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 create standard curves using Excel and then use them to determine the concentration level of unknown samples. We will also show how to find the associated line algebraically. The focus will be on linear functions or graphs that can be turned into linear functions by a scale (axis) change. We will accomplish this by learning how to:

Enter Data into an Excel Spreadsheet
Create and Modify Graphs
Using Chart Wizard to Plot the Data
Selecting Chart Type
Source Data
Chart Options
Location
Add Data
Format Graph
Find a Standard Curve Graphically and Algebraically
Create Trendlines to find Standard Curves in Excel
Display equation
Display r2 value

Lab Assignment Part 1: Standard Curve for Protein Measurements:

A standard curve for protein concentration is often created using known concentrations of bovine serum albumin. The assay is called the Bradford assay; it is a colorimetric assay. The reagent turns blue when it binds to amino acids present in protein. The intensity of the color is best measured with a spectrophotometer (A device for comparing two light radiations, wavelength by wavelength). In the case of the Bradford assay the greater the absorbance, the higher the protein concentration.

A series of tests were performed on some samples and the following measurements were obtained using a spectrophotometer:
Protein
Concentration
(mg/ml)
Absorbance (A)
0.28
0.078
0.56
0.143
0.84
0.393
1.12
0.473
1.40
0.527
TASKS:
1. Enter this data into Excel
2. Create a graph of the data that is appropriately titled and labeled (Include your name on the graph)
3. Print out the graph
4. Use a straight edge to sketch a line that “best” approximates the trend of this data.
5. Estimate the slope and y-intercept and use them to find the equation of the associated line using the slope-intercept form of a line: y = mx + b
6. Pick two points on the line that you’ve drawn [(x1,y1) and (x2,y2)] and use these points to find the equation of this