Coalescence modeling of cancer sequencing data

49 Pages·2016·0.94 MB·English

by  Andrzej Polański

Coalescence modeling of
cancer sequencing data
Andrzej Polanski
Silesian University of Technology, Gliwice, Poland
15 September, 2016
M T E : I ,
ODELING UMOR VOLUTION NITIATION
G P
ROWTH AND ROGRESSION
PLAN
• Coalescent model
• Motivation for use in cancer sequencing data
• Methods
• Results
• Conclusions
What is coalescent model ?
Coalescent is a mathematical tool for modeling phylogenetic trees of
samples drawn from evolving populations. It has been used for
statistical inference on genetic parameters and structures of evolving
populations.
What is coalescent model ?
• Kingman J.F.C. , (1982), The Coalescent,
Stoch. Proc. Appl., vol. 13, pp. 235-248, 1982.
• Kimura M, (1983), The neutral theory
of molecular evolution, Cambridge (UK):
Cambridge University Press.
Wright-Fisher model of reproduction
Genetic drift
Individuals = fragments of DNA
Generations Alleles: A : A :
1 2
Reproduction = DNA replication = sampling with
replacement
G
1
Hypotheses:
• Discrete, non-overlapping generations
• Haploid individuals or diploid population
G
2
with panmixia = random mating)
...
• Constant population size
• No selection (all individuals are equally fit)
G
• No recombination
n
• No substructure (no geographical structure)
...
Wright-Fisher model: reproduction + mutation
Mutation
G
k introduces
genetic variability to
the evolution process
• Poisson process with intensity  measured per
locus (per site) per generation. Spatial
characterization of places and effects caused,
further specifies a mutation model. Most often
G applied:
k+1
 Infinite sites model, where it is assumed that each
mutation takes place at a DNA site that never
mutated before;
Coalescent approach
One looks at the past of an n - sample of sequences taken at present.
Possible events that happen in the past are coalescences leading to
common ancestors of sequences, and mutations along branches of
ancestral tree.
Coalescent approach
G
1
s t
2 2
G
2
... s t
3 3
t
s
4
4
G
n
s t
5 5
1 2 3 4 5 1 2 3 4 5
Coalescent versus other approaches
Analytical results
Coalescent
Coalescent simulations
Branching processes
Forward random simulations
Coalescent
Changing population size
Coalescent
Selection
Substructure