Time-Variable Networks in Candida Glabrata

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

Transcript of Time-Variable Networks in Candida Glabrata

Time-Variable Gene Regulation Networks in Candida Glabrata

Michael P.H. Stumpf & Thomas Thorne

Theoretical Systems Biology Group, Division of MolecularBiosciences, Imperial College London

12th June 2011

Networks: Mapping Processes and Understanding

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Time-Variable Networks in Candida Glabrata Stumpf&Thorne 1 of 11

Biology is Dynamic — Networks Change with Time

A

AP

AP

B

• Inferred regulatory network structures represent correlations rather than direct interactions.

• Gene products may require activation and need to be transported into the nucleus toinfluence regulation; or complexes formed by signalling cascades may be required toactivate transcription.

• Many factors that are not a part of a traditional regulatory network model can also influenceregulatory interactions.

• These relationships may change depending on external signals or other factors.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 2 of 11

Biology is Dynamic — Networks Change with Time

A AP

AP

B

• Inferred regulatory network structures represent correlations rather than direct interactions.

• Gene products may require activation and need to be transported into the nucleus toinfluence regulation; or complexes formed by signalling cascades may be required toactivate transcription.

• Many factors that are not a part of a traditional regulatory network model can also influenceregulatory interactions.

• These relationships may change depending on external signals or other factors.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 2 of 11

Biology is Dynamic — Networks Change with Time

A

AP

AP

B

• Inferred regulatory network structures represent correlations rather than direct interactions.

• Gene products may require activation and need to be transported into the nucleus toinfluence regulation; or complexes formed by signalling cascades may be required toactivate transcription.

• Many factors that are not a part of a traditional regulatory network model can also influenceregulatory interactions.

• These relationships may change depending on external signals or other factors.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 2 of 11

Biology is Dynamic — Networks Change with Time

A

AP

AP

B

• Inferred regulatory network structures represent correlations rather than direct interactions.

• Gene products may require activation and need to be transported into the nucleus toinfluence regulation; or complexes formed by signalling cascades may be required toactivate transcription.

• Many factors that are not a part of a traditional regulatory network model can also influenceregulatory interactions.

• These relationships may change depending on external signals or other factors.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 2 of 11

Capturing Biological Dynamics — Changepoint Models forNetworks

• We can include hidden factors that my change the regulatory interactions taking place in our model byallowing 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 differentnetwork 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 SystemsBiology, 4:130, 2010.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 3 of 11

Capturing Biological Dynamics — Changepoint Models forNetworks

• We can include hidden factors that my change the regulatory interactions taking place in our model byallowing 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 differentnetwork 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 SystemsBiology, 4:130, 2010.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 3 of 11

The Chinese Restaurant Process

. . .

θ1 θ2 θ3 θ4

H

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

The Chinese Restaurant Process

. . .

θ1 θ2 θ3 θ4

H

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

The Chinese Restaurant Process

. . .

θ1 θ2 θ3 θ4

H

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

The Chinese Restaurant Process

. . .

θ1 θ2 θ3 θ4

H

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

The Chinese Restaurant Process

. . .

θ1 θ2 θ3 θ4

H

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

What We Want to Know is Often Not Measured: Hidden MarkovModels

• Here we measure transcriptomic data, whereas the action is all due to proteins andtheir interactions among themselves and with DNA/RNA.

• We measure mRNA expression (yi ) which is influenced by a network (si ) that is notor cannot be observed directly.

• We allow the network to change and learn this change from the observed data.

s1

y1

θs1

πs1

s2

y2

θs2

s3

y3

θs3

. . . sT

. . . yT

θsT

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 5 of 11

What We Want to Know is Often Not Measured: Hidden MarkovModels

• Here we measure transcriptomic data, whereas the action is all due to proteins andtheir interactions among themselves and with DNA/RNA.

• We measure mRNA expression (yi ) which is influenced by a network (si ) that is notor cannot be observed directly.

• We allow the network to change and learn this change from the observed data.

s1

y1

θs1

πs1

s2

y2

θs2

s3

y3

θs3

. . . sT

. . . yT

θsT

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 5 of 11

What We Want to Know is Often Not Measured: Hidden MarkovModels

• Here we measure transcriptomic data, whereas the action is all due to proteins andtheir interactions among themselves and with DNA/RNA.

• We measure mRNA expression (yi ) which is influenced by a network (si ) that is notor cannot be observed directly.

• We allow the network to change and learn this change from the observed data.

s1

y1

θs1

πs1

s2

y2

θs2

s3

y3

θs3

. . . sT

. . . yT

θsT

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 5 of 11

Systems at Different Times are Related: The Chinese RestaurantFranchise

α

θ2 θ1 θ1 θ3 θ2 θ2

θ1 θ2 θ3 θ ′ ∼ H

γ

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 6 of 11

Systems at Different Times are Related: The Chinese RestaurantFranchise

α

θ2 θ1 θ1 θ3 θ2 θ2

θ1 θ2 θ3 θ ′ ∼ H

γ

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 6 of 11

Systems at Different Times are Related: The Chinese RestaurantFranchise

α

θ2 θ1 θ1 θ3 θ2 θ2

θ1 θ2 θ3 θ ′ ∼ H

γ

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 6 of 11

Systems at Different Times are Related: The Chinese RestaurantFranchise

H

γ β

α πi,·

s0 s1 s2 sn

y1 y2 yn

• Base measure H• Shared state distribution β• Transition distributions πi,·

• State sequence s0, . . . , sn

• Observations y1, . . . , yn

Chinese restaurant franchise analogyStates correspond to restaurants, dishes served correspond to transitions to one of the shared set ofstates and customers to observations

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 6 of 11

Biological Systems do Not Change Wildly (Assumption!): HiddenStates are Correlated

s1 s2 s3 s4 s5 s6 s7 s8 s9

Observations y1 y2 y3 y4 y5 y6 y7 y8 y9

Time point 1 2 3 4 5 6 7 8 9Time-Variable Networks in Candida Glabrata Stumpf&Thorne 7 of 11

Regulatory Interactions During the S. cerevisae Cell Cycle

Expression data for S. cerevisae over two cell cycles, at 25 time points.

1 2

3 4

Fre

quen

cy

0 10 20 30 40 50 60 70 80 90 105 120

0.0

0.2

0.4

0.6

0.8

1.0

T. Pramila, W. Wu, S. Miles, W.S. Noble et al., The Forkhead transcription factor Hcm1 regulates chromosome segregation genes and fills the S-phase gap inthe transcriptional circuitry of the cell cycle. Genes Dev Aug 15;20(16):2266-78, 2006.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 8 of 11

Candida glabrata osmotic stress response (0.5M NaCl)

SPT16

FPS1

EMC6

SMX3

ISD11

MKS1

CAGL0K04235g

FPS1

VMA22 SRB8

SMX3

CAGL0H00704g

ISD11

BUD31 CAGL0K06127g

YJR085C

CUE22

1

Time point (mins)

Fre

quen

cy

0.0

0.2

0.4

0.6

0.8

1.0

15 30 60 90 120 150 180 240

Two distinct regulatoryarchitectures appear tocontrol the expression of thegenes involved in osmoticstress response in C.glabrata.

Temporal DependenciesT<30min:

ISD11→ SMX3

T>30min:

ISD11→ BUD31

SMX3→ BUD31

Interactions change with timeand may be contingent onpast interactions.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 9 of 11

Candida glabrata osmotic stress response (0.5M NaCl)

SPT16

FPS1

EMC6

SMX3

ISD11

MKS1

CAGL0K04235g

FPS1

VMA22 SRB8

SMX3

CAGL0H00704g

ISD11

BUD31 CAGL0K06127g

YJR085C

CUE22

1

Time point (mins)

Fre

quen

cy

0.0

0.2

0.4

0.6

0.8

1.0

15 30 60 90 120 150 180 240

Two distinct regulatoryarchitectures appear tocontrol the expression of thegenes involved in osmoticstress response in C.glabrata.

Temporal DependenciesT<30min:

ISD11→ SMX3

T>30min:

ISD11→ BUD31

SMX3→ BUD31

Interactions change with timeand may be contingent onpast interactions.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 9 of 11

Capturing Biological Dynamics

From Stamp-Collecting to Dynamics to Insights

All science iseither physics orstamp collecting.

Ernest Rutherford.

• Temporally resolved data sheds light on transient dynamics. The transientdynamics in turn determine the ultimate outcome.

• It is hard to see what can be learned from data that is not temporally resolved.Many of the results have only anecdotal value compared to time-course data.

• If resources are limited then we would suggest generating data at additionaltime-points over generating replicate data: we can use statistical methods to assessand cope with noise but have no way of “guessing” transient behaviour.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 10 of 11

Capturing Biological Dynamics

From Stamp-Collecting to Dynamics to Insights

All science iseither physics orstamp collecting.

Ernest Rutherford.

• Temporally resolved data sheds light on transient dynamics. The transientdynamics in turn determine the ultimate outcome.

• It is hard to see what can be learned from data that is not temporally resolved.Many of the results have only anecdotal value compared to time-course data.

• If resources are limited then we would suggest generating data at additionaltime-points over generating replicate data: we can use statistical methods to assessand cope with noise but have no way of “guessing” transient behaviour.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 10 of 11

Capturing Biological Dynamics

From Stamp-Collecting to Dynamics to Insights

All science iseither physics orstamp collecting.

Ernest Rutherford.

• Temporally resolved data sheds light on transient dynamics. The transientdynamics in turn determine the ultimate outcome.

• It is hard to see what can be learned from data that is not temporally resolved.Many of the results have only anecdotal value compared to time-course data.

• If resources are limited then we would suggest generating data at additionaltime-points over generating replicate data: we can use statistical methods to assessand cope with noise but have no way of “guessing” transient behaviour.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 10 of 11

Capturing Biological Dynamics

From Stamp-Collecting to Dynamics to Insights

All science iseither physics orstamp collecting.

Ernest Rutherford.

• Temporally resolved data sheds light on transient dynamics. The transientdynamics in turn determine the ultimate outcome.

• It is hard to see what can be learned from data that is not temporally resolved.Many of the results have only anecdotal value compared to time-course data.

• If resources are limited then we would suggest generating data at additionaltime-points over generating replicate data: we can use statistical methods to assessand cope with noise but have no way of “guessing” transient behaviour.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 10 of 11

Capturing Biological Dynamics

From Stamp-Collecting to Dynamics to Insights

All science iseither physics orstamp collecting.

Ernest Rutherford.

• Temporally resolved data sheds light on transient dynamics. The transientdynamics in turn determine the ultimate outcome.

• It is hard to see what can be learned from data that is not temporally resolved.Many of the results have only anecdotal value compared to time-course data.

• If resources are limited then we would suggest generating data at additionaltime-points over generating replicate data: we can use statistical methods to assessand cope with noise but have no way of “guessing” transient behaviour.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 10 of 11

Capturing Biological Dynamics

From Stamp-Collecting to Dynamics to Insights

All science iseither physics orstamp collecting.

Ernest Rutherford.

• Temporally resolved data sheds light on transient dynamics. The transientdynamics in turn determine the ultimate outcome.

• It is hard to see what can be learned from data that is not temporally resolved.Many of the results have only anecdotal value compared to time-course data.

• If resources are limited then we would suggest generating data at additionaltime-points over generating replicate data: we can use statistical methods to assessand cope with noise but have no way of “guessing” transient behaviour.

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 10 of 11

Acknowledgements

Imperial College London

• Thomas Thorne

• Justina Zurauskine• Paul Kirk• Daniel Silk

Exter University• Andrew McDonagh• Melanie Puttnam• Lauren Ames• Ken Haynes

Time-Variable Networks in Candida Glabrata Stumpf&Thorne 11 of 11