The Hitachi Software MiraiBio Group Blog

Standard Curves are used in chemistry to determine the concentration of a substance. The X axis of a standard curve has units of concentration, while the Y axis usually has units of transmission or absorption of light of a particular frequency dependent on the substance of interest (usually a florescent reporter or dye). A standard curve is represented by an equation that is fit to a series of observations using known concentrations. These observations are plotted and an equation corresponding to the model being tested is regressively fit to the data. After establishing a standard curve for a particular substance, unknown concentrations can be evaluated by taking a measurement and selecting the value on the X axis (concentration) corresponding to the point on the standard curve with the appropriate Y value.

The fitness of a standard curve is described by the R-square value, a statistical measure of how accurately an equation approximates real data points. This value varies from zero (no accuracy) to one (totally accurate), and is calculated from the ratio of the covariance of the observed X and Y values and the product of the standard deviations of X and Y, with respect to the values predicted by the model equation. In general, an R-square value greater than 0.5 demonstrates some predictive power in the model equation, but values greater than 0.95 are desired for most applications.

Several factors should be considered in determining the predictive strength, or fitness of a standard curve. Of these the most important is the number of observations used to fit the model equation. Generally, more observations are better than less, and, in most cases, several trails at each concentration will yield better results. Using too few concentrations may give misleading results and compromise the validity of the standard. When taking multiple observations at a single concentration, researchers should use the average if the experimental errors of each observation are co-dependent, but if each observation is independent every data point should be used. Experimental observations are dependent if, for instance, multiple observations are made using the same sample. In most cases observations are independent (taken from different samples), and multiple data points at each concentration are used for curve fitting. In general, a valid standard curve can be generated using eight or more concentrations, with three observations taken at each concentration.

The standard curve used is another important factor in determining the validity of a standard. The type of equation used (linear, polynomial, exponential, sigmoidal, etc.) depends on the physical model which describes the system under observation. Researchers should adhere to the appropriate physical model even if another equation produces a higher R-square value. In particular, researchers should be aware that a polynomial series can be fit to nearly any data set simply by increasing the order of the series (the largest exponent used), but in most cases these curves do not represent a physical model and have no predictive power. In addition, the R-square value of a given model equation can be misleading if too few concentrations (data points) are used in the fit, or if only a single observation at each concentration is taken. In general, the choice of model equation depends on the physical model describing the system, not on the R-square value.

Users of MiraiBio’s MasterPlex QT software in conjunction with xMAP microsphere technology have a variety of powerful tools for fitting standard curves to their observations. MasterPlex QT makes fitting a standard curve easier by simplifying the collection of standard data and providing a graphic user interface for entering solution concentrations, managing repeated trials, and selecting a model equation. Users can import, export, and save standards, compare multiple standards in a single screen, and apply a given standard to their experimental observations.

To view a Flash tutorial on how to generate standard curves with MasterPlex QT, visit http://www.miraibio.com/images/flash/qt/AbsoluteQuantification.htm