Serial Dilution Sources Of Error In Measurement Physics

A common practice in immunoassay is the use of sequential dilutions of an initial stock solution of the antigen of interest to obtain standard samples in a desired concentration range. Nonlinear, heteroscedastic regression models are a common framework for analysis, and the usual methods for fitting the model assume that measured responses on the standards are independent. However, the dilution procedure introduces a propagation of random measurement error that may invalidate this assumption.

We demonstrate that failure to account for serial dilution error in calibration inference on unknown samples leads to serious inaccuracy of assessments of assay precision such as confidence intervals and precision profiles. Techniques for taking serial dilution error into account based on data from multiple assay runs are discussed and are shown to yield valid calibration inferences.

Overview Source: Laboratory of Dr. Jill Venton - University of Virginia Calibration curves are used to understand the instrumental response to an analyte and predict the concentration in an unknown sample. Generally, a set of standard samples are made at various concentrations with a range than includes the unknown of interest and the instrumental response at each concentration is recorded.

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Propagation of Errors in Dilution Problems When a calculation is done in lab, it is important to round the result to the number of significant figures indicated by the precision of. A serial dilution is a series of sequential dilutions used to reduce a dense culture of cells to a more usable concentration. The easiest method is to make a series of 1 in 10 dilutions.

For more accuracy and to understand the error, the response at each concentration can be repeated so an error bar is obtained. The data are then fit with a function so that unknown concentrations can be predicted. Typically the response is linear, however, a curve can be made with other functions as long as the function is known. The calibration curve can be used to calculate the limit of detection and limit of quantitation. When making solutions for a calibration curve, each solution can be made separately. However, that can take a lot of starting material and be time consuming. Another method for making many different concentrations of a solution is to use serial dilutions.

With serial dilutions, a concentrated sample is diluted down in a stepwise manner to make lower concentrations. The next sample is made from the previous dilution, and the dilution factor is often kept constant. The advantage is that only one initial solution is needed. The disadvantage is that any errors in solution making—pipetting, massing, etc.—get propagated as more solutions are made.

Thus, care must be taken when making the initial solution. Cite this Video JoVE Science Education Database. Analytical Chemistry. Calibration Curves.

JoVE, Cambridge, MA, (2019). Principles Calibration curves can be used to predict the concentration of an unknown sample. To be completely accurate, the standard samples should be run in the same matrix as the unknown sample.

A sample matrix is the components of the sample other than the analyte of interest, including the solvent and all salts, proteins, metal ions, etc. That might be present in the sample.

In practice, running calibration samples in the same matrix as the unknown is sometimes difficult, as the unknown sample may be from a complex biological or environmental sample. Thus, many calibration curves are made in a sample matrix that closely approximates the real sample, such as artificial cerebral spinal fluid or artificial urine, but may not be exact.

The range of concentrations of the calibration curve should bracket that in the expected unknown sample. Ideally a few concentrations above and below the expected concentration sample are measured. Many calibration curves are linear and can be fit with the basic equation y=mx+b, where m is the slope and b is the y-intercept. However, not all curves are linear and sometimes to get a line, one or both set of axes will be on a logarithmic scale.

Linear regression is typically performed using a computer program and the most common method is to use a least squares fitting. With a linear regression analysis, an R 2 value, called the coefficient of determination, is given. For a simple single regression, R 2 is the square of the correlation coefficient (r) and provides information about how far away the y values are from the predicted line. A perfect line would have an R 2 value of 1, and most R 2 values for calibration curves are over 0.95. When the calibration curve is linear, the slope is a measure of sensitivity: how much the signal changes for a change in concentration. A steeper line with a larger slope indicates a more sensitive measurement. A calibration curve can also help define the linear range, the range of concentrations that the instrument gives a linear response.