The Scientific Process is a method by which humans systematically ask questions of nature in order to understand how things work. It is based on the idea that nature works according to regular repeating rules and that by careful, systematic observation, we can discover those rules. The ideas of science are that humans can find things out directly from experience without having to depend on other humans (or books, etc.) for knowledge, and that the rules that are deduced can be used to make predictions about the outcome of future events so we can plan effective actions. Scientists write down the conclusions they reach so that other people can benefit from them without having to do every experiment personally. However, they must always report the experimental methods and evidence from which the conclusions were drawn so that others can repeat the experiments or independently evaluate the evidence. Scientific principles that have received wide acceptance have been tested in many ways, from many sides, by many people and have been debated and discussed until everyone is quite sure that the evidence all supports the principle as stated.
Never would a major principle be based on the work of one person. If later evidence appears that is in conflict with even the most highly respected scientific principle, the principle would have to be restated to reflect the new knowledge.
Science is limited in scope: if some things do not function according to rules, or if the rules involve too many variables in too many types of interactions for the human mind to unravel, then those things cannot be solved by the scientific method —at least for now. It does no good to ask nature for the name of the capital of Nebraska. Humans chose the name in an arbitrary manner; it does not obey a rule of nature. Nor have humans yet successfully unraveled all the variables involved in human interactions so no firm predictions can be made about how political groups such as Congress will behave. Why do some works of art move many people deeply while others do not? There are many important spheres of human life, including value systems and emotions, which cannot be tested or predicted by science.
It is important for modern humans to understand which parts of our lives can be enriched by science and which require other skills and knowledge from us. As complete human beings who make decisions and choices about our lives, including ethical and moral ones, we need to use scientific knowledge and the scientific process in appropriate coordination with the skills and values of other disciplines.
In the scientific method, facts about nature are obtained through direct observation and measurement of events, usually under controlled conditions that comprise an experiment. Then these facts are interpreted and analyzed to obtain
Standard Curve Analysis for DNA Quantitation
Mary Colavito and Ruth Logan, 2013
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Standard Curve Analysis for DNA Quantitation
Colavito and Logan, 2013 an understanding of the rules that controlled the observed events. Scientists are always careful to separate facts (direct observations and measurements) from interpretation, and to always show how interpretation is related to and derived from facts.
In general, all facts must be used or incorporated into an interpretation since to ignore some might involve omitting important information that has a bearing on the rules that are being sought. All facts contain unplanned variables or conditions (error) that will cause the scientist to make an inappropriate conclusion if not discovered, so part of every analysis involves trying to expose such variables in order to reveal and remove their causes if possible and to correct the analysis of the phenomenon for their effects.
Scientists finally draw a conclusion about each experiment or step that they complete in discovering rules of nature. These usually represent a restatement of a hypothesis that guided their initial experimental design. In their simplest form, hypothesis and conclusion statements are similar and represent a precisely described relationship between two measurable variables. It is this form that we will practice and use.
You will have opportunities to learn about and practice the scientific process throughout this semester and the next two (Biology 22 and 23) since full understanding of where scientific information comes from and confident use of the process are very important to anyone becoming a scientist.
In this first laboratory session, you will gain experience with measurements and methods that enhance the accuracy of experimentation. The goals of this exercise are to:
1. Separate the cellular components of a plant cell to obtain plant DNA.
2. Develop a consistent process for measuring the concentration of a component in solution.
3. Process data to make a standard curve graph. Graphs are pictorial representations of the process studied in the experiment.
4. Use the standard curve graph to determine the concentration of the unknown DNA solution.
5. Use collective standard curve data to evaluate the variability that occurs during experimentation.
6. Formulate a laboratory report that presents the data and your interpretation of the data.
The exercise is divided into three parts, which should be completed in the following order:
A. Strawberry DNA Extraction
B. Standard Curve Preparation
C. DNA Quantitation
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Materials used in this laboratory are non-hazardous. Solids can be discarded in the trash basket. To insure optimum safety, blue-stained solutions should be poured into the chemical waste container. All other solutions can be safely poured down the sink drains.
Each student should perform the DNA isolation individually.
1. Place one strawberry in a zip-loc bag and seal the top of the bag completely.
2. Use a balance to weigh the strawberry and record the result below:
__________ grams.
3. Mash the strawberry with your hands for about 2 minutes.
4. Add 10 ml of DNA Extraction Buffer.
This buffer contains detergent and salt (sodium chloride). How do
these two components affect the strawberry cells?
5. Reseal bag and mash the strawberry again for 2 minutes.
6. Line a plastic funnel with cheesecloth. Place the funnel in a 150 ml beaker.
7. Cut a corner from the zip-loc bag and empty the strawberry solution into the cheesecloth.
8. Gently squeeze the solution into the funnel and allow it to collect in the beaker. There may also be some foam but this does not interfere with obtaining the DNA. Discard the cheesecloth along with the pulp that remained inside.
This step recovers the cellular material that is soluble in the extraction buffer.
9. Transfer one-third to one-half of the strawberry solution to a 15 ml tube.
You should be able to measure at least 4 cm of dark solution from the bottom of the tube, not counting foam.
10. Using a plastic transfer pipette, slowly add ice-cold ethanol down the side of the tube so that it forms a layer on top of the strawberry solution.
Continue adding the ethanol until the tube is about three-quarters filled and you see the DNA appearing as a white, wispy material at the interface between the strawberry solution and ethanol.
What is the effect of ethanol on the DNA?
11. Place a wooden stick into the tube at the solution-ethanol interface and rotate gently to wind the DNA around the stick.
12. Add 0.5 ml of 70% ethanol to a 1.5 ml microcentrifuge tube. Transfer the
DNA from the stick into this solution. The material will be sticky and you may need to scrape the stick against the edge of the tube or use the transfer pipette to push the DNA from the stick. Use an additional 0.5 ml of
70% ethanol to completely transfer the DNA, ending with a total volume of
1 ml in the microcentrifuge tube.
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13. Collect the DNA by spinning the tube in a microcentrifuge for 1 minute at high speed. For this and all subsequent centrifugations, follow your instructor’s directions for loading, balancing and operating the microcentrifuge and be sure to accommodate the tubes of your classmates.
14. At the end of centrifugation, the ethanol solution will be the liquid supernatant and the DNA will be found in a solid pellet on the side of the tube near the bottom. Remove as much of the ethanol as possible without disturbing the DNA pellet. You can invert the tube over another tube or waste beaker and allow the supernatant to drain away. If necessary, use a transfer pipette or a tissue to take the residual ethanol from the tube.
15. Let the tube air dry for 5 minutes.
16. Add 5 drops of 0.2% methylene blue to the DNA pellet. Use the wooden stick or a transfer pipette to mix the dye with the DNA. Allow this mixture to incubate at room temperature for 5 minutes.
Methylene blue is a dye that binds to DNA as well as to proteins.
17. Using a transfer pipette, fill the microcentrifuge tube with tap water. Close the tube and mix the contents by inverting the tube or vigorously tapping the bottom of the tube with your finger. Spin the tube in the microcentrifuge at high speed for 1 minute.
Water is used to remove excess methylene blue dye that is not bound to DNA.
18. Remove as much of the water as possible without disturbing the DNA pellet. Refill the microcentrifuge tube with tap water and repeat the mixing step. Spin the tube in the microcentrifuge at high speed for 1 minute.
19. Remove as much of the water as possible without disturbing the DNA pellet. Using a transfer pipette, resuspend the DNA in 1 ml tap water by taking it up and down in a transfer pipette repeatedly. Transfer to a small glass cuvette and add 4 ml of tap water. Uniformly resuspend the bluestained DNA in the 5 ml solution by pipetting up and down repeatedly.
This treatment will break the long DNA strands somewhat, but will still allow detection of the amount of DNA recovered.
20. Your stained DNA solution is highly stable and should be saved for the remainder of the laboratory period or until the next laboratory ses sion. Follow your instructor’s directions for sealing and labeling the tube to preserve your sample for later analysis. As part of the standard curve analysis, read and record the absorbance of the 5 ml DNAcontaining solution at 550 nm. (See part C: DNA Quantitation)
You will use this value along with your standard curve to determine the concentration of DNA recovered from a single strawberry.
21. Clear your work area in preparation for the next part of the experiment.
Rinse all used glassware and invert on a paper towel to dry. Discard all solids in the trash. Pour any blue-stained solutions in the chemical waste bucket. Wipe any spilled liquids from the bench top.
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A standard curve is a common experimental tool used to determine the concentration of a solution. Light absorbed by a series of known concentrations of the solution is measured and a graph is produced that relates absorbance to concentration. The graph can be used to extrapolate the concentration of an unknown solution once its absorbance is obtained. For this part of the exercise, you will systematically dilute a concentrated solution of methylene blue and read the absorbance of each solution using a spectrophotometer. This data will be plotted for a standard curve. You will also measure the absorbance of your stained DNA solution and use the standard curve to determine the yield of DNA that you obtained from a single strawberry. In addition, standard curve data from all laboratory groups will be combined and analyzed to better understand the variability that arises during scientific experimentation. The instructions for producing the standard curve follow the introduction to the spectrophotometer, the instrument used to measure light absorbance.
INTRODUCTION TO THE SPECTROPHOTOMETER
The spectrophotometer is an instrument used to measure the amount of light that can pass through a solution. This, in turn, can be used as a measure of the concentration of a substance in the solution because of Beer’s Law which states that the concentration of a substance in solution is directly proportional to the amount of light absorbed by the solution, and inversely proportional to the logarithm of the fraction of light transmitted by the solution.
Absorbance = log
10
I o
= a s
x Concentration I
Where: I o
= incident light intensity
I = final light intensity
a s
= extinction coefficient (a constant)
% Transmittance
Absorbance
Concentration (mg/mL) Concentration (mg/mL)
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Beer’s law only holds if the “incident light” (the light which enters the solution) is monochromatic, that is, composed of light of a single wavelength. Normal white light is a mixture of many different wavelengths between 380nm and 750nm
(nanometer = 10 -9 meter). Our eyes and brain interpret these different wavelengths as different colors. Some approximate equivalencies between wavelength and color are given below:
400-435 nm Violet
435-480 nm Blue
480-580 nm Green 595-610 nm Orange
580-595 nm Yellow 610-750 nm Red
The spectrophotometer can separate white light into its component wavelengths by means of a prism (diffraction grating). The operator of the instrument can select incident light of any wavelength by turning the dial that rotates this prism.
The light enters a cuvette that contains the test solution and part of it will be absorbed if the substance in the solution is “active” (that is, chemically able to absorb light) at this wavelength. Unabsorbed light (transmitted light) strikes a photocell on the other side of the cuvette and generates an electric current which is registered on a galvanometer scale. The operator of the spectrophotometer can read the “percent transmittance” (%T) or the absorbance (Abs) directly on the meter.
Since the amount of light absorbed by a solution is directly proportional to the concentration of that solution, while the percent transmittance is related to the concentration as an inverse logarithmic function, we usually use the absorbance scale rather than the percent transmittance scale to determine the concentration of a solution. This makes the determination much easier than it would be otherwise: for example, if the concentration of an unknown solution were half that of a known solution, its absorbance would also be half that of the known solution.
Since the absorbance of an unknown solution is directly proportional to its concentration, we can easily determine its concentration by comparing its absorbance with the absorbance of a solution of known concentration.
Absorbance(Abs) (known) = Absorbance (unknown)
Concentration (known) Concentration (unknown)
Therefore:
Concentration (unknown) = Concentration (known) X Absorbance (unknown)
Absorbance (known)
Since all experimental techniques are subject to variability (error), it is usual to find the absorbance of a particular solution more than once, then to use a statistical method to find a probable value for the measurement.
A standard curve, showing the relationship between absorbance and concentration, can be prepared for any substance at any specific wavelength.
This can then be used to determine the concentration of unknown solutions in the future. An example of a standard curve and its use are given on the next page.
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An example of a standard curve using Potassium Permanganate dissolved in water.
Dilutions of a solution containing potassium permanganate were prepared and their concentrations calculated from that of the original solution. Each sample was placed into a spectrophotometer calibrated at 550 nm and its absorbance was read. The following table of data was produced:
Concentration of
Potassium Permanganate (g/L)
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
Abs
550nm
0.140
0.257
0.377
0.498
0.628
0.72
0.85
0.96
1.1
1.2
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 0.02
0.04
0.06
0.08
Concentration of Potassium Permanganate (g/L)
0.1
0.12
Figure 1: Standard Curve of Light Absorbance by Potassium Permanganate. Samples of known concentration were prepared and the absorbance of each sample was measured with a spectrophotometer. A trend line of y = 11.965x + 0.0174 with R 2 =0.9991 is superimposed.
Notice that the trend line shows the central tendency of the data. It does not connect the points and does not extend beyond the range of x axis values.
How to use the curve: If a solution of unknown concentration has an absorbance of 0.358, we could find its concentration from the standard curve. Its concentration would be about 0.028 g/L.
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Calibrating and Reading the Spectrophotometer
All instruments must be calibrated before use so that they will register the same type of information each time we make a measurement. The Spectronic 200 spectrophotometer is calibrated against the solvent of the system being tested as follows:
1. Using the switch at the back of the instrument, turn on the spectrophotometer.
2. When the screen reading “Initialization” appears, check to see that there are no cuvettes inside and then press enter. Wait until the “Home Menu” appears. [After initialization, you can use the key with a house symbol to return to the main menu if needed.]
3. On the “Home Menu” screen, use the arrow keys to select “Spec 20+ D
Emulation”.
4. Using the circular dial, set the wavelength to 550 nm. Turn the knob for
10 nm changes; press the center and rotate for 1 nm changes.
5. Set the Mode to Absorbance by using the right arrow key.
6. Fill a cuvette (small, thin walled, glass tube) with at least 5 ml of the solvent being used. For our first experiment, the solvent is tap water.
Be sure there are no air bubbles or floating objects in the solution, and wipe all drops and finger prints off the outside of the cuvette so that the light will only pass through glass and solvent. Repeat the steps of removing bubbles and fingerprints every time you use a cuvette.
7. Handling the cuvette only by the upper rim, place it into either of the tube holders in the spectrophotometer and close the lid. Press the key labeled “0.00” and wait until the “Data” display shows 0 absorbance.
This should define the conditions under which the most light possible will pass through solutions during the experiment (since experimental samples should contain both solvent and solute). Remove the solventfilled cuvette.
8. Place 5 ml of an experimental sample into a cuvette. Remove any bubbles, drops, or fingerprints from it, place it into one of the tube holders inside the spectrophotometer and close the lid. Under “Data” read the absorbance of the sample record the numbers in a table in your notebook.
Absorbance (Abs.) is the name of a variable and of its units. There is no further unit name for absorbance.
Practice using the spectrophotometer until its operation is familiar and easy for you.
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DILUTION OF METHYLENE BLUE SOLUTIONS AND ABSORBANCE
MEASUREMENTS FOR STANDARD CURVE PREPARATION
Each group of 4-5 students should produce one set of dilutions and obtain the absorbance readings for those samples. Group data will be collected and combined so that variation in class data can be analyzed.
1. Obtain about 3 mL of Methylene Blue stock solution from the lab bench.
Its concentration is 0.1%. Identify the test tubes (larger), cuvettes (smaller with much clearer glass), measuring pipets, pipetting bulb, and two beakers on the bench in front of you. Fill the larger beaker with tap water.
2. Use the table on the next page to plan a series of dilutions of the 0.1%
Methylene Blue stock solution. Begin by preparing 30 mL of a 1:10 dilution of the stock solution in the smaller beaker. Then use this diluted solution to prepare 5 mL volumes of all of the less concentrated solutions in the test tubes.
Sample Calculation : Making the 1:10 dilution of the stock solution yields a concentration of 0.01% Methylene Blue. Let’s say that you wish to produce a 5 mL solution that is 0.006% Methylene Blue. You can use the following equation to calculate the amount of the 0.01% solution to use:
Concentration
1
x Volume
1
= Concentration
2
x Volume
2
Let the 0.01% solution be Solution 1 and the 0.006% solution be solution
2. Then the equation will read 0.01% x Volume
1
= 0.006% x 5 mL, and
Volume
1
= 3 mL. This means you would use 3 mL of the 0.01% solution and add 2 mL of water to produce a 5 mL solution of 0.006% Methylene
Blue.
3. Prepare the dilutions in the series, one at a time, by pipetting measured amounts of methylene blue solution and tap water into test tubes (not cuvettes). Use pipetting bulbs; do not pipet by mouth. Remember to calculate all dilutions so as to produce concentrations with ONE significant figure, since your starting concentration has just one significant digit.
Record all of your activities, both in dilution preparation and reading absorbance values, in the table on the next page.
4. Mix the contents of the large test tube by pouring it into a cuvette .
Be certain that you have at least five mL of solution so that the solution completely fills the light path in the spectrophotometer chamber.
5. After calibrating the spectrophotometer with tap water (repeat every twenty minutes or so), and removing any bubbles, drops, or fingerprints, place the cuvette into the spectrophotometer chamber. Measure and record the absorbance of each solution at 550nm. Remember to watch for the correct number of significant digits.
6. Repeat the above until you have obtained at all 10 data points with concentrations from 0.001% to 0.01% as shown on Table 1. Ideally, the absorbance values should fall in the range of ~0.05 to >1.0.For inclusion in a spreadsheet of class data, report the last two columns of numbers from your table to your instructor, that is, report “final concentration” and
“absorbance”.
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0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
Table 1. Data table for recording all steps in the procedures used to prepare samples of Methylene Blue of known concentration and to measure their absorbance at 550nm. The last two columns of data will be used for the construction of the Standard Curve. Report this data to your instructor at the end of the laboratory period.
Dilution Procedure Used
Starting concentration of Methylene
Blue (%)
0.1
(stock solution)
Amount of
Methylene
Blue
Solution
3 mL
Amount of
Tap
Water
Added
27 mL
Total
Volume
30 mL
5 mL
Final concentration of Methylene
Blue (%)
0.01
(Read Abs first, then use for all other dilutions)
0.009
Abs
550nm
5 mL
5 mL
5 mL
5 mL
5 mL
5 mL
5 mL
5 mL
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
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1
Student
Name
Each student, still working in a group of 4 or 5, will determine the absorbance of the strawberry DNA solution produced in Part A.
1. Follow the procedures in Part B for calibrating the spectrophotometer at 550 nm with tap water as the solvent.
2. Removing any bubbles, drops, or fingerprints, read the absorbance of each student’s blue-stained strawberry DNA solution at 550 nm. Record the data in
Column 2 of Table 2, below.
3. (After the laboratory period.) Complete Table 2 by following the directions and applying the conversion factors described beneath it. Record your value for
Column 7 on the class spreadsheet provided by your instructor. Using the class spreadsheet, determine the standard deviation for the DNA Yield values.
4. Clean your working space by rinsing all glassware and leaving it inverted to dry.
Wipe any spilled liquids from the bench. Discard all solids in the trash. Pour any blue-stained solutions in the chemical waste bucket. Turn off the spectrophotometer, cover it, and coil its cord.
Table 2: Data table for determining the amount of DNA extracted from strawberries.
Each row represents a sample prepared by a different student.
2
Weight of
Strawberry
(g)
3
Abs
550
for
Methylene
Blue-stained
DNA solution
4
Concentration of Solution (%)
(from standard curve)
5
Concentration of DNA
(micrograms/mL)
6
Total Amount of DNA
Recovered
(micrograms)
7
DNA Yield
(micrograms
DNA/gram of strawberry)
Column 4: Determine the concentration of the solution by using the standard curve values generated with the data from Table 1. This value is expressed as a percentage of methylene blue, corresponding to the x-axis of the standard curve.
Column 5: For this calculation you need a conversion factor that relates the concentration of DNA in solution to the percentage of methylene blue detected by the standard curve assay. Use the following relationship: 0.001% Methylene Blue corresponds to 0.086 micrograms/milliliter of DNA. This value was determined by comparing methylene blue staining with an alternate method of measuring DNA concentration.
Column 6: The value in Column 4, in micrograms per mL, should be corrected for the total volume of 5 mL for the blue-stained solution.
Column 7: The value in Column 5, in micrograms, should be divided by the weight of the strawberry in grams to determine the DNA yield.
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Laboratory Report 1 will emphasize the presentation and interpretation of data collected from the strawberry DNA extraction and standard curve analysis. There will therefore be three sections, results, discussion and conclusion. Refer to the lab manual section on
“How to Write a Scientific Report” for general information on what to include in these sections. “Introduction to Error Analysis”, provided at the end of this document may also be helpful. Specific details relating to this report are provided below.
For this report, the Results section will contain the following:
1. Text: Present a paragraph that introduces the reader to the way in which the data will be presented and describes what the reader should notice about each figure and table. You can comment on the mathematical relationships between the variables that are shown in the figures. Provide objective information, without any interpretation in this section. Note that the results text is separate from all of the figure and table captions.
2. Figure 1: Using your group’s data , prepare a graph of Absorbance versus
Concentration for the data compiled in Table 1 of the lab manual instructions.
Include only the data for your lab group. Be sure that the independent variable
(concentration of Methylene Blue) is on the X-axis and the dependent variable
(Abs
550nm
) is on the Y-axis. Use a graphing program like Excel to plot the graph and insert a trend line. Write a full caption, including a title and brief description of the data presented, and place it below the figure. It should describe the central concept of the graph and show the source and purpose of the data. Be sure to include the equation of the trend line in the caption.
3. Figure 2: Using data from the class spreadsheet , prepare a graph of the
AVERAGE (mean) Absorbance versus Concentration for the standard curve analysis. Use Excel to calculate mean values for absorbencies at each concentration as well as the standard deviation for these values. Each mean value will be a point on the graph. Be sure that the independent variable
(concentration of Methylene Blue) is on the X-axis and the dependent variable
(Mean Abs
550nm
) is on the Y-axis. The standard deviation values will be represented by error bars on the graph. Write a full caption, including a title and brief description of the data presented, and place it below the figure. It should describe the central concept of the graph and show the source and purpose of the data.
4. Table 1: Use this format to present the data related to DNA Quantitation of your own strawberry DNA extraction . You may use the layout of Table 2 from the lab manual instructions or apply another design of your choice. Be sure that the format allows you to report all of the information from Columns 2-7 of Table 2.
Your table will have a single row of data, showing the yield you obtained from a single strawberry. Make sure that you use your group’s standard curve (Figure 1 in this report) to determine the concentration in Column 4 of this table. You do not need to present calculations, but can do so if you prefer. Write a full caption, including a title and brief description of the data presented, and place it above the table. In the brief description, be sure to include the mean + 1 standard deviation for the DNA Yield, calculated from the class data.
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For this report, the Discussion section should be an integrated interpretation of the data presented. Although the specifics are provided here in outline form, your discussion should be written as a series of paragraphs that form a cohesive unit for describing your data analysis.
1. Figure 1: Describe the relationship between the variables that is observed in this graph. What is the basis for this relationship? Consider events at the molecular level that provide the mechanism for this relationship. How well does the data fit the expected pattern? By what criteria are you evaluating the fit of the data? What are some possible sources of error that could have contributed to deviations from the expected values?
2. Figure 2: When interpreting this graph, focus on the variability demonstrated by the data. How well does the data fit the expected pattern? By what criteria are you evaluating the fit of the data? What can be determined from Figure 2 that cannot be seen from Figure 1? What are some possible sources of error that could have contributed to deviations from the expected values? [Note that you do not need to repeat your analysis of the relationship between the variables in Figure 2 unless you wish to present some additional information that was not pertinent to
Figure 1.]
3. Table 1: Describe the usefulness of standard curve analysis in determining the amount of DNA extracted from strawberry cells. How can you be sure that you were measuring DNA as opposed to another cellular component? Comment on whether the yield of DNA is reasonable in comparison to the class results. What are some possible sources of error that could have occurred in this portion of the experiment?
The Conclusion section should be a concise summary of the relationship(s) observed between the variables studied. Be sure that each relationship is precisely described, using mathematical terms when possible. A comment regarding the variation observed for the class data would also appropriately reflect the goals of this lab exercise.
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Working scientists soon discover that many measurements do not exactly represent the object or process being measured. It requires skill, some insight, and quite a bit of creativity to understand where the additional information may have come from, how it influenced the measurement, and whether a representative measurement can be derived from the flawed one. This task makes up a very large part of the analysis of any experiment so understanding and practicing it is a very important skill to develop. Statistics are used to provide consistent methods for treating data and, since these methods are widely used, the characteristics of data treated by these methods are well understood.
MEASUREMENTS AND ERROR
In biology, as in all sciences, measurements play a key role in the experimental process. A measurement is a precise and objective description or representation of a real phenomenon. In order for measurements to be meaningful, they must be reliable. Reliability is established by defining the conditions under which measurements are taken and examining the variability in the resulting measurements. Usually measurements are repeated enough times to insure confidence that reproducible values can be obtained. Examination of the variability also involves a calculation of the limits of accuracy in the measuring procedure. In this experiment, we will measure the absorbance of solutions of known concentrations of Methylene Blue and will use the calculated value of one standard deviation as the limit of accuracy among the measurements.
Error can be conceived of as variation from an unknown and immeasurable, hypothetically true value that is usually taken to be the mean or the most frequent measurement in a set of data. Error is a part of any measurement and variation is a property of any set of data. Its sources are usually intrinsic (inherent variability in the subject being measured, which is sometimes quite large in biological studies) and/or systematic (variability due to the measurement process).
One of the great achievements of modern science has been to show that variations (i.e. errors) in measurements are strikingly similar regardless of the object being measured. This general similarity has been incorporated into the
Normal Law of Error, which allows us to estimate the measurement error itself and to analyze the nature of variation. The task now is to use this law to describe in precise mathematical terms the distribution of a specific measurement taken in the class in such a way that the common features of the sample group and the variability are revealed. How does the frequency distribution of this measurement compare to the usual bell-shaped normal curve of error? One possible distribution is shown in Figure 1 below.
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100.00%
80.00%
60.00%
40.00%
20.00%
0.00%
3s 2s 1s X 1s 2s 3s
Figure 1: Example of a normal curve of error. This hypothetical curve was constructed by assigning an arbitrary value to the mean and a percentage of that value to the appropriate standard deviation multiples away from the mean.
As Figure 1 suggests, most sets of measurements exhibit two identifying characteristics: one, a tendency to group around a central value (the mean is usually the most probable measurement), and two, a degree of variability or spread away from the central value (the standard deviation is a measure of the variability--or error--in the set of measurements.) The Normal Law of Error defines these two characteristics as follows:
1. The mean - the average value obtained by dividing the sum of a sample of quantities by the total number of quantities added. For a set of N measurements
__ with values symbolized X
1
, X
2
, X
3
,----X
N
, the mean (X) is calculated as follows:
_
X =

X i
/N where X i
stands for the individual measured values from 1 to N.
2. The standard deviation - a measure of variability relative to the mean, whose formula is:
________
/ _
s = /

(X i
-X) 2
√ N-1
_ where s is the standard deviation, X i
- X is the difference between each value and the mean (these are squared to eliminate any negative values), and N is the total number of individual measurements.
The mean and the standard deviation are two constants whose value can be calculated easily from any set of data in which a single variable has been measured many times under a single set of conditions. Together they are
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Standard Curve Analysis for DNA Quantitation
Colavito and Logan, 2013 usually sufficient for the reconstruction of the distribution of data in the form of a curve fitted to the histogram whose height is proportional to the mean and whose width is determined by the standard deviation. More importantly, these two constants serve as a shorthand representation of the original sample, thereby furnishing a concise basis for the interpretation and comparison of measurements.
The standard deviation is a mathematically defined characteristic that is based on the number of measurements that should fall within any given interval centered on the mean. This function is pictured in Figure 1, showing a normal curve of error in which the horizontal scale is marked off in multiples of the standard deviation on either side of the mean. In any normal distribution, the expected distribution of measurements is approximately:
66% of the values lie within mean ± ls
95% of the values lie within mean ± 2s
99% of the values lie within mean ± 3s
The method of calculating the mean and standard deviation is shown in Table 1 for a small sample of five hypothetical measurements.
Table 1: Sample Calculation of Mean and Standard Deviation from a set of five data measurements.
Measurement Measurement minus mean
Square of difference
X i
35
27
_
X i
–X
7
-1
(X
_ i
– X)
49
1
2
24
31
-4
3
16
9
23
140
_
Mean = X = 140 = 28
-5 25
100
5
__
Standard Deviation = S = / 100 = √25 = 5
√ 5-1
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Standard Curve Analysis for DNA Quantitation
Colavito and Logan, 2013
At this point it is worth emphasizing the steps taken in the process of condensing a collection of measurements into a useful form. These steps are:
1. Sorting the raw data into arbitrary groups defined by regular intervals
2. Reporting the grouped and ordered data in a table or histogram.
3. Calculating the mean and the standard deviation.
4. Analyzing the measurements to see their pattern of variability and describing the variability characteristics in the data sample.
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