Models of Polyclonal Tumor Initiation in the Mouse Intestine
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Models of Polyclonal Tumor Initiation in the Mouse Intestine Shuang Huang Dec. 7 th Fall 2007 Shapiro Fellowship Under Prof. M. A. Newton and Dr. R. Halberg
Transcript of Models of Polyclonal Tumor Initiation in the Mouse Intestine
Models of Polyclonal Tumor Initiation in the Mouse Intestine
Shuang HuangDec. 7th
Fall 2007 Shapiro FellowshipUnder Prof. M. A. Newton and Dr. R. Halberg
Tumor origin: Monoclonal vs Polyclonal
l Monoclonal- Single initiation event- Normal cell converts to a cancer state- All cells in tumor are descendents of this progenitor.
l Polyclonal- Multiple initiation events contributing to the tumor
Chimera [Thliveris et al 2005]
Heterotypic Tumor
Heterotypic Tumor
l
My Project
l Develop statistical models for the probability of heterotypic or pure tumors.
l Frequencies of heterotypic (H), blue (B), or white (W) tumors are observable.
l Using such multinomial data, we could compare different models for P(H), P(B), P(W).
Formation of Polyclonal Tumor
l Two models:RecruitmentSelection
l Data: images showing the chimeric patchwork in mouse intestine.
Example binary imagel Represents a small section in intestine:
Recruitment
l Single initiation event at position Xl X may be nonuniformly distributed ~ fl Recruitment distanceδl Model: all cells in
are converted to tumor.(Normal) à (Initiation) à (Recruitment)
( ) { : }disc x y y xδ δ= − ≤
origin of pure tumor
origin ofheterotypic
tumor
Recruitment
Events:
Problem: Compute P(B), P(W) and P(H).
c
B=[ Tumor is pure blue ]W=[ Tumor is pure white ]H=(B W)∪
Recruitment
l DefineThe green part below is :
Obviously, is the part of blue.Similarly, we can define:
( ) { : cells in disc ( ) are pure blue}Bd x xδδ =( )Bd δ
( ) { : cells in disc ( ) are pure white}Wd x xδδ =
(0)Bd
Computation
l Setl The position X has pdf:l To be a pdf, it requires: l Then
( ) 1{ }c x x is blue= ( ) 0( )
( ) 1c x
f xc x
αβ
== =
( ) ( )1{ ( )} ( ( ))
( ) ( )1{ ( )} ( ( ))
( ) 1 ( ) ( )
B B
W W
P B f x x d dx Area d
P W f x x d dx Area d
P H P B P W
δ β δ
δ α δ
= ∈ = ⋅
= ∈ = ⋅
= − −
∫∫
( (0)) ( (0)) 1W BArea d Area dα β⋅ + ⋅ =
Computation
( ) 1 ( ) ( )1 (1 ( )) ( (0))
(1 ( )) ( (0))1 ( (0)) ( (0))
( (0)) ( ) ( (0)) ( )( (0)) ( ) ( (0)) ( )
b B
w W
B W
B b W W
B b W W
P H P B P WF Area d
F Area dArea d Area d
Area d F Area d FArea d F Area d F
α δ
β δ
α β
α δ β δ
α δ β δ
= − −= − −
− −
= − −
+ +
= ⋅ ⋅ + ⋅ ⋅
Result
Selection
l Multiple initiation eventsl e.g. n=2, at position X,Y ~ fl Conditional onl Model: all cells in
are converted to tumor.(Normal) à (Initiation) à (Selection)
{ }E Y X δ= − =
/ 2 (( ) / 2)disc X Yδ +
Discussion – Future work
l Combine information of different images.
l Develop models further.
l Compare the prediction of these 2 models in multiple biological context.
l What does the calculation tell us about biology.
Reference
[1] Andrew T. Thliveris, Richard B.Halberg, Linda Clipson, William F. Dove, Ruth Sullivan, Mary Kay Washington, Stephen Stanhope, and Michael A. Newton. Polyclonality of familial murine adenomas: Analyses of mouse chimeras with low tumor multiplicity suggest short-range interactions. PNAS May10, 2005. vol.102, no.19
[2] Michael A. Newton. On estimating the polyclonal fraction in lineage-marker studies of tumor origin. Biostatistics(2006), 7,4, pp. 503-514
[3] Michael A. Newton, Linda Clipson, Andrew T. Thliveris, and Richard B. Halberg, A Statistical Test of the Hypothesis that Polyclonal Intestinal Tumors Arise by Random Collision of Initiated Clones. Biometrics.
