Network Inference Using Steady- State Data and Goldbeter- Koshland - - PowerPoint PPT Presentation

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Network Inference Using Steady- State Data and Goldbeter- Koshland - - PowerPoint PPT Presentation

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Network Inference Using Steady- State Data and Goldbeter- Koshland Kinetics C.J.Oates 1 , 2 , B.T.Hennessy 3 , Y.Lu 4 , G.B.Mills 4 and S.Mukherjee 2 , 1 1 Dept. Biochemistry, Nederlands Kanker Instituut 2 Depts. Statistics & Complexity, Univ.

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SLIDE 1

Network Inference Using Steady- State Data and Goldbeter- Koshland Kinetics C.J.Oates1,2, B.T.Hennessy3, Y.Lu4, G.B.Mills4 and S.Mukherjee2,1

1 Dept. Biochemistry, Nederlands Kanker Instituut 2 Depts. Statistics & Complexity, Univ. Warwick 3 Dept. Med. Oncol., Beaumont Hospital, Dublin 4 Dept. Sys. Bio., Tex. M.D.Anderson Cancer Ctr.

c.oates@nki.nl; s.mukherjee@nki.nl

9th September, 2012

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SLIDE 2

Outline

What is network inference?

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 2 / 25

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SLIDE 3

Outline

What is network inference? Problems with the linear model

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 2 / 25

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SLIDE 4

Outline

What is network inference? Problems with the linear model Problems with steady-state data

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 2 / 25

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SLIDE 5

Outline

What is network inference? Problems with the linear model Problems with steady-state data “Kinetics-driven” inference

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 2 / 25

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SLIDE 6

Outline

What is network inference? Problems with the linear model Problems with steady-state data “Kinetics-driven” inference Preliminary results

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 2 / 25

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SLIDE 7

Problems with the linear model

✏

  • ☎ ☎ ☎
  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 3 / 25

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SLIDE 8

Problems with the linear model

The linear model in regression notation: y ✏ β0 β1x1 β2x2 ☎ ☎ ☎ βpxp ǫ

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 3 / 25

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SLIDE 9

Problems with the linear model

The linear model in regression notation: y ✏ β0 β1x1 β2x2 ☎ ☎ ☎ βpxp ǫ As usual we consider the following quantities:

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 3 / 25

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SLIDE 10

Problems with the linear model

The linear model in regression notation: y ✏ β0 β1x1 β2x2 ☎ ☎ ☎ βpxp ǫ As usual we consider the following quantities: An (observed) response y (phosphoprotein)

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 3 / 25

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SLIDE 11

Problems with the linear model

The linear model in regression notation: y ✏ β0 β1x1 β2x2 ☎ ☎ ☎ βpxp ǫ As usual we consider the following quantities: An (observed) response y (phosphoprotein) (Known) covariates x1, x2, . . . , xp (other phosphoproteins)

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 3 / 25

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SLIDE 12

Problems with the linear model

The linear model in regression notation: y ✏ β0 β1x1 β2x2 ☎ ☎ ☎ βpxp ǫ As usual we consider the following quantities: An (observed) response y (phosphoprotein) (Known) covariates x1, x2, . . . , xp (other phosphoproteins) (Unknown) regression coefficients β0, β1, β2, . . . , βp

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 3 / 25

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SLIDE 13

Problems with the linear model

The linear model in regression notation: y ✏ β0 β1x1 β2x2 ☎ ☎ ☎ βpxp ǫ As usual we consider the following quantities: An (observed) response y (phosphoprotein) (Known) covariates x1, x2, . . . , xp (other phosphoproteins) (Unknown) regression coefficients β0, β1, β2, . . . , βp There are two subsets of covariates which may be of interest:

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 3 / 25

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SLIDE 14

Problems with the linear model

The linear model in regression notation: y ✏ β0 β1x1 β2x2 ☎ ☎ ☎ βpxp ǫ As usual we consider the following quantities: An (observed) response y (phosphoprotein) (Known) covariates x1, x2, . . . , xp (other phosphoproteins) (Unknown) regression coefficients β0, β1, β2, . . . , βp There are two subsets of covariates which may be of interest: Covariates P which, together, are (in some sense) optimal for prediction of response

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 3 / 25

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SLIDE 15

Problems with the linear model

The linear model in regression notation: y ✏ β0 β1x1 β2x2 ☎ ☎ ☎ βpxp ǫ As usual we consider the following quantities: An (observed) response y (phosphoprotein) (Known) covariates x1, x2, . . . , xp (other phosphoproteins) (Unknown) regression coefficients β0, β1, β2, . . . , βp There are two subsets of covariates which may be of interest: Covariates P which, together, are (in some sense) optimal for prediction of response Covariates C such that each member of C directly causes the response, in the interventional sense (Pearl, 2009)

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 3 / 25

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SLIDE 16

Problems with the linear model

The linear model in regression notation: y ✏ β0 β1x1 β2x2 ☎ ☎ ☎ βpxp ǫ As usual we consider the following quantities: An (observed) response y (phosphoprotein) (Known) covariates x1, x2, . . . , xp (other phosphoproteins) (Unknown) regression coefficients β0, β1, β2, . . . , βp There are two subsets of covariates which may be of interest: Covariates P which, together, are (in some sense) optimal for prediction of response Covariates C such that each member of C directly causes the response, in the interventional sense (Pearl, 2009) In signalling network inference we aim to find C.

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 3 / 25

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SLIDE 17

Example: P ✘ C

Consider the simple system of structural equations: X1 :✏ ǫ1 X2 :✏ X1 0.1ǫ2 X3 :✏ X2 0.01ǫ3 where ǫj ✒ N♣0, 1q are i.i.d. Then X3 is a much better predictor of X2 than X1, even though X3 does not drive the variation in X2.

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 4 / 25

X1 X2 X3

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Biological goals are often the prioritisation of interventional experiments (e.g. knock down, knock out, etc.) rather than prediction per se.

➓ ➓ ➓ ➓ ➓

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 5 / 25

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SLIDE 19

Biological goals are often the prioritisation of interventional experiments (e.g. knock down, knock out, etc.) rather than prediction per se. However, mainstream bioinformatics approaches rely on variable selection techniques developed for prediction.

➓ ➓ ➓ ➓ ➓

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 5 / 25

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SLIDE 20

Biological goals are often the prioritisation of interventional experiments (e.g. knock down, knock out, etc.) rather than prediction per se. However, mainstream bioinformatics approaches rely on variable selection techniques developed for prediction. Commonly used procedures are

➓ Bayesian variable selection (median model is predictive optimal) ➓ L1 penalisation (lower MSE than MLE) ➓ ➓ ➓

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 5 / 25

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SLIDE 21

Biological goals are often the prioritisation of interventional experiments (e.g. knock down, knock out, etc.) rather than prediction per se. However, mainstream bioinformatics approaches rely on variable selection techniques developed for prediction. Commonly used procedures are

➓ Bayesian variable selection (median model is predictive optimal) ➓ L1 penalisation (lower MSE than MLE)

Linear regression based approaches have drawbacks in this setting:

➓ ➓ ➓

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 5 / 25

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SLIDE 22

Biological goals are often the prioritisation of interventional experiments (e.g. knock down, knock out, etc.) rather than prediction per se. However, mainstream bioinformatics approaches rely on variable selection techniques developed for prediction. Commonly used procedures are

➓ Bayesian variable selection (median model is predictive optimal) ➓ L1 penalisation (lower MSE than MLE)

Linear regression based approaches have drawbacks in this setting:

➓ Model misspecification may lead to inefficient or inconsistent

estimation (Heagerty and Kurland, 2001; Lv and Liu, 2010).

➓ ➓

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 5 / 25

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SLIDE 23

Biological goals are often the prioritisation of interventional experiments (e.g. knock down, knock out, etc.) rather than prediction per se. However, mainstream bioinformatics approaches rely on variable selection techniques developed for prediction. Commonly used procedures are

➓ Bayesian variable selection (median model is predictive optimal) ➓ L1 penalisation (lower MSE than MLE)

Linear regression based approaches have drawbacks in this setting:

➓ Model misspecification may lead to inefficient or inconsistent

estimation (Heagerty and Kurland, 2001; Lv and Liu, 2010).

➓ Variates may be highly correlated. ➓

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 5 / 25

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SLIDE 24

Biological goals are often the prioritisation of interventional experiments (e.g. knock down, knock out, etc.) rather than prediction per se. However, mainstream bioinformatics approaches rely on variable selection techniques developed for prediction. Commonly used procedures are

➓ Bayesian variable selection (median model is predictive optimal) ➓ L1 penalisation (lower MSE than MLE)

Linear regression based approaches have drawbacks in this setting:

➓ Model misspecification may lead to inefficient or inconsistent

estimation (Heagerty and Kurland, 2001; Lv and Liu, 2010).

➓ Variates may be highly correlated. ➓ Symmetry of the linear equivalence precludes identification of

underlying causal relationships (Pearl, 2009).

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 5 / 25

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SLIDE 25

Example: Symmetry of the linear equivalence

Consider the same system of structural equations: X1 :✏ ǫ1 X2 :✏ X1 0.1ǫ2 X3 :✏ X2 0.01ǫ3 where ǫj ✒ N♣0, 1q are i.i.d. X3 highly correlated with X2 Only the undirected graph is recoverable from observation.

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 6 / 25

X1 X2 X3

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SLIDE 26

Example: Nonlinearity aids causal inference

tX1, X2✉ ✏ tweight, height✉

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 7 / 25

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SLIDE 27

A bit more generally

✏ ♣

♣ q

q P P ♣ q

♣ q③t ✉

♣

♣ q③t ✉

☎ ❧♦ ♦♠♦ ♦♥ ☎ ❧♦ ♦♠♦ ♦♥q

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 8 / 25

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SLIDE 28

A bit more generally

Any nonlinearity will do, as long as the inverse isn’t physically plausible. ✏ ♣

♣ q

q P P ♣ q

♣ q③t ✉

♣

♣ q③t ✉

☎ ❧♦ ♦♠♦ ♦♥ ☎ ❧♦ ♦♠♦ ♦♥q

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 8 / 25

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SLIDE 29

A bit more generally

Any nonlinearity will do, as long as the inverse isn’t physically plausible. Consider functional relationships Xi ✏ fi♣XPa♣iq, ǫiq belonging to a functional model class fi P F. P ♣ q

♣ q③t ✉

♣

♣ q③t ✉

☎ ❧♦ ♦♠♦ ♦♥ ☎ ❧♦ ♦♠♦ ♦♥q

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 8 / 25

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SLIDE 30

A bit more generally

Any nonlinearity will do, as long as the inverse isn’t physically plausible. Consider functional relationships Xi ✏ fi♣XPa♣iq, ǫiq belonging to a functional model class fi P F. The underlying causal structure is identifiable if, for each i, each j P Pa♣iq and each XPa♣iq③tj✉, the functional fi♣XPa♣iq③tj✉, ☎ ❧♦ ♦♠♦ ♦♥

Xj

, ☎ ❧♦ ♦♠♦ ♦♥

ǫi

q is bivariate identifiable in F (Peters et al., 2011).

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 8 / 25

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SLIDE 31

Any nonlinearity will do...

r s ✏ ✂ r s ✂ r s r s

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 9 / 25

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SLIDE 32

Any nonlinearity will do...

r s ✏ ✂ r s ✂ r s r s

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 9 / 25

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SLIDE 33

Any nonlinearity will do...

This nonlinearity is captured by the Michaelis-Menten functional drproducts dt ✏ V ✂ renzymes ✂ rsubstrates K rsubstrates

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 9 / 25

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SLIDE 34

Problems with steady-state data

✏ ♣

♣ q

q ✏ ♣ q P ✾ ✏ ✁ ✾ ✏ ✁ ✏ ✏

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 10 / 25

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SLIDE 35

Problems with steady-state data

In the dynamical setting, define causality as a nontrivial dependence dXi dt ✏ fi♣XPa♣iq, U; θiq where XC ✏ ♣XcqcPC. ✾ ✏ ✁ ✾ ✏ ✁ ✏ ✏

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 10 / 25

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SLIDE 36

Problems with steady-state data

In the dynamical setting, define causality as a nontrivial dependence dXi dt ✏ fi♣XPa♣iq, U; θiq where XC ✏ ♣XcqcPC.

Example: Nonidentifiability at equilibrium

Consider the following dynamical system: ✾ X1 :✏ ✁X2 ✾ X2 :✏ ✁X1 At equilibrium x2 :✏ 0, x1 :✏ 0, so it is not possible to infer causal structure at equilibrium.

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 10 / 25

Gdyn U1 U2 X1 X2 Gequ U1 U2 X1 X2

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SLIDE 37

Faithfulness at equilibrium

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 11 / 25

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SLIDE 38

Faithfulness at equilibrium

PROBLEM: The equilibrium distribution may be unfaithful to the causal structure derived from dynamics.

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 11 / 25

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SLIDE 39

Faithfulness at equilibrium

PROBLEM: The equilibrium distribution may be unfaithful to the causal structure derived from dynamics. Intervention in an equilibrium model Gequ forces the system out of equilibrium, into Gdyn (Dash, 2003). Gdyn Gequ ˆ Gdyn ˆ Gequ

equilibrate manipulate

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 11 / 25

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SLIDE 40

Faithfulness at equilibrium

PROBLEM: The equilibrium distribution may be unfaithful to the causal structure derived from dynamics. Intervention in an equilibrium model Gequ forces the system out of equilibrium, into Gdyn (Dash, 2003). Gdyn Gequ ˆ Gdyn ˆ Gequ

equilibrate manipulate

This must be a commutative diagram. i.e. the operators “manipulation” and “equilibrate” must commute.

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 11 / 25

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SLIDE 41

Example: Faithfulness at equilibrium

Consider the following dynamical system: ✾ X1 :✏ ✁X1 ✾ X2 :✏ ✁X2 ✁ X1 Here the equilibrium relations are x1 :✏ 0, x2 :✏ ✁x1, so Gequ is faithful. ✾ ✏ ✁

  • ♣

♣ q

q ✾ ✏ ✁

  • ♣

♣ q

q

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 12 / 25

Gdyn U1 X1 X2 Gequ U1 X1 X2

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SLIDE 42

Example: Faithfulness at equilibrium

Consider the following dynamical system: ✾ X1 :✏ ✁X1 ✾ X2 :✏ ✁X2 ✁ X1 Here the equilibrium relations are x1 :✏ 0, x2 :✏ ✁x1, so Gequ is faithful. More generally, for systems of the form ✾ X1 :✏ ✁X1 g1♣XPa♣1q, U1q . . . ✾ Xp :✏ ✁Xp gp♣XPa♣pq, Upq, Gequ will be faithful to the equilibrium distribution.

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 12 / 25

Gdyn U1 X1 X2 Gequ U1 X1 X2

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SLIDE 43

A model for protein phosphorylation

U1 X1 U2 X2 X3 U3 U4 X4

P P ✏ ✁

  • ➳

P

  • ✁

➦

P

✠

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 13 / 25

Ui ✏ concentration of unphosphorylated i Xi ✏ concentration of phosphorylated i

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SLIDE 44

A model for protein phosphorylation

U1 X1 U2 X2 X3 U3 U4 X4

The rate of phosphorylation of protein p depends on the concentration of enzymes XE, E P E, and inhibitors XI, I P IE, of those enzymes: dXi dt :✏ ✁V0Xi ➳

EPE

VEXEUi Ui KE ✁ 1 ➦

IPIE XI KI

✠

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 13 / 25

Ui ✏ concentration of unphosphorylated i Xi ✏ concentration of phosphorylated i

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SLIDE 45

Such equations result in the equilibrium relations xi :✏ ➳

EPE

♣VE④V0qxEUi Ui KE ✁ 1 ➦

IPIE xI KI

✠. ♣ q⑤ ♣ q ✒ ☎ ✆ ☎ ✆ ➳

P

♣ ④ q

  • ✁

➦

P

✠ ☞ ✌ ☞ ✌

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 14 / 25

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SLIDE 46

Such equations result in the equilibrium relations xi :✏ ➳

EPE

♣VE④V0qxEUi Ui KE ✁ 1 ➦

IPIE xI KI

✠. Introducing uncertainty, we arrive at the conditional probability model log♣xiq⑤x♣iq, Ui, θi ✒ N ☎ ✆log ☎ ✆ ➳

EPE

♣VE④V0qxEUi Ui KE ✁ 1 ➦

IPIE xI KI

✠ ☞ ✌, σ2 ☞ ✌.

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 14 / 25

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SLIDE 47

Inference by MCMC sampling

E P Ei XE I P Ii,E XI Ui Xi σ V0 VE KE VI KI ✏ ↕

P

♣t ✉ ✂ q ✏ →

P

♣ q

♣t ✉ ✂

♣ qq

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 15 / 25

V ⑤K, σ, M ✒ Gamma♣2, 1④2q K⑤σ, M ✒ Gamma♣2, 1④2q σ⑤M ✒ InvGamma♣6, 1q M ✒ Uniform

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SLIDE 48

Inference by MCMC sampling

E P Ei XE I P Ii,E XI Ui Xi σ V0 VE KE VI KI A Reversible Jump sampler was constructed over the joint space of structure and parameters: S ✏ ↕

kPK

♣tk✉ ✂ Θkq, k ✏ →

EPEM♣kq

♣tE✉ ✂ IM♣kq

E

q

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 15 / 25

V ⑤K, σ, M ✒ Gamma♣2, 1④2q K⑤σ, M ✒ Gamma♣2, 1④2q σ⑤M ✒ InvGamma♣6, 1q M ✒ Uniform

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SLIDE 49

Metropolis-Hastings proposal mechanisms:

  • 1. Update parameters V , K, σ
  • 2. Update structure

(a) Add/remove a kinase E to Ei (b) Add/remove an inhibitor I P Ii,E (c) Swap a kinase (d) Swap an inhibitor

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 16 / 25

Move

  • Accept. Rate

1 55% 2(a) 7% 2(b) 10% 2(c) 7% 2(d) 9%

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SLIDE 50

Metropolis-Hastings proposal mechanisms:

  • 1. Update parameters V , K, σ
  • 2. Update structure

(a) Add/remove a kinase E to Ei (b) Add/remove an inhibitor I P Ii,E (c) Swap a kinase (d) Swap an inhibitor

0.5 1 1.5 2 2.5 3 x 10

4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Iterations Estimated Posterior Edge Probabilities

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 16 / 25

Move

  • Accept. Rate

1 55% 2(a) 7% 2(b) 10% 2(c) 7% 2(d) 9%

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SLIDE 51

Empirical results: Simulation study (Xu et al., 2010)

EGFR EGFR SOS SOS SOS C3G C3G EPAC EPAC RAS RAS RAP1 RAP1 RAF RAF RAF BRAF BRAF PKA PKA MEK MEK ERK ERK GAP PKAA EPACA Cilostamide

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 17 / 25

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SLIDE 52

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 False Positive Rate True Positive Rate Averaged Receiver Operating Characteristic Curves G.K. Kinetics Lin.Bayes Adj.Lin.Bayes Lin.LASSO Adj.Lin.LASSO

n=8,σ = 0.2

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 18 / 25

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SLIDE 53

0.4 0.5 0.6 0.7 0.8 0.9 1

  • Lin. Lasso Adj.
  • Lin. Lasso
  • Lin. Bayes Adj.
  • Lin. Bayes

G.K. Kinetics n = 8, σ = 0.2 n = 16, σ = 0.2 n = 24, σ = 0.2 n = 24, σ = 0 Area Under ROC Curve

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 19 / 25

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SLIDE 54

Empirical results: Real data

Protein Species Log(expression) Basal Luminal

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 20 / 25

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SLIDE 55

Inference for p-S6

5 10 15 20 25 30 35 40 0.5 1 G.K. Kinetics 5 10 15 20 25 30 35 40 0.5

  • Lin. Bayes

5 10 15 20 25 30 35 40 0.1 0.2

  • Lin. Bayes Adj.

5 10 15 20 25 30 35 40 0.2 0.4

  • Lin. Lasso

5 10 15 20 25 30 35 40 0.5 1

  • Lin. Lasso Adj.

Phosphorylated Proteins (ranked by scores) incorrect proteins p70S6K

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 21 / 25

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SLIDE 56

p70S6K

Inference for regulators of p-S6

G.K. Kinetics

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 22 / 25

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SLIDE 57

Target: Akt p70S6K S6 p53 G.K. Kinetics 4 3 1 8

  • Lin. Bayes

10 9 15 32

  • Lin. Bayes Adj.

14 8 8 14

  • Lin. Lasso

NA 8 NA NA

  • Lin. Lasso Adj.

NA 12 NA NA Total # Candidates: 36 37 36 37

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 23 / 25

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SLIDE 58

Summary

In this talk we have

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 24 / 25

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SLIDE 59

Summary

In this talk we have seen theoretically how kinetics may be exploited to infer causes rather than correlations

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 24 / 25

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SLIDE 60

Summary

In this talk we have seen theoretically how kinetics may be exploited to infer causes rather than correlations discussed why, for signalling, network structure ought to be identifiable from steady-state data

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 24 / 25

slide-61
SLIDE 61

Summary

In this talk we have seen theoretically how kinetics may be exploited to infer causes rather than correlations discussed why, for signalling, network structure ought to be identifiable from steady-state data seen empirical evidence in favour of “kinetics-driven” inference.

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 24 / 25

slide-62
SLIDE 62

Summary

In this talk we have seen theoretically how kinetics may be exploited to infer causes rather than correlations discussed why, for signalling, network structure ought to be identifiable from steady-state data seen empirical evidence in favour of “kinetics-driven” inference. Interesting directions for future research include

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 24 / 25

slide-63
SLIDE 63

Summary

In this talk we have seen theoretically how kinetics may be exploited to infer causes rather than correlations discussed why, for signalling, network structure ought to be identifiable from steady-state data seen empirical evidence in favour of “kinetics-driven” inference. Interesting directions for future research include systematic experimental validation in the mammalian setting

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 24 / 25

slide-64
SLIDE 64

Summary

In this talk we have seen theoretically how kinetics may be exploited to infer causes rather than correlations discussed why, for signalling, network structure ought to be identifiable from steady-state data seen empirical evidence in favour of “kinetics-driven” inference. Interesting directions for future research include systematic experimental validation in the mammalian setting expanding the repertoire of kinetic equations.

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 24 / 25

slide-65
SLIDE 65

References and Acknowledgments

1. Cho, H., Fryzlewicz, P. (2012) High dimensional variable selection via tilting, Journal of the Royal Statistical Society, Series B, to appear. 2. Dash, D. (2003) Caveats for Causal Reasoning with Equilibrium Models, PhD thesis, Intelligent Systems Program, University

  • f Pittsburgh.

3. Heagerty, P.J., Kurland, B.F. (2001) Misspecified Maximum Likelihood Estimates and Generalised Linear Mixed Models, Biometrika, 88(4), 973-985. 4. Lv, J., Liu, J.S. (2010) Model Selection Principles in Misspecified Models, Technical Report, arXiv:1005.5483v1. 5. Pearl, J. (2009) Causal inference in statistics: An overview, Statistics Surveys, 3, 96-146. 6. Peters, J. et al. (2011) Identifiability of Causal Graphs using Functional Models, Proceedings of the 27th Annual Conference: Uncertainty in Artificial Intelligence (UAI-11), 589-598. 7. Xu, T. et al. (2010) Inferring signaling pathway topologies from multiple perturbation measurements of specific biochemical species, Science Signaling, 3(113), ra20. Financial support was provided by NCI CCSG support grant CA016672, NIH U54 CA112970, UK EPSRC EP/E501311/1 and the Cancer Systems Biology Center grant from the Netherlands Organisation for Scientific Research.

Sister paper: Causal Variable Selection Using Equilibrium Relations from Nonlinear Dynamics, Workshop on Causal Structure Learning, UAI2012.

  • C. Oates (Nederlands Kanker Instituut)

Kinetics-Driven Inference September 2012 25 / 25