A Novel Method and Simple On-line Tool for Maximum Likelihood Calibration of Immunoblots and other Measurements that are Quantified in Batches

Experimental measurements require calibration to transform measured signals into physically meaningful values. The conventional approach has two steps: the experimenter deduces a conversion function using measurements on standards and then calibrates (or normalizes) measurements on unknown samples with this function. The deduction of the conversion function from only the standard measurements causes the results to be quite sensitive to experimental noise. It also implies that any data collected without reliable standards must be discarded. Here we show that a new \"1-step calibration method\" reduces these problems for the common situation in which samples are measured in batches, where a batch could be an immunoblot (Western blot), an enzyme-linked immunosorbent assay (ELISA), a sequence of spectra, or a microarray, provided that some sample measurements are replicated across multiple batches. The 1-step method computes all calibration results iteratively from all measurements. It returns the most probable values for the sample compositions under the assumptions of a statistical model, making them the maximum likelihood predictors. It is less sensitive to measurement error on standards and enables use of some batches that do not include standards. In direct comparison of both real and simulated immunoblot data, the 1-step method consistently exhibited smaller errors than the conventional \"2-step\" method. These results suggest that the 1-step method is likely to be most useful for cases where experimenters want to analyze existing data that are missing some standard measurements and where experimenters want to extract the best results possible from their data. Simple open source software for both methods is available for download or on-line use.\n\nAuthor SummaryMost quantitative measurements do not return the physical quantities that are of interest, but some instrument-specific response value instead. These measurements are then converted to physical quantities through a conversion function, which the experimenter deduces from instrument responses for one or more standard samples of known composition. This is called calibration or normalization. For example, we recently performed quantitative immunoblotting on a large number of samples, each replicated on multiple blots, and then calibrated the measurements to yield protein concentrations relative to those in a standard sample. We found that the conventional calibration approach of treating the samples in each blot independently of the samples in other blots produced inaccurate results because this approach is completely dependent on the standard measurements, which were sometimes missing or erroneous in our data. Thus, we developed a new calibration approach in which we fit a statistical model to the entire data set simultaneously. This method, which applies to a very wide range of calibration problems, was substantially more accurate during validation tests and can be shown to return the most accurate results possible within the assumptions of the model. It is particularly useful when some standard measurements are missing from data sets or when experimenters want the best possible results.