MSDefenseTalk2008

A"Bayesian"Sta,s,cal"Approach"to"Modeling"Gene"Regulatory"Pathways"in"

Human"Placental"Data"

Elinor"Velasquez"Dept."of"Biology"

San"Francisco"State"University"

Outline"of"talk"

•  Introduc,on"•  The"experimental"approach"

•  Results"from"experiments"

•  Discussion"•  Conclusions"and"future"work"•  Acknowledgements"

Introduc,on"

Overall"Goal"

hMp://www.biotechnologycenter.org/hio/assets/hisimages/placenta/placenta44.jpg"

To use a bioinformatics model for which to better understand the human placenta

The"human"placenta"

http://www.uchsc.edu/winnlab/index.html

EGFR"pathway"

•  "EGFR,"cell"surface"receptor"for"epidermal"growth"factors"

•  "Poten,ally"important"gene"for"the"placenta"

British Journal of Cancer (2006) 94, 184 – 188

EGFR"regulates"gene"expression""

EGFR

ANGPT2 CSPG2 DCN

Causal"rela,onships""

EGFR

ANGPT2 CSPG2 DCN

Example"of"a"gene"regulatory"network"

Gene""1"

Gene"2"

Gene""3"

Gene""5"

Gene""6"Gene"

"4"

Defini,on"of"a"Bayesian"network"

•  There"exist"nodes"(disks)"

•  There"are"edges"(arrows)"between"some"of"the"nodes"

•  Causality"is"implied"by"the"edges"

•  Acyclic"

Gene""1"

Gene"2"

Gene""3"

Gene""5"

Gene""6"Gene"

"4"

The"experimental"approach"

What"is"a"probe"set?"

•  Several"oligonucleo,des"designed"to"hybridize"to"various"parts"of"the"mRNA"generated"from"a"single"gene""

Probe set

mRNA

gene

Data"collected"from"microarrays"

•  Data"comes"from"experiments"conducted"by"Virginia"Winn"et"al."at"the"SJ"Fisher"lab,"UCSF"

•  Gene"expression"profiling"experiments"

45000 dots (25-mer oligo probe sets)

representing the human genome

cRNA

hybridization

Microarray"data"

•  The"normalized"log"2"intensity"values"were"centered"to"the"median"value"of"each"probe"set,"by"Winn"et"al."

•  Red"denotes"the"up"regulated"expression"and"green"denotes"the"down"regulated"expression"rela,ve"to"the"median"value"

Genes differentially expressed in the basal plate of placentas: Rows contain data from a single basal plate cRNA sample and columns correspond to a single probeset.

http://www.uchsc.edu/winnlab/index.html

Summary"of"data"used"in"bioinforma,cs"experiments"

•  36"placentas"•  509"probe"sets"(418"genes)"

•  Probe"sets"chosen"according"to"pcvalue"(p"<"0.05)"

•  Timecseries"data"from"14c16"weeks"to"term"

Average expression value

Outline"of"bioinforma,cs"experimental"design"

•  Create"a"naïve"Bayesian"network"using"the"probe"set"data"•  Score"that"network"•  Randomly"add/delete"an"edge"and"rescore"the"Bayesian

"network"•  Con,nue"un,l"best"score"reached"•  Combine"probe"sets"to"create"the"gene"regulatory"pathways"for

"the"placenta"

PS#1#

PS##2# PS#

3#

PS#4#

Naïve"Bayesian"network"

•  Choose"a"root"node"•  All"other"nodes"branch"off"of"the"root"node"

•  PS1"is"the"parent"node"

PS#1#

PS##2# PS#

3#

PS#4#

Step"1:"Create"a"naïve"Bayesian"network"

•  Use"data"from"one",me"segment"•  Choose"Weeks"23c24"data"(6"placentas)"

PS1

PS2 PS3 PS4

Placenta"data"for"Weeks"23c24"

201984 corresponds to EGFR

236034, 211148, 205572 correspond to ANGPT2

204620 corresponds to CSPG2

209335 corresponds to DCN

Step"2:"Score"the"naïve"Bayesian"network"

•  We"want"to"score"this"network:"

201984

236064 204620 211148

The"network"score"is"a"func,on"of"condi,onal"probabili,es"

•  Probability"is"defined"to"be"the"chance"that"something"will"happen"

•  Condi,onal"probability,"""""Prob(N"|"Pa(N)),"is"the"probability"of"child"node"N"given"parent"of"N"

•  Example:"Given"a"parent"201984’s"node"has"an"associated"expression"value"10,"what"is"the"probability"that"its"child"node,"204620,"has"an"expression"value"of"8?"

201984

204620

Condi,onal"probability"

•  EGFR"(201984)"is"the"parent"node"and""""has"value"10.""•  CSPG2"(204620)"is"the"child"node"and"has""""value"8"two",mes"

•  Condi,onal"probability"="2/6"

201984

204620

Score"for"naïve"network"

•  The"score"of"the"naive"network"equals"the"product"of"all"the"nonzero"condi,onal"probabili,es"associated"with"the"network:"

•  P(N1,"N2,"N3,"N4)"""=""Π"P(Ni"|"pa(Ni))"

•  P(N1,"N2,"N3,"N4)"""="?"201984

204620

i=1

4

236064 211148

Step"3:"Delete/Add"an"edge"

•  The"score"becomes"?."•  Since"the"score"is"a"probability,"we"want"the"score"to"be"high."

•  The"previous"network"is"the"beMer"choice."

201984

236064

204620

211148

Final"Network"for"four"probe"sets/three"genes"

EGFR

ANGPT2 CSPG2

How"do"we"create"all"possible"networks?"

•  1"probe"set"1"Bayesian"network"•  2"probe"sets"2"possible"Bayesian"networks"•  3"probe"sets"12"possible"Bayesian"networks"•  4"probe"sets"144"possible"Bayesian"networks"•  5"probe"sets">"4800"possible"Bayesian"networks!"•  6"probe"sets"…"??"•  And"so"on…"

Welcome"to"“Modern"Heuris,cs”"•  Step"1."Representa,on"of"a"model"•  Step"2."The"evalua,on"func,on"•  Step"3."Defining"the"search"problem"

•  Step"4."Neighborhoods"and"local"op,ma"score

local

change

Step"1:"Representa,on"of"the"model""

•  The"model"is"a"gene"regulatory"pathway."

•  The"number"of"possible"pathways"is"so"large"as"to"forbid"an"exhaus,ve"search"for"the"best"answer."

•  It’s"complicated"so"we"have"to"simplify."

•  We"are"going"to"assume"a"Bayesian"model"for"our"probe"set:""

PS#1#

PS##2# PS#

3#

PS#4#

Step"2."The"evalua,on"func,on"

•  Introduce"the"idea"of"randomness."

•  Choose"100"networks"randomly."Each"node"is"randomly"chosen"with"probability"p.#

•  Simplify:#Assume"the"network"has"a"Dirichlet"distribu,on"which"is"similar"to"a"mul,nomial"distribu,on.#

www.wikipedia.com

The"new"scoring"func,on"

•  Probability"of"a"fixed"network"given"the"specified"database"equals"product"of"condi,onal"probabili,es",mes"the"Dirichlet"distribu,on:"

Local"Search"for"Possible"Network"

•  HillcClimbing"is"a"tradi,onal"method"for"search"techniques"

•  Can"get"caught"on"local"maxima"

•  K2"is"a"type"of"hillcclimbing"algorithm"

From http://content.answers.com/

score

local

change

MRC2

ATP5E

ERG

PECAM1 IL2RB CECAM1 CYP19A1

USP6NL

EGFR

ADAM9

GLB1

CCNG2

RAP2B

P4HA1

BAMBI

INHBA

CSPG2

DCN COL3A1

COL1A2

SPP1

ANGPT2

SFRP1

Time Segment:

Week 14-16 weeks

Results"for"the"Human"Placenta"

Gene"egfr"regulated"by:"

Gene"Regulatory"Network"for"Gene"egfr#

CCNG2

PLAU CSPG2

DCN

ADAM9

PECAM1 INHBA

COL1A2

Sorware"

•  Weka"sorware"system"from"the"University"of"Waikato,"New"Zealand"

•  hMp://www.cs.waikato.ac.nz/~ml/index.html"

Future"Direc,ons"

•  A"threecdimensional"viewer"with"numerical"values"will"be"implemented"to"use"with"the"Weka"sorware""

•  Use"molecular"gene,cs"techniques"to"validate"a"por,on"of"the"results"

•  Design"a"gene,c"programming"algorithm"(evolu,onary"algorithm)"to"create"a"Bayesian"network"

Acknowledgements"

•  Le,cia"MárquezcMagaña"and"laboratory"members"(San"Francisco"State"University)"

•  Susan"J."Fisher""(U.C."San"Francisco)"•  MaMhew"Gormley"(U.C."San"Francisco)"

•  M.B.R.S.cR.I.S.E."Grant""5"c"R25cGM59298"