When considering an interaction between two biochemical molecules, one of the key things you might like to demonstrate is that the interaction is specific. A specific interaction is when two things come together in a particular, repeatable way. This specificity is important when you consider that biochemical molecules are rather similar in their chemical composition—it's all organic chemistry.

If specificity is so important, how do you demonstrate specificity? Saturation. If there is a single, specific binding site on a molecule, and you know the concentration of that molecule in solution, the interaction with another molecule will increase until you hit the equivalent concentration, until you saturate the site of interaction. After that adding more of the second molecule will have no addtional effect. All the sites of interaction are already filled. The system is said to be saturated.

In order to demonstrate this theme, we need to be able measure solution volumes carefully and prepare solutions at different concentrations.

To illustrate these themes, we'll start with a paper in which the authors develop a reporter assay for the activity of luteinizing hormone. That paper is Tang D, Song X, Du Y, Wang J, Lei Y and Chen B (2024) Development of a reporter gene-based assay for the bioactivity determination of rhLH pharmaceutical products Anal Biochem 686 115413.

The adjustable volume micropipette is the standard tool for measuring small volumes of aqueous solutions. We have two particular instruments, the p1000 and the p200. The shorthand is easy to decode, the number is the maximum volume the instrument measures in units of microliters. Recalling that 1000 μL is 1 mL (μ is 1 x 10-6; m is 1 x 10-3, they differ by a factor of 1000), the p1000 will measure a maximum volume of 1 mL and the p200, 0.2 mL. At the smaller end, the minimum volume each instrument can measure well is twenty percent of the maximum volume, 200 μL and 20 μL respectively. It is, of course, by design that the two instruments converge at 200 μL.

The first challenge to using the micropipettes is setting the instrument to the correct volume. Starting with the p1000, the numerical scale is three digits. The upper digit represents the thousands place. Note that this digit is red on the p1000, that's the warning that this place only has two accessable values, zero and one, less than 1000 or 1000 exactly (in adjusting the instruments, you shouldn't go above or below the limit by more than a few microliters or the internal mechanism may jam). The middle digit is the hundreds place (note that it is black, the hint that it can hold any digit from zero to nine). The last digit is the tens place. To set the individual microliters on the p1000, use the tick marks on the bottom dial. Each tick is two microliters, set the instrument to the white gap for odd microliter volumes.

Let's try a few examples on reading the volumes on the p1000.

Show Answer	Show Answer	Show Answer

The P200 is similar in that the dial has three numerals, the place values just shift down, hundreds (note that this digit is black, it can read 0, 1 or 2), tens, ones and finally the tick marks are each two tenths of a microliter.

Try a few examples with the p200.

Show Answer	Show Answer	Show Answer

Setting the correct volume is just the first step to using the micropipette well. The method is rather straight forward and will, with a modicum of experience, become second nature. It outline form it looks like:

1. Set the desired volume.
2. Fit a tip to the instrument.
3. Depress the plunger to the first stop. There are two stops on the plunger, the first is the correct volume for measuring, the second, for ejection, pushes a bit more air out to make sure that your entire volume is ejected. The second stop has a bit more tension that should be easy to feel. The only catch is that if you are near the low end of the volume range, the travel to the first stop is very small.
4. Place that tip in the solution to measure.
5. Slowly release the plunger. Your volume should be one smooth, continuous column of liquid. Air bubbles or turbulent flow suggest that you may be too quick with the thumb.
6. Transfer the tip to the vessel collecting your volume and slowly depress the plunger through the first stop to the second to eject your volume.

Let's put it all together and get a visual feeling for measuring different volumes. Place a square of parafilm on the bench and set the P200 to 200 μL. Dispense 200 μL of water toward one corner of the parafilm. Reset to 100 μL and dispense next to the first drop, along the diagonal. If you dispense too fast, the drops tend to run together. This is good training for being slow and steady with the tool. Repeat the process for 50 μL and 25 μL. When you are finished, appreciate the series of drops where each drop is one half the volume of the previous drop. While this is fun practice, it also sets up the theme of dilutions.

As we saw in the Tang et al. paper, it is common to use a wide concentration range in many assays. A convenient way to make that concentration range is with a serial dilution. The "serial" here refers to a dilution series in which each new solution is a fixed fraction the previous solution.

The two most common serial dilutions are the two–fold and ten–fold serial dilutions. In the two–fold dilution, each dilution is one half the concentration of the previous solution (similar to the volume series you made in working with the micropipettes). This dilution style is most useful when you need a number of concentrations which are close to one another, tightly spaced points along your independent variable axis. The ten–fold serial dilution produces a much wider concentration range in the same number of points. Each dilution is one tenth the concentration of the previous solution. Another way to think about this dilution is that with each dilution, the concentration is reduced by an order of magnitude. This allows for testing a wide concentration range with a small number of solutions. Tang et al. used a scheme similar to the ten–fold serial dilution (you'll note that their concentration axis in Figure 5 has points that don't fall exactly on the orders of magnitude—don't worry, we'll cover making a specific dilution to an arbitrary concentration a little bit later) to cover a range of about 0.001 to 1000 mIU/mL in rhLH concentration.

A convenient feature of the serial dilution is that the method is very similar regardless of the dilution factor involved. Once you've done one, it is relatively easy to modify the protocol for another—all you really have to change is the volume involved.

The basic method for the two–fold is that you start with a stock solution that is the highest concentration of interest in a volume of twice the final volume that you'll need for your work (or usually a bit more as you often have to do things twice or three times). You then set out one tube for each dilution that you would like to prepare and fill each of those tubes with a volume of your buffer equal to the final volume you would like for each solution. Then the serial dilution can begin. Half the volume of the stock solution is removed from the first tube and added to the second and mixed. Our first tube is now at both the correct concentration (stock) and the correct final volume (one half the starting volume). The second tube is at the correct concentration (one half the stock concentration) but twice the desired volume. To make that the correct volume, and start the third concentration, remove half the volume of tube two and place it in tube three and mix. Tube two is now the correct volume and concentration, and you begin to get the picture. The transfer of half the volume continues to the final tube. How do you solve the volume problem for the final tube? Easy, discard half the volume to waste collection.

Drop your stock solution tube of bromocresol green (commonly used a pH indicator, note that it isn't green at this pH) in the rack with the seven empty tubes to the right. Fill each empty tube with 750 μL of acetate buffer. Remove 750 μL from your stock and add it to the second tube. Cap the second tube and invert to mix. Repeat the process from tube 2 to tube 3, 3 to 4 and so on until you've completed the series. Discard 750 μL from the last tube. Leave this dilution series in your rack, we'll use it later.

Drop your stock solution tube of bromocresol green in the rack with the seven empty tubes to the right. Fill each empty tube with 900 μL of acetate buffer. Remove 100 μL from your stock, place in tube two, cap and mix. Complete the dilution series by transferring 100 μL from the current tube to the next with mixing for each step. Discard 100 μL from the final tube.

Congratulations, you've completed the mechanics of the serial dilutions. Now it's time to analyze what you've done. Place a white paper towel down on the bench and spread the two–fold and ten–fold serial dilutions next to each other. You may remove the label from the stock tube for better visualization. You may also label each series with a marker on the top of the tube for safety.

Do you agree that the ten‐fold serial dilution creates a much greater concentration range? Record a qualitative description of the two series.

Qualitative is nice, but wouldn't a quantitative measure be better?

Since we know the concentrations of each sample in your dilution series (hint: the first is 0.2 mg/mL and each subsequent solution is one half the concentration of the previous one), we can measure the absorbance of each solution at 460 nm to prepare a standard curve of absorbance as a function of dye concentration.

Rotate the left knob on the front face of the Spec 20D clockwise until the machine turns powers. Wait a couple minutes for the lamp to warm and produce a stable light. Using the knob on the top of the instrument, dial the wavelength of 460 nm. There is also a lever on the front left of the instrument, make sure that lever is toward the range containing 460 nm. Begin to blank or zero the instrument with the chamber empty and the lid down (top of the instrument, left). Using the left knob on the front, dial 0.000 transmittance (don't worry, we'll get absorbance eventually, it's easier to zero in transmittance mode and negative zero is as good as zero). Fill the cuvette with ≈1000 μL of acetate buffer as a blank. The cuvette has a triangle at the top. Put the cuvette into the cuvette adapter such that you can see the triangle. Open the chamber and insert the cuvette adapter so that the triangle is pointing right, toward the wavelength knob. Close the lid and using the right knob on the face of the instrument, dial one hundred percent transmittance. Do note that the right knob will rotate several turns. Depending on what the instrument was last used for, this might be a slight adjustment or might require many revolutions. When you have the instrument blanked, you can push the mode button on the face to select absorbance mode. The instrument will read 0.000 (or something very close). Transmitting all the incident light is equivalent to absorbing none.

With the Spec 20D blanked, it's time to measure the absorbance of each dilution. Remove the cuvette, discard the buffer, rinse and dry the cuvette. Repeat the process with each dilution recording the absorbance of each sample. The smallest concentration will have very little absrobance at this wavelength, the stock concentration should have an absorbance in the neighborhood of 1.100. Plot absorbance as a function of concentration. Be sure to label each axis with identity and units (you can use OD, short for optical density, as the absorbance units). Add a linear trendline to your data, asking Excel to show both the equation (useful later) and the "R-squared" value. This last value is the square of the correlation coefficient, a measure of how well the data correlate each axis. If the line of best fit bisects each point perfectly, R2 will be 1.0, errors in dilution and measurement will lower this value. Here's an example to provide an objective; you do not have to match my style.

Since we've made a standard curve from the two–fold serial dilution, there must be one more thing that will use those data. There is. We saw it in Tang et al. paper, they covered a several order of magnitude concentration range, but not every concentration was exactly ten times the concentration of the previous point. How did they do that?

$$M_1V_1=M_2V_2$$

Or the version with C for concentrations, if you prefer.

That's right, concentration volume concentration volume. With this relationship, we can make any dilution we want (within our limits of the ability to measure volumes, of course). Not so sure? Let's try it out with the first step of our two–fold serial dilution. Recall that we added 750 μL of 0.2 mg/mL bromocresol green to 750 μL of acetate buffer making a final volume of 1500 μL. Let's translate that to the equation:

$$M_1V_1=M_2V_2$$ $$0.2~mg/mL \times 750~\mu L=M_2 \times 1500~\mu L$$

Solving for the final concentration

$${{0.2~mg/mL \times750~\mu L}\over{1500~\mu L}}=M_2$$ $$M_2=0.1~mg/mL.$$

The final concentration is 0.1 mg/mL, exactly half of the starting concentration. That's the two–fold dilution. And it's the key to being able to make (within limits) any dilution anytime, anywhere.

Let's take a practical example which turns the calculation around slightly from the analysis of a dilution to the calculation of a new one. You have a stock solution which is 3.45 M. You want to make at 500. mL of solution at a concentration of 1.67 M. What volume of stock solution do you use?

Ask yourself this question, "What volume of 3.45 M stock do I need to dilute to make 1.67 M solution in a volume of 500. mL? And then translate into the equation

$$M_1V_1=M_2V_2$$ $$3.45~M \times V_1=1.67~M \times 500.~mL$$ $$V_1 = {{1.67~M \times 500.~mL} \over {3.45~M}}$$ $$V_1 = 242~mL$$

That means I mix 242 mL of my 3.45 M stock with 258 mL of buffer to make 500 mL of solution at a concentration of 1.67 M. Relatively straight forward.

But you ask, "Is there a sanity check I can make to be sure that calculation is reasonable?"

Yes, there is. Think about something called the "dilution factor." The dilution factor is a ratio of the stock concentration to the final concentration. In our example

$$dilution~factor = {3.45~M \over 1.67~M}$$ $$dilution~factor = 2.06.$$

Since the dilution factor for this dilution is just a little over two, our stock solution should be just a little bit less than one half the final volume (think back to what we did in the two–fold serial dilution if this gives you pause). Using 242 mL of stock in a solution of 500 mL total volume is just a bit less than half. Check.

Complete honesty. Our molecular biology friends will usually work dilution problems solely by dilution factor. They will calculate the dilution factor as we did above and then divide their desired total volume by that dilution factor to come to 242 mL. It looks remarkably like, in the end, our explicit calculation, using two concentrations and a volume. Why the difference? When you're working with cell culture and unpurified cell extracts, buffers often have multiple components, making it challenging to give a molar concentration. They offen work with a buffer where the working strength is labeled as 1X (one times the working concentration). That buffer may be made as a stock solution at 5X (five times the working concentration). Diluting that stock to the working concentration is easy—almost no calculator required. It's due to the complex solutions that they tend to think about that all dilutions are written in this style. A style which is just M1V1, M2V2, but in two steps.

Using the 0.4 mg/mL bromocresol green stock, make four dilutions dilutions which will fall on your standard curve. Prepare 800 μL of bromocresol green at concentrations of 0.052 mg/mL, 0.084 mg/mL, 0.091 mg/mL and 0.150 mg/mL. Measure the absorbance of each of these solutions. Use the equation for your standard curve to calculate the theoretical absorbance from your two fold serial dilution. Calculate a percent error for each dilution according to the equation

$$Percent~Error = {{(Measured - Theoretical)}\over{Theoretical}} \times 100\%$$

1. Read the volume from the micropipette scale. How did you know which instrument you were looking at in this example?

2. You are tasked with diluting a sample 10,000–fold using a 10–fold serial dilution protocol. However, your lab is running very low on tubes so you may only use the minimum number necessary. What is that number of tubes? Explain.
3. If tubes are really as scarce as indicated in the above problem, how might you change the protocol to use fewer tubes? You are limited to using only a P200 and P1000 to measure volumes. There are several ways to approach this challenge; you have options. You do not need to find the optimal (one tube) solution, that would be challenging with the tools you have for the job, and you could always "borrow" some tubes from the lab across the hall.
4. You have been given a large volume of a stock solution which is at a concentration of 650 μg/mL and asked to make 1000 μL of that reagent at a concentration of 125 μg/mL. How do you do that?

Include the following in your laboratory report:

1. A paragraph (or more) describing the qualitative difference between the two fold and ten fold serial dilutions. Please address the similarity of the technique, the relative concentration spread of your eight dilutions from each series and speculate on why you might choose one series or the other for a particular titration of your own choosing.
2. Your standard curve, fully labeled with linear trendline, equation and R2. Comment on the beauty of these data being sure to answer the question. "I am satisfied with this work?"
3. Please provide all data and calculations from the "Making Specific Dilutions" section.
4. Answer all questions, with full calculations where you need them.

Each student should prepare and submit a unique lab report. Your group data and calculations related to the protocol will be similar. You should write unique prose and answer the questions individually.