Kara M Dismuke Week 10 Journal

Outline

Introduction

Regulation of gene expression

• important process in cell
• takes static information (in DNA) and transmits it into protein molecules (that serve various functions)
• requires recognition of specific promoter sequences
• the effects of transcription change with as the cell changes/develops

Microarrays

• document changes in gene expression over time
  • analysis these changes can enable one to see a relationship between genes and their regulators
• use microarray data to track the interaction between genes and their regulators

Saccharomyces cerevisiae

• gene-expression data gathered from genome-wide microarrays
• data analyzed using clustering methods
• data modeled using singular value decomposition
• genes were grouped according to their transcriptional regulatory networks (i.e. relationship between the genes and their respective regulators/promoters)

Previous Studies

• use differential equations to try to develop a linear model that reflects the transcription pattern of each of the genes being studied
• Woolf and Wang: used "fuzzy logic" to try to do this
  • Nachman: used kinetic model and Bayesian networks
  • Bar-Joseph: used genomic information and analysis of gene expression data
    • Wang and Makita: building of Bar-Joseph approach, the looked at the analysis of the promoter sequences and the sigma factor binding sequence motif

This Paper

• alternative method b/c uses a nonlinear differential equation model
• Procedure
  • choose set of all potential regulators (chose pool of 184)
  • choose set of target genes of S. cerevisiae (chose 40)
  • picks genes from possible regulators and applies model to then compare results to information known about the target gene
    • repeated to exhaust all possibilites
    • determine which regulators correctly model gene expression model
• compare results and make conclusions using results from other studies & also a comparison of the linear model
• result: this method can correctly identify a target gene's specific regulator and can say whether or not that regulator is an activator or repressor

Results

Dynamic model of transcription control

Model's Assumptions

• recursive action of regulators on target gene (over time)
• regulatory effect on gene can be expressed with a combination of its regulators

Equations

EQUATION 1

• b: parameter that represents the initial delay or unspecific bias from regulatory effects associated with gene expression
• g: regulatory effect for particular gene
• wj: regulatory weights
• yj: expression level of regulators
• j=1,2,...m
  • m: the number of regulators controlling the gene

EQUATION 2

• ρ: regulatory effects of other genes
• x: effect of degradation
• degradation: x = k*z where k is a constant in this kinetic equation
• ρ and x make up the rate of expression of a target gene (dz/dt)

EQUATION 3

• • z: target expression level
  • complete model for control of target gene expression z

EQUATION 4

• k1: maximal rate of expression
• k2: rate of degradation of target gene product
• simplification of Equation 3

EQUATION 5

• y: approximated with polynomial of degree n

EQUATION 6

• Once we have the expression profiles Z {z(t)} of the target and Y {y(t)} of the regulator genes, we search for gene profiles that minimize the mean square error function.
• t: 1,2,...Q
  • Q: data points computed using Equation 4
• {zc(t)}: reconstructed profile of z(t) in Z at all time points

EQUATION 7

• Linear form of the model
• parameters di (i=0,1,2): computed by minimizing error in function 6

Computational Algorithm

• estimate expression profile of target gene in order to choose a set of potential regulators for a particular target gene
  • search for potential regulators uses Equations 4 and 6
• approximate regulator gene profile by polynomial of degree n
• Algorithm

1. 1. fit regulators using Equation 5
   2. choose target gene
   3. choose a regulatory gene from pool of possible regulators
   4. use least squares minimization on the target and regulator genes
   5. repeat for all possible regulators (step 3)
   6. choose regulators that best satisfy criterion
   7. repeat for all target genes (step two)

• procedure in algorithm was done 100 times for each pair of regulator and target gene
• optimization done using Levenberg-Marquardt procedure
  • uses Runge-Kutta procedure (MATLAB's ode45 function)

Definitions

1. transcription
   • Transcription is the first step of gene expression, in which a particular segment of DNA is copied into RNA by the enzyme RNA polymerase. Both RNA and DNA are nucleic acids, which use base pairs of nucleotides as a complementary language that can be converted back and forth from DNA to RNA by the action of the correct enzymes. During transcription, a DNA sequence is read by an RNA polymerase, which produces a complementary, antiparallel RNA strand called a primary transcript. As opposed to DNA replication, transcription results in an RNA complement that includes the nucleotide uracil (U) in all instances where thymine (T) would have occurred in a DNA complement. Also unlike DNA replication where DNA is synthesized, transcription does not involve an RNA primer to initiate RNA synthesis.Although Transcription is nice.
   • http://www.biology-online.org/dictionary/Transcription
2. RNA polymerase
   • An enzyme that is responsible for making rna from a dna template. In all cells RNAP is needed for constructing rna chains from a dna template, a process termed transcription. In scientific terms, RNAP is a nucleotidyl transferase that polymerizes ribonucleotides at the 3' end of an rna transcript. Rna polymerase enzymes are essential and are found in all organisms, cells, and many viruses.
   • http://www.biology-online.org/dictionary/RNA_polymerase
3. promoter
   • A site in a DNA molecule at which RNA polymerase and transcription factors bind to initiate transcription of mRNA.
   • http://www.biology-online.org/dictionary/Promoter
4. activator
   • A DNA-binding transcription metabolite that positively modulates an allosteric Enzyme or regulates one or more genes by increasing the rate of transcription.
   • http://www.biology-online.org/dictionary/Activator
5. repressor
   • A regulatory protein that binds to an operator and blocks transcription of the genes of an opreon
   • http://www.biology-online.org/dictionary/Repressor
6. regulator
   • In genetics, a regulator pertains to a gene that codes for substances capable of repressing expression of another gene.
   • http://www.biology-online.org/dictionary/Regulator
7. mRNA
   • Abbreviated form for messenger ribonucleic acid, the type of RNA that codes for the chemical blueprint for a protein (during protein synthesis).
   • http://www.biology-online.org/dictionary/Mrna
8. gene expression
   • The conversion of the information from the gene into mRNA via transcription and then to protein via translation resulting in the phenotypic manifestation of the gene.
   • http://www.biology-online.org/dictionary/Gene_Expression
9. punative
   • Denoting a supposition or inference based on what was commonly believed, reputed, or deemed rather than on a direct evidence
   • http://www.biology-online.org/dictionary/Putative
10. combinatorial
    • Any system using a random assortment of components at any positions in the linear arrangement of atoms, i.e., a combinatorial library of mutations could contain positions where all four bases have been randomly inserted.
    • http://www.biology-online.org/dictionary/Combinatorial