BIOL388/S25:Week 10

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BIOL 388-01: Biomathematical Modeling

MATH 388-01: Survey of Biomathematics

Loyola Marymount University

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Preliminary Tasks

  • If necessary, follow the instructions on the Help page to turn on file extensions, control where the browser downloads files, and decompress files.

Microarray Data Analysis

We will be working on the protocols in class in the next few class sessions. Based on the progress that is made during class, the milestone of what needs to be completed by the Week 10 journal deadline will be announced in class. We will continue with this protocol for the Week 11 assignment.

Keeping an electronic lab notebook

Since you don't have access to keeping an electronic notebook on the wiki, please keep one in your preferred format (Word document, Google Doc, etc.). The sections you need to have in your notebook are Purpose, Methods/Results (one combined section), Data & Files, Conclusion, Acknowledgments, and References.

  • An electronic laboratory notebook records all the manipulations you perform on the data and the answers to the questions throughout the protocol. Like a paper lab notebook found in a wet lab, it should contain enough information so that you or someone else could reproduce what you did using only the information from the notebook.
    • We will be performing a series of computations on a microarray dataset, primarily using Microsoft Excel. In the interests of reproducible research, it is appropriate to copy and paste the methods from this assignment into your notebook.
    • You must then modify the general instructions (which are generic to the whole class) to your own data analysis, recording the specific modifications and equations that you used on your dataset.
    • The protocol is written in the imperative tense because it is telling you what to do. Your notebook should be in the past tense because it is recording what you did.
    • Record the answers to the questions posed in the protocol at the place in which they appear in the method. You do not need to separate them out in a different results section.
    • All files generated in the protocol must be uploaded to Brightspace. In the "Data & Files" section of your notebook, list all of the filenames and write one brief sentence about the contents of that file.
    • You will write a summary paragraph that gives the conclusions from this week's analysis.

Homework Partners

Overview

This is a list of steps required to analyze DNA microarray data.

  1. Quantitate the fluorescence signal in each spot
  2. Calculate the ratio of red/green fluorescence
  3. Log2 transform the ratios
    • Steps 1-3 have been performed for you by the GenePix Pro software (which runs the microarray scanner).
  4. Normalize the ratios on each microarray slide
  5. Normalize the ratios for a set of slides in an experiment
  6. Perform statistical analysis on the ratios
  7. Compare individual genes with known data
    • We will perform steps 6-7 in Microsoft Excel
  8. Pattern finding algorithms (clustering)
  9. Map onto biological pathways
  10. Identifying regulatory transcription factors responsible for observed changes in gene expression (YEASTRACT)
  11. Dynamical systems modeling of the gene regulatory network (GRNmap)
  12. Viewing modeling results in GRNsight

Experimental Design and Getting Ready

The data used in this exercise is publicly available at the NCBI GEO database in record GSE83656.

  • Begin by downloading the Excel file for your group's strain (links are on Brightspace).
  • NOTE: before beginning any analysis, immediately change the filename (Save As...) so that it contains your initials to distinguish it from other students' work.
  • In the Excel spreadsheet, there is a worksheet labeled "Master_Sheet_<STRAIN>", where <STRAIN> is replaced by the strain designation, wt, dCIN5, or dGLN3.
    • In this worksheet, each row contains the data for one gene (one spot on the microarray).
    • The first column contains the "MasterIndex", which numbers all of the rows sequentially in the worksheet so that we can always use it to sort the genes into the order they were in when we started.
    • The second column (labeled "ID") contains the Systematic Name (gene identifier) from the Saccharomyces Genome Database.
    • The third column contains the Standard Name for each of the genes.
    • Each subsequent column contains the log2 ratio of the red/green fluorescence from each microarray hybridized in the experiment (steps 1-5 above having been performed for you already), for each strain starting with wild type and proceeding in alphabetical order by strain deletion.
    • Each of the column headings from the data begin with the experiment name ("wt" for wild type S. cerevisiae data, "dCIN5" for the Δcin5 data, etc.). "LogFC" stands for "Log2 Fold Change" which is the Log2 red/green ratio. The timepoints are designated as "t" followed by a number in minutes. Replicates are numbered as "-0", "-1", "-2", etc. after the timepoint.
      • The timepoints are t15, t30, t60 (cold shock at 13°C) and t90 and t120 (cold shock at 13°C followed by 30 or 60 minutes of recovery at 30°C).
  • Begin by recording in your electronic lab notebook, the strain that you will analyze, the filename, the number of replicates for each strain and each time point in your data.


Statistical Analysis Part 1: ANOVA

The purpose of the within-stain ANOVA test is to determine if any genes had a gene expression change that was significantly different than zero at any timepoint.

  1. Create a new worksheet, naming it "(STRAIN)_ANOVA" as appropriate. For example, you might call yours "wt_ANOVA" or "dCIN5_ANOVA".
  2. Copy all data from the "Master_Sheet" worksheet and paste it in your new worksheet.
  3. At the top of the first column to the right of your data, create five column headers of the form (STRAIN)_AvgLogFC_(TIME) where STRAIN is your strain designation and (TIME) is 15, 30, 60, 90, and 120.
  4. In the cell below the (STRAIN)_AvgLogFC_t15 header, type =AVERAGE(
  5. Then highlight all the data in row 2 associated with t15, press the closing paren key (shift 0),and press the "enter" key.
  6. This cell now contains the average of the log fold change data from the first gene at t=15 minutes.
  7. Click on this cell and position your cursor at the bottom right corner. You should see your cursor change to a thin black plus sign (not a chubby white one). When it does, double click, and the formula will magically be copied to the entire column of 6188 other genes.
  8. Repeat steps (4) through (8) with the t30, t60, t90, and the t120 data.
  9. Now in the first empty column to the right of the (STRAIN)_AvgLogFC_t120 calculation, create the column header (STRAIN)_ss_HO.
  10. In the first cell below this header, type =SUMSQ(
  11. Highlight all the LogFC data in row 2 (but not the AvgLogFC), press the closing paren key (shift 0),and press the "enter" key.
  12. In the next empty column to the right of (STRAIN)_ss_HO, create the column headers (STRAIN)_ss_(TIME) as in (3).
  13. Make a note of how many data points you have at each time point for your strain. For most of the strains, it will be 4, but for the wild type it will be "4" or "5". Count carefully. Also, make a note of the total number of data points. Again, for most strains, this will be 20, but for example, for wt it should be 23 (double-check).
  14. In the first cell below the header (STRAIN)_ss_t15, type =SUMSQ(<range of cells for logFC_t15>)-COUNTA(<range of cells for logFC_t15>)*<AvgLogFC_t15>^2 and hit enter.
    • The COUNTA function counts the number of cells in the specified range that have data in them (i.e., does not count cells with missing values).
    • The phrase <range of cells for logFC_t15> should be replaced by the data range associated with t15.
    • The phrase <AvgLogFC_t15> should be replaced by the cell number in which you computed the AvgLogFC for t15, and the "^2" squares that value.
    • Upon completion of this single computation, use the Step (7) trick to copy the formula throughout the column.
  15. Repeat this computation for the t30 through t120 data points. Again, be sure to get the data for each time point, type the right number of data points, and get the average from the appropriate cell for each time point, and copy the formula to the whole column for each computation.
  16. In the first column to the right of (STRAIN)_ss_t120, create the column header (STRAIN)_SS_full.
  17. In the first row below this header, type =sum(<range of cells containing "ss" for each timepoint>) and hit enter.
  18. In the next two columns to the right, create the headers (STRAIN)_Fstat and (STRAIN)_p-value.
  19. Recall the number of data points from (13): call that total n.
  20. In the first cell of the (STRAIN)_Fstat column, type =((n-5)/5)*(<(STRAIN)_ss_HO>-<(STRAIN)_SS_full>)/<(STRAIN)_SS_full> and hit enter.
    • Don't actually type the n but instead use the number from (13). Also note that "5" is the number of timepoints.
    • Replace the phrase (STRAIN)_ss_HO with the cell designation.
    • Replace the phrase <(STRAIN)_SS_full> with the cell designation.
    • Copy to the whole column.
  21. In the first cell below the (STRAIN)_p-value header, type =FDIST(<(STRAIN)_Fstat>,5,n-5) replacing the phrase <(STRAIN)_Fstat> with the cell designation and the "n" as in (13) with the number of data points total. Copy to the whole column.
  22. Before we move on to the next step, we will perform a quick sanity check to see if we did all of these computations correctly.
    • Click on cell A1 and click on the Data tab. Select the Filter icon (looks like a funnel). Little drop-down arrows should appear at the top of each column. This will enable us to filter the data according to criteria we set.
    • Click on the drop-down arrow on your (STRAIN)_p-value column. Select "Number Filters". In the window that appears, set a criterion that will filter your data so that the p value has to be less than 0.05.
    • Excel will now only display the rows that correspond to data meeting that filtering criterion. A number will appear in the lower left hand corner of the window giving you the number of rows that meet that criterion. We will check our results with each other to make sure that the computations were performed correctly.
    • Be sure to undo any filters that you have applied before making any additional calculations.

Stopping point for Tuesday, March 25. Be sure to upload your spreadsheet to the assignment on Brightspace by Thursday, March 27, 12:01am.

Calculate the Bonferroni and p value Correction

Note: Be sure to undo any filters that you have applied before continuing with the next steps.

  1. Now we will perform adjustments to the p value to correct for the multiple testing problem. Label the next two columns to the right with the same label, (STRAIN)_Bonferroni_p-value.
  2. Type the equation =<(STRAIN)_p-value>*6189, Upon completion of this single computation, use the Step (10) trick to copy the formula throughout the column.
  3. Replace any corrected p value that is greater than 1 by the number 1 by typing the following formula into the first cell below the second (STRAIN)_Bonferroni_p-value header: =IF((STRAIN)_Bonferroni_p-value>1,1,(STRAIN)_Bonferroni_p-value), where "(STRAIN)_Bonferroni_p-value" refers to the cell in which the first Bonferroni p value computation was made. Use the Step (10) trick to copy the formula throughout the column.

Calculate the Benjamini & Hochberg p value Correction

  1. Insert a new worksheet named "(STRAIN)_ANOVA_B-H".
  2. Copy and paste the "MasterIndex", "ID", and "Standard Name" columns from your previous worksheet into the first two columns of the new worksheet.
  3. For the following, use Paste special > Paste values. Copy your unadjusted p values from your ANOVA worksheet and paste it into Column D.
  4. Select all of columns A, B, C, and D. Sort by ascending values on Column D. Click the sort button from A to Z on the toolbar, in the window that appears, sort by column D, smallest to largest.
  5. Type the header "Rank" in cell E1. We will create a series of numbers in ascending order from 1 to 6189 in this column. This is the p value rank, smallest to largest. Type "1" into cell E2 and "2" into cell E3. Select both cells E2 and E3. Double-click on the plus sign on the lower right-hand corner of your selection to fill the column with a series of numbers from 1 to 6189.
  6. Now you can calculate the Benjamini and Hochberg p value correction. Type (STRAIN)_B-H_p-value in cell F1. Type the following formula in cell F2: =(D2*6189)/E2 and press enter. Copy that equation to the entire column.
  7. Type "STRAIN_B-H_p-value" into cell G1.
  8. Type the following formula into cell G2: =IF(F2>1,1,F2) and press enter. Copy that equation to the entire column.
  9. Select columns A through G. Now sort them by your MasterIndex in Column A in ascending order.
  10. Copy column G and use Paste special > Paste values to paste it into the next column on the right of your ANOVA sheet.
  • Zip and upload the .xlsx file that you have just created to Brightspace.


Sanity Check: Number of genes significantly changed

Before we move on to further analysis of the data, we want to perform a more extensive sanity check to make sure that we performed our data analysis correctly. We are going to find out the number of genes that are significantly changed at various p value cut-offs.

  • Go to your (STRAIN)_ANOVA worksheet.
  • Select row 1 (the row with your column headers) and select the menu item Data > Filter > Autofilter (The funnel icon on the Data tab). Little drop-down arrows should appear at the top of each column. This will enable us to filter the data according to criteria we set.
  • Click on the drop-down arrow for the unadjusted p value. Set a criterion that will filter your data so that the p value has to be less than 0.05.
    • How many genes have p < 0.05? and what is the percentage (out of 6189)?
    • How many genes have p < 0.01? and what is the percentage (out of 6189)?
    • How many genes have p < 0.001? and what is the percentage (out of 6189)?
    • How many genes have p < 0.0001? and what is the percentage (out of 6189)?
    • Note that it is a good idea to create a new worksheet in your workbook to record the answers to these questions. Then you can write a formula in Excel to automatically calculate the percentage for you.
  • When we use a p value cut-off of p < 0.05, what we are saying is that you would have seen a gene expression change that deviates this far from zero by chance less than 5% of the time.
  • We have just performed 6189 hypothesis tests. Another way to state what we are seeing with p < 0.05 is that we would expect to see this a gene expression change for at least one of the timepoints by chance in about 5% of our tests, or 309 times. Since we have more than 309 genes that pass this cut off, we know that some genes are significantly changed. However, we don't know which ones. To apply a more stringent criterion to our p values, we performed the Bonferroni and Benjamini and Hochberg corrections to these unadjusted p values. The Bonferroni correction is very stringent. The Benjamini-Hochberg correction is less stringent. To see this relationship, filter your data to determine the following:
    • How many genes are p < 0.05 for the Bonferroni-corrected p value? and what is the percentage (out of 6189)?
    • How many genes are p < 0.05 for the Benjamini and Hochberg-corrected p value? and what is the percentage (out of 6189)?
  • In summary, the p value cut-off should not be thought of as some magical number at which data becomes "significant". Instead, it is a moveable confidence level. If we want to be very confident of our data, use a small p value cut-off. If we are OK with being less confident about a gene expression change and want to include more genes in our analysis, we can use a larger p value cut-off.
  • We will compare the numbers we get between the wild type strain and the other strains studied, organized as a table. Use the sample PowerPoint slide posted on Brightspace to see how your table should be formatted. Upload your slide to Brightspace.
    • Note that since the wild type data is being analyzed by one of the groups in the class, it will be sufficient for this week to supply just the data for your strain. We will do the comparison with wild type at a later date.
  • Comparing results with known data: the expression of the gene NSR1 (ID: YGR159C)is known to be induced by cold shock. Find NSR1 in your dataset. What is its unadjusted, Bonferroni-corrected, and B-H-corrected p values? What is its average Log fold change at each of the timepoints in the experiment? Note that the average Log fold change is what we called "STRAIN)_AvgLogFC_(TIME)" in step 3 of the ANOVA analysis. Does NSR1 change expression due to cold shock in this experiment?

Data and Files

As a reminder, what you need to upload to Brightspace is:

  • Your electronic lab notebook.
  • Your Excel workbook with all of your calculations.
    • Note that you will be working with this workbook for the next week or two, adding computations to it. Save the new versions with the same filename.
  • Your PowerPoint slide with a summary table of p values.
    • You will also be adding to the PowerPoint presentation during subsequent steps in the analysis.
  • The input .txt file that you used to run stem.

Conclusion (Summary Paragraph)

  • Write a summary paragraph that gives the conclusions from this week's analysis.

Shared Journal Assignment

  • Submit your journal entry on the Discussion Board on Brightspace.

View & Read

Reflection

  • Answer the following questions:
    1. What are your initial reactions to hearing about this case?
    2. What role did data sharing play in uncovering this fraud?
    3. What additional information would you like to know about this case? (We will be visiting it again in subsequent weeks in the course.)
  • Please feel free to respond or comment on your classmates' reflections.


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