Differential Contribution of Transmembrane Domains IV, V, VI, and VII to Human Angiotensin II Type 1 Receptor Homomer Formation*

G protein-coupled receptors (GPCRs) play an important role in drug therapy and represent one of the largest families of drug targets. The angiotensin II type 1 receptor (AT1R) is notable as it has a central role in the treatment of cardiovascular disease. Blockade of AT1R signaling has been shown to alleviate hypertension and improve outcomes in patients with heart failure. Despite this, it has become apparent that our initial understanding of AT1R signaling is oversimplified. There is considerable evidence to suggest that AT1R signaling is highly modified in the presence of receptor-receptor interactions, but there is very little structural data available to explain this phenomenon even with the recent elucidation of the AT1R crystal structure. The current study investigates the involvement of transmembrane domains in AT1R homomer assembly with the goal of identifying hydrophobic interfaces that contribute to receptor-receptor affinity. A recently published crystal structure of the AT1R was used to guide site-directed mutagenesis of outward-facing hydrophobic residues within the transmembrane region of the AT1R. Bioluminescence resonance energy transfer was employed to analyze how receptor mutation affects the assembly of AT1R homomers with a specific focus on hydrophobic residues. Mutations within transmembrane domains IV, V, VI, and VII had no effect on angiotensin-mediated β-arrestin1 recruitment; however, they exhibited differential effects on the assembly of AT1R into oligomeric complexes. Our results demonstrate the importance of hydrophobic amino acids at the AT1R transmembrane interface and provide the first glimpse of the requirements for AT1R complex assembly.

and VII (respectively) facilitate receptor activation (16,17). Little information has been derived from the crystal structure in relation to potential oligomeric domains. To identify some of the regions required for homomerization of the AT1R, sitedirected mutagenesis was performed on hydrophobic amino acid residues identified as facing toward the lipophilic environment and expressed within the transmembrane region. Expression of mutated constructs of these residues either in combination or individually was used to assess their contribution to AT1R-AT1R affinity as measured by bioluminescence resonance energy transfer. Our experiments suggest that various transmembrane domains contribute to the homomerization of AT1R.

Results
Selection of Amino Acids for Mutagenesis-Accessible surface area (ASA) is defined as the area of the molecular surface that is in contact with solvent. This unit of this measurement is square angstroms. The concept of accessible surface area provides a quantitative definition of the exterior and interior of proteins and other macromolecules. The fractional surface ASA is calculated by comparing the accessible surface area against a table that lists average areas and provides an intrinsic measure of hydrophobicity. Fractional ASA was measured using the web server VADAR. Visual inspection of the AT1R structure was used to determine a fractional ASA threshold that would identify amino acid residues oriented toward the phospholipid environment in the transmembrane region (TM). Some amino acids within TMs IV to VII with a fractional ASA greater than 0.3 were selected for mutagenesis (Fig. 1). Variations in observed fractional ASA between the two models could be explained by variations in the crystal structures, as explained in Zhang et al. (15), where they performed a comparison of the two crystal structures. The amino acids selected were highly hydrophobic. We focused on TMs IV to VII, based on literature showing the involvement of these TMs in the formation of oligomers of several other GPCRs. For example, it has been proposed that TM IV could act as a hinge in the ␦ opioid receptor, whereas TM V was involved in the dimerization of ␤1AR, M3R, and CXCR4 (18).  TM IV is highly accessible to the phospholipid environment with ϳ70% of amino acids in this region exceeding a fractional ASA of 0.3 (Fig. 1A). A combination of 5 amino acids found in TM IV were selected for mutagenesis. The combination of mutations was selected based on the orientation of each amino acid side chain in respect to one another with the idea to mutate different planar views. Two orientations are possible for TM IV, either facing TM III or facing TM V. An isoleucine at position 150 and a leucine at position 154 mutated into alanines were selected to represent the TM III-facing orientation, while mutations of the isoleucine 151 and leucines 155 and 158 into alanines were selected for TM V-facing orientation of TM IV. Finally, one amino acid from each face was also selected to form an AT1R mutant receptor where both TM IV faces would be partially mutated. Residues 154 and 158 were mutated into alanines.
The crystal structure of the AT1R is missing several partial side chains in TM V, so we used SCWRL (19) to optimize the side chains for the incomplete TM V region. Based on this optimization, TM V also presents at least 60% of its amino acids, showing a fractional ASA higher than 0.3 (Fig. 1B). Three of these amino acids were selected for mutagenesis based of their hydrophobicity, their orientation toward the lipid environment, and central location within the TM. Thus, Leu 202 , Phe 206 , and Ile 210 were mutated to alanines.
Approximately 25-30% of TMs VI and VII residues exhibit a fractional ASA higher than 0.3, and some residues within these regions with high ASA facing toward the lipid environment were mutated. Interestingly, several amino acids in TM VI (Leu 247 , Phe 251 , and Ile 250 ) showed symmetry with hydrophobic residues in TM VII (Ile 286 , Phe 293 , and Leu 297 ), and these residues were selected for mutagenesis into alanines (Fig. 1, C and D). Graphical representation of the amino acids mutated within the AT1R crystal structure is found in Fig. 2.
Total and Cell Surface Expression Levels Are Similar between WT and Mutant AT1Rs-In preparation for BRET 2 experiments, each mutant and WT AT1R construct was tagged with a C-terminal GFP 10 or Rluc2. This also provided an opportunity to assess overall receptor expression. Using transiently transfected HEK293A cells, receptor expression was quantified as net GFP 10 fluorescence and Rluc2 luminescence. Net values were defined as total emission minus the emission of a pcDNA3.1 control. Upon excitation, there was no significant difference between the net fluorescence of the GFP 10 -tagged WT AT1R and each tagged mutant receptor construct (Fig.  3A). Similar results were obtained with Rluc2-tagged constructs (Fig. 3B). We also quantified cell surface expression of each receptor using On-Cell Western TM analysis. Similar levels of cell surface expression were observed between the WT and each mutant receptor (Fig. 3C). The ability of each receptor to induce inositol phosphate-1 (IP1) production in response to a fixed concentration of angiotensin II (Ang II) was used as a functional indicator of cell surface expression. Each of the WT and mutant receptor constructs produced a similar level of IP1 in the presence of Ang II (Fig. 3D). Together, these results indicate that the mutations had no effect on receptor expression at the cell surface.

Receptor Mutants Have an Arrestin Recruitment Profile
Similar to That of the WT AT1R-In addition to quantifying overall receptor expression, we sought to characterize whether or not each GFP 10 -tagged receptor construct was responsive to Ang II. To quantify Ang II-induced ␤-arrestin1 recruitment, a BRET 2 experiment was developed using a ␤-arrestin1 construct that was tagged with a C-terminal Rluc2. A fixed amount of each GFP 10 -tagged receptor construct was co-transfected with ␤-ar-restin1-Rluc2 in HEK293A cells, and arrestin recruitment was quantified in the presence of increasing concentrations of Ang II. A sigmoidal dose-response curve was produced for each receptor construct (Fig. 4). Each mutant receptor also displayed dose-response parameters (E Min , EC 50 , and E Max ) that were similar to the WT AT1R-GFP 10 construct (Table 1). Here, the same WT AT1R-arrestin curve was displayed in all panels for comparison purposes. These experiments indicate FIGURE 2. Ribbon diagrams of AT1R exposing mutated residues. Ribbon diagrams based on the AT1R crystal structure are depicted showing the TM residues that were mutated. Each TM and exposed residue is color-coded following this legend: TM I (gray); TM II (magenta); TM III (yellow); TM IV (blue) (Ile 150 and Leu 154 (cyan); Ile 151 and Leu 155 (blue); Leu 158 (black)); TM V (Leu 202 , Phe 206 , Ile 210 ) (red); TM VI (Leu 247 , Phe 251 , Ile 258 ) (green); TM VII (Ile 286 , Phe 293 , Leu 297 ) (orange). Mutated residues are shown for TM IV (A), TM V (B), TM VI (C), and TM VII (D). FEBRUARY 24, 2017 • VOLUME 292 • NUMBER 8 that each mutant receptor is functional and expressed at the cell surface, also suggesting that the receptor constructs are folded properly.

AT1R Homomer Formation
Mutation of Selected Outward-facing Residues Attenuates Receptor-Receptor Affinity-BRET 2 saturation experiments were designed to quantify receptor-receptor affinity. As mentioned under "Experimental Procedures," WT AT1R-Rluc2 were held constant while AT1R-GFP 10 levels varied. Using a non-linear regression (one-phase decay), B max and K D determinations were taken as the BRET max and BRET 50 , respectively. The GFP 10 -tagged AT1R mutants from TM IV were then paired with WT AT1R-Rluc2, and their BRET max and BRET 50 were measured ( Table 2). Mutations of residues Ile 150 and Leu 154 (facing toward TM III) (Fig. 5A) and mutations of residues Ile 151 , Leu 155 , and Leu 158 from TM IV (facing toward TM V) both led to an increase in BRET 50 , but did not affect BRET max values (Fig. 5B). Combination of mutations from each face of TM IV (Leu 154 and Leu 158 ) also affected BRET 50 values, but did not change the BRET max (Fig. 5C).
TM V mutant at residues Leu 202 , Phe 206 , and Ile 210 (Fig. 5D) and TM VI mutant at residues Leu 247 , Phe 251 , and Ile 258 (Fig.  5E) also increased BRET 50 values, but did not alter the BRET max when combined with WT AT1R in BRET experiments. Muta-tion of residues Ile 286 , Phe 293 , and Leu 297 ( Fig. 5F) resulted in an increased BRET 50 , and the BRET max values, although not significantly altered, showed a trend toward decreased BRET max values. Here, the same WT AT1R curve was displayed in all panels for clarity and comparison purposes. A potassium ion channel known as hERG was tagged with GFP 10 and used as negative control as it can be assumed that it does not interact with the AT1R.
Our data suggest that mutations in TM IV, V, VI, or VII alone are not sufficient to completely disrupt the AT1R-AT1R interaction. We therefore proceeded to combine different mutants from various TMs to determine whether disruption of the potential interaction sites of two TMs would disrupt BRET between AT1R receptors. We first tested the combination of mutant Ile 151 , Leu 155 , and Leu 158 from TM IV (facing TM V) and TM V mutant Leu 202 , Phe 206 , and Ile 210 . Our results suggest that, in contrast to what was observed with each mutant receptor when paired with WT AT1R, BRET max values were altered by ϳ50% with this combination (Fig. 6A). When the same TM IV mutant was combined with either TM VI or TM VII mutants, the BRET saturation curves adopted a linear trend similar to the hERG-GFP 10 negative control, suggesting that the interaction was completely abolished. Combination of TM  V with either TM VI or TM VII also inhibited the generation of a BRET signal, suggesting that combinations of mutations within the TM IV/V face with the TM VI/VII face are sufficient to disrupt AT1R homomerization. Similar results were obtained by co-immunoprecipitation of these constructs (Fig. 6B). Combination of mutations within TMs IV and V would likely disrupt only one side of all potential receptor interfaces and lead to partial disruption of AT1R-AT1R homomerization.

Discussion
GPCRs form one of the largest classes of drug targets in a variety of diseases ranging from depression to heart disease and cancer. Despite their important role, it has been difficult to obtain crystal structures of these receptors. Currently, less than 5% of all GPCRs structures have been resolved. This shortcoming is compounded by a general lack of knowledge about oligomeric structures. Only a handful of crystal structures exist for receptor homodimers such as for the -(21) and -opioid (22) receptors, ␤1AR (23), and CXCR4 (24).
Arrestin recruitment is often used to demonstrate GPCR activation. As an extracellular ligand, Ang II stimulates ␤-arrestin1 recruitment to the AT1R. Our data show that specific mutations within TMs IV to VII of the AT1R do not impact ␤-arrestin1 recruitment to the receptor. This also indicates that the mutant receptors we examined are functional and expressed at the cell surface.
Despite the emergence of a three-dimensional crystal structure of the AT1R (14), little is known about the structural requirements for AT1R homomer formation. In previous studies,   Values are represented as the mean Ϯ S.E. and are each compared with WT AT1R (n ϭ 6; *, p Ͻ 0.05; **, p Ͻ 0.05; two-tailed, unpaired t test).

AT1R Homomer Formation
FEBRUARY 24, 2017 • VOLUME 292 • NUMBER 8 peptides representing transmembrane segments of receptors have been utilized to compete for protein-protein interactions involving that segment. Up to now, studies have shown an important role for various combinations of TMs IV to VIII in the dimerization of receptors such as -opioid receptor, ␤1AR, M3R, and CXCR4, among others (21,(23)(24)(25). For the AT1R, one study showed previously that an AT1R TM IV peptide could partially disrupt AT1R-AT1R and AT1R-secretin receptor BRET (26). In another study, mutation of TM IV did not have any effect on homodimerization of AT1R, evaluated by intact receptor BRET (27). The authors suggested that receptor complexes can be formed through individual monomers, monomers associating with dimers, dimers associating with dimers, and perhaps even more complex forms. Within any of these complexes, there is also the possibility of having various distinct interfaces between the interacting partners.
In this study, we utilized mutation of individual TMs or combination of various TMs to evaluate their effect on AT1R homomerization. TM IV has been at the heart of the studies of AT1R dimerization up to now. Within the TM IV helix, amino acids can prominently be exposed toward the lipid environment in two separate orientations: facing TM III, or facing TM V. We designed constructs that would mutate each face individually, and one where residues from each face would be mutated. Our results tend to confirm that any of the faces of TM IV alone or the mutation of both TM IV faces is not sufficient to completely disrupt homomeric AT1R interactions. This does, however, lead to a significant increase in BRET 50 and, therefore, a decrease in homomer affinity.
Mutations in other individual AT1R TMs (TM V to TM VII) are not sufficient to completely disrupt homomeric interactions as BRET max values were unchanged, but our results suggest that they do have some involvement in the AT1R-AT1R interaction. BRET 50 values were significantly increased in the presence of all of the mutations that were examined, which indicates that there is a reduction in AT1R-AT1R affinity. Combinations of constructs exhibiting mutations in two different TMs were able to significantly change the BRET values achieved. The TM IV/TM V combination of mutations leads to an increase in BRET 50 between the AT1R homomer partners, again suggesting a reduction in homomer affinity. However, combinations of AT1R TM IV/TM VI, TM IV/TM VII, TM V/TM VI, and TM V/TM VII all abolished AT1R homomer formation as they produced a linear BRET 2 saturation curve that was similar to the negative control. Based on the crystal structure information available for the AT1R (Fig. 7) and other GPCRs, it appears that different TMs could associate together to form single, asymmetrical interaction interfaces. Based on our results and interpretation of the results from other groups, it is possible to extrapolate that at least two faces could be involved in AT1R homomer formation, where TM IV/TM V could represent one planar side, while TM VI and TM VII could represent another interface (Fig. 7, continuous lines). It is also possible that TM I and TM IV could shape another interface, as suggested by a previous study where TM I and TM IV disrupted AT1R receptor-receptor interactions (26). Finally, it could be possible that a fourth face consisting of TMs I and VII could exist (Fig. 7, dashed lines), although no experimental evidence of this has been reported yet. Because homomerization required mutation in at least two different TMs to eliminate the BRET signal, it is possible that AT1R homomers form higher order oligomers, as suggested by the fact that combination of mutations in non-adjacent TMs, in different planar views (such the TM IV/TM VI or TM IV/TM VII combinations), could limit the interaction. However, at this point, it is impossible for us to determine the exact number of protomers involved in these AT1R homomer complexes. The AT1R has a central role in the treatment of cardiovascular disease and is involved in a multitude of pathological conditions. However, the realization that this GPCR forms oligomeric complexes has complicated our understanding of AT1R pharmacology. Characterization of the basic structural requirements for the formation of such complexes will help further our understanding of AT1R oligomerization. This work provides fundamental information about how these receptors can be targeted and modulated for the formation of specific receptor complexes based on their structural organization.
Mutant Candidate Identification-Protein Data Bank (PDB) entries 4YAY (14) and 4ZUD (15) were processed using SCWRL4 (19) to obtain backbone-dependent rotamer librarybased side chain atom positioning for residues that were not fully resolved crystallographically. Of the regions analyzed, this affected only TM V. The web server VADAR 1.8 (28) was used to measure the fractional ASA of the side chain. Fractional ASA is normalized relative to the ASA of the given residue in a tripeptide flanked by two Gly residues. These data were used to  FEBRUARY 24, 2017 • VOLUME 292 • NUMBER 8 determine which amino acids were exposed to the phospholipid bilayer of the AT1R crystal structure. Amino acid groups with a fractional ASA greater than 0.3 and a similar orientation with respect to one another were selected as candidates for mutagenesis. Amino acid candidates were selected for mutagenesis only if they were found in the membrane-spanning region, which was defined using UniProt (29). Molecular graphics and analyses were performed with the UCSF Chimera package (30).

AT1R Homomer Formation
Mutagenesis-AT1R TM mutants were developed using the QuikChange TM site-directed mutagenesis method that was designed by Stratagene (La Jolla, CA). Forward and reverse oligonucleotide primers were designed using the online QuikChange TM Primer Design software that is provided by Agilent Technologies. Successful mutagenesis was confirmed using the automated DNA sequencing service (GENEWIZ, Inc., South Plainfield, NJ). AT1R containing the desired amino acid substitutions was tagged with either GFP10 (a GFP variant used for BRET2) or Rluc2 at the C-terminal domain between the XhoI-XbaI cut sites.
Cell Culture and Transfection-HEK293A cells were cultured in DMEM that was supplemented with 10% (v/v) fetal bovine serum and 1% penicillin-streptomycin. 300,000 cells were seeded in 6-well plates and incubated at 37°C in a humidified environment of 5% CO 2 . After 24 h, the cells were subjected to PEI-induced transfection. Transfection solutions were prepared such that there was a 3:1 ratio of PEI:DNA in each well. The transfection solution was removed after 24 h and replaced with DMEM that was supplemented as described above. Following an additional 24-h incubation period, the supplemented medium was replaced with minimal DMEM. All experiments were performed 72 h after transfection.
Total Receptor Expression-Cells were divided among the wells of a 6-well plate, and then transfected with 1.0 g of a specific AT1R-GFP 10 or AT1R-Rluc2 construct. Following transfection, each well was harvested with 1 ml of PBS and subjected to centrifugation (2350 ϫ g). The resulting cell pellets were resuspended with 90 l of PBS and transferred to a 96-well plate. Overall receptor expression was quantified using fluorescence spectroscopy. The PerkinElmer EnVision 2104 Multila-bel Reader was used to quantify GFP 10 fluorescence (relative fluorescence units) with an excitation filter set at 410 nm and an emission filter set at 515 nm. Rluc2 luminescence was measured in the presence of coelenterazine-400a (5 M) using a 410-nm emission filter. Wallac EnVision Manager software was used to process the data output. These values were analyzed using GraphPad Prism.
In-Cell and On-Cell Western TM Analyses-For On-Cell Western TM analyses, HEK293A cells in a 6-well plate were transfected with 1 g of each construct, and the next day, 20,000 cells were seeded in a 96-well plate. 24 h later, the cells were fixed for 10 min at room temperature with 4% paraformaldehyde and washed three times with 0.1 M PBS for 5 min each. Cells were incubated with LI-COR Odyssey blocking solution (LI-COR Biosciences, Lincoln, NE) for 1 h at room temperature. Cells were incubated with primary antibody solutions directed against N-terminal AT1R (1:500; SC-1173, Santa Cruz Biotechnologies, Santa Cruz, CA) diluted in antibody dilution buffer (0.1 M PBS and 1% (w/v) BSA in distilled H 2 O) overnight at 4°C. Cells were washed three times with 0.1 M PBS for 5 min each. Cells were incubated in IR CW680 dye (1:500; Rockland Immunochemicals) for 1 h at room temperature. Cells were then washed three times with 0.1 M PBS for 5 min each. Cells were allowed to air-dry overnight. On-Cell Western TM data were then collected using the Odyssey imaging system and software (version 3.0; LI-COR). The same cells were then used to quantify total AT1R protein levels using the In-Cell Western TM technique where the same buffers and antibodies are used but 0.3% Triton X-100 is used to permeabilize the cells. The On-Cell Western TM AT1R levels were divided by the In-Cell Western TM (total) AT1R levels to determine the fraction of AT1R expressed at the plasma membrane. Background fluorescence was subtracted from each measurement, and values were expressed as percentage of net.
Inositol Phosphate-1 Production-IP1 production was determined using the IP-One Assay Kit (Cisbio Bioassays, Bedford, MA). Cells were transfected in a 6-well plate with 1 g of each construct. 24 h later, the cells were then harvested and distributed at 20,000 cells/well (7 l) in a white 384-well plate using stimulation buffer. The next day, cells were stimulated at 37°C for 30 min with Ang II (Sigma-Aldrich Canada; 1 M). Cells were then lysed with 3 l of IP1-d2. After the addition of 3 l of Ab-cryptate, cells were incubated for 1 h at room temperature under agitation. FRET signals were then measured.
Dose-response Experiments-Ang II-induced recruitment of ␤-arrestin1-Rluc2 to each mutant or WT AT1R-GFP 10 construct was examined using a dose-response experiment. Recruitment was quantified using BRET 2 at a fixed acceptor/ donor ratio of 6.0. Concentrations of human Ang II that ranged from 0 to 1 M were added to the corresponding wells of a 6-well plate, and stimulation took place over a 10-min period at 37°C and 5% CO 2 . Cells were harvested with 1 ml of ice-cold PBS and subjected to centrifugation at 2350 ϫ g. The resulting cell pellets were resuspended with 90 l of PBS and transferred to a 96-well plate. A 10-l aliquot of coelenterazine-400a was added to each well to yield a final concentration of 5 M per well. BRET 2 was quantified using a PerkinElmer EnVision 2104 Multilabel Reader with emission filters set at 410 and 515 nm to observe donor and acceptor emission, respectively. Wallac EnVision Manager software was used to process BRET 2 ratios (acceptor emission:donor emission). These values were analyzed using GraphPad Prism.
BRET 2 Saturation Experiments-BRET2 saturation experiments were performed using recombinant human AT1R (WT or mutant) that was tagged with either a C-terminal GFP 10 or a C-terminal Rluc2. The amount of transfected AT1R-Rluc2 (donor) was held constant at 1.00 g/well, while the amount of transfected AT1R-GFP 10 (acceptor) ranged from 0.25 to 5.00 g/well in a six-well plate. The cells were verified for successful transfection using fluorescence microscopy and harvested with 1 ml of PBS. Following centrifugation (2350 ϫ g), cell pellets were resuspended with 90 l of PBS and transferred to a 96-well plate. A 10-l aliquot of coelenterazine-400a (50 M) was added to each well to yield a final concentration of 5 M per well. BRET 2 was quantified using the PerkinElmer EnVision 2104 Multilabel Reader with emission filters set at 410 and 515 nm to observe donor and acceptor emission, respectively. Wallac EnVision Manager software was used to process BRET 2 ratios (acceptor emission:donor emission). BRET 2 efficiency was calculated using the following formula: (BRET 2 ratio Ϫ background)/positive control. These values were analyzed using GraphPad Prism.
Protein Collection, Immunoprecipitation, and Western Blotting-48 h after transfection, medium was aspirated from wells, and cells were collected in ice-cold PBS. The cell pellet was then lysed in 100 l of cold radioimmunoprecipitation assay buffer containing 50 mM Tris (pH 7.4), 150 mM NaCl, 0.5% sodium deoxycholate, 1% Nonidet P-40, 0.1% SDS, and a Roche Applied Science COMPLETE protease inhibitor tablet. Samples were nutated for 30 min at 4°C with BSA-treated Sepharose beads to remove cellular debris and centrifuged for 10 min to isolate the protein-rich supernatant. For co-immunoprecipitation, samples were gently incubated with relevant antibodies at 4°C for 30 min to precipitate each protein of interest. This was followed by the addition of protein A-Sepharose beads and an overnight incubation under the same conditions. The next day, samples were rinsed three times with radioimmunoprecipitation assay buffer. Both Western blots and co-immunoprecipitation sam-ples were then incubated at 65°C for 5 min prior to resolution using SDS-PAGE. Proteins were then transferred to nitrocellulose membranes, blocked with 5% milk powder in TBS, and shaken overnight at 4°C in milk containing the relevant primary antibody. The next day, membranes were washed with TBS containing 0.1% Tween 20 and incubated with HRPconjugated secondary antibodies for 1 h in TBS milk. Following another wash with TBS-Tween, membranes were visualized with Western Lightning Plus-ECL Chemiluminescence Substrate.
Author Contributions-B. M. Y. developed the experimental approach, conducted the majority of the experiments, analyzed the results, and wrote the paper. E. N. conducted a portion of the experiments. M. A. J. C. developed some receptor mutants and wrote a portion of this paper. J. K. R. helped identify amino acid candidates for mutagenesis and performed some modeling. D. J. D. conceived the idea for the project, performed some experiments, and wrote the paper.