Brianna N. Samuels-Week 6

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Purpose

  • to use our gene regulatory network to create a model and further analyze the data using the newly constructed model

Materials and Methods

Creating the GRNmap Input Workbook

production_rates sheet

  • contains initial guesses for the production rate parameters
  • Assuming that the system is in steady state with the relative expression of all genes equal to 1, (P/2) - lambda = 0, where lambda is the degradation rate, is a reasonable initial guess.
  • The sheet should contain two columns (from left to right) entitled, "id", "production_rate".
    • The "production_rate" column should then contain the initial guesses for the P parameter as described above, rounded to four decimal places.
      • The production rates are provided in a Microsoft Access database, which you can download from here.

degradation_rates sheet

  • contains degradation rates for all genes in the network, which are provided by the user.
  • Currently, the Dahlquist Lab is using data based on published mRNA half-life data from Neymotin et al. (2006).
    • We converted the half-life data values to the degradation rates by taking the natural log of the half-life and dividing by 2.
  • The sheet should contain two columns (from left to right) entitled "id", and "degradation_rate".
    • The id is an identifier that the user will use to identify a particular gene.
    • The "degradation_rate" column should then contain the absolute value of the degradation rate for the corresponding gene as described above, rounded to four decimal places.
      • To obtain these values, you will use the same file, [Microsoft Access database, which you can Expression-and-Degradation-rate-database_2019.accdb that you used to obtain the production rates in the first worksheet. Again, you can copy and paste the values one-by-one or you can follow the instructions to execute a query, substituting the appropriate "degradation_rates" table in the query. Note that you don't need to re-import your "network" table, you just need to create and execute the query.

Expression Data Sheets for Individual Yeast Strains

  • Expression data can be provided for either a single strain or multiple strains of yeast (for example, the wild type strain and a transcription factor deletion strain).
    • Each strain will have its own sheet in the workbook.
    • Each sheet should be given a unique name that follows the convention "STRAIN_log2_expression", where the word "STRAIN" is replaced by the strain designation, which will appear in the optimization_diagnostics sheet.
      • You should have included the transcription factors GLN3, HAP4, and ZAP1 in your network. Thus, we will use the expression data from the dGLN3, dHAP4, dZAP1 deletion strains in our workbooks as well, naming the worksheets "dgln3_log2_expression", "dhap4_log2_expression", and "dzap1_expression".
  • The sheet should have the following columns in this order:
    1. "id": list of all genes. The genes should be listed in the same order in all the sheets in the Excel workbook.
    2. The next series of columns should contain the expression data for each gene at a given timepoint given as log2 ratios (log2 fold changes). The column header should be the time at which the data were collected, without any units. For example, the 15 minute timepoint would have a column header "15" and the 30 minute timepoint would have the column header "30". GRNmap supports replicate data for each of the timepoints. Replicate data for the same timepoint should be in columns immediately next to each other and have the same column headers. For example, three replicates of the 15 minute timepoint would have "15", "15", "15" as the column headers.
    3. If data are provided for multiple strains, each strain should have data for the same timepoints, although the number of replicates can vary.
  • Include the data for the 15, 30, and 60 minute timepoints, but not the 90 or 120 minute timepoints.
  • The data you will be using is contained in the Expression-and-Degradation-rate-database_2019.accdb file that you used to obtain the production and degradation rates.

network sheet

  • The network you derived from the YEASTRACT database for the Week 5 assignment can be copied and pasted into this sheet directly. You may need to edit the contents of cell A1, but the rest should be good to go (especially since you previewed it in GRNsight). The description below just explains what is already in this worksheet.
    • This sheet contains an adjacency matrix representation of the gene regulatory network.
    • The columns correspond to the transcription factors and the rows correspond to the target genes controlled by those transcription factors.
    • A “1” means there is an edge connecting them and a “0” means that there is no edge connecting them.
    • The upper-left cell (A1) should contain the text “cols regulators/rows targets”. This text is there as a reminder of the direction of the regulatory relationships specified by the adjacency matrix.
    • The rest of row 1 should contain the names of the transcription factors that are controlling the other genes in the network, one transcription factor name per column.
    • The rest of column A should contain the names of the target genes that are being controlled by the transcription factors heading each of the columns in the matrix, one target gene name per row.
    • The transcription factor names should correspond to the "id" in the other sheets in the workbook. They should be capitalized the same way and occur in the same order along the top and side of the matrix. The matrix needs to be symmetric, i.e., the same transcription factors should appear along the top and left side of the matrix. The genes should be listed in the same order in all the sheets in the Excel workbook.
    • Each cell in the matrix should then contain a zero (0) if there is no regulatory relationship between those two transcription factors, or a one (1) if there is a regulatory relationship between them. Again, the columns correspond to the transcription factors and the rows correspond to the target genes controlled by those transcription factors.

network_weights sheet

  • These are the initial guesses for the estimation of the weight parameters, w.
  • Since these weights are initial guesses which will be optimized by GRNmap, the content of this sheet can be identical to the "network" sheet.

optimization_parameters sheet

  • The optimization_parameters sheet should have two columns (from left to right) entitled, "optimization_parameter" and "value".
  • You should copy this worksheet from the sample workbook provided. The only row that you need to modify is row 15, "Strain". Include just the strain designations for which you have a corresponding STRAIN_log2_expression sheet. If you don't have the dgln3, dhap4, or dzap1 expression sheets, then you will delete those from this row. If you do so, make sure that you don't leave any gaps between cells.
  • What follows below is an explanation of what the optimization_parameters mean.
    • alpha: Penalty term weighting (from the L-curve analysis)
    • kk_max: Number of times to re-run the optimization loop. In some cases re-starting the optimization loop can improve performance of the estimation.
    • MaxIter: Number of times MATLAB iterates through the optimization scheme. If this is set too low, MATLAB will stop before the parameters are optimized.
    • TolFun: How different two least squares evaluations should be before the program determines that it is not making any improvement
    • MaxFunEval: maximum number of times the program will evaluate the least squares cost
    • TolX: How close successive least squares cost evaluations should be before the program determines that it is not making any improvement.
    • production_function: = Sigmoid (case-insensitive) if sigmoidal model, =MM (case-insensitive) if Michaelis-Menten model
    • L_curve: =0 if an L-curve analysis should NOT be run or =1 if an L-curve analysis SHOULD be run. The L-curve analysis will automatically run sequential rounds of estimation for an array of fixed alpha values (0.8, 0.5, 0.2, 0.1,0.08, 0.05,0.02,0.01, 0.008, 0.005, 0.002, 0.001, 0.0008, 0.0005, 0.0002, and 0.0001). GRNmap makes a copy of the user's selected input workbook and changes alpha to the first alpha in the list. The estimation runs and the resulting parameter values are used as the initial guesses for the next round of estimation with the next alpha value. This process repeats until all alpha values have been run. New input and output workbooks are generated for each alpha value, although currently, the graphs are only saved for the last run.
    • estimate_params =1 if want to estimate parameters and =0 if the user wants to do just one forward run
    • make_graphs =1 to output graphs; =0 to not output graphs
    • fix_P =1 if the user does not want to estimate the production rate, P, parameter, just use the initial guess and never change; =0 to estimate
    • fix_b =1 if the user does not want to estimate the b parameter, just use the initial guess and never change; =0 to estimate
    • expression_timepoints: A row containing a list of the time points when the data was collected experimentally. Should correspond to the timepoint column headers in the STRAIN_log2_expression sheets.
    • Strain: A row containing a list of all of the strains for which there is expression data in the workbook. Should correspond to the "STRAIN" portion of the names of the STRAIN_log2_expression sheets for each strain. Note that GRNmap will run the model for the wild type network (all genes present in the network) and for networks where the gene deleted from the designated STRAIN has been deleted from the network.
    • simulation_timepoints: A row containing a list of the time points at which to evaluate the differential equations to generate the simulated data. This does not need to correspond to the actual measurement times, but should be in the same units (e.g. minutes).

threshold_b sheet

  • These are the initial guesses for the estimation of the threshold_b parameters.
  • There should be two columns.
    • The left-most column should contain the header "id" and list the standard names for the genes in the model in the same order as in the other sheets.
    • The second column should have the header "threshold_b" and should contain the initial guesses, we are going to use all 0.

Results

GRNmap Input Workbook

Sample Workbook

Scientific Conclusion

This week we were asked to create an input workbook that we would use to create a model later down the road. This required us to use estimated guesses for production rates based off the degradation rates. In this case we estimated that the production rates would be about twice the degradation rates. We also made initial guesses for the weights and the threshold values. In order to create this workbook we needed to use our own data as well as values provided from a different workbook with all the values necessary. It is very important that everything is done in the right order and looks the same/similar to the sample otherwise we will have issues trying to create the model next week.

Acknowledgements

  • Homework Partners: Desiree Gonzalez Ava Lekander communicated through text to answer questions about query and running the model
  • Asked for help with production rate and degradation rate values for two transcription factors from Dr. Dahlquist
  • Used sample workbook provided from Dr. Dahlquist
  • Copied wiki syntax from Angela Abarquez
  • Except for what is noted above, this individual journal entry was completed by me and not copied from another source.

References

  • Dahlquist, K. & Fitpatrick, B. (2019). "BIOL388/S19: Week 6" Biomathematical Modeling, Loyola Marymount University. Accessed from:Week 6 Assignment Page
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