Talk given in the "Integrative Genomics" session at the 18th Congress of the International Society for Human and Animal Mycology

1. Time-Variable Gene Regulation Networks in Candida Glabrata
Michael P.H. Stumpf & Thomas Thorne
Theoretical Systems Biology Group, Division of Molecular
Biosciences, Imperial College London
12th June 2011

2. Networks: Mapping Processes and Understanding
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3 3 Erkner <> Ostkreuz rU Spindlersfeld <> Schöneweide (nur Mo-Fr) (only Mon-Fri) 3 3 Nollendorfplatz <> Krumme Lanke 7 7 Rathaus Spandau <> Rudow S+U-Bahn-Nachtverkehr 2 7 S+U-Bahn nighttime traffic 2 7
rQ rQ Ring > im Uhrzeigersinn 5 5 Strausberg Nord <> Spandau 9 Flughafen Berlin-Schönefeld <> Pankow 4 Nollendorfplatz <> Innsbrucker Platz 8 8 Wittenau <> Hermannstraße nur Fr/Sa ca. 0:30-5:30 Uhr Fri/Sat ca. 0:30 am-5:30 am
rW rW Ring > gegen Uhrzeigersinn 7 7 Ahrensfelde <> Potsdam Hbf 9 Flughafen Berlin-Schönefeld <> Treptower Park 5 5 Hönow <> Alexanderplatz 9 9 Osloer Straße <> Rathaus Steglitz Sa/So und vor Feiertagen ca. 0:30-7:00 Uhr Sat/Sun and prior to holidays ca. 0:30 am-7:00 am © 2011 Kartographie Berliner Verkehrsbetriebe (BVG)
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 1 of 11

3. Biology is Dynamic — Networks Change with Time
A B
• Inferred regulatory network structures represent correlations rather than direct interactions.
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 2 of 11

4. Biology is Dynamic — Networks Change with Time
P
A A
• Inferred regulatory network structures represent correlations rather than direct interactions.
• Gene products may require activation and need to be transported into the nucleus to
influence regulation; or complexes formed by signalling cascades may be required to
activate transcription.
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 2 of 11

5. Biology is Dynamic — Networks Change with Time
P
A A
• Inferred regulatory network structures represent correlations rather than direct interactions.
• Gene products may require activation and need to be transported into the nucleus to
influence regulation; or complexes formed by signalling cascades may be required to
activate transcription.
• Many factors that are not a part of a traditional regulatory network model can also influence
regulatory interactions.
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 2 of 11

6. Biology is Dynamic — Networks Change with Time
P
A A B
• Inferred regulatory network structures represent correlations rather than direct interactions.
• Gene products may require activation and need to be transported into the nucleus to
influence regulation; or complexes formed by signalling cascades may be required to
activate transcription.
• Many factors that are not a part of a traditional regulatory network model can also influence
regulatory interactions.
• These relationships may change depending on external signals or other factors.
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 2 of 11

7. Capturing Biological Dynamics — Changepoint Models for
Networks
• We can include hidden factors that my change the regulatory interactions taking place in our model by
allowing the regulatory network structure to vary between timepoints and/or conditions.
• In changepoint models the time series is divided into a number of segments, allowing a different
network structure in each.
• Using Bayesian inference it is possible to infer the posterior distribution of changepoint positions.
`
S. Lebre, J. Becq, F. Devaux, M. P. H. Stumpf, G. Lelandais, Statistical inference of the time-varying structure of gene-regulation networks. BMC Systems
Biology, 4:130, 2010.
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 3 of 11

8. Capturing Biological Dynamics — Changepoint Models for
Networks
• We can include hidden factors that my change the regulatory interactions taking place in our model by
allowing the regulatory network structure to vary between timepoints and/or conditions.
• In changepoint models the time series is divided into a number of segments, allowing a different
network structure in each.
• Using Bayesian inference it is possible to infer the posterior distribution of changepoint positions.
Time point 1 2 3 4 5 6 7 8 9 10
`
S. Lebre, J. Becq, F. Devaux, M. P. H. Stumpf, G. Lelandais, Statistical inference of the time-varying structure of gene-regulation networks. BMC Systems
Biology, 4:130, 2010.
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 3 of 11

9. The Chinese Restaurant Process
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 4 of 11

10. The Chinese Restaurant Process
θ1 θ2 θ3 θ4
Analogy for the Dirichlet process due to Pitman and Dubins
´ ´ ´ ´
D. Aldous, Exchangeability and Related Topics. In l’Ecole d’ete de probabilites de Saint-Flour, XIII, pages 1-198. 1983
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 4 of 11

11. The Chinese Restaurant Process
θ1 θ2 θ3 θ4
H
Analogy for the Dirichlet process due to Pitman and Dubins
´ ´ ´ ´
D. Aldous, Exchangeability and Related Topics. In l’Ecole d’ete de probabilites de Saint-Flour, XIII, pages 1-198. 1983
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 4 of 11

12. The Chinese Restaurant Process
θ1 θ2 θ3 θ4 θ5
Analogy for the Dirichlet process due to Pitman and Dubins
´ ´ ´ ´
D. Aldous, Exchangeability and Related Topics. In l’Ecole d’ete de probabilites de Saint-Flour, XIII, pages 1-198. 1983
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 4 of 11

13. The Chinese Restaurant Process
...
θ1 θ2 θ3 θ4 θ5
H
Analogy for the Dirichlet process due to Pitman and Dubins
´ ´ ´ ´
D. Aldous, Exchangeability and Related Topics. In l’Ecole d’ete de probabilites de Saint-Flour, XIII, pages 1-198. 1983
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 4 of 11

14. What We Want to Know is Often Not Measured: Hidden Markov
Models
• Here we measure transcriptomic data, whereas the action is all due to proteins and
their interactions among themselves and with DNA/RNA.
• We measure mRNA expression (yi ) which is influenced by a network (si ) that is not
or cannot be observed directly.
• We allow the network to change and learn this change from the observed data.
π s1
s1
θs1
y1
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 5 of 11

15. What We Want to Know is Often Not Measured: Hidden Markov
Models
• Here we measure transcriptomic data, whereas the action is all due to proteins and
their interactions among themselves and with DNA/RNA.
• We measure mRNA expression (yi ) which is influenced by a network (si ) that is not
or cannot be observed directly.
• We allow the network to change and learn this change from the observed data.
s1 s2
θs1 θs2
y1 y2
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 5 of 11

16. What We Want to Know is Often Not Measured: Hidden Markov
Models
• Here we measure transcriptomic data, whereas the action is all due to proteins and
their interactions among themselves and with DNA/RNA.
• We measure mRNA expression (yi ) which is influenced by a network (si ) that is not
or cannot be observed directly.
• We allow the network to change and learn this change from the observed data.
s1 s2 s3 ... sT
θs1 θs2 θs3 θsT
y1 y2 y3 ... yT
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 5 of 11

17. Systems at Different Times are Related: The Chinese Restaurant
Franchise
θ2 θ1 θ1 θ3 θ2 θ2
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 6 of 11

18. Systems at Different Times are Related: The Chinese Restaurant
Franchise
θ2 θ1 θ1 θ3 θ2 θ2
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 6 of 11

19. Systems at Different Times are Related: The Chinese Restaurant
Franchise
α
θ2 θ1 θ1 θ3 θ2 θ2
γ
θ1 θ2 θ3 θ ∼H
Time-Variable Networks in Candida Glabrata Stumpf&Thorne 6 of 11