pH. Electrostatic interaction influence at each folding stage was also analyzed. Finally, the pK_a values were calculated for the folded protein (using CpHMD and TKSA) and the unfolded protein (using only CpHMD). The computational pK_a values are in good agreement with the experimental values, considering the simplicity of the models. Thus, these coarse-grained models were found to be a computationally fast and cheap alternative to explore and provide useful insight into biological systems.

Methods

The TK model with solvent accessibility: TKSA

In the model proposed by Tanford and Kirkwood (TK), the protein is modeled by a spherical cavity with dielectric constant, ε_p, and radius, b, surrounded by an electrolyte solution treated according to the Debye-Hückel theory (22). A solvent static accessibility parameter for each charged residue was incorporated by Shire et al. (41) into the TK model. This modification was introduced to overcome the uncertainty of an adjustable charge-burial parameter beneath the dielectric interface and to allow for the irregular protein-solvent interface. With this change, the model proposed by Tanford and Kirkwood is now referred to as the “Tanford-Kirkwood model with a solvent accessibility” (TKSA) (41, 42, 43). The interaction energy, U_ij, between two charged residues is given by

$$U_{ij}=e^2\left(\frac{A_{ij}-B_{ij}}{2b}-\frac{C_{ij}}{2a}\right)\left(1-S{A}_{ij}\right),$$ (1)

where e is the elementary charge; b is the radius of the protein; a is the closest possible approach distance of an ion; A_ij, B_ij, and C_ij are parameters obtained from the analytical solution of the TK model, which are functions of the distance between charged residues, the dielectric constants, and the salt concentration (22, 44, 45); and SA_ij is the average of the solvent accessible surface area of residues i and j (41, 42, 46).

Once the electrostatic energy of the ionizable residues of the protein is determined, it is necessary to sample all the possible protonation states (23, 47). For a protein with n ionizable residues, there are χ = 2ⁿ different protonation states. The free energy, ΔG_N(χ), for a protein in its native state and for given state of protonation χ is given by

$$\Delta G_N\left(\chi \right)=-RT\left(\text{ln}10\right)\sum _{i=1}^n\left(q_i+x_i\right)\text{p}{K}_{\text{a},\text{ref},\text{i}}+\frac{1}{2}\sum _{i,j=1}^n{U}_{ij}\left(q_i+x_i\right)\left(q_j+x_j\right),$$ (2)

where R is the ideal gas constant; T is the temperature in Kelvin scale; q_i is the charge of the ionizable residue i in its deprotonated state; x_i is 0 or 1, depending on the protonation state of the residue i; and pK_a,ref,i is the reference compound pK_a value of the ith ionizable residue (pK_a,ref values are 3.6 for C-terminal, 4.0 for Aspartic acid, 4.5 for Glutamic acid, 6.3 for Histidine, 7.5 for N-terminal, 10.6 for Lysine, and 12.0 for Arginine).

The probability that the protein is in its native state with a particular state of protonation, ρ_N(χ), is

$${\rho }_N\left(\chi \right)=\frac{1}{Z_N}\text{exp}\left[-\frac{\Delta G_N\left(\chi \right)}{RT}-\nu \left(\chi \right)\left(\text{ln}10\right)\text{pH}\right],$$ (3)

where ν(χ) is the number of ionizable residues that are protonated in the state of protonation χ, and Z_N is the partition function for the protein in its native state.

The average total electrostatic energy, 〈W_qq〉, is given by the average over all protonation states, taking into account Eq. 3:

$$\langle W_{qq}\rangle =\sum _{\chi }\left[\frac{1}{2}\sum _{i,j=1}^n{U}_{ij}\left(q_i+x_i\right)\left(q_j+x_j\right)\right]{\rho }_N\left(\chi \right).$$ (4)

Ibarra-Molero et al. (23) and Makhatadze have shown that the contribution of electrostatic interaction energy to free energy, ΔG_qq, can be described by the negative of the average total electrostatic energy of the native state, that is, ΔG_qq ≈ −〈W_qq〉.

Constant-pH molecular dynamics simulations

In the structure-based model (SBM), the residues of a protein are represented by individual beads centered in C_α position (18, 48, 49, 50, 51). The energy of the protein is given by a Hamiltonian equation in which only the native interactions based on its native topology are taken into account (48). The first simplification of this model does not take into account the charged residues in the protein; the electrostatic interactions are therefore inserted by adding charged points at beads, which represent acidic/basic residues (7, 14, 19, 52). The interaction between charged residues is given by a Coulomb screening potential. The energy in a given configuration Γ with regard to configuration Γ_o, the native structure, is given by

$$\begin{array}{c}V\left(\text{Γ},{\text{Γ}}_o\right)=\sum _{\text{bonds}}{\mathit{ϵ}}_r{\left(r-r_o\right)}^2+\sum _{\text{angles}}{\mathit{ϵ}}_{\theta }{\left(\theta -{\theta }_o\right)}^2\\ +\sum _{\text{dihedrals}}{\mathit{ϵ}}_{\varphi }\left\{\left[1-\text{cos}\left(\varphi -{\varphi }_o\right)\right]+\frac{1}{2}\left[1-\text{cos}\left(3\left(\varphi -{\varphi }_o\right)\right)\right]\right\}\\ +\sum _{\text{contacts}}{\mathit{ϵ}}_C\left[5{\left(\frac{d_{ij}}{r_{ij}}\right)}^{12}-6{\left(\frac{d_{ij}}{r_{ij}}\right)}^{10}\right]+\sum _{\text{non}\text{-}\text{contacts}}{\mathit{ϵ}}_{NC}{\left(\frac{{\sigma }_{NC}}{r_{ij}}\right)}^{12}\\ +\sum _{\text{electrostatics}}{K}_{\text{electrostatics}}\frac{q_i{q}_j\text{exp}\left(-\kappa r_{ij}\right)}{{\mathit{ϵ}}_K{r}_{ij}},\end{array}$$ (5)

where r_o represents the distance between two subsequent residues, and θ_o and ϕ_o are the angles formed by three and four subsequent residues, respectively. All of them are taken from the native structure. Factor d_ij represents the distance between pairs of residues i and j (i < j – 3), ε_C = 2.5 kJ/mol, ε_r = 100 ε_C, ε_θ = 20 ε_C, ε_ϕ = ε_NC = ε_C, σ_NC = 4 Å (48), and K_{electrostatic} = 1390 kJ Å/(mol⋅e²) (7, 15, 19). The charges of residues i and j are q_i and q_j, respectively; κ is the inverse of Debye length (53); and ε_K = 80 is the dielectric constant.

Protonation/deprotonation criterion

The CpHMD method was utilized in this study. It associates a standard MD simulation with the Metropolis Monte Carlo method (MC) for sampling protein protonation states (19, 21, 54, 55, 56, 57, 58). During the simulation, the MD is regularly halted, a MC step is taken, and a random titratable residue is considered to change its protonation. The transition energy, ΔE, for this step is appraised according to Eq. 6, in which the positive and negative signs mean protonation and deprotonation, respectively. The acidic or basic residues are represented by ξ, where acidic residues present ξ = −1 and basic residues ξ = +1:

$$\Delta E=\pm \xi k_{\text{B}}T\text{ln}\left(10\right)\left(\text{pH}-\text{p}{K}_{\text{a},\text{ref}}\right)+\Delta E_{\text{elec}}.$$ (6)

In Eq. 6, k_B is the Boltzmann constant and T is the temperature. The first term is the contribution due to the presence of a proton bath at a given concentration determined by pH; the second one is the contribution of the compound model; and the last one, ΔE_elec, is the electrostatic energy variation for the protonation state change of the titratable residue. The protonation/deprotonation is determined by the Metropolis criterion (59). Thus, if the MC step is accepted, the protonation/deprotonation of the residue will change to the new state, and the MD will continue. However, if the new state is not accepted, there is no need for updating, and the residue continues with its unchanged protonation state.

Titration curves and pK_a calculation

The pK_a values were calculated by fitting of titration curves using the Hill equation (60):

$$\alpha =\frac{1}{1+{10}^{n\left(\text{p}{K}_{\text{a}}-\text{pH}\right)}},$$ (7)

where α is the ionization degree of each acidic residue calculated by the average of the absolute valency (|Z|) generated by the simulations, and n is the Hill coefficient. This coefficient is also computed using the fit of the Eq. 7.

Simulation details

The CpHMD-SBM algorithm was implemented using Espresso Package version 3.2 in NVT ensemble and Langevin thermostat (61, 62). In the folding simulations, the protein was initialized in its native state with all titratable residues protonated. An equilibration process was executed with 10⁷ steps and 10⁹ steps to generate the trajectory with a time step of 0.5 fs. The data was stored every 1000 MD steps, and the Monte Carlo titration procedure was carried out every 2000 steps (19). The free energy and specific heat profiles were obtained using the weighted histogram method (63, 64, 65), calculated from different simulations at 25 temperatures for pH ranging from 1.0 to 12.0 for high and low salt concentrations. The reaction coordinate used to describe the folding was defined as the fraction of formed native contacts (Q). A native contact was considered formed when the distance between the residue i and j (i < j − 3) was shorter than 1.2 d_ij from the native structure. The native contact map was determined by contact-of-structural-units software (66). The mutant protein PGB1-QDD was built from PGB1 protein with PDB: 1PGB using Modeler software version 9.17 (67). The protein 3D structure graphic in Fig. 1 A was created with the UCSF Chimera package (68) and the protein sequence in Fig. 1 B was generated with Aline software (69). The TKSA method was implemented in PYTHON 2.7, and the solvent accessible surface area (SASA) was calculated with Surface Racer software (70). The TKSA method was performed for each of the 19 charged residues in PGB1-QDD and was simulated for pH from 1.0 to 12.0 at intervals of 0.5.

Results and Discussion

Electrostatic energy calculations: TKSA

In this section the contribution of electrostatic energy to protein free energy was calculated with the TKSA method. The sum of electrostatic energy of each charged residue is here referred to as ΔG_elec. The ΔG_elec of PGB1-QDD was calculated in a range of pH from 1.0 to 12.0, and the stability pH-dependent profile is presented in Fig. 2.

Figure 2.

Electrostatic energy contribution to free energy native state stability ΔG_elec as a function of pH in kJ/mol. The values were calculated from TKSA simulation analysis for 23 different pH values from 1.0 to 12.0. The solid circles represent values for 0.15 M of a monovalent salt concentration in simulation and the open squares represent values of 2.0 M of salt concentration. (Inset) Plot shows the experimental results of the free energy difference between the unfolded and the native state ΔG° from 1PGB-QDD as a function of pH in kJ/mol. The solid circles represent values for 0.15 M of NaCl, and the open squares represent values for 2.00 M of NaCl (adapted from (37)).

The data presented in Fig. 2 of ΔG_elec as a function of pH have similar behavior with slight differences for high and low salt concentrations in simulations via the TKSA method. The TKSA simulation results indicate that high levels of salt concentration do not eliminate the electrostatic interaction of surface charges and the pH dependence of protein native state stability is still strong (37). The peak of TKSA curves indicates that the protein PGB1-QDD native state is more stable around its isoelectric point, which is close to pH 4.5 for both high and low salt concentrations. The TKSA result has a level of good agreement with experimental data (37) for low salt concentrations shown as an inset in Fig. 2, and the correlation value between TKSA and experimental data is 0.83. On the other hand, for high salt concentrations, there is not a strong correlation between the TKSA and experimental results and the correlation value is 0.44. The weak correlation is due to the differences between the results for lower pH values. The behavior of experimental data for lower pH values does not present a significant stability difference from 2 M of NaCl (37), shown in Fig. 2 (inset). The correlation between TKSA and experimental data became stronger if only values of pH > 3.0 are taken into account and the new correlation value is then 0.95.

Another result obtained from TKSA simulation is the contribution of each charged residue to protein stability (23, 27, 71). Fig. 3 shows the TKSA analysis for pH values 2.5, 4.5, 7.5, and 10.0 for low salt concentrations. For pH 2.5 in Fig. 3 A, there are eight residues with ΔG_qq < 0.0, which contribute favorably to protein stability. The other 11 residues have energy values close to 0 with ΔG_qq ≈ 0.0. The total electrostatic free energy ΔG_elec for pH 2.5 is −38.22 kJ⋅mol⁻¹, and is calculated as the sum of ΔG_qq of all charged residues (23, 24, 71). The major contribution to stability comes from six residues: K04, E15, E27, K31, D47, and K50. These six residues make an important energetic contribution to all pH values and they are responsible for 86 ± 6.2% of all favorable interaction for pH values 2.5, 4.5, 7.5, and 10.0, shown in Fig. 3. The side chains of these residues are not fully exposed to solvent, with SASA$\le 55\text{\%}$. However, the short distance between their ionizable groups of opposite charge (<2.95 ± 0.56 Å) promotes the high energetic contribution of these groups to protein stability (the side chains of K04, E15, E27, K31, D47, and K50 are highlighted in Fig. 1 A). At pH 4.5 in Fig. 3 B, similar to pH 2.5 analysis, the major electrostatic energy contribution comes from the six residues mentioned above. At pH 4.5, there are 12 residues with ΔG_qq < 0.0 and the other seven residues have energy values close to 0, with ΔG_qq ≈ 0.0. The total electrostatic free energy ΔG_elec for pH 4.5 is −44.09 kJ⋅mol⁻¹, which is the pH that maximizes protein stability in experiments (37) and also in the TKSA simulation shown in Fig. 2. For pH 7.5, shown in Fig. 3 C, there are also 12 residues with ΔG_qq < 0.0 similar to pH 4.5. There are seven residues with ΔG_qq > 0.0 contributing with unfavorable electrostatic interactions to native state stability. These seven residues—D08, D36, D37, D40, E42, D46, and E56—are all acidic residues in their deprotonated state with charge −1. The protonation/deprotonation events are detailed in the pK_a comparison section. The positive ΔG_qq values of these seven residues make the greatest contribution to decreasing the native state stability of PGB1-QDD, and the total electrostatic free energy ΔG_elec for pH 7.5 is −35.63 kJ⋅mol⁻¹. In Fig. 3 C, the red bars highlight the residues whose side chains are exposed to solvent >50% with SASA = 73 ± 14% for residues D36, D37, D40, and E42. The positive ΔG_qq energy contribution and the side chain exposed >50% to solvent indicate that mutations in these residues should lead the protein to a more stable native state based on optimization of the electrostatic interactions on the protein surface (23, 24, 25, 26, 27, 71, 72, 73). The TKSA result for pH 10.0 is shown in Fig. 3 D with nine residues ΔG_qq < 0.0, three residues with ΔG_qq close to 0, and seven residues with ΔG_qq > 0.0. The discussion of the favorable and unfavorable electrostatic energy contribution of each residue in pH 10.0 is similar to what has been discussed for pH 7.5. There is an increase of ΔG_qq for acidic residues. The positive energy contribution passes from 12.2 kJ⋅mol⁻¹ in pH 7.5 to 14.5 kJ⋅mol⁻¹ in pH 10.0. The residue E19 had a significant variation from negative value ΔG_qq = −1.07 kJ⋅mol⁻¹ to a slightly positive contribution ΔG_qq = 0.15 kJ⋅mol⁻¹. The N-terminal also had a significant variation due to the fact that it becomes deprotonated with charge 0 in pH 10.0 and its energy contribution is close to 0. The total electrostatic free energy ΔG_elec for pH 10.0 is −31.12 kJ⋅mol⁻¹.

Figure 3.

Charge–charge interaction energy ΔG_qq calculated by the TKSA model for each ionizable residue. (A–D) Given here are the energy profiles of pH values 2.5, 4.5, 7.5 and 10.0, respectively. The red bars indicate the residues with the side chain exposed to solvent with SASA ≥ 50% and positive energy contribution to native state stability, most of these residues are located between D36 and E42. To see this figure in color, go online.

pH and ionic strength effects on 1PGB-QDD folding: CpHMD-SBM-C_α

The previous section indicates that the drive interaction responsible for PGB1-QDD stability is electrostatic. However, the TKSA model takes into account only the static native structure of the protein in its calculations, whereas experimental data suggests that the unfolded state of PGB1-QDD is also important to its stability (37). Thus, in this section, CpHMD-SBM simulations were utilized, which can explore the effects of the unfolded and transition states on protein stability. 1PGB-QDD was therefore simulated at four different pH values (2.5, 4.5, 7.5, and 10.0) and three ionic strengths (low salt ≈ 0.01 M, intermediate salt ≈ 0.1 M, and high salt ≈ 0.4 M).

Heat capacity (C_v) and free energy profiles of PGB1-QDD were calculated to explore the role of pH and ionic strength on protein folding thermodynamics (Fig. 4). In Fig. 4 A, C_v is presented as a function of temperature in Kelvin and in reduced units T^∗. T^∗ is calculated by T^∗ = k_BT/ε_C, where ε_C is a simulation parameter, which can be chosen arbitrarily because all other parameters of the SBM model are written in function of ε_C. Thus, the direct comparison between absolute temperatures obtained by experiments and simulations must be done carefully. Therefore, in this study, the comparison between experimental and computational heat capacity is made observing the relative variation of the temperatures and the qualitative behavior of the curves. Heat capacity curves obtained by Lindman et al. (37) using differential scanning calorimetry present low ΔC_p values in a large range of solution conditions, which indicates that 1PGB-QDD is stable in a wide range of temperatures. However, heat capacity calculated computationally does not present a shift between the baseline for the protein in its folded and unfolded states. This difference between simulation and experiment is caused by a simplification in the force field of the CpHMD-SBM-C_α model, which does not take into account the temperature dependence in its interactions (see Eq. 5).

Figure 4.

Thermodynamic properties of 1PGB-QDD folding. (A) Shown here are heat capacities at constant volume (C_v) in low, intermediate, and high salt concentrations. Solid black lines are for pH 2.5, short dashed red lines are for pH 4.5, long dashed blue lines are for pH 7.5, and dashed/dotted green lines are for pH 10.0. (B) Given here are free energy curves as a function of the reaction coordinate Q for the same three salt concentrations. All systems are at T close to T_M (melting temperature) of pH 7.5 in each ionic strength. It is considered that the melting temperature corresponds to the peak of C_v. To see this figure in color, go online.

In these CpHMD-SBM-C_α computational results, electrostatic screening at the high salt concentration is too strong, making the pH effect on protein stability almost insignificant. Thus, it is not possible to see a significant variation in 1PGB-QDD thermodynamic properties at this ionic strength. As expected, the pH effect becomes more evident in the protein at low and intermediate salt concentrations, but the higher stability remains at pH 4.5. At the low salt concentration, the difference between the C_v peaks of each pH curve was maximized. The transition barrier between the folded and unfolded state in protein near T_M was not affected by salting, with the barrier close to 2.0 ε_C. In general, the thermodynamic properties calculated by CpHMD-SBM are in qualitative agreement with the experimental results.

The comparison between experimental and computational T_M is presented in Fig. 5. The general behavior T_M for computational results in each salt concentration shows a good level of agreement with the experimental data, with the T_M peak at pH 4.5 for all systems. At low pH, there is a decrease of T_M mostly in low and intermediate salt concentrations. In this case, both experiments and simulations agree that a high ionic strength contributes to 1PGB-QDD stability. However, when the protein has a pH higher than 4.5, the highest stability in the simulations occurs at low salt concentration, followed by intermediate and high salt concentrations. On the other hand, experimental results at pH 7.5 and 10.0 indicate that the electrostatic screening caused by a high salt concentration helps to stabilize 1PGB-QDD. This difference between experimental and computational results is caused by the electrostatic energy calculated in the simulation, and this interaction will be explored below.

Figure 5.

Values of melting temperature T_M^∗ in reduced temperature as a function of pH. Black circles are for low salt, red squares are for an intermediate ionic strength, and blue diamonds are for high salt concentration. Inset graphic presents the experimental results of T_M^∗ as a function of pH in similar salt conditions to simulation (adapted from (37)). Dashed lines connecting symbols help guide the eye. To see this figure in color, go online.

The effect of electrostatic interaction and charge regulation on each folding stage of 1PGB-QDD can be evaluated by an analysis of Fig. 6. This figure presents a 2D map of the distribution of electrostatic energy as a function of Q. The net charge q in each highly populated region of distribution of electrostatic energy was also calculated and included in Fig. 6.

Figure 6.

2D map of the distribution of electrostatic energy as a function of the reaction coordinate Q for pH 2.5, 4.5, 7.5, and 10.0. The color map represents the probability distribution of the electrostatic energy and Q, normalized by its highest value. All the systems are at T ≈ T_M and intermediate salt concentration. The value q represents the net charge of 1PGB-QDD in each minimum. To see this figure in color, go online.

Previous results showed that the highest stability of 1PGB-QDD occurs at pH 4.5. This is because the protein in this condition has the lowest mean electrostatic energy 〈E_elec〉 compared to the protein at pH 2.5, 7.5, and 10.0. For both folded and unfolded states, the 〈E_elec〉 is near −4 ε_C and net charge q = −1, not favoring any state in comparison to each other. A similar discussion applies to the protein at pH 7.5: the folded and unfolded states have 〈E_elec〉 close to −2 ε_C and q = −5 (experimental net charge (37) is −6). An increase in mean electrostatic energy promotes a loss of stability and is caused by this negative q, although, even with a high negative net charge, 〈E_elec〉 is kept negative. This favorable energy explains the fact that low salt concentration promotes more stability in 1PGB-QDD at pH 7.5 than intermediate and high salt concentrations (Fig. 5), which does not agree with the experimental results. Although the net charge is similar (experimental q = −6 and computational q = −5), the arrangement of charges in the C_α model can be different from the more realistic case, and creates more regions of favorable interaction. At pH 10.0, the same thing occurs: the protein has a high negative q = −7 or q = −6 and a negative value of 〈E_elec〉 close to −1 ε_C.

Fig. 6 also shows that the pH effect at pH 4.5 and 7.5 is strong enough to keep the protein net charge, irrespective of its conformational state. However, at the extreme pH values 2.5 and 10.0, some differences in electrostatic energy and net charge arise, depending on the folding stages. In these cases, the charge regulation is more evident, and the interaction between charged groups becomes fundamental for their protonation states. With the protein at pH 2.5, the 2D map presents two populated regions in the unfolded state, one with 〈E_elec〉 close to 1 ε_C (q = 5) and other near 2.0 ε_C (q = 6), the second being the most populated. In the folded state, in this same pH condition, three populated regions arise—the most populated with the highest 〈E_elec〉 = 4 ε_C and q = 7; an intermediate region in 〈E_elec〉 = 2 ε_C and q = 6; and the lowest populated region with 〈E_elec〉 = 1 ε_C and q = 5. The loss of stability at this low pH condition may be associated with the fact that 〈E_elec〉 of the unfolded protein is lower than 〈E_elec〉 in folded state. Thus, the electrostatic interaction favors the unfolded state.

Comparison between computational and experimental pK_a

In this final section, the experimental pK_a and the pK_a calculated by TKSA (for folded state), and CpHMD (for folded and unfolded states), were compared to evaluate the sampling of charges using these models for different pH conditions. The computational pK_a and the Hill coefficient n were calculated fitting individual titration curves with the Hill equation (60) (examples of these curves are presented in Fig. 7). The Hill coefficient values are associated with the correlation between titratable groups. For the cases where n = 1, the electrostatic energy is constant throughout the titration; for n > 1, the attraction between the charged groups tends to change linearly with pH; and when the Hill coefficient is <1, the repulsion changes linearly with pH (74). For 1PGB-QDD, the experimental and computational n values tend to be near or <1. The highest discrepancy between these values occurs for the results of TKSA model, which presents low Hill coefficients. This discrepancy is caused by the residues that are electrostatically coupled, because this model does not take into account the MD and the protein is held in its compact crystal structure.

Figure 7.

Titration curves of residue D22: ionization degree α as a function of pH. (A) The value α is calculated for the folded 1PGB-QDD using the CpHMD model. (B) The value α is calculated for the unfolded 1PGB-QDD via the CpHMD model. (C) The value α is calculated for the folded protein using the TKSA model. Red curves are the fit of the Hill equation (Eq. 7). To see this figure in color, go online.

The results are presented in Table 1. The errors in pK_a values were calculated using a set of three different simulations, and an error <0.1 pK_a unit was obtained for each ionizable residue. Thus, these error values were omitted from Table 1.

Table 1.

Comparison between Experimental and Computational pK_a Values for the Acidic Residues in Folded and Unfolded 1PGB-QDD Protein

Residue	Experimentala				CpHMDb				TKSAc
	pKa Folded	n Folded	pKa Unfolded	n Unfolded	pKa Folded	n Folded	pKa Unfolded	n Unfolded	pKa Folded	n Folded
D08	4.9	0.7	3.7	0.9	3.5	0.8	3.5	0.9	4.2	0.5
E15	4.6	0.9	4.4	0.9	4.0	0.8	4.1	0.9	1.8	0.8
E19	3.9	1.0	4.5	0.8	4.0	0.8	4.4	0.9	4.0	0.9
D22	3.0	1.0	3.9	0.9	3.7	0.8	3.9	0.9	3.4	0.8
E27	4.8	0.8	4.4	0.9	3.5	0.8	3.7	0.9	0.6	0.6
D36	4.2	0.8	4.1	0.8	4.1	0.7	4.2	0.7	4.1	0.8
D37	6.5	1.1	4.2	0.8	4.1	0.7	4.3	0.7	4.0	0.7
D40	4.1	0.7	4.2	0.7	4.0	0.7	4.1	0.8	4.3	0.7
E42	4.8	0.7	4.4	0.9	4.6	0.8	4.7	0.8	5.0	0.7
D46	3.8	0.9	4.0	0.9	4.0	0.7	4.1	0.8	4.0	0.7
D47	3.1	0.9	3.9	0.9	3.6	0.7	3.8	0.8	2.9	0.8
E56	3.8	0.6	4.7	0.8	4.6	0.7	4.4	0.9	6.5	0.4
C-ter	3.1	0.7	3.6	0.7	—	—	—	—	3.5	0.6

Error values for all cases are <0.1 units and have been omitted. Experimental values are from (74).

^aThe experimental pK_a and n values for the acidic residues measured by Lindman et al. (74).

^bThe computational pK_a and n values fitting the individual titration curves with the Hill equation; simulation using CpHMD.

^cThe computational pK_a and n values fitting the individual titration curves with the Hill equation; simulation using TKSA.

Only differences higher than 1.0 pK_a unit between experimental and computational values were considered significant (19). Comparing the experimental pK_a of folded 1PGB-QDD protein and the values calculated using TKSA, only four residues presented a difference higher than 1.0 pK_a unit. This is a good level of agreement considering the simplicity of the model, which can output the results in <1 h. E15 and E27 have a downshift in computational pK_a that may be caused by the overrated interaction calculated in this model that these residues make with K04 and K21, respectively. D37 has a large upshift in its experimental pK_a, which may be caused by the desolvation effects associated with side-chain burial (74) that TKSA is not taking into account sufficiently. Finally, the residue E56 has two charged groups that cause a large electrostatic repulsion in the TKSA model; this repulsion may explain the high upshift in its computational pK_a value.

Using CpHMD, the comparison with the experimental results is even better, with only three residues of folded 1PGB-QDD presenting >1.0 pK_a unit of difference between the simulation and the experimental pK_a values. E27 has a similar downshift in pK_a values to that obtained using TKSA; the reason for this difference is the high interaction that this residue makes with K04. In the case of D08, the downshift of 1.4 pK_a units obtained in computational results could be caused by a model limitation. Considering the native structure of the protein, the distance between the C_α of D08 and C_α K13 is near 5.1 Å, whereas the distance between the carboxyl group of D08 and ammonium group of K13 is close to 8.3 Å. This difference in the distances promotes a more favorable interaction between these residues in CpHMD, resulting in this disagreement between experimental and simulation results. In residue D37, as previously stated, desolvation effects have a strong impact on its experimental pK_a value and the CpHMD model does not treat this effect adequately. When the pK_a of the unfolded protein was considered, the agreement between experimental values and CpHMD values is remarkable: in no case does the difference between these values exceed 1.0 pK_a unit.

Conclusions

In this study, the protein 1PGB-QDD was studied by two coarse-grained models with the objective of evaluating the pH and salting effect on protein stability. The results of this study were compared with experimental results. The first model tested here was TKSA, which analyzes the effect of each ionizable residue in the electrostatic free energy of the protein in its native state. Using this simple model, it was possible to quantify the importance of each charged residue in 1PGB-QDD stability. The comparison between TKSA calculations and experimental results also indicates that the driving force of this stability is the electrostatic interaction. The second model used in this study was CpHMD-SBM, which was able to explore the protein folding process in constant pH (19). With CpHMD-SBM simulations, the folded and unfolded states and the transition between these states could be studied. The pH effect in 1PGB-QDD stability explored by simulation was found to be in good agreement with the experimental data. Similarly, the salt effect was evaluated, and the simulations obtained the same general behavior in protein stability as the experiments. Finally, pK_a was calculated using TKSA in the folded protein and CpHMD-SBM for folded and unfolded 1PGB-QDD. The pK_a values calculated by the two models are near experimental values. Therefore, most of the effects associated with pH and ionic strength variations in 1PGB-QDD stability were qualitatively described by both coarse-grained models.

Author Contributions

V.M.d.O., V.d.G.C., and V.B.P.L. designed research. V.M.d.O. and V.d.G.C. performed research. Data were analyzed by V.M.d.O., V.d.G.C., F.B.d.S., D.L.Z.C., and S.J.d.C. All authors contributed to the manuscript writing.

Editor: Nathan Baker.