Natalie Williams Week 10: Difference between revisions
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*Degradation is shown with a first order chemical reaction --> x = k*z | *Degradation is shown with a first order chemical reaction --> x = k*z | ||
*ρ = regulatory effect g of regulators transformed by a sigmoidal transfer | *ρ = regulatory effect g of regulators transformed by a sigmoidal transfer | ||
The entire model for control of target gene expression ''z'': | The entire model for control of target gene expression ''z'': <br> | ||
[http://nar.oxfordjournals.org/content/35/1/279/embed/mml-math-3.gif| Equation 3] | [http://nar.oxfordjournals.org/content/35/1/279/embed/mml-math-3.gif| Equation 3] | ||
*k2: rate of degradation of target gene product | *k2: rate of degradation of target gene product | ||
| Line 51: | Line 51: | ||
*The simplified version - Equation 4 - was used to figure out regulators of the target genes | *The simplified version - Equation 4 - was used to figure out regulators of the target genes | ||
*''n'' has to be chosen to represent the large amounts of changes in gene expression for each individual experiment | *''n'' has to be chosen to represent the large amounts of changes in gene expression for each individual experiment | ||
These expression profiles <b>Z</b> {z(t)} for the target and <b>Y</b> {y(t)} for regulating genes measure at time points ranging from 1,2...Q were used to look at and analyze the gene profiles to minimize the average square error. | These expression profiles <b>Z</b> {z(t)} for the target and <b>Y</b> {y(t)} for regulating genes measure at time points ranging from 1,2...Q were used to look at and analyze the gene profiles to minimize the average square error. <br> | ||
[http://nar.oxfordjournals.org/content/35/1/279/embed/mml-math-6.gif| Equation 6] | [http://nar.oxfordjournals.org/content/35/1/279/embed/mml-math-6.gif| Equation 6] | ||
*{z^c(t)}: altered profile of z(t) for all Z at time points t=1,2,...Q, | *{z^c(t)}: altered profile of z(t) for all Z at time points t=1,2,...Q, | ||
| Line 57: | Line 57: | ||
The issue began to focus on how to get the best results with the minimal amount of error. | The issue began to focus on how to get the best results with the minimal amount of error. | ||
<br> | <br> | ||
The | The [http://nar.oxfordjournals.org/content/35/1/279/embed/mml-math-7.gif| linear model] was then compared to the nonlinear model. | ||
*The parameters (d) came from the minimization of errors in function 6. | *The parameters (d) came from the minimization of errors in function 6. | ||
====Computational algorithm==== | ====Computational algorithm==== | ||
Revision as of 13:57, 21 March 2015
Outline of Nonlinear differential equation model for quantification of transcriptional regulation applied to microarray data of Saccharomyces cerevisiae
Introduction
- Gene regulation makes a working copy of the genetic information of DNA sequences into proteins and/or functional RNAs.
- Promoting regions must be recognized by transcription regulatory proteins which bind RNA polymerase to the DNA strand.
- Microarray developments have made it easier to follow the changes of the cell's gene expression over time.
- Analyzing this microarray data, we could better understand the relationships between genes and their transcription factor regulators.
- Because these relationships collectively form a network among the genes, it should be possible to construct networks by studying the results of microarray data.
- Budding yeast, Saccharomyces cerevisiae, has been studied extensively in the lab.
- There is a lot of knowledge about its genome.
- Expression data was collected and analyzed to figure out what genes were being used at a specific stage of the cell cycle.
- Genes were grouped based on where their regulators bound to promoter regions.
- Methods in which networks were produced previously:
- A generalized linear model was going to be created to described regulators and guess the pattern of regulators and their target genes.
- A kinetic model with Bayesian networks was used to predict gene regulatory networks as well as the proteins that regulate genes expression.
- Including both information from the genome and gene expression data named another method to predicting networks.
- Another research furthered this method by using promoter regions or the sigma factor.
- An alternative method used in this paper:
- A model based on nonlinear differential equation model was used.
- It called for all potential regulators
- Genes from a group of potential regulators are picked and the model is applied to try to fit the gene expression results of the target genes.
- This is done for all potential regulators
- A model based on nonlinear differential equation model was used.
- In this model:
- There were 40 target genes;
- 184 possible regulators were identified;
- The data were analyzed using a linear model; and,
- Results from the linear model were compared to that of the nonlinear differential equation system to see how well it predicted the target genes' profiles.
Results
Dynamic model of transcriptional control
- For the model, an assumption that there is repeated interactions between regulators and target genes over time.
- The model also assumes there is combinatorial control among the regulators for target genes.
- yj: expression level regulators
- wj: regulatory weights
- g: regulator effect of a specific gene
- j =1,2,...m, where m is number of regulators controlling a gene
- b: parameter for transcription initiation delay/unspecific bias caused by regulator effects associated with gene expression
Rate of expression of target gene (dz/dt) is given by regulatory effects of other genes ρ & the effect of degradation x.
Equation2
- Degradation is shown with a first order chemical reaction --> x = k*z
- ρ = regulatory effect g of regulators transformed by a sigmoidal transfer
The entire model for control of target gene expression z:
Equation 3
- k2: rate of degradation of target gene product
- k1: rate of expression
However, Equation 3 can be simplified to Equation 4
Equation 4
- y is approximated with a polynomial of degree n
- Coefficients were taken from experimental gene expression data using a least squares approximation.
- An assumption that all the weight errors for all points were the same.
- The simplified version - Equation 4 - was used to figure out regulators of the target genes
- n has to be chosen to represent the large amounts of changes in gene expression for each individual experiment
These expression profiles Z {z(t)} for the target and Y {y(t)} for regulating genes measure at time points ranging from 1,2...Q were used to look at and analyze the gene profiles to minimize the average square error.
Equation 6
- {z^c(t)}: altered profile of z(t) for all Z at time points t=1,2,...Q,
- Q: data points calculated from Equation 4
The issue began to focus on how to get the best results with the minimal amount of error.
The linear model was then compared to the nonlinear model.
- The parameters (d) came from the minimization of errors in function 6.
Computational algorithm
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