# A probabilistic dynamical model for quantitative inference of the regulatory mechanism of transcription

Guido Sanguinetti, University of Edinburgh
Magnus Rattray, University of Manchester
Neil D. Lawrence, University of Sheffield

Bioinformatics 22, pp 1753-1759

#### Abstract

Motivation: Quantitative estimation of the regulatory relationship between transcription factors and genes is a fundamental stepping stone when trying to develop models of cellular processes. This task, however, is difficult for a number of reasons: transcription factors’ expression levels are often low and noisy, and many transcription factors are post-transcriptionally regulated. It is therefore useful to infer the activity of the transcription factors from the expression levels of their target genes.\ \ Results: We introduce a novel probabilistic model to infer transcription factor activities from microarray data when the structure of the regulatory network is known. The model is based on regression, retaining the computational efficiency to allow genome-wide investigation, but is rendered more flexible by sampling regression coefficients independently for each gene. This allows us to determine the strength with which a transcription factor regulates each of its target genes, therefore providing a quantitative description of the transcriptional regulatory network. The probabilistic nature of the model also means that we can associate credibility intervals to our estimates of the activities. We demonstrate our model on two yeast data sets. In both cases the network structure was obtained using Chromatine Immunoprecipitation data. We show how predictions from our model are consistent with the underlying biology and offer novel quantitative insights into the regulatory structure of the yeast cell.\ \ Availability: MATLAB code is available from http://umber.sbs.man.ac.uk/resources/puma.

  @Article{sanguinetti-chipdyno06, title = {A probabilistic dynamical model for quantitative inference of the regulatory mechanism of transcription}, journal = {Bioinformatics}, author = {Guido Sanguinetti and Magnus Rattray and Neil D. Lawrence}, pages = {1753}, year = {2006}, volume = {22}, number = {14}, month = {00}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2006-01-01-sanguinetti-chipdyno06.md}, url = {http://inverseprobability.com/publications/sanguinetti-chipdyno06.html}, abstract = {**Motivation:** Quantitative estimation of the regulatory relationship between transcription factors and genes is a fundamental stepping stone when trying to develop models of cellular processes. This task, however, is difficult for a number of reasons: transcription factors’ expression levels are often low and noisy, and many transcription factors are post-transcriptionally regulated. It is therefore useful to infer the activity of the transcription factors from the expression levels of their target genes.\ \ **Results:** We introduce a novel probabilistic model to infer transcription factor activities from microarray data when the structure of the regulatory network is known. The model is based on regression, retaining the computational efficiency to allow genome-wide investigation, but is rendered more flexible by sampling regression coefficients independently for each gene. This allows us to determine the strength with which a transcription factor regulates each of its target genes, therefore providing a quantitative description of the transcriptional regulatory network. The probabilistic nature of the model also means that we can associate credibility intervals to our estimates of the activities. We demonstrate our model on two yeast data sets. In both cases the network structure was obtained using Chromatine Immunoprecipitation data. We show how predictions from our model are consistent with the underlying biology and offer novel quantitative insights into the regulatory structure of the yeast cell.\ \ **Availability:** MATLAB code is available from .}, key = {Sanguinetti-chipdyno06}, doi = {10.1093/bioinformatics/btl154}, linkpdf = {http://bioinformatics.oxfordjournals.org/cgi/reprint/22/14/1753}, linksoftware = {https://github.com/SheffieldML/chipdyno/}, group = {gene networks,shefml,puma} }
 %T A probabilistic dynamical model for quantitative inference of the regulatory mechanism of transcription %A Guido Sanguinetti and Magnus Rattray and Neil D. Lawrence %B %C Bioinformatics %D %F sanguinetti-chipdyno06 %J Bioinformatics %P 1753--1759 %R 10.1093/bioinformatics/btl154 %U http://inverseprobability.com/publications/sanguinetti-chipdyno06.html %V 22 %N 14 %X **Motivation:** Quantitative estimation of the regulatory relationship between transcription factors and genes is a fundamental stepping stone when trying to develop models of cellular processes. This task, however, is difficult for a number of reasons: transcription factors’ expression levels are often low and noisy, and many transcription factors are post-transcriptionally regulated. It is therefore useful to infer the activity of the transcription factors from the expression levels of their target genes.\ \ **Results:** We introduce a novel probabilistic model to infer transcription factor activities from microarray data when the structure of the regulatory network is known. The model is based on regression, retaining the computational efficiency to allow genome-wide investigation, but is rendered more flexible by sampling regression coefficients independently for each gene. This allows us to determine the strength with which a transcription factor regulates each of its target genes, therefore providing a quantitative description of the transcriptional regulatory network. The probabilistic nature of the model also means that we can associate credibility intervals to our estimates of the activities. We demonstrate our model on two yeast data sets. In both cases the network structure was obtained using Chromatine Immunoprecipitation data. We show how predictions from our model are consistent with the underlying biology and offer novel quantitative insights into the regulatory structure of the yeast cell.\ \ **Availability:** MATLAB code is available from . 
 TY - CPAPER TI - A probabilistic dynamical model for quantitative inference of the regulatory mechanism of transcription AU - Guido Sanguinetti AU - Magnus Rattray AU - Neil D. Lawrence PY - 2006/01/01 DA - 2006/01/01 ID - sanguinetti-chipdyno06 SP - 1753 EP - 1759 DO - 10.1093/bioinformatics/btl154 L1 - http://bioinformatics.oxfordjournals.org/cgi/reprint/22/14/1753 UR - http://inverseprobability.com/publications/sanguinetti-chipdyno06.html AB - **Motivation:** Quantitative estimation of the regulatory relationship between transcription factors and genes is a fundamental stepping stone when trying to develop models of cellular processes. This task, however, is difficult for a number of reasons: transcription factors’ expression levels are often low and noisy, and many transcription factors are post-transcriptionally regulated. It is therefore useful to infer the activity of the transcription factors from the expression levels of their target genes.\ \ **Results:** We introduce a novel probabilistic model to infer transcription factor activities from microarray data when the structure of the regulatory network is known. The model is based on regression, retaining the computational efficiency to allow genome-wide investigation, but is rendered more flexible by sampling regression coefficients independently for each gene. This allows us to determine the strength with which a transcription factor regulates each of its target genes, therefore providing a quantitative description of the transcriptional regulatory network. The probabilistic nature of the model also means that we can associate credibility intervals to our estimates of the activities. We demonstrate our model on two yeast data sets. In both cases the network structure was obtained using Chromatine Immunoprecipitation data. We show how predictions from our model are consistent with the underlying biology and offer novel quantitative insights into the regulatory structure of the yeast cell.\ \ **Availability:** MATLAB code is available from . ER - 
 Sanguinetti, G., Rattray, M. & Lawrence, N.D.. (2006). A probabilistic dynamical model for quantitative inference of the regulatory mechanism of transcription. Bioinformatics 22(14):1753-1759