Plasmid constructs
The human glycine receptor α3 (NCBI: NP_006520.2), β (NCBI: NP_000815.1) and EP2(NCBI: NP_000947.2) sequence were amplified from cDNA clones (McDermott Center, UT Southwestern Medical center). The α3em sequence was generated by deletion 9 amnio acids of M3/M4 loop (residues A329-S337). α3S346Eem is the addition of S346E mutation site based on α3em. For the βem construct, we used the previously described βem construct3,5. M3/M4 loop (residues N334-N377) was replaced by GGSSAAA-monomeric enhanced green fluorescent protein (EGFP)-SGSGSG. A PA-tag (GVAMPGAEDDVV) and PreScission Protease site (LEVLFQ/GP) were inserted following signal peptide. The α3em and α3wt sequence were subcloned into BacMam expression vector57. The β wild type sequence were introduced into pLVX-IRES-ZsGreen1 vector (Clonetech) for electrophysiology. The human prostaglandin E2 receptor EP2 sequence was inserted into pLVX-IRES-mCherry vector (Clonetech) for electrophysiology. We designed constructs of α3FRET, α3S346EFRET and βFRET based on α3em, α3S346Eem, and βem for smFRET imaging, respectively. α3FRET and α3S346EFRET introduced a mutation C41V and inserted an A1 tag (GDSLDMLEWSLM) between α3S380 and α3P381. βFRET introduced a mutation C115S. All mutations were introduced using sites-directed mutagenesis.
Protein expression
Protein α3β and α3S346Eβ was expressed as described before4,5. The α3em, α3S346Eem, α3FRET, α3S346EFRET, βem and βFRET plasmids were transformed into DH10BacY competent cells (Geneva Biotech) to produce bacmids. The bacmids were transfected into Sf9 cells (ATCC, CRL-1711) to generate baculovirus and then recombinant baculovirus titers were measured. Virus was added at MOI (multiplicity of infection) of 2 (at 3βem:1α3em ratio) to HEK293S GnTI- cells (ATCC, CRL-3022) at a density of 2.5×106 cells/ml. 10 mM sodium butyrate was added, and culture temperature was turned to 30 °C after transduction 12h. Cells were collected after induction 60h by centrifugation at 30,000 g for 20 minutes at 4 °C and stored at −80 °C until further use.
Protein α3β GlyR purification and saposin nanodisc reconstitution for Cryo-EM data collection
Cell pellets were thawed and resuspended in lysis buffer (40 mM Tris pH 8.0, 50 mM NaCl, 2 mM MgCl2, 1 mM CaCl2, 2 mM Glycine, 20 μg/ml Dnase, 2 μg/ml leupeptin, 2 μM pepstatin, 0.8 μM aprotinin, 0.2 mM PMSF) rotated at 4 °C for 30 min under constant stirring, then cell debris was collected by centrifugation at 40,000g for 20 min. The cell debris was dounced and centrifugated at 40,000g at 4 °C for 20 min. The pellets were further homogenized and solubilized with buffer A (40 mM Tris pH 8.0, 200 mM NaCl, 2 mM MgCl2, 1 mM CaCl2, 2 mM Glycine, 20 μg/ml DNase, 2 μg/ml leupeptin, 2 μM pepstatin, 0.8 μM aprotinin, 0.2 mM PMSF, 0.75% (w/v) DDM, 0.075% (w/v) CHS and 0.075% (w/v) Na Cholate) for 40 min at 4 °C. Supernatant was collected from solubilized membranes by centrifugation at 40,000g for 30 min, and then PA-tag antibody (NZ-1) resin58 added to supernatant. The resin was collected and washed with 10 CV buffer B (20 mM Tris pH 8.0, 200 mM NaCl, 2 mM MgCl2, 1 mM CaCl2, 2 mM Glycine, 0.2 mM PMSF, 0.05% (w/v) DDM (Anatrace), 0.005% (w/v) CHS (Anatrace), 0.001% (w/v) Na Cholate (Anatrace)). Then resin bound with protein were mixed with PreScission protease (1:30 v/v) at RT for 1h to cleave PA tag. The flow through was collected, and resin were washed with another 2 CV buffer B. All proteins were pooled and concentrated to load onto Superose6 increase 10/300 GL column (GE Healthcare) in SEC buffer (20 mM Tris pH8.0, 200 mM NaCl, 2 mM Glycine, 0.05%(w/v) DDM, 0.005% CHS). Reconstitution of α3β GlyR into saposin nanodisc was modified from the published protocol5. 1:30:200 molar ratio of α3β: saposin: brain polar lipids extract (BPE) (Avanti) was used. α3β GlyR protein mixed with BPE at room temperature (RT) for 10 min. Saposin protein was added and the mixture was put at RT for another 2 min. The mixture was diluted with buffer (20 mM Tris pH 8.0, 200 mM NaCl, 2 mM Glycine) and incubate on ice for 30 min. Then bio-beads SM-2 (Bio-Rad) were added to the mixture and rotated overnight at 4 °C. After 12h, old bio-beads were removed and the fresh bio-beads were added for another 10h. The mixture was centrifuged for 30min at 4 ℃ before loading onto Superose 6 increase size exclusion column in SEC buffer (20 mM Tris-HCl pH 8.0, 200 mM NaCl, 2 mM glycine).
Protein (α3β and α3S346Eβ GlyRs) purification in digitonin for Cryo-EM data collection
Cell lysis and protein solubilization by detergent follow the similar protocol as the protein purification for saposin nanodisc reconstitution. Briefly, solubilized membranes were cleared by centrifugation at 40,000g for 30 min. Supernatant was collected and added to PA-tag antibody (NZ-1) resin at RT. The resin was collected and washed with 5 CV buffer B and 5CV buffer C (20 mM Tris pH 8.0, 200 mM NaCl, 2mM MgCl2, 1 mM CaCl2, 2 mM Glycine, 0.06% (w/v) digitonin (Sigma-Aldrich)). Then, beads were mixed with PreScission protease (1:30 v/v) to cleave PA tag at RT for 1h. The resin was collected to get flow through, then resin was washed another 2 CV buffer C. Flow through and 2CV washed buffer C were pooled and concentrated to load onto Superose6 increase 10/300 GL column in SEC buffer (20 mM Tris-HCl pH8.0, 200 mM NaCl, 2 mM Glycine, 0.06%(w/v) digitonin). Good peak fractions were collected and concentrated to 6 mg/ml for grids freeze. For the sample with 2, 6-DTBP the buffer used throughout the purification process contained 500 μM 2, 6-DTBP and another 500 μM 2, 6-DTBP was added to cryo-EM sample for 1h before grid freezing.
Cryo-EM sample preparation, data collection and image processing
3 mM final concentration (1 × CMC) of Fluorinated fos-choline 8 (Anatrace) was added into cryo-EM sample immediately before freezing. Grids (Quantifoil R1.2/1.3 400-mesh Au holey carbon grid) were glow-discharged. An FEI Vitrobot Mark IV Vitrobot (Thermo Fisher) was used to plunge freeze the grids after application of 3 µl sample at 4℃ under 100% humidity.
Micrographs were collected using a Titan Krios microscope (Thermo Fisher) with a K3 Summit direct electron detector (Gatan) operating at 300 kV using the SerialEM data acquisition software. The GIF-Quantum energy filter was set to a slit width of 20 eV. Images were recorded with the pixel size of 0.415 Å in the super-resolution counting mode. Micrographs were dose-fractioned into 50 frames with a dose rate of 1.4 e-/Å/frame.
2-fold binning (0.83 Å pixel size after binning), motion correction and dose weighting of the movie frames were carried out using the Motioncorr2 program59. CTF correction was carried out using the CTFFIND 4 program60. The following image processing steps were performed in RELION 461. Particles were initially picked using the Laplacian-of-Gaussian blobs and subjected to 2D classification to obtain good class-averages. Then good 2D classes were used as template for reference-based auto picking. Resulting particles were extracted with 4-fold binning for a further round of 2D classification. Good 2D class-averages were selected and subjected to 3D classification using an initial model downloaded from EMDB database (EMD-23148)3. For the α3β-gly GlyR in digitonin sample, 1 out of 6 classes in 3D classification appeared with good density for the entire channel (Extended Data Fig.2b). A single density blob for GFP was identified for the heteromeric α3β GlyR in digitonin sample. The density arising from GFP fusion on the βem subunit served as fiducial marker to differentiate the β subunit from the structurally similar α subunits. A further 3D classification into 4 classes with non-binned particles (0.83 Å pixel size) without particle alignment was performed. Partial signal subtraction62 was carried out to focus on the TMD. 1 indistinguishable good class resulted in a final of 19,993 particles. After reverting particles to un-subtracted version, CTF refinement, Bayesian polishing in RELION and non-uniform refinement63 in cryoSPARC64, an overall resolution of 3.8 Å was achieved, with local resolutions exceeding 3.5 Å in many regions (Extended Data Fig. 2c, d, e). For the α3β-gly GlyR in nanodisc sample, 1 out of 3 classes in 3D classification appeared with good density for the entire channel (Extended Data Fig.2g). A single density blob for GFP was identified for the heteromeric α3β-gly GlyR in nanodisc sample. A further 3D classification into 3 classes with non-binned particles (0.83 Å pixel size) without particle alignment was performed. 1 indistinguishable good class resulted in a final of 40,868 particles. After reverting particles to un-subtracted version, CTF refinement, Bayesian polishing in RELION and non-uniform refinement in cryoSPARC, an overall resolution of 3.8 Å was achieved, with local resolutions exceeding 3.5 Å in many regions (Extended Data Fig. 2h, i, j). For the α3S346Eβ-gly GlyR in digitonin, 1 out of 4 classes in 3D classification appeared with good density for the entire channel (Extended Data Fig.3b). A single density blob for GFP was identified for the heteromeric α3S346Eβ-gly GlyR sample. A further 3D classification into 4 classes with non-binned particles (0.83 Å pixel size) without particle alignment was performed. 1 indistinguishable good class resulted in a final of 9,628 particles. After reverting particles to un-subtracted version, CTF refinement, Bayesian polishing in RELION and non-uniform refinement in cryoSPARC, an overall resolution of 3.7 Å was achieved, with local resolutions exceeding 3.0 Å in many regions (Extended Data Fig. 3c, d, e).
For the α3S346Eβ-gly/2, 6-DTBP GlyR in digitonin sample, 1 out of 6 classes in 3D classification appeared with good density for the entire channel (Extended Data Fig.3g). A single density blob for GFP was identified for the heteromeric GlyR α3S346Eβ-gly/2, 6-DTBP GlyR sample. A further 3D classification into 4 classes with non-binned particles (0.83 Å pixel size) without particle alignment was performed. 1 indistinguishable good class resulted in a final of 22,755 particles. After reverting particles to un-subtracted version, CTF refinement, Bayesian polishing in RELION and non-uniform refinement in cryoSPARC, an overall resolution of 3.6 Å was achieved, with local resolutions exceeding 2.5 Å in many regions (Extended Data Fig. 3h, i, j). Resolutions were estimated by applying a soft mask around the protein densities with the Fourier Shell Correlation (FCS) 0.143 criterion. Local resolutions were calculated using Resmap65.
Model building and refinement
Models of α3β-gly (in digitonin and nanodisc) and α3S346Eβ-gly GlyRs were bulit by fitting the structure of heteromeric human α1β desensitized state (PDB ID: 8DN4)5 into the Cryo-EM density maps of α3β-gly (in digitonin and nanodisc) and α3S346Eβ-gly GlyRs using Chimera66 and Coot67. Model of α3S346Eβ-gly/2, 6-DTBP GlyR was bulit by fitting the structure of heteromeric human α1β expanded-open state (PDB ID: 8DN2)5 into the Cryo-EM density map of α3S346Eβ-gly/2, 6-DTBP using Chimera66 and Coot67. The atomic model was manually adjusted in Coot. The final models were refined with real-space refinement module and validated with comprehensive validation module in PHENIX package68,69. Fourier shell correlation (FSC) curves were calculated between refined atomic model and the work/free half maps as well as the full map to assess the correlation between the model and density map. Statistics of cryo-EM data processing and model refinement are listed in Extended Data Table 1. Pore radii were calculated using the HOLE program70. Figures were prepared in UCSF Chimera66, ChimeraX71, and PyMOL72.
The final model of α3β-gly in nanodisc contained the α3 and β subunit amino acids except the following: α3 subunit of chain A (total 422aa, 349aa built, 73aa not built) A1-P7, K312-F328, D338-D382 and Q428 - D431; α3 subunit of chain B (total 422aa, 340aa built, 82aa not built) A1-M8, H311-F328, D338-D382 and H423- D431; α3 subunit of chain C (total 422aa, 345aa built, 77aa not built) A1-A6, H311-F327, D338-D382 and H423-D431; α3 subunit of chain D (total 422aa, 342aa built, 25aa not built) A1-M8, H311-F327, D338-M384, H427-D431. β subunit (total 444aa, 348aa built, 74aa not built) K1-R28, GSSAAA-EGFP-SGSGSG insertion and V378-P442.
The final model of α3β-gly in digitonin contained amino acids except the following: α3 subunit of chain A (total 422aa, 345aa built, 77aa not built) A1-M8, E313-F327, D338-R384 and H427-D431; α3 subunit of chain B (total 422aa, 340aa built, 82aa not built) A1-M8, K311-F327, D338-R384 and H423-D431; α3 subunit of chain C (total 422aa, 343aa built,79aa not built) A1-M8, E313-F327, D338-R384 and H423-D431; α3 subunit of chain D (total 422aa, 343aa built, 79aa not built) A1-M8, H311- F327, D338-K386 and H427-D431. The model of β subunit forα3β-gly in digitonin is the same as α3β GlyR-gly in nanodisc.
The final model of α3S346Eβ-gly contained amino acids except the following: α3 subunit of chain A (total 422aa, 343aa built, 79aa not built) A1-P7,H311-F327, D338-R385 and D425-D431; α3 subunit of chain B (total 422aa, 331aa built, 81aa not built) A1-P7, H311- F327, D338-R385 and H423-D431; α3 subunit of chain C (total 422aa, 336aa built, 31aa not built) A1-P7, H311-F327, D338-R385 and H423- D431; α3 subunit of chain D (total 422aa, 342aa built, 80aa not built) A1-P7, H311-F327, D338-R385 and H423- D431. The model of β subunit of α3S346Eβ-gly is the same as α3β GlyR-gly in nanodisc.
The final model of α3S346Eβ-gly/2, 6-DTBP contained the α3 and β subunit amino acids except the following: α3 subunit of chain A (total 422aa, 344aa built, 78aa not built) A1-M8, K312-F327, D338- R385 and I426- D431; α3 subunit of chain B (total 422aa, 334aa built, 81aa not built) A1-M8, K312-F327, D338- R385 and H423- D431; α3 subunit of chain C (total 422aa, 341aa built, 83aa not built) A1-P7, H311-F327, D338- R385 and H423- D431; α3 subunit of chain D (total 422aa, 345aa built, 79aa not built) A1-P7, H311-F327, D338-R385 and H427-D431. The model of α3S346Eβ-gly/2, 6-DTBP β subunit is the same as α3β GlyR -gly in nanodisc.
Fluorescence-Detection Size-Exclusion Chromatography (FSEC) expression assay
Fluorescence was detected using the RF-20Axs fluorescence detector for HPLC (Shimadzu, Japan) (GFP excitation: 480 nm, emission: 512 nm) as EGFP was fused into βem construct for FSEC assay. 2 μl of Lipofectamine 3000 (Thermo Fisher Scientific, US) mixing with 1 μg of plasmid (at 1α3:3β ratio) was transfected into HEK293T cells for 12 well plate each well. Cells were incubated in a CO2 incubator (37 °C, 8% CO2) for 48 h after transfection and solubilized with 50 μl buffer B for 1 h. After centrifugation (40,000 g, 30 min), 50 μl of the sample was applied to a Superose 6 Increase 10/300 GL column (GE Healthcare) equilibrated with buffer D (20 mM Tris pH 8.0, 200 mM NaCl, 2 mM glycine, 0.025%DDM) for the FSEC assay.
Whole cell patch clamp
The glycine EC50 values were measured on α3β GlyR and α3S346Eβ GlyR expressed in HEK293T cells (ATCC, CRL-3216). Plasmids were transiently transfected using Lipofectamine 3000 reagent (Invitrogen). Total 0.8 μg of DNA was transfected at 1α3:3β ratios for 35 mm dish. Whole-cell recordings were made after 17-24h transfected at 22 ℃. GFP fluorescence was used to identify the cells expressing the heteromeric α3β and α3S346Eβ GlyRs. The bath solution contained (in mM): 10 HEPES-NaOH pH 7.4, 10 KCl, 125 NaCl, 2 MgCl2, 1 CaCl2 and 10 glucoses. The pipette solution contained (in mM): 10 HEPES-NaOH pH 7.4, 150 KCl, 5 NaCl, 2 MgCl2, 1 CaCl2 and 5 EGTA. The resistance of borosilicate glass pipettes between 2∼7 MΩ. The voltage held at -70 mV and a Digidata 1550B digitizer (Molecular Devices) was connected to an Axopatch 200B amplifier (Molecular Devices) for data acquisition. Analog signals were filtered at 1 kHz and subsequently sampled at 20 kHz and stored on a computer running pClamp 10.5 software. Data analysis was performed by Origin 2018 software (Origin Lab). Hill1 equation was used to fit the dose-response data and derive the EC50 (k) and Hill coefficient (n). For glycine dose response experiment, we fit the data using equation , where I is current, I0 is the basal current (accounting mostly for leak, very close to 0), Imax is the maximum current and x is glycine concentration. All start point is fixed at 0 during fit. Measurements were from 7-11 cells, mean and S.E.M. values were calculated for each data point.
For experiments of PGE2 modulation GlyR, total 1 μg of plasmid (0.6 μg GlyR at 1α3:3β ratios and 0.4 μg EP2) was transfected for 35 mm dish. Whole-cell recordings were made after 17-24h transfected at 22 ℃. Both in presence of GFP (GlyR) and mCherry (EP2) fluorescences were used to identify the cells co-expressing the heteromeric α3β GlyR and EP2 receptor. PGE2 (10 μM concentration used) was applied by perfusion system at a rate of 1-2 ml/min. At least 5 times current response evoked by 1 mM glycine was recorded before application of PGE2. After application PGE2 for about 2 minutes, the currents reached steady state. This steady state of inhibition kept another 3 min with PGE2 application. Then bath solution without PGE2 was applied to wash out.
2, 6-DTBP (100 μM concentration used) was also applied by perfusion system at a rate of 1-2 ml/min. After 3 to 5 times current response evoked by 30 μM glycine of baseline recording, 2, 6-DTBP (100 μM) was applied to bath solution for 4-6 min until the currents increase reaching saturation. The increase in current is recorded every 40 seconds.
Protein purification and labeling for smFRET
Cell lysis and protein solubilization by detergent follow the protocol as the protein purification for saposin nanodisc reconstitution excepting that 20 mM HEPES-NaOH, pH7.4 was used instead of 20 mM Tris-HCl, pH8.0. Peak fractions of protein were collected and concentrated to 1 mg/ml. αFRETβFRET was equally divided into two parts. One part protein was labeled with CoA-LD555 and LD655-MAL.The protocol as described below: 10 μM TCEP was added to protein then incubated for 30 min on ice. αFRETβFRET was labeled first by incubating protein with LD655-MAL at 1:3 (protein: LD655-MAL) molar ratio at 4 ℃ for overnight in the dark. αFRETβFRET was labeled further by incubating protein with 20 μM AcpS, 10 μM CoA-LD555, 20 mM MgCl2, 20 mM HEPES-Na, pH 7.4 at RT for 4h protecting from light. Another part of the protein was labeled with LD555-MAL and LD655-MAL in the dark at 1:3:3 molar ratio (protein: LD555-MAL: LD655-MAL). To remove free dye, the solution with labelled protein was then loaded onto PD-10 desalting column (GE Healthcare) equilibrated in the buffer E (20 mM HEPES-NaOH, pH7.4, 200 mM NaCl, 0.03% (w/v) DDM, 0.003% (w/v) CHS), and the resulting flow-through was loaded onto a second desalting column equilibrated in buffer E. The flow through containing pure labeled protein was centrifuged at 18,000g for 1 h at 4 ° C to remove insoluble aggregates. FRET-Labeled αFRETβFRET were aliquoted and frozen at -80 °C, and freshly thawed before the experiments.
Glass slides preparation for smFRET imaging
The glass slides are cleaned by soaking for 1.5 h at room temperature in piranha solution (≥98% H2SO4 and 30% H2O2 in a 3:1 ratio) in jugs. The procedure is carried out in a hood. The glass slides were sonicated for 3 times for 10s/time (once at the started soaking, once at 45 min and once at the end) and the washed with ddH2O for 5 times in jug. Then the treated glass slides are further soaked in 1M KOH for another 30 min and washed for 5 times using running ddH2O. During soaking with KOH, the glass slides were sonicated for another 3 times for 1mim/time (once at the started soaking, once at 15 min and once at the end). After washing procedures, the glass slides are drained on air in a vertical position. The soaked glass slides were covered with 25% mPEG-sliane 5k (Sigma-Aldrich) with 1% Biotin mPEG-silane 5k (Sigma-Aldrich) at 90oC on metal plate covering by Petri dish for 30 min. Finally, the glass slides were washed with running ddH2O and then drained on air in a vertical position. Coated glass slides were stored at -20 °C until further use.
TIRF-based single-molecule FRET imaging
For direct immobilization of αFRETβFRET, the imaging surface was first exposed to 0.2 μM NeutrAvidin (Thermo Fisher Scientific) and then 50 nM Biotin Anti-GFP antibody (abcam, ab6658) in buffer F (50 mM HEPES-NaOH, pH7.4, 150 mM NaCl). The surface was washed and exchanged into imaging buffer (50 mM HEPES-NaOH pH 7.4, 150 mM NaCl, 10 mM MgCl2, 0.8% (w/v) glucose). FRET-labeled GlyR variants was diluted to 0.7 nM and bound to a NeutrAvidin/ Biotin anti GFPab-coated glass slide surface for 30 min in imaging buffer with 2 μM 25-nucleotide DNA duplex (IDT) and 10 mg/ml BSA (Jackson Immunoresearch) as surface blocking agents. To measure smFRET in apo state, imaging was performed in imaging buffer. To measure the effect of glycine on smFRET value, imaging was performed in imaging buffer added 2mM glycine. To detect the modulating of 2, 6-DTBP on M3/M4 loop, imaging was performed in imaging buffer added 2 mM glycine and 500 μM 2, 6-DTBP and waiting for 30min before imaging recording. TIRF-based smFRET imaging experiments were performed at 22 °C with a custom-built TIRF microscope. Fluorescence emission from LD555 and LD655 was collected by a 60X, 1.27 NA water immersion objective (Leica), spectrally split in a MultiCam Device (Cairn) and collected with two synchronized Flash 4.0 V3 camera (C13440-20CU, Hamamatsu) with 2x2 pixel binning. SmFRET imaging recordings were performed by exciting with the Gem 560 nm laser (Laser Quantum) laser at 50 mW and acquiring 200 frames per movie at a 200 ms/frame rate in both donor and acceptor channels.
Analysis of TIRF-based single-molecule data
Image movies were analyzed with Cornell SPARTAN version 3.7.073 following manual. Molecules were detected as local intensity maxima in an image combing with donor and acceptor channels (aligned using the iterative closest points algorithm) averaged over the first 10 frames and background subtracted with threshold 100. The distances of molecules smaller than 3.5 pixels were excluded from analysis. Traces were extracted from the selected intensity maxima by summing the 9 most intense pixels for each fluorescence channel. Selected traces were saved for further analysis if they met the following criteria for experiments recorded with 200 ms (10 ms) time resolution: FRET lifetime > 5, donor acceptor correlation coefficient -1 to 0.5, signal-to-noise >8, #cy3 blinks<4 and remove overlapping traces. Saved races is then manually viewed and selected as all FRET section for further analysis according following criteria: Donor-acceptor fluorescence exchange time more than 5s (25 frames); Donor and acceptor fluorescence were found to bleach in a single step. Single-molecule traces showing dynamics before photobleaching. More than 180 typically molecules at each condition were manually selected, and FRET values for individual each conduction was accumulated in histograms. Histogram distributions were analyzed with a double Gaussian equation to reveal reoccurring mean FRET values using Origin 2018 software (OriginLab). The correlation results of Gaussian fitting analysis were listed on Extended Data Table 2 and 3. FRET histograms showed in results are averaged from the first 25 frames (total 5s).
Plotting and statistics
Glycine dose-response curves fitting was used Origin 2018 software (OriginLab). Plotting for PGE2 and 2, 6-DTBP modulation GlyRs were carried out by GraphPad Prism (GraphPad Software). Plotting, distribution fitting and statistics for all single-molecule data were carried out using Origin 2018 (OriginLab). All errors represent the S.E.M.