Abstract
The PDZ domain is an interaction motif that recognizes and binds the C-terminal peptides of target proteins. PDZ domains are ubiquitous in nature and help assemble multiprotein complexes that control cellular organization and signaling cascades. We present an optimized energy function to predict the binding free energy (ΔΔG) of PDZ domain/peptide interactions computationally. Geometry-optimized models of PDZ domain/peptide interfaces were built using Rosetta, and protein and peptide side chain and backbone degrees of freedom are minimized simultaneously. Using leave-one-out cross-validation, Rosetta’s energy function is adjusted to reproduce experimentally determined ΔΔG values with a correlation coefficient of 0.66 and a standard deviation of 0.79 kcal mol−1. The energy function places an increased weight on hydrogen bonding interactions when compared to a previously developed method to analyze protein/protein interactions. Binding free enthalpies (ΔΔH) and entropies (ΔS) are predicted with reduced accuracies of R = 0.60 and R = 0.17, respectively. The computational method improves prediction of PDZ domain specificity from sequence and allows design of novel PDZ domain/peptide interactions.
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Introduction
Protein/peptide interactions play an important biological role in an array of cellular processes. One motif frequently used for such interactions is the well characterized PDZ (PSD-95, Discs large, Zona occludens 1) domain [1]. Within Homo sapiens, Drosophila melanogaster, and Caenorhabditis elegans, Schultz et al. [2] have estimated the existence of 440 PDZ domains in 259 different proteins, 133 PDZ domains in 86 proteins, and 138 PDZ domains in 96 proteins, respectively. PDZ domains perform critical roles in signaling cascades of bacteria, yeast, plants, and animals [3] by acting as intracellular scaffolding proteins [4, 5]. Pathogens disrupt host-signaling processes using linear peptide motifs to target PDZ binding sites [6]. Developing inhibitors of these interactions is one avenue of therapeutic development [7]. The wide-spread presence of the PDZ domain in nature and its integral role in numerous biological processes and diseases make it an ideal focus for studying the specificity of protein/peptide interactions.
PDZ domains bind peptides through strong backbone hydrogen bonds
PDZ domains are typically composed of 80–90 amino acids [8] and consist of a central bent six-stranded β-sheet surrounded by two α-helices. The peptide binding interface (Fig. 1) lies at the edge of the β-sheet. The peptide binds in an extended, antiparallel conformation, using the unsatisfied hydrogen bonding capabilities of PDZ β-strand 2 (β2) to extend the β-sheet by one additional strand. The ligand also engages in side-chain interactions with the second α-helix (α2) of the PDZ domain, which lines the other side of the binding groove. The binding pocket contains a characteristic hydrophobic loop (β1:β2) that binds the peptide carboxy-terminus through the formation of three hydrogen bond interactions. Overall, the interface is characterized by strong backbone–backbone hydrogen bonding contacts within a hydrophobic environment [9].
PDZ domain specificity is governed by side-chain interactions
Although the general binding mode of PDZ domains is the same, different proteins interact with different targets. While specificity in the PDZ family has been studied extensively, an unambiguous classification of the PDZ domain remains a challenge [6]. Generally, PDZ domains have been grouped into three classes (I, II, and III) depending on the characteristics of the β1:β2 loop [6] and position −2 (P−2) of the ligand (see Fig. 1). Class I domains have a G-L/Y-G-F β1:β2 loop that binds C-terminal peptide residues of sequence X-S/T-X-V/I/L (P−3-P0) [9]. Additionally, the peptide hydroxyl group at P−2 makes an important hydrogen bonding contact with the histidine side chain of α21 [6]. Class II proteins have a similar β1:β2 loop sequence of X-L/V-G-F/I/L that binds peptide sequences having a hydrophobic amino acid at position P−2 (X-ø-X-ø) [8]. Class III domains are less widespread and have a G-L-G-F β1:β2 loop sequence that binds peptides having an acidic amino acid at P−2 (X-D/E-X-ø) [10, 11].
PDZ class I, II, and III proteins and their peptides have variable sequence similarities (between 5% and 90%) but are structurally highly similar. Indeed, Stiffler et al. [12] found only a weak correlation between sequence identity and PDZ domain specificity. Instead, Stiffler developed a modified position specific scoring matrix based on the profiles of peptides which bind to a domain. Chen et al. [13] later developed a method that incorporated structural information on protein/peptide residue pairs within close proximity of each other. The model was capable of predicting PDZ domain specificity for multiple species from primary sequences and it was argued that including structural information via the protein/peptide residue position specific interaction matrix was sufficient to predict the specificity of PDZ domains.
PDZ domains display a diverse and finely tuned specificity profile
PDZ domain classification can be extended beyond the three naïve classes discussed here. Specificity within these classes depends upon other differences in the protein/peptide interface that result in a diversified sequence profile. Tonikian et al. [6] performed profiling of 91 point mutants of a model PDZ domain to create a specificity map. Using this map, 82 protein domains of the PDZ family were reclassified into 16 classes distinguished by specificity for peptide residues up to the P−6 position. While sequence-based analysis alone reveals diverse specificity profiles, the inclusion of structure-based information should provide a more general model for predicting PDZ specificity. Such a physical model would be a useful tool for PDZ domain classification, specificity prediction, and design.
The Rosetta protein modeling software predicts specificity of protein/protein interfaces
In a series of experiments, Kortemme et al. [14] demonstrated the power of the knowledge-based energy function of the modeling software Rosetta to characterize and design protein/protein interfaces. A model for protein/protein binding was created using a data set of alanine mutants at protein/protein interfaces. The model was able to predict successfully the results of alanine scanning experiments on globular proteins (743 mutations) and 19 protein/protein interfaces (233 mutations) with low standard deviations of 0.8 kcal mol−1 and 1.1 kcal mol−1, respectively [14]. The model was applied to create new DNase-inhibitor protein pairs with altered specificities that functioned both in vitro and in vivo [15]. It was also used to fuse domains of two homing endonucleases, creating a chimera that recognized a new DNA target and functioned as a highly specific artificial endonuclease [16].
While this model proved successful in modeling protein/protein interfaces, the derived parameterization is not optimal for protein/peptide interfaces as these are characterized by distinct features that require a tailored parameterization, such as smaller hydrophobic surface area and a greater dependence of hydrogen bonding interactions. Sood and Baker explored the use of Rosetta to design elongated p53 and dystroglycan-based peptides that bind with increased affinity to Mdm2 oncoprotein and dystrophin, respectively. These studies included backbone flexibility and allowed side-chain flexibility through repacking of a rotamer library but used the standard Rosetta energy function with a packing score derived from the change in solvent accessible surface area [17]. Sood and Baker found that sampling of the backbone conformation improved recovery of sequence diversity in designed peptides and in cases where the algorithm fails, insufficient sampling of backbone degrees of freedom explains the error.
A Rosetta parameterization tailored for PDZ domain/peptide interfaces
It is the objective of the present work to develop a model for predicting the specificity of PDZ domains using the protein structure prediction program Rosetta. Saro et al. [18] conducted isothermal titration calorimetry (ITC) measurements on a series of peptides binding the third PDZ domain (PDZ3) of postsynaptic density 95 protein (PSD-95), a class I domain. They recorded the thermodynamic properties ΔΔG, ΔΔH, and TΔS for a series of six-residue peptides of sequence (X-X-X-T-X-V), with different X amino acids influencing binding. We parameterize Rosetta to accurately predict these thermodynamic parameters.
Methods
Dataset for energy function parameterization
The dataset contains free energy (ΔΔG), enthalpy (ΔΔH), and entropy (TΔS) measurements for binding of 28 peptides to the PDZ3 domain of PSD-95 (Table 1) [18]. The crystal structure of the PDZ3 domain of PSD-95 with the highest resolution (1.54 Å) from the PDB was used for structural modeling (PDBID 1TP5).
The crystal structure was determined in complex with the peptide KKETWV.
Introduction of mutations and initial minimization of structural models
RosettaDesign [19] protocols allow in silico mutation of amino acids. Briefly, the side chain of the amino acid in question is removed and replaced with the side chain of the target amino acid. The conformation of the introduced amino acid is chosen from a backbone-dependent rotamer library [20] to minimize the Rosetta energy function. First, the tryptophan at position P−1 of 1TP5 was reverted to a glutamate to match the base peptide KKETEV used in the study by Saro et al. [18]. Following this modification, the 28 PDZ domain/peptide complexes were built (Table 1, Fig. 2b). All models underwent gradient minimization using Rosetta to remove initial clashes (Fig. 2c) [21]. The protocol involves eight rounds of gradient-based minimization of all torsional degrees of freedom, which is alternated with side chain repacking using a rotamer library. The all-atom RMSD of the structure changed by 0.40 Å on average with a maximum of 0.51 Å observed for complex 6 containing the KKETEF mutant peptide.
RosettaDock generation of structural models for protein/peptide complexes
To generate minimized models for energy evaluation, all bound structures underwent a small perturbation protocol applied to the transformational degrees of freedom in the protein/peptide complex using RosettaDock (Fig. 2e) [22]. This rigid body motion is complemented by a simultaneous optimization of side chain coordinates through a fast repacking protocol. The backbone coordinates of protein and peptide are held fixed in the process.
The protocol is setup in an iterative fashion. First a random small perturbation of up to 0.1 Å translation and up to 2° rotation is made to the rigid body degrees of freedom. Then the side chain conformations are allowed to change by substituting discrete rotamers from a library of conformations commonly seen in the PDB. If the substitution results in a lower total energy, Rosetta keeps the new conformation of the protein. If the energy is higher, Rosetta may still accept the substitution with a probability inversely proportional to the energy increase (Metropolis criterion). On average, around 50 of these iterations are completed in order to find the best combination of amino acid side chain conformations. The output model is the lowest energy complex observed throughout the entire trajectory. Lastly, a gradient-based minimization on the rigid body degrees of freedom moves the final model into the nearest local minimum in the Rosetta energy landscape. A total of 100 bound models were generated for each complex. The 5 models with the lowest overall energy were selected for further analysis (Fig. 2g).
Modeling apo structures in Rosetta
The unbound (apo) structures were created by removing the peptide from the binding pocket and away from the protein by a distance sufficiently large to prevent any interaction (> 100 Å). The side chains, which were allowed to move during the docking protocol, were allowed to rearrange using repacking algorithms [19]. A total of 100 models was generated for each of the mutants, and the total Rosetta energy was used to select a single most favorable unbound conformation for each of the 28 complexes (Fig. 2h).
Calculation and evaluation of binding free energy
The Rosetta energy function contains six energy terms. Van der Waals energies are modeled using a Lennard-Jones 12-6 potential. The potential is split into an attractive (atr) and a repulsive (rep) component. Rosetta introduces a solvation energy (sol) that imposes a penalty for polar atoms buried in the core of a protein accounting for the exposure preferences of polar and non-polar atoms [23]. Side chain conformational probabilities are reflected by an energy (dun) derived from rotamer probabilities [20]. Electrostatic interactions are mimicked by a knowledge-based pair-wise potential (pair) derived from statistics over the PDB. Hydrogen bonds (hbnd) are captured by an orientation dependent potential [24]. Note that, in the past, hydrogen bonds have been classified into three classes: long-range backbone–backbone (lr-bb), backbone–side chain (bb-sc), and side chain–side chain (sc-sc) hydrogen bonds [14].
Within each structure, all residues were individually evaluated. To obtain the total energy of the model, the sum over all amino acids was computed and averaged over the top five bound structures (Fig. 2g). For the unbound models energies from the single structure with lowest Rosetta energy were used directly (Fig. 2h). The binding free energy was computed for each of the above-mentioned terms \( \Delta \Delta E_{binding}^{term} \) using:
\( \Delta \mathop {E}\limits_i \,_{bound}^{term} \) is the Rosetta energy one of the five complex models, respectively; \( \Delta E_{unbound}^{term} \) is the Rosetta energy of the single unbound model.
Multiple linear regression is used to parameterize an overall free energy function
To obtain an energy function optimized for the analysis of protein/peptide interactions (Fig. 2i), a multiple linear regression (MLR) analysis was used. Each of the \( \Delta E_{binding}^{term} \) terms is affiliated with a weight wterm:
The bias is introduced to account for contributions to the binding free energy not represented in the Rosetta energy function, such as the loss in entropy. The bias assumes that these contributions are constant, an obvious limitation of the present model.
The weights were determined by performing a leave-one-out (LOO) cross validation analysis. In a round-robin setup, 27 of the 28 mutants with known experimental binding affinities were used to determine an optimal weight set given these 27 data points. Afterwards, the binding free energy of the 28th mutant was predicted and compared with the experiment to enter a correlation analysis. This experiment was repeated for all 28 mutants.
To determine whether an energy term contributes significantly to an optimal energy function for protein/peptide interfaces, energy terms were removed systematically. The subset of energy terms that resulted in the optimal correlation coefficient within the cross-validation experiment was used. The final weight set reported consists of the average weights and standard deviations over of all 28 experiments. The protocol was implemented using the Mathematica software package (Fig. 2j).
Results
The physical model for protein/peptide interactions depends on van der Waals, solvation, and hydrogen bonding
The optimal weight set was determined by a LOO cross validation analysis as described in the Methods section. Of the six Rosetta energy terms considered, only van der Waals attraction (atr), solvation (sol), and hydrogen bonding energies (hbnd), contributed to an energy function that optimally reproduced experimentally determined binding free energies:
The correlation coefficient for the independent dataset is 0.66 (Fig. 3).
Known characteristics of the PDZ binding domain are mirrored within the model
Figure 1 displays the per amino acid changes in free energy upon peptide binding for the PSD-95 PDZ3 in complex with the peptide KKETEV as determined by our model. Strong backbone–backbone hydrogen bonds between the class I domain and the peptide residues V(P0) and T(P−2) agree with the anti-parallel β-strand binding motif of the PDZ domain that forms two backbone hydrogen bonds for every other amino acid. In this particular case, the C-terminal amino acid V(P0) engages in three hydrogen bonds. This alternative pattern is further highlighted by E(P−1) and E(P−3), which contribute only 0.1 and −0.3 kcal mol−1 to the binding free energy, respectively. In contrast, V(P0) and T(P−2) contribute −3.1 and −3.0 kcal mol−1, respectively.
In addition to hydrogen bonding interactions, important salt bridges and van der Waals interactions are involved in binding the peptide tightly. H(α21) is the most important residue within α2 for binding the peptide as it forms a hydrogen bond with T(P−2) through side chain hydrogen bonding, and engages in van der Waals interactions with K(P−4). L(α28) and K(α29) interact with V(P−0) through van der Waals attractive interactions. This creates a favorable, hydrophobic environment for the non-polar valine side chain and amplifies the strength of the hydrogen bonds formed between the peptide carboxyl terminus and F(β21), G(β1:β28), and L(β1:β27).
Enthalpic and entropic contributions to the binding free energy map to different components of the Rosetta energy function
The investigation was extended to other thermodynamic characteristics of protein/peptide binding including enthalpy and entropy (Table 2). The independent correlation observed for the binding enthalpy ΔΔHbinding is with 0.60 only slightly reduced from the value observed for the Gibbs binding free energy (0.66, Fig. 3). In contrast, when correlating with respect to experimentally measured entropy changes the independent correlation drops to 0.17.
Specificity prediction for 12 PDZ domains with available crystal structures
For the specificity analysis, a set of 12 PDZ protein/peptide complexes with available crystal structures was used (Table 3). All experimentally determined structures with resolutions of 2.30 Å or better were considered (PDBID 1BE9 [10], 1N7F [25], 1OBY [26, 27], 1RZX [28], 1TP3, 1TP5, 1V1T [29], 1W9E [29], 1W9O [29], 1W9Q [30, 31], 2I04 [32], 2QT5 [33]). Structures used in the specificity analysis were initially separated into their protein and peptide components. Peptides were truncated to include five carboxy-terminal residues. All possible combinations between PDZ domains and peptides were created yielding a total of 144 complexes. Each complex was refined using the protocol described above (Fig. 2).
The binding energies for each complex were then computed using the PDZ optimized weight set. The heat map in Fig. 4a shows that the PDZ optimized weight set captures specificity within each PDZ class. The complexes group into two blocks reflecting the two classes of PDZ domains. Figure 4b shows the receiver operating characteristics (ROC) curve where a complex is regarded as a true complex if both peptide and protein come from the same PDZ class. The area under the curve is 78%, 28% better than a random predictor.
Discussion
Energy function weights from LOO analysis are stable
The deviations from a perfect correlation are attributed to imperfection in the Rosetta energy function, which is simplified to only contain pair-wise decomposable energetic terms [34]. The small standard deviations observed for the individual weights (Table 4) demonstrate internal consistency as the analysis of all 28 complexes yielded very similar weight sets.
Table 4 compares the weight set obtained in the present analysis with a weight set optimized for protein/protein interfaces [35] and the default weight set. Specializing the energy function should allow prediction of binding affinities at a higher accuracy than seen for a more generalized function such as that put forth by Kortemme [14]. The weights derived here deviate from the default Rosetta weights, highlighting the importance of a customized computational model for protein/peptide binding. The weight set is optimized to predict the binding free energies PDZ domains. In particular, the hydrogen bonding weight is increased substantially relative to other weights. This result can be explained in part by the backbone hydrogen bonds between peptide and PDZ domain. These hydrogen bonds contribute significantly to the stability of the PDZ-domain/peptide interface. However, as these hydrogen bonds are present in all PDZ domain/peptide complexes, they do not govern specificity but contribute an approximately equal amount to all interfaces studied.
Our results indicate that a high weight on side chain hydrogen bonds is particularly important for accurate specificity prediction. Interestingly, a holistic weighting with a single hydrogen bonding weight gave the best results. This is in contrast to the earlier reported optimal weight set for protein/protein interfaces where hydrogen bonds contributed differently depending on the level of solvent exposure [35]. Beyond this aspect, changes in the weight set are small.
Energy function components capture enthalpic but not entropic contributions
The weighted energy terms vary significantly when correlated to the different thermodynamic binding properties. Enthalpy is best predicted from hydrogen bonding (hbnd) and electrostatic (pair) interactions; entropy correlates best with a combination of hydrogen bonding (hbnd) and rotamer probability. Overall we expected that Rosetta-derived energy terms correlate best with binding free energies. Their knowledge-based character can be well aligned with the definition of free energy in statistical thermodynamics. Hence, every one of the Rosetta energy terms contains both entropic contributions and enthalpic contributions. However, the term can be dominated by one of the two if it is better represented by the simplified two-body equations used within Rosetta. Our results demonstrate that entropic contributions are least accurately reflected and prevent Rosetta from predicting to higher degrees of accuracy.
Computed binding energies correctly classify PDZ domains
The correlation of the binding energies within each class is apparent, but the computed binding energies across all PDZ complexes do not accurately rank the complexes. However when holding either the protein or the peptide constant, the binding energies display a better correlation with specificity as seen in Fig. 4c, d. This may reflect the need to sample a greater conformational space. In fact, Sood and Baker [17] found a better recovery of peptides sequence profiles upon introducing backbone flexibility into their design protocol.
Summary
This study presents a physical model for PDZ domain/peptide interactions. Parameterization of the Rosetta energy function was achieved by fitting a linear model to experimentally determined binding free energies for 28 PDZ domain/peptide complexes. The energy function is dominated by van der Waals attractive, solvation, and hydrogen bonding interactions. It reproduces well-known determinants of PDZ domain/peptide interactions such as an alternating pattern of backbone hydrogen bonding to the second strand of the PDZ domain (β2) and side chain interactions with the second helix (α2). While the Gibbs free energy correlates well with experimental values (R = 0.66), correlation of enthalpy (R = 0.60) and particularly entropy (R = 0.17) is reduced. This reduction is attributed to the knowledge-based nature of Rosetta energy functions, which aligns well with the definition of free energy in statistical mechanics. The resulting weight set was able to classify a given PDZ/peptide complex 28% better than a random predictor.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Kaufmann, K., Shen, N., Mizoue, L. et al. A physical model for PDZ-domain/peptide interactions. J Mol Model 17, 315–324 (2011). https://doi.org/10.1007/s00894-010-0725-5
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DOI: https://doi.org/10.1007/s00894-010-0725-5