• Precision – “refers to the extent of agreement among repeated measurements of an experimental value”(13).  It can also be described as reproducibility or repeatability (14). For example, say you want to pipette 125 μL of water in 5 different tubes. If you measure the volume of water in each tube and they all come out to 125 μL, then you can confidently say that you have 100% precision. It also gives you confidence in the calibration of your pipette in that it delivers reproducible results multiple times.

2. Accuracy – “is defined as the difference between the experimental value and the true value of the quantity” (13). Think about the example specified above. If you obtain the same result as above, but you programmed the pipette to dispense 75 μL you can say that your pipette’s accuracy is off by 50 μL (125 μL – 75 μL = 50 μL) but the precision (or reproducibility) is excellent. This could mean that your pipette is not calibrated accurately and is, therefore, a problem that you need to fix before using this pipette. Now, 50 μL might not seem like a large volume until you place this in context with your experiments. Again, remember your entire Polymerase Chain Reaction volume is 50 μL! 

If we were to expand this concept to the general scientific field, reproducibility is the key to making proper observations. We design our experiments such that we test a variable using a specific technique and our output is some form of measurement. We then process this measurement and analyze it by making correlations about its meaning as it pertains to our test hypothesis. But what about errors? How do they occur and how can we minimize them? Well, a lot of errors can be minimized using good laboratory practices (much like what you are doing with this pipetting exercise). In science we like to divide errors into 2 broad concepts:

Whereby, x = individual values and n = number of observations

However, we also need to convey the reproducibility of our experiment and the mean does not give us this information. For example, we can have 3 data points with a mean of 2. The individual data points can be various number combinations. For example, they can all be 2, which would indicate high precision and reproducibility of our data. Alternatively, the mean can reflect a data set of 1, 2, and 3, which would indicate that we have a much lower reproducibility rate and a spread of 1 from the mean.  Therefore, percent error and standard deviation calculations are used to determine the measure of accuracy and precision, respectively.

Whereby x= value of the sample, x bar = mean of the samples and n = number of samples.

Pipetting 101

The following information on how to use a micropipettor has been adapted and modified from (15) and (16). Micropipettes (or pipettes) are air displacement pipettes used routinely in the research field to dispense small volumes (usually 0.5 µL – 1000 µL). They typically come in five sizes which are capable of pipetting five ranges of volumes: P10 =0.5-10 µL, P20 = 2- 20 µL, P100 = 10-100 µL, P200 = 20-200 µL and P1000 = 100-1000 µL. The pipettes require disposable plastic tips for use (16).

The following is an illustration of a Gilson micropipettor. You may also encounter Eppendorf and VWR pipettes which follow a similar design (16):

Figure 1: Parts of a pipette. Image made by Felicia. Pictures courtesy of Felicia Vulcu and Vivian Leong.

Now it’s your turn: please drag the appropriate pipette description to each of the four highlighted labels:

Pictures were taken by Felicia Vulcu, in collaboration with Vivian Leong.

Laboratory Calculations -some basic rules 

And now it’s time to switch gears and go over some basic solution calculations. This section is extremely important and we will be using it for every single lab, so please spend some time and go over these general points and watch the corresponding e-content on this topic.

Please watch the following module to learn more about making solutions and performing calculations: Solutions and Dilutions Video

It is very important to keep in mind that concentration is a RATIO. Concentrations are the currency of most laboratory work as scientists typically report work in concentrations. This is because a concentration is very reproducible and it provides the scientists with a lot of information, namely the amount of a solute and the total solution volume. This is enough information to reproduce the solution.

For example, telling someone you made a salt solution of 1 gram/ 100 mL is very helpful. Telling someone you used 1 gram of salt in your experiments is wildly unhelpful and not reproducible at all. Please get into the habit of reporting laboratory information in the form of concentrations whenever possible.

The other important tip is to ALWAYS, ALWAYS include the units. Treat them almost like numbers and fractions. For example: 

Super cool and awesome! Why? Because if you are ever in doubt of how to proceed with a calculation, you can obtain a ton of clues by following the units. Always follow the units.

Some basic formulas to keep in mind:

C₁V₁ = C₂V₂

Whereby C = concentration, V = volume, ₁ and ₂ refer to “stock” and “final, respectively

Tip: this equation only really works if you fully understand what you are trying to do in the lab. 

Molarity: “equal to the number of moles of a solute that are dissolved per liter of solution, M = mol/L”. (19) Memorize this but also understand it. Do not confuse “M” with “mol or mole”. M is a concentration: mole/L (a ratio).

mole = 6.02 x 10²³ atoms (Avogadro’s number), however, some atoms are heavier than others therefore 1 mole of 1 element weighs a different amount than a mole of another element.

Weight of a mole of given element = atomic weight in grams or Gram Atomic Weight, see Periodic Table. Example: 1 mole carbon = 12.0 grams

By definition: a 1 Molar solution of a compound contains 1 mole of that compound dissolved in 1 Liter of the total solution.

The formula to use is: C = n/V, where C = concentration, n = number (e.g. in moles) and V = volume

Mass per Volume, where C = m/V (same as above except m = mass).

Percent Volume per Volume, such as 20 % (v/v). The designation % (v/v) describes the number of mL of liquid solute per 100 mL total volume. These units are used when the solute is a liquid such as glycerol or ethanol. Therefore, a 20 % (v/v) solution of glycerol implies 20 mL of glycerol in a total 100 mL solvent volume (in this example the solvent is water). To prepare this solution you would measure out 20 mL glycerol and add it to 80 mL water for a total of 100 mL.

Percent Weight per Volume, such as 20 % (w/v). The designation % (w/v) describes the number of grams of solute per 100 mL total volume. If you are asked to prepare a 25 % (w/v) solution you weigh out 25 grams of your solute and add it to your solvent (example, water) to a final total volume of 100 mL. Note that this makes the assumption that the added solute does NOT contribute significantly to the final volume.

However, this is not always the case so to ensure that your concentration is never prepared wrong add the solute to a volume of solvent (or water) that is LESS than the final volume, dissolve the solute, THEN add solvent (or water) to the final total volume.

Fold Concentration, such as 100 X Buffer B. The “X” unit means that the concentration of each solute in this solution is a given number of times more concentrated than each is in a 1X solution. The usual assumption is that the final working solution is at a 1X concentration (although this is NOT always the case), irrespective of the units (mol/L, g/L, etc.). Thus, if a reagent should be at a final working concentration of 2 mg/mL and you need to make a 100X stock, you would use:

The polymerase chain reaction (PCR) is an amazing technique that mimics the basic concepts of DNA replication.  In this process, the 2 strands of the DNA double helix separate and act as templates for newly formed DNA. 

This technique was successfully accomplished by Dr. Kari Mullis who received the Nobel Prize in 1993. The entire reaction depends on one key ingredient: a thermostable polymerase (enzyme). The enzyme must be thermostable as PCR relies on extreme temperature shifts to separate DNA strands allowing DNA primers to anneal and the polymerase to copy and produce new strands of DNA. 

The main components of a PCR reaction are as follows:

– A thermostable polymerase (such as Taq DNA polymerase)

– dNTPs (monomeric building blocks for DNA: dCTP, dATP, dTTP, dGTP)

– DNA template (this can be any source of DNA, from genomic to plasmid, as long as it contains your gene of interest)

– Primers (this is a set of DNA primers that flank the start and end of your gene of interest). The primers are chemically generated oligonucleotides. 

– Buffer (contains lots of really important things, like pH maintenance and Magnesium, which are required for a successful PCR)

                                                                                       Image created by Felicia.

The entire reaction process can be described by these 3 temperature settings (note: some of these temperatures need to be optimized depending on the DNA to be amplified, and the type of thermostable polymerase used):

95°C – (Denaturation step) “template” DNA is separated. In cellular DNA replication, this strand separation would be performed by enzymes. You can mimic this function using temperature in the PCR tube. By increasing the temperature to really high levels you can break down the hydrogen bonds that keep the two strands together.

37-72°C – (Annealing step) oligonucleotide “primers” anneal to separated DNA strands. Annealing refers to the association of DNA primers to the complementary template due to hydrogen bonds that form between complementary base pairs. There are 2 primers, one complementary to the beginning of the DNA gene sequence to be amplified, and one complementary to the end of the DNA gene sequence to be amplified. In this way the primers flank the DNA sequence to be amplified! Please keep in mind that this reaction is taking place in a test tube and only borrows concepts of DNA replication. One very important distinction between PCR and cellular DNA replication is that in a polymerase chain reaction the primers are made of DNA.

This cycle can be repeated for 24-30 cycles, doubling the number of copies of target DNA with each cycle giving us an exponential amplification. Assuming 100% efficiency, we can calculate the number of target DNA sequences at the end of the PCR cycle if we know the number of cycles and the number of copies of the target sequence initially present in the reaction:

Whereby N = number of copies after amplification, t = number of cycles, N₀ = number of copies initially present in the reaction