BIOL398-04/S15:Jeffrey Crosson Week 10

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Jeffrey Crosson


Outline of "Nonlinear differential equation model for quantification of transcriptional regulation applied to microarray data of Saccharomyces cerevisiae"

  1. Introduction
    1. Gene expression
      1. One of the most important processes in a cell
      2. Depends on transcriptional regulatory proteins
        1. Their programs are modified when
          1. Cell progresses through development
          2. Cell reacts to changing environment
        2. These changes are recorded with microarray
          1. Analysis of dynamics allows for discovery of causal relations
          2. Can reverse engineer the gene network
      3. Saccharomyces cerevisiae has been extensively studied
        1. Gene expression for its whole genome has been collected
  2. Results
    1. Dynamic model of transcriptional control
      1. A result of previous work on the dynamic simulation of genetic networks
      2. Assumes the recursive action of regulators on the target gene over time
      3. Assumes the regulatory effect on the expression can be expressed as a combinatorial action of its regulators
      4. The polynomial fit is an approximation of the true expression profile
      5. Gene profiles that minimize the mean square error function are sought for
      6. The result allows the parameters in the differential equation to be estimated
    2. Computational Algorithm
      1. The aim is to find a set of potential regulators of a certain target gene by estimating its expression profile
      2. It searches from a group of transcriptional regulators using least squares minimization, the differential equation, and the error function
      3. The missing data points and fluctuation in gene expression profiles is compensated for by approximating the regulator gene profiles by a polynomial of degree n
    3. Dataset Selection
      1. The eukaryotic cell cycle dataset published by Spellman and others was chosen to evaluate the performance of the model
      2. The dataset records changes in gene expressions using microarrays at 18 points in time over two cell cycle periods
      3. 800 genes were identified whose expression was associated with the cell cycle, but the real number of regulators controlling the cell cycle is much smaller
      4. Therefore 184 potential regulator genes were selected for the identification of yeast cell cycle regulators
      5. 40 target genes were selected
    4. Inference of Regulators
      1. The data is in form of log base 2 of ratio between RNA amount and value of standard
      2. Least squares minimization for each target gene for all potential regulators
      3. Approximation of unknown real profile is the least squares best fit of polynomial of degree n to target gene expression profile z
    5. Comparison to Linear
      1. It took the nonlinear model less attempts to find the correct regulator
      2. Regulators that are repressors have an opposite curve as the target genes and reconstructed target curve
      3. Regulators that are activators have a similar curve as the target genes and the reconstructed target curve
    6. Discussion
      1. The nonlinear model effectively paired target gene expression with its regulator
      2. The nonlinear algorithm selected the most probable regulator and provided information about how well it controls the target gene
      3. The model does not test indirect controls of target genes
      4. Regulators are selected from a pool through sequence analysis
      5. Transcriptional regulation also is controlled by proteins which cannot be recorded by microarrays
      6. This nonlinear algorithm can lead to further attempts at modeling gene regulatory networks
      7. Combinatorial control and larger networks can be created with smaller medium-scale gene regulatory networks
      8. In the future, the speed of the algorithm will have additional features that will allow it to consider other factors