Development of statistical methods for DNA copy number analysis in - PowerPoint PPT Presentation

Development of statistical methods for DNA copy number analysis in cancerology Morgane Pierre-Jean Supervisors : Catherine Matias and Pierre Neuvial Laboratoire de Mathématique et de Modélisation d’Evry, LaMME December 2nd, 2016

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Outline Introduction 1 2 Segmentation 3 Heterogeneity Model 4 Simulations Application to real data sets 5 6 Conclusion Morgane Pierre-Jean Development of statistical methods for DNA copy number data 2/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Outline 1 Introduction Alterations in tumor cells Notion of Heterogeneity 2 Segmentation 3 Heterogeneity Model 4 Simulations 5 Application to real data sets 6 Conclusion Morgane Pierre-Jean Development of statistical methods for DNA copy number data 3/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Alterations in tumor cells Objectives Alterations in tumor cells can be observed at several levels Gene expression DNA structure Mutations DNA copy number Why study genetic alterations in cancers ? Help to diagnosis Identify biomarkers linked to drug resistance Personalized treatments Morgane Pierre-Jean Development of statistical methods for DNA copy number data 4/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Alterations in tumor cells Objectives Alterations in tumor cells can be observed at several levels Gene expression DNA structure Mutations DNA copy number Why study genetic alterations in cancers ? Help to diagnosis Identify biomarkers linked to drug resistance Personalized treatments Morgane Pierre-Jean Development of statistical methods for DNA copy number data 4/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Alterations in tumor cells Illustration of alterations at level of DNA copy number Tumor Matched Normal Tumor with deletion with deletion (diploid) (diploid) with gain with gain copy-neutral LOH - BB BB A B AB A BB ABB BB B BB BB - BB B B BBB ) - A B A AB B AB A A ) A A AA A A AA A A AA ) Morgane Pierre-Jean Development of statistical methods for DNA copy number data 5/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Alterations in tumor cells Human Karyotype (a) Normal cell (b) Tumor cell Morgane Pierre-Jean Development of statistical methods for DNA copy number data 6/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Alterations in tumor cells How to measure DNA copy number more precisely ? CGH arrays (measuring total DNA copy number) SNP arrays (measuring quantity of alleles for predefined SNPs) Sequencing technologies (WGS or WES) Morgane Pierre-Jean Development of statistical methods for DNA copy number data 7/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Alterations in tumor cells What kind of signals from SNPs arrays ? Total copy number B allele fraction N B c j = N A j + N B j b j = j c j Morgane Pierre-Jean Development of statistical methods for DNA copy number data 8/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Alterations in tumor cells What kind of signals from SNPs arrays ? Total copy number B allele fraction N B c j = N A j + N B j b j = j c j Morgane Pierre-Jean Development of statistical methods for DNA copy number data 8/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Notion of Heterogeneity Notion of heterogeneity in cancers Differences between tumors of the same disease in different patients (inter-tumor heterogeneity) Differences between cancer cells within a single tumor of one patient (intra-tumor heterogeneity). Morgane Pierre-Jean Development of statistical methods for DNA copy number data 9/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Notion of Heterogeneity Heterogeneity illustration (a) Tumor sample (b) Copy-number profile = 0 . 6 × ( ) ( ) + 0 . 2 × + 0 . 2 × ( ) Morgane Pierre-Jean Development of statistical methods for DNA copy number data 10/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Notion of Heterogeneity Heterogeneity illustration (a) Tumor sample (b) Copy-number profile = 0 . 6 × ( ) ( ) + 0 × + 0 . 4 × ( ) Morgane Pierre-Jean Development of statistical methods for DNA copy number data 11/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Notion of Heterogeneity Mathematical modelization y 1 • ∈ R J and y 2 • ∈ R J the observed DNA copy number profiles y 1 • = w 11 z 1 • + w 12 z 2 • + w 13 z 3 • y 2 • = w 21 z 1 • + w 22 z 2 • + w 23 z 3 • = 0 . 6 × ( ) = 0 . 6 × ( ) ( ) ( ) + 0 . 2 × + 0 × + 0 . 2 × ( ) + 0 . 4 × ( ) Find w and z for the two profiles Morgane Pierre-Jean Development of statistical methods for DNA copy number data 12/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Notion of Heterogeneity Mathematical modelization y 1 • ∈ R J and y 2 • ∈ R J the observed DNA copy number profiles y 1 • = w 11 z 1 • + w 12 z 2 • + w 13 z 3 • y 2 • = w 21 z 1 • + w 22 z 2 • + w 23 z 3 • = 0 . 6 × ( ) = 0 . 6 × ( ) ( ) ( ) + 0 . 2 × + 0 × + 0 . 2 × ( ) + 0 . 4 × ( ) Find w and z for the two profiles Morgane Pierre-Jean Development of statistical methods for DNA copy number data 12/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Notion of Heterogeneity General mathematical modelization Let y i • ∈ R J the observed DNA copy number profiles p � y i • = w ik z k • + ǫ k = 1 Latent profiles assumed to be shared between the observed profiles p n w ik z k • � 2 under some constraints. � � Minimize � y i • − i = 1 k = 1 Morgane Pierre-Jean Development of statistical methods for DNA copy number data 13/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Notion of Heterogeneity Related works Matrix Factorization problem W , Z � Y − WZ � 2 min F Penalized latent models to infer heterogeneity Fused Lasso latent model FLlat (Nowak et al., 2011) CGH analysis with Dictionary Learning e-FLlat (Masecchia et al., 2013) Evolutionary history by next-generation sequencing Canopy (Jiang et al., 2016) Morgane Pierre-Jean Development of statistical methods for DNA copy number data 14/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Notion of Heterogeneity InCaSCN- Inferring Cancer Subclone using Copy Number Features of method joint segmentation of all n profiles ⇒ S − 1 breakpoints (Pierre-Jean et al., Briefings in Bionformatics, 2015) Integration of B allele fraction information by using transformations Biological interpretation of constraints on latent profiles of TCN and BAF and weight matrix W Morgane Pierre-Jean Development of statistical methods for DNA copy number data 15/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Outline 1 Introduction 2 Segmentation Models Recursive Binary Segmentation for multiple samples 3 Heterogeneity Model 4 Simulations 5 Application to real data sets 6 Conclusion Morgane Pierre-Jean Development of statistical methods for DNA copy number data 16/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion What is segmentation ? Total copy B allele fraction number N B c j = N A j + N B j b j = j c j Morgane Pierre-Jean Development of statistical methods for DNA copy number data 17/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion What is segmentation ? Total copy B allele fraction Decrease of number Heterozygosity N B d j = 2 × | b j − 1 c j = N A j + N B j b j = 2 | j c j Morgane Pierre-Jean Development of statistical methods for DNA copy number data 17/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion What is segmentation ? Total copy B allele fraction Decrease of number Heterozygosity N B d j = 2 × | b j − 1 c j = N A j + N B j b j = 2 | j c j Morgane Pierre-Jean Development of statistical methods for DNA copy number data 17/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion What is segmentation ? Total copy B allele fraction Decrease of number Heterozygosity N B d j = 2 × | b j − 1 c j = N A j + N B j b j = 2 | j c j Morgane Pierre-Jean Development of statistical methods for DNA copy number data 17/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Models Segmentation methods Multiple change-point Recursive Total variation Hidden Markov Models Kernel methods Morgane Pierre-Jean Development of statistical methods for DNA copy number data 18/ 55

Introduction Segmentation Heterogeneity Model Simulations Application Conclusion Models Segmentation methods Multiple change-point Recursive Total variation Hidden Markov Models Kernel methods Morgane Pierre-Jean Development of statistical methods for DNA copy number data 18/ 55