Activity 3.1.5 Unlocking the Secrets in Our Genes
Introduction
In Activity 3.1.4, you performed a simulated DNA microarray to compare the gene
expression of a smoker’s lung cells and lung cells from a non-smoker. Researchers
could use this information to learn more about the progression of lung cancer and
potentially design treatment strategies.
But are all cases of cancer the same? Is the gene expression the same in Mike Smith’s
osteosarcoma as all other patients with osteosarcoma? What if scientists want to learn
more about how cancer affects gene expression patterns in different people? Mike
Smith’s doctor has enrolled Mike in a research study to answer this question. The
research study will investigate three genes thought to be associated with osteosarcoma.
By taking samples from various patients, researchers can then calculate the similarities
between the gene expression patterns of these three genes.
One popular method to calculate the similarities between individual genes is called the
Pearson Correlation Coefficient. This method measures how gene expression levels
from two genes go up and down together. In this activity, you will use the Pearson
Correlation Coefficient method to determine the correlation coefficient between three
genes thought to be associated with osteosarcoma.
Equipment




Computer with Microsoft Excel software
Activity 3.1.5 Student Resource Sheet
Laboratory Journal
Scientific Calculator
Procedure
Part I: Transforming Ratios
Once the data from a DNA microarray is converted into ratios, it is then useful to convert
the ratios to a base 2 logarithm (Log2) in order to perform statistical analysis of the data.
A logarithm is the power to which a base must be raised to produce a desired value. In
the case of a base 2 logarithm, for every increase or decrease of one, there is a two fold
change. For example:
Log2(0.0625) = -4
Log2(0.125) = -3
Log2(0.25) = -2
Log2(0.5) = -1
Log2(1) = 0
Log2(2) = 1
Log2(4) = 2
Log2(8)= 3
Log2(16) = 4
© 2010 Project Lead The Way, Inc.
Medical Interventions Activity 3.1.5 Unlocking The Secrets In Our Genes – Page 1
The gene expression ratios in base 2 logarithm form can be used to give meaning to
DNA microarray results:
 When the ratio is positive, it means that the gene is induced by tumor formation.
This means that the gene transcription was more active in cancer cells than in
normal cells.
 When the ratio is negative, it means that the gene is suppressed by tumor
formation. This means that the gene transcription was less active in cancer cells
than in normal cells.
 When the ratio is equal to one, the gene is not affected by tumor formation. This
means that the gene transcription was the same in cancer cells as it was in
normal cells.
 When the ratio is zero, the gene is not expressed in either cell.
In order to understand why scientists convert gene expression ratios to base 2
logarithms, we will look at the gene expression ratios from three different patients:
Table One: Gene Expression Ratios for Three Osteosarcoma Patients
Gene 1
Gene 2
Gene 3
Mike Smith (Patient 1)
1.4
1.1
0.5
Patient 2
2.3
1.33
0.65
Patient 3
3.1
1.82
0.25
1. Obtain a Student Resource Sheet from your teacher.
2. Graph the gene expression ratios from Table One. Follow steps 1-14 on the Student
Resource Sheet for directions on how to create your graph.
3. Create a new data table converting the gene expression ratios into base 2
logarithms and graph the information. Follow steps 15-19 on the Students Resource
Sheet for directions on how to do this.
4. Print two copies of your data tables and graphs. Attach one copy into your laboratory
journal. Hand in the other copy to your teacher.
5. Answer Conclusion questions 1 – 3.
Part II: Calculate the Mean and Standard Deviation
Now that you have converted the gene expression ratios for the osteosarcoma patients
into base 2 logarithm form, you will now calculate the mean, or average of the gene
expression values, and the standard deviation, the measure of how spread out the gene
expression values are.
6. Note that your teacher will assign you either Gene 2 or Gene 3. Work with a partner
to complete the remainder of the steps in Part II and Part III for this assigned gene.
Use the completed data table for Gene 1, found below, as your example to help you
complete steps 7-13. Notice that the transformed gene expression ratios have been
rounded to the nearest hundredth. For all calculations, you round to the nearest
hundredth where appropriate. If a calculation is smaller than 0.005, round this
number to 0.01.
© 2010 Project Lead The Way, Inc.
Medical Interventions Activity 3.1.5 Unlocking The Secrets In Our Genes – Page 2
Example: Mean and Standard Deviation for Gene 1:
Gene Expressions
Deviance
(Log2)
Mike Smith (Patient 1)
0.49
0.49 - 1.11 = -0.62
Patient 2
1.20
1.20 - 1.11 = 0.09
Patient 3
1.63
1.63 - 1.11 = 0.52
Mean = (0.49 + 1.20 + 1.63) ÷ 3 = 1.11
Sum of Squared Deviances = 0.38 + 0.01 + 0.27 = 0.66
(Sum of Squared Deviances) ÷ 2 = 0.66 ÷ 2 = 0.33
Standard Deviation = √ (0.33) = 0.57
Deviance2
(-0.62) 2 = 0.38
(0.09) 2 = 0.01
(0.52) 2 = 0.27
7. Fill-in the “Gene Expressions (Log2)” column for your assigned gene in Table Two
below.
Table Two: Mean and Standard Deviation for Assigned Gene:
Gene Expressions
(Log2)
Deviance
(Log2 Gene
Expression – Mean)
Deviance2
Mike Smith (Patient 1)
Patient 2
Patient 3
Mean =
Sum of Squared Deviances =
(Sum of Squared Deviances) ÷ 2 =
Standard Deviation =
8. Calculate the mean for your assigned gene. Do this by adding the gene expressions
for your assigned gene together and divide by three. Fill-in the calculated mean for
your gene in Table Two.
9. Calculate the deviance for each gene expression (how far each of the gene
expression ratios is from the mean). Do this by subtracting the mean from each of
the gene expressions. Fill-in the “Deviance” columns for each gene in Table Two.
10. Square all of the deviances for each gene. Fill-in the “Deviance2” column for each
gene in Table Two.
11. Calculate the sum of all the squared deviances for each gene. Fill-in this information
in the “Sum of Squared Deviances =” row in Table Two.
12. Divide the sum you got in step 11 by 2 (this is the total number of genes minus 1).
Fill-in this information in the “(Sum of Squared Deviances) ÷ 2 “ row in Table Two.
13. Calculate the square root of the result from step 12. The result of this calculation is
the standard deviation. Fill-in the standard deviation in Table Two.
Part III: Normalize the Gene Expression Values
The next step toward determining the correlation coefficient between the gene
expression patterns between Gene 1 and your assigned gene is to normalize the gene
expression values. Normalizing the gene expression values removes the statistical error
from the data.
© 2010 Project Lead The Way, Inc.
Medical Interventions Activity 3.1.5 Unlocking The Secrets In Our Genes – Page 3
14. Use the completed data table for gene one as your example, found below, to help
you as you complete step 15.
Example: Normalized Gene Expressions for Gene 1:
Gene Expressions (Log2)
Mike Smith (Patient 1)
Patient 2
Patient 3
0.49
1.20
1.63
Normalized Gene
Expressions
-0.62 ÷ 0.57 = -1.09
0.09 ÷ 0.57 = 0.16
0.52 ÷ 0.57 = 0.91
15. Normalize the gene expression values for each patient for your assigned gene by
dividing the deviance by the standard deviation. Fill-in the normalized gene
expressions in Table Three, found below as well as Table Four.
Table Three: Normalized Gene Expressions for Assigned Gene:
Normalized Gene
Gene Expressions (Log2)
Expressions
(Deviance ÷ Std Deviation)
Mike Smith (Patient 1)
Patient 2
Patient 3
16. Work with a group that was assigned the other gene to fill-in the data table below.
Table Four: Normalized Gene Expressions for All Three Genes:
Gene 1:
Gene 2:
Mike Smith (Patient 1):
-1.09
Patient 2:
0.16
Patient 3:
0.91
Gene 3:
Part IV: Calculate the Correlation Coefficient
The correlation coefficient will indicate the relationship between two genes.
 When the correlation coefficient is positive, it means that the gene expressions
behave similarly. The larger the correlation coefficient, the stronger the
relationship.
 When the correlation coefficient is negative, it means that the gene expressions
behave in opposite ways. The farther away the correlation coefficient is from
zero, the stronger the relationship.
 When the correlation coefficient is one, it means that the gene expressions are
identical.
 When the correlation coefficient is zero, it means that the gene expressions
behave in an unrelated manner.
17. Multiply each patient’s normalized gene expression for gene 1 by his or her
normalized gene expression for gene 2. Complete these calculations in the
“Gene 1 Compared with Gene 2” column in Table Five below. For example, for
Mike Smith, you should do the following calculation:
-1.09 x -0.89 = 0.97
© 2010 Project Lead The Way, Inc.
Medical Interventions Activity 3.1.5 Unlocking The Secrets In Our Genes – Page 4
Table Five: Correlation Coefficients
Gene 1
Compared
with Gene 2:
(-1.09) x (Mike Smith (Patient 1):
0.89) = 0.97
(0.16) x (-0.16)
Patient 2:
= -0.03
(0.91) x (1.05)
Patient 3:
= 0.96
0.97 + -0.03 +
Sum Product =
0.96 = 1.90
Correlation Coefficient
1.90 ÷ 3 =
(Sum Product ÷ 3) =
0.63
Gene 1
Compared with
Gene 3:
Gene 2 Compared
with Gene 3:
18. Calculate the Sum Product (also called the Dot Product) for Gene 1 Compared with
Gene 2. Do this by adding all of the products for each patient together. Complete
this calculation in the “Sum Product” row for Gene 1 Compared with Gene 2 in Table
Five. For example, for Gene 1 Compared with Gene 2, you should do the following
calculation: 0.97 + -0.03 + 0.96 = 1.90
19. Divide the Sum Product by 3 (because there are three patients that we are looking
at). The result is called the Correlation Coefficient. Complete this calculation in the
“Correlation Coefficient” row in Table Five. For example, to determine the
Correlation Coefficient for Gene 1 Compared with Gene 2, you should do the
following calculation: 1.90 ÷ 3 = 0.63
20. Use Gene 1 Compared with Gene 2 as your example and repeat steps 17 – 19 to
calculate the Correlation Coefficients for Gene 1 Compared with Gene 3 and for
Gene 2 Compared with Gene 3. Fill-in the remainder of Table Five. Show your work.
21. Answer the remaining Conclusion questions.
Conclusion Questions
1. How do the two graphs compare? Looking at the graphs, explain why you think
scientists convert the gene expression ratios into logarithmic form?
2. Using the graph of log2 ratios, which genes do you think are induced by tumor
formation? Which genes do you think are suppressed by tumor formation?
© 2010 Project Lead The Way, Inc.
Medical Interventions Activity 3.1.5 Unlocking The Secrets In Our Genes – Page 5
3. Using the graph of log2 ratios, which genes would you select for further study of
osteosarcoma? Explain your choice(s).
4. What does the correlation coefficient indicate about the similarities between the
gene expression for Gene 1 and the gene expression for Gene 2? What does this
number indicate about how these genes might be expressed in different
osteosarcoma patients?
5. What does the correlation coefficient indicate about the similarities between the
gene expression for Gene 1 and the gene expression for Gene 3? What does this
number indicate about how these genes might be expressed in different
osteosarcoma patients?
6. What does the correlation coefficient indicate about the similarities between the
gene expression for Gene 2 and the gene expression for Gene 3? What does this
number indicate about how these genes might be expressed in different
osteosarcoma patients?
7. Why would doctors and researchers want to know the correlation coefficient for a
specific gene in a sample of patients with the same type of cancer? How can this
data help cancer patients or evaluate risk?
8. We used the Pearson Correlation Coefficient method to analyze DNA microarray
results of three patients with the same type of cancer. How could you use this same
method to learn more about cancer cells before and after a particular treatment?
Web Portfolio
1) In a short paragraph describe why special calculations are needed for microarray
results as well as what you have learned about the Pearson Correlation Coefficient.
© 2010 Project Lead The Way, Inc.
Medical Interventions Activity 3.1.5 Unlocking The Secrets In Our Genes – Page 6