Site Directed Spin Labeling and EPR Spectroscopic Studies of Pentameric Ligand-Gated Ion Channels

1. Site-Directed Mutagenesis and Cys Mutations

1. Cloning and Mutagenesis
   NOTE: GLIC wild type (wt) ³⁵ has a single-native cysteine (C27), which is mutated to serine to create a cysteine-less background. Cysteine mutations are introduced on the cysteine-less background by site-directed mutagenesis using primers that carry a cysteine codon at the desired position³⁶.
   1. Mix 5 μl of 10x reaction buffer, 1 μl of 100 ng/μl cysteine-less GLIC template DNA³⁵, 0.5 μl each of 40 μM forward and reverse primer³⁶, 1 μl of dNTPs (100 mM), and 41 μl of deionized water. Pipette the sample a few times to mix it thoroughly, spin (6,000 rpm) and finally add 1 μl of DNA polymerase.
   2. Set the thermo-cycler to the following protocol:
      1. Denaturation at 95 ºC for 4 min.
      2. Denaturation at 95 ºC for 30 sec.
      3. Annealing at 55 ºC for 1 min.
      4. Elongation at 68 ºC for 10 min (roughly 1 min per kb plasmid length).
      5. Repeat steps 1.1.2.2 – 1.1.2.4 for 18 cycles.
      6. A final elongation at 68 ºC for 10 min.
      7. Holding temperature at 4 ºC
         NOTE: Annealing temperature is calculated based on the primer Tm.
   3. Add 1 μl of DpnI to the reaction mixture, mix thoroughly by pipetting, and spin down (6,000 rpm) for 1 min. Incubate for 2 hr at 37 °C.
2. Transformation
   1. Thaw E. coli competent cells on ice. Aliquot 30 μl of cells into a 14 ml sterile transformation tube and add 1 μl of digested DNA to the cells. Mix by tapping on the side of the tube. Incubate for 20 min on ice.
   2. Place the tube in a 42 ºC water bath for 45 sec and then place it back on ice for 2 min. Add 400 μl sterile SOC media and shake the cells in an incubator at 37 ºC for 1 hr.
   3. Plate 100 μl of cells on LB plates containing kanamycin (50 μM) and 1% glucose. Incubate the plates O/N at 37 ºC.
   4. Harvest a single colony from the plate and inoculate in 5 ml O/N cultures containing LB/kanamycin media. Incubate the culture O/N (~16 hr) at 37 ºC in an incubator shaker.
   5. Extract DNA from the O/N culture by minipreparation³⁷. Quantify the yield of DNA using a spectrophotometer by measuring the absorbance at 260 nm wavelength. The concentration should be ~100 – 200 ng/μl. Confirm the presence of mutation by standard recombinant DNA sequencing strategies ^38,39.

2. GLIC Expression and Purification

1. Transformation
   1. Following the steps described in section 1.2, transform 30 μl of C43 competent cells with 1 μl (~100 – 200 ng/μl) of the plasmid containing the gene coding for GLIC along with a Human Rhinovirus (HRV)-3C protease cleavage site (For the plasmid and gene sequence, refer to the supplemental text) ³⁵ (from step 1.2.5).
   2. Plate 100 μl of cells on LB-agar plates containing 1% glucose and 50 μg/ml kanamycin, and incubate them O/N (~16 hr) at 37 ºC in an incubator.
   3. Check visually for colonies and ensure that they are not over-grown or show the presence of satellite colonies. Promptly seal the plates with parafilm and store them at 4 ºC.
2. Setting up O/N-cultures and Preparation of growth media
   1. Pick a single isolated colony using loop inoculating wire and transfer into a 100 ml sterile flask containing 20 ml of Luria Broth (LB) media supplemented with sterile 1% glucose and 50 μg/ml kanamycin. Incubate them O/N (~16 hr) at 37 ºC in a shaker at 250 rpm.
   2. Autoclave 900 ml Terrific Broth (TB) media (See Media and Buffer Composition) in 2.8 L Fernbach glass flasks for the bacterial culture in steam cycle at 121 ºC for 20 min.
3. Setting up large growth cultures
   1. Add 100 ml of sterile potassium phosphate buffer (See Media and Buffer Composition) to the autoclaved TB media. Add sterile glucose (0.2% final concentration), kanamycin (50 μg/ml), and 10 ml of the O/N culture. Incubate at 37 ºC in a shaker at 250 rpm.
   2. Check the optical density at 600 nm wavelength (OD₆₀₀) using densitometer or a spectrophotometer every hour until it reaches 0.5 (~2 hr). At this point reduce the speed to 150 rpm and lower the temperature to 18 ºC. Monitor the OD₆₀₀ every 30 min until it reaches 0.8 (~1 hr).
   3. Add 50 ml of glycerol and continue shaking the culture until the OD₆₀₀ reaches 1.0 – 1.2 (~15 – 30 min).
      NOTE: Under these conditions, it takes about an hour for the culture to reach 18 ºC from 37 ºC. It is important that glycerol is added to the culture after it has cooled to 18 ºC.
   4. Induce the cells with 200 μM IPTG (isopropyl-thio-β-galactoside) and reset the shaker back to 250 rpm and incubate further for ~16 hr at 18 ºC.
4. Protein Purification
   1. Ensure that the OD₆₀₀ at the end of 16 hr is ~16 – 18. Harvest the cells in 1.0 L centrifuge bottles by spinning at 8,500 x g, 4.0 ºC for 15 min. Decant the supernatant and weigh the bottle with the cell pellet. Calculate the weight of the pellet by subtracting weight of the empty bottle from the total weight.
      NOTE: The expected cell pellet weight is ~30 – 35 g/L. Although, it is to be noted that there may be variability in the final OD₆₀₀ and cell pellet weight across mutants.
   2. Re-suspend the bacterial pellet in 150 ml of ice-cold Buffer A (100 mM NaCl, 20 mM Tris, pH 7.4) per 1.0 L of culture. Add DNase I (100 μg/ml) and protease inhibitors (phenylmethyl sulfonyl fluoride (1 mM), leupeptin (2.0 μg/ml), aprotinin (2.0 μg/ml), and pepstatin A (1 μg/ml)).
   3. Homogenize the cells by passing them through a cell disrupter in a 4.0 ºC cold room. Repeat the process three times so that most of the bacteria is lysed. Centrifuge the cells at 14,000 x g for 15 min and pipette the supernatant out and transfer into a clean centrifuge tube. Discard the pellet, which contains un-lysed cells and inclusion bodies.
   4. Centrifuge the supernatant at 168,000 x g for 1 hr. Carefully decant the supernatant without disturbing the membrane pellet.
   5. Pool the membrane pellet from 1 L of culture and re-suspend it in Buffer A (supplemented with 10% glycerol) to a final volume of 50 ml. Add 0.5 g of n-Docecyl-β-D-Maltopyranoside (DDM) to the membrane suspension and nutate for 2 hr at 4.0 ºC.
   6. After membrane solubilization, remove cell debris from the lysate by centrifugation at 168,000 x g for 1hr. In the meantime prepare amylose resin. Transfer 3 ml of resin using a pipette into an empty polypropylene chromatography column. Wash the resin by passing 10 bed volumes of water 3 times and then with 10 bed volumes of Buffer A containing 0.5 mM DDM.
   7. After centrifugation, gently take the supernatant out using a pipette and transfer to a clean 50 ml conical tube. For batch-wise binding, add pre-equilibrated amylose resin to the conical tube. Bind the extracted protein to amylose resin by nutating the mixture for 2 hr at 4.0 ºC.
   8. Pass the entire slurry through a chromatography column and collect the flow-through. Then pass the entire collected flow-through over the resin a second time to maximize binding.
   9. Pass 10 bed volumes of buffer A with 0.5 mM DDM, 0.5 mM tris(2-carboxyethyl)phosphine (TCEP) and 1 mM ethylenediaminetetraacetic acid (EDTA) to remove unbound proteins.
   10. Elute the GLIC protein with 10 ml of Buffer A containing 40 mM maltose in addition to 0.5 mM DDM and 0.05 mM TCEP. TCEP prevents oxidation of cysteine side-chains. Collect the entire elute.
   11. Concentrate the eluted protein using centrifugal concentrator (Molecular Weight Cut-off = 50 KDa) to 4 – 6 mg/ml and add HRV-3C protease (200 μg per 10 mg protein) and incubate O/N at 4.0 ºC.
       NOTE: Ascertain the completion of protease digestion by running the samples on SDS PAGE gel (See step 2.5.5 and Figure 1).
5. Site-Directed Spin-labeling
   1. Make about 100 μl of 200 mM stock of (1-oxyl-2,2,5,5-tetramethyl-Δ3-pyrroline-3-methyl) MTSL ⁴⁰ in DMSO and store the stock at -20 ºC in 25 μl aliquots.
   2. Use the protease-digested sample for spin-labeling with MTSL. Add 10-fold molar excess of MTSL spin-label (GLIC monomer: MTSL in 1:10 molar ratio). Incubate on ice for 1 hr. Add a second shot of spin label at a 5-fold molar excess ratio and incubate for another hour.
      NOTE: For buried positions (with low spin labeling efficiency, described below), a 30 times molar excess of spin label is added and the protein is incubated for 6 hr.
   3. Pass the sample through a size-exclusion Fast Protein Liquid Chromatography (FPLC) column that is pre-equilibrated with Buffer A and 0.5 mM DDM to separate the cleaved MBP and the excess free spin-label from GLIC pentamers. Collect 1 ml fractions for a total of 30 ml elution. Pool the fractions containing GLIC pentamers (Figure 1). Follow the manufacturer's instruction to run the FPLC.
   4. Determine the concentration of the sample using a spectrophotometer by measuring the absorbance at 280 nm wavelength. Molar extinction coefficient and the estimated molecular weight of GLIC monomer are 49,850 M^-1 cm^-1 and 36,380 Da, respectively. Concentrate the protein solution using a centrifugal concentrator (Molecular Weight Cut-off = 50 KDa) to a final concentration of ~8-10 mg/ml and place it on ice. The sample is now ready for reconstitution.
   5. As an additional quality check to ensure that the preparation is biochemically homogenous, run a reducing (1.0% β-ME) SDS-PAGE gel.
      NOTE: The commassie stained gel should show a single band at ~33 kDa corresponding to the GLIC monomer (Figure 1).
   6. For the spin-labeled mutants suspected of exhibiting dipolar broadening, under-label the samples in the presence of diamagnetic label ⁴¹. Incubate the eluted-protein with 0.1-fold MTSL and incubate on ice for 1.0 hr. Afterwards, add 20-fold molar excess of diamagnetic label (1-acetoxy-2,2,5,5-tetramethyl-Δ3-pyrroline-3-methyl) methane thiosulfonate.
      NOTE: The diamagnetic reagent used here is iso-steric to the paramagnetic label with an identical labeling chemistry.
   7. Incubate the sample on ice for 2 hr. Pass the sample through a size exclusion chromatography column that is pre-equilibrated with Buffer A and 0.5 mM DDM as in Step 2.5.3.
6. Efficiency of spin labeling
   1. Spin-labeling efficiency is defined as the ratio of the spin-label concentration to the concentration of cysteine side-chain (GLIC-monomer). To determine the efficiency of spin-labeling of the sample, the integrated intensity of the sample will be compared with a standard of known concentration using a calibration plot. Make solutions of an EPR standard (such as 2,2,6,6-tetramethyl-1-piperidinyloxyl: TEMPO) in a range of concentrations (10 – 250 μM) by dissolving in water.
   2. Measure the EPR signal for each of these solutions and determine the area under the curve (double integration of the EPR signal) for each concentration (as described in Steps 6.1). Generate a calibration curve by plotting the measured area as a function of the TEMPO concentration and fitting with a straight line.
      NOTE: The area under a derivative EPR signal is a better description of the spectral intensity than the peak to peak amplitude. Integrating the first-derivative EPR signal will give the absorption spectrum, a second integration will then give the area under the absorption spectrum (which is proportional to the spin concentration). Ensure a constant baseline both in the low-field and high field region of the spectrum.
   3. Measure the concentration of the spin-labeled protein in the detergent using a spectrophotometer (as in step 2.5.4). Now measure the EPR signal of the sample and then determine the area of the double integral of the EPR signal following steps in section 6.1. By using the calibration plot, determine the concentration of the label which corresponds to the measured EPR signal. Calculate the spin labeling efficiency as the molar ratio of spin label and protein concentration.

3. GLIC Reconstitution in Asolectin Membranes

1. Liposome Preparation
   1. Rinse a clean 25 ml round bottom flask with 5 ml of chloroform and dry the flask in a stream of N₂ gas in the fume hood. Transfer 10 mg of asolectin (soybean polar extract 25 mg/ml stock in chloroform) into the flask and dry the lipids under a continuous stream of N₂ gas.
      NOTE: The choice of lipids for reconstitution is based on findings from experiments in section 4.
   2. When the chloroform has evaporated, place the flask in a vacuum for 1 hr to ensure complete drying. Add 1 ml of reconstitution Buffer A to the dried lipid and vortex the flask vigorously to get the lipid pellet into suspension.
   3. To prepare small unilamellar vesicles, sonicate the lipid suspension in a cold bath sonicator until the vesicle solution becomes more or less translucent and no clumps are observed (roughly 10 – 15 min). To this mixture, add DDM to a final concentration of 4 mM and incubate at RT for 30 min.
2. Reconstitution
   1. Add the purified protein from step 2.5.4 to the lipid mixture.
      NOTE: The protein-to-lipid ratio depends upon the type of experiment. For macroscopic current measurements, a 1:10,000 ratio is used. For EPR studies, reconstitution is done at a higher protein to lipid ratio (1:2,500) to maximize the signal. It is previously shown that at these concentrations, no lateral aggregation is observed⁴².
      NOTE: Typical working amount of GLIC for EPR is ~1 mg, although based on the position probed, lower amounts would work as well.
   2. Incubate the sample at 4 ºC for 1 hr with gentle rotation then dilute the sample to 15 ml with Buffer A.
      NOTE: This step brings the detergent concentration below the critical micellar concentration (CMC).
   3. Remove the residual detergent in the suspension by adding polystyrene beads (with hydrophobic pores that trap detergent). Add 80 mg of clean the beads and incubate the liposome suspension O/N on a nutator at 4 ºC^.
      1. To prepare the beads for use, weigh ~100 mg and transfer them to a 50 ml conical tube. Add 10 ml of methanol, shake vigorously, spin down the beads at 8,000 x g for 2 min, and decant the methanol. Repeat this process of methanol wash three times. Repeat the same process with 30 ml of deionized water, washing three times.
   4. The next day, transfer the liposome to a 25 ml ultracentrifuge tube using a column filter to remove the beads and further dilute the sample to 25 ml. Centrifuge the samples at 168,000 x g for 2 hr. Decant the supernatant and re-suspend the pellet using 100 μl of Buffer B.

4. Determine Optimal Lipid Composition for Reconstitution by FRET

1. Use a fluorescence resonance energy transfer (FRET)-based assay to determine the membrane composition that maintains the protein monodisperse.
2. Purify wt GLIC (with the native cysteine, C27) by following steps described in section 2. Label the protein at a 10:1 (label/monomer) molar ratio with either fluorescein-maleimide or tetramethylrhodamine-maleimide using steps in section 2.5.
3. Following steps in section 3.2 for reconstitution, prepare three different samples for each lipid composition to be tested; First, fluorescein-labeled GLIC in a molar ratio of 1: 1,500 (pentamer: lipid). Second, rhodamine-labeled GLIC in a molar ratio of 1: 1,500 (pentamer: lipid). Third, mix detergent solubilized fluorescein and rhodamine labeled GLIC (1:1 molar ratio). Reconstitute this mixture in 1: 750 (pentamer: lipid) ratio.
   NOTE: We used three lipid systems: asolectin, POPC:POPG (3:1 molar ratio), and E. coli polar extract. The protein to lipid reconstitution ratio in the FRET experiment is higher than that used for EPR measurements (1:750 in comparison to 1: 1,500 used for EPR studies).
4. Dilute the liposome suspension (to reduce the light scattering signal; ~5 μl in 995 μl of Buffer A) then pipette the sample into a quartz cuvette and place it in a fluorimeter.
5. Set the excitation wavelength at 490 (which corresponds to the absorption maxima for the donor:fluorescein). Using manufacturer's instructions, record the emission spectra from 500 nm to 660 nm.
   NOTE: For the fluorescein-labeled GLIC sample, you will see a peak at 518 nm (corresponding to fluorescein emission) with no peak at 572 nm (corresponding to rhodamine emission). For the rhodamine-labeled GLIC sample, you will not see a peak at 518 nm but instead at 572 nm arising from direct excitation of rhodamine at 490 nm. For the sample containing both fluorescein and rhodamine labels, a decrease in fluorescein peak intensity and a corresponding increase in rhodamine peak is a FRET signal that is likely an indicator of lateral aggregation of the protein on the membrane.
6. Monitor the amplitude of rhodamine emission at 572 nm at various time intervals (from 0 – 24 hr) recording at every hour for the first 6 hr and then after O/N incubation (Figure 2). For each interval, measure the fluorescence intensity at 572 nm (for rhodamine: Ia) and at 518 nm (for fluorescein: Id). Subtract the contribution of direct rhodamine activation (sample 2 in step 4.3) from Ia (Iac). Determine the FRET ratio as Iac/(Iac + Ib). Compare FRET at different time intervals and across different lipid compositions.
   NOTE: As a control, perform step 4.5 and 4.6 for detergent solubilized samples and compare the emission spectra to those from reconstituted liposomes. Use an equimolar mixture of labeled protein in detergent (described in step 4.3) and dilute in Buffer A supplemented with 0.5 mM DDM. It is expected that detergent samples will show minimal FRET signal.

5. Functional Measurements by Patch-clamp Recordings

1. Prepare proteoliposomes for patch-clamp measurements in exactly the same way as for EPR studies (Section 3.1).
   NOTE: However, adjust the protein:lipid ratio based on the type of measurement being made (Single-channel vs Macroscopic recordings). Flash-freeze the proteoliposomes in liquid nitrogen and store at -80 ºC until use. Typically, reconstitute GLIC in 1: 10,000 protein: lipid (molar ratio) for macroscopic currents and 1: 50,000 molar ratio for single-channel recordings.
2. Thaw liposomes on ice. Rinse a clean glass slide with water and ethanol and dry completely. Place a 10 μl drop of the proteoliposome on the center of the slide and dry O/N in a desiccator at 4 ^oC under vacuum.
3. Re-hydrate the dried proteoliposomes by adding 20 μl of Buffer B (150 mM NaCl, 10 mM HEPES, pH 7.0) and place the slide in a petriplate on top of a moist filter paper. Cover the plate and allow the rehydration to proceed for about 2 hr.
   NOTE: This process yields giant multi-lamellar liposomes that are conducive to patch from.
4. Pull patch pipettes from thin-walled borosilicate glass capillaries (~1 – 2 μm tip diameter) using Manufacturer's recommended setting on the pipette puller. Heat-polish using a fire-forge to a resistance of 1.5 – 2MΩ when filled with Buffer B.
5. Fill the recording chamber with Buffer B using a pipette and attach the Ag/AgCl ground electrode. Using a 2 μl pipette tip, gently dislodge the liposomes from the edge and transfer 1 μl of the suspension on the recording chamber. Wait a few minutes for the liposomes to settle to the bottom.
6. Fill the patch-pipette with Buffer B using a nonmetallic syringe needle and mount it on the amplifier head-stage. Identify a single-isolated vesicle to patch. Apply a slight positive pressure to prevent the patch-pipette from clogging, and insert the tip into the recording chamber.
7. Apply test pulses to measure the pipette resistance and compensate for the pipette voltage offset. Approach the vesicle, and when contact is made, apply a slight negative pressure to gently pull the vesicle against the patch pipette to form a gigaohm seal.
8. Monitor the resistance of the pipette during the entire process. Once the gigaohm seal is formed, withdraw the pipette carefully away from the liposome to form an inside-out patch. Turn off the test pulse.
9. Set the holding potential to -100 mV, and apply a pH pulse. Low pH was obtained using 10 mM sodium citrate Buffer C (150 mM NaCl, 10 mM citrate, pH 3.0). (Figure 3)
   NOTE: Recordings are made at a sampling frequency of 10 kHz for macroscopic and 40 kHz for single channel measurements.

6. EPR Measurements

1. Continuous-Wave EPR Spectroscopy
   1. Transfer the liposome suspension from Step 3.2 into a 200 μl tube and pellet the samples using a centrifuge. Discard the supernatant and sample is ready for EPR measurements.
      NOTE: For EPR measurements, it is important to remove as much buffer from the liposome sample as possible. Since aqueous samples absorb the electric part of the microwave resulting in heating and loss of sensitivity.
   2. To carry out buffer exchange, transfer 20 μl of liposome pellet using a pipette to a microfuge tube. Add 180 μl of Buffer D (100 mM NaCl, 10 mM citrate, pH 3.0) and incubate at 42 ºC water bath for 5 min. Centrifuge the sample, remove the supernatant using a pipette and repeat the process three times to ensure complete buffer exchange.
      NOTE: Alternatively, buffer exchange can be made by subjecting the samples to multiple freeze/thaw cycles.
   3. Gas permeable plastic capillaries are suitable for measurements of both spectral line-shapes and solvent accessibility. Tap the capillary onto the pelleted proteoliposome to draw the sample inside and seal the end with bone wax.
      NOTE: Typical sample volumes are ~5 μl and a desirable spin concentration is 150 μM. If the objective is to measure line shapes alone, one can use 0.4 mm OD quartz capillary tubes. If necessary, a pipette could be used for filling the sample inside the capillary.
   4. Operate the spectrometer
      1. Perform CW-EPR measurements at RT (292 – 297 K) on an X-band spectrometer equipped with a dielectric resonator as per the manufacturers' instruction manual.
      2. Turn on the water chiller, power supply, and microwave bridge console. Allow the system to thermally equilibrate for about 30 min before the recording. Open the acquisition software.
      3. Insert the sample tube/capillary into the resonator, make sure that the section of the tube filled with sample is at the center of the resonator cavity. Tune the resonator as per the instruction on the spectrometer manual.
      4. Record the first derivative absorption spectrum by field sweep at an incident microwave power of 1.0 mW, a modulation frequency of 100 kHz and a sweep width of 100 G. Determine the optimal power for the experiment by carrying out a progressive power saturation experiment where the peak-to-peak height of the first derivative CW EPR signal is measured as a function of the square root of the incident microwave power.
         NOTE: At lower microwave powers, the intensity of the signal increases in proportion to the square root of the power as long the equilibrium population of the spin states is unaffected. However, if power is further increased, the spin-lattice relaxation can no longer maintain the equilibrium population difference of the two spin states and the signal amplitude starts to plateau or "saturate." Beyond this point, the signal amplitude may actually decrease with increasing observe power due to population inversion of spin sates. In addition, for broadened spectra with extensive wings where a well-defined flat baseline is not visible, extend the sweep width to 150 – 200 G to prevent area loss.
      5. Start with using a modulation amplitude of 1.0 G.
         NOTE: This value is sample-dependent and adjusted to decrease the low frequency noise in the signal. If too large a value is used, it may distort or broaden the signal.
      6. Set the time constant and conversion time to 20.48 msec, sweep time to 20.97 sec, and resolution to 1024 points.
         NOTE: The time constant is also based on the sample and is adjusted to filter out high frequency noise.
      7. After the first scan, set the center field at the center of the EPR signal and choose sweep width such that the trace includes the signal and sufficient baseline on either side.
         NOTE: Also, to improve the signal/noise ratio, increase the number of scans based on the strength of the EPR signal. Include sweep width and number of points
      8. Measure the accessibility of the spin label to collisional relaxing agents O₂ or ethylenediaminediacetic acid (NiEDDA) using power saturation protocols²⁷ described in step 6.1.4.4.
         NOTE: Prepare NiEDDA as described previously ²⁶.
      9. First perfuse the sample in the cavity with N₂ for 5 min (to flush out O₂). Measure the spectra for each microwave power between 5 – 35 dB in steps of 3 dB with a sweep width of 30 G.
      10. Then perfuse the sample in the cavity with air for 10 min and measure the spectra at different microwave powers (5 – 35 dB in steps of 3 dB) as in the step 6.1.4.9.
      11. Incubate 20 μl of liposome pellet with 180 μl of 50 mM NiEDDA (in Buffer B or Buffer D) in a 42 ºC water-bath for 5 min. Centrifuge the sample and remove the supernatant using a pipette. Load the sample into the capillary and place it in the resonator cavity. Repeat step 6.1.4.9.
          NOTE: The principle behind the experiment is that the interaction with paramagnetic relaxing agents through Heisenberg spin exchange would prevent saturation of the signal and population inversion. Water soluble NiEDDA and lipid soluble molecular O₂ are used as reporters for water (both bulk and intraprotein vestibules) and membrane exposed positions on the protein, respectively.
2. Data Analysis:
   NOTE: The analysis of EPR data involves the following steps:^{14,22,23,25-27}
   1. Calculate the mobility of the spin probe (ΔH_o^-1), as the inverse of the central line width of the first derivative absorption spectrum. ΔH_o^-1 is reflective of the motional freedom or the dynamics of the probe.
   2. Calculate the accessibility parameter (П), which is an estimate of the accessibility of the probe to other paramagnetic collisional relaxing agents, using steps described below.
      NOTE: Interaction of the spin-probe with paramagnetic relaxing agents enhances the spin-lattice relaxation rate (T₁) of the nitroxide by Heisenberg spin exchange.²⁷
      1. Estimate the accessibility parameter (П) from power saturation experiments (6.1.4.8) in which the vertical peak-to-peak amplitude of the central line of the first derivative EPR spectrum is measured at different microwave power.²⁵ Plot the amplitude of the signal as a function of the square-root of the microwave power and fit with the following equation ²⁷.
         
         NOTE: Where A is the amplitude of the signal, is a measure of the homogeneity of the saturation of the resonance line (which is usually between 0.5 and 1.5), I is a scaling factor, P is the incident power, and the represents the value at which the first derivative amplitude is half of its unsaturated value.
3. Calculate ΔP_1/2 as the difference in P_1/2 values in the presence (O₂ or NiEDDA) and absence (perfused with N₂) of paramagnetic relaxing agents. Calculate the accessibility parameter (П) using the equation:
   
   NOTE: Where P_1/2^reference and ΔH_o^reference are the half maximal power saturation value and the central line width, respectively, for the reference standard (such as DPPH (2,2-diphenyl-1-picrylhydrazyl))²⁷.