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"Laboratory Math"

Throughout this course and in future laboratory courses in biosciences, should you take them, your success will depend in part on how efficiently you apply your knowledge of mathematics to real problems. This week we will focus on the ability to apply simple mathematics in the laboratory itself, as described under "Objectives" below. Your work will begin with a colorimetric assay for determining protein concentration, called the biuret (bye•you•rett) assay, followed by some dilutions and yield calculations.

The principles that you learn in this study will apply to your very next laboratory study, for which you will also need to determine protein concentrations. The general principles you learn here apply to a great many applications in research and in medicine.

A lot of background material is linked to this page. It goes into solutions, dilutions, assays, etc. in greater depth than you will need for this week, so you don't need to review all of it. In fact, if you are able to complete pre-lab #1 without much trouble, you'll be good to go. Do remember, though, that when you do more than the minimum you'll enjoy the benefits of your effort sooner or later.

Objectives

Here's a summary of the laboratory work for this week.

1. Prepare protein standards from a stock solution of bovine serum albumin
2. Prepare unknowns for assay
3. Conduct a biuret assay: add color reagent, let the color develop, read absorbances in a spectrophotometer
4. Plot a standard curve of absorbance versus amount of protein
5. Determine protein concentrations for your unknowns
6. Estimate total protein (yield) for each unknown tested
7. Conduct dilutions of your unknowns and check your work using the biuret assay
8. Calibrate your set of automatic pipettors
9. Troubleshooting practice: deliberately miscalibrate a spectrophotometer and observe the results

Expectations during and following the laboratory work

Preparation and laboratory work

To prepare for the laboratory work please go through each section below and write down the information that you need. You should make it a weekly habit to prepare an outline of the work to be done. In the laboratory itself, enter all of your procedures and observations directly into your notebook.

When you have everything ready to go, please complete and submit the first pre-laboratory assignment (Pre-Lab #1). If you start to complete the pre-laboratory assignment and find that you need more information, you are welcome to go back and find what you need. It is not a timed test.

This course enrolls students with widely diverse backgrounds and varying levels of experience. To help even things out, the weekly lecture will cover general principles related to the week's work. An orientation talk in the laboratory itself will go over safety concerns and specific methodology such as how to use our pipettors or how to calibrate and use our spectrophotometers.

Links to support documents are listed in each section below. You need not go through all of them. There is a lot of redundancy and a lot of extra information that is useful but not essential. Choose the learning method that suits you best. Once you understand the concepts and find the information that you need, move to the next part. Laboratory "veterans" who have already conducted many if not all of these kinds of activities may be able to prepare adequately by merely skimming some of the reference materials. Others among you may never have made up a solution or used an automatic pipettor, and will have to review the materials more thoroughly. You do not have to follow every single link and you certainly don't have to take notes on everything here. The link below takes you to a Powerpoint presentation (slides and notes) used for the first week of classes a few semesters ago. It presents relevant material on solutions, dilutions, and assays.

Monday lecture

Prepare biuret reagent

This section applies to courses/semesters in which students prepare the reagent themselves. To save time, we may use reagent that has already been prepared and begin with the protein assay itself.

Biruet protein assay

• Biuret reagent and assay [web page]

Solutions/dilutions, terms & units

• Mixtures and solutions [web page (the NEXT buttons take you through all of the web references on solutons/dilutions] [Powerpoint slides/text]
• Materials for solution making [web page] [Powerpoint slides/text]
• Terms and units, including SI units and prefixes [solutions –web page] [dimensions and units web page] [dimensions and units pdf]
• Formulas for solutions [web page] [Powerpoint slides/text (with examples)]
• Examples: making solutions [web page]
• Video/audio/slide presentations on mixtures, solutions, dilutions (covers the same material as the Powerpoint slides/text above)

Dimensions, units, graphing, significant figures

• S & E references

In the laboratory you and a partner are to work as a team to prepare one 200 ml batch of biuret reagent. Each of you must be prepared to do the work. Decide on the volume of distilled water to begin with, the mass (in grams) to use for each component, and the order in which to dissolve the components. Depending on past experience you may need to consult

It is VERY EASY to make a mistake when you prepare a solution with multiple components. Your outline should detail exactly what to do, each step of the way. If you then check off each item and enter the step into your notebook you can avoid mistakes and/or be prepared to go back and find out what went wrong if the assay fails.

The reference materials on the biruet assay describe how to prepare 250 ml of reagent . Because we have 250 ml flasks, let's scale down the formula to prepare 200 ml biuret reagent so that we don't create a potential hazard by filling a flask up to the neck. Note the recommended sequence for mixing components. The final composition of your reagent will be 0.9% Sodium potassium tartrate, 0.3% Copper sulfate • 5 H2O, 0.5% Potassium iodide, and 0.08 M NaOH (f.w. 40.0).

***CAUTION*** Strong bases are extremely hazardous. You must wear protective eyewear, and be especially careful handling the assay solution. The copper sulfate will take about 10 minutes to dissolve, with vigorous stirring. In the meantime, you can prepare the reference and standards for the assay. When all components are dissolved in the NaOH solution, bring the final volume to 200 ml with distilled water and stir to mix completely.

When you have finished making the reagent, test it. Double check that you finished bringing the reagent to final volume. Next, add 0.25 ml 20 mg/ml BSA to a sample tube and add 4.5 ml reagent to the tube. Within a couple of minutes you should see a definite color change from light blue to purple. If there is no color change, then use stock reagent from the laboratory to complete your assay, and check your notes to track down your mistake.

Prepare protein standards

• Using an automatic pipettor [Video/audio/slide presentation] [Powerpoint slides/text] (also covered in the pre-lab talk)
• Colorimetric assays [web page (NEXT button take you to principles of spectrophotometry)]

In the laboratory each of you will independently prepare protein standards for the assay. You should start by labeling each tube near the top with a marking pen. The assay tubes will be read directly in the spectrophotometer by shining a light through the tube and measuring attenuation of transmitted light (absorbance). Any marks made near the bottom of a tube will interfere with the light path.

The description of the biuret method calls for 1 ml of calibration standard or unknown per tube plus 9 ml color reagent. Our spectrophotometer tubes conveniently hold 5 ml, so let's scale down the assay by a factor of 2 by preparing each standard or unknown to 0.5 ml final volume before adding reagent. When all tubes are ready you will add 4.5 ml color reagent to each tube to give a final volume of 5 ml. We expect the relationship between absorbance at 550 nm and amount protein to be linear over a range of amounts from 0.5 to 10 mg protein, so you will want to determine the relationship between absorbance and amount of protein throughout that entire range.

For the protein standard we will use a stock solution of 20 mg/ml bovine serum albumin (BSA). BSA is a fairly cheap and available protein that is used for many purposes in biosciences laboratories. Prepare 6 or 7 standards in 13 x 100 mm culture tubes, containing amounts of protein from 0.5 mg to 10 mg. You will need to determine what volumes of BSA to add to each of your assay tubes to represent the desired amount of protein.

EXAMPLE: Suppose one of your standards is to contain 3 mg protein. One ml stock BSA solution contains 20 mg protein, so for this standard you will need a volume of (3 ÷ 20) x 1 ml, which is 0.15 ml (150 µl). A volume of 150 µl of 20 mg/ml BSA contains 3 mg of protein.

The volume of sample in an assay tube influences absorbance because it dilutes the color reagent that you add to it. Samples containing identical amounts of protein will give different absorbance values if the sample volumes before adding color reagent are different. We don't worry about the error when the sample volume is very small relative to the volume of color reagent (1-2% of reagent volume, for example), but the sample volumes in our Biuret assay dilute the color reagent up to 10%. To bring all standards to the same volume we can use distilled water, because simply diluting a sample with water doesn't change the amount of protein in the tube.

For each standard of volume less than 0.5 ml dilute the stock solution with distilled water to bring the volume to 0.5 ml prior to adding color reagent. EXAMPLE: Each assay tube is to be prepared to a volume of 0.5 ml before adding color reagent. A standard with 3 mg BSA contains a volume of 0.15 ml 20 mg/ml BSA. To bring the volume to 0.5 ml you need to add 0.35 ml (350 µl) distilled water.In addition to your standards you will need a reference tube for calibrating the spectrophotometer. Prior to adding color reagent it should contain 0.5 ml water only.

Prepare unknowns for assay

In the laboratory each of you will independently prepare unknowns for the assay. Your unknowns are from a hypothetical fractionation of a crude protein extract to obtain a pure enzyme. The original extract (fraction A) was gradually purified to produce fractions B, C, D, E, and F. Each fraction will be divided up into small samples, known in "lab language" as aliquots (al'•ih•kwats). Each of you is to select two aliquots, including one from set A-C, and one from set D-F. You know nothing about the concentration of protein in any aliquot.

You will have to treat the unknowns exactly as you treated the standards, so that the only variable is amount of protein. A complication is that you know nothing about the concentrations of the unknowns. You could pipet 0.5 ml each unknown into respective tubes and run the assay on them, but if any of them has concentration greater than 20 mg/ml its absorbance might be out of range. We could avoid the problem by using just 0.05 ml (50 µl) each sample, but what if a sample is of low concentration? There won't be enough protein to detect, and you will have to waste time re-doing the sample.

You may have figured out by now that we can save time by preparing two assay tubes for each sample. Lob 0.5 ml into one tube and 50 µl into the other, and chances are one of the tubes will contain an amount of protein that you can measure. Remember to record the original volume of sample in each tube, then bring all unknowns to 0.5 ml. For example, if you prepare a tube with 50 µl sample you’ll need to add 450 µl water to bring it to 0.5 ml.

Conduct the assay

• Principles and use of a Spectronic 20 spectrophotometer [web page]

In the laboratory, each of you is to conduct his/her own assay. When all standards and samples are ready add 4.5 ml color reagent to each tube containing standards and unknowns, using a serological pipette. Practice using the pipette to deliver distilled water before using it for color reagent. Spilling water is no big deal, but spilling a solution containing NaOH will pose a hazard. Delivery of color reagent will mix the materials adequately, so it will not be necessary to vortex the tubes. Let them stand for 10 minutes before reading and recording absorbances according to instructions given in the laboratory. Meantime you might go ahead and calibrate the instrument that you intend to use.

Prepare a standard curve

• Example of a standard curve [web page]
• Fundamentals of graphing [html] [pdf]

In the laboratory, each of you is to plot a standard curve. Plot absorbance at 550 nm versus milligrams BSA in your notebook. For the best readability, the standard curve should be proportioned so that both axes are the same length and the standard curve data fills the field from origin to upper right of the curve. If you have a direct proportion the curve will be linear and make a 45 degree angle with each axis. Make it nice and big.

Determine protein concentrations

• Determine a concentration from a standard curve [web page]
• Error analysis and significant figures (just the first part) [html] [pdf]

If you run out of time (i.e., it is approaching 5:00 pm), we may ask you to complete this and the remaining parts outside of the laboratory, entering the calculations in your notebook without conducting the actual procedures.

In the laboratory you are to determine the amount of protein corresponding to the absorbance reading for each of your sample tubes containing unknowns. Determine protein concentration from this amount and the volume of undiluted sample used in the tube, recording all of the information in your notebook. See the recommended reference for details. The reference also explains what to do when more than one absorbance reading falls in the linear portion of your standard curve.

Remember that a major learning objective is to be able to round quantities to reflect limits on the precision with which you obtain your measurements. Unfortunately, students seldom address significant figures unless they are specifically told to do so. Even with the most careful technique we cannot count on a colorimetric assay to be accurate to more than two significant figures (e.g., report 3.147 mg/ml as 3.1 mg/ml). Remember to use appropriate physically meaningful units for a physical quantity.

Pre-lab #1 gives you some examples, for practice.

Determining protein yield (fraction yield)

• Tissue fractionation and yields [web page (just page one for now)]

After determining protein concentrations for your samples, estimate the total amount of protein in the stock solutions from which your aliquots were taken. If these stocks were from a cell or tissue fractionation, then these amounts would tell us how much of the total protein of the original cells or tissues remain in each fraction. If applicable, use an appropriate prefix on your mass unit to simplify expression of yield. As always, don't forget to round off the number. Here are hypothetical volumes corresponding to each fraction A-F.

For the very first investigative study (laboratory week 2) you will conduct a tissue fractionation and estimate fraction yields. One mistake that students frequently make is to estimate a yield based upon the aliquot volume and not the fraction volume. The amount of protein in an aliquot is not scientifically relevant, since it is based upon the arbitrary choice of aliquot volume. The estimate will differ if you took an aliquot of 1, 2, or 5 milliliters, for example.

Pre-lab #1 gives you a yield determination problem, for practice.

Dilutions

• Making dilutions [web page] [Powerpoint slides/text (includes information on stock solutions]
• Working with stock solutions [web page]

Your instructor or teaching assistant will check your work after you estimate protein yields for your two unknowns. We will help you correct any mistakes you might have made, and will give you the actual concentrations to compare with your estimates. You will then be asked to dilute each sample two ways and, time permitting, to check your work by repeating the biuret assay on the diluted samples (use your earlier standard curve to estimate concentrations).

Sample A, B, or C
Dilute 200 microliters sample to a final concentration of 5 mg/ml
Prepare a portion of sample to 500 microliters final volume, concentration 4 mg/ml

Sample D, E, or F
Dilute 500 microliters sample to a final concentration of 2 mg/ml
Prepare a portion of sample to 500 microliters final volume, concentration 2 mg/ml

Pre-lab #1 gives you some examples, for practice.