Sarah Carratt 4.12.11

Sources for this Week

• Sontag et al (2004) Bioinformatics
• Kim et al. (2007) Comp Bio Chem
• Vu and Vohradsky (2007) Nucleic Acid Res

Gene Regulation and Modeling

• Focused on measuring RNA and modeling dynamic behavior of proteins that RNA spins off
• High activity in RNA should mean high protein behavior
• Low activity in RNA should mean low protein behavior

Modeling in Network Construction

• Qualitative, not just quantitative/numbers
• Active genes working simultaneously → transcription factors
  • Define "simultaneously"
• Database represents a model built through experiments and literature

Clustering

• Define distance metric (this is what it means for two things to be close together)
• Easily build matrix of closeness once distance is defined
• Clustering is more subtle
  • time 1 graphed vs time 2...dot plot!
  • two+ clusters that are distinct, separate based on where they fall..."an art"

Matrices

• 1's and 0's
• Changes in G1 produces changes in G3 if that box is 1
• Arrows in diagram show effector/affectee relationship
• Called an adjacency matrix → graph theory
• Graph theory is a way to put structures to pictures?
• When handed adjacency matrix...which ways do the arrows go?

Functions

• How does quantity of protein present relate to genes?
• Do we know if relationships are activation or repression?
  • Back to microarrays...up or down?
• What does activation mean?
  • Positive log fold change
  • Produce more/Do more
  • Increase in rate of change (production = rate↑)
• What does repression mean?
  • Negative log fold change
  • Slow, stop, reduce synthesis/activity
  • Produce less
  • Decrease in production rate

Network Picture

• Takes the matrix to cartoon land
• Provides qualitative information about production
• All arrows are about production
• Does the arrow = activation or production?
• Degradation=decrease contrary to production

Degradation

• Production - Degradation
• Half life is measure of degradation (time of how long it takes half of a sample to degrade)
• Pure degradation modul
• x = quantity at time t
• dx/dt = -λ·x(t)
  • λ=fraction of quantity degraded in unit of time (units = 1/time)
• Start with fixed amount, X = x(0)
• x(t) = e^-λtX
• d/dt(e^-λt) = -λe^-λtX
• dx/dt(e^-λt) = -λe^-λtX
• Half life = t_H
  • x(0) = X
  • x(t_H)= 1/2X = e^-λt_HX
  • 1/2= e^-λt_H
  • 2= e^λt_H
  • λ=log(2)/t_H
    • ln of 2 ≈ 0.69
  • t_H = ln(2)/λ

Production

• Production goes up in presence of x₂
• Move x₂ means higher rate
• What does the graph look like?
  • POSITIVE!!! (duh)
• Production Functions
  • (A) Linear
    • a +bx
  • (B) Michaelis-Menten
    • Vx/(K+x)
  • (C) Sigmoidal
    • approximates a switch
      • starts near zero, increases slowly, jumps up near saturation value and stays there
    • on-off + transition
      • S(x) = 1/(1+e^-x)
      • large numbers are close to 1
      • small numbers close to zero
      • has a symmetry (skew symmetry about a point)

OUR EQUATION

P₁/(1+e^{w₂(t₂-t₂)}) - λ₁x₁(t)