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  • Writer's pictureJessica Liu

Beyond the Line: Mastering the Art and Science of Standard Curves

Consider this scenario: you are a new student research assistant tasked with determining the amount of protein in a solution. You know that there is a technique called the Bradford protein assay, in which the solution color changes depending on the amount of protein present. You also know that color is based on light absorbance, which can be measured using an instrument called a spectrophotometer. However, what you don’t know is what color corresponds to what amount of protein. So: what can you do?


Make a standard curve, of course!

     

The importance of a standard curve

     

Standard curves give the relationship between the concentration of a substance and the measured parameter. In the case of the Bradford protein assay, it will give the relationship between the amount of protein and the absorbance values. To prepare a standard curve, you can dissolve a known amount of protein and measure their absorbances. Then, using the standard curve and the absorbance value of your unknown sample, you can estimate the amount of protein present. 

A graph with concentration plotted on the y-axis and absorbance plotted on the x-axis. The graph shows multiple linear data points, as well as a line of best fit

Many other techniques besides the Bradford protein assay will require standard curves. For example, enzyme-linked immunosorbent assays (ELISAs), release profiles, and many spectroscopy methods will all use standard curves. Standard curves have important uses in and out of the lab. If you need to measure the amount of drug released from a pill, how much pollutant is in a pond, even how much sugar is in your soda, you might need to make a standard curve. 


How to make a standard curve


Now that we’ve seen how useful standard curves can be, we’ll learn how to make them.


First, we start with a solution of a known concentration of the substance we want to measure in our samples. For example, if we are measuring protein, we will obtain a solution with a known amount of protein. This is our stock solution.


Next, using our protein stock solution, we will prepare a standard curve. This involves diluting the stock solution to lower concentrations. What we use to dilute the solutions, called the diluent, should be the same solvent that the samples are in; for example, if the samples are in water, the diluent should also be water. One common technique used to obtain the diluted solutions is called serial dilution, in which we dilute the previous solutions in a step-wise fashion. For example, to prepare a standard curve with concentrations of 0 mg/mL, 1.25 mg/mL, 2.5 mg/mL, 5 mg/mL, and 10 mg/mL from a 100 mg/mL stock solution, we can dilute the stock solution ten times to prepare the 10 mg/mL solution. Then, some of the 10 mg/mL solution can be diluted to prepare a 5 mg/mL solution, which itself can be diluted to prepare a 2.5 mg/mL solution, etc. The 0 mg/mL solution is just water.


A cartoon schematic showing 6 test tubes in a row with colored liquid in each tube. The tube on the far left shows the darkest colour liquid and the liquid in the rest of the tubes gets progressively lighter in colour. This visually illustrates the serial dilutioion processn
Created using Biorender

Once the standard curve solutions have been prepared, we can add them to wells in a 96-well plate. The samples should be added to the plate in equal volumes as the standard curve. After the samples and standards have been added, a colorimetric reaction, such as a Bradford Assay or BCA assay, is typically performed to measure the amount of protein in each well using an instrument called a spectrophotometer.  The spectrophotometer ‘reads’ the plate and measures how much light is absorbed in the sample – the more protein there is, the more color that is produced during the colorimetric reaction, which translates as more light absorbed during the spectrophotometer reading. 


After we’ve obtained the reading, we can generate a standard curve by plotting the absorbance values from the spectrophotometer against the amount of protein in the standard curve wells. Usually, the standard curve can be fit with a linear regression; other times, the behavior is more complex, and may need to be fit with a quadratic or sigmoidal curve. Regardless, after performing the regression, we will obtain an equation which can be used to calculate the amount of analyte in the samples based on the absorbance values of the sample wells.

Two graphs side-by-side. The right graph has concentration plotted on the y-axis and fluorescence plotted on the x-axis. Several linear data points are shown with a line of best fit. The graph on the right shows concentration plotted on the y-axis and absorbance plotted on the x-axis. Several lines are plotted with a line of best fit illustrating a quadratic line.

What makes a good standard curve?


A standard curve will only be accurate if it covers the expected concentration of the samples. It should have at least 5 points, and there should be two or more standard curve points both above and below where the samples fall. If the samples are far away from the points on the curve, the results will be less accurate.

A cartoon schematic showing various outcomes of data range. Ideally, the data points of the standard curve should range in value such that the data point of the unknown sample falls within the range. If the unknown sample data point falls less than or greater than the range, the accuracy of the standard curve is affected

Additionally, once we’ve generated a standard curve, we must determine how good the fit of the curve is. Sometimes, there may be errors caused by the user, such as pipetting mistakes. If the volumes in the plate are not equal, then for any light-based assay, the detected absorbance will not be the same (think back to Beer’s law!). The R2 value of the regression, which ranges from 0-1, will tell us how good the fit is. Although assay-dependent, typically we want an R2 of 0.95 or higher. 

A cartoon schematic illustrating the line of best fit. A line of best fit with a R-squared value close to 1 represents an accurate and confident standard curve. Graphs with a standard curve with a R-squared value less than 0.95 is less accurate

The best way to get a high R2 is to practice, so now that you understand the basics of preparing standard curves, you should try it out!



 

A little bit about guest writer Jessica Lui:

She is a PhD student at Columbia University studying biomedical engineering, focusing on biomaterials for cartilage regeneration. Outside the lab, she is passionate about good food, mentorship of young women in STEM, as well as science communication!

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