Lymphocyte activation is a multistep process. The cellular events following the evolvement of immunological synapses between lymphocytes and their target cells lead to the activation of a number of intracellular second messengers. Of those, Ca2+ is an essential element for early activation (1, 2). Increased intracellular Ca2+ content is an irreversible step toward an activated state of a lymphocyte (3). Therefore, intracellular Ca2+ content presents important information about the status and kinetics of lymphocyte activation (4). Furthermore, monitoring lymphocytes' Ca2+ content is a valuable approach to assess the impact of disease and/or drugs on lymphocyte activation properties (5).
Several methods are available for the determination of intracellular Ca2+ levels (6–8). Indo-1 has been the most commonly used fluorophore in flow cytometric Ca2+ measurements; it has an excitation peak at 330–346 nm, depending upon the Ca2+ concentration, and requires a UV-capable laser with a line between 325 and 360 nm for excitation (6). Ratiometric analysis with Indo-1 is accomplished as the peak fluorescence emission for Ca2+ bound is 405 and 475 nm for Ca2+-free Indo-1. Hence, Ca2+ flux may be determined by calculating the ratio of the mean fluorescence intensity of Indo-1 emission at 405 nm/475 nm. Although Indo-1 requires the use of a UV-capable laser for excitation, this has had an advantage of preserving access to a 488-nm line, which allows the simultaneous use of fluorescein-conjugated antibodies.
An alternative to Indo-1 is the combination of Fluo-3 and Fura Red dyes. On binding Ca2+, the fluorescence intensity of Fluo-3 at 530 nm increases whereas that of Fura Red at 695 nm decreases when excited by 488-nm laser line. The ratio of fluorescence emissions of Fluo-3 to Fura Red is informative about intracellular Ca2+ levels; hence, its alteration is suitable for monitoring cell activation. [The advantage of simultaneous use of two dyes instead of one is that this approach is relatively insensitive to small fluctuations in the dye content on a cell by cell basis (9).]
Flow cytometry provides an opportunity to sequentially determine calcium levels even in several millions of cells over time and gain data about characteristics of lymphocyte kinetics. The characterization and interpretation of this huge number of data present, however, a great challenge. Commercially available softwares (10, 11) enable the calculation of average or median values of light intensity measured during a given time period, smooth curves (using average or median smoothing), and provide the graphical illustration of kinetics. Some of the most important parameters such as maximal values and slopes of the curves may be also estimated. These do not take into account, however, the specific (i.e., non-normal) distribution of measurement data and do not utilize the additional information provided by the huge number of individual measurement data.
Now we present a robust algorithm that provides an opportunity for the mathematical characterization of calcium-flux kinetics and the direct statistical comparison of individual flow cytometry-kinetic measurements.
MATERIALS AND METHODS
Fluo-3-AM (Cat. No. F-1242) and Fura Red-AM (Cat. No. F-3021) were from Invitrogen (Carlsbad, CA. Fluo-3 AM and Fura Red AM were solubilized to 10 mg/ml with dimethyl sulfoxide (Sigma, Bonnem, Belgium, Cat. No. D5879), with 10% Pluronic F127 (Invitrogen, Karlsbad, CA, Cat. No. P-3000MP), and stored protected from light at −20°C. Hank's Balanced Salt Solution (Modified 10X Cat. No. 55225-100M) was from Sigma and diluted using sterile, endotoxin-free, water. APC-labeled anti-CD4 (Cat. No. 555349) was from BD Pharmingen (San Jose, CA).
Peripheral blood mononuclear cells were separated by a standard density gradient centrifugation (Ficoll Paque, 25 minutes, 400 g, 22°C) from 10 ml of freshly drawn peripheral venous blood collected in lithium heparin treated tubes. Blood was drawn from healthy adult volunteers who gave informed consent to donate blood to this purpose. An independent institutional ethical committee approved their contribution. Peripheral blood mononuclear cells contained in the interphase were washed twice in phosphate buffer saline. The viability of cells was assessed by trypan blue exclusion (it was over 90% in every experiment).
Flow Cytometric Calcium Measurements
Cells were loaded with 4 μg/ml Fluo-3 AM and 10 μg/ml Fura Red AM for 30 minutes at 30°C. Cells were washed once and stained with APC-labeled anti-CD4. After washing, cells were kept at room temperature (21°C) at the dark. A 500-μl aliquot was warmed to 37°C prior to fluxing. First, a baseline (30 s) level was recorded. Then, the tube was removed, and different amounts of phytohemagglutinin (Sigma, Bonnem, Belgium Cat. No: L8754) (5–25 μg/ml) were added and the tube was replaced.
We used a FACSAria (BD, San Jose, CA) flow cytometer equipped with 488- and 633-nm lasers. Fluo-3 and Fura Red signals were separated with a 610-nm short pass dichroic filter and fluo-3 detected at 530/30-nm and Fura Red at 695/40-nm band pass filters.
The lymphocytic population was initially defined in a forward and side scatter gate. A second gate (logical) was then created around the CD4+ cells. Recording was commenced as soon as cells traversed the laser line and continued for up to 10 minutes (600 s). We applied ionomycin (1 mg/ml) stimulation as a positive control to verify dye loading. Data were saved as FCS 3.0 files and analyzed with R software's (12) Bioconductor's rflowcyt package (13).
Analysis of Published Data
In addition to our measurements, we also aimed to demonstrate the robustness of our algorithm by analyzing calcium-flux data obtained under other experimental conditions. For this purpose, a recent publication was selected that analyzed calcium flux of CD3+ cells and Jurkat cells with thapsigargin and anti-CD3 stimulus using Fluo-3 and Fura Red ratio and Indo-1 as well (14).
Measured intensity ratios were calculated and plotted against time. We analyzed kinetics on two ways: with usual methods (i.e., average and median smoothing; Fig. 1) and by fitting different functions on median values of data per time unit.
The kinetics the data follow may differ from measurement to measurement. We applied the following algorithm to find the function best fitting to the actual measurement to be analyzed.
First, we divided the measurement period up to equal time intervals. We fitted different functions (e.g., linear regression, logistic function, hormesis function) with nonlinear least square regression to median values and tested with F-test which function fits the best. On statistical function fitting analysis performed on many independent (but each at least 10 minutes long) calcium-flux measurements, the hormesis function (Fig. 2) fitted the best to the fluorescence intensity values measured against time in the majority of experiments. In some conditions, however, logistic function (that can be regarded as a special case for hormesis function) proved to be the optimal fit.
The hormesis function is described by the following formula:
where c, starting value; d, ending value−f; e, site of inflection if f = 0; b, proportional to gradient at inflection if f = 0; and f, level of cut-down. Logistic function is identical to hormesis function in that specific case when f equals to 0; for that purpose, these functions will be mentioned in a common term as “hormesis.”
The biologically relevant parameters such as time to reach peak; maximum value (peak); time to reach first 50% value (ascending); and time to reach second 50% value (descending) are calculated from these parameters. Furthermore, these parameters provide a suitable basis for the comparison of the activation reactions measured during individual measurements.
To utilize the advantages of the large number of measurement data acquired, functions were fitted for each percentile; the parameters of each fitted function were calculated along with the statistical distribution of each parameter (Fig. 3). These parameters can be statistically compared with Mann–Whitney test. Further details are available through the Internet at the following address: http://calciumflux.intralab.eu.
We calculated the parameters of calcium-flux kinetics after different stimuli including phytohemagglutinin for CD4+ cells, anti-CD3+, and thapsigargin for CD3+ and Jurkat cells. Calculations were performed with the traditional median smoothing approach and with our algorithm (Table 1).
Table 1. Parameters of calcium-flux kinetics calculated with the traditional approach and our new algorithm at different stimuli and dye concentrations (a) Parameters of calcium-flux kinetics at different concentrations of Fluo 3/Fura Red and Indo 1 dyes after stimulation of Jurkat cells with CD3 antibody or thapsigargine
Dye concent-ration (μM)
Peak (fold compared with baseline)
Time to reach peak (second)
Time to reach first 50%—ascending phase (second)
Time to reach second 50%—descending phase (second)
Peak (fold compared with baseline) median [quartile]
Time to reach peak (second) median [quartile]
Time to reach first 50%—ascending phase (second) median [quartile]
Time to reach second 50%—descending phase (second) median [quartile]
C = constant line, L = logistic function, and H = hormesis function.
Significantly different compared with sample without stimulation (0 concentration level).
Significantly different compared with first concentration level.
Significantly different compared with second concentration level.
Traditional approach applies smoothing method (moving median) whereas our algorithm applies function fitting to describe calcium-flux characteristics. After a baseline period, we applied different stimulate to activate CD4+, CD3+ lymphocytes, and Jurkat cells. Intensity values are expressed as fold changes compared with the baseline. All data except CD4+ cells activated by PHA-A and stained with Fluo3/FuraRed were presented in Ref.14.
5 μg/ml anti-CD3 stimulation, Fluo-3/Fura Red dyes
We also compared the parameters derived from our algorithm between different strengths of stimuli and detected significant differences in some biologically relevant parameters (Table 1 and Fig. 2). Note that when results obtained with the same stimulatory but different dye concentrations were compared, some parameters (particularly time to reach 50% value before and after the peak) were extremely sensitive for such a variation whereas others (e.g., peak value and time to reach peak) were comparable.
Available approaches used for the analysis of flow cytometry-derived calcium-flux data are based on smoothing and subjective comparison of the smoothed curves (15). The smoothing is often realized by moving average or median smoothing technique (16, 17). Smoothing of average, however, does not take into account the fact that the distribution of flow cytometry data is non-normal (18). Using techniques that assume normality (such as those calculating average or standard deviation) leads to incorrect smoothing (see Fig. 1). The use of moving median for the characterization of flow cytometry data is a more convenient approach because of non-normal distribution of data. However, there have been no attempts to fit any function on median values, and, as a result, the mathematical description of kinetics with parameters was not solved. The lack of descriptive parameters prevented the correct characterization of individual curves as well.
The present article demonstrates our algorithm that solves this problem through fitting hormesis function to calcium-flux data. Hormesis was originally defined as an adaptive response characterized by biphasic dose responses of generally similar quantitative features with respect to amplitude and range of the stimulatory response that are either directly induced or the result of compensatory biological processes following an initial disruption in homeostasis (19). The phenomenon itself was first observed for toxins and other stressors (20).
Using this type of function, we were able to describe calcium-flux kinetics with five well-defined parameters that characterize the nonlinear shape of calcium-flux curves. These are starting value, peak (fold increase compared with the baseline), time to reach maximum (peak), and time to reach 50% values before and after the peak. In addition to their suitability for the mathematical description of curves, these parameters may be also of biological importance. We think that the introduction of these parameters would largely improve the evaluation of calcium-flux measurements; however, in this study, we did not attempt to reveal the exact biological information that could be derived from these parameters. Methods applied so far were subject to nonstandardized evaluation that depends largely on the observers' personal experience; moreover, different authors characterized their experiments with different descriptive statistics (21, 22). Our approach can be a common basis for the communication between different investigators when flow cytometry calcium-flux kinetic data are planned to be compared.
The introduction of parameters' distribution provides an opportunity for the statistical comparison between individual calcium-flux measurements. Indeed, our algorithm clearly demonstrated significant differences in curves after biologically relevant stimulatory actions.
The use of a function over the estimation of activation level at designated time points provides an opportunity for the introduction of new parameters. These may help to better characterize the biological process of cell activation. For instance, we calculated with the aid of hormesis function the time to reach 50% values before and after the peak. However, these new parameters are extremely sensitive to even slight changes in measurement conditions (i.e., different dye concentrations). Further research will shed light on the particular usage of these parameters.
We concluded that our algorithm is a suitable method for the mathematical characterization and comparison of flow cytometry calcium-flux data obtained in activated lymphocytes. To facilitate its use during the routine practice with flow cytometry calcium-flux assay, we established a homepage (http://calciumflux.intralab.eu.) that provides an opportunity to load and calculate flow cytometry calcium-flux data for anyone who is interested.
A.T. and B.V. are recipients of Bolyai Fellowship.