A Search-Based Approach for Bayesian Inference of the T -cell - - PowerPoint PPT Presentation

SLIDE 1

A Search-Based Approach for Bayesian Inference of the T

• cell Signaling Network

Mitchell Koch

• Dept. of Computer Science

Rice University mkoch@rice.edu

BIOT

• 2007

Bradley Broom

• Dept. of Bioinf. & Comp. Biology

M.D. Anderson Cancer Center bmbroom@mdanderson.org Devika Subramanian

• Dept. of Computer Science

Rice University devika@rice.edu

SLIDE 2

Signaling & metabolic networks

• Consist of interacting

proteins, genes and, small molecules

• Underlie the major

functions of living cells

• Goal: learn these

networks from experimental data, particularly how they are altered in diseased cells

SLIDE 3

Challenges

• The cell is a complex stochastic domain:

signal transduction, metabolic and regulatory pathways all interconnected.

• We only observe mRNA levels and/or

protein levels.

• Measurements are noisy.
• Limited amount of data.

SLIDE 4

Building models from data

A B C

HIGH HIGH … LOW MED … HIGH LOW …

A B C

SLIDE 5

Bayesian network

A B C

P(BHI) = 0.8

B P(AHI)

HIGH 0.9 LOW 0.2

A B P(CHI)

HIGH HIGH 0.99 HIGH LOW 0.9 LOW HIGH 0.5 LOW LOW 0.1

SLIDE 6

Learning Bayesian networks

• Scoring function
• Impossible to find highest scoring

network

• Super-exponential number of possible

networks

• Use heuristic search procedures

SLIDE 7

Identifying Significant Edges

• Very many high-scoring networks
• Each over-fitted to data
• Find edges that occur frequently in good

networks

• Two approaches:
• Markov Chain Monte Carlo (MCMC)
• Bootstrap aggregation
• Select edges occurring above threshold t

SLIDE 8

A Search-Based Approach for Bayesian Inference of the T

• cell Signaling Network

SLIDE 9

Sachs, et al.

Science, 2005 MCMC (Markov Chain Monte Carlo) technique

Our scenario is akin to the magnetic furnace model proposed by Axford and McKenzie (14–16) and to ideas invoking reconnection of mesoscale loops (38, 39). We adopt from the furnace model the idea that reconnection plays a major role, as it will release plasma, set free magnetic energy, and produce Alfve ´n waves. However, our model

• f the nascent solar wind is intrinsically 3-D,

and the magnetic field geometry is derived

• empirically. The plasma is accelerated in the

funnel above a critical height of 5 Mm but

• riginates below from the neighboring loops.

The initial heating of the solar wind plasma is achieved in the side loops. References and Notes

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Heliosphere, J. R. Jokipii, C. P. Sonett, M. S. Giampapa,

• Eds. (Arizona University Press, Tucson, 1997), pp. 31–66.
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L5 (2003).

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424, 1025 (2004).

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(2002).

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428, 629 (2004).

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596, 621 (2003).

• 31. J. P. Delaboudinie

`re et al., Solar Phys. 162, 291 (1995).

• 32. Materials and methods are available as supporting

material on Science Online.

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˚. Nordlund, Astrophys. J. 617, L85 (2004).

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• Astron. Astrophys. 346, 285 (1999).
• 37. T. J. M. Boyd and J. J. Sanderson, Plasma Dynamics

(Thomas Nelson and Sons, London, 1969).

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Wang, Astron. Astrophys. 316, 355 (1996).

• 39. L. A. Fisk, J. Geophys. Res. 108, 1157 (2003).
• 40. The National Natural Science Foundation of China

supported C.-Y.T., C.Z., and L. Z. under projects with the contract nos. 40336053, 40174045 and 40436015; J.-X.Wang, contract no. 10233050; and L.-D.X., contract no. 40436015. The foundation Major Project of National Basic Research supported C.-Y.T., C.Z., L.-D.X., L. Z., and J.-X.W. under contract

• no. G-200078405. C.-Y.T. is supported by the Beijing

Education Project XK100010404. The SUMER project is financially supported by DLR, CNES, NASA, and the ESA PRODEX program (Swiss contribution). SUMER, EIT, and MDI are instruments on SOHO, an ESA and NASA mission. We thank the teams of MDI and EIT for providing the magnetic field data and the context image. Supporting Online Material www.sciencemag.org/cgi/content/full/308/5721/519/ DC1 Materials and Methods

• Fig. S1

References 6 January 2005; accepted 1 March 2005 10.1126/science.1109447

Causal Protein-Signaling Networks Derived from Multiparameter Single-Cell Data

Karen Sachs,1* Omar Perez,2* Dana Pe’er,3* Douglas A. Lauffenburger,1. Garry P. Nolan2. Machine learning was applied for the automated derivation of causal influ- ences in cellular signaling networks. This derivation relied on the simultaneous measurement of multiple phosphorylated protein and phospholipid components in thousands of individual primary human immune system cells. Perturbing these cells with molecular interventions drove the ordering of connections between pathway components, wherein Bayesian network computational methods auto- matically elucidated most of the traditionally reported signaling relationships and predicted novel interpathway network causalities, which we verified ex-

• perimentally. Reconstruction of network models from physiologically relevant

primary single cells might be applied to understanding native-state tissue signal- ing biology, complex drug actions, and dysfunctional signaling in diseased cells. Extracellular cues trigger a cascade of infor- mation flow, in which signaling molecules become chemically, physically, or location- ally modified; gain new functional capabil- ities; and affect subsequent molecules in the cascade, culminating in a phenotypic cellular

• response. Mapping of signaling pathways typ-

ically has involved intuitive inferences arising from the aggregation of studies of individual pathway components from diverse experimen- tal systems. Although pathways are often con- ceptualized as distinct entities responding to specific triggers, it is now understood that in- terpathway cross-talk and other properties of networks reflect underlying complexities that cannot be explained by the consideration of individual pathways or model systems in isola-

• tion. To properly understand normal cellular

responses and their potential disregulation in disease, a global multivariate approach is re- quired (1). Bayesian networks (2), a form of graphical models, have been proffered as a promising framework for modeling complex systems such as cell signaling cascades, be- cause they can represent probabilistic depen- dence relationships among multiple interacting components (3–5). Bayesian network models illustrate the effects of pathway components on each other (that is, the dependence of each biomolecule in the pathway on other biomol- ecules) in the form of an influence diagram. These models can be automatically derived from experimental data through a statistically founded computational procedure termed net- work inference. Although the relationships are statistical in nature, they can sometimes be in- terpreted as causal influence connections when interventional data are used; for example, with the use of kinase-specific inhibitors (6, 7). There are several attractive properties of Bayesian networks for the inference of sig- naling pathways from biological data sets. Bayesian networks can represent complex stochastic nonlinear relationships among mul- tiple interacting molecules, and their proba- bilistic nature can accommodate noise that is inherent to biologically derived data. They can describe direct molecular interactions as well as indirect influences that proceed through additional unobserved components, a property crucial for discovering previously unknown effects and unknown components. Therefore, very complex relationships that likely exist in 1Biological Engineering Division, Massachusetts Insti- tute of Technology (MIT), Cambridge, MA 02139, USA. 2Stanford University School of Medicine, The Baxter Laboratory of Genetic Pharmacology, Department of Microbiology and Immunology, Stanford, CA 94305,

• USA. 3Harvard Medical School, Department of Genet-

ics, Boston, MA 02115, USA. *These authors contributed equally to this work. .To whom correspondence should be addressed. E-mail: lauffen@mit.edu (D.A.L.); gnolan@stanford.edu (G.P.N.) R E S E A R C H A R T I C L E S www.sciencemag.org SCIENCE VOL 308 22 APRIL 2005 523

• n June 1, 2007

www.sciencemag.org Downloaded from

CORRECTED 19 AUGUST 2005; SEE LAST PAGE

SLIDE 10

Processing pipeline

SLIDE 11

(Source: Eaton & Murphy, 2007)

SLIDE 12

PKC Raf PKA Jnk Plcγ PIP3 Mek PIP2 Erk Akt P38

Biologically Accepted Network

(Source: Sachs, et al., 2005)

SLIDE 13

(20 links) (15 links) Accepted Network Consensus Network

PKC Raf PKA Jnk Plcγ PIP3 Mek PIP2 Erk Akt P38 PKC Raf PKA Jnk Plcγ PIP3 Mek PIP2 Erk Akt P38

SLIDE 14

Ellis & Wong

Order-sampling MCMC

Learning Causal Bayesian Network Structures from Experimental Data

Byron Ellis Baxter Labs in Genetic Pharmacology Stanford University Medical School Stanford University, Stanford, CA 94305 email: bcellis@stanford.edu Wing Hung Wong Department of Statistics Stanford University, Stanford, CA 94305 email: whwong@stanford.edu

SLIDE 15

Eaton & Murphy

AI & Statistics, 2007 Structure-MCMC

Exact Bayesian structure learning from uncertain interventions

Daniel Eaton Computer Science Dept. University of British Columbia deaton@cs.ubc.ca Kevin Murphy Computer Science Dept. University of British Columbia murphyk@cs.ubc.ca

Abstract

We show how to extend the dynamic program- ming algorithm of Koivisto [KS04, Koi06], which computes the exact posterior marginal edge probabilities p(Gij = 1|D) of a DAG G given data D, to the case where the data is ob- tained by interventions (experiments). In partic- ular, we consider the case where the targets of the interventions are a priori unknown. We show that it is possible to learn the targets of interven- tion at the same time as learning the causal struc-

• ture. We apply our exact technique to a biolog-

ical data set that had previously been analyzed using MCMC [SPP+05, EW06].

1 Introduction

The use of Bayesian networks to represent causal models has become increasingly popular [Pea00, SGS00]. In par- ticular, there is much interest in learning the structure of these models from data. Given observational data, it is only possible to identify the structure up to Markov equivalence. For example, the three models X→Y →Z, X←Y ←Z, and X←Y →Z all encode the same conditional independency statement, X ⊥ Z|Y . To distinguish between such models, we need interventional (experimental) data [EGS05]. Most previous work has focused on the case of “perfect” interventions, in which it is assumed that an intervention sets a single variable to a specific state (as in a random- ized experiment). This is the basis of Pearl’s “do-calculus” (as in the verb “to do”) [Pea00]. A perfect intervention essentially “cuts off” the influence of the parents to the in- tervened node, and can be modeled as a structural change by performing “graph surgery” (removing incoming edges from the intervened node). Although some real-world interventions can be modeled in this way (such as gene knockouts), most interventions are not so precise in their effects. One possible relaxation of this model is to assume that interventions are “stochastic”, meaning that they induce a distribution over states rather than a specific state [KHNA04]. A further relaxation is to assume that the ef- fect of an intervention does not render the node indepen- dent of its parents, but simply changes the parameters of the local distribution; this has been called a “mechanism change” [TP01b, TP01a] or “parametric change” [EGS06]. For many situations, this is a more realistic model than per- fect interventions, since it is often impossible to force vari- ables into specific states. In this paper, we propose a further relaxation of the notion

• f intervention, and consider the case where the targets of

intervention are uncertain. This extension is motivated by problems in molecular biology, where the effects of various chemicals that are added are not precisely known. In par- ticular, each chemical may affect a hidden variable, which can in turn affect multiple observed variables, often in un- known ways. We model this by adding the intervention nodes to the graph, and then performing structure learning in this extended, two-layered graph. Our contributions are three-fold. First, we show how to combine models of intervention — perfect, imperfect and uncertain — with a recently proposed algorithm for effi- ciently determining the exact posterior probabilities of the edges in a graph [KS04, Koi06]. Second, we show em- pirically that it is possible to infer the true causal graph structure, even when the targets of interventions are uncer- tain, provided the interventions are able to affect enough

• nodes. Third, we apply our exact methodology to a biologi-

cal dataset that had previously been analyzed using MCMC [SPP+05, EW06].

2 Models of intervention

We will first describe our probability model under the as- sumption that there are no interventions. Then we will de- scribe ways to model the many kinds of interventions that have been proposed in the literature, culminating in our model of uncertain interventions. This will serve to situ- ate our model in the context of previous work.

SLIDE 16

Our network learning strategy

• Dirichlet Prior Score Metric (DPSM)
• Small λ (λ=0.1 or λ=1)
• Model averaging by bootstrap aggregation
• Very many resamples (2500)
• Greedy hill-climbing search algorithm with

randomized restarts

• Friedman’s sparse candidate algorithm

SLIDE 17

Experimental results

• Learning experiment
• Synthetic validation experiment

SLIDE 18

Learning experiment

• Uses discretized data from Sachs et al.
• Also used by Eaton&Murphy and Ellis&Wong
• Deciding which edges to report
• Two thresholds:
• Arbitrary high threshold: 0.99
• Threshold from permutation test: 0.6

SLIDE 19

Resulting Bayesian Network

From consensus model Not in consensus model Not in consensus model and 0.6 < frequency < 0.99 Reversed from consensus model In consensus model but missing from graph Reversed from consensus model and 0.6 < frequency < 0.99

PIP2 PKC Plcγ PKA PIP3 Raf Jnk Akt Erk P38 Mek

SLIDE 20

Comparison to previous analyses

With respect to the Sachs consensus network Correct Reversed Incorrect Missing gbayesnet t = 0.99 gbayesnet t = 0.6 Eaton & Murphy Ellis & Wong

16 1 5 3 16 2 12 2 16 2 9 2 8 4 8 8

SLIDE 21

Graph comparison

Ours Eaton & Murphy’s

PKC Raf PKA Jnk Plcγ PIP3 Mek Akt PIP2 Erk P38 PIP2 PKC Plcγ PKA PIP3 Raf Jnk Akt Erk P38 Mek

SLIDE 22

“Incorrect” ≠ Wrong

SLIDE 23

Verification experiment

• Learned CPTs for consensus model from

Sachs data

• Generated 60 synthetic data sets with 5400

data points each from consensus model

• Learned model from each of 60 syn. datasets
• Learned models contain
• 17 to 18 edges from consensus network
• No additional edges occur at high frequency

SLIDE 24

Typical result graph

Threshold: 0.6; Correct: 14, Reversed: 3, Incorrect: 0, Missing: 3

PKC Raf PKA Jnk Plcγ PIP3 Mek PIP2 Erk Akt P38

SLIDE 25

Incorrect edges and frequency of occurrence

From To Freq

Raf Jnk 0.648 Raf Erk 0.819 Plcγ P38 0.963 PKA Plcγ 0.976 PKC PIP3 0.983 Jnk PIP3 0.984

From To Freq

PKC Erk 0.987 Mek Jnk 0.995 Mek Plcγ 0.999 Jnk P38 1.000 Mek Akt 1.000 Raf Akt 1.000

SLIDE 26

Conclusions

• Identification of promising edges not in

consensus model of Sachs et al.

• Despite different method, close agreement

with Eaton & Murphy.

• Unlikely that these are artifacts of the

learning process.

• Could be artifacts of discretization.
• Planning biological validation experiments

SLIDE 27

Thanks — Questions?