1. Nonparametric Bayesian inference for perturbed and orthologous gene regulatory networks
Christopher A. Penfold
Vicky Buchanan-Wollaston
Katherine J. Denby
And
David L. Wild
Published in Bioinformatics

2. Motivation
Reverse engineering of Gene Regulation Networks– interesting area of research
Previous assumptions– multiple time series data assumes identical topology
Whereas as in reality different sets of transcription factors (but overlapping) are expected to bind in different conditions
How to handle the information from this somewhat diverse set of multiple datasets?

3. Some researchers used non-parametric Bayesian learning strategies  but for those techniques to be computationally feasible the no. of transcription factors (TFs) , that can bind to the promoter region of a gene, need to be limited.
However, recent studies a large no. of TFs have the potential to bind to any gene

4. However, it is noticed that the no
However, it is noticed that the no. of TFs binding under some specific conditions are fewer.
So, it is of interest to find this subset of TFs w.r.t each specific condition applied which can result in a different GRN.

5. Causal Structure Identification
The CSI algorithm (Klemm, 2008; Penfold and Wild, 2011) and related approaches (Äijö and Lähdesmäki, 2009) have previously been used to reverse engineer GRNs and shown to perform well
The discrete-time version of CSI assumes that the mRNA expression level of a particular gene in a larger set, i∈G, as:

6. where xi(t) represents the expression level of gene i at time t, Pa(i)⊆G represents the genes encoding for TFs binding the promoter regions of gene i (parents of gene i) with xPa(i)(t) the vector expression level of those parents at time t, and f (·) represents some unknown (non-linear) function capturing the dynamics of the system.

7. y and matrix X :

8. Usually the parent genes are not known as a prior so, that data is used to infer them as follows:
where T ⊆G represents the set of all transcription
factors and θk the set of hyperparameters for the k-th parental set.
The distribution depends on the values of the parameters for which the Expectation Maximization is being used

9. Finally, a distribution over causal network structures, P(M), can be assembled from the distribution over individual parental sets, constituting the CSI algorithm:

10. Hierarchical modelling for CSI
In this framework, the joint distribution for all model parameters conditioned on the data is factorised as:

12. The conditional distribution for the parents of gene i in dataset j given the hyperparent is chosen to correspond to a Gibbs distribution:

13. Again, a network structure can be assembled from the parent distributions for each node, with a hypernetwork assembled from the the distributions over hyperparents:

14. Results

15. Combining hierarchical modelling and yeast one-hybrid
YIH used to identify the genes capable of binding to the promoter region .
In this study a gene RD29A was used and previous study suggests 9 such genes.
However, in this study, time series data was collected using 6 timestamps under different conditions.

17. Thank you!