lecture21

							CSCI5461: Functional Genomics, Systems Biology and Bioinformatics




                    Inferring transcriptional
                  networks using Bayesian
                                     models
                        Rui Kuang and Chad Myers

            Department of Computer Science and Engineering
                        University of Minnesota
Announcements
 1-2 pg. project proposals due 4/8!
(come talk to us if you have any questions
  about formulating a plan)
 Email me by today if you would like us to
  organize a group for you
 Get started on your projects ASAP
Outline for today
 Wrap-up of function prediction paper
 Background on transcriptional regulatory
  networks
 Brief introduction to Bayesian networks
 Paper discussion: inferring transcriptional
  regulatory networks from expression data
  using Bayesian networks
 A reminder about gene transcription
                    Transcription
                       Factors
                                                     RNA polymerase
                      (proteins)
                                                          (protein)

                     C T A A T G T . . .
5’                                                                     3’
3’                                                                     5’
                     G A T T A C A . . .
Binding sites

     Transcription factors recognize transcription factor binding sites and bind
     to them, forming a complex.

     RNA polymerase binds the complex.


                      Protein-DNA interaction!
                                                                        (eukaryotes)
            Gene Transcription
               Transcription
                  Factors
                                     RNA polymerase
                (proteins)
                                        (protein)

               C T A A T G T . . .
5’                                                    3’
3’                                                    5’
               G A T T A C A . . .


     Transcription factors recognize transcription
     factor binding sites and bind to them, forming a
     complex.

     RNA polymerase binds the complex.
                                       (eukaryotes)
Gene Transcription



5’                                       3’
3’                                       5’




     The two strands are separated


                               (eukaryotes)
Gene Transcription



5’                                        3’
3’                                        5’




     An RNA copy of the 5’→3’ sequence is
     created from the 3’→5’ template until a
     termination sequence is reached
                                (eukaryotes)
Regulatory Networks
Can we learn these networks from expression data?




               ?
A different kind of network:
Bayesian networks
• Probabilistic graphical models that capture dependence relations
between random variables

• Can represent prior knowledge/belief

• Can be learned from data or constructed by experts in the field

• Two general uses:

    o Make inferences about variables we can’t observe

    o Framework for automatic structure/dependence learning from
    observed data
The sprinkler Bayes net
                                Prior probability that it is cloudy




                                         Conditional probability that
• What are the conditional
                                         rains when it’s cloudy
independence relations
implied?
                             Probability that grass is wet when
• What is the joint          the sprinkler is off and it rains
probability?
    What can we do with Bayes nets?




   We can compute the likelihood of observing some combination of events (i.e.)
    P(cloudy (C), sprinkler’s on (S), raining (R))

            P(C,S, R)  P(C) P(S | C) P(R | S, C)  P(C) P(S | C) P(R | C)  .5 * .1* .4  .02
    What can we do with Bayes nets?

We can also make inferences
about the most likely states
given partial evidence

(e.g. say the grass is wet, and
we want to know which is more
likely: it’s raining or the
sprinkler’s on? )




                                  Remember:

                                  P(A|B) = P(A,B) / P(B)
Continuous vs. discrete nodes
  Discrete               Continuous


                               A               B



                                        C

                         P(C A, B) ~ N (c0  c1a  c2b, 2 )



             (hybrid models also possible)
Applying Bayes nets to
transcriptional network inference
               Exp. 1   ..........   Exp. P   Gene 4     Gene 2        Gene 3
     Gene 1    0.78     ..........   0.50

     Gene 2    0.73     ..........   0.09

     Gene 3    0.99     ..........   0.56
                                                                           Gene 1
     .....     .....    ..........   .....
                                               Gene 5
     Gene N    0.28     ..........   0.89
                                                                  Gene 6
              Microarray data                     Transcriptional regulatory
                                                           network

 Challenges:

 • We don’t know either the structure or the conditional probabilities!

 • Expression data are noisy

 • Even if expression data were perfect, they don’t capture the complete
 picture (e.g. post-transcriptional/translational regulation)