MA 61 Precalculus for Biology Majors
Lab I: Applications of Linear Functions
Standard curves
A standard curve is a quantitative research tool. It is a method of plotting known assay data to determine the concentration of an unknown substance, particularly proteins and DNA. The assay is first performed with various known concentrations of a substance similar to that being measured. A new standard curve is constructed each time you set up a new series of tests, since we must account for variations in experimental conditions (solution preparation, spectrophotometer sensitivity, temperature, etc.) The particular assay procedure used may measure absorbance, optical density, luminescence, fluorescence, radioactivity, Rf or something else.
This data obtained from a set of known samples is then used to make a standard curve, by plotting the concentration on the x-axis, and assay measurement on the y-axis. If the data exhibits a linear relationship the standard curve will be a straight line. The same assay is then performed with samples of unknown concentration. To analyze the data, one locates the measurement on the y-axis that corresponds to the assay measurement of the unknown substance and follows a line to intersect the standard curve. The corresponding value on the x-axis is the concentration of substance in the unknown sample.
A line in a two variables is defined by the equation y = mx + b. The y variable can be expressed in terms of a constant (b) and a slope (m) times the x variable. The constant is also referred to as the intercept (or more specifically the y-intercept), and the slope as the regression coefficient. A correlation coefficient (R) is also computed. R is a quantity that gives the quality of a least squares fitting to the original data. The closer R is to 1 the better the approximation. Typically an R-value greater than 0.97 (or an R2 value of 0.95 or higher) is needed for a good linear approximation.
In this lab we will learn how to...