Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,*,*,Analysis of DNA Damage and Repair in Colonic Crypts,Raymond J.Carroll,Texas A&M University,:/stat.tamu.edu/carroll,Postdoctoral Training Program:,1,Acknowledgments,Jeffrey Morris,M.D.Anderson,Lead author,Naisyin Wang,(adducts and structure),Marina Vannucci,Texas A&M(wavelets),Phil Brown,University of Canterbury(wavelets),Joanne Lupton,Biology of Nutrition at Texas A&M(problems and data!),2,Outline,Introduction,Colon Carcinogenesis Studies,Hierarchical Functional Model,DNA Damage,:regional correlations,Crypt Cell Architecture,:modeling where the cells are located,DNA Repair,:Wavelet-based Estimation of Hierarchical Functions,Conclusions,3,Some Background,General Goal,:Study how diet affects colon carcinogenesis.,Model,:Carcinogen-induced colon cancer in rats.,Early Carcinogenesis,:DNA damage to cells,and associated repair and cell death(apoptosis),If not,repaired,or,removed,Mutation,Colon cancer,4,Some Background,We are especially interested in anatomical effects,Regions,of the colon,e.g.,proximal(front)and distal(back),There are some major differences in early carcinogenesis between these two regions,Localized,phenomena:cell locations,Apoptosis and DNA adducts differ by location in,colonic,crypts,5,Colon Sliced and Laid Out,Aberrant Colon Crypts,Normal Colon Crypts,6,Architecture of Colon Crypts:Crosssectional View,Stem Cells,:,Mother cells near bottom,Depth,in crypt age of cells,Suggests importance of depth,Relative Cell Position:,0=bottom,1=top,crypts,Lumen,7,Architecture of Colon Crypt:Expanded View,The cells are more easily visible here,Note that the cells seem smaller at the crypt bottom,8,Architecture of Colon Crypt,The general idea is to slice the colon crypt,The cells along the left wall are assayed,9,Colon Carcinogenesis Studies,Rats are,fed different diets,exposed to carcinogen(and/or radiation),euthanized.,DNA adducts,DNA repair,apoptosis,measured through imaging experiments,Hierarchical structure of data,Diet groups-rats-crypts-cells/pixels,Hierarchical longitudinal(in cell depth)data,10,Coordinated Response,Rats were exposed to a potent carcinogen(AOM),At both the proximal and distal regions of the colon,20 crypts were assayed,The,rat-level,function is g,dr,(t),For each cell within each crypt,the level of DNA damage was assessed by measuring the DNA adduct levels,Question:how is DNA damage related in the proximal and distal regions,across rats?,We call this,coordinated response,11,Coordinated Response as Correlation,We are interested in the“correlation of the DNA damage in the proximal region with that of the distal region,Are different regions of the colon responding(effectively)independently to carcinogen exposure?,This sort of interrelationship of response is what is being studied in our group.,It is not cell signaling in the classic sense,We will have data on this in the near future,12,Coordinated Response,Correlation in the usual sense is not possible,Let Y(,t,)=DNA adduct in a proximal cell measured by immunohistochemical staining intensity at,cell depth t,Let Z(,t,)=DNA adduct in a distal cell at,cell depth t,We cannot calculate correlation(Y,Z)(,t,)in the usual way,the same cell cannot be in both locations,Coordinated response then has to be measured at a higher level,13,Coordinated Response:Hierarchical Functional Model,Let d=diet group,Let r=rat,Let c=crypt,Let t=t,drc,=cell position,Let Y,drc,(t)=,adduct level in the proximal region,The,diet-level,function is,g,d,(t),Our aim,:estimate the correlation between proximal and distal regions as a function of cell depth at the,rat level,14,Coordinated Response:Average then Smooth,If cell depths were identical for each crypt,we could solve this by“average then smooth,That is,average over all crypts at any given depth,then estimate the correlation as a function of depth,The estimated correlation would of course account for the averaging over a finite number of crypts,Problem,:data are not of this structure,Cell locations,vary from crypt to crypt,Number of cells,varies from crypt-to-crypt,15,Coordinated Response:Smooth then Average,Instead,we smoothed crypts via,nonparametric regression,Then,average,the smooth fits over the crypts(on a grid of depths),Then,compute,the correlation as before,We actually fit REML to the fitted functions at the crypt level,Problem,:Is there any effect due to the initial smooth?,16,Coordinated Response:Asymptotics,General theory,available:kernel regression,Allows explicit calculations,Can we estimate the correlation function just as well as if the crypt-level functions were known?,Complex,higher order expansions necessary,The asymptotic theory is for large numbers of,Rats,Crypts,Cells,17,Coordinated Response:Asymptotics,Possibility#1:,Use standard methods,at the crypt level,Optimal at the crypt level,Double-smoothing phenomenon(at crypt then across crypts),Effect of smoothing does not disappear,