A gain and dynamic range independent index to quantify spillover spread to aid panel design in flow cytometry

Concept of SQI

The SQI value is defined as the difference in median fluorescent intensity (MFI) between the 99th percentile and the 50th percentile in detector B, of the positive population of fluorochrome X (Fig. 1). Detector B is the recipient detector where spread from fluorochrome X is being registered. This value is a measure of total spread including spillover fluorescence in a secondary detector. Some examples of SQI can be found in Fig. 2. The following abbreviations are used to describe the calculation procedure as explained in Fig. 1.

• X^B50 = 50th percentile of compensated positive population of fluorochrome X in detector B.

• X^B99 = 99th percentile of compensated positive population of fluorochrome X in detector B.

• Un^B50 = 50th percentile of compensated unstained population of in detector B.

• YSt^B50 = 50th percentile of compensated stained population of fluorochrome Y in detector B.

• NFY^B = Normalization factor of fluorochrome Y in detector B (Normalization Factor, in Fig. 1).

• (YSt^B50 – Un^B50) = The difference between the positive and negative populations (scale units) (Difference 2, D in Fig. 1).

If P (any constant number, in this article we have used P = 9000) is the number of photons received by the detector B and (YSt^B50 – Un^B50) are the number of scale units of detector B that represent P.

Then (YSt^B50–Un^B50) ≡ P, but not equal.

1 scale unit in detector B = P/(YSt^B50 – Un^B50) = NFY^B

If SQI value X^B = Spread of fluorochrome X in detector B,

Then SQI X^B = (X^{B99ber of photons received by the detecto} – X^B50) × NFY^B.

By applying the stated normalization factor, the SQI value is made independent from voltage/gain settings of the detectors, and dynamic range. The normalization factor is founded on two assumptions. First, the number of incoming photons remains the same when settings of the secondary detector are changed. This means that changing the detector voltage/gain will not change the excitation of the fluorochrome by the laser and the number of emitting photons will remain same when they pass through the same filters and mirrors. Second, differences in signal intensities are linearly proportional to changes in detector settings. This means that the conversion of photons into photo electrons is constant. In one gain setting, 1 photon converts into 3 photoelectron and 5 photons into 15 photoelectrons, while in another gain setting, if 1 photon converts to 5 photoelectrons, then 5 photons must convert into 25 photoelectrons.

The normalization factor allows for the SQI value to be determined without prior optimization of detector settings, provided that all obtained data is within the linear range and negative values are outside the detector noise. P is the difference in number of photons that are coming from positive and negative population in detector B. This number will stay practically constant when saturatedly stained samples will be maximally excited. The lasers of almost all of the presently available cytometers are designed to get maximal excitation. For this reason, we can get the same P values in all commercial cytometers. Maximal excitation makes P practically a constant. The constant nature of P in these terms allows for direct comparison of SQI values between instruments with different dynamic ranges. SQI showed a high degree of reproducibility in an average of three runs on the Fusion (Supplementary Fig. S1). In the discussion, we elaborate on the conditions that must be met. Importantly, when multiple fluorochromes are associated with the same detector, the same amount of spread results in a higher SQI in secondary detectors when associated with dim fluorochromes (Supplementary Table S1).

Classification of SQI values

Since there are no clear consensus or characteristics that divide spread in categories^14,15, we created a different, semi-quantitative method to categorize SQI outcome as described below:

For example, 262,144 is the total number of scale units for BD machines (Fusion and Symphony). SQI between 0 to 120, 121 to 220, 221 to 300 and 300 + matches nicely with 0 to 0.5%, 0.5% to 1%, 1% to 1.5% and 1.5% + of scale unit occupancy respectively. Comparing percent of scale units occupied with SQI will provide the user with a better understanding of spread between different types of machines (Table 1) and between multiple machines of the same type (Table 2). We have color coded SQI values in 4 categories (Tables 1 and 2): 1–120 (Green); 121–220 (Yellow); 221–300 (Orange); and 300 + (Red). While Green and yellow both provide acceptable discriminative power in most cases, Green should be reserved for markers with low or unknown expression levels. Values with an Orange or Red SQI value should be used for markers on distinctly separated cell populations or for markers with exclusive expression on specific cell subsets. For example, if BV421 is combined with Alexa Fluor 647 (AF647), the SQI value is 20 (Green). Note that the SQI value is not zero due to measurement error of the autofluorescent signal and biological variance. In comparison, if PE-Cy5 is combined with AF647 the SQI value is 611 (Red). At these different levels of spread, 15% and 5% double positive events were identified respectively (Supplementary Fig. S2). Double positive events are those which are outside the spreading error, received by the secondary/recipient detector (R670). The lower number of double positive events registered for the PE Cy5 compare to BV421 because of the need to account the higher spreading error coming from the PE Cy5.

Intrinsic Spillover Spread values are dependent on detector voltage/gain settings

The ISS value of BV605 changed in the recipient detector when voltage of the primary detector changed, because the intensity difference (ΔF) between the positive and negative populations incorrectly describes a change in photonic input in the secondary detector (Fig. 2A). Importantly, the variance as represented by the rSD and SQI value remained the same. When voltages of both the detector were reduced, the rSD and ISS values were lower too (Fig. 2A–C). Conversely, the SQI value was unchanged. In Fig. 2D we only reduced the PMT voltage of the secondary detector which decreased the ΔF of the secondary detector resulting in increasing the related ISS.

SQI values are independent of detector gain settings

Our main goal is to quantify spread independent of detector voltage/gain. The normalization factor was introduced for this reason. We devised this simple experiment to test the accuracy of the normalization factor. Single stained beads were measured with two different PMT voltage sets. The voltage was manipulated to position the positive population to ~ 110,000 MFI or 50,000 MFI in all detectors. The SQI values were the same in both voltage sets, but the ISS values were quite different (Table 3). This observation is possible because SQI does not include any component from the primary detector. When the voltage of detector B was decreased, the spread from fluorochrome X in detector B was reduced, but the intensity of fluorochrome Y, which was used to calculate normalization factor, reduced proportionally, rendering SQI values independent of detector voltage. In contrast, when the same data were used to obtain the conventional Spillover Spread Matrices, the lower voltage set showed lower ISS values (Table 3). In another scenario, a series of voltages were applied in which the voltage of the secondary detector was kept constant, but the voltage of the primary detector was changed gradually (Fig. 3A,B). Alternatively, the voltage of the primary detector was kept constant, and the voltage of the secondary detector was changed (Fig. 3C,D). In both cases the SQI values remained the same, however, the ISS values changed considerably.

Application of SQI: compare instruments with different dynamic range

To investigate which instrument is the best for running a given panel in terms of spread, we compared the SQI values between a Fusion, Symphony, Quanteon and a CytoFLEX (Table 1). The CytoFLEX showed the lowest number of SQI values above 120. The other instruments showed a higher number of values above 120. The Quanteon and CytoFLEX had the lowest number of SQI values over 300. The Quanteon had the highest number of SQI values between 120 to 199.

Application of SQI: compare instrument performance

While all three Fusions had similar optical configuration and laser power, Fusion 3 performed best with only 6 instances of 300 + range. The performance of The Fusion 1 was considered worst with 12 occurrences of Range values over 300. The findings are summarized in Table 2. The results suggest that Fusion 3 is more suitable for the most sensitive experiments.

Application of SQI: investigate the effect of instrument characteristics on spread

SQI was used to investigate the effect of high and low laser powers in Fusion 2 which showed some interesting findings. At an output power of 140 mW, the Red laser resulted in lower spillover spread from APC and APC-R700 compared to lower output power of 100 mW (Table 2). In other cases, higher laser power showed minimal effect on spread. For instance, at 100 mW, the 405 nm laser showed virtually the same spread in all three violet detectors as compared to measurement at 85 mW (Supplementary Table 2). Our data indicates that in our systems, higher laser powers other than for the red laser, doesn’t lower the data spread (Table 2).

Validation assay

To test the usefulness of SQI, we ran two small panels separately. The experiment was performed on Cytek Aurora, a full spectral cytometer. Antibodies in both panels have identical clones and the exact same amount of antibody was used. In Panel 2, we replaced CD3-BV605, CD45-Alexa Fluor 488 with CD3-APC-R700 and CD45-BV650. We did this change to introduce more spread in the APC and PerCP-eFluor 710 detectors. We also choose BUV395, a dim fluorochrome with CD25 (low expression) to show clearly the adverse effect of lowering the gain. Both panels were run four times separately using four different gain settings (details are in material and methods). When analyzing for specific populations (Supplementary Fig. S3), ISS and SQI calculated using beads to show with change of gain, SQI remains the same but ISS drops (Supplementary Fig. S4). Further, reducing gain resulted in the loss of data resolution of the specific populations, marked by the black arrows in panel 1, and spread-induced masking of the specific populations, marked by the red arrows in panel 2 (Supplementary Fig. S4). These data, combined with the single color SQI with these same antibodies (Supplementary Table S4), demonstrate that BV650 and APC-R700 would produce much larger spread in APC and PerCP-eFluor 710 detectors resulting in masking of dimly expressing cells. This data confirms that SQI works nicely with full spectral cytometers as well as conventional cytometers.