Team:TU Munich/Modeling/Priors

From 2012.igem.org

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{{Team:TU_Munich/Header}}
{{Team:TU_Munich/Header}}
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{{Team:TU_Munich/ExCol}}
= Prior Data =
= Prior Data =
<hr/>
<hr/>
== Yeast mRNA Degradation Rate ==
== Yeast mRNA Degradation Rate ==
<hr/>
<hr/>
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[[File:TUM12_mRNA_degradation.png|300px|thumb|right|Picture taken from Wang et. Al 2001]]
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<div class="show">
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[[File:TUM12_PriormRNAdecay.jpg|300px||right|]]
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[[File:TUM12_mRNA_degradation.png|300px|thumb|right|'''Fig. 1''' Genome-wide mRNA decay rate. Picture taken from Wang et. al. 2002]]
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Data was obtained from the Paper (Wang et. Al 2001 [http://www.pnas.org/content/99/9/5860.long]) and processed by [http://arohatgi.info/WebPlotDigitizer/app/] to obtain raw data.
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[[File:TUM12_PriormRNAdecay.jpg|300px|thumb|right|'''Fig. 2''' Approximated probability density for the genome-wide mRNA decay rate.]]
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Using a least-squared error approximation the distribution of the half life time in was approximated as '''noncentral ''t''-distribution''' with parameters &mu; = 1.769 and &nu; = 20.59;.
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Data was obtained from the Paper [[http://www.ncbi.nlm.nih.gov/pubmed/11972065 Wang et al., 2002]] and processed by [[http://arohatgi.info/webplotdigitizer/app/ Rohatgi, 2012]] to obtain raw data.
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Using a least-squared error approximation the distribution of the half life time in was approximated as '''noncentral ''t''-distribution''' with parameters &mu; = 1.769 and &nu; = 20.59.
<pre>
<pre>
dataGraph = [
dataGraph = [
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0.9999935434718044,0.005142624707842157
0.9999935434718044,0.005142624707842157
];
];
-
 
+
%scale the data
X = round(dataGraph(:,1)*90);
X = round(dataGraph(:,1)*90);
-
 
y = round(dataGraph(:,2)*2000);
y = round(dataGraph(:,2)*2000);
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</pre>
</pre>
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The matlab nctpdf.m script needs to compute the limit of an infinite series to calculate the probabilities for the noncentral ''t''-distribution. As this the function will be called several million times during the generation of samples, the computation was quite time consuming and the funtion was approximated using chebyshev interpolation [[http://www2.maths.ox.ac.uk/chebfun/ Trefethen, 2012]].
 +
</div>
== Yeast Protein Degradation Rate ==
== Yeast Protein Degradation Rate ==
<hr/>
<hr/>
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<div>
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For the Degradation Rate the N-end rule (Varshavsky 1997 [http://openwetware.org/images/c/c2/The_N-end_Rule_Pathway_of_Protein_Degradation.pdf]) served as approximation for the half life time.
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For the Degradation Rate the N-end rule [[http://www.ncbi.nlm.nih.gov/pubmed/9112437 Varshavsky, 1997]] served as approximation for the half life time.
It states that the half life time in ''S. cerevisiae'' can be approximated based on the amino acid after the initial start codon.
It states that the half life time in ''S. cerevisiae'' can be approximated based on the amino acid after the initial start codon.
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As these values do not give enough information to infer a proper distribution, only the two lower bounds 5 h and 30 h will serve as approximate lower bounds for the optimization routines.
As these values do not give enough information to infer a proper distribution, only the two lower bounds 5 h and 30 h will serve as approximate lower bounds for the optimization routines.
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</div>
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== Yeast Transcription Rate Rate ==
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== Yeast Transcription Rate ==
<hr/>
<hr/>
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[[File:TUM12_mRNA_transcription.png|300px|thumb|right|Picture taken from Pelechano et al. 2010]]
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<div>
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[[File:TUM12_PriormRNAtrans.jpg|318px||right|]]
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[[File:TUM12_mRNA_transcription.png|300px|thumb|right|'''Fig. 3''' Genome-wide transcription rate. Picture taken from Pelechano et al. 2010]]
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Data was obtained from the Paper (Pelechano et al. 2010 [http://www.pnas.org/content/99/9/5860.long]) and processed by [http://arohatgi.info/WebPlotDigitizer/app/] to obtain raw data.
+
[[File:TUM12_PriormRNAtrans.jpg|300px|thumb|right|'''Fig. 4''' Approximated probability density for the genome-wide transcription rate.]]
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Using a least-squared error approximation the distribution of the transcription rate was approximated as ''log-normal distribution''' with parameters &mu; = -1.492 and &sigma; = 0.661;.
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Data was obtained from the Paper [[http://www.ncbi.nlm.nih.gov/pubmed/21103382 Pelechano et al., 2010]] and processed by [[http://arohatgi.info/webplotdigitizer/app/ Rohatgi, 2012]] to obtain raw data.
 +
Using a least-squared error approximation the distribution of the transcription rate was approximated as '''log-normal distribution''' with parameters &mu; = -1.492 and &sigma; = 0.661;.
<pre>
<pre>
dataGraph = [
dataGraph = [
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k=fminunc(@(z) sum((y-z(3)*lognpdf(x,z(1),z(2))).^2),k);
k=fminunc(@(z) sum((y-z(3)*lognpdf(x,z(1),z(2))).^2),k);
</pre>
</pre>
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<hr/>
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</div>
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<hr/>
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==Reference==
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----
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=Reference=
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*[[http://www.ncbi.nlm.nih.gov/pubmed/21103382 Pelechano et al., 2010]] Pelechano, V., Chávez, S., and Pérez-Ortín, J. E. (2010). A complete set of nascent transcription rates for yeast genes. ''PLoS One'', 5(11):e15442.
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*[[http://arohatgi.info/webplotdigitizer/app/ Rohatgi, 2012]] Rohatgi, A. (2012). http://arohatgi.info/webplotdigitizer/app/.
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*[[http://www2.maths.ox.ac.uk/chebfun/ Trefethen, 2012]] Trefethen, N. (2012). http://www2.maths.ox.ac.uk/chebfun/.
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*[[http://www.ncbi.nlm.nih.gov/pubmed/9112437 Varshavsky, 1997]] Varshavsky, A. (1997). The n-end rule pathway of protein degradation. ''Genes Cells'', 2(1):13–28.
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*[[http://www.ncbi.nlm.nih.gov/pubmed/11972065 Wang et al., 2002]] Wang, Y., Liu, C. L., Storey, J. D., Tibshirani, R. J., Herschlag, D., and Brown, P. O. (2002). Precision and functional specificity in mrna decay. ''Proc Natl Acad Sci U S A'', 99(9):5860–5.

Latest revision as of 19:43, 26 October 2012

Contents

Prior Data

Yeast mRNA Degradation Rate

Fig. 1 Genome-wide mRNA decay rate. Picture taken from Wang et. al. 2002
Fig. 2 Approximated probability density for the genome-wide mRNA decay rate.

Data was obtained from the Paper http://www.ncbi.nlm.nih.gov/pubmed/11972065 Wang et al., 2002 and processed by http://arohatgi.info/webplotdigitizer/app/ Rohatgi, 2012 to obtain raw data. Using a least-squared error approximation the distribution of the half life time in was approximated as noncentral t-distribution with parameters μ = 1.769 and ν = 20.59. 

dataGraph = [
0.0018691649126431735,0.0016851538590669062
0.05978099456360327,0.01885629059542104
0.11548146330755026,0.21910551258377348
0.17122389948476902,0.396902157771723
0.2253457470848775,0.4417136917136917
0.2815821076690642,0.3552607791738227
0.3359848142456839,0.249812760682326
0.39216629434020744,0.19272091011221448
0.4465173486912618,0.11490683229813668
0.5026600896166115,0.07854043723608946
0.5569239808370243,0.04735863431515607
0.6111394480959699,0.04208365077930302
0.667233765059852,0.031624075102336016
0.7233280820237343,0.021164499425369035
0.777540321018582,0.017616637181854626
0.8373665112795547,0.010604847561369285
0.8897063570976615,0.008787334874291503
0.9420462029157682,0.006969822187213598
0.9999935434718044,0.005142624707842157
];
%scale the data
X = round(dataGraph(:,1)*90);
y = round(dataGraph(:,2)*2000);

k(1) = 1.769292045467269;
k(2) = 20.589996419308118;
k(3) = 24852.48237036381;

k=fminunc(@(z) sum((y-z(3)*nctpdf(X,z(1),z(2))).^2),k);
k=fminunc(@(z) sum((y-z(3)*nctpdf(X,z(1),z(2))).^2),k);
k=fminunc(@(z) sum((y-z(3)*nctpdf(X,z(1),z(2))).^2),k);
k=fminunc(@(z) sum((y-z(3)*nctpdf(X,z(1),z(2))).^2),k);
k=fminunc(@(z) sum((y-z(3)*nctpdf(X,z(1),z(2))).^2),k);

The matlab nctpdf.m script needs to compute the limit of an infinite series to calculate the probabilities for the noncentral t-distribution. As this the function will be called several million times during the generation of samples, the computation was quite time consuming and the funtion was approximated using chebyshev interpolation http://www2.maths.ox.ac.uk/chebfun/ Trefethen, 2012.

Yeast Protein Degradation Rate

For the Degradation Rate the N-end rule http://www.ncbi.nlm.nih.gov/pubmed/9112437 Varshavsky, 1997 served as approximation for the half life time. It states that the half life time in S. cerevisiae can be approximated based on the amino acid after the initial start codon.

Residue ! Half-life
Arg 2 min
Lys, Phe, Leu, Trp, His, Asp, Asn 3 min
Tyr, Gln 10 min
Ile, Glu 30 min
Pro > 5 h
Cys, Ala, Ser, Thr, Gly, Val, Met > 30 h

As these values do not give enough information to infer a proper distribution, only the two lower bounds 5 h and 30 h will serve as approximate lower bounds for the optimization routines.

Yeast Transcription Rate

Fig. 3 Genome-wide transcription rate. Picture taken from Pelechano et al. 2010
Fig. 4 Approximated probability density for the genome-wide transcription rate.

Data was obtained from the Paper http://www.ncbi.nlm.nih.gov/pubmed/21103382 Pelechano et al., 2010 and processed by http://arohatgi.info/webplotdigitizer/app/ Rohatgi, 2012 to obtain raw data. Using a least-squared error approximation the distribution of the transcription rate was approximated as log-normal distribution with parameters μ = -1.492 and σ = 0.661;. 

dataGraph = [
-1.8,0.3442950751957339
-1.6,1.3525375039897853
-1.4,3.5492668181220783
-1.2,11.28874786429094
-1.0,23.213749272450762
-0.8,26.31522126884587
-0.6,18.273455248681024
-0.4,7.913623476840467
-0.2,3.7755111620134825
0,1.9559339854677913
0.2,0.6458759692833385
0.4,0.12767315671880167
];

x = 10.^dataGraph(:,1);
y = dataGraph(:,2);

k(1) = -0.8;
k(2) = 0.2;
k(3) = 25;

k=fminunc(@(z) sum((y-z(3)*lognpdf(x,z(1),z(2))).^2),k);
k=fminunc(@(z) sum((y-z(3)*lognpdf(x,z(1),z(2))).^2),k);
k=fminunc(@(z) sum((y-z(3)*lognpdf(x,z(1),z(2))).^2),k);
k=fminunc(@(z) sum((y-z(3)*lognpdf(x,z(1),z(2))).^2),k);

Reference

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