EP1960922A1 - Method for processing and error reduction for standardized quantitative data in biological networks - Google Patents

Abstract

The present invention is related to a method to quantitate a set of samples obtained from quantification o f a gel or blot, minimizing errors and eliminating the correlation structure of errors in quantitative gel-, immunoblotting (Western Blotting, Northern Blotting or Southern Blotting) analysis. In the first step, raw quantified data from at least one randomized loaded series of samples o f at least one gel or blot is loaded into the algorithm. In a subsequent step, a blotting error for at least one normalizer and/or calibrator with at least one gel or blot is est imated via an approximation function. Still further, a smooth first signal estimate of at least one molecule of interest is created by a functional relationship or an approximation and said first estimate of the at least one molecule of interest is corrected at hand of the estimated blotting error. Another step, dependent on the result of the correction, corrected data for the at least one molecule o f interest or the original values are further processed. Finally, the processed and/or merged data of the at least one molecule of interest is saved.

Description

Method for Processing and Error Reduction for Standardized Quantitative Data in Biological Networks

Discussion of Prior Art Complex cellular networks regulate biological responses and subtle changes can trigger the onset of diseases. Critical for the control of cellular growth, differentiation and survival is the stoichiometry of the cellular components involved and the timing as well as the amplitude of signal activation. To elucidate key regulatory mechanisms and to reliably identify changes in aberrant cells, data generation has to progress from qualitative information gathering to the acquisition of quantitative data. Standardized procedures and reliable normalization methods are essential to facilitate the generation of high quality quantitative data and comparability of independent experiments.

A newly emerging field that is in high demand for quantitative data is systems biology. It is an approach to understand general design principles and predict the dynamic behavior of cellular networks by mathematical modeling, especially in signal transduction, transcriptional control and metabolism. The aim is to delineate the dynamic behavior of complex biological networks, identification of systems properties and the prediction of targets for perturbation. However, the major limitation at present is the lack of reliable quantitative data. To determine the quantitative accuracy of models and to capture the characteristic dynamic behavior of systems, techniques that quantitatively and selectively measure biochemical reactions within the cell have to be developed. In order to conduct a systems-level analysis, a comprehensive set of quantitative and time-resolved data is required. Recent reports show that by combining quantitative data generated with fluorescence microscopy, electrophoretic mobility shift assays, or quantitative immunoblotting new biological knowledge can be obtained.

One of the most widely used techniques to determine proteins in mixtures is immunoblotting which is based on separation of proteins according to their molecular weight by SDS polyacrylamide electrophoresis and blotting to a membrane. The presence of specific proteins on the membrane is detected by antibodies in combination with the utilization of chemiluminescent substrates and exposure to X-ray films. However, since the linear range of X-ray films is very limited, quantification by CCD camera detection is preferable. For rare proteins such as certain signaling components, pre-purification by immunoprecipitation is required prior to immunoblotting which potentially increases the error due to the multiple steps involved in the procedure. Up to now, only relative values have been generated by immunoblotting that are difficult to compare from experiment to experiment. Thus, reliable procedures for error reduction and data processing are required to use immunoblotting for the generation of high quality quantitative data.

Signaling pathways have been primarily studied in the context of cell lines that are easy to propagate. However, since cell lines have lost restrictive growth control mechanisms, it is of great importance to analyze the systems behavior of signaling pathways in primary cells.

To generate reliable results with primary cells standard operating procedures (SOP) have to be developed for the preparation of the cells from animals or patients and their cultivation.

Mammalian cells either grow in suspension or attached to a support. Suspension cells are primarily cells of hematopoietic origin and are particularly suited for biochemical studies on cell populations with high temporal resolution, since they permit bulk stimulation and rapid sampling. For biochemical studies in adherent cells, separate stimulations are required for each time point potentially resulting in a higher sample-to-sample-variation.

Even more difficult is the analysis of proteins in patient samples. To eliminate technical errors and ensure comparability of results, reliable normalization procedures have to be developed.

Summary of the Invention

According to the present invention, the erythropoetin-receptor (EpoR) induced activation of ERKl in the hematopoietic suspension cell line BaF3-HA-EpoR and the interleukin (IL)-6 induced activation of the signal transducer and activator of transcription (STAT)3 in adherent primary murine hepatocytes are used as model systems to establish a robust procedure for the generation of high-quality data by quantitative immunoblotting. To reduce systematical errors and noise, an error determination is performed, utilizing randomized sample loading, employing normalizers and calibrators and developed normalization criteria. As a consequence thereof, reliable and accurate time-resolved data of phosphorylated and total protein concentration of cells can be acquired and absolute concentrations can be determined permitting systems-level analysis of signaling pathways in primary cells such as hepatocytes and other cell lines and primary cells. Determination of Molecules per Cell To determine the concentration of signaling components in cells and to compare data generated by independent experiments, relative signals obtained by quantitative immunoblotting have to be converted to absolute numbers such as molecules per cell. A total cellular lysate of BaF3-HA-EpoR cells was analyzed in parallel with a dilution series of purified recombinant ERK2 standards by immunoblotting using an anti-ERK-antibody as shown in Figure Ia, upper panel. The measurements obtained by Lumilmager analysis for the purified ERK2 were plotted against the number of molecules loaded on the gel. A linear regression passing through the origin could be calculated as shown in Figure Ia, lower panel, demonstrating in conjunction with extensive other studies that the CCD camera device applied facilitated linear detection over at least two orders of magnitude. A linear regression model was used to convert the signals of endogenous ERKl and ERK2 in the total cellular lysate, estimating that 107 000 ERKl molecules and 318 000 ERK2 molecules are present in the cytoplasm of one BaF3-HA-EpoR cell. This determination can be performed for proteins analyzed on the same immunoblot and sharing the same antibody epitope. Since the detection by Lumilmager analysis is proportional to the number of epitopes, it can be even applied to proteins with different molecular weight such as isoforms or partial fusion proteins, in consequence permitting the concomitant determination of multiple signaling components.

Error Determination of the Measurement Process

To estimate inherent noise on the data generated by the immunoblotting technique, error determinations were performed. A serial dilution of purified recombinant ERK2 protein was analyzed eight times by immunoblotting using an anti-ERK antibody (according to Figure Ib, upper panel) and quantified by Lumilmager analysis based on CCD camera detection. The estimated error was calculated as the standard deviation of the Lumilmager measurements. Plotting signal strength versus estimated error revealed that the expected error behavior, e.g. of the CCD camera photon counting process, cannot be recovered. The systematical error inherent in this technique can phenomenologically be described by a sublinear function. Within the measurement range, about 20% error for each data point is estimated, whereas for weaker signals this number is increased as shown in Figure Ib, lower panel. This noise comprises different contributions:

(i) pipetting errors are constant within a lane, but, however, stay uncorrelated from lane to lane, further, (ii) blotting errors which arise from inhomogeneities of the gel or the blot are highly correlated from lane to lane as well as within a lane and still further, (iii) uncorrelated errors resulting from antibody-detection.

Eliminating Correlated Errors by Randomized Sample Loading

To determine steps predominantly contributing to the error obtained by quantitative immunoblotting analysis, a time-course of erythropoetin (Epo) induced activation of ERKl in BaF3-HA-EpoR cells is monitored. Identical samples of total cellular lysates were loaded in a randomized fashion on two gels and subsequently transferred to membranes (see Figure 2a, blot 1 and blot 2) and analyzed by three repetitive cycles of ERK antibody reprobing and application of the chemiluminescent substrate. Quantification of the immunoblotting signals showed that data obtained from neighboring lanes was strongly correlated. To eliminate the effects of errors (i) and (iii) as listed above, uncorrelated from lane to lane a smoothing spline is employed. The apparent different results for identical samples reveal the relative contribution of the different types of errors. Pipetting errors (i) and uncorrelated errors from antibody detection (iii) had surprisingly little effect on the results, whereas the blotting error leads to substantial systematical errors as shown in Figure 2b, upper panel. Detailed analysis of large data sets revealed a strong correlation between neighboring lanes in immunoblotting analysis resulting in aberrant spurious dynamic behavior. In order to separate this spatial correlation from true temporal dynamics in time-course data, a standard operating procedure to randomize samples is disclosed. Consecutive time points are loaded randomly on the gel, separated by a minimum number of lanes. This loading scheme is varied from experiment to experiment in order to minimize gel border effects. This procedure thereby ensures that the errors are uncorrelated (Figure 2b, lower panel) and thus facilitates the detection of true dynamic behavior.

Criteria-Based Data Normalization To reduce the effect of the blotting error and improve the data quality, endogenous proteins were used as normalizers. The time-course of Epo-induced phosphorylation of ERKl and ERK2 was detected by immunoblotting using a phosphospecific anti-pERKl/2 antibody (Figure 3 a). Subsequently, the antibody was removed and the blot was first reprobed with an anti-ERKl/2 antibody to determine the total amount of ERKl and ERK2 in the cytoplasmic lysates and second with a mixture of antibodies against endogenous proteins. These proteins which were termed "normalizers" are highly expressed, their levels are not changed during the course of the experiment and antibodies that permit efficient detection are available. The blotting errors dependent not only on the experiment but also on the position of a protein within a blot as evidenced by the analysis of β-Actin (42kDa), PDI (protein disulfide isomerase, 58 kDa) and Hsc70 (heat shock cognate protein 70, 73 kDa) covering the entire separation range of the polyacrylamide gel. Therefore, the signal of a normalizer of similar molecular weight as the protein of interest, in the case of ERKl β- Actin, was used to distinguish blotting error from the true protein concentration. The levels of pERKl and ERKl were normalized with a smoothing spline applied to the β-Actin signal. By this procedure, it was achieved to compensate for blotting errors in the signals and generate data that was for example in line with the assumption of constant concentration of ERKl over the entire observation time. By employing purified ERK2 as standard, total protein levels of ERKl could be determined as shown in Figure 3b. Absolute concentrations of phosphorylated ERKl were estimated by analyzing the fraction of protein that migrates at a higher position in the polyacrylamide gel.

Recombinant Proteins as Calibrators for Immunoprecipitation

For certain proteins, immunoblotting is not sufficient to generate quantitative data and the protein of interest has to be prepurified prior to electrophoresis by immunoprecipitation (IP). This is due to antibodies with weak affinity to the protein or cross-reaction to other proteins, resulting in a high background. Another example of favoring immuno- precipitation is the use of generic phospho-tyrosine antibodies. Since normalizers are not captured by the antibodies in the immunoprecipitation, a method was established to correct against blotting errors as well as inaccuracies in the multi-step immunoprecipitation procedure and normalize the results obtained. Proteins are generated, sharing the same epitope as the protein of interest but differing in molecular weight, termed calibrators. Adding a defined amount of calibrator to the lysate prior to immunoprecipitation allows for normalizing the results obtained from the Lumilmager. The protein domain containing the epitope of the antibody used for immunoprecipitation is fused to a protein tag for purification (see Figure 4a). Using only a part of the protein, calibrators of large or membrane proteins could easily be expressed in E. coli and purified using affinity beads. The concentration of the calibrators is determined by using a Coomassie Blue-stained gel with a bovine serum albumine dilution series. To determine the optimal amount of calibrator to be added to the immunoprecipitation and to prevent saturation of the antibodies, an increasing amount of calibrator GST-EpoR was added to lysates of BaF3- HA-EpoR cells prior to immunoprecipitation (see Figure 4b). The concentration of calibrator added to the lysates is plotted versus signals of the HA-EpoR and the calibrator quantified with the Lumilmager enables to define a linear relationship for GST-EpoR within a range of 2.5 to 100 ng of calibrator addition. The addition of calibrator has no effect on the signal for the HA-EpoR up to concentrations of 500 ng of GST-EpoR, indicating that the antibody is in large excess as compared to HA-EpoR. This indicates that immunoprecipitation cannot only be used for quantitative data generation but as well for conversion of relative values to absolute protein concentration. Using this data, it is calculated that 40 ng of calibrator should be added to the lysate to obtain a signal comparable to the HA-EpoR (see Figure 4c).

Calibrators for Error Reduction

The impact of calibrators on data quality is demonstrated by a chronologically loaded and a randomized immunoblot of an EpoR time-course experiment. BaF3-HA-EpoR cells were stimulated with Epo up to 10 minutes, taking samples every 30 seconds. 40 ng of GST- EpoR were added to each immunoprecipitation reaction, see Figure 5. This calibrator can be used to correct against gel errors, improving data quality. However, if a calibrator yields weak signals or a normalizer of the wrong molecular weight is chosen, correction steps can even be detrimental to the data obtained. Therefore, criteria for data correction in immunoprecipitation experiments as described have been developed. One condition necessary for these criteria is randomized sample loading. It was shown that by combining randomized sample loading with calibrators on normalizers, standard deviation of immunoblotting data is improved more than twofold. In both experiments as depicted in Figure 5, signals could be corrected using the calibrator, but only in the time-course with randomized sample loading all correlated errors could be removed. Quantitative immunoprecipitation and immunoblotting allows accurate determination of protein concentrations. In quantitative immunoprecipitation using a calibrator, the signals obtained from the Lumilmager can be converted into molecules per cell as described. Calibrators allow for simultaneous normalization of the signals and determination of the absolute concentration of the protein of interest. In contrast to standards, no additional lanes are used for the quantification, since the molecular weight of the calibrator differs from the one of the measured protein and is loaded on the same lane.

High Quality Time-Course Data of Primary Hepatocvtes To validate the approach, the effect of standard operation procedures on data generation from primary hepatocyte time-courses were investigated. Sample randomization was combined with criteria-mediated error reduction using calibrators and normalizers to obtain high quality quantitative data. By loading time points alternating on more than one gel, the number of data points can be increased beyond gel capacity as best shown in Figure 6. Employing the proposed mathematical methods, it was achievable to combine the signals and to generate time-course data with high temporal resolution, see Figure 6b. The sampling rate of the data has to be matched to the time-course of the signal. Rapid changes in the signal have to be measured with a sufficient amount of data points to allow smoothing by splines, to give an example. Adding GST-STAT3 as calibrator and measuring Calnexin and Hsc70 as normalizers, quantitative data with a low standard deviation was generated. Still further, the method is applicable robustly for both immunoprecipitation and immunoblotting experiments. Both measurements result in approximately the same time-course dynamics for phosphorylated and total cytoplasmic STAT3 indicating high reproducibility of the results.

According to the present invention, the use of randomized sample loading, the application of criteria-based use of normalizers and calibrators and computational data processing generates high quality quantitative data by immunoblotting. By systematically determining the steps contributing to the error attached to the data, inhomogeneities in the gel and transfer thereof were identified as the major source for correlated error, whereas variations in antibody incubation and substrate development could be better controlled and had less impact on data quality. Correlations of the errors could be destroyed by randomized sample loading and error reduction was achieved by the use of normalizers or calibrators in combination with computational data processing. This method yielded reproducible data for samples analyzed on separate blots thus establishing comparability of results obtained in unrelated experiments, independent from the environmental conditions, and duration of experiment to name but a few.

Randomized sample analysis in general constitutes a strategy to prevent error correlations. By simulations of typical time-course experiments, it was demonstrated that the randomization reduces the standard deviation of immunoblotting data by more than twofold. Thus, sample randomization has proven a simple procedure that significantly improves data quality without increasing experimental efforts. To reduce errors inherent in blotting techniques such as inhomogeneities in the gel as well as transfer, normalizers present at a similar position as the molecule of interest in the blot and detectable with a strong constant signal are preferably used. Several proteins of different molecular weight have been identified to be reliably used as normalizers. To ensure correctness of data normalization, approximation functions such as a polynomial spline or other approximation functions using polynoms and data-handling criteria have been developed. The criteria compare the standard deviation of both the normalized and the unprocessed data to a first estimate. Only in the case when the normalized values are closer to the smoothing spline, normalization by computational data processing is reasonable and results in significantly improved data quality. The first estimate can be calculated as the mean value of replicates, as a proportional, linear, polynomial or sigmoidal function if the functional relationship is known or as a smoothing spline if the functional relationship is unknown.

Similarly, calibrators added in immunoprecipitation experiments permit criteria-based data normalization. Importantly, calibrators in addition facilitate the conversion of relative signals into absolute values such as molecules per cell. This can also be achieved by co- loading known amounts of recombinant proteins detected by the same antibody as the protein of interest on the protein gel. Purified protein standards of several proteins are commercially available or can be generated in bacteria and insect cells. By determining the concentration of components in cells, the generation of absolute values enables additional information on absolute protein concentrations which not only can be used to compare signals derived from independent immunoblot experiments but as well to determine the stoichiometry of cellular components and to identify the number of a given protein in a single cell. The measurement of chemical kinetic parameters and molecular concentrations in vivo is crucial for the development of a functional mathematical model of a cell. Using the approach according to the present invention, absolute concentrations of proteins can be determined in cells. To identify kinetic parameters, highly resolved time-course data obtained according to standard operating procedures are generated. By fitting the a priori unknown parameters to time-course data, chemical kinetic parameters representing an in vivo situation are estimated. The knowledge of the error of each data point is critical for efficient parameter fitting. The proposed criteria-based data normalization calculates standard deviations providing this information.

The proposed methods can be applied as well to other blotting techniques, including "Northern" and "Southern" blotting, measuring DNA and RNA concentrations, respectively. Inhomogeneities in gel and transfer are likely to cause correlated errors in blotting data. This correlations can be destroyed by randomization, while the errors can be reduced with criteria-mediated normalization.

The developed criteria-mediated error corrections are suitable for any type of data acquisition. To validate a normalization procedure, the standard deviation of the normalized and the unprocessed values to an estimator of the data is compared. Smoothing splines have been applied as estimators which work well for sufficiently dense sampled data. Only if the standard deviation of the normalized values is smaller, the normalization procedure is valid, otherwise the unprocessed data should be used.

Quantitative data generation is promising to become an increasingly important factor in current biology, enabling researchers to quantitatively understand biological processes and interfere against diseases. Advancing the established technique of quantitative immunoblotting to a robust and reliable method for data acquisition provides a valuable tool for biomedical research.

Description of the Drawings

The present invention is hereinafter further described by a description of the accompanying drawings in which: Figure 1 shows (a) a conversion of relative values to an absolute protein concentration and error estimation of quantitative immunoblotting and (b) calculation of the estimated error of quantified signal given a standard deviation of the data,

Figure 2 shows (a) two SDS polyacrylamide gels using two distinct randomized sample loading orders and (b) the correlated errors when arranged in gel loading order, Figure 3 shows (a) a correction of phosphorylated and total ERKl signals using normalizers and (b) a spline-smoothed signal to normalize pERKl and ERKl signals having similar molecular weights,

Figure 4 shows (a) a domain structure of HA-EpoR schematically depicted, (b)

BaF3-HA-EpoR cells starved, stimulated with 50 units/ml Epo for 5 minutes and lysed and (c) concentrations of the calibrator being plotted versus the signals obtained for the HA-EpoR and the GST-EpoR calibrator,

Figure 5 shows corrections of HA-EpoR signals with GST-EpoR calibrator,

Figure 6 shows quantitative data generation with primary hepatocytes with primary mouse hepatocytes prepared from mouse livers according to (a) and calibrated immunoprecipitation data with GST-STAT3 converted to molecules per cell (b),

Figure 7 shows a flowchart of the method according to the present invention,

Figure 8 shows the effect of randomization on immunoblotting data, showing in A pipetting and blotting error, B simulated data, C spline-smoothed data and D autocorrelation of residuals,

Figure 9 shows the normalization of simulated time-course data depicting a valid procedure according to the criteria established according to the present invention A pipetting and blotting error, B randomized data, C normalized data and D lane-correlation of residuals, Figure 10 shows the normalization of simulated time-course data depicting a rejected procedure according to the criteria established according to the present invention A pipetting and blotting error, B randomized data, C normalized data and D lane-correlation of residuals,

Figure 11.1, 11.2, respectively, show an estimated blotting error in Figure 11.1 and a stimulation time course in Figure 11.2,

Figure 12 shows the emerging of two gels shown in the upper left panel data from experiment and in the upper right panel a normalization non- improving the data, in the lower left panel a scaling of estimated data sets and in the lower right panel a determined common data set.

Preferred Embodiments

Methods for Performing the Present Invention: Cell lines and primary Cell Cultures

According to the present invention, the retroviral expression vector pMOWS containing HA-EpoR cDNA was introduced into BaF3 cells by retroviral transduction. Cell lines stably expressing the HA-EpoR (BaF3-HA-EpoR) were selected and maintained in RPMI 1640 (Invitrogen, Carlsbad, CA) in the presence of puromycin.

Primary hepatocytes were isolated from 6-8 week old male Black 6 mice (Charles River, Wilmington, MA). Livers were perfused with Hanks buffer supplemented with collagenase II (Biochrom, Berlin, Germany). Intact liver capsules were transferred into Williams' medium (Biochrom, Berlin, Germany) supplemented with fetal calf serum, insulin, L- glutamine and dexamethasone. Hepatocytes were removed from the capsules, enriched by centrifugation and cultivated on collagen I-coated dishes (BD Biosciences, Franklin Lakes, NJ) in Williams' medium E (Biochrom, Berlin, Germany) supplemented with L-glutamine and dexamethasone.

Expression, Purification and Quantification of Recombinant Proteins Inactive purified ERK2 was purchased from Cell Signaling Technologies, Beverly, MA. The cytoplasmic domain of the EpoR was cloned into pGEX-2T (Amersham Biosciences, Piscataway, NJ) and expressed in E. coli BL21 CodonPlus-RIL bacteria (Stratagene, La Jolla, CA). Proteins were extracted by lysozyme lysis and sonification. Glutathione agarose beads (Sigma- Aldrich, St. Louis, MO) were added to lysates and proteins were recovered by addition of reduced glutathione (Sigma- Aldrich, St. Louis, MO). For quantification of purchased and purified proteins, dilution series of purified BSA (Sigma- Aldrich, St. Louis, MO) and the recombinant proteins were separated by 10% SDS polyacrylamide gel electrophoresis and stained with Coomassie Brillant Blue. The gel was documented using trans-illumination mode of a Lumilmager (Roche Diagnostics, Mannheim, Germany). Proteins were quantified using LumiAnalyst software (Roche Diagnostics, Mannheim, Germany).

Time-course Experiments

BaF3-HA-EpoR cells were starved in RPMI 1640 (Invitrogen, Carlsbad, CA) supplemented with 1 mg/ml BSA (Sigma-Aldrich, St. Louis, MO) for 5 h and were stimulated with 50 units/ml Epo (Cilag-Jansen, Bad Homburg, Germany). For each time point, 10⁷ cells were taken from the pool of cells and lysed by the addition of 2x Nonidet P-40 lysis buffer to terminate the reaction.

2 x 10⁶ primary hepatocytes were cultivated for 24 h after plating on collagen I-coated 60 mm dishes (BD Biosciences, Franklin Lakes, NJ) in Williams' medium E (Biochrom,

Berlin, Germany) supplemented with L-glutamine and dexamethasone. Cells were starved for 5 h in Williams' medium E supplemented with L-glutamine. Each dish was stimulated with 40 ng/ml IL-6 in Williams' medium E with L-glutamine. The medium of the cells was removed, Ix Nonidet P-40 lysis buffer was added and cells were collected using a cell scraper.

Quantitative Immunoprecipitation and Immunoblotting For immunoprecipitation, cytosolic lysates were incubated with anti-EpoR (Santa Cruz, La Jolla, CA) or anti-STAT3 antibodies (Cell Signaling Technologies, Beverly, MA). Immunoprecipitated proteins and total cellular lysates were separated by SDS polyacrylamide gel electrophoresis and transferred to PVDF or nitrocellulose membranes. Proteins were fixed with Ponceau S stain (Sigma-Aldrich, St. Louis, MO), followed by immunoblotting analysis using the anti-phosphotyrosine monoclonal antibody 4G10 (Upstate Biotechnology, Lake Placid, NY), the anti-tyrosinephosphorylated STAT3 antibody or the anti-doublephosphorylated p44/42 MAPK antibody (both Cell Signaling Technologies, Beverly, MA). Antibodies were removed by treating the blots with β- mercaptoethanol and SDS as described. Reprobes were performed using anti-EpoR (Santa Cruz, La Jolla, CA), anti-STAT3 or anti-p44/42 MAPK (both Cell Signaling Technologies, Beverly, MA) antibodies. For normalization, antibodies against β-Actin (Sigma-Aldrich, St. Louis, MO), PDI, Hsc70 and Calnexin (all Stressgen, Victoria, Canada) were used. Secondary horseradish peroxidase coupled antibodies (anti-rabbit HRP, anti-mouse HRP, protein A HRP) were purchased from Amersham Biosciences, Piscataway, NJ. Immunoblots against phosphorylated EpoR and total EpoR were incubated with ECL substrate (Amersham Biosciences, Piscataway, NJ) for 1 min, and exposed for 10 min on a Lumilmager (Roche Diagnostics). All other immunoblots were incubated with ECL Advance substrate (Amersham Biosciences, Piscataway, NJ) for 2 min, and exposed for 1 min on a Lumilmager (Roche Diagnostics, Mannheim, Germany). For quantifications, LumiAnalyst software (Roche Diagnostics, Mannheim, Germany) was used.

Spline Approximation and Signal Normalization

Smoothing splines are applied to the noisy data in order to estimate the actual values. Their smoothness is determined by generalized cross-validation, minimizing the mean square error between the estimated time-course and the data. Smoothing splines employing cross validation are freely available from the mgcv library of the statistics program "R". Splines are used for criteria-mediated error reduction.

Turning now to the figures, Figure 1 shows a conversion of relative values to absolute protein concentrations and error estimation of quantitative immunoblotting (a), upper panel. A dilution series of recombinant ERK2 protein as well as 100 μg of total cellular lysate prepared from BaF3-HA-EpoR cells was analyzed by quantitative immunoblotting with anti-ERK antibodies. The BLU-values (biomedical light units) of the dilution series were plotted against the number of molecules loaded on the gel (amount [g] / MW_ERK2 [g/mol] x N_A [molecules/mo I]) and a linear regression through the origin was calculated. The slope was used for converting the signals of the total cellular lysate to molecules per cell. Error bars represent estimated errors of total ERK2 dilution series as determined in part (b) of Figure 1. Part (b) of Figure 1 shows a dilution series of purified ERK2 separated eight times by a 10% SDS polyacrylamide gel and transferred to a membrane that was probed with anti-ERK antibody and subsequently developed with ECL or ECL advance. The estimated error of the quantified signals was calculated as the standard deviation of the data. To determine the noise inherent in this technique, the signal strength was plotted versus estimated error and was described by a sublinear function showing a 20% error for each data point within the measurement range.

According to Figure 2, randomized sample loading ensures uncorrelated errors. According to part (a) of Figure 2, BaF3-HA-EpoR cells were starved and stimulated with 50 units/ml Epo for 9.5 minutes, with samples of 1 x 10⁷ cells taken every 30 seconds. Cells were lysed and 75 μg total cellular lysate of each time point were separated by two 17.5% SDS polyacrylamide gels using two distinct randomized sample loading orders. Each immunoblot was analyzed by three repetitive cycles of detection with anti-ERK antibodies and subsequent removal of the antibodies by treatment with β-mercaptoethanol and SDS. The obtained signals for ERKl were quantified by Lumilmager analysis. According to figure 2, part (b), the data shows strongly correlated errors when arranged in gel loading order which are specific for a particular blot but are not affected by reprobing procedures. By arranging the data in chronological order, these correlations are eliminated and the data can be smoothed by spline approximations - to give an example - indicated by solid lines. According to the graphs shown in Figure 3, a correction of phosphorylated and total ERKl signals using normalizers is depicted. According to Figure 3, part (a), BaF3-HA-EpoR cells were starved and stimulated with 50 units/ml Epo for 9.5 minutes, with samples of 1 x 10⁷ cells taken every 30 seconds. Cells were lysed and 75 μg total cellular lysate of each time point were separated by a 17.5% SDS polyacrylamide gel. The immunoblot was analyzed with anti-pERK antibodies, reprobed first with anti-ERK antibodies and after that with an anti-Hsc70/anti-PDI/anti-β-Actin antibody mixture. All signals were quantified by Lumilmager analysis. According to Figure 3, part (b), the β-Actin signal was spline- smoothed and used to normalize pERKl and ERKl signals, having similar molecular weights. pERKl and ERKl signals were converted to molecules per cell numbers using the protein standard depicted in accordance with Figure 1. Smoothing spline curves through original and normalized data are given in solid lines. According to Figure 4, a titration of recombinant protein calibrators in immuno- precipitation is disclosed. According to Figure 4, part (a), the domain structure of HA- EpoR is schematically depicted and the binding epitope for the anti-EpoR antibody is indicated. The calibrator GST-EpoR consists of the protein domain containing the antibody binding site fused to a protein tag for purification. According to Figure 4, part (b), BaF3- HA-EpoR cells were starved, stimulated with 50 units/ml Epo for 5 min and lysed. Increasing amounts of recombinant GST-EpoR were added to the lysates and both the GST-EpoR calibrator and the HA-EpoR were immunoprecipitated with anti-EpoR antibodies. The samples were separated on a 10% SDS polyacrylamide gel. The immunoblot was analyzed with anti-EpoR antibodies and quantified by Lumilmager analysis. According to Figure 4, part (c), concentrations of the calibrator were plotted versus the signals obtained for the HA-EpoR and the GST-EpoR calibrator. A solid line depicts the linear relationship between the calibrator concentration added to the lysate and the detected signal within a range of 2.5 to 100 ng of calibrator addition. The solid line depicting the average signal of the HA-EpoR intersects at 40 ng of GST-EpoR indicating comparable signals for the calibrator and the HA-EpoR.

In Figure 5 according to the drawing, a correction of HA-EpoR signals with GST-EpoR calibrator is shown. According to Figure 5, BaF3-HA-EpoR cells were starved and stimulated with 50 units/ml Epo for the indicated time. 1 x 10⁷ cells were lysed and 40 ng of GST-EpoR were added to each lysate. Immunoprecipitation was performed using anti- EpoR antibodies, followed by separation on a 10% SDS polyacrylamide gel. The experiment was repeated with randomized sample loading. The immunoblot was analyzed with anti-pTyr and anti-EpoR antibodies and quantified by Lumilmager analysis. Time after Epo-stimulation was plotted against the signals of HA-EpoR and the calibrator GST- EpoR. A spline smoothing the calibrator signal was used to calibrate pEpoR signals, whereas the EpoR signal was calibrated and converted to molecules per cell. In both experiments, signals could be corrected using the calibrator, but only in the time-course with randomized sample loading the correlated errors could be removed. Splines are given in solid lines.

According to Figure 6, a quantitative data generation with primary hepatocytes is shown.

According to Figure 6, part (a), primary mouse hepatocytes were prepared from mouse livers. 2 x 10⁶ cells for each time point were cultivated on collagen coated dishes and starved. 40 ng/ml IL-6 was added and the cells were lysed at the indicated time points. 100 μg of total cellular lysates were separated by two 10% SDS polyacrylamide gels, while the remaining lysates were subjected to immunoprecipitation using anti-STAT3 antibodies before separating by two 10% SDS polyacrylamide gels. Sample loading was randomized with every second time point on the second gel. Quantitative immunoblotting was performed with anti-pSTAT3, anti-STAT3, and an anti-Calnexin/anti-Hsc70 mixture. According to Figure 6, part (b), immunoprecipitation data was calibrated with GST- STATS and converted to molecules per cell, while total cellular lysate data was normalized with Calnexin/Hsc70 signals and the data-points were spline-smoothed as indicated by solid lines.

In Figure 7, a flowchart for the method according to the present invention is given.

A user input file with general information, A, further a gel information file with gel specific information, labelled B, and raw blotting data labelled C are entered and allow in step 10 a start of the method by reading raw data from one or more gels or blotted membranes. In step 20 according to the flowchart given in Figure 7, an estimation of the blotting error is performed. A smooth curve for every normalizer in gel domain via a spline approximation is obtained. Normalizer is meant as an abbreviation for normalizer or calibrator proteins. In the gel domain the dependency of the data on the slot index is expressed, whereas in the time domain the dependency on the time variable is expressed or on the dose concentration for response experiments. If necessary, in step 20 average normalizers which have a neighbored position on the gel into one curve after minimizing the difference of their splines. The smooth curve represents the blotting error estimation. It is to be pointed out that the time and the gel domain are not equal but correspond rather in random manner to each other.

According to method step 30, a first estimation for the proteins of interest is performed. Given functional relationships or a spline approximation are used to get a smooth first signal estimate of every protein of interest within the time domain.

In step 40, a correction of every protein of interest is possible if desired. Every protein of interest can be corrected by division with a blotting error estimate. If the least square distance of the protein of interest data values to its first estimate decreases, the normalization was successful. Otherwise, the original values are used for further processing instead of the normalized data. According to method step 50, by optimized scaling multigel molecules of interest can be merged. For this, the molecules should be measured alternatingly over the different gels. To obtain one time-course or one dose response sequence, dilution series or other experimental settings, relative scaling of the different gels is minimized.

In finishing step 60, the processed and possibly merged data, is saved together with estimated smooth signals in chronological order.

Error Classification

Immunoblotting as a technique for quantitative analysis of protein concentrations has several sources of noise, which can be divided into three classes:

(i) pipetting errors f(j) change the amount of each protein in the j-th lane by the same factor, reflecting, e.g., the different amount of lysate loaded on each gel lane

(ii) blotting errors gθ_? ^m), observed as brighter and darker areas, arise from inhomogeneities of the gel and transfer to the membrane. They are highly correlated for neighboring lanes, j, and rows, m.

(iii) contributions independent from the loaded protein concentrations which are modeled as Gaussian noise, η (j, m) .

Error contributions from pipetting are small compared to the highly correlated errors of the blotting technique. The effects of the concentration x^* (t_y ) of a given protein in the lysate at a time t,, resulting in the measured concentration xyt_j ), can be described by equation 1: x(t_j )= [l + g {j, m)] [l + f {j)x (t_j )+η {j, m)\ .

Here, the time point t _} after stimulation corresponds to lane j , the smooth systematic error g depends on the lane index j and on the molecular weight m measured in kD. The pipetting error / depends only on the lane number j , since it changes the amount of all proteins in a lane by the same factor. Errors arising from (i) and (iii) are uncorrelated among different lanes, resulting in (/(/ )/(/)) = 0 and (η {j,m)r[ {f,m)) = 0 for j≠ f .

In the following, normalizers and calibrators are used as well as a randomized, non- chronological loading of the lanes to identify and reduce the highly correlated blotting errors, g(j,m).

Elimination of the Blotting Error

The highly correlated errors arising from the blotting technique vary gradually over the lanes and make it difficult to extract the true values. To eliminate the correlations among the lanes, non-chronological gel loading is employed. Here, the subsequent time-points after stimulation are loaded on the gel in a randomized fashon under the condition that consecutive time points are separated by minimum number of 4 lanes for 20 time-points. By applying this method, the errors between consecutive time points are uncorrelated. An estimation of the true time-course from the data by rearranging the time points in chronological order can be estimated. As shown in Figure 8, graph (c), a cubic spline is employed whose smoothness is determined by generalized cross-validation. This technique demands statistical independent errors as generated by the randomized gel loading. The estimation of a time-course from noisy data by smoothing splines has been worked out in detail. It is emphasized that a sufficiently dense grid of time-points is necessary to keep the bias of this method small.

For the case that a normalizer protein, x_n {j), can be measured with a similar molecular weight as the molecule of interest, it is possible to estimate the blotting error g{j,m) as X_n (j) = const by definition. The true signal is then given by equation 2:

x. V,

Here, x_n(t) denotes the smoothing spline generated from the data set {jc_B(t₇ )| by keeping the lane ordering of the randomly loaded gels. Smoothing of the data is performed in order to average over error contributions arising from pipetting, f(j) and other sources of noise, r\ (j,m) . Further, by x^*{t) and x(t) the time-courses of the smoothing splines generated from the chronological ordered data sets ) , are expected to be significantly smaller than the residuals without employing a normalizer, x'yt_j j-xyt_j ) , as already applied for the blotting errors in the first case. This in turn provides for a reliable measure for the quality of the used normalizer protein.

Error Reduction via Randomization and Normalizers - Simulation Study Simulations of typical immunoblotting experiments were performed by generating a simulated signal with quadratic rise and exponential decay and a maximum at half lane number, equidistant Iy sampled according to graph B of Figure 8. this simulates a typical time-course experiment after stimulation with a hormone. The true signal jc^*(t_y ) was processed with two main sources of errors in the previous section, a pipetting and a blotting error. In detail:

1. A multiplicative, uncorrelated pipetting error was applied as shown in Figure 8, graph A representing errors derived from unequal cell number or errors in pipetting the cellular lysates: x'(_tj ) = x% ) - (1 + σεC/)) ε(/)e M<U).

2. A multiplicative, strongly correlated blotting error was applied, representing errors from differences in migration in the SDS polyacrylamide gel or unequal transfer to the membrane: with the blotting error g[j) represented by a sine function with mean zero and phase, amplitude and frequency consistent with experimental observations.

The processing was applied to a chronological and to a randomized true signal, x_r ^* _and and ^xl_hmn ' respectively, leading to "measurements" as given in graph B of Figure 8. It is noted that the chronological signal is rather smooth but changes the characteristic of the true signal as follows: The maximum occurs earlier and a new minimum is observed at t = 15. The randomized signal on the other hand is very noisy but does not introduce systematic effects. The smoothed processed randomized signal x_rand is very close to the true time- course, whereas the smoothed processed chronological signal x_chron still keeps correlated deviations from the true signal, see graph C of Figure 8. The correlation structure of the deviations can be investigated via the autocorrelation function as shown in Figure 8, graph D. For uncorrelated errors, the autocorrelation function should drop from 1 at τ = 0 into the 95% confidence interval for τ = 0. This is not the case for the processed chronologically signal which can lead to misleading conclusions if methods are applied which assume uncorrelated noise. Besides visual inspection of the autocorrelation function, the improvement of data quality by means of a randomized gel loading can be quantified by the error reduction factor:

For the illustrated data set, the achieved reduction of the standard deviation was CC - 0.45. The reduction can only be quantified when the actual values are available which is not the case in experimental measurements. Hence, the question arises whether a general error reduction factor can be established by randomizing or whether it depends on experimental parameters like the number of lanes, strength of signal maximum, blotting error or pipetting error. A simulation study showed that for small pipetting errors an error reduction factor of 0.45 ± 0.1 could be established independently from other parameters.

Quantifying the Error Reduction using Randomization and Calibrators To determine the usefulness of randomization for the improvement of data quality, several parameters were varied including the number of lanes (10 to 100), the number of sine periods of the blotting error (0.8 to 2.2), the strength of the blotting error (ratio of smallest to largest value ranging from 1.5 to 10), the maximum signal strength (0.1 to 20) and the strength of the pipetting error (σ ranging from 0 to 1). During the variation of one parameter, the other parameters were fixed:

• Number of lanes: 20

• Number of sine periods of the blotting error: 1

• Strength of the blotting error (max/min): 3

• Maximum signal strength: 2

• Standard deviation of the pipetting error: 0.1

At least 15 lanes should be used to achieve an optimal improvement. For the other investigated parameter ranges no strong effect is observed for all variations except for the strength of the pipetting error. Since pipetting errors are uncorrelated, they cannot be reduced by randomization - if the fraction of the pipetting errors increases, the randomization takes less effects. In general, randomization decreases the standard deviation in quantitative immunoblotting to about 0.45 of the value without randomization, as long as the pipetting error is not too large. An approach to control the pipetting error in experiments is sampling the same number of cells for each time point or measuring and adjusting total protein concentration.

Criteria for Employing Normalization with Normalizers and Calibrators

Calibrators and normalizers possess a constant concentration. Fluctuations occur only as measurement errors. Since the blotting error changes gradually from lane to lane and other errors like the pipetting error are rather uncorrelated, the blotting error can be estimated by smoothing the calibrator or normalizer signal, e.g. with a smoothing spline. Based on this blotting error estimate, the protein of interest can be normalized. However, since the blotting error is a local property of the gel, normalizers and calibrators are required with a similar molecular weight as the protein of interest. If the molecular weight of the normalizer is different and hence runs on a significantly different region on the gel, it does not reflect the blotting error for the molecule of interest. Therefore, criteria for employing normalizers and calibrators have to be developed.

Figure 9, graph A shows a simulated blotting error and a good estimation, corresponding to the smoothed signal of an appropriate normalizer in a real experiment. Smoothing the processed randomized signal leads to an acceptable estimation of the true signal. Smoothing the normalized signal yields virtually the true signal itself, as best shown in graph C of Figure 9. Even the correlation structure of the estimation error in the gel domain is improved. The estimation of the blotting error given in Figure 10, graph A is inaccurate: A strong phase shift is to be observed, corresponding to a skewed gradient of the blotting error depending on the position on the blot. In this situation, normalizing the data increases the deviation of the estimated signal from the true signal. Hence, a criterion whether a normalization is applicable would be a decreased standard deviation of the estimated signal. This, though, requires knowledge of the time course which is not available. Instead, the smoothed curve of the randomized but not yet normalized signal is used as first estimate of the true signal. If the normalizer is applicable, a new estimate can be calculated based on the randomized and normalized data, otherwise the former estimate is kept. The shown simulated data sets have the following standard deviations: • Figure 9:

- Randomized (true): 0.533

- Randomized (estimation): 0.722

- Randomized, normalized (true): 0.157

- Randomized, normalized (estimation): 0.515

• Figure 10:

- Randomized (true): 0.533

- Randomized (estimation): 0.722

- Randomized, normalized (true): 1.208

- Randomized, normalized (estimation): 1.068

The estimated error decreases in case of Figure 9 and increases in case of Figure 10 if a normalizer is used. Hence, the normalization procedure is only applicable in the first case, reducing the true standard deviation from 0.533 to 0.157. In the other case it would increase the standard deviation from 0.533 to 1.208. This procedure works robustly for normalizers and calibrators, as long as randomized gel loading is applied.

Application to Stimulation Experiment

The randomizing and normalization procedure was applied on an erythropoetin (Epo)- induced time-course experiment resulting in phosphorylation of ERKl and ERK2. Samples were loaded randomly and separated on 17.5% SDS polyacrylamide gel and transferred to membranes that were developed with chemiluminescent substrates and quantified with the Lumi-Imager. The standard deviation of the signals to their spline approximation was calculated to 2.524 for pERKl and 0.455 for pERK2. Normalization with β-Actin reduced the standard deviation to the spline approximation to 1.878 for pERKl and 0.262 for pERK2. The reduced lane-correlation for the normalized data is a second quality criterion. In this case, the correlation structure of the systematical blotting error could be disrupted validating the normalization. IV. Calculation of Molecules per Cell

Quantification of a protein P measured by immunoblotting is performed via chemiluminescence detection yielding total intensities P_blu which are proportional to the total number of molecules P_tmlc on the blot. The linear relationship reads:

"tmlc ^{~ a '} "blue with a proportionality factor a and 0 y-axis interception. The factor a has to be determined for each protein species and for every blot, since the amount of antibody added varies for different blots and the antibody affinity differs for different proteins.

The reference protein R realized by a standard or calibrator protein should

- contain the same epitope binding to the antibody as the protein of interest;

- have a known molecular weight R_mw ,

- be added to the lysate with a known amount R . The total number of reference proteins in the lysate is given as

^tmlc ^{= '} ^A

R mw with Avogadro constant N _A = 6.022^• 10²³. If the imaging unit measures the intensity R_blu , the proportionality factor can be calculated as a ₌ R_mlc _ R_tmlcN_AR_g

J? J? J?

^Λblu ^Λblu ^Λmw

If possible, one should measure the reference protein several times and estimate a by linear regression. This provides also a standard for the deviation for a .

Calibrator proteins harbor the same antibody epitope as the molecule of interest, P, however, yet possess a different molecular weight than P resulting in a distinct band in the immunoblot analysis. If analysis of total cellular lysates are performed, a few lanes of the immunoblot have to be used for the standard protein to facilitate parallel detection.

P_tmlc is the total number of the molecules of the investigated lysate. If the number of cells in the lysate is available, the molecule number per cell can be calculated as p P tmlc

rmlc ~ ^'

# cells

Figures 11.1 and 11.2, respectively, show a blotting error estimation and normalization. The upper panel in Figure 11.1 shows a blotting error estimated with two endogenous normalizer proteins Hsc70 and Calnexin. Figure 11.2 shows original ( O) and normalized data points (*). The normalized data points have a smaller standard deviation to the first estimate consisting of the spline-smoothed original data than the original data points themselves. Hence, the normalization is valid and the normalized data are used as processed data.

In Figure 12, the merging of two gels is shown, graph A of Figure 12 shows data from an experiment, measured with two gels. According to graph B of Figure 12, the normalization cannot improve the data of the second gel ( O). After scaling the estimated data sets according to graph C of Figure 12, the common data set can be determined as given in graph D of Figure 12. According to graph C of Figure 12, the two splines are approximated to one another until a minimum deviation between the splines is obtained. To approve the description of the dynamic behavior of the protein, sampling is extended beyond gel capacity, in this case 31 time points.

Claims

Claims

1. Method to quantitate a set of samples obtained from quantification of a gel or blotted membrane and minimizing errors in quantitative gel or blotting analysis including the following method steps: a) reading raw data from at least one randomized loaded sample of at least one gel or blotted membrane with at least one molecule of interest and at least one corresponding normalizer or calibrator molecule,

b) estimating a blotting error for at least one normalizer or calibrator within said at least one gel or blotted membrane via an approximation function,

c) creating a smooth first signal estimate of at least one molecule of interest by a known functional relationship of the concentration and an independent variable like e.g. time or dose of estimation or an approximation, if a continuous functional relationship exists but the function is unknown,

d) said first signal estimate of the at least one molecule of interest is corrected at hand of the estimated blotting error according to step b),

e) dependent on the result of the correction according to step d), corrected data for the at least one molecule of interest or the original values are further processed, and

f) processed and/or merged data of the at least one molecule of interest is saved in a non-random order.

2. Method to quantitate a set of samples according to claim 1, wherein according to step a), the randomized sample loading is performed in a non-chronological order.

3. Method to quantitate a set of samples according to claim 2, wherein subsequent time points are separated by a minimum number of n/5 lanes for n time points.

4. Method to quantitate a set of samples according to claim 1, wherein in steps b) and c), respectively, an approximation function is given by either a mean value, a proportional, linear, polynomial or sigmoidal Hill function or a cubic spline, whose smoothness is determined by generalized cross-validation.

5. Method to quantitate a set of samples according to claim 1, wherein according to step b), a normalizer x_n {j) is used, the blotting error g g{j, m) is estimated as x_n ^* (j) = const and normalized data is given by

X_n [t_j ) normalized smoothing spline with mean 1.

6. Method to quantitate a set of samples according to claim 1, wherein in step b) normalizer and/or calibrators are applied for processing a constant concentration and/or a constant molecular weight.

7. Method to quantitate a set of samples according to claim 1, wherein in step c) the normalization is qualified as being successful if the error average least square distance of the data of at least one molecule of interest decreases to its first estimate.

8. Method to quantitate a set of samples according to claim 1, wherein in step c) the normalization is qualified as being unsuccessful if a least square distance of the data of at least one molecule of interest increases to its first estimate and original values are used for further processing.

9. Method to quantitate a set of samples according to claim 1, wherein by randomization of sample loading, a standard deviation of immunoblotting data is reduced at least about two-fold.

10. Method to quantitate a set of samples according to claim 1, wherein in step b) normalizers and/or calibrators are provided, present at a similar position as the molecule of interest in a gel or blot, being detectable with a strong constant signal.

11. Method to quantitate a set of samples according to claim 1, wherein normalized data according to step d) is compared with respect to the standard deviation of both the normalized and the unprocessed data to a smoothing data spline, or a mean value, a proportional, a linear, a polynomial or a sigmoidal Hill function of the unprocessed data serving as first estimate.

12. A computer programme comprising a computing routine(s) stored on a computer readable medium for reading raw data from at least one randomized loaded series of sample of at least one gel or blotted membrane, estimating a blotting error for at least one normalizer and/or calibrator within said at least one gel via an approximation function, creating a smooth first signal estimate of at least one molecule of interest created by a functional relationship or approximation, correcting said first estimate of the at least one molecule of interest at hand of the estimated blotting error, processing dependent on the result of the corrected data for the at least one molecule of interest or the original values and processing and/or merging data of the at least one molecule of interest.

13. A computer programme according to claim 12, wherein the normalized data is calculated by

^■u-÷ 'M₁ ⁾

Xn \t, an error reduction factor is calculated by

with x_rand being the normalized data, x_mw being the unprocessed data and x^* being the first estimate of the unprocessed data.

14. A computer programme according to claim 12, wherein measured concentrations x[t ) are described by the equation

x(t)= V + g {j,m)] [l + f {j)x (t)+x\ {j,m)\

15. Method to quantitate a set of samples according to claim 1, wherein according to step f), the merged data derived from multiple gels or blots by minimizing the mean square distance between the approximation of each gel or blot, either a mean value, a proportional, a linear, a polynomial or a sigmoidal Hill function or a cubic spline whose smoothness is determined by generized cross validation by scaling of the data is applied.

16. Use of the method according to one or more of the preceding claims for error reduction for standardized quantitative data in biological networks, particularly in gel, immunoblotting (Western Blotting), Northern Blotting and Southern Blotting analysis.