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 = tH
 * x(0) = X
 * x(tH)= 1/2X = e-λtHX
 * 1/2= e-λtH
 * 2= eλtH
 * λ=log(2)/tH
 * ln of 2 ≈ 0.69
 * tH = 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+ew2(t2-t2)) - λ1x1(t)