# Modelling transcriptional regulation using Gaussian Processes

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

in Advances in Neural Information Processing Systems 19, pp 785-792

### Errata

• Equation after equation (5): the square outside the $\exp(\gamma_k)$ term should be inside the bracket. Same applies to equation after equation (6)
Thanks to: Pei Gao and David Luengo
• Equation after equation (5): there is a missing $t$ on the second line of the equation after $D_j$.
Thanks to: Pei Gao
• Equation (10): There is a missing log on the left hand side of the equation.
Thanks to: Pei Gao
• Equation (10): The sign before log(\sigma_{ji}^2) should be positive, not negative.
Thanks to: Pei Gao
• Equation (7): We missed the mean function which should be subtracted from the genes observations, $\mathbf{x}$, to get the posterior mean prediction. It was also misimplemented in the original code, but since everything needs to be offset to fit the earlier results we didn't notice. It is correct in the later journal paper \cite{Gao:latent08}
Thanks to: Pei Gao and James Anderson

#### Abstract

Modelling the dynamics of transcriptional processes in the cell requires the knowledge of a number of key biological quantities. While some of them are relatively easy to measure, such as mRNA decay rates and mRNA abundance levels, it is still very hard to measure the active concentration levels of the transcription factor proteins that drive the process and the sensitivity of target genes to these concentrations. In this paper we show how these quantities for a given transcription factor can be inferred from gene expression levels of a set of known target genes. We treat the protein concentration as a latent function with a Gaussian Process prior, and include the sensitivities, mRNA decay rates and baseline expression levels as hyperparameters. We apply this procedure to a human leukemia dataset, focusing on the tumour repressor p53 and obtaining results in good accordance with recent biological studies.

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 %T Modelling transcriptional regulation using Gaussian Processes %A Neil D. Lawrence and Guido Sanguinetti and Magnus Rattray %B %C Advances in Neural Information Processing Systems %D %E Bernhard Schölkopf and John C. Platt and Thomas Hofmann %F lawrence-transcriptionalgp06 %I MIT Press %P 785--792 %R %U http://inverseprobability.com/publications/lawrence-transcriptionalgp06.html %V 19 %X Modelling the dynamics of transcriptional processes in the cell requires the knowledge of a number of key biological quantities. While some of them are relatively easy to measure, such as mRNA decay rates and mRNA abundance levels, it is still very hard to measure the active concentration levels of the transcription factor proteins that drive the process and the sensitivity of target genes to these concentrations. In this paper we show how these quantities for a given transcription factor can be inferred from gene expression levels of a set of known target genes. We treat the protein concentration as a latent function with a Gaussian Process prior, and include the sensitivities, mRNA decay rates and baseline expression levels as hyperparameters. We apply this procedure to a human leukemia dataset, focusing on the tumour repressor p53 and obtaining results in good accordance with recent biological studies. 
 TY - CPAPER TI - Modelling transcriptional regulation using Gaussian Processes AU - Neil D. Lawrence AU - Guido Sanguinetti AU - Magnus Rattray BT - Advances in Neural Information Processing Systems PY - 2007/01/01 DA - 2007/01/01 ED - Bernhard Schölkopf ED - John C. Platt ED - Thomas Hofmann ID - lawrence-transcriptionalgp06 PB - MIT Press SP - 785 EP - 792 L1 - ftp://ftp.dcs.shef.ac.uk/home/neil/gpsim.pdf UR - http://inverseprobability.com/publications/lawrence-transcriptionalgp06.html AB - Modelling the dynamics of transcriptional processes in the cell requires the knowledge of a number of key biological quantities. While some of them are relatively easy to measure, such as mRNA decay rates and mRNA abundance levels, it is still very hard to measure the active concentration levels of the transcription factor proteins that drive the process and the sensitivity of target genes to these concentrations. In this paper we show how these quantities for a given transcription factor can be inferred from gene expression levels of a set of known target genes. We treat the protein concentration as a latent function with a Gaussian Process prior, and include the sensitivities, mRNA decay rates and baseline expression levels as hyperparameters. We apply this procedure to a human leukemia dataset, focusing on the tumour repressor p53 and obtaining results in good accordance with recent biological studies. ER - 
 Lawrence, N.D., Sanguinetti, G. & Rattray, M.. (2007). Modelling transcriptional regulation using Gaussian Processes. Advances in Neural Information Processing Systems 19:785-792