Computer implemented method for quantitative comparison of biological reactions

Field of the invention

The invention disclosed herein relates to computer implemented methods for quantitative comparison of important characteristics of biological reactions, advantageously biological activation reactions measured in individual measurements performed in biological specimens, in particular intracellular or transmembrane calcium flux measurements, wherein said reaction results in characteristic alteration of the concentration of a characteristic substance, in particular calcium, in a cell or cellular compartment upon an activating or modifying stimulus. The invention further concerns a method for identifying modulators of biological activation reactions. The invention also concerns reagent kits for quantitative comparison of important characteristics of biological reactions measured in individual measurements performed in biological samples.

Background of the invention

Numerous biological reactions result in a characteristic alteration of the concentration (e.g. increasing and subsequent decreasing in time) of a characteristic substance (e.g. calcium, in the case of e.g. lymphocyte activation) in a cell or cellular compartment upon an activating stimulus. It is often an important task to compare different significant characteristics of activation reactions of the same type performed in separate, individual activation measurements e.g. for comparing the intensity of different stimuli or effects of different activation modulating substances. Such comparison, however, cannot be performed objectively and statistically unless there is definite function known which would suitably fit the signal intensity values (being proportional to the actual concentration of the above mentioned characteristic substance) measured against time in the individual measurements.

Lymphocyte activation, a characteristic representative of the above mentioned activation reactions, is a multi-step process. 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, Ca ²⁺ is an essential element for early activation (1,2): increased intracellular Ca ²⁺ content is an irreversible step toward an activated state of a lymphocyte. Therefore, intracellular Ca ²⁺ content presents important information about the status and kinetics of lymphocyte activation (3). Furthermore, monitoring lymphocytes' Ca ²⁺ content is a valuable approach to assess the impact of disease and/or treatment on lymphocyte activation properties (4).

Several methods are available for the determination of intracellular Ca ²⁺ levels (5,6,7). Of those, colorimetric methods are commonly used. The fluorescence intensity of Fluo-3 increases upon binding Ca ²⁺ and that of Fura Red decreases. Hence the fluorescence emissions of Fluo-3 to

Fura Red can be used for ratiometric analysis of Ca ²⁺ using the commonly available 488 nm wavelength with laser. The ratio of these two parameters is comparatively insensitive to small changes in fluctuations in the fluorescence signal on a cell by cell basis that may be observed in a single parameter (8).

Fluorescence activated cell-sorting (FACS) is a commonly used form of flow cytometry. FACS is an instrument developed for the determination of cells with well-characterized cell surface properties. For this purpose fluorescent dyes bound to antibodies or dyes that form complexes with intracellular molecules (such as ions) are used. Fluorescent dyes excited with the energy of laser emit light on a specific wavelength.

Kinetic analyses define the change of a specific parameter over time, such as the change in intracellular calcium concentration that occurs when e.g. lymphocytes are activated. This change in calcium concentration is detected using fluorescent calcium-binding dyes and flow cytometry.

FACS offers numerous advantages over traditional techniques for measuring intracellular Ca ²⁺ , in that relatively large numbers of cells and sequential samples can be tested. FACS 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 interpretation of this huge number of data represents, however, a difficult task. Available approaches used for the analysis of FACS-derived calcium flux data fit curves to the measured values and calculate some descriptive parameters. However, they do not take into account the distribution and complexity of individual measurement points and, as a result, important information is lost.

Available programs (9, 10, 11 and 12) enable the calculation of different mean or median values of light intensity measured in individual cells during an interval, smooth curves and illustrate the kinetics. Some of the most important parameters such as maximal values and slopes of the curves may be also determined.

Calcium flux is a commonly used technique in today's immunological methodology. In a PubMed search performed on 3/29/07 the term ,,calcium flux" results in 1262 papers. The technique itself is well known and accepted by the most prestigious journals (Nature, Cell, Immunity etc.). Since there is no generally accepted evaluation for the results, authors usually present their data in two formats: they show representative "raw" dot plots or representative mean values after smoothing techniques.

Some representative examples of the presentation of results according to the state of the art can be seen in the following documents:

"Raw" dot plots

Xu S et al, Cbp deficiency alters Csk localization in lipid rafts but does not affect T-cell development. MoI Cell Biol. 2005, 25(19):8486-95. Figure 3.c on page 8490.

Gavin MA et al., Homeostasis and anergy of CD4(+)CD25(+) suppressor T cells in vivo. Nat. Immunol. 2002, 3(1):33-41. Figure 3. on page 34.

Kohm AP et al., Treatment with nonmitogenic anti-CD3 monoclonal antibody induces CD4+ T cell unresponsiveness and functional reversal of established experimental autoimmune encephalomyelitis. J. Immunol. 2005, 174(8):4525-34. Figure 5.c on page 4530

Mean values after smoothing

Shui JW et al., Hematopoietic progenitor kinase 1 negatively regulates T cell receptor signaling and T cell-mediated immune responses. Nat. Immunol. 2007, 8(1):84-91. Figure 6.b on page 89.

Lamoureux J et al., Leukotriene D4 enhances immunoglobulin production in CD40-activated human B lymphocytes. J. Allergy. Clin. Immunol. 2006, 117(4):924-30. Figure 3 on page 927.

Yi JS et al., Electron transport complex I is required for CD8+ T cell function. J. Immunol. 2006, 15;177(2):852-62. Figure 6.a on page 857.

Currently used analytic tools do not utilize, however, the advantage presented by the huge number of individual measurement data that would largely increase the statistical power when activation curves are compared.

The usual method of analyzing data is that representative plots are shown and then semi- quantitatively ("looks different") the authors conclude whether according to their opinion there was or was not a difference to be observed. Currently, no exact method is available to correctly compare two calcium flux measurements.

The object of the present invention was, therefore, to develop a new method that provides opportunities for the quantitative numeric characterization of biological activation reactions, in particular kinetic calcium-flux measurements and enables the direct statistical comparison of the characteristic parameters of individual FACS-kinetic measurements.

Detailed description of the invention

Upon statistical function fitting analysis performed on many individual calcium flux measurements performed in FACS instruments using a large number of different functions, the present inventors have surprisingly found, that the so called Cedergreen-Ritz-Streibig's modified logistic dose response function (14) and the hermesis function and the hermfesis function statistically acceptably fits the fluorescence intensity values (being proportional to the intracellular calcium concentration) measured against time and the important parameters of the said function are suitable for the quantitative comparison of the activation reactions measured in separate, individual measurements.

Instead of using slope, maximum or minimum values for the description of the curves, we introduced other parameters more closely defining the nonlinear shape of calcium flux curves. These biological parameters are the following: time to reach peak; fold increase at peak compared to baseline; time to reach 50% values before the peak; time to reach 50% values after the peak 50%.

The present inventors wanted to describe the sequential alteration of measurement data during a kinetic FACS assay. Therefore we aimed to find a function that best fits to the sequential measurement data.

The major points of our function selection method were the following:

• fitting functions to the measurement data

• assessing the way which function is best fitting to measurement data

• assessing the most important and biologically relevant parameters of the function

• development of the comparison method between individual measurements.

1. Finding a function:

We have divided the measurement period up to equal time intervals (e.g. for a 10 minutes long period we use 250 intervals) and calculated the 1 ^th quantile of the points for each interval (for details, see below). We have fitted the functions listed below with non-linear least square regression to quantile values. (This method is almost equivalent with the quantile regression method, but this approach is much faster and requires less computational capacity.) Before each fitting, we have estimated the parameters with the aid of the lowess method. constant line: y=a (a: constant value) (a is the same as the mean of the medians); linear regression line: y=a*x+b (a: gradient, b: intercept); polynomial function: y=c+a*x ^λ b (c: starting value, a: factor, b: proportional to gradient); logistic function: y=c+(d-c)/(l+(x/e) ^λ b) (c: starting value, d: ending value, e: place of 50% value, b: proportional to gradient at 50% value);

Cedergreen-Ritz-Streibig's function: y=c+(d-c+f*exp(-l/(x ^λ 0.25)))/(l+(x/e) ^λ b) (b, c, e same as previous, f: level of cut-down, d+f: ending value); hermesis function: y=c+(d-c+f/(l+(x/e) ^λ g))/(l+(x/e) ^λ b) (b, c, e, f same as previous, g: proportional to gradient at 50% value of cut-down function); hermfesis function: y=c+(d-c+(c-d)/(l+(x/e) ^λ g))/(l+(x/e) ^λ b) (b, c, e same as previous, g: proportional to gradient at 50% value of cut-down function); where the following restrictions apply: b and g are always <0; e is always >0.

2. The calculated mathematical parameters are used to determine the above mentioned biological parameters with numerical approximation.

3. Biological parameters expressing the alteration of intensity are divided by the starting value's median in order to standardize the process.

constant line: constant value linear regression line: starting value ending value polynomial function: starting value dynamic coefficient logistic function: starting value ending value time to reach 50% value gradient at the 50% value (speed of increase) Cedergreen-Ritz-Streibig's starting value modified logistic dose response time to reach peak function & hermfflesis functions: maximum value (peak) time to reach first 50% value (ascending) time to reach second 50% value (descending).

For the determination of statistical distribution of biological parameters for statistical comparison, two possible ways can be applied: a. The specific function originally fitted to median values is also fitted to each percentile value and the corresponding biological parameters are calculated. This approach is useful for statistical description of empirical distribution of the parameters of the functions. b. 1000 datasets are created with bootstrap method from measurement data. The specific function originally fitted to median values is fitted to the medians of each bootstrapped dataset. This approach is useful for statistical description of the parameters of the function fitted to the median.

Different measurements can be compared according to the distribution of the parameters of the fitted function. For comparison, Mann- Whitney test (for the approach 'a') or Bootstrap confidence interval comparison (for the approach 'b') can be used.

The invention, therefore, concerns a computer implemented method for quantitative comparison of important characteristics of a biological reaction, measured in individual measurements performed in biological specimens, wherein said biological reaction results in a characteristic alteration of the concentration of a characteristic substance in a cell or cellular compartment upon an activating or modifying stimulus. Said method comprises the following steps: a) providing a first biological specimen comprising at least one biological entity being capable of alteration upon an activating or modifying stimulus and at least one detectable marker provid-

ing a detectable signal the intensity of which being proportional to the concentration of said characteristic substance; b) activating said at least one biological entity by applying an activating or modifying stimulus; c) measuring the intensity of said detectable signal against time; c) fitting any of the following functions: a Cedergreen-Ritz-Streibig's modified logistic dose response function, a hermesis function or a hermfesis function to said measured values of said detectable signal and identifying the best fitting function; d) determining at least one characteristic parameter of said best fitting function; e) comparing said at least one characteristic parameter of said best fitting function with the same parameter of another function obtained for a second activated biological specimen in accordance with the above steps a)-d); f) determining, on the basis of the difference between said at least one characteristic parameters, whether the accomplishment of said biological reaction measured in said second biological specimen was significantly different in one or more important characteristics than the accomplishment of said biological reaction measured in said first biological specimen.

In a preferred embodiment of the method of the invention said characteristic alteration of the concentration of said characteristic substance consists of increasing and subsequent decreasing of said concentration in time.

In a further advantageous embodiment of the method of invention said activation measurement is a measurement of intracellular or transmembrane calcium flux.

In another preferred embodiment of the method of the invention said at least one biological entity is at least one cell.

In a further preferred embodiment of the method of the invention said at least one cell is at least one nucleated blood cell, advantageously a lymphocyte.

In a further preferred embodiment of the method of the invention said detectable marker is a compound forming a detectable complex with said characteristic compound.

In a further preferred embodiment of the method of the invention said characteristic compound is calcium.

In a further preferred embodiment of the method of the invention said detectable signal is fluorescence.

In a further preferred embodiment of the method of the invention said measurement is done in a flow cytometric device, advantageously, in a fluorescence activated cell-sorting (FACS) device or in an optical device, preferably a fluorescent microscope or a confocal microscope.

In a further advantageous embodiment of the method of the invention said function fitting in the above step c) comprises the following:

i) dividing the measured time period up to numerous equal intervals; ii) determining, by power analysis, the number of quantiles to be used (default: 90), and calculating the quantile probabilities distributed equally; and iii) applying the following method for each quantile (default: i=5-95):

- calculating the 1 ^th quantile of the measured values for each interval;

- fitting a Cedergreen-Ritz-Streibig's modified logistic dose response function with non-linear least square regression to the quantile values, taking the starting values of the parameters from the (i-l) ^λ fit.

In a further preferred embodiment in the above method said function fitting step c) comprises the following: i) dividing the measured time period up to numerous equal intervals; then ii) for statistical description of empirical distribution of the parameters of the functions, the specific function originally fitted to median values is also fitted to each percentile value and the corresponding biological parameters are calculated, or for statistical description of the parameters of the function fitted to the median, 1000 data sets are created with bootstrap method from measurement data and the specific function originally fitted to median values is fitted to the medians of each bootstrapped data set.

In another advantageous embodiment of the method of the invention said determination of said at least one characteristic parameter in the above step d) is done with numerical approximation up to le-6 precision and normalization of said parameters is done corresponding to the perpendicular axis with the median of the starting value.

In a further advantageous embodiment of the method of the invention said comparison of said at least one characteristic parameters of said different functions in the above step e) is done using any of the following: Wilcoxon non-parametric homogeneity test, a Mann- Whitney test or a Bootstrap confidence interval comparison.

In a further preferred embodiment of the method of the invention said measurement is done by a fluorimeter, a luminometer or other similar device capable of repeated measurements of light intensity.

In a further preferred embodiment of the method of the invention said at least one characteristic parameter of said Cedergreen-Ritz-Streibig's function or said hermesis function or said herm- fesis function is selected from the group comprising: time to reach peak; fold increase at peak compared to baseline; time to reach 50% value before the peak; and time to reach 50% value after the peak.

The invention further provides a method for identifying a modulator of a biological activation process, which method comprises the following steps:

a) determining a first at least one characteristic parameter of a first best fitting function being characteristic to a biological activation process in accordance with the above described steps a)-d); b) determining a second at least one characteristic parameter of a second best fitting function in accordance with the above described steps a)-d), wherein said step b) is performed in the presence of a substance supposedly being a modulator of said biological activation process; c) determining, on the basis of a significant difference between said first and second at least one characteristic parameter, whether said substance is a modulator of said biological activation process.

The invention also provides reagent kits for quantitative comparison of important characteristics of a biological reaction measured in individual measurements performed in biological specimens, wherein said biological reaction results in a characteristic alteration of the concentration of a characteristic substance in a cell or cell compartment upon an activating or modifying stimulus, said kit comprising: a) detectable marker providing a detectable signal the intensity of which being proportional to the concentration of said characteristic substance and b) information carrying medium comprising information concerning the performance of the methods according to the invention.

The reagent kit according to the invention may additionally comprise means facilitating fitting of a function selected from the group comprising a Cedergreen-Ritz-Streibig's function, a herme- sis function and a hermfesis function to signal intensity data measured against time or an information carrying medium comprising information concerning parameters of one or more of said functions fitted to signal intensity values measured in activation measurements performed in biological specimens, wherein said biological reaction resulted in a characteristic alteration of the concentration of a characteristic substance in a cell or cell compartment upon an activating stimulus.

Brief description of the drawings

Figure IA: A characteristic state of the art calcium flux measurement where Fluo-3/ FuraRed ratiometric values are plotted against time and one point corresponds to one measurement data.

Figure IB: Smoothing with traditional approach with commercially available software (FlowJo®). For the data points of figure IA the mean is calculated at each time point with the moving average 'smoothing' method and these values are plotted against time, the line corresponds to the moving average.

Figure 2: A diagram showing how different functions fit to a characteristic calcium flux measurement (fitting was done on the same measured data that is presented in Fig. 1). The figure

shows the calculated median values and four different fitted functions: a constant line, a linear regression line, a logistic function and a Cedergreen-Ritz-Streibig's function.

Figure 3: A Cedergreen-Ritz-Streibig's modified logistic dose response function was fitted (same measured data which is presented in Fig. 1 and Fig. 2) to each percentile values between 5 ^th and 95 ^th percentile. This figure presents the value of calculated parameters (n=90)

Figure 4: A histogram that relates to the peak values of 2 different measurements compared to the baseline. The majority of data is between 0.9 and 1.5 in both scenarios, but there is a shift to higher values when activation stimulus is more pronounced (filled and empty bars correspond to parameters obtained at 10 and 25 μg/ml of phyohaemagglutinin activation, respectively).

Figure 5 A and 5B: Fluo-3 imaging of intracellular Ca ²⁺ . These figures show the calcium- flux and the fitted Cedergreen-Ritz-Streibig's modified logistic function for two different cells examined in a fluorescent confocal microscope.

Examples

In the following illustrative examples are shown demonstrating the applicability of the methods of the invention for the quantitative comparison of important characteristics of biological activation reactions measured in individual activation measurements performed in biological specimens.

Example 1: Kinetic analysis of flow cytometry-acquired calcium-flux data

Fluo-3-AM (Cat. No. F- 1242) and Fura Red-AM (Cat. No. F-3021) were from Molecular Probes (Eugene, Oregon, USA). Fluo-3 AM and Fura Red AM were solubilized to 10 mg/ml with dimethyl sulfoxide (DMSO, Sigma), with 10% Pluronic F 127 (Sigma), and stored protected from light at -20 ⁰ C. Hank's Balanced Salt Solution, (HBSS Modified 1OX Cat. No. 55225-100M) was from Sigma and diluted using sterile, endotoxin free, water. APC labeled anti CD3 was from BD Pharmingen.

Human peripheral blood mononuclear cells (PBMC) were obtained from healthy volunteers. PBMCs were separated by a standard density gradient centrifugation (Ficoll Paque, 25 minutes, 40Og, 22°C) from 10 ml freshly drawn peripheral venous blood collected in Lithium heparin treated tubes. PBMC contained in the interphase were washed twice HBSS. Cell viability was routinely assessed by Trypan Blue exclusion and cells were more than 90% viable.

Loading conditions

Cells were loaded with 4 μg/ml Fluo-3 AM and 10 μg/ml Fura Red AM for 30 min at 30 ⁰ C. Cells were washed once, and stained with APC-labeled anti-CD4. After washing, cells were kept at room temperature (21 ⁰ C) at the dark. A 500 μl aliquot was warmed to 37°C prior to fluxing. First a baseline (30 s) level was recorded. Than the tube was removed, and different amounts of

phytohemagglutinin (PHA) (1-25 μg/ml) addeu and the tube replaced. 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. Data were saved as FCS 3.0 files, and analyzed with R software's (10) Bioconductor's "rflowcyt" package (11). To develop this method a total of 100 Ca-flux experiments with different stimuli were carried out. Representative plots are shown.

Flow cytometer

We used a FACSAria (BD San Jose USA) flow cytometer equipped with a 488 nm and a 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.

Analysis

Widely used calculations (such as those applied by commercially available flow cytometry analytic softwares) Fluo-3/ FuraRed ratiometric values are plotted against time (figure 1). Then the mean is calculated at each time point with the moving average 'smoothing' method. This enables the estimation of particular values of the curves such as maximum values and time to reach the peak.

The aim of our method was to describe the sequential alteration of measurement data during a kinetic FACS assay. Therefore we aimed to find a function that best fits to the sequential measurement data. For comparison we fitted on the median values of measurement plots a constant line; a linear regression line; a logistic function and a Cedergreen-Ritz-Streibig's function. We show on figure 2 a plot of the median values and the 4 fitted functions. Of those, Cedergreen-Ritz- Streibig's function fitted the best according to the F-test.

The biologically relevant parameters of Cedergreen-Ritz-Streibig's function are the following: starting value; time to reach peak; maximum value (peak); time to reach first 50% value (ascending); time to reach second 50% value (descending).

Comparison between individual measurements

We determined the empirical distribution of the best fitting functions' parameters with the following method (fig. 3):

• We divided the measurement period up to equal and numerous intervals (as above)

• With power analysis we determined the number of quantiles to be used (default: 90) and calculated the quantile probabilities distributed equally

• For each quantile (default: i=5-95) we applied the following: o For each interval we calculated the 1 ^th quantile of the points o We fitted the appropriate function with non-linear least square regression to the quantile values. The starting values of the parameters were taken from the (i-l) ^th fit.

o We determined the above mentioneu parameters with numerical approximation up to le-6 precision

• We normalized the parameters corresponding to the perpendicular axis (for Cedergreen- Ritz-Streibig's function these are starting value and peak) with the median of the starting value, thus the parameters will be comparable between different measurements

Results

We measured relative cellular calcium levels after different PHA stimuli and calculated relative calcium response using mean (with moving average) and the approach of the present invention. Significant differences were obtained between time to reach peak, fold increase at peak compared to baseline and time to reach 50% values before the peak at 5, 10 and 25 μg/ml PHA concentrations (table 1).

Table 1

Table 1 (continued)

The parameters were compared with Wilcoxon rank test and the test revealed significant differences between time to reach peak; peak values; time to reach first 50% (ascending phase) and time to reach second 50% (descending phase) measured at 5, 10 and 25 μg/ml PHA-levels. Comparison of the original calculation method with the method of the present invention (table 2):

Table 2

* denotes estimated data determined graphically by the present inventors using the smoothed curves provided by Flow Jo

Histogram of the peak values of two different measurements (10 and 25 ug/1 PHA) are shown on figure 4.

Example 2 Kinetic analysis of calcium-flux data measured in individual cells with confocal microscopy

Lung epithelial cells were stained with Fluo-3, incubated in pH 7.4 puffer, and at time period 2.2, 5.0 mg ATP was added. The measurements were made by fluorimeter.

Fluo-3 imaging of intracellular Ca ²⁺

Cytosolic Ca ²⁺ concentration was measured with confocal microscopy after cells were loaded with the permeant form of the fluorescence dye, Fluo-3 -acetoxymethyl ester (Fluo-3/AM). Fluo-3 fluorescence was measured at an emission wavelength of 525 nm in response to excitation wavelength of 488 nm. Cells were incubated in Dulbecco's phosphate buffered saline containing 2 mM CaCl ₂ and 1 mM MgCl ₂ in the presence of 4 μM Fluo-3/AM and 1 mg/ml Pluronic F- 127 dissolved in DMSO for 120 min to allow loading of the dye into the cells. After loading, coverslips were rinsed at least for 10 min in Dulbecco's phosphate buffered saline to remove extracellular Fluo-3/AM. Two glass capillary tubes were inserted into the top of the chamber out of the patch

of the excitation light. One tube was extended iu the bottom of the chamber and connected by way of polyethylene tubing to an infusion pump. The other capillary tube was positioned at the top of the chamber and served to remove fluid. The volume of the chamber was ~1.5 ml, and the flow rate was ~5 ml/min. It is important to note that switch in perfusion solutions is removed in time and space for the chamber, such that a 10-15 sec time lag exists before agonist is exposed to the cells. Experiments were performed at room temperature.

Below the serial measurement data obtained from five independent cells are presented. Ceder- green-Ritz-Streibig's modified logistic function was fitted to the values. The calculated parameters are presented in table 3.

Table 3

Figure 5 A and 5B shows the calcium- flux and the fitted Cedergreen-Ritz-Streibig's modified logistic function for cell number 1 and 2 respectively.

This example clearly demonstrates that the suitable fitting of the Cedergreen-Ritz-Streibig's modified logistic function applied in the present invention is not due to any specific feature of the calcium flux measurement performed in a FACS equipment but an inherent characteristic of the measured calcium flux activation reaction itself.

On the basis of the above experimental examples, it can be clearly seen that the method of the present invention shows statistically significant differences between calcium flux kinetic parameters measured at slightly different activator concentrations where traditional methods can not show significant differences. The comparison method of the present invention is sensitive to even minor differences, and, hence, dramatically decreases the number of measurements required to investigate the activation characteristics of biological entities being capable of activation, e.g. lymphocytes.

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