Free energy landscape of a minimalist salt bridge model

Abstract

Salt bridges are essential to protein stability and dynamics. Despite the importance, there has been scarce of detailed discussion on how salt bridge partners interact with each other in distinct solvent exposed environments. In this study, employing a recent generalized orthogonal space tempering (gOST) method, we enabled efficient molecular dynamics simulation of repetitive breaking and reforming of salt bridge structures within a minimalist salt‐bridge model, the Asp‐Arg dipeptide and thereby were able to map its detailed free energy landscape in aqueous solution. Free energy surface analysis shows that although individually‐solvated states are more favorable, salt‐bridge states still occupy a noticeable portion of the overall population. Notably, the competing forces, e.g. intercharge attractions that drive the formation of salt bridges and solvation forces that pull the charged groups away from each other, are energetically comparable. As the result, the salt bridge stability is highly tunable by local environments; for instance when local water molecules are perturbed to interact more strongly with each other, the population of the salt‐bridge states is likely to increase. Our results reveal the critical role of local solvent structures in modulating salt‐bridge partner interactions and imply the importance of water fluctuations on conformational dynamics that involves solvent accessible salt bridge formations.

Introduction

Salt bridges, formed between oppositely charged protein side‐chain residues, are among the most common intermolecular interactions involved in protein structures. From a common viewpoint, salt bridge structures prefer being formed in protein interiors because due to low dielectric screening, attractive forces between the charge partners are significantly stronger; and in the high dielectric bulk environment, solvation forces on individual charged species tend to be greater than dielectrically screened salt bridge attractive forces and therefore, salt bridge partners are more likely to be separated. Notably, protein surfaces are usually populated with charged side‐chain residues, many of which are within the vicinity of potentially forming salt‐bridge structures. Despite being spatially close, because solvent accessible environments surrounding protein surfaces are generally assumed to be similar to the bulk solution, a general notion had been that salt bridge partners residing on protein surfaces should favor being separated and thus their roles in protein stability and functions is very likely modest.

In the past decades, an ever‐increasing number of protein structures allow for detailed examination of salt bridge partner interactions in solvent accessible environments. As shown by protein structure analysis studies,1, 2, 3 although protein surface charged residues are solvent accessible, these charge species still have certain propensity of forming tight salt bridge structures; moreover, computational analysis shows that structurally identified solvent exposed salt bridges usually play a stabilizing role.4 Interestingly, engineering such solvent exposed salt bridges that enhance protein stability has been shown to be challenging.5 As often observed from molecular dynamics (MD) simulation studies on protein conformational changes such as protein folding, solvent accessible salt bridge structures not only can form but also are likely to be pivotal to associated conformational pathways.6, 7, 8, 9, 10, 11 Furthermore, a recent experimental investigation reveals that solvent exposed salt bridge formation can facilitate folding kinetics.12 The above observations all indicate that charged residues in solvent accessible environments should be able to play more important roles than simply enhance protein solubility. Indeed, because local protein environments can influence water fluctuations, water molecules near protein surfaces are expected to have distinct structural and dynamic features from those in the bulk solution. Therefore the empirical assumption that the bulk solution can generally resemble protein surface solvent accessible environments needs to be carefully evaluated. Furthermore, how salt bridge partners interact with each other in distinct solvent accessible environments and how the formation of salt bridge structures interplays with water dynamics remain important questions to answer.

As an initial step, in this study, we analyzed the Asp‐Arg dipeptide, a minimalist salt bridge model, specifically seeking to understand how the charged side‐chain groups interact with each other in solvent exposed environments. Taking advantage of our recent generalized orthogonal space tempering (gOST) method, we successfully mapped detailed free energy surfaces of the model peptide. From our analysis, we show that although individually solvated states are more favorable, salt‐bridge states still occupy a noticeable portion of the overall population. Notably, the competing forces, e.g. inter‐charge attractions that drive the salt‐bridge formation and solvation forces that pull the charges away from each other, are actually energetically comparable; therefore, salt bridge stability is highly tunable by local environments. Moreover we show that under certain conditions when local water structures are perturbed, salt‐bridge states can become more populated. Our results reveal the critical role of local solvent structures in modulating salt‐bridge partner interactions and imply the importance of water fluctuations on conformational dynamics that involves solvent accessible salt bridge formations.

Results and Discussion

Salt bridge states occupy a noticeable portion of the overall population

As shown in Figure 2(a), along the gOST simulation trajectory with a total length of 175 nanoseconds (ns), six one‐way trips occurred between the two end scaling parameter states ( $\lambda =0.999$ and $\lambda =1.049)$. As the result of the gOST sampling treatment, the conformation can quickly move back and forth between individually‐solvated (IS) states and salt‐bridge (SB) states; this can be easily seen from the time‐dependent changes [Fig. 2(b)] of the SB distance, e.g. the distance between the two charged groups (the carboxylate group of the aspartate residue and the guanidinium group of the arginine residue). Based on Eq. (3), we can accurately construct the SB distance dependent free energy surface. The free energy profile [Fig. 2(c)] shows that the two major regions, e.g. the SB region and the IS region, are connected by an apparent transition state, which corresponds to the SB distance of about 5.3 Å. As expected, the SB region is narrower and the IS region is much broader with the co‐existence of multiple subregions. Notably, free energy changes along the SB distance are generally small. This indicated that instead of being dominated by forces favoring the IS states, the relative distribution between the SB states and the IS states is subtly governed by a fine balance between inter‐salt‐bridge‐partner attractions and solvation forces on individual charge groups. Converted from the free energy profile, the probability distribution allows us to estimate the fraction of the overall population of the SB states to be around 5%. Although this value agrees with the general notion that in aqueous solution, salt bridge partners prefer being separated, apparently the overall SB population of 5% is still quite noticeable, at least not as trivial as commonly assumed. Indeed, this value is in good accord with the estimated fraction of the SB structures formed on protein surfaces when the SB partners are located on adjacent residues.

Figure 2.

The gOST simulation enables repetitive breaking and reforming of salt‐bridge structures. (a) The time‐dependent scaling parameter changes. (b) The time‐dependent salt‐bridge distance changes. (c) The free energy profile along the salt‐bridge distance.

The backbone conformation influences the propensity of salt bridge structures formed between adjacent residues

Our minimalist model specifically represents cases when the SB partners reside on adjacent residues. Due to possible spatial constraint, the salt bridge propensity may vary with changes of the backbone conformation. In this simple dipeptide model, the most relevant order parameter that describes possible coupling between the backbone conformation and the salt bridge formation is the dihedral angle $\theta$ defined as: $C_{\beta }\left(\mathrm{A}\mathrm{s}\mathrm{p}\right)-C_{\alpha }\left(\mathrm{A}\mathrm{s}\mathrm{p}\right)-C_{\alpha }\left(\mathrm{A}\mathrm{r}\mathrm{g}\right)-C_{\beta }\left(\mathrm{A}\mathrm{r}\mathrm{g}\right)$. As shown in Figure 3(a), the gOST simulation allows this dihedral angle to be thoroughly sampled. The two‐dimensional free energy surface [Fig. 3(b)] shows that the backbone conformation has two primary distributions: one around $\theta ={25}^{\mathrm{o}}$, which corresponds to more compact conformations, and the other around $\theta ={-110}^{\mathrm{o}}$, which corresponds to more stretched conformations. The free energy surface shows that salt bridges can only be formed when the backbone adopts a compact conformation.

Figure 3.

The gOST simulation enables thorough sampling of backbone conformations. (a) The time‐dependent changes of the dihedral angle $\theta$: $C_{\beta }\left(\mathrm{A}\mathrm{s}\mathrm{p}\right)-C_{\alpha }\left(\mathrm{A}\mathrm{s}\mathrm{p}\right)-C_{\alpha }\left(\mathrm{A}\mathrm{r}\mathrm{g}\right)-C_{\beta }\left(\mathrm{A}\mathrm{r}\mathrm{g}\right)$. (b) The free energy surface along the salt‐bridge distance and the dihedral angle $\theta$.

The free energy surface in the SB region features three states; two majors ones around $\theta ={25}^{\mathrm{o}}$ and the minor one around $\theta ={-45}^{\mathrm{o}}$. The two major SB states correspond to the two characteristic double‐hydrogen‐bond salt bridge structures that are possibly formed between the charged groups of the arginine and aspartate residues; and in the minor SB state, only one hydrogen bond is formed between the charged groups, therefore the backbone conformation is more extended. The free energy surface in the IS region features two subregions: the broader one around $\theta ={25}^{\mathrm{o}}$ with more compact backbone conformations and the narrower one around $\theta ={-110}^{\mathrm{o}}$ with more extended backbone conformations. In the broader IS subregion, there exist the global free energy minimum state at the SB distance of about 8.0 Å. The fact that the global free energy minimum is located at a medium distance, where solvation forces have not been fully developed and charge attraction forces still remain, further suggests that two competing interactions indeed subtly compromise.

Compensating fluctuations of solute‐solvent and solute‐solute interactions drive the forming and breaking of salt bridge structures

In order to understand how water structures surrounding SB partners influence salt bridge formations, we constructed the two‐dimensional free energy surface along both the SB distance and the essential solute‐solvent interaction energy (UPW, as defined in Computational Details) [Fig. 4(a)]. This free energy surface reveals that the forming and breaking of salt bridge structures are driven by solute‐solvent interaction fluctuations: (a) weak solute‐solvent interactions naturally leads to the formation of salt bridge structures; (b) the strengthening of the solute‐solvent interaction (to around −190 kcal/mol) gives rise to the transition state, in which the salt bridge is breaking while the charged group solvation is still being developed; and (c) with the completion of the charged group solvation, favorable IS states spontaneously form. Interestingly during the transition, the solute‐solvent and solute‐solute interactions intimately interplay. As shown by the free energy surface in Figure 4(b), the essential solute‐solvent interaction energy (U _PW) and the solute‐solution interaction energy (U _PP, as defined in Computational Details) not only fluctuate in the opposite direction but also closely compensate each other. This further confirms that associated with the forming and breaking of salt bridge structures, two compensating effects, e.g. salt bridge partner attractions and solvation forces on individual charge groups, are finely balanced. Therefore the salt bridge stability is very likely to be easily tunable by local solvent environments.

Figure 4.

Compensating fluctuations of solute‐solvent and solute‐solution interactions drives the breaking and forming of salt‐ bridge structures. (a) The free energy surface along the salt‐bridge distance and the essential solute‐solvent interaction energy (U _PW). (b) The free energy surface along the essential solute‐solvent interaction energy (U _PW) and the solute‐solute interaction energy (U _PP).

Minor local environment perturbations lead to increasingly populated SB states

To probe how local solvent environments can modulate salt bridge stabilities, we planned to exam some representative perturbed conditions, particularly to find out how the salt bridge propensity can be enhanced. Considering the simplicity of this model, we decided to choose a few $\lambda$‐perturbed states in Eq. (1) to serve as target conditions for examination. Using the same set of samples collected from the gOST simulation, based on Eq. (3), we can construct the SB distance dependent distributions for these perturbed conditions. As shown in Figure 5, with the increasing of the scaling factor $\lambda$, the SB region becomes more populated. In the mean time, the population of the major IS state (around the SB distance of 8.0 Å) monotonically decreases. And its neighboring flatter IS region (around the SB distance of 9.0 Å) has a shaper distribution developed; after $\lambda$ is larger than 1.03, this region turns into the most populated IS state.

Figure 5.

The salt‐bridge distance dependent distributions under various perturbed conditions.

When the scaling factor $\lambda$ is larger than 1, with the increasing of this factor, solute‐solute interactions grow faster than solute‐solvent interactions and at the same time, the effective surface tension on the solute increases as well. Such perturbations are analogous to physical situations when local water‐water interactions become stronger, for instance when the local environment becomes more hydrophobic. The above numerical perturbation experiment further indicates that the salt bridge propensity is highly tunable by the local solvent environment. Particularly when the local protein environment pushes solvent molecules to form stronger interactions with each other, the solute‐solvent interaction is naturally weakened and as the consequence, salt‐bridge structures can be more easily formed.

Computational Details

Due to intimate coupling with slow water fluctuations, salt‐bridge structures may form and break in timescales that are difficult for canonical ensemble MD simulation methods to achieve adequate sampling. Therefore, we employed a recent “predictive” enhanced sampling method, the generalized orthogonal space tempering technique (gOST), to carry out our MD simulation study. In this section, we first briefly introduce the gOST algorithm and then describe the simulation and analysis details.

Generalized orthogonal space tempering (gOST) method

In gOST, we first construct an expanded energy function:

$$U_{\lambda }=\lambda U_{\mathrm{s}\mathrm{s}}\left({\mathbf{X}}_{\mathit{N}}\right)+\mathrm{S}\mathrm{E}\left(\lambda \right)U_{se}\left({\mathbf{X}}_{\mathit{N}}\right)+\left[\mathrm{S}\mathrm{A}\mathrm{S}\mathrm{A}\left(\lambda \right)-1\right]U_{\mathrm{s}\mathrm{a}\mathrm{s}\mathrm{a}}\left({\mathbf{X}}_{\mathit{N}}\right)+U_e\left({\mathbf{X}}_{\mathit{N}}\right),$$ (1)

where $U_{\mathrm{s}\mathrm{s}}\left(X_N\right)$ and $U_{\mathrm{s}\mathrm{e}}\left(X_N\right)$, respectively represent selected solute‐solute and solute‐solvent interactions that are subject to the scaling perturbation treatment; $U_e\left(X_N\right)$ represents the remaining “environmental” interactions; and $U_{\mathrm{s}\mathrm{a}\mathrm{s}\mathrm{a}}\left({\mathit{X}}_{\mathit{N}}\right)$ represents the solvent accessible surface area (SASA) energy that is commonly used to model non‐polar solvation contributions.13 To be general, while $U_{\mathrm{s}\mathrm{s}}\left(X_N\right)$ is straightly scaled by a factor $\lambda$, $U_{\mathrm{s}\mathrm{e}}\left(X_N\right)$ is scaled by a $\lambda$‐dependent function $\mathrm{S}\mathrm{E}\left(\lambda \right)$ and $U_{\mathrm{s}\mathrm{a}\mathrm{s}\mathrm{a}}\left({\mathit{X}}_{\mathit{N}}\right)$ is scaled by another pre‐chosen $\lambda$‐dependent function, $\mathrm{S}\mathrm{A}\mathrm{S}\mathrm{A}\left(\lambda \right)-1$. Except for the $U_{\mathrm{s}\mathrm{a}\mathrm{s}\mathrm{a}}\left({\mathit{X}}_{\mathit{N}}\right)$ related term, such an expanded energy function is commonly used in other enhanced‐sampling techniques, for instance simulated scaling (ST)14 and Hamiltonian replica exchange method (HREM),15, 16, 17 etc. In gOST, the $\left[\mathrm{S}\mathrm{A}\mathrm{S}\mathrm{A}\left(\lambda \right)-1\right]U_{\mathrm{s}\mathrm{a}\mathrm{s}\mathrm{a}}\left({\mathit{X}}_{\mathit{N}}\right)$ term is introduced to effectively vary the surface tension surrounding the solute molecule and so indirectly perturbs near‐solute solvent‐solvent interactions.

Notably, although switching $\lambda$ may lead to a shifted distribution, it can take very long time for a configuration to dynamically evolve to new “important” regions. To overcome this slow configuration response problem, we introduced the orthogonal space sampling (OSS) scheme,18, 19, 20, 21 as exemplified by the orthogonal space random walk (OSRW)18, 19, 20 and orthogonal space tempering (OST)21 methods. To more robustly accelerate configuration responses in aqueous solution, recently we devised a generalized orthogonal space tempering (gOST) algorithm, which can be expressed via the following modified potential:

$$U_{\mathrm{m}}=U_{\mathrm{\lambda }}+f_{\mathrm{m}}\left(\lambda \right)+\alpha g_{\mathrm{m}}\left(\lambda ,{\varphi }_1,{\varphi }_2\right),$$ (2)

where $U_{\lambda }$ is the same as in Eq. (1). Here, the scaling factor $\lambda$ is treated as a one‐dimension particle or a monotonic function of a one‐dimension particle; in this study, we used the function introduced in the original OST method. To achieve $\lambda$ space random walks, the target function of $f_{\mathrm{m}}\left(\lambda \right)$ is set as $-G_{\mathrm{o}}\left(\lambda \right)$, the negative of the $\lambda$‐dependent free energy function under the $H_{\lambda }$ ensemble; and to synchronously accelerate configuration responses, the target function of $g_{\mathrm{m}}\left(\lambda ,{\varphi }_1,{\varphi }_2\right)$ is set as $-G_{\mathrm{f}}\left(\lambda ,{\varphi }_1,{\varphi }_2\right)$, the negative of the free energy function along $\left(\lambda ,{\varphi }_1,{\varphi }_2\right)$ under the ensemble of $H_{\lambda }-G_{\mathrm{o}}\left(\lambda \right)$. Here, ${\varphi }_1$ and ${\varphi }_2$ respectively denote $U_{\mathrm{s}\mathrm{s}}\left({\mathit{X}}_{\mathit{N}}\right)+\frac{\mathrm{d}\mathrm{S}\mathrm{A}\mathrm{S}\mathrm{A}\left(\lambda \right)}{\mathrm{d}\lambda }{U}_{\mathrm{s}\mathrm{a}\mathrm{s}\mathrm{a}}\left({\mathit{X}}_{\mathit{N}}\right)$ and $\frac{\mathrm{d}\mathrm{S}\mathrm{E}\left(\lambda \right)}{\mathrm{d}\lambda }{U}_{\mathrm{s}\mathrm{e}}\left({\mathit{X}}_{\mathit{N}}\right)$, which are the two compensating components of the generalized force order parameter $\partial H_{\lambda }/\partial \lambda$. The parameter $\alpha$ controls the magnitude of response fluctuation enlargement.

The OST algorithm is an adaptive sampling method. To recursively generate target biasing potentials $g_{\mathrm{m}}\left(\lambda ,{\varphi }_1,{\varphi }_2\right)$ and $f_{\mathrm{m}}\left(\lambda \right)$, an extended‐dynamics based “double‐integration” recursion strategy was designed.21 For gOST, a straightforward generalization of the original “double‐integration” recursion approach was developed.

Model and general molecular dynamics simulation setups

In our model, we have a neutrally blocked Asp‐Arg dipeptide (Fig. 1) solvated in a truncated octahedral water box; potassium and chloride ions were added to have the ionic strength adjusted to be around 0.15M. The peptide and ions were modeled with the CHARMM2222/CMAP23 force field and water molecules were treated with the modified TIP3P model.24 The particle mesh Ewald (PME) method25 was used to calculate long‐range electrostatic interactions; in real space energy and force calculations, short‐range electrostatic interactions were switched off at 12 Å. All the simulations were performed under the NPT ensemble. The temperature was set as 300 K and the pressure was set as 1 atm; the Nóse‐Hoover thermostat26 was utilized to maintain the constant temperature and the Langevin piston algorithm27 was employed to maintain the constant pressure. The SHAKE algorithm was used to constrain all the bonds that involve water hydrogen atoms. The MD simulation time step was set as 1 femto‐second (fs).

Figure 1.

The structure of our minimalist salt bridge model: the Asp‐Arg peptide. The termini are neutrally blocked.

Details on the generalized orthogonal space tempering simulation

The gOST algorithm was implemented in our customized version of the CHARMM program.28, 29 In this study, we selected all the intra‐peptide torsional terms (including the CMAP terms) and the electrostatic energy terms into $U_{\mathrm{s}\mathrm{s}}\left({\mathit{X}}_{\mathit{N}}\right)$ and all the electrostatic interactions between the peptide and the solvent environment (including both water molecules and ions) into $U_{\mathrm{s}\mathrm{e}}\left({\mathit{X}}_{\mathit{N}}\right)$; in the Results and Discussion section, these energy components, $U_{\mathrm{s}\mathrm{s}}\left({\mathit{X}}_{\mathit{N}}\right)$ and $U_{\mathrm{s}\mathrm{e}}\left({\mathit{X}}_{\mathit{N}}\right)$, are respectively denoted as $U_{\mathrm{P}\mathrm{P}}$ and $U_{\mathrm{P}\mathrm{W}}$. For $\mathrm{S}\mathrm{E}\left(\lambda \right)$, we picked $\sqrt{\lambda };$ 30, 31, 32 and for $U_{\mathrm{s}\mathrm{a}\mathrm{s}\mathrm{a}}\left({\mathit{X}}_{\mathit{N}}\right)$, we used a solvent‐accessible‐surface‐area energy function form33, 34 in the CHARMM program. We collected experimentally determined temperature‐dependent water surface tension changes $\gamma \left(T_{\mathrm{m}}\right)$ and set $\mathrm{S}\mathrm{A}\mathrm{S}\mathrm{A}\left(\lambda \right)$ as a B‐spline function that connects the collected‐points based on the relationship $\mathrm{S}\mathrm{A}\mathrm{S}\mathrm{A}\left(\lambda \right)=\gamma \left(\frac{300K}{{\lambda }^2}\right)/\gamma \left(300 \mathrm{K}\right)$.

Generalized orthogonal space tempering simulation result analysis

For a collective variable set $\mathit{S}$ of interest, the free energy surface can be constructed based on the following equation,

$$G_{\mathrm{o}}\left(\mathit{S}\right)=-k{T}_{\mathrm{o}}\mathrm{l}\mathrm{n}\sum _t{e}^{\frac{U_{\mathrm{m}}\left(t\right)-U_{\mathrm{T}}\left(t\right)}{k{T}_o}}\delta \left(\mathit{S}\left[{\mathbf{X}}_{\mathit{N}}\left(t\right)\right]-\mathit{S}\right)+ \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t},$$ (3)

where $t$ represents scheduled sample‐collection time‐steps in the near‐equilibrium phase of the simulation and $U_{\mathrm{T}}\left(t\right)$ stands for the potential energy function of the targeted ensemble.

Concluding Remarks

Salt bridge is an essential structural component in proteins. On protein surfaces, salt bridges not only can form but also may play critical roles in facilitating protein conformational transitions. Despite the importance, there has been scarce of detailed discussion on how salt bridge partners interact with each other in distinct solvent accessible environments. In this study, we computationally analyzed a minimalist salt‐bridge model, the Asp‐Arg dipeptide using a recent generalized orthogonal space tempering sampling method, which allowed us to achieve efficient molecular dynamics simulation of repetitive breaking and reforming of salt bridge structures and thereafter map the detailed free energy landscape of the model peptide in aqueous solution. Free energy calculation results show that although individually‐solvated states are more favorable, salt‐bridge states still occupy a noticeable portion of the overall population. Notably none of the competing forces, e.g. inter‐charge attractions that drive the formation of salt bridges and solvation forces that pull the charged groups away from each other, is absolutely dominant; instead they subtly compromise. As a consequence, the salt bridge stability is highly tunable by local environments. Furthermore, we show that when local water structures are perturbed, salt‐bridge states can become more populated. This provides a simple explanation on why stabilizing salt bridges may form on solvent exposed protein surfaces.

This study reveals the critical role of local solvent structures in modulating salt‐bridge partner interactions and implies the importance of water fluctuations on conformational dynamics that involves solvent accessible salt bridge formations. Although this study was only performed on a simple minimalist peptide model, our understanding is general. We will undertake further study on solvent exposed salt‐bridge partner interactions in the context of real protein systems.