From 2012.igem.org

Revision as of 15:51, 6 September 2012

Prior Data

Yeast mRNA Degradation Rate

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. 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
];

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);

Yeast Protein Degradation Rate

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. It states that the half life time in S. cerevisiae can be approximated based on the amino acid after the initial start codon.

Yeast Transcription Rate Rate

Data was obtained from the Paper (Pelechano et. Al 2001 [http://www.pnas.org/content/99/9/5860.long]) and processed by [http://arohatgi.info/WebPlotDigitizer/app/] 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);

figure(1)
clf
plot(linspace(-2.8,0.8,100),k(3)*lognpdf(linspace(-2.8,0.8,100),k(1),k(2)),'r-')
hold on
plot(x,y,'g*')

Reference