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Sittampalam GS, Coussens NP, Brimacombe K, et al., editors. Assay Guidance Manual [Internet]. Bethesda (MD): Eli Lilly & Company and the National Center for Advancing Translational Sciences; 2004-.

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# Calculations and Instrumentation used for Radioligand Binding Assays

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Published ; Last Update: October 1, 2012.

## Abstract

Radioligand binding assays are a “work horse” in biological laboratories and have been adapted for HTS and lead optimization support in drug discovery. The instrumentation is highly specialized to measure radioactivity of the labels on binding ligands and requires specialized calculation procedures. In this chapter, the author thoroughly and systematically describes the instrumentation and calculation principles used in data analysis. Sample calculations are shown along with definitions of terms and important steps in setting up the instrumentation. This is a very useful chapter for beginners, as well as a refresher for experienced investigators.

## Introduction

The purpose of this chapter is to 1) describe common calculations used in radioligand binding assays and 2) outline steps for setting up and using microplate scintillation counters (Microbeta Trilux and TopCount).

When performing calculations such as those described on the following pages, it is advised to use unit dimension equations. This ensures that values have the appropriate units for the designated purpose. Unit dimension equations are used through this chapter.

### Determination of Counting Efficiency

Microplate scintillation counters, used for reading Scintillation Proximity Assay (SPA) and filtration assays, detect flashes of light (photons) that occur when a released radioactive particle interacts with and excites a fluor molecule. Not all of the radioactive particles emitted will be detected as photons by the counting instrument. The output from the scintillation counter is the number of photons detected per unit time, typically expressed in counts per minute (CPM). The ratio between CPM detected by the instrument and actual disintegrations per minute (DPM) of the isotope is termed efficiency. The efficiency of counting depends on the geometry of the detector, scintillation properties of the fluor and the energy of the particular isotope. Determination of DPM is important for making conversions to calculate molar concentrations of radioligands, and it is also important if a comparison between different instruments is required. For data that will be normalized (e.g. % Inhibition), CPM can be used as a direct readout from the instrument.

The efficiency for each isotope counting condition should be independently determined for an instrument. Steps to determine average instrument efficiency are shown in the example below for an SPA assay using a [3H]-labeled radioligand and YSi SPA beads:

#### Example Determination of Efficiency

[3H]-labeled SPA Beads can be prepared by incubating [3H]-labeled biotin with YSi streptavidin beads and washing them (using centrifugation) to remove any unbound radioactivity. Alternatively, a reaction associated with an assay (e.g. WGA beads, membranes, radioligand) can be used.

1.

Remove a 300 μl aliquot of [3H]-SPA beads to a 1.5 ml polypropylene tube.

2.

Centrifuge the tube for 5 seconds in a microfuge to pellet the [3H]-SPA beads.

3.

Remove the supernatant. Dispose of it properly, treating it as potential radioactive waste.

4.

Add 300 μl of PBS and mix beads. Repeat centrifugation and remove supernatant.

5.

Resuspend in a final volume of 300 μl PBS.

6.

For a Microbeta, pipette 25 μl of beads into three different wells of a microplate. Add 175 μl of PBS. Allow the beads to settle overnight.

7.

Count the microplate and determine the average CPM for the three replicates (example: 52,800 CPM).

8.

Add 25 μl of beads to three different scintillation vials containing scintillation cocktail. Count the vials on a liquid scintillation counter, which is capable of returning results in DPM, and determine the average for the three replicates (example: 140,582 DPM).

9.

Determine efficiency using the following equation:

For [125I], a gamma counter with a known efficiency can be used for the determination of the total DPM.

Some typical instrument efficiencies for common isotope configurations on a Trilux Microbeta are shown in Table 1.

#### Table 1:

Typical instrument efficiencies for common isotope configurations on a Trilux Microbeta. These are approximate efficiencies for comparison and actual efficiencies for your instrument should be determined independently.

These are approximate efficiencies for comparison. Actual efficiencies for your instrument should be determined independently. In addition, some counting conditions require special “window settings” that can impact the apparent efficiency. Alterations or repairs to an instrument (e.g. adjustment of photomultiplier tubes (PMT’s)) may also require determination of an updated efficiency value.

### Conversion from CPM to DPM

DPM are calculated from the equation shown below, where efficiency is expressed as a decimal percent. Determination of instrument efficiency (Eff) is described above.

Example:

1000 CPM detected in an assay using Polyvinyltoluene (PVT) SPA beads and 3H.

The instrument efficiency was determined to be 22%.

 DPM = CPM/Efficiency = 1000/0.22 = 4545

### Specific Activity (SA)

The amount of radioactivity per unit mole for a radioligand is referred to as the specific activity (often abbreviated as SA) and is typically given in units of Ci/mmol by the manufacturer. Since raw data from assays using radioactivity are in CPM or DPM, conversion of the specific activity from Ci/mmol to CPM/fmol or DPM/fmol is usually more convenient for further data analysis.

Conversion Factors: 1 Ci = 2.22 x 1012 DPM

1012 fmol = 1 mmol

Equation to convert Ci/mmol to DPM/fmol:

DPM/fmol = [Specific activity (Ci/mmol) x [2.22 x 1012 DPM/Ci] x [mmol/1012 fmol] = SA x 2.22

Example: SA = 2000 Ci/mmol

DPM/fmol = SA x 2.22 = 2000 x 2.22 = 4440 DPM/fmol

Equation to Convert Ci/mmol to CPM/fmol:

CPM/fmol = [SA (Ci/mmol) x [2.22 x 1012 DPM/Ci] x [mmol/1012 fmol] x Efficiency (CPM/DPM) = SA x 2.22 x Eff

Example: Instrument efficiency = 40%, SA = 2000 Ci/mmol

CPM/fmol = SA x 2.22 x Eff = 2000 x 2.22. x 0.4 = 1776 CPM/fmol

### Nominal Concentration of a Radioligand

The theoretical or nominal concentration of a radioligand stock solution can be calculated from the stated radioactive concentration (RAC, in μCi/ml) and the specific activity (SA, in Ci/mmol) using the equation shown below:

Example: Radioactive concentration (RAC): 50 μCi/ml

Specific Activity (SA): 2000 Ci/mmol

Conversion factor: 1 Ci = 106 μCi

[Radioligand] = RAC/SA = (50 μCi/ml ÷ 2000 Ci/mmol) x 1 Ci/106 μCi = 2.5 x 10-8 mmol/ml

= 2.5 x 10-8 M

= 25 nM

This is the nominal concentration of the stock on the reference date. To estimate the concentration on any other day, see the Radioactive Decay section to determine the fraction remaining and the resulting concentration. See also the Dilution of Stock section to prepare a dilution of a stock radioligand.

### Actual Concentration of a Radioligand

When performing radioligand binding assays, a rough estimate for the concentration of radioligand used in the assay can be computed using the information supplied with the material. This is called the theoretical or nominal concentration (shown above). In order to calculate the actual concentration of the radioligand used in an assay more accurately, one should count an aliquot of the stock mix and obtain the CPM or DPM for that aliquot, then use the equation below.

Equation to convert CPM to pM:

Example: Counted a 50 μl aliquot of a stock mix, which yielded 50,000 CPM; SA = 1776 CPM/fmol (see above for calculation).

If values are in DPM, one should use specific activity (SA) expressed in DPM/fmol. Use appropriate unit conversions to determine the concentration in nM, μM, etc.

It is best practice to use the actual concentration of radioligand determined for each assay in calculations such as Ki, rather than the theoretical or nominal concentration.

Radioactive decay is a random event and follows an exponential decay trend. You can calculate the fraction remaining in a radioactive sample if you know the date (reference date) when the specific activity or radioactive concentration was known using the following equation:

where t1/2 is the half-life of the isotope (time it takes for half the isotope to decay), and time is the number of days before or after the known reference date. The term (-0.693/t1/2) is also referred to as the decay rate constant, Kdecay.

Example: [125I] radioligand with a known specific activity on 10/1/07.

Half-life for [125I] = 60 days.

Fraction remaining on 10/20/07 (20 days):

0.794 or 79.4% remaining

The fraction remaining following radioactive decay can also be determined from tables. Note that for the activity on a day prior to the stated reference date, the fraction remaining will be greater than 1.

An assumption typically made is that radioactive decay results in unlabeled decay product(s), which no longer bind to the target or receptor of interest. This implies that the specific activity remains constant over time and that the concentration of ligand changes with time. This assumption may not be valid with all radioligands used.

### Half-Life

Table 2 shows half-lives (time for half of the isotope to decay) for common isotopes, along with typical values for specific activity of a single-labeled molecule. One should always consult the manufacturer's information for the exact specific activity of a radioligand.

#### Table 2:

Half-lives for common isotopes and typical values for specific activity of a single-labeled molecule. One should always consult the manufacturer’s information for the exact specific activity of a radioligand.

Note that half lives (even for the same isotope) can vary from one manufacturer to another. In addition, if software is used for tracking of decay of isotope inventories, one must make sure that the half life value used is consistent throughout.

### Dilution of Stock

To calculate the amount of a radioligand stock solution required to prepare a specific volume of a dilution, the parameters listed below will be needed. The values listed for each parameter are for use in the example calculations.

Specific Activity (SA): 2000 Ci/mmol

Half-life for isotope: 60 days (I-125)

Reference date: 10/1/07

Date of preparation: 10/20/07

Volume of final diluted mix: 50 ml

Desired concentration of final diluted mix: 0.1 nM

1.

Determine nominal stock concentration – described above in Stock Concentration section:

[Radioligand] = RAC/SA = (50 μCi/ml ÷ 2000 Ci/mmol) x 1 Ci/106 μCi = 2.5 x 10-8 mmol/ml

= 2.5 x 10-8 M

= 25 nM

2) Determine stock concentration on day of use – described in Radioactive Decay section above:

Date of use – Reference Date = 20 days

0.794 or 79.4% remaining

Therefore, stock concentration on day of use = 0.794 x 25 nM = 19.85 nM

3) Determine amount of stock required:

C1V1 = C2V2 solving for V1, yields V1 = C2V2/C1 = (50 ml x 0.1 nM)/19.85 nM = 0.252 ml

This is the theoretical or nominal concentration. To determine actual concentration, count an aliquot of the diluted mix and calculate as shown in the Actual Concentration of Radioligand section above.

## Instrumentation

### Microbeta Trilux

#### General Concepts

A Microbeta Trilux comes with either 6 or 12 detectors. Each detector is comprised of two photomultiplier tubes (PMT’s), one on top of the sample and one on the bottom. The PMT’s operate using conventional coincidence circuitry, as shown in Figure 1.

#### Figure 1:

Diagram of a Microbeta Detector. Each detector includes two photomultiplier tubes that operate in coincidence counting mode. In this mode, background photons not related to the sample are eliminated because they do not possess the energy required for (more...)

Each detector counts only a portion of a 96-well microplate (16 wells per detector on the 6-detector Microbeta model, ~9 wells on the 12-detector model). The area of the plate counted by each detector of a 6- or 12-detector model is shown in Figure 2.

#### Figure 2:

The area of the plate counted by each detector of a 6- or 12-detector model of a Microbeta Detector.

Although the use of multiple detectors can increase throughput, since the performance of PMT’s are not identical, a calibration procedure (Normalization) is required. An identical sample is counted by all of the detectors, and a relative efficiency (fractional value) is determined. If an activity (DPM) for the sample is known, this can be inputted into the software, and the detectors are normalized to this activity. This will result in the efficiency factors being lower than if the detectors are normalized against each other. As an example, the typical efficiency relative to activity for [3H] with SPA beads is 0.20 – 0.30. When the detectors are normalized against each other, the relative efficiencies should be 0.9 – 1.0.

#### Modes of Normalization

There are two ways to normalize the Trilux with a single sample in well G11 (for 96 well plate):

1.

Relative to the detector with the highest reading (CCPM = CPM)

2.

Relative to the activity inputted in well G11 (CCPM = DPM)

The basic principle for each of these modes is shown at the end of this section. The sample to be used for normalization must be in well G11. Both normalization protocols are set up the same way, with one additional step for mode 2, when results in DPM are desired. There are other features for Standardization (e.g. using quench curves) or Easy DPM, Paralux, etc. that are not discussed in this document.

#### Setup of a Normalization Protocol

1.

Click on the Protocols button at the top of the Microbeta software toolbar.

2.

Select Normalizations followed by the Open button.

3. Click on the New button to create a new normalization protocol.

4. Select the appropriate label from the pull-down menu in the pop-up dialog box and click OK. Do not check SPA unless you want to use Paralux counting mode (consult instrument manual).

In many cases, particularly with YSi SPA beads, you should select Other and use the manual energy spectrum window settings shown in the table below in Step 6. The default settings were designed for PVT SPA beads.

5. Under the General tab, type in a name for the protocol and select a number for the protocol from the pull-down list (only unused, available protocol numbers are listed).

If it is desired to express results in DPM: Check the Isotope activity box and input a number for the activity (in DPM) that is in well G11. This activity should be determined by counting an identical aliquot in a liquid scintillation counter (for 3H) or a gamma counter (for 125I) that has a known efficiency (DPM = CPM/Efficiency). In this example, replicate aliquots of YSi SPA beads were counted in a liquid scintillation counter with an average of 140,782 DPM. An identical aliquot was placed in well G11 of a microplate for normalization. The value 140,782 is entered into the area on the General tab, as shown below.

6. If Other was selected as the label, the energy spectrum window settings may need to be manually defined. By default it will appear under the Other tab as a window from 5 to 1024, an open energy spectrum window.

Uncheck the box next to Use defaults. The window settings for Low and High can now be changed.

Table 3 indicates the suggested settings for several isotopes and types of SPA beads and Cytostar-T plates. The screen capture below shows the Other tab, after new window settings have been inputted for tritium YSi SPA beads and the Microbeta (Table from www.perkinelmer.com).

#### Table 3:

suggested settings for several isotopes and types of SPA beads and Cytostar-T plates

7. Click OK to save the normalization protocol.

#### Setup of a General Counting Protocol

A Normalization protocol is linked to a General Counting protocol, in order to define the counting parameters (i.e. isotope, window settings, etc.) and the detector efficiencies (relative to the highest detector reading or relative to DPM activity) needed to correct raw counting data.

1.

Click on the Protocols button at the top of the Microbeta software toolbar.

2.

Select General followed by the Open button.

3. Click on the New button to create a new General counting protocol.

4. In the Edit Counting Protocol window, type in a name for the protocol in the Identification space. Select a protocol number from the pull-down list to the right of the Identification name. Only unused protocol numbers will appear in this pull-down list.

5. Select the isotope from the pull-down list. Once the isotope is selected, Normalization protocols that have been created using that isotope will appear in the Normalization pull-down area. Select the appropriate Normalization protocol to link to the General counting protocol. Note that an underscore (_) before the name of a Normalization protocol indicates that the Normalization plate has not been counted yet. Once the Normalization data has been stored, an (n) will appear before the name of the Normalization protocol.

6. Change the Counting time if desired (default is 1 min). The other tabs in the Edit Counting Protocol window (Corrections, Counting Control, Other) usually do not need to be modified unless special counting circumstances are being used.

7. Click OK to save the General counting protocol. Click Yes on the dialog box that pops up.

8. From the Protocol group General window, the General counting protocols can be edited.

9. The Protocol button allows editing of the protocol parameters (i.e. counting time).

10. The Plate map button allows selection of microplate wells to count (default set to entire plate).

11. The Output button allows selection of file and printing options. There are a couple of changes that should be made in the output as outlined below:

If the instrument is connected to a network and does not have a dedicated printer attached to the PC controller, it may be desirable to deselect the printing option. Quality printouts of the data directly from the instrument to a network laser printer are difficult. Deselect Generate print output in the Print tab.

Under the File 1 tab, it is advisable to change the path where data files are electronically stored. By default, they are stored in the Results subdirectory where the Microbeta software is stored. This can be dangerous, as the Normalization parameters are also stored in that subdirectory. Accidental deletion or moving of Normalization protocol results files will render the Normalization protocols useless. To prevent this, direct General counting output to a different subdirectory.

Under the File 1 Items tab, if you do not want the electronic data file to have the data expressed as 96 numbers in a column (for a 96-well plate), deselect the Column section box. The data file will have results in plate format only (8 x 12 array for 96-well microplates).

The suggested outline shown above is for general counting conditions. One should consult instrument owners or the manufacturer for advanced counting options such as cross-talk correction, background correction or manual setting of count windows.

Figure 3 demonstrates the linking of a Normalization protocol to a General counting protocol for a 12-detector Trilux using either a relative detector efficiency set up or anefficiency relative to a known activity. Similar linking occurs for a 6 detector instrument.

#### Figure 3:

Linking of a Normalization protocol to a General counting protocol for a 12-detector Trilux using either a relative detector efficiency set up or an efficiency relative to a known activity.

### TopCount

#### General Concepts

The TopCount is different than the Microbeta because it uses a single photomultiplier tube (PMT) counting from the top of the microplate instead of one PMT on top and one on bottom. Consequently, the TopCount determines background from true photon events using a time-resolved discrimination method of scintillation counting. This means that appropriate scintillators (known as slow scintillators) must be used for proper signal detection (Figure 4). The TopCount is available in 6- and 12-detector models.

#### Figure 4:

Diagram of TopCount Pulse Discrimination. Appropriate slow scintillators must be used to allow the photon energy to dissipate in a time resolved manner (multiple pulses detected during resolving time). Single pulses detected by the PMT during the resolving (more...)

Normalization of the TopCount is similar to the Microbeta, except that Well A10 is used by the detectors as the common read well. In addition, the TopCount NXT software does not have a provision to enter in an activity (in DPM) for the normalization amount on the plate. Therefore, results are always reported in corrected CPM, with the detectors normalized relative to each other. Efficiency of the TopCount must be determined manually, and the correction factor must be applied to determine DPM activity. Further information about normalization procedures and applications for the TopCount can be obtained from the manufacturer.

A stepwise procedure for setting up a counting protocol on a TopCount NXT is shown below.

#### Setup of Counting Assay

1.

Click on the Assay Wizard icon located in the tool bar at the top of the software window (hold the mouse over a button to obtain a description of each icon).

2.

Select Create a New Assay.

3.

Define the assay name and number; select CPM as the Assay Type; select the desired plate type if requested.

4.

Accept the default selection of Unknowns, unless you need to add Totals and Blanks for additional calculations.

5.

Select Counting Options including delays and repeats, and select the Radionuclide from the drop-down list. Table 4 lists preset window settings on the TopCount NXT.

6. Define printed and ASCII file outputs, as well as post-processing user application programs.

7.

Select Instrument Correction Factors.

8.

Establish Instrument Correction Factors.

9.

Define Sample Map and finish Setup.

10.

The first time the Assay Protocol is selected, a normalization plate with a sample of activity in well A10 will be expected. Future runs will count plates using the stored normalization parameters.

#### Table 4:

Preset window settings on the TopCount NXT.

## Uniformity Plate

To test instrument detector variation, a uniformity plate with the same level of radioactivity in all wells is generated. The counting results are analyzed for each detector, as well as across the plate by columns and rows, to determine if any detectors require adjustment. Periodic counting of a uniformity plate (called a Performance Check) can identify detector drift or other instrument problems. This procedure can be performed regardless of the instrument type or the number of detectors.

Since many assays are performed in a concentration response mode, a gradient signal across the plate is an expected result. An example of how a Performance Check using a uniformity plate can assist in reducing instrument variability is shown in Figure 5.

#### Figure 5:

Example a performance check, which reduces instrument variability.

To generate a 96-well microplate for [125I] SPA beads, labeled beads are prepared using WGA beads, [125I]-ligand and receptor membranes. A brief procedure is described below:

Add receptor membranes, [125I]-ligand and WGA SPA beads in an appropriate buffer in a single tube. After a incubation time (consistent with the biological system), add 200 μl of diluted bead mixture per well using a 12-channel pipette. Change tips for each row. Allow beads to settle overnight (stable counting conditions) or centrifuge if the receptor/ligand interaction is not stable. Count radioactivity in Microbeta (use clear bottom plate) or TopCount (use opaque bottom plate

Results for a typical read using a clear bottom plate and a 12-detector Microbeta Trilux are shown in Figure 6. The relative efficiency between all 12 detectors is >95%.

#### Figure 6:

Results for a typical read using a clear bottom plate and a 12-detector Microbeta Trilux.

## Color Quench Correction

If colored compounds are to be tested and are present during the counting step (as in a non-separation technique such as SPA) color quenching may be present. This occurs when the photons emitted by the fluor are absorbed by the colored compound resulting in attenuation of signal. The emission spectra (~420 nm max) of SPA beads detectable in the Trilux and TopCount and the absorption spectra for common colors are shown in Figure 7.

#### Figure 7:

The emission spectra (~420 nm max) of SPA beads detectable in the Trilux and TopCount and the absorption spectra for common colors. Diagrams from PE LAS.

For the Trilux and TopCount, compounds that are red, yellow or orange (absorption max ~400 nm) have the biggest impact on signal attenuation (with PVT or YSi SPA beads) if they are present while reading the plates.

Correction of color quenching can be performed within the software of the Trilux or TopCount using a prepared quench curve. Typically, this is performed with a yellow dye, such as tartrazine.

## Abbreviations

CPM = Counts per minute

DPM = Disintegrations per minute

SA = Specific activity, example: Ci/mmol

RAC = Radioactive concentration, example: µCi/ml or mCi/ml

Eff = Efficiency, defined as CPM/DPM

PMT = Photomultiplier tube, detects photons of light emitted by a source (e.g. fluor)

SPA = Scintillation Proximity Assay

YSi = Yttrium silicate, a rare earth metal based SPA bead

PVT = Polyvinyltoluene, a plastic-based SPA bead

PE LAS = Perkin Elmer Life and Analytical Sciences

*

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Bookshelf ID: NBK91997PMID: 22553868

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