# Team:TU Munich/Modeling/Priors

### From 2012.igem.org

## Contents |

# Prior Data

## Yeast mRNA Degradation Rate

Data was obtained from the Paper [Wang et al., 2002] and processed by [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 [Trefethen, 2012].

## Yeast Protein Degradation Rate

For the Degradation Rate the N-end rule [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

Data was obtained from the Paper [Pelechano et al., 2010] and processed by [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

- [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. - [Rohatgi, 2012] Rohatgi, A. (2012). http://arohatgi.info/webplotdigitizer/app/.
- [Trefethen, 2012] Trefethen, N. (2012). http://www2.maths.ox.ac.uk/chebfun/.
- [Varshavsky, 1997] Varshavsky, A. (1997). The n-end rule pathway of protein degradation.
*Genes Cells*, 2(1):13–28. - [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.