# BIOL398-04/S15:Jeffrey Crosson Week 10

### From OpenWetWare

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

- Introduction
- Gene expression
- One of the most important processes in a cell
- Depends on transcriptional regulatory proteins
- Their programs are modified when
- Cell progresses through development
- Cell reacts to changing environment

- These changes are recorded with microarray
- Analysis of dynamics allows for discovery of causal relations
- Can reverse engineer the gene network

- Their programs are modified when
- Saccharomyces cerevisiae has been extensively studied
- Gene expression for its whole genome has been collected

- Gene expression
- Results
- Dynamic model of transcriptional control
- A result of previous work on the dynamic simulation of genetic networks
- Assumes the recursive action of regulators on the target gene over time
- Assumes the regulatory effect on the expression can be expressed as a combinatorial action of its regulators
- The polynomial fit is an approximation of the true expression profile
- Gene profiles that minimize the mean square error function are sought for
- The result allows the parameters in the differential equation to be estimated

- Computational Algorithm
- The aim is to find a set of potential regulators of a certain target gene by estimating its expression profile
- It searches from a group of transcriptional regulators using least squares minimization, the differential equation, and the error function
- 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

- Dataset Selection
- The eukaryotic cell cycle dataset published by Spellman and others was chosen to evaluate the performance of the model
- The dataset records changes in gene expressions using microarrays at 18 points in time over two cell cycle periods
- 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
- Therefore 184 potential regulator genes were selected for the identification of yeast cell cycle regulators
- 40 target genes were selected

- Inference of Regulators
- The data is in form of log base 2 of ratio between RNA amount and value of standard
- Least squares minimization for each target gene for all potential regulators
- Approximation of unknown real profile is the least squares best fit of polynomial of degree n to target gene expression profile z

- Comparison to Linear
- It took the nonlinear model less attempts to find the correct regulator
- Regulators that are repressors have an opposite curve as the target genes and reconstructed target curve
- Regulators that are activators have a similar curve as the target genes and the reconstructed target curve

- Discussion
- The nonlinear model effectively paired target gene expression with its regulator
- The nonlinear algorithm selected the most probable regulator and provided information about how well it controls the target gene
- The model does not test indirect controls of target genes
- Regulators are selected from a pool through sequence analysis
- Transcriptional regulation also is controlled by proteins which cannot be recorded by microarrays
- This nonlinear algorithm can lead to further attempts at modeling gene regulatory networks
- Combinatorial control and larger networks can be created with smaller medium-scale gene regulatory networks
- In the future, the speed of the algorithm will have additional features that will allow it to consider other factors

- Dynamic model of transcriptional control