MathBench > Measurement

Straight Lines/ Standard Curves

Looking back

What you are practicing here is called calibration, or creating a standard curve. You need to do this when you use a spec.

Often, when you use a measuring tool, it has already been calibrated – for example, someone a long time ago figured out how to use the pipetman to measure 10 microliters, 20 microliters, 30 microliters... and then that kind-hearted person created a volume indicator to make it easy for you to use the pipetman. That means that you (being a person using the pipetman) don't need to figure out every pipetman all over again.

It's very convenient to have our measuring tools come precalibrated – that's why we use an electronic scale and graduated cylinders and so on. But not everything can be pre-calibrated. Sometimes the calibration has to depend either on environmental conditions or on the thing that you're trying to measure. In that case, you need to do the calibration yourself.

Specs, of course, don't come pre-calibrated. When you use a spectrophotometer, you need to calibrate it yourself. Why? Because there are thousands of different kinds solutions you could measure. Each one has its own extinction coefficient. This process of calibration is also called “creating a standard curve”. That is “standard” as in something you can measure against, and “curve” as in a function drawn on a graph. The word curve is a little unfortunate, since straight lines are anything but curvy, but that's the word we use.

Once you have the standard curve, you can use it in one of two ways:

1. Figure out the function which represents that curve, and use that function to translate your measurements -- that's why you had to find “e”.
2. Simply read the translation from the curve itself – this is faster but less accurate, plus you have to carry a graph around.

The reason I spent so much time on this is that biology (and science in general) is full of instruments that need to be calibrated and standard curves that need to be figured out. Once you understand the logic of what you're doing, all of the procedures make intuitive sense.

Just the facts, please

A graph representing a DIRECTLY PROPORTIONAL relationship is always a straight line passing through (0,0).

You can measure the slope of this graph by finding the value of y at x=1.

If that's not feasible, you can find the first feasible value of y, then divide by the value of x.

The slope of the graph is the same as the rate of change of y.

The relationship between light absorbed and gunk is directly proportional, and can be written as

OD = e c,

where OD=optical density, e=extinction coefficient (a rate), and c = concentration.

In order to calibrate a spec, you need to know the best wavelength to use, which generally is some wavelength other than the color of the solution being tested.

Once you know the wavelength, you need to create a series of different concentrations and measure the OD of each (with the spec).

You use this data to calculate "e" (the slope of the line).

Once you know e, you can solve the equation above for c, like this:

c = OD / e,

which allows you to measure the OD of any similar solution and calculate its concentration.




If you want a printer-friendly version of this module, you can find it here in a Microsoft Word document. This printer-friendly version should be used only to review, as it does not contain any of the interactive material, and only a skeletal version of problems solved in the module.