# Sarah Carratt 4.12.11

### From OpenWetWare

## Contents |

## 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
^{-λt}X - d/dt(e
^{-λt}) = -λe^{-λt}X - dx/dt(e
^{-λt}) = -λe^{-λt}X - Half life = t
_{H}- x(0) = X
- x(t
_{H})= 1/2X = e^{-λtH}X - 1/2= e
^{-λtH} - 2= e
^{λtH} - λ=log(2)/t
_{H}- ln of 2 ≈ 0.69

- t
_{H}= ln(2)/λ

## Production

- Production goes up in presence of x
_{2} - Move x
_{2}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)**

- approximates a switch

- (A) Linear

## OUR EQUATION

P_{1}/(1+e^{w2(t2-t2)}) - λ_{1}x_{1}(t)