Sarah Carratt 4.12.11: Difference between revisions
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==Sources for this Week== | |||
*[http://bioinformatics.oxfordjournals.org/content/early/2004/03/22/bioinformatics.bth173.full.pdf Sontag et al (2004) ''Bioinformatics''] | |||
*[http://sbie.kaist.ac.kr/ftp/Inferring%20gene%20regulatory%20networks%20from%20temporal%20expression%20profiles%20under%20time-delay%20and%20noise%20%5Bcbac-200708%5D.pdf Kim ''et al.'' (2007) ''Comp Bio Chem''] | |||
*[http://nar.oxfordjournals.org/content/35/1/279.short Vu and Vohradsky (2007) ''Nucleic Acid Res''] | |||
==Gene Regulation and Modeling== | ==Gene Regulation and Modeling== | ||
*Focused on measuring RNA and modeling dynamic behavior of proteins that RNA spins off | *Focused on measuring RNA and modeling dynamic behavior of proteins that RNA spins off | ||
Line 9: | Line 15: | ||
**Define "simultaneously" | **Define "simultaneously" | ||
*Database represents a model built through experiments and literature | *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 | *Easily build matrix of closeness once distance is defined | ||
*Clustering is more subtle | *Clustering is more subtle | ||
**time 1 graphed vs time 2...dot plot! | **time 1 graphed vs time 2...dot plot! | ||
**two+ clusters that are distinct, separate based on where they fall..."an art" | **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<sup>-λt</sup>X | |||
*d/dt(e<sup>-λt</sup>) = -λe<sup>-λt</sup>X | |||
*dx/dt(e<sup>-λt</sup>) = -λe<sup>-λt</sup>X | |||
*Half life = t<sub>H</sub> | |||
**x(0) = X | |||
**x(t<sub>H</sub>)= 1/2X = e<sup>-λt<sub>H</sub></sup>X | |||
**1/2= e<sup>-λt<sub>H</sub></sup> | |||
**2= e<sup>λt<sub>H</sub></sup> | |||
**λ=log(2)/t<sub>H</sub> | |||
***ln of 2 ≈ 0.69 | |||
**t<sub>H</sub> = ln(2)/λ | |||
==Production== | |||
*Production goes up in presence of x<sub>2</sub> | |||
*Move x<sub>2</sub> 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<sup>-x</sup>)''' | |||
****'''large numbers are close to 1''' | |||
****'''small numbers close to zero''' | |||
****'''has a symmetry (skew symmetry about a point)''' | |||
==OUR EQUATION== | |||
P<sub>1</sub>/(1+e<sup>w<sub>2</sub>(t<sub>2</sub>-t<sub>2</sub>)</sup>) - λ<sub>1</sub>x<sub>1</sub>(t) |
Latest revision as of 09:32, 14 April 2011
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)
- approximates a switch
- (A) Linear
OUR EQUATION
P1/(1+ew2(t2-t2)) - λ1x1(t)