Protein Frustration Reveals Orthosteric and Allosteric Active Sites in GPCR:G Protein Complexes

Abstract

The folded structure of a protein is understood to be an optimal energy state. However, previous studies have shown that certain amino acid residue positions that play a critical role in protein function are often in a suboptimal energy state or “frustrated”. Here, we leverage over 1200 three-dimensional structures of G protein-coupled receptors (GPCRs) to demonstrate that residues at the interface between GPCR and its ligand or G protein contain a higher density of frustrated residues compared to other structural regions in the receptor. Likewise, the Gα subunit of the trimeric G proteins shows multiple clusters of highly frustrated residues on its surface that overlap with their effector protein (Gbγ, RGS, Adenylyl cyclase, Ric8) binding interfaces. Our study highlights the use of protein frustration as one of the multiple structural properties to identify protein–protein interfaces and for prospective prediction of potential ligand binding sites.

Introduction

The folding of the three-dimensional structure of protein complexes is driven by an interplay of physical and chemical interactions to minimize its free energy. However, not all regions within a protein or its complex end up in a stable low-energy state; some regions are in a suboptimal energy state or “frustrated”. Protein frustration refers to the presence of competing interactions that prevent these regions from achieving their optimal, in isolation, energy state, resulting in local energetic conflicts. Rather than being detrimental, frustration often plays a crucial role in biological function. Regions of high frustration are frequently associated with functional hotspotssites where proteins interact with other molecules such as ligands or other proteins, undergo conformational changes, or catalyze chemical reactions. These regions tend to be evolutionarily conserved and are strategically positioned to maintain functional flexibility while ensuring overall structural stability.

In protein complexes, the study of frustration has provided insights into key functional sites such as binding interfaces, allosteric sites, and regions critical for enzymatic activity. By mapping the frustration landscape of a protein or protein complex, previous studies have shown how such energetic compromises are made to accommodate specific functional requirements. This approach has been increasingly employed in structural biology and drug discovery, offering a powerful framework for understanding protein function and guiding the design of therapeutics.

G protein-coupled receptors (GPCRs) form the largest superfamily of membrane proteins in the human genome, and they are also the largest target family for drug design. They serve as critical mediators of cellular communication by transducing extracellular signals, such as hormones, neurotransmitters, and sensory stimuli, into intracellular responses. This versatility is achieved through their ability to interact with a wide range of ligands and activate downstream signaling pathways via trimeric G proteins and other effectors. Despite their central role in drug development, designing ligands with high specificity and efficacy for GPCRs remains challenging. Their highly conserved structural framework, particularly in the transmembrane domain, poses challenges for designing drugs that selectively modulate specific GPCR subtypes without off-target effects. The dynamic nature of GPCRs, their ability to adopt multiple conformations, and the diversity of their ligand binding mechanisms add complexity to the task. Analysis of the available three-dimensional structures of GPCRs has shown that ligands bind to multiple binding sites other than the orthosteric binding site and modulate receptor activity.

A critical step in rational drug design is the identification of protein and/or ligand binding sites on the proteins of interest. These binding sites can be orthosteric, where endogenous ligands bind, or allosteric, which provide alternative regulatory sites. Understanding and identification of these sites are essential for designing molecules that can modulate proteins’ natural activity.

In this study, we systematically mapped the frustration profiles of over 1200 crystal structures of GPCRs and showed that receptor interfaces with ligands and effectors contain higher densities of highly frustrated residues. The correlation between frustration and protein function was further demonstrated in the Gα subunits of G proteins, in which clusters of frustrated residues were found on the interface between Ras-like and all helical domain as well as the interfaces with effector proteins. Subsequently, we showed that frustration in protein surface cavities can be used in conjunction with other structural properties to predict binding sites of GPCR allosteric modulators.

Results

A Protocol to Calculate Average Frustration per Residue from Multiple GPCR Structures

In this work, we have calculated the frustration of all the residue pairs using FrustratometeR. We downloaded 1283 three-dimensional structures of GPCRs that comprise class A (1007), class B (169), class C (80), class D (5), and class F (22) structures from GPCRdb.org as of August 15, 2024 (see Supporting Information, Table S1). This data set includes 850 active-state GPCR structures bound to either G protein (680) or b-arrestin (12) and 410 inactive-state structures bound to antagonists (232) or inverse agonists (48). For each of these structures, we employed mutational frustration FrustratometeR (V0.1.0, https://github.com/proteinphysiologylab/frustratometeR) to calculate the frustration index of every residue pair (see Methods, Figure S1). The FrustratometeR toolkit is based on the coarse-grained force field AWSEM. In each structure, each pair of residues from the output of FrustratometeR was classified as a highly frustrated (HF) pair if the z-score is less than −1, neutrally frustrated (NF) (z-score is between 0.78 and −1), or minimally frustrated (MF) pair with the z-score greater than 0.78 (Figure A).

1.

Workflow for calculating frustration. A) Residue pairwise frustration calculated using FrustratometeR (version 0.1.0, https://github.com/proteinphysiologylab/frustratometeR). Green dashed and solid lines refer to minimally frustrated pairs, either water-mediated or direct-contacts, respectively. Red dashed and solid lines refer to highly frustrated pairs either through water-mediated or direct-contacts, respectively. B) Procedure for conversion of the t pairwise frustration to single-residue frustration density. Residues within 5 Å of a given residue are considered for calculating frustration density. C) Workflow for calculating mean frustration density for each residue position in GPCR three-dimensional structures using the common residue numbering system derived from sequence alignments used for GPCRs.

We defined the frustration level of a protein–protein interface (PPI) as the percentage of HF or MF residue pairs in the interface to the total number of pairs in the interface (see Methods). We then calculated the residue-based frustration as the sum of the frustration index of all the residue pairs within 5 Å of the reference residue (Figure B). The percentages of HF, NF, and MF pairs within 5 Å are calculated and assigned to the residue as its score in each of the three categories. We refer to these scores as HF density, NF density, and MF density, respectively. For each class of GPCRs, we aligned the residues by their generic numbering system (Ballesteros-Weinstein numbering system for class A, Wootten numbering system for classes B1 and B2, Pin numbering system for class C, Wang numbering system for class F) and calculated the mean values of HF density, NF density, and MF density for each residue position (alignment of class A GPCR as an example shown in Figure C). Residues in the top quartile of high frustration density are referred to as HF residues, while those in the top quartile of minimal frustration density are referred to as MF residues.

Frustration Is Correlated to Experimentally Measured Function and Stability in Class A GPCRs

Figures A,B show HF and MF residues in class A GPCRs using the Ballesteros-Weinstein numbering system (a total of 1007 structures, including both active and inactive state conformations) projected on the structure of adenosine 2A receptor A_2AR (PDB ID: 5G53). Notably, we observed a high density of HF residues at the GPCR:G protein interface (red spheres in Figure A), including the intracellular loops, whereas most of the MF residues were in the transmembrane helices (green spheres in Figure B), rather than extracellular or intracellular loop regions. These observations suggest that HF residues may be linked to GPCR activity, given the importance of the GPCR:G protein interaction site for receptor function, while MF residues may support GPCR stability through the structural integrity of the transmembrane region. However, such patterns are not observed beyond the top quartile for both HF and MF residues (Figure S2). To find experimental support for this observation, we used receiver operating characteristic (ROC) analysis to check how well the HF density value of each residue calculated across all class A GPCRs retrieves the experimental positives.

2.

Frustration is correlated to the function and stability of Class A GPCRs. A, B) The HF residues (A) and MF residues (B) by their BW positions in class A GPCR (using 5G53 as template for displaying). C) The ROC comparing HF residues in AT1R and functional critical residues identified from Alanine scanning yields an Area Under the Curve (AUC) of 0.65. D) The ROC compares MF residues and thermostable residue mutations from Alanine scanning of adenosine A_2A receptor (A_2AR), β1-adrenergic receptor (β1AR), and neurotensin receptor (NTSR1), yielding an average AUC of 0.66. The average in ROC curve is shown as an orange line, while the standard deviation of the ROC curve is shown as a gray shade. E, F) Percentage of HF residues (E) and MF residues (F) formed with each selected residue compared to GPCR:Gα interface residues and all other GPCR residues. G) HF residues around the ligand binding site among the Adrenoceptor family (PDB ID: 8JJL). H) Percentage of HF residues in binding interfaces of the G protein, peptide ligands, and small molecule ligands, and the rest of the TM region. Statistical comparisons against the TM region were performed using Welch’s t test (two-sided). Peptide agonist: p = 1.19 × 10^–49; peptide antagonist: p = 2.23 × 10^–3; small-molecule agonist: p = 6.88 × 10^–7; small-molecule antagonist: p = 2.50 × 10^–3.

We used the experimental measurements of the change in the receptor coupling to the G protein upon mutation of each amino acid in the Angiotensin II receptor 1 (AT1R) to alanine. Briefly, the functional responses of each AT1R mutant for Gαq coupling were measured with the protein kinase C (PKC)–BRET biosensor. The dose-dependent responses to angiotensin II stimulation showed the level of change in both EC50 and Emax of angiotensin II in each AT1R mutant. The ROC analysis shown in Figure C was performed using the frustration density calculated for each residue in AT1R and the measured difference in the receptor activity RA (Emax/EC50) between the mutant and the wild type AT1R. This analysis yielded an Area Under the Curve (AUC) of 0.65 (Figure C), which is modest correlation showing that HF density calculation of each residue from a single crystal structure recapitulates the receptor G protein coupling sensitivity better than random. Similarly, we used the MF density of each residue to check how well they retrieve the thermostability data from experiments. The thermostability data for the inactive adenosine receptor (A_2AR), active b1-adrenergic receptor (β1AR), and active neurotensin receptor 1 (NTSR1) were taken from previously published data. The experimental thermostability measurements were performed on antagonist cyanopindolol bound turkey β1AR, agonist 5′-N-ethylcarboxamidoadenosine (NECA) bound adenosine receptor A_2AR, antagonist ZM-241385 bound A_2AR, and agonist NTS1 bound rat neurotensin receptor NTSR1. Briefly, the experimental thermostability was measured by doing an alanine scanning mutation of each residue in each of these receptors and heating the detergent-solubilized mutant to an elevated temperature (∼28–32 °C), cooling to 0 °C, and the amount of correctly folded receptor was determined by a radioligand (either an agonist or antagonist or both) binding assay. In that work by Tate and colleagues, the thermostability of the wild type receptor was taken as 100%, and any mutants that showed 100% or higher ligand binding compared to the wild-type receptor were defined as thermostable. The ROC analysis of this data yielded AUC of 0.66 (Figure D), which shows modest recovery of the thermostable mutants by minimally frustrated residues.

Taken together, these results supported our hypothesis that HF residues are likely associated with GPCR function while MF residues contribute to GPCR stability. It should be noted that many of these residues contribute to both stability and function, but the frustration density shows the extent of leaning toward either stability or function.

We further investigated the location of the structural regions of the HF and MF residues (Figure S3A-F). Four distinct HF clusters of residues emerged: 1) the GPCR:G protein interface, 2) helix 8 (H8), 3) the well-characterized sodium binding site, and 4) three HF residues within the extracellular TM region, located near the orthosteric ligand binding site. The GPCR:G protein interface is well-established as critical for G protein coupling and hence the GPCR activity. Taking a closer examination, we observed that the bottom of transmembrane (TM) helices TM5 and TM6 within this interface contains a higher number of HF density residues compared to other TM helices. Notably, the intracellular (IC) region of TM5 and TM6 connects to intracellular loop 3 (ICL3), which, as shown in previous studies, , plays a key role in GPCR activity and G-protein selectivity. This observation supported our hypothesis that HF residues could be linked to GPCR activity. Such conclusions have been derived in previous studies of frustration in different proteins. Residues in ICL2 were also highly frustrated (Figure A). Due to the higher sequence diversity and difference in length in the loop regions, ICL1, ICL2, and ICL3 lack sufficient common residue positions for a systematic frustration analysis across all GPCRs. Therefore, we assessed each three-dimensional structure individually to evaluate the frustration differences between loop and TM regions (see the Methods section for details, Figure S1). Comparisons revealed that loop residues are generally more frustrated than TM residues, with a higher percentage of HF residues and a lower percentage of MF residues (Figure S3A-F). ICL2 is known to undergo a disorder-to-order structural transition during GPCR activation, so the high percentage of HF residues observed in ICL2 indeed correlates with GPCR activity. Recent studies have shown that helix 8 is critical for GPCR activity and G protein selectivity, − while the sodium binding site is a well-known activation motif in class A GPCRs. The high percentage of HF residues observed in both regions (Figure A) further supports our hypothesis.

Effect of Different Crystallization Conditions and Constructs

To study the effect of the GPCR constructs that were used to stabilize the receptors such as fusion constructs and/or thermostable mutants on the calculated frustration, we have compared frustration calculated for the A2A adenosine receptor in the fusion versus nonfusion constructs and thermostabilizing mutations versus wild type. As shown in Figures S3G and S3H, 60 to 80% of the HF and MF residues are shared across different experimental conditions. For the μ-opioid receptor, we analyzed fusion versus nonfusion constructs, thermostabilized versus wild-type variants, and dimeric versus monomeric forms, as illustrated in Figure S3I–K. Again, 60–80% of the HF and MF residues are shared across different experimental conditions, indicating that these conditions have only a mild effect on the overall protein frustration profile.

To examine if the protein frustration can help assess GPCR models in the absence of experimentally determined structures, we studied a set of biogenic amine receptors using the experimental structures and AlphaFold3 (AF3) models. We studied dopamine receptors (active: D3, PDB ID 7CMV; inactive: D2, PDB ID 5WIU), serotonin receptors (active: 5-HT1E, PDB ID 7E33; inactive: 5-HT2A, PDB ID 7WC9), adrenoceptors (active: β3, PDB ID 9IJE; inactive: β2, PDB ID 2RH1), and histamine receptors (active: H4, PDB ID 8YN9; inactive: H3, PDB ID 7F61). These eight systems have the highest resolution structures within each receptor subfamily. For each receptor, the inactive state AlphaFold models were obtained from UniProt, while the active state models were generated using AF3 on a local GPU cluster. The active state of the AlphaFold models was confirmed by the distance between transmembrane helix 3 (TM3) and TM6, an important marker of class A GPCR activation. GPCR and Gα subunit sequences were retrieved from UniProt, and ligand SMILES representations were downloaded from the Protein Data Bank. For each active state, we generated 10 AF3 models and selected the highest-scoring model for downstream analysis. The overlap of HF and MF residues between the AF3 models and the experimental structures is shown in Figure S3L. Approximately 80% of the HF residues and nearly 90% of the MF residues are shared between the predicted and experimental structures. These findings indicate that AF3 predicted models recapitulate the overall local frustration patterns observed in experimentally determined structures. However, this agreement may not extend to orphan receptors or receptors with limited homology to the GPCRs represented in the Protein Data Bank.

Frustration Patterns in Orthosteric Ligand Binding Sites in GPCRs

Our study thus far suggested that frustration can serve as one of multiple structural features for identifying functionally critical residues in GPCRs. We observed that the GPCR:G protein interface contains more HF residues compared to other regions of the GPCR (Figures E, F). In contrast to the GPCR:G protein interface, the orthosteric ligand binding site showed fewer HF residues in the extracellular region. The orthosteric ligands in class A GPCRs bind in different structural locations, and therefore the number of common residue positions that we could average across class A GPCRs was very low. This variability could explain why we observed fewer HF residues around the orthosteric ligand binding site. Indeed, when analyzing only the adrenoceptor family of GPCRs (Figure G), we observed a higher number of HF residues around the ligand binding site. To overcome the variability in ligand size, we calculated the percentage of HF residues in the binding interface of orthosteric ligands, categorized by their sizes and modalities (Figure H). The TM residues that are not part of any binding interface were used as a control and labeled “TM”. While G-protein interface and peptide ligand interfaces all have a higher percentage of HF residues compared to TM residues, signifying higher frustration in these interfaces, such cannot be easily claimed for small molecule ligands. In fact, small molecule antagonist binding interface is less frustrated than TM. We speculate that this observation may arise because antagonists bind to and stabilize the receptor in an inactive conformation. In contrast, agonists promote receptor activation, which requires greater conformational flexibility. Accordingly, we observe a higher number of highly frustrated residues in the agonist-binding site, which may facilitate the dynamic motions necessary for allosteric communication between the ligand-binding pocket and the G protein coupling interface in GPCRs.

Analysis of Frustration in Structures with Different Ligand Binding Poses

To analyze if different poses of the same ligand in the same receptor give rise to different frustration patterns, we analyzed 31 A2A adenosine receptor structures cocrystallized with antagonist ZM241385 (Table S2). We aligned all of the 30 structures to the reference used with PDB ID: 3EML. The ligand binding pose in the structure, PDB ID: 3PWH, is distinct relative to the other 30 structures (Figure S4A). The residues contacting the ligand were grouped as unique to 3PWH, present only in the other structures (common pose), or shared across all structures. We plotted the average frustration density for the common-pose residues (Figures S4B and S4C), with shaded ranges representing their full variability. The frustration values for the unique pose found in 3PWH are shown as points. Three residues (67, 177, 264) in 3PWH had highly frustrated scores outside the common pose range, and four residues (168, 271, 274, 267) had minimally frustrated scores outside that range. Except for residue 274, these residues showed higher HF and lower MF density values than the common poses, indicating increased local frustration in the alternative binding pose of 3PWH. Overall, the alternative ligand pose in 3PWH is also associated with an elevated level of frustration at several binding-site residues.

Evolutionary Properties of Highly and Minimally Frustrated Residues in GPCRs

If frustration is a functionally significant property, it is likely to be subject to evolutionary constraints. To investigate this, we assessed whether frustration correlates with sequence conservation and coevolution across Class A GPCRs. Using multiple sequence alignment (MSA) of 287 endogenous (without olfactory receptors) human Class A GPCRs, we calculated the conservation score (C_i) based on Von Neumann entropy (S_i) (see Methods). Specifically, for each alignment position, we constructed a density matrix ρ from the relative frequencies of amino acids, incorporating their chemical similarities through the BLOSUM50 similarity matrix. Because the maximum possible entropy in this setup is 1, the conservation score at each position is C _i = 1 – S _i . Applying this methodology to GPCR MSA revealed a substantial difference in average conservation between minimally and highly frustrated residues (Figures A, B). MF residues were approximately 40% conserved, in contrast to only ∼20% for HF residues. This 2-fold increase in conservation for MF residues implies stronger evolutionary constraints.

3.

Sequence conservation and frustration. A. Population density plot of the conservation score of highly/neutral/minimally frustrated residues. B. Mapping of the conservation score for all residues in Class A GPCR alignment. Sets of minimally and highly frustrated residues are highlighted (green and red) and show a higher overall conservation score compared to neutral residues (gray). C. Population density plot of the coevolution score of highly/neutral/minimally frustrated residues. D. Mapping of the coevolution score for all residues in Class A GPCR alignment. Sets of minimally and highly frustrated residues are highlighted (green and red) and show a higher overall coevolution score compared to neutral residues (gray).

Next, we calculated the mutual information-based coevolution scores. Mutual information between two positions in the alignment measures how much knowing the amino acid at one position in the alignment reduces uncertainty about the amino acid at another position. We calculated the coevolution score for all positions in the same MSA (see the Methods section, Figures C, D). HF residues have coevolution scores one standard deviation above average. In contrast, MF residues clustered around average coevolution score values. These findings point to a compensatory or interdependent relationship for HF residues, whereas the elevated evolutionary stability of MF residues (high conservation, lower coevolution) suggests they act as structural “anchors.”

Other Classes of GPCR Show a Similar Signature of Frustration

We extended our study to include class B1 (137 structures, both active and inactive conformations, using the Wootten residue numbering scheme for this class), class B2 (32 structures, Wootten numbering scheme), class C (80 structures, Pin numbering scheme), class D (5 structures, Fungal numbering scheme), and class F (22 structures, Wang numbering scheme) GPCRs. The frustration patterns across these GPCR classes showed trends similar to those observed in class A GPCRs (Figure ).

4.

Location of highly and minimally frustrated residues in different GPCR classes. Frustration profiles were aligned using generic GPCR numbering for each class, Class B1 (Wootten), Class B2 (Wootten), Class C (Pin), and Class F (Wang), and averaged across available structures. HF and MF residues were mapped on representative structures Class B1: 6X19, Class B2: 7WU5, Class C: 7MTS, Class D: 7AD3, Class F: 6XBK. Native ligands are shown as cyan sticks to highlight the position of the orthosteric ligand binding site. On the right, snake plots show HF and MF residues, mapped on representative plots for each class: GLP-1 receptor (Class B1), ADGRF1 (Class B2), mGlu2 receptor (Class C), STE2 receptor (Class D), and SMO receptor (Class F).

The G protein binding sites and helix 8 exhibit high frustration, indicating the functional importance of both regions across all of the GPCR classes. The orthosteric ligand binding sites on the extracellular (EC) side are also highly frustrated, except in class C GPCRs, where their orthosteric binding sites are in the EC domain rather than within the TM bundles. The EC domains and loop regions also exhibit high frustration, reflecting their critical roles in receptor function (Figure S5). For example, the EC domain of the GLP-1 receptor, which facilitates GLP-1 binding, displays high frustration. Similarly, the EC domain of the metabotropic glutamate mGlu2 receptor, known as the Venus flytrap domain, is highly frustrated and essential for glutamate binding and receptor dimerization. , In class D, Ste2 receptor, both the dimerization interface and ligand-binding sites are highly frustrated. Likewise, the EC domain of the Smoothened receptor, which includes a cysteine-rich domain, exhibits high frustration at binding sites for oxysterols, highlighting its role in the Sonic Hedgehog signaling pathway. Finally, the central region of the TM bundle shows lower frustration, as indicated by a higher proportion of minimally frustrated residues.

The Protein–Protein Interface on the Gα Subunit Is Highly Frustrated

The trimeric G protein has three subunits, namely Gα, Gβ, and Gγ. The Gα subunit has multiple subtypes. In this section, we analyze the frustration residue pairs in the Gα subunit of the trimeric G proteins. We began by analyzing the GPCR:Gα interface. Like GPCRs, G proteins have a Common G alpha Numbering (CGN) system, which allows us to align different Gα subtypes (Gα_S, Gα_I/O, Gα_Q/11, and Gα_12/13 for which three-dimensional structures are available) and calculate the average frustration for each aligned residue position. By combining CGN numbering for Gα protein with residue numbering for GPCRs, we identified the frustration residue pairs along the GPCR:G protein interface (Figure A). We observed high numbers of both HF and MF pairs between TM3, TM5, and ICL2 of the GPCR and the H5 helix of the G protein (Figure B).

5.

Residue pairwise frustration in the GPCR:Gα interface. A) A structural overview of the interface between GPCR and Gα. AHD is the all-helical domain of the Gα subunit. The Ras domain of Gα is shown in a gray cartoon. The Gbγ subunits are shown in a pink surface. B) HF (top) and MF (bottom) pairs between GPCR and Gα across all structural regions. C) HF (top) and MF (bottom) pairs between GPCR and the H5 helix of Gα. The thickness of the line reflects the percentage of said pairs occurring in all structures.

Since the H5 helix is known to be critical for Gα coupling to GPCR, we examined the residues forming HF and MF pairs on the 27 amino acids of the H5 helix (Figure C). The HF and MF residues on the H5 helix in the Ga protein are distinct: the middle section of H5 (H5.09-H5.19) contains the HF pairs, whereas the C terminus of H5 (H5.20-H5.26) contains the MF pairs. This observation suggests that the C terminus tip of the H5 helix is likely crucial for providing stability to the GPCR:G protein complex. The middle section of the H5 contributes to selectivity of the Gα couplings. These observations have experimental support from previous studies. −

The Gα subunit of the G protein has four major subfamilies (Gα_S, Gα_I/O, Gα_Q/11, and Gα_12/13) and samples three conformational states: GDP-bound trimer state, GPCR-bound complex state, and GTP-bound monomeric state. We downloaded 637 three-dimensional structures of Gα proteins in monomeric and effector-bound (84), trimeric (3), and GPCR-bound (550) conformations as of August 15th, 2024. We first calculated the frustration density of residues in the Ga subunit in the GDP-bound trimer state. Surprisingly, in the GDP-bound trimer state, which is the “off” state, the H5 helix does not contain any HF residues, even though we observed that residues on H5 are highly frustrated when coupled to GPCRs. Most of the HF residues are found at the interface between the Ras domain and AHD, with additional HF residues located in the Gα-Gβγ interface and other regions along the Gα-GPCR interface outside of H5 (Figure A). The Ras-AHD interface is crucial for nucleotide binding, and it has been shown that the AHD domain demonstrates dynamic motion with respect to the Ras domain during GPCR-dependent activation to enable the nucleotide release and exchange. , These well-established concepts indicate that the Ras-AHD interface is critical for G protein function, so the high frustration observed there aligns with functionality. Similarly, the Gα-Gβγ interface is essential for G protein activity due to the requirement for Gα-Gβγ association and dissociation, agreeing with our observation of the number of HF residues in that region. Multiple studies have shown that G proteins interact with multiple partners (doi:10.1016/j.jbc.2024.105756), including and not limited to, Regulators of G protein Signaling (RGS), Gβγ subunits, adenylyl cyclase, Ric8, and RapGap1a. Given that high frustration is often associated with functional regions and that G proteins engage a diverse set of binding partners (Figure C), we propose that the widespread distribution of highly frustrated residues across G protein domains reflects their role in mediating these multiple interactions and allosteric communication.

6.

Frustration profiles of Gα in Gβγ-bound trimer and high frustration interface characterization of Gα in the three states. A) High frustration (red spheres - left) and minimal frustration (green spheres - right) residues in the Gα subunit in the GDP-bound Gα Gβγ-bound trimer state. B) Venn diagram of the HFRs in three conformational states (GDP-bound trimeric state, GPCR-bound intermediate state, and GTP-bound Gα monomeric state) illustrating the common and distinct HFRs in the three states in Gα_S (left) and Gα_I‑1 (right). C) Alignment of Gα Ras domain with protein effectors of Gα; frustration profile from the GPCR-bound trimer state is shown.

We compared the similarities in distributions of HF and MF residues among the GDP-bound trimer, GPCR-bound complex, and GTP-bound monomeric states in two Gα subtypes, namely Gα_S and Gα_I‑1 (Figures A, B, and S6A). Interestingly, 39 of the HF residues in Gα_S and 40 HF residues in Gα_I‑1 are common to all three conformational states (Figure B). As shown in Figure C, the highly frustrated residues are located on different protein (such as GPCR, Gbγ, RGS, Ric8, adenylyl cyclase) binding interfaces in the Gα subunit, indicating that protein binding interfaces are frustrated. The information on the protein binding interfaces on the Gα subunit was derived from the three-dimensional structures available in the protein data bank on August 15th, 2024.

We then examined the distribution of the HF residues that are common to Gα_S and Gα_I‑1 in the Ras domain structures. We observed a high number of common HF residues in the HG-hgh4-H4 region in both Gα_S and Gα_I‑1 (Figures S6B and S6C, respectively). This region is the hinge of Ras-AHD domain movement and part of the Ras-AHD interface and therefore possesses significant functional importance. The same analysis was also done for the shared MF residues. Similarly, many MF residues were shared among the three states (Figure S6D), and they are located mostly on structured regions (β1, β3, β4, β5, and α3) of the Ras domain of Gα_S and Gα_I‑1 subunits (Figures S6E and S6F, respectively). This implies their importance in structural stability. When comparing frustration in G proteins and GPCRs, a significant difference emerges: the distributions of HF and MF residues were less clearly separated in G proteins. In GPCRs, MF residues were primarily located in the TM bundle, whereas in G proteins, HF and MF residues showed a notable overlap in different structural regions (Figure S6A). One possible explanation for this difference is that G proteins have multiple functions and interact with various downstream proteins. As a result, much of the G protein surface is likely functionally relevant in different contexts, leading to a generally higher level of frustration: we noticed that the Ras domain is more frustrated than the AHD, consistent with its role as the primary functional region of the Gα subunit.

We categorized residues in both GPCRs (Figure S7A) and G proteins (Figure S7B) into polar and nonpolar groups and compared their frustration profiles. Our statistical analysis reveals a consistent trend across both protein types: polar residues exhibit a higher density of highly frustrated residues and a lower density of minimally frustrated residues. Conversely, nonpolar residues tend to be minimally frustrated, consistent with their role in stabilizing the hydrophobic core. Interestingly, these trends remain consistent for both GPCRs (transmembrane proteins) and G proteins (globular proteins). These results support the idea that highly frustrated sites are often enriched with polar or charged residues, which are frequently associated with functional sites rather than with purely structural stability.

Application of Frustration in Identifying Allosteric Modulator Sites in GPCRs

Allosteric modulators are sought after in GPCR drug design, yet remain a challenge. These modulators bind to allosteric sites and either enhance (positive allosteric modulators, PAMs) or reduce (negative allosteric modulators, NAMs) the pharmacological properties of the orthosteric ligands. To investigate whether residue frustration density can be used to identify such sites, we used all available class A GPCR structures containing PAMs or NAMs from GPCRdb.org and clustered the PAM and NAM binding sites based on the geometric center of the ligand heavy atoms. This analysis revealed six locations of the binding sites for PAMs and four for NAMs (Figures S8A and S8B). When examining those binding sites on structures without PAM/NAM bound, we found that PAM binding sites contain a higher percentage of HF residues and NAM binding sites have a lower percentage of HF residues than the TM region (Figure A). The TM region is defined as the region in the transmembrane domain that does not contain the binding sites. This observation is like that of agonists and antagonists shown in Figure H. Additionally, each PAM/NAM binding site contains several HF residues (Figures S8A and S8B). We observed a similar trend for the PAMs and NAMs in other GPCR classes (Figure S8C). This finding further supports the use of frustration as one of the multiple structural properties for identifying potential allosteric ligand-binding sites in GPCRs. Next, we analyzed how allosteric modulator sites can be identified by using the structure with no allosteric modulators bound to the receptor. Such information will be useful for the design of allosteric modulators for GPCRs.

7.

Predicting GPCR allosteric modulator binding sites using frustration. A) Mean of the percentage of HF residues in PAM, NAM, and Cholesterol endogenous modulator binding sites. G-protein binding sites and TM regions are used as positive and negative controls, respectively. Statistical comparisons were performed using Welch’s t test (G-protein vs PAM, p = 0.956; Cholesterol vs TM, p = 9.12 × 10^–102) and two-sided Mann–Whitney U test (PAM vs NAM, p = 0.015; NAM vs TM, p = 0.022). Error bars represent SEM. B) Schematics of applying frustration to identify true PAM/NAM binding sites. C) The workflow to identify GPCR PAM/NAM sites using frustration. D) Ranking of true PAM and NAM binding sites (for all class A GPCRs where structures with PAM and NAM are available) among all putative binding pockets in the TM regions. The Y-axis reports the transformed score 1 – percentile rank, such that higher values indicate higher-ranking (more top-positioned) binding sites. E) In the D1 structure (PDB ID: 7JOZ), the known PAM binding site is the most frustrated among all putative binding sites in the TM regions. All putative binding sites discovered by Fpocket are shown as spheres and colored by their mean HF density.

As a case study, we compiled all Class A GPCRs with known PAM or NAM coresolved in the structures. We used the structures without the modulator for the frustration analysis to identify potential sites, while the structures with the modulator bound were used for validation. These receptors also have three-dimensional structures without the modulators. The GPCRs with known PAMs include human CB1R, FFAR1, D1R, GPBA, HCA2, M2AChR, M4AChR, MRGPRX1, TSH, β2AR, NTSR1, and rat NTSR1, while those with known NAMs include human C5a1R, CB1R, M1AChR, and β2AR. We collected all active-state structures without PAMs and all inactive-state structures without NAMs. We developed a protocol to identify a modulator binding site as enumerated below (Figures B, C):

• 1.Potential ligand binding sites were identified in each three-dimensional structure using the fpocket algorithm.
• 2.The mean HF density of all residues in a binding pocket for each putative ligand binding site was calculated.
• 3.The putative binding sites for each structure were ranked from the most to the least frustrated.

We observed that the true PAM binding site ranks second by the average HF density in the case of the b2AR. However, the correct PAM binding site falls within the top quartile of the average HF density distribution, and the NAMs site falls within the last quartile of the average HF density (Figures D, E). This suggests that frustration can be used in identifying PAM/NAM binding pockets, which, followed by virtual ligand screening in these sites, could aid modulator design.

Several studies have shown that cholesterol has both direct and indirect effects on stabilizing GPCR conformational states. We analyzed the frustration of the residues in the cholesterol-binding site of those GPCRs for which we have structures with cholesterol bound (Table S3). As shown in Figure A, the cholesterol binding sites are less frustrated than the PAM or NAM sites.

Discussion

Previous studies of energetic frustration have shown that highly frustrated residues are frequently located at active sites in proteins. Here, we leverage the vast database of published GPCR structures to demonstrate that protein frustration can also identify sites of interaction with ligands and G protein heterotrimers. Interestingly, protein frustration reveals high frustration not only in the orthosteric ligand-binding site but also in the allosteric sites, which are not sites of action of the endogenous ligands. Our study demonstrates that evolution might have optimized residues at protein–protein interfaces to be passivated by the coupling interaction. In parallel, we find that protein frustration is a helpful tool to facilitate interactions in engineered complexes to enhance the efficiency of molecular degraders that operate at these non-native interfaces. Hence, protein frustration serves as an accessible tool to evaluate the chemistry of engineered interfaces to facilitate complexation.

In this study, we computed residue-level frustration for over 1200 GPCRs and their complexes with G proteins. Our analysis revealed that highly frustrated residues cluster predominantly at the G-protein-coupling interface and ligand-binding sites of GPCRs. Our calculated results were validated experimentally using the mutations of these highly frustrated sites affecting G protein coupling. This was established by correlating frustration scores with experimentally measured coupling strengths using bioluminescence resonance energy transfer (BRET) assays. In contrast, minimally frustrated residues are predominantly located within the central regions of transmembrane helices. These residues contribute to receptor stability and align well with the thermostability experimental data. Moreover, minimally frustrated residues tend to be more evolutionarily conserved than highly frustrated ones, whereas highly frustrated residues exhibit greater coevolutionary values.

Our findings suggest that analyzing frustration from static structural snapshots can serve as a powerful approach to identifying novel druggable allosteric sites in GPCRs. Interestingly, agonist binding sites show a higher density of highly frustrated residues compared with antagonist sites, potentially allowing greater flexibility to facilitate the conformational changes required for receptor activation.

Analysis of the Gα subunit of trimeric G proteins regardless of subtype (Gα_S, Gα_I/O, Gα_Q/11, and Gα_12/13) or activation state (“on”/“off”) revealed multiple clusters of highly frustrated surface residues. These clusters coincide with known interfaces for a range of effectors, including Gβγ, GPCRs, RGS proteins, Ric8, and adenylyl cyclase. Within the H5 helix, which is a critical structural element for GPCR coupling, we observed that minimally frustrated residues at the helix tip may stabilize GPCR binding, while highly frustrated residues midhelix could act as a lever to facilitate nucleotide exchange by modulating the opening and closing of the binding site. This dynamic behavior has been previously described in molecular dynamics simulations. In conclusion, our work underscores the value of understanding residue-specific energy landscapes in protein complexes. Such insights can inform novel strategies for designing therapeutics that target dynamic protein–protein interfaces.

Pitfalls of the Approach

Several methodological limitations should be considered when interpreting the results of this study. First, the structural coverage of GPCRs in the Protein Data Bank remains heavily biased toward class A receptors. The limited availability of experimentally resolved structures for class B, class C, class D, and class F in comparison to class A GPCRs limits the generalizability of frustration-based analyses for these subfamilies. As additional structures from underrepresented GPCR classes become available, future studies will be needed to determine whether the frustration patterns identified here remain true across the broader GPCR superfamily. Second, the number of available structures cocrystallized with PAMs or NAMs also remains limited. This constrains our ability to systematically evaluate how allosteric modulators shape the frustration landscape of the GPCRs. Without matched sets of modulator-bound and modulator-free structures, it is difficult to decouple allosteric effects on local frustration from conformational heterogeneity arising from differences in crystallization conditions, receptor constructs, or resolution. Expanding this analysis as more PAM- and NAM-bound structures are deposited will be an important direction for future work.

Third, the software we used to calculate residue-based frustration, Frustratometer, uses a coarse-grain force field AWSEM that does not take into account the effect of ligand or the protonation states of amino acids. Please note that this could affect the level of frustration in the residues near the ligand binding sites. However, since we are comparing frustrations between GPCR structures, we expect that the conclusions from this study will not be impacted. The combination of protein frustration analysis and other computational methods that offer all-atom-level resolutions will provide a more comprehensive understanding of protein function and stability.

Materials and Methods

Frustration Calculation via FrustratometeR

FrustratometeR was downloaded and installed on the local cluster from the GitHub repository (https://github.com/proteinphysiologylab/frustratometeR) in a Conda environment. Mutational frustration was calculated for each structure with a R submission script, with all other parameters set to default. Briefly, in the FrustratometeR procedure, each amino acid pair is mutated in silico to all other amino acids and the energy distribution for all the mutated pairs (decoy pairs) is calculated with respect to the energy of the wild type pair. The wild type residue pair energy is subsequently converted into a z-score ( $zscor{e}_{wildtype}=\frac{E_{wildtype}-\mu }{\sigma }$ , where μ and σ are the mean and standard deviation of the decoy energy distribution, respectively). The z-score is a measure of the wild type contact energy relative to all other amino acid substitutions at these residue positions, and hence an estimation as to whether a residue is in an energetically optimal or suboptimal state. The results included two files: [pdb].pdb_mutational, which is the pairwise frustration data, and [pdb].pdb_mutationa_5adens, which is the frustration density of each residue within 5 Å. Both were then parsed using in-house scripts for further analyses.

The frustration level of a protein–protein interface is defined as $PPIFrustration(\%)=\frac{n_{frust}}{n_{total}}\times 100\%$ , where n _frust is the number of highly or minimally frustrated interface pairs, and n _total is the total number of residue pairs in the interface.

GPCR Structure Information

A total of 1283 GPCR structures were collected from GPCRdb (https://gpcrdb.org/) for analysis, including 1007 class A, 137 class B1, 32 class B2, 80 class C, 5 class D, and 22 class F GPCRs (Table S1). This data set includes 850 active-state GPCR structures bound to either G protein (680) or arrestin (13) and 410 inactive-state structures bound to antagonists (232) or inverse agonists (48). Species and chain information was retrieved from GPCRdb (https://gpcrdb.org/structure/) using the Structure API. PDB structure files were downloaded on August 15, 2024.

G Protein Structure Information

A total of 636 Gα structures were collected from GproteinDB (https://gproteindb.org/) for analysis, including 3 Gα-Gβγ trimer, 25 Gα monomer, 57 Gα-effector complex, and 551 GPCR:Gα:Gβγ complex. Structures that were labeled to have chimeric Gα were excluded. These structures are grouped based on Gα states into GPCR:Gα complex (551), Gα-Gβγ trimer (3), and Gα monomer (82). Species and chain information was retrieved from RCSB (https://www.rcsb.org/) using the REST API.

B Factor Calculation per Residue

To compare the HF density of each residue with the B factor, we calculated the per residue B factor. For each residue, the B-factors of all heavy atoms obtained from the PDB structures were averaged, and the resulting mean value was used as the B-factor of the residue. To assess the quality of the downloaded structures, and whether structural quality can affect frustration, we plotted the density distribution of B factor against both HF density and MF density (Figures S9A, S9B). We calculated the Spearman’s ρ value between high frustration (Figure S9A) and minimal frustration (Figure S9B) per residue. Highly frustrated residues showed a moderate positive correlation with B-factors (ρ = 0.383, p < 0.001), whereas minimally frustrated residues exhibited a moderate negative correlation (ρ = −0.502, p < 0.001). The stronger correlation observed for minimally frustrated residues likely reflects the fact that both minimal frustration and low B-factors could come from structural stability. In contrast, the association between high frustration and elevated B-factors is weaker. While conformational flexibility can contribute to increased B-factors, it is not their sole determinant. Elevated B-factors may also arise from factors unrelated to frustration, such as crystal packing effects, partial disorder, or crystallization conditions. As a result, not all residues with high B-factors are expected to exhibit high frustration.

Contact Analysis

We employed “get_static_contacts.py” module from GetContacts (http://getcontacts.github.io/) for contact analysis. The output TSV file was further processed using in-house code to retrieve the residues lining up the interface. Briefly, given the chain ID of interest, the entity containing the chain was kept in each row; the residue number was extracted from the entities, from which a unique list was created.

GPCR:Gα Frustration Pairs

Class-A-GPCR:Gα complex data were used in this analysis. Frustration pair information was parsed from [pdb].pdb_mutational files. Pairs made between GPCR and Gα that are classified as either highly or minimally frustrated were kept for analysis. Residues of each structure were first converted to BW and CGN for GPCR and Gα, respectively. A super set of contacts was collected and grouped by the contacts’ structural regions, according to BW and CGN. The plot was generated using the Python Matplotlib.pyplot package. The frequencies of each contact present were calculated and used as the width of lines.

Per-Residue Frustration Density, Mean Residue Frustration Density, and Mean Region Frustration Density Calculation

The per-residue frustration density ρ _i was computed as

$${\rho }_i^X=\frac{n_i^X}{n_i^H+n_i^N+n_i^M}$$ 1

where each residue i interacts with residues within a 5 Å sphere (n _i ), generating frustrated pairs categorized as highly frustrated (n _i ), neutrally frustrated (n _i ), or minimally frustrated (n _i ). The frustration type is denoted by X ∈ {H, N, M}. For GPCR per-residue frustration density, frustration profiles were aligned using generic GPCR numbering specific to each class: Class A (Ballosteros-Weinstein), Classes B1 and B2 (Wootten), Class C (Pin), Class D (fungal²⁶), and Class F (Wang). For G protein per-residue frustration density, Common G protein Numbering (CGN) was employed for alignment.

The mean residue frustration density η _i representing the frustration of a GPCR or G protein residue across s PDBs was computed as

$$\begin{array}{c}{\eta }_i^X=\frac{1}{S}\sum _{s=1}^S{\rho }_i^X(s)\end{array}$$ 2

where the per-residue frustration density ρ _i is averaged across S structures. For GPCR calculation, per-residue frustration densities for each generic GPCR number were extracted from individual PDBs, and their mean value was calculated to represent the mean residue frustration density for that generic GPCR number. For G protein calculation, per-residue frustration densities for each CGN were extracted from individual structures, and their mean value was calculated to represent the mean residue frustration for that CGN.

Quartile analysis was performed for each GPCR class, and generic GPCR residues in the top quartile for high and minimal frustration were plotted onto representative structures in PYMOL. Quartile analysis was done on the GPCR:Gα complex, Gα-Gβγ trimer, and Gα monomer groups separately, and CGN positions in the top quartile were plotted onto the representative structures in PYMOL.

The mean region frustration density η _R , representing the frustration of a GPCR structural region R across S structures, was computed as

$$\begin{array}{c}{\eta }_R^X=\frac{1}{S}\sum _{s=1}^S\left(\frac{1}{|R|}\sum _{i\in R}{\rho }_{i,s}^X\right)\end{array}$$ 3

where we compute the mean frustration density for a region R in each structure S, denoted as η _R,s , by averaging the frustration densities ρ _i,s of all residues i in the region R. Here, |R| represents the total number of residues in region R. We then compute η _R by averaging η _R,s over the available S structures. A graphical representation of the schematics is depicted in Figure S1.

Common Highly Frustrated Residues in Different Gα States

The top quartile of most frustrated CGN positions was collected from the GPCR:Gα complex, Gα-Gβγ trimer, and Gα monomer groups. Only G_I‑1 and G_S subtypes have trimer structures, and therefore we only included structures of these two subtypes. CGN positions from HN helix and AHD regions were removed from the pool, because most GPCR:Gα complex structures do not have AHD regions, and most Gα monomer structures do not have an HN helix. The Venn diagram was plotted using the Python matplotlib_venn package. Then, common highly frustrated GCN positions were grouped by the structural regions. The radial plots were created using the Python Matplotlib.pyplot package using polar coordinates. Results from contact analysis were incorporated to plot the contacting region outer rings. If one GCN position from a structural region is in an interface, then the region is considered part of the interface.

Allosteric Modulator Binding Pocket Identification and Clustering

The structures of class A GPCRs containing resolved PAM or NAM were collected and fed into the Python environment via the MDAnalysis package. For each structure, the coordinates of allosteric modulator heavy atoms were extracted, and the geometric center of the modulator was calculated using NumPy. The geometric centers of all available PAMs and NAMs were clustered separately by using K-mean clustering in the SciPy package. The optimal number of clusters fed into the K-means algorithm was determined by minimizing the within-cluster sum of squares.

Defining Interface Residues in Apo Structures

Bound structures of the same GPCR and same state (active: agonist-bound, inactive: antagonist-bound) were used for defining interface residues in the apo structures.

Interface Residue Polarization Analysis

For amino acid polarization analysis, residues were classified as polar [R, N, D, Q, E, H, K, S, T, Y] or nonpolar [A, C, G, I, L, M, F, P, W, and V] based on their side chain properties.

Coevolutionary Analysis

We employed mutual information, an information-theoretic measure, to detect potential coevolutionary, structural, and functional connections between pairs of alignment sites. Given a multiple sequence alignment of n sequences and p positions, the coevolutionary score is derived from calculating the mutual information between positions according to

$$\begin{array}{c}I(X,Y)=\sum _{x\in X}{P}_{X,Y}\sum _{y\in Y}\log \frac{P_{X,Y}(x,y)}{P_X(x)P_y(y)}\end{array}$$ 4

Here, P _X (x) is the probability of observing an amino acid X at position x in the alignment, and P _X,Y (x, y) is the joint probability of seeing an amino acid X at position x together with amino acid Y at position y. To highlight key interactions, the Z-score for positions x and y is then determined as

$$\begin{array}{c}{Z}_{XY}=\frac{I_{XY}-⟨I⟩}{{\sigma }_{XY}}\end{array}$$ 5

Once the coevolutionary scores for all position pairs have been computed using eqs and , we condense these pairwise values into a single cumulative Z-score for each residue and rank them in descending order. Our premise is that residues exhibiting high Z-scores play important structural or functional roles, whereas those with lower Z-scores could be essential to the receptor stability. We obtained the MSA of 287 human class A GPCR sequences for this step from GPCRdb (https://gpcrdb.org).

Conservation Analysis

For the conservation analysis, we used an MSA of 287 human class A GPCR sequences, obtained from the GPCR database (https://gpcrdb.org/). We computed a conservation score C _i using Von Neumann entropy S _i that incorporates chemical similarities among amino acids to yield a more robust metric of conservation across the alignment

$$\begin{array}{c}{S}_i=-\sum {\lambda }_i{\log }_{20}{\lambda }_i\end{array}$$ 6

where λ _i is the eigenvalues of ρ, a density matrix based on the relative frequencies P(Y) of amino acids at each position in combination with a similarity matrix (BLOSUM50):

$$\begin{array}{c}\rho =\mathrm{diag}(P(A),P(B),\mathrm{...},P(Y))\times \end{array}$$ 7

The final conservation score is found by subtracting the entropy from the maximum possible value, 1. Thus, C _i = 1 – S _i .

The PDB IDs used in this study are available in the Supporting Information. The raw FrustratometeR results generated in this study are openly available on Zenodo (DOI 10.5281/zenodo.16740185). The scripts used in structure retrieval, FrustratometeR job submission, and analyses are openly available on GitHub (https://github.com/Wenyuan-Wei/frustration_manuscript_script_lib).

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.6c00203.

• Method schematics, visualization and statistical distribution of HF and MF of additional quartiles of residues, A2AR ligand pose analysis, visualization of HF and MF residues in other states of G protein, polarity distribution of Class A GPCR, visualization of PAM/NAM binding site, method validation, and the PDB IDs of structures used for analyses in the manuscript, A2AR ligand pose analysis, and cholesterol binding site analysis (PDF)

⊥.

W.W., R.D.M., and T.Y. contributed equally to this work.

W.W.: data curation, formal analysis, investigation, software, validation, visualization, writing-original draft, writing-review and editing. R.D.M.: data curation, formal analysis, investigation, software, validation, visualization, writing-original draft, writing-review and editing. T.Y.: data curation, formal analysis, investigation, software, validation, visualization, writing-original draft, writing-review and editing. E.M.: data curation, formal analysis, investigation, software, visualization. I.R.S.: formal analysis, investigation, software. V.S.: supervision, funding acquisition. S.B.: supervision, validation, funding acquisition. A.S.R.: supervision, validation, funding acquisition. S.S.: supervision, validation, funding acquisition. N.M.: formal analysis, software, conceptualization, supervision, validation, writing-original draft, writing-review and editing. N.V.: conceptualization, supervision, resources, funding acquisition, writing-review and editing.

The authors declare no competing financial interest.