A serial dilution is the repeated dilution of a solution to amplify the dilution factor quickly. It’s commonly performed in experiments requiring highly diluted solutions, such as those involving concentration curves on a logarithmic scale or when you are determining the density of bacteria. Serial dilutions A sequential set of dilutions in which the stock for each dilution in the series is the working solution from previous dilution. In effect, except for the last dilution, each dilution is both a stock and a working solution. The DF for the entire series as a whole is the product of the DF's of each individual dilution. So, when i did the serial dilution for BSA standard, i used RIPA as diluent. But i found that the standard curve look so abnormal n weird. As i know that, detergent can affect the Bradford assay. Start studying Proteins and Dilutions. Learn vocabulary, terms, and more with flashcards, games, and other study tools. A standard curve, also known as a calibration curve, is a type of graph used as a quantitative research technique. Multiple samples with known properties are measured and graphed, which then allows the same properties to be determined for unknown samples by interpolation on the graph.
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There are a variety of methods that can be used to determine protein concentrations. One specific method uses the Bradford assay, a colorimetric protein assay, which involves the binding of Coomassie® Brilliant Blue G-250 to proteins under acidic conditions. Coomassie Brilliant Blue is known to bind to basic and aromatic amino acid residues.1 Upon binding to a protein, the absorbance maximum for the Bradford reagent shifts from 465nm to595nm. The absorbance of the dye at 595nm is indicative of the protein concentration. In order to successfully determine the unknown concentration of the bovine serum albumin (BSA), a standard calibration curve was created via the serial dilution of a standard solution of bovine serum albumin(BSA). The absorbance of the BSA standard was analyzed after the Bradford reagent was mixed with the solutions according to the experimental procedure.2 The calibration curve was determined accordingly and followed the equation y= 0.0018x + 0.3978 Subsequently, dilutions were made of the BSA of unknown concentration according to the standard Bradford assay procedure.2 Following the dilutions, the absorbences of the samples were determined via a spectrophotometer. Consequently, the concentration of the unknown samples was determined by multiplying the values of the absorbences by the dilution factor used. The concentration of the unknown sample of protein was determined to be 2323.3 with a deviation of ± 598. Therefore, the complete expression was 2323.3 ± 598. During the experiment, it was observed that the Bradford Assay was an effective method for determining unknown concentrations of protein samples of about 1µg/mL. This method proved to be a quick and fairly accurate approach for determining an unknown protein concentration because this approach is highly sensitive to low protein concentrations.
Introduction:
The Bradford protein assay is a spectroscopic analytical method used to measure the concentration of protein samples in solution. It is a popular protein assay because it is fairly simple to conduct and is sensitive to relatively minute concentrations of proteins in sample. The framework of the Bradford assay relies on the reagent Coomassie Brilliant Blue G-250 dye which binds to proteins under acidic conditions. The dye reagent effectively reacts with arginine residues and less effectively with phenylalanine, tryptophan, tyrosine, lysine, and histidine residues. The binding of the dye to a protein under the appropriate conditions causes a shift in the wavelength of maximum absorption from 465nm to 595 nm.1 The concentration of the protein is then directly related to the absorption values of the samples at 595nm.
Most commonly, a calibration curve is constructed using bovine serum albumin (BSA). The Bradford assay requires the reagent Coomassie Brilliant Blue G-250 dissolved in an acidic solution.3
Advantages of the Bradford assay encompass the observance a stable color which varies according to proteins. The dye’s response to protein sample is only linear for a small range of the total sample group. An advantage of the reagent, Coomassie Brilliant Blue G-250, is that has a sensitivity of about 30ng.4However, some disadvantages include: the discoloration of protein samples, variation between different protein samples, and the destruction of the protein sample used in the assay. Due to the variation between proteins, the choice of the standard is quite important.5
The experiment conducted aimed to acquire, through the use of the Bradford assay, a standard curve for the bovine serum albumin solutions and to ultimately determine the concentration of an unknown sample of bovine serum albumin. The standard curve is obtained by performing serial dilutions of the standard samples and then adding the Bradford reagent. First, A blank sample in a disposable cuvette is prepared in which water and the Bradford reagent are added. The absorbances of the blank and the protein samples are recorded through the use of s spectrophotometer. A standard curve can then obtained by graphing the absorbance of the samples versus their concentrations. To find the concentration of the unknown samples, dilutions were performed on the scale the of a 10x and 50x dilution factor so that the relative concentrations fall in the range of .01 to 0.1 . Finally, after the absorbances of the unknown samples are determined, the concentration of the unknown is determined by finding the location on the graph that corresponds to the absorbance of the standard. Subsequently, the concentration of the unknown sample can be found by multiplying the concentration found from the graph by the dilution factor.
Experimental:
The standard and unknown solution of bovine serum albumin along with any chemicals used was obtained from Sigma Aldrich unless noted otherwise. The de-ionized water used in this experiment was obtained from the Baylor Science Building located in Waco, Texas. The spectrophotometer used was a Beckman DU 520 General Purpose Ultraviolet/Visual Spectrophotometer manufactured in Fullerton, California.
In this experiment, serial dilutions were made of a standard solution of BSA using de-ionized water to give six samples of standard solutions ranging in concentration from 117 to 1000 . Each test tube was covered with para-film to prevent evaporation of the sample. Shortly thereafter, a 10x dilution of the unknown sample(A1) was made. This was performed by adding .9 mL of de-ionized water to .1 mL of the unknown BSA sample. Next, a 50x dilution was performed for the sample A2 where .4mL of de-ionized water was added to .1mL of the unknown BSA solution from A1. After this, .1mL of de-ionized water was pipeted into an empty plastic cuvette along with the Bradford reagent. Each of the BSA samples of unknown concentration were pipeted(.1mL) into clean and labeled test tubes. Approximately, 3mL of dye was added to each of the test tubes. The test tubes were shaken gently to ensure a homogenous solution and then allowed to incubate for approximately 7 minutes. The Beckman Spectrophotometer was calibrated to read at a wavelength of 595 nm. The blank cuvette which contained the de-ionized water and the Bradford reagent was run through the spectrophotometer. Next, the absorbences of the standard BSA solutions were recorded by running them through the spectrophotometer starting with the least concentrated and going to the most concentrated. Using the same method mentioned above, the absorbances for the unknown A1 and A2 samples were measured and recorded. The recorded data can be viewed in the accompanying tables that follow.
In order to determine the unknown concentration of the BSA sample, the standard curve had to be analyzed. The equation of the line of best fit for the points above was found to be : Y= .0018x + .03978. It is important to note that three points were omitted from the graph(above) due to their non-linear relationship with the rest of the data points. Had these points been included in the graph the equation of the line would have been Y= 0.001x + .3559 and the R2 value would have been 0.8586. Thus, when calculating the unknown concentrations, the values that would have been obtained from this equation would be negative. As the date points began to taper off, it was a sign that the linear nature of the line was disappearing. The R2 value of the line was 0.972. This indicated that the points fell very close to the line of best fit. Paragon ntfs serial v149. The unknown concentrations were determined by finding the concentration that corresponded to the absorbance. This was then multiplied by the dilution factor to give the actual concentration of the unknown BSA solution samples. The mean value for the unknown concentration was determined to be is 2323.3 ± 598 .
Finally, it is important to point out that in Table 1, the absorbance value for sample #7 was found to be 1.118. This absorbance value was omitted from the standard curve because it did not follow the linear relationship of the standard dilution curve. Furthermore, it was determined that this abnormal value was a result of not taking 100 µL out of tube 7 and then adding the Bradford dye. Rather, what occurred was the final volume that accumulated in tube 7 was not taken account for and thus resulted in an abnormally high absorbance value. A potential source of error that could have affected the value of our absorbance values could have possibly come from experimental error. This could have come in the form of our spectrophotometer not operating properly due to improper calibration or the UV lamp malfunctioning. Consequently, this would have resulted in a deviation of absorbance values and affected the concentration values of the protein samples of unknown concentration.
Calculations: Download full hd mp4 movies.
To perform the calculations below, the equation of the standard curve was used alongside graphical analysis.
A1: Y= .0018x + .03978
.534=.0018x + .03978
x= 274.6µg/mL
Because this was a 10x dilution, the original concentration is:
(274.6µg/mL)(10)= 2746 µg/mL
A2: Y= .0018x + .03978
.1082=.0018x + .03978
x= 38.01µg/mL
Because this was a 50x dilution, the original concentration is:
(38.01µg/mL)(50)= 1900.6 µg/mL
Mean Value: =
= 2323.3
Standard Deviation Calculation:
= 597.8 The amazing spider man setup.exe download highly compressed.
This value is the standard deviation for the unknown concentrations.
Descargar premiere pro cc gratis 32 bits. Therefore, the deviation is 2323.3 ± 598 .
Mean calculation for unknown class data
A1 = .534
A2 = .1082
Discussion:
The objectives of this experiment were met. Using the Bradford method, it was possible to construct a standard curve for the standard solution of bovine serum albumin and determine the unknown concentration of a bovine serum albumin solution. By using the standard curve constructed from the standard solutions, it was possible to determine the concentrations of the unknown dilutions through the use of the Bradford method.
Usually, it is observed that when the concentration of a protein sample increases, the absorbance also increases. This occurs because the specific wavelength of light emitted is absorbed by the delocalized pi electrons in the aromatic side chains of the amino acids tyrosine, tryptophan, and phenylalanine. Also, Beer’s law states that the absorbance is equal to the path length times the concentration times the coefficient. Therefore, it is the increase in concentration of aromatic side chains that causes the absorbance to increase as the amount of protein is increased. With the addition of the Bradford reagent ( Coomassie Brilliant Blue G-250) and successful binding to proteins, the wavelength of maximum absorption of the dye shifts from 465nm to 595nm. According to the data for the standard curve, it was observed that there was a positive linear relationship for the lower protein concentrations. It was also observed that some of the higher values began to taper off and fit a non-linear relationship. Therefore, these “outlier” data points were discarded. The line of best fit for the data points was found to have the equation Y= .0018x + .03978 and an R2 value of 0.9718. The R2 value of 0.9718 indicated that the data points fell within minimal deviation from the line of best fit. Furthermore, the y value in the equation indicated the absorbance while the x value indicated the concentration of the protein.
The unknown concentrations were determined by using the line of best fit. Essentially, the unknown concentration was found by finding the corresponding concentration for each of the measured absorbances. Then, the actual concentrations of the unknown sample of bovine serum albumin could be found by multiplying those concentration values by the dilution factor. It was determined that the average protein concentration of our unknown sample of bovine serum albumin was 2323.3 ± 598 This value was found by averaging the values of the two unknown samples listed in the Calculations section.
Lastly, another route to determining the concentration of a protein sample is through the use of the extinction coefficient of protein. This methodology employs the use of the equation A=ECL. Where A is the absorbance, E is the extinction coefficient value for a certain protein, C is the concentration of the protein in mg/mL, and L is the length of the cuvette used. This method is a more concrete way of determining the concentration of a protein sample and allows one to insert the unknown values and solve for a variable. One drawback to this method is that it does not allow one to interpret the values to a great degree. However, by using the Bradford assay one can construct a standard curve based on the methods described in the paper and interpret the results in a more graphical manner. This method relies on plotting the standard curve and determining the unknown protein concentrations by using points on the line of best fit that coincide with the absorbances recorded for the samples of unknown concentration.
Abstract
Reverse phase protein arrays (RPPAs) are a powerful high-throughput tool for measuring protein concentrations in a large number of samples. In RPPA technology, the original samples are often diluted successively multiple times, forming dilution series to extend the dynamic range of the measurements and to increase confidence in quantitation. An RPPA experiment is equivalent to running multiple ELISA assays concurrently except that there is usually no known protein concentration from which one can construct a standard response curve. Here, we describe a new method called ‘serial dilution curve for RPPA data analysis’. Compared with the existing methods, the new method has the advantage of using fewer parameters and offering a simple way of visualizing the raw data. We showed how the method can be used to examine data quality and to obtain robust quantification of protein concentrations.
Availability: A computer program in R for using serial dilution curve for RPPA data analysis is freely available at http://odin.mdacc.tmc.edu/~zhangli/RPPA.
Contact:[email protected]
1 INTRODUCTION
The reverse phase protein array (RPPA) is an emerging high-throughput technique in proteomics (for reviews, see Borrebaeck and Wingren, 2007; Charboneau et al., 2002; Lv and Liu, 2007; Poetz et al., 2005; Sheehan et al., 2005). This technology has been successfully applied in a number of basic and clinical studies (Amit et al., 2007; Aoki et al., 2007; Fan et al., 2007; Pluder et al., 2006; Sahin et al., 2007; Tibes et al., 2006; Yokoyama, et al., 2007). A single array slide can be used to measure hundreds of samples for a protein. The protein level across the slide is detected by binding of a highly specific and sensitive primary antibody followed by detection using amplification linked to fluorescence, dye deposition, near infrared or nanoshells. Because protein concentrations can vary over many orders of magnitude in patient or cell line samples, it is desirable to have accurate measurements of protein concentrations over a wide dynamic range. To extend the dynamic range of the measurements, each sample is diluted multiple times successively and spotted on an RPPA slide so that if a protein concentration in the original sample is close to saturation, the sample can still be measured at diluted spots.
Multiple methods are available for analysis of RPPA data (Hu et al., 2007; Kreutz et al., 2007; Mircean et al., 2005). Typically, the methods are based on modeling the response curve, which describes the relationship between the observed signal and the protein concentration. Mircean et al. (2005) realized that since it is the same protein being measured for all the samples spotted on an RPPA slide, the same response curve should be suitable for all these samples. Based on this assumption, Microean et al. proposed a robust linear-square method to quantify the protein levels. However, an obvious drawback of the method is that it fails to recognize saturation effects for proteins at high levels. Recently, Hu et al. (2007) developed an alternative method using a non-linear, non-parametric approach to model the response curve.
In this study, we show an alternative approach to RPPA data analysis. Instead of modeling the response curve, we construct a new model, serial dilution curve, which characterizes the relationship between signals in successive dilution steps. The advantage of this approach is two fold: (i) the signals in successive dilutions can be related to each other in explicit formula in which the underlying unknown protein concentrations do not appear. This allows a low-dimensional non-linear optimization to estimate the key parameters of the map between protein concentration and signal intensity. The estimated map can then be applied to the observed signals to estimate the underlying abundances; (ii) it leads to an intuitive display of raw data, which is very useful for checking data quality and interpreting the model.
2 METHODS2.1 Serial dilution curveOur new method is based on the recognition that the relationship between signals in successive dilution steps uniquely determines the response curve. Typically, a response curve is a monotonic, s-shaped curve. It can be described by the Sips model (Sips, 1948):
(1)
where a is the background noise; b is the response rate in the linear range; M is the maximum or saturation level, x is the concentration of the protein. Sips model has been widely used to describe adsorption including binding of DNA (Glazer et al., 2006) and proteins on solid surface (Vijayendran and Leckband, 2001). Generally, γ≠1 applies to conditions in which the free energy of binding of the solute molecules can take a range of values instead of a unique value (Sips, 1948), i.e. there is some hereterogeneity in the solute molecules or the surface receptors. When the range of the free energy of binding shrinks to a singular point, γ approaches to 1, in which case it is equivalent to the conventional Langmiur model. With RPPA technology, one can only determine the relative protein concentration. Thus, x can be chosen on an arbitrary scale. For simplicity, we set x on a scale (i.e. a physical unit of x) so that b=1. Thus,
(2)
On this scale, protein concentration equals the background subtracted signal (S−a) when γ=1 and saturation effect can be ignored.Starting from Equation (2), we can see that if the protein concentration is diluted from x to x/dk at the k-th dilution step, where d>1, the expected signal would be:
(3)
Combine the cases for Sk+1 and Sk and eliminate x, we have:
(4)
Equation (3) describes Sk as a function of Sk+1, which we call the serial dilution curve, with three unknown parameters: a, M and γ (d is known). These parameters have graphical interpretations from the plot. As shown in Figure 1, the curve has two intersection points with identity line: one at background level, Sk=Sk+1=a, the other at the saturation level, Sk=
Bsa Standard Curve ConcentrationsSk+1=M. At the left side in Figure 1, the saturation effect is of no concern and the relationship between Sk and Sk+1 is approximately linear,
(5)
Serial dilution plot. Each point in the serial dilution plot is composed of an observed signal Sk at dilution step k (on x-axis) and a corresponding signal Sk+1 of the same sample at the dilution step k+1 (on y-axis). The curve was produced using Equation (3). The curve has two intersection points with the identity line: (a, a) and (M, M).
Serial dilution plot. Each point in the serial dilution plot is composed of an observed signal Sk at dilution step k (on x-axis) and a corresponding signal Sk+1 of the same sample at the dilution step k+1 (on y-axis). The curve was produced using Equation (3). The curve has two intersection points with the identity line: (a, a) and (M, M).
Thus, dγ corresponds to the slope in the linear range in the serial dilution plot.
Equation (4) suggests a new model for displaying and analyzing RPPA data. It is important to note that Equation (4) does not contain protein concentration. Thus, it permits an appealing way of displaying the raw data without model specification or parameterization. Based on the plot like Figure 1, we can infer the parameters (a, M and γ) from the graph or through model fitting without knowing the protein concentrations in the samples. Model fitting with Equation (4) is relatively simpler than that with model fitting with Equation (2), which involves much more unknown parameters as in the existing methods of RPPA data analysis. Altogether, the number of unknown parameters in the model with Equation (2) is three plus the number of protein samples (each dilution series count as one sample), which can be in the hundreds. In contrast, Equation (4) only involves three unknown parameters.
2.2 Parameterization of the serial dilution curve
To find the optimal parameters, we used a weighted non-linear regression model using Equation (4) as the model and taking a, D=dγ, M as parameters. We assumed the observed signals have multiplicative errors except for the signals close to zero. The weight used in the regression model is 1/(m+|S|), where m=5, which is taken as the minimal error from signal quantification from the scanner used to obtain RPPA data. The starting values of a, D and M were taken to be max(m, min(S)), d, max(S), respectively. The nls function implemented in R-language (Ihaka and Gentleman, 1996) was used to optimize the parameters. The m is set to be the lower bound of a.
2.3 Estimating protein concentrations
Given the parameters in Equation (4) and signals of a dilution series of a particular sample (let these be S0, S1, S2,…, SK), to obtain protein concentration in the original undiluted sample, we used the following procedure. First, if all these signals are greater than M/r, the protein concentration is marked to be saturated.
This threshold value of M/r is set according to an approximate estimate of the 95% confidence interval (CI) of the signals at the saturated spots. Under multiplicative error model, assume that the error rate of the observed signals is ɛ=10%, and the saturation level is M, we expect the CI to be [M/(1+2×ɛ), M(1+2×ɛ)]=[M/1.2, 1.2M]. Similarly, at background level a, we expect the 95% CI to be [a/(1+2×ɛ), a(1+2×ɛ)]=[a/1.2, 1.2a]. In general, r should be >1 and can be reduced if precision of signals is improved.
If all the signals except one are >M/r and the exception is not SK, is also marked to be saturated. Similarly, if all the signals are <ar, is marked to be undetected. If all of them except one are >M/r and the exception is not S0, is also marked to be undetected. The minimum and maximum of are set to be
(6)
(7)
respectively. The above steps were taken to stabilize the protein concentration estimates for out of linear-range measurements.If is not marked saturated or undetected, we proceed to make an estimate of We choose to remove signals >M/r or <ar. Then, we convert each of the remaining signals Sj to xj as
(8)
where j denotes the j-th dilution step. To remove outliers among xjs, we identify an outlier among xjs as where mad(x) is the median absolute deviation of x. Here, x is the vector of all xjs. Note that the outliers can also be identified from the serial dilution plot as points far away from the dilution curve (e.g. Fig. 3A).Finally, we give the estimate of the dilution series as a weighted average of xjs:
(9)
where
(10)
the partial derivatives are derived and computed according to Equation (8); Δ a, ΔM and Δγ are standard deviations of a,M, γ, respectively, which are obtained from the nls function in R. The estimated error of is obtained from (Σwj)−1/2.
3 RESULTS
To test the utility of the serial dilution curve for analyzing RPPA data, we first applied the method to simulated data, which was composed according to the Sips model [See Equation (2) in Section 2], with background level a=100, saturation level M=50 000 and γ=1, dilution factor d=2. We added multiplicative noise (error rate=0.15) to nominal signals and generated data as shown in Figure 2A. The multiplicative error model has been previously suggested (Kreutz et al., 2007). The samples were diluted to 1/2, 1/4 and 1/8 of their original concentrations serially. Figure 2B shows the serial dilution plot, which contains all data in the dilution series. Each point in the serial dilution plot is composed of an observed signal at dilution step k (on y-axis) and a corresponding signal of the same sample at the dilution step k+1 (on x-axis).
Computer simulations. (A) Computer generated data with serial dilutions. Red, yellow, green, blue represent undiluted concentrations, 1/2, 1/4, 1/8 original concentrations, respectively. (B) Serial dilution plot. The blue line shows the estimated serial dilution curve. (C) The estimated versus the ‘true’ concentrations. The dashed lines show the upper (shown in green) and lower (shown in blue) bounds of the estimated concentrations according to Equations (5) and (6). The red line shows the identity lines. (D) Estimated error rates. CV=estimated error/estimated concentration. (E) Signal versus estimated concentrations. Red, yellow, green, blue represent undiluted concentrations, 1/2, 1/4, 1/8 original concentrations, respectively.
Computer simulations. (A) Computer generated data with serial dilutions. Red, yellow, green, blue represent undiluted concentrations, 1/2, 1/4, 1/8 original concentrations, respectively. (B) Serial dilution plot. The blue line shows the estimated serial dilution curve. (C) The estimated versus the ‘true’ concentrations. The dashed lines show the upper (shown in green) and lower (shown in blue) bounds of the estimated concentrations according to Equations (5) and (6). The red line shows the identity lines. (D) Estimated error rates. CV=estimated error/estimated concentration. (E) Signal versus estimated concentrations. Red, yellow, green, blue represent undiluted concentrations, 1/2, 1/4, 1/8 original concentrations, respectively.
We found that our algorithm was able to recover the ‘true’ parameters from the simulated signals accurately. The values of a, M and γ were found to be 98± 5, 49 800± 520, 1.05±0.01, respectively. The estimated protein concentrations are also accurate (Figure 2C), except for the cases which are clearly out of the linear range. The lower and the upper bound of the range were calculated using Equations (6) and (7) and shown as dashed lines in Figure 2C. Note that setting the lower and upper bound helps to stabilize the estimates of protein concentration on logarithm scale, so that small changes in observed signals do not incur large changes in the estimates. Compare Figure 2A and C, one can also see that the linear range is much wider in the latter, showing that the dilution series can greatly expand the linear response range of the measurements.
We have also tested our algorithm with experimental data. Figure 3 shows a typical example of RPPA dataset. The experimental methods used to produce the array data were described by Fan et al. (2007). From the serial dilution plot (Fig. 3A), we notice many outliers (marked by red plus signs) near both x- and y-axis. Inspection of the original scanned image revealed that these outliers were produced by a faulty background subtraction method that extracted signals from the scanned image. The image quantification method took median pixel intensities from local regions outside the spotted area as the background level. However, occasionally the protein samples seemed to spill over the spotted area, which caused grossly overestimated background levels, which in turn led to grossly underestimated signals.
Example of a practical dataset. The measured protein is beta actin, which serves as a control standard for measurements. (A) Serial dilution plot. Points shown in red were regarded as outliers or saturated (circled). (B) Signal versus estimated concentration. The signals of undiluted samples are shown in red, 1/2 diluted samples in green and 1/4 diluted samples in blue. (C) Estimated error rates. CV=estimated error/estimated concentration. Each point represents result from one serial dilution. (D) Estimated protein concentrations from replicated dilution series of the same samples.
Example of a practical dataset. The measured protein is beta actin, which serves as a control standard for measurements. (A) Serial dilution plot. Points shown in red were regarded as outliers or saturated (circled). (B) Signal versus estimated concentration. The signals of undiluted samples are shown in red, 1/2 diluted samples in green and 1/4 diluted samples in blue. (C) Estimated error rates. CV=estimated error/estimated concentration. Each point represents result from one serial dilution. (D) Estimated protein concentrations from replicated dilution series of the same samples.
Figure 3A also showed that all the signals are bounded below 65 000 (the points close to the upper bound are marked by the red circles). This was caused by imaging software that set the maximum pixel intensity to be 65 536. Thus, the real signals must have been truncated for these spots. We therefore removed the points shown in red in Figure 3A before fitting the serial dilution curve. The estimated parameters are a=5, M=63 602, γ=0.57. The estimated protein concentrations were shown in Figure 3B.
Sometimes RRPA experiment may fail to yield meaningful measurements of proteins. In Figure 4, we show an example that has quality problems. The experimental methods used to produce the array data was described by Tibes et al. (2006). Using methods as described in Section 2.2, the background was estimated to be 1000, saturation level: 4751, dilution factor: 1.11. The black line is the identity line and the blue line is the serial dilution curve. The serial dilution curve (blue) is very close to the identity line (black), indicating that after dilution, the signals tend to stay at the same levels as before. This implies that the dilution had failed to produce the expected reduction of signals. The exact cause of this effect is unclear. From our observations, such pattern often occurs in the slides that have faint signals. Furthermore, because the serial dilution curve is approximately linear, the saturation level cannot be accurately determined.
Example of data with quality problems. This is a serial dilution plot. The measured protein is GAPDH. The red symbols show the outliers. The background is estimated to be 1000, saturation level: 4751, dilution factor: 1.11. The black line is the identity line and the blue line is the serial dilution curve.
Example of data with quality problems. This is a serial dilution plot. The measured protein is GAPDH. The red symbols show the outliers. The background is estimated to be 1000, saturation level: 4751, dilution factor: 1.11. The black line is the identity line and the blue line is the serial dilution curve.
To evaluate data quality on an array, we find the following two measures to be most important according to our empirical experience.
4 DISCUSSION
Graphical display of data plays a very important role in data analysis. For RPPA data, it is conventional to plot the observed signals against the estimated protein concentrations. However, because the estimated protein concentrations depend on the models as well as the estimated parameters, when the signals seem to fit poorly to the estimated concentrations, it is not clear whether it is due to a suboptimal model or to noisy data. Making the serial dilution plot per se requires no model selection or parameter fitting. The plot presents the entire set of observables on an array in their original values. From the plot one can identify the background level, saturation level, which signals are in the linear range, and which signals are outliers (as in Fig. 3A). Fitting a serial dilution curve needs only three parameters, which is much simpler than fitting the response curve, which requires estimating the protein concentrations as additional parameters.
From simulated RPPA data, we showed that our algorithm can yield robust and accurate estimates of protein concentrations. From practical RPPA data, we saw some of the data points did not follow the serial dilution curve. There may be multiple causes of the abnormal points, such as saturation or failure of binding. It should be noted that the response curve in RPPA technology is sensitive to a large number of factors, including the amount and duration of sample incubation, specific and non-specific interactions of reporter molecules and surface chemistry in the microarrays (Seurynck-Servoss et al., 2007). These factors complicate the interpretation of RPPA data. Non-parametric models (Hu et al.2007) take fewer assumptions about the hybridization kinetics in RPPA technology. Hence, the non-parametric models are more flexible, and in some cases they may fit better with observed RPPA data. The disadvantage of non-parametric models is that the parameters are less interpretable, while the parameters in Sips model are physically meaningful and can be used to optimize the conditions for RPPA experiments. We believe the method developed in this study will have broad utility in RRPA applications.
Funding: M. D. Anderson Cancer Center start-up fund; MDACC Institutional Research Grant (to L.Z.).
Conflict of Interest: none declared.
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