A Probabilistic Dynamical Model for Quantitative Inference of the Regulatory Mechanism of Transcription. Guido Sanguinetti, Magnus Rattray and Neil D. Lawrence. Talk plan. Overview of the problem Extending regression Introducing dynamics Modelling separately concentrations What next?.
Guido Sanguinetti, Magnus Rattray and Neil D. Lawrence
Easy to measure
Hard to measure
TFs are often low expressed, noisy
TFs are post-transcriptionally regulated
TFs interact non-trivially with each other
bmt is the transcription factor activity (TFA) of TF m at time t, monotonically linked to protein concentrations (Liao et al, Boulesteix and Strimmer, Gao et al,...)
Modify the regression model to allow different TFAs for different genes and experiments
Reduce the number of parameters by placing a prior distribution over the gene-specific TFAs. The choice of the prior distribution depends on the situation we model. E.g., for independent samples we may assume TFAs at different time points to be independent
This is equivalent to assuming TFAs vary smoothly
The likelihood can be estimated efficiently using the sparsity
of the covariance and recursion relations.
TFAs can be estimated a posteriori using Bayes’s
Theorem and moment matching
Error bars associated with each TFA are given by the squared root of the diagonal entries in the posterior covariance.
Mean TFAs can be obtained by averaging gene-specific TFAs over the target genes.
TFA for CTS1
TFA for SCW11
TFA for YER124C
TFA for YKL151C
Under a factorization assumption on the approximating
distribution q, the E-step becomes exactly solvable via
fixed point equations.
The left hand picture shows the expression level of ACE2
in the yeast cell cycle, the middle shows the inferred protein
concentration and right shows the significance of the activities.