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Paula Tataru

Paula Tataru defended her PhD thesis on using mathematical modeling and computational tools to analyze population genetics and molecular data. Her research involved using stochastic context-free grammars, hidden Markov models, discrete time Markov chains, and continuous time Markov chains to study problems involving RNA structure prediction, motif discovery, identity-by-descent modeling, and modeling allele frequency data. She described these modeling techniques and their applications to several of her published works and papers in preparation.

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T a t a r uP a u l a Deciphering the story in our DNA PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Aarhus, January23rd 2015 Inference of population history and patterns from molecular data Supervisors: Christian N.S. Pedersen & Asger Hobolth
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Math Computer science My PhD studies 2 Bioinformatics
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Mathematical modeling Implementation My PhD studies 2 Bioinformatics
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Mathematical modeling Implementation My PhD studies 2 Bioinformatics Population genetics Sequence analysis Pattern matching Structural bioinformatics
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Mathematical modeling toolbox 3 SCFG DFA DTMC HMM CTMC
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Mathematical modeling toolbox 3 Stochastic Context Free Grammar Deterministic Finite Automaton Discrete Time Markov Chain Hidden Markov Model Continuous Time Markov Chain
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Research overview 4 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC Population genetics Sequence analysis Pattern matching Structural bioinformatics
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Research overview 4 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC Population genetics Sequence analysis Pattern matching Structural bioinformatics
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Research overview 4 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC Population genetics Sequence analysis Pattern matching Structural bioinformatics
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 5 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 5 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Evolution of a population forward in time › Follow the change of the allele count Populations genetics: the Wright-Fisher model 6 individuals generations(time) 3 2 4 3 4 5 5 allele count 1. Modeling toolbox
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Allele count per generation in a population of size N › States {0, 1, …, N} 0 ≤ i, j ≤ N › Transitions binomial Discrete Time Markov Chain 7 ji Bin(i | j/N) Bin(j | N, i/N) Bin(j | N, j/N)Bin(i | N, i/N) 0.23 0.20 0.33 0.08 1 0.26 DTMC 3 2 4 3 4 5 5 allele count 1. Modeling toolbox
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre individuals generations(time) › Allele count per generation in a population of size N › Difficult to measure Hidden Markov Model 8 3 2 4 3 4 5 5 allele count 1. Modeling toolbox
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre individuals generations(time) › Allele count per generation in a population of size N › Difficult to measure › Directly affects allele count of a sample of size n Hidden Markov Model 8 3 2 4 3 4 5 5 allele count 1. Modeling toolbox
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre individuals generations(time) › Allele count per generation in a population of size N › Difficult to measure › Directly affects allele count of a sample of size n Hidden Markov Model 8 3 2 4 3 4 5 5 allele count 2 1 2 2 2 3 3 sample 1. Modeling toolbox
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre individuals generations(time) › Allele count per generation in a population of size N › Difficult to measure › Directly affects allele count of a sample of size n Hidden Markov Model 8 3 2 4 3 4 5 5 allele count 2 1 2 2 2 3 3 sample Hidden Markov chain 1. Modeling toolbox
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre individuals generations(time) › Allele count per generation in a population of size N › Difficult to measure › Directly affects allele count of a sample of size n Hidden Markov Model 8 3 2 4 3 4 5 5 allele count 2 1 2 2 2 3 3 sample Observable data 1. Modeling toolbox
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Hidden Markov Model › Transitions (DTMC) binomial › Emissions (data) binomial 9 i Bin(i | N, i/N) 0: Bin(0 | n, i/N) 1: Bin(1 | n, i/N) 2: Bin(2 | n, i/N) 3: Bin(3 | n, i/N) Bin(j |N, j/N) 0: Bin(0 | n, j/N) 1: Bin(1 | n, j/N) 2: Bin(2 | n, j/N) 3: Bin(3 | n, j/N) jBin(i | N, j/N) Bin(j | N, i/N) 1. Modeling toolbox
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Hidden Markov Model › Standard algorithms › Forward Likelihood of data › Viterbi Global decoding › Posterior decoding Local decoding 10 i Bin(i | N, i/N) 0: Bin(0 | n, i/N) 1: Bin(1 | n, i/N) 2: Bin(2 | n, i/N) 3: Bin(3 | n, i/N) Bin(j |N, j/N) 0: Bin(0 | n, j/N) 1: Bin(1 | n, j/N) 2: Bin(2 | n, j/N) 3: Bin(3 | n, j/N) jBin(i | N, j/N) Bin(j | N, i/N) 1. Modeling toolbox
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Allele count in time in a population of size N › States {0, 1, …, N} 0 < i < N › Rates ri = i (N-i) / N Continuous Time Markov Chain 11 i CTMC i-1 i+1 ri ri+1ri-1 - 2 ri -2 ri-1 - 2 ri+1 ri 1. Modeling toolbox
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Allele count in time in a population of size N › States {0, 1, …, N} 0 < i < N › Rates ri = i (N-i) / N Continuous Time Markov Chain 11 i allele count in DTMC 3 2 4 3 4 5 5 0.23 0.20 0.330.08 10.26 CTMC i-1 i+1 ri ri+1ri-1 - 2 ri -2 ri-1 - 2 ri+1 ri 1/2 3 3 3 4 t2 t6 2 4 5 t1 t4t2 1/2 1/2 1/2 1/2 1/2 allele count in CTMC 1. Modeling toolbox
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 12 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 12 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › DTMC describes sequences › Allele count in a population › DFA encodes pattern › (i)+ (i+1)+ (i+2)+ 13 i+2 0 1 2 k i+1 i+2 3 i i k, i+2 i+1 i+1 ii i+2 k i+1 M. M. Nielsen, P. Tataru, T. Madsen, A. Hobolth, and J. S. Pedersen. Motif discovery in ranked lists of sequences. In preparation. ji Bin(i | j/N) Bin(j | N, i/N) Bin(j | N, j/N)Bin(i | N, i/N) Motif discovery for DTMCs using DFAs 3 2 4 3 4 5 5 2. Brief overview
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Motif discovery for DTMCs using DFAs 14 M. M. Nielsen, P. Tataru, T. Madsen, A. Hobolth, and J. S. Pedersen. Motif discovery in ranked lists of sequences. In preparation. › Does the pattern (i)+ (i+1)+ (i+2)+ occur more frequently in specific environments? Populations DTMC sequences … 2 4 3 4 5 5 generations (time) Environment 2. Brief overview
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Motif discovery for DTMCs using DFAs 14 M. M. Nielsen, P. Tataru, T. Madsen, A. Hobolth, and J. S. Pedersen. Motif discovery in ranked lists of sequences. In preparation. › Does the pattern (i)+ (i+1)+ (i+2)+ occur more frequently in specific environments? Populations DTMC sequences … 2 4 3 4 5 5 generations (time) Environment › Contribution › DFA › New approach to significance (random walk) 2. Brief overview
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › HMM describes problem › Allele count in a population › DFA encodes pattern › (i)+ (i+1)+ (i+2)+ Restricted algorithms for HMMs using DFAs 15 P. Tataru, A. Sand, A. Hobolth, T. Mailund, and C. N. Pedersen. Algorithms for hidden Markov models restricted to occurrences of regular expressions. Biology, 2(4):1282–1295, 2013 i Bin(i | N, i/N) 0: Bin(0 | n, i/N) 1: Bin(1 | n, i/N) 2: Bin(2 | n, i/N) 3: Bin(3 | n, i/N) Bin(j |N, j/N) 0: Bin(0 | n, j/N) 1: Bin(1 | n, j/N) 2: Bin(2 | n, j/N) 3: Bin(3 | n, j/N) jBin(i | N, j/N) Bin(j | N, i/N) i+2 0 1 2 k i+1 i+2 3 i i k, i+2 i+1 i+1 ii i+2 k i+1 2 1 2 2 2 3 3 3 2 4 3 4 5 5 2. Brief overview
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Restricted algorithms for HMMs using DFAs 16 P. Tataru, A. Sand, A. Hobolth, T. Mailund, and C. N. Pedersen. Algorithms for hidden Markov models restricted to occurrences of regular expressions. Biology, 2(4):1282–1295, 2013 i Bin(i | N, i/N) 0: Bin(0 | n, i/N) 1: Bin(1 | n, i/N) 2: Bin(2 | n, i/N) 3: Bin(3 | n, i/N) Bin(j |N, j/N) 0: Bin(0 | n, j/N) 1: Bin(1 | n, j/N) 2: Bin(2 | n, j/N) 3: Bin(3 | n, j/N) jBin(i | N, j/N) Bin(j | N, i/N) i+2 0 1 2 k i+1 i+2 3 i i k, i+2 i+1 i+1 ii i+2 k i+1 › Contribution: new algorithms › Calculate distribution of #pattern occurrences › Adapt decoding algorithms to include #pattern occurrences 2. Brief overview
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Restricted algorithms for HMMs using DFAs 17 P. Tataru, A. Sand, A. Hobolth, T. Mailund, and C. N. Pedersen. Algorithms for hidden Markov models restricted to occurrences of regular expressions. Biology, 2(4):1282–1295, 2013 2. Brief overview
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Conditional expectations for CTMCs 18 P. Tataru and A. Hobolth. Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains. BMC Bioinformatics, 12(1):465, 2011 1/2 3 3 3 4 t2 t6 2 4 5 t1 t4t2 1/2 1/2 1/2 1/2 1/2 ii-1 i+1 ri ri+1ri-1 - 2 ri -2 ri-1 - 2 ri+1 ri 2. Brief overview
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Required expectations › Time › Jumps Conditional expectations for CTMCs 18 P. Tataru and A. Hobolth. Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains. BMC Bioinformatics, 12(1):465, 2011 ii-1 i+1 ri ri+1ri-1 - 2 ri -2 ri-1 - 2 ri+1 ri 3 5 t 2. Brief overview
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Required expectations › Time › Jumps › Contribution: compare and extend existing methods › Accuracy › Speed Conditional expectations for CTMCs 18 P. Tataru and A. Hobolth. Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains. BMC Bioinformatics, 12(1):465, 2011 ii-1 i+1 ri ri+1ri-1 - 2 ri -2 ri-1 - 2 ri+1 ri 3 5 t 2. Brief overview
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Beta with spikes: approximate Wright-Fisher 19 P. Tataru, T. Bataillon, and A. Hobolth. Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach. In preparation individuals generations(time) 3 2 4 3 4 5 5 allele count 2. Brief overview
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Beta with spikes: approximate Wright-Fisher 19 P. Tataru, T. Bataillon, and A. Hobolth. Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach. In preparation › What is the distribution of allele count in the current generation? 2. Brief overview individuals generations(time) 3 2 4 3 4 5 5 allele count
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Beta with spikes: approximate Wright-Fisher 19 P. Tataru, T. Bataillon, and A. Hobolth. Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach. In preparation individuals generations(time) 3 2 4 3 4 5 5 allele count › What is the distribution of allele count in the current generation? › Use the beta distribution › Contribution: › Add spikes (better fit) › Include selection 2. Brief overview
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Beta with spikes: approximate Wright-Fisher 20 P. Tataru, T. Bataillon, and A. Hobolth. Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach. In preparation 2. Brief overview
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 21 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 21 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Trace the genealogy of sampled individuals backward in time 22 individuals generations(time) Populations genetics: the coalescent model 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Trace the genealogy of sampled individuals backward in time 22 individuals generations(time) Populations genetics: the coalescent model 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Trace the genealogy of sampled individuals backward in time › Coalescent process terminates when reaching MRCA › Time to coalescent event: CTMC 22 individuals generations(time) Populations genetics: the coalescent model MRCA 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Recombination 23 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 › Multiple sequences and loci analysis › HMM: hidden states = (possible) coalescent trees for each locus › CTMC: probability of the alleles at the leaves 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Identity by descent 25 IBD tract 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre diCal-IBD: CTMCs and HMMs 26 › IBD applications › Association mapping › Demography inference › Detection of selection P. Tataru, J. A. Nirody, and Y. S. Song. diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals. Bioinformatics, 30(23):3430-3431, 2014 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre diCal-IBD: CTMCs and HMMs 26 › IBD applications › Association mapping › Demography inference › Detection of selection › First method to use the coalescent with recombination › One of the first methods to use sequence data P. Tataru, J. A. Nirody, and Y. S. Song. diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals. Bioinformatics, 30(23):3430-3431, 2014 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre diCal-IBD: CTMCs and HMMs 26 › IBD applications › Association mapping › Demography inference › Detection of selection › First method to use the coalescent with recombination › One of the first methods to use sequence data › Outperforms SNP-based methods › Comparable with sequence-based method P. Tataru, J. A. Nirody, and Y. S. Song. diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals. Bioinformatics, 30(23):3430-3431, 2014 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre diCal-IBD: CTMCs and HMMs 27 P. Tataru, J. A. Nirody, and Y. S. Song. diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals. Bioinformatics, 30(23):3430-3431, 2014 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Selection and IBD 28 › IBD tract length depends on MRCA › The more recent the MRCA, the longer the tract › Recent MRCA can be an indication of positive selection › IBD can be used for detecting positive selection1 › Standing variation 1Albrechtsen A et al. Genetics 2010;186:295-308 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Selection and IBD 29 › IBD segment length depends on MRCA › The more recent the MRCA, the longer the segment › Recent MRCA can be an indication of recent selection › IBD can be used for detecting selection › Standing variation 1Albrechtsen A et al. Genetics 2010;186:295-308 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The SLC24A5 gene: diCal-IBD 30 P. Tataru, J. A. Nirody, and Y. S. Song. diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals. Bioinformatics, 30(23):3430-3431, 2014 SLC24A5 › Major influence on natural skin color variation › Under positive selection in Europeans1 1Wilde S et al. PNAS 2014;111(13):4832-4837 3. Overview: diCal-IBD
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 31 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Population genetics: Methods vs Data 32
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Population genetics: Methods vs Data 32 diCal ARGWeaver MSMC ms MaCS PSMC coalHMM Kim Tree
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Population genetics: Methods vs Data 32 Beta with spikes diCal-IBD diCal ARGWeaver MSMC ms MaCS PSMC coalHMM Kim Tree
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Population genetics: Methods vs Data 32 Beta with spikes diCal-IBD diCal ARGWeaver MSMC ms MaCS PSMC coalHMM Kim Tree Data
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Population genetics: Methods vs Data 32 Beta with spikes diCal-IBD diCal ARGWeaver MSMC ms MaCS PSMC coalHMM Kim Tree Data
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Population genetics: Methods vs Data 32 Beta with spikes diCal-IBD diCal ARGWeaver MSMC ms MaCS PSMC coalHMM Kim Tree Data dimension reduction
PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre 33 Thank you for your attention!

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PaulaTataru_PhD_defense

  • 1. T a t a r uP a u l a Deciphering the story in our DNA PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Aarhus, January23rd 2015 Inference of population history and patterns from molecular data Supervisors: Christian N.S. Pedersen & Asger Hobolth
  • 2. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Math Computer science My PhD studies 2 Bioinformatics
  • 3. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Mathematical modeling Implementation My PhD studies 2 Bioinformatics
  • 4. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Mathematical modeling Implementation My PhD studies 2 Bioinformatics Population genetics Sequence analysis Pattern matching Structural bioinformatics
  • 5. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Mathematical modeling toolbox 3 SCFG DFA DTMC HMM CTMC
  • 6. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Mathematical modeling toolbox 3 Stochastic Context Free Grammar Deterministic Finite Automaton Discrete Time Markov Chain Hidden Markov Model Continuous Time Markov Chain
  • 7. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Research overview 4 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC Population genetics Sequence analysis Pattern matching Structural bioinformatics
  • 8. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Research overview 4 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC Population genetics Sequence analysis Pattern matching Structural bioinformatics
  • 9. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Research overview 4 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC Population genetics Sequence analysis Pattern matching Structural bioinformatics
  • 10. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 5 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
  • 11. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 5 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
  • 12. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Evolution of a population forward in time › Follow the change of the allele count Populations genetics: the Wright-Fisher model 6 individuals generations(time) 3 2 4 3 4 5 5 allele count 1. Modeling toolbox
  • 13. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Allele count per generation in a population of size N › States {0, 1, …, N} 0 ≤ i, j ≤ N › Transitions binomial Discrete Time Markov Chain 7 ji Bin(i | j/N) Bin(j | N, i/N) Bin(j | N, j/N)Bin(i | N, i/N) 0.23 0.20 0.33 0.08 1 0.26 DTMC 3 2 4 3 4 5 5 allele count 1. Modeling toolbox
  • 14. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre individuals generations(time) › Allele count per generation in a population of size N › Difficult to measure Hidden Markov Model 8 3 2 4 3 4 5 5 allele count 1. Modeling toolbox
  • 15. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre individuals generations(time) › Allele count per generation in a population of size N › Difficult to measure › Directly affects allele count of a sample of size n Hidden Markov Model 8 3 2 4 3 4 5 5 allele count 1. Modeling toolbox
  • 16. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre individuals generations(time) › Allele count per generation in a population of size N › Difficult to measure › Directly affects allele count of a sample of size n Hidden Markov Model 8 3 2 4 3 4 5 5 allele count 2 1 2 2 2 3 3 sample 1. Modeling toolbox
  • 17. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre individuals generations(time) › Allele count per generation in a population of size N › Difficult to measure › Directly affects allele count of a sample of size n Hidden Markov Model 8 3 2 4 3 4 5 5 allele count 2 1 2 2 2 3 3 sample Hidden Markov chain 1. Modeling toolbox
  • 18. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre individuals generations(time) › Allele count per generation in a population of size N › Difficult to measure › Directly affects allele count of a sample of size n Hidden Markov Model 8 3 2 4 3 4 5 5 allele count 2 1 2 2 2 3 3 sample Observable data 1. Modeling toolbox
  • 19. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Hidden Markov Model › Transitions (DTMC) binomial › Emissions (data) binomial 9 i Bin(i | N, i/N) 0: Bin(0 | n, i/N) 1: Bin(1 | n, i/N) 2: Bin(2 | n, i/N) 3: Bin(3 | n, i/N) Bin(j |N, j/N) 0: Bin(0 | n, j/N) 1: Bin(1 | n, j/N) 2: Bin(2 | n, j/N) 3: Bin(3 | n, j/N) jBin(i | N, j/N) Bin(j | N, i/N) 1. Modeling toolbox
  • 20. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Hidden Markov Model › Standard algorithms › Forward Likelihood of data › Viterbi Global decoding › Posterior decoding Local decoding 10 i Bin(i | N, i/N) 0: Bin(0 | n, i/N) 1: Bin(1 | n, i/N) 2: Bin(2 | n, i/N) 3: Bin(3 | n, i/N) Bin(j |N, j/N) 0: Bin(0 | n, j/N) 1: Bin(1 | n, j/N) 2: Bin(2 | n, j/N) 3: Bin(3 | n, j/N) jBin(i | N, j/N) Bin(j | N, i/N) 1. Modeling toolbox
  • 21. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Allele count in time in a population of size N › States {0, 1, …, N} 0 < i < N › Rates ri = i (N-i) / N Continuous Time Markov Chain 11 i CTMC i-1 i+1 ri ri+1ri-1 - 2 ri -2 ri-1 - 2 ri+1 ri 1. Modeling toolbox
  • 22. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Allele count in time in a population of size N › States {0, 1, …, N} 0 < i < N › Rates ri = i (N-i) / N Continuous Time Markov Chain 11 i allele count in DTMC 3 2 4 3 4 5 5 0.23 0.20 0.330.08 10.26 CTMC i-1 i+1 ri ri+1ri-1 - 2 ri -2 ri-1 - 2 ri+1 ri 1/2 3 3 3 4 t2 t6 2 4 5 t1 t4t2 1/2 1/2 1/2 1/2 1/2 allele count in CTMC 1. Modeling toolbox
  • 23. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 12 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
  • 24. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 12 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
  • 25. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › DTMC describes sequences › Allele count in a population › DFA encodes pattern › (i)+ (i+1)+ (i+2)+ 13 i+2 0 1 2 k i+1 i+2 3 i i k, i+2 i+1 i+1 ii i+2 k i+1 M. M. Nielsen, P. Tataru, T. Madsen, A. Hobolth, and J. S. Pedersen. Motif discovery in ranked lists of sequences. In preparation. ji Bin(i | j/N) Bin(j | N, i/N) Bin(j | N, j/N)Bin(i | N, i/N) Motif discovery for DTMCs using DFAs 3 2 4 3 4 5 5 2. Brief overview
  • 26. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Motif discovery for DTMCs using DFAs 14 M. M. Nielsen, P. Tataru, T. Madsen, A. Hobolth, and J. S. Pedersen. Motif discovery in ranked lists of sequences. In preparation. › Does the pattern (i)+ (i+1)+ (i+2)+ occur more frequently in specific environments? Populations DTMC sequences … 2 4 3 4 5 5 generations (time) Environment 2. Brief overview
  • 27. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Motif discovery for DTMCs using DFAs 14 M. M. Nielsen, P. Tataru, T. Madsen, A. Hobolth, and J. S. Pedersen. Motif discovery in ranked lists of sequences. In preparation. › Does the pattern (i)+ (i+1)+ (i+2)+ occur more frequently in specific environments? Populations DTMC sequences … 2 4 3 4 5 5 generations (time) Environment › Contribution › DFA › New approach to significance (random walk) 2. Brief overview
  • 28. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › HMM describes problem › Allele count in a population › DFA encodes pattern › (i)+ (i+1)+ (i+2)+ Restricted algorithms for HMMs using DFAs 15 P. Tataru, A. Sand, A. Hobolth, T. Mailund, and C. N. Pedersen. Algorithms for hidden Markov models restricted to occurrences of regular expressions. Biology, 2(4):1282–1295, 2013 i Bin(i | N, i/N) 0: Bin(0 | n, i/N) 1: Bin(1 | n, i/N) 2: Bin(2 | n, i/N) 3: Bin(3 | n, i/N) Bin(j |N, j/N) 0: Bin(0 | n, j/N) 1: Bin(1 | n, j/N) 2: Bin(2 | n, j/N) 3: Bin(3 | n, j/N) jBin(i | N, j/N) Bin(j | N, i/N) i+2 0 1 2 k i+1 i+2 3 i i k, i+2 i+1 i+1 ii i+2 k i+1 2 1 2 2 2 3 3 3 2 4 3 4 5 5 2. Brief overview
  • 29. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Restricted algorithms for HMMs using DFAs 16 P. Tataru, A. Sand, A. Hobolth, T. Mailund, and C. N. Pedersen. Algorithms for hidden Markov models restricted to occurrences of regular expressions. Biology, 2(4):1282–1295, 2013 i Bin(i | N, i/N) 0: Bin(0 | n, i/N) 1: Bin(1 | n, i/N) 2: Bin(2 | n, i/N) 3: Bin(3 | n, i/N) Bin(j |N, j/N) 0: Bin(0 | n, j/N) 1: Bin(1 | n, j/N) 2: Bin(2 | n, j/N) 3: Bin(3 | n, j/N) jBin(i | N, j/N) Bin(j | N, i/N) i+2 0 1 2 k i+1 i+2 3 i i k, i+2 i+1 i+1 ii i+2 k i+1 › Contribution: new algorithms › Calculate distribution of #pattern occurrences › Adapt decoding algorithms to include #pattern occurrences 2. Brief overview
  • 30. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Restricted algorithms for HMMs using DFAs 17 P. Tataru, A. Sand, A. Hobolth, T. Mailund, and C. N. Pedersen. Algorithms for hidden Markov models restricted to occurrences of regular expressions. Biology, 2(4):1282–1295, 2013 2. Brief overview
  • 31. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Conditional expectations for CTMCs 18 P. Tataru and A. Hobolth. Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains. BMC Bioinformatics, 12(1):465, 2011 1/2 3 3 3 4 t2 t6 2 4 5 t1 t4t2 1/2 1/2 1/2 1/2 1/2 ii-1 i+1 ri ri+1ri-1 - 2 ri -2 ri-1 - 2 ri+1 ri 2. Brief overview
  • 32. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Required expectations › Time › Jumps Conditional expectations for CTMCs 18 P. Tataru and A. Hobolth. Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains. BMC Bioinformatics, 12(1):465, 2011 ii-1 i+1 ri ri+1ri-1 - 2 ri -2 ri-1 - 2 ri+1 ri 3 5 t 2. Brief overview
  • 33. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Required expectations › Time › Jumps › Contribution: compare and extend existing methods › Accuracy › Speed Conditional expectations for CTMCs 18 P. Tataru and A. Hobolth. Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains. BMC Bioinformatics, 12(1):465, 2011 ii-1 i+1 ri ri+1ri-1 - 2 ri -2 ri-1 - 2 ri+1 ri 3 5 t 2. Brief overview
  • 34. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Beta with spikes: approximate Wright-Fisher 19 P. Tataru, T. Bataillon, and A. Hobolth. Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach. In preparation individuals generations(time) 3 2 4 3 4 5 5 allele count 2. Brief overview
  • 35. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Beta with spikes: approximate Wright-Fisher 19 P. Tataru, T. Bataillon, and A. Hobolth. Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach. In preparation › What is the distribution of allele count in the current generation? 2. Brief overview individuals generations(time) 3 2 4 3 4 5 5 allele count
  • 36. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Beta with spikes: approximate Wright-Fisher 19 P. Tataru, T. Bataillon, and A. Hobolth. Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach. In preparation individuals generations(time) 3 2 4 3 4 5 5 allele count › What is the distribution of allele count in the current generation? › Use the beta distribution › Contribution: › Add spikes (better fit) › Include selection 2. Brief overview
  • 37. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Beta with spikes: approximate Wright-Fisher 20 P. Tataru, T. Bataillon, and A. Hobolth. Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach. In preparation 2. Brief overview
  • 38. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 21 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
  • 39. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 21 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
  • 40. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Trace the genealogy of sampled individuals backward in time 22 individuals generations(time) Populations genetics: the coalescent model 3. Overview: diCal-IBD
  • 41. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Trace the genealogy of sampled individuals backward in time 22 individuals generations(time) Populations genetics: the coalescent model 3. Overview: diCal-IBD
  • 42. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre › Trace the genealogy of sampled individuals backward in time › Coalescent process terminates when reaching MRCA › Time to coalescent event: CTMC 22 individuals generations(time) Populations genetics: the coalescent model MRCA 3. Overview: diCal-IBD
  • 43. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Recombination 23 3. Overview: diCal-IBD
  • 44. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 3. Overview: diCal-IBD
  • 45. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 3. Overview: diCal-IBD
  • 46. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 3. Overview: diCal-IBD
  • 47. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 3. Overview: diCal-IBD
  • 48. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 3. Overview: diCal-IBD
  • 49. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 3. Overview: diCal-IBD
  • 50. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The coalescent model: adding recombination 24 › Multiple sequences and loci analysis › HMM: hidden states = (possible) coalescent trees for each locus › CTMC: probability of the alleles at the leaves 3. Overview: diCal-IBD
  • 51. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Identity by descent 25 IBD tract 3. Overview: diCal-IBD
  • 52. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre diCal-IBD: CTMCs and HMMs 26 › IBD applications › Association mapping › Demography inference › Detection of selection P. Tataru, J. A. Nirody, and Y. S. Song. diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals. Bioinformatics, 30(23):3430-3431, 2014 3. Overview: diCal-IBD
  • 53. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre diCal-IBD: CTMCs and HMMs 26 › IBD applications › Association mapping › Demography inference › Detection of selection › First method to use the coalescent with recombination › One of the first methods to use sequence data P. Tataru, J. A. Nirody, and Y. S. Song. diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals. Bioinformatics, 30(23):3430-3431, 2014 3. Overview: diCal-IBD
  • 54. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre diCal-IBD: CTMCs and HMMs 26 › IBD applications › Association mapping › Demography inference › Detection of selection › First method to use the coalescent with recombination › One of the first methods to use sequence data › Outperforms SNP-based methods › Comparable with sequence-based method P. Tataru, J. A. Nirody, and Y. S. Song. diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals. Bioinformatics, 30(23):3430-3431, 2014 3. Overview: diCal-IBD
  • 55. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre diCal-IBD: CTMCs and HMMs 27 P. Tataru, J. A. Nirody, and Y. S. Song. diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals. Bioinformatics, 30(23):3430-3431, 2014 3. Overview: diCal-IBD
  • 56. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Selection and IBD 28 › IBD tract length depends on MRCA › The more recent the MRCA, the longer the tract › Recent MRCA can be an indication of positive selection › IBD can be used for detecting positive selection1 › Standing variation 1Albrechtsen A et al. Genetics 2010;186:295-308 3. Overview: diCal-IBD
  • 57. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Selection and IBD 29 › IBD segment length depends on MRCA › The more recent the MRCA, the longer the segment › Recent MRCA can be an indication of recent selection › IBD can be used for detecting selection › Standing variation 1Albrechtsen A et al. Genetics 2010;186:295-308 3. Overview: diCal-IBD
  • 58. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre The SLC24A5 gene: diCal-IBD 30 P. Tataru, J. A. Nirody, and Y. S. Song. diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals. Bioinformatics, 30(23):3430-3431, 2014 SLC24A5 › Major influence on natural skin color variation › Under positive selection in Europeans1 1Wilde S et al. PNAS 2014;111(13):4832-4837 3. Overview: diCal-IBD
  • 59. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Outline 31 • 2012 BMC Bioinformatics Evolving stochastic context-free grammars for RNA secondary structure prediction SCFG • 2013 Bioinformatics Oxfold: kinetic folding of RNA using stochastic context-free grammars and evolutionary information SCFG Population genetics Sequence analysis Pattern matching Structural bioinformatics SCFG DFA DTMC HMM CTMC1 • 2011 BMC Bioinformatics Comparison of methods for calculating conditional expectations of sufficient statistics for continuous time Markov chains CTMC • 2013 Biology Algorithms for hidden Markov models restricted to occurrences of regular expressions HMM & DFA • In preparation Motif discovery in ranked lists of sequences DTMC & DFA • In preparation Modeling allele frequency data under a Wright-Fisher model of drift, mutation and selection: the Beta distribution approach DTMC 2 • 2014 Bioinformatics diCal-IBD: demography-aware inference of identity-by-descent tracts in unrelated individuals CTMC & HMM 3
  • 60. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Population genetics: Methods vs Data 32
  • 61. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Population genetics: Methods vs Data 32 diCal ARGWeaver MSMC ms MaCS PSMC coalHMM Kim Tree
  • 62. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Population genetics: Methods vs Data 32 Beta with spikes diCal-IBD diCal ARGWeaver MSMC ms MaCS PSMC coalHMM Kim Tree
  • 63. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Population genetics: Methods vs Data 32 Beta with spikes diCal-IBD diCal ARGWeaver MSMC ms MaCS PSMC coalHMM Kim Tree Data
  • 64. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Population genetics: Methods vs Data 32 Beta with spikes diCal-IBD diCal ARGWeaver MSMC ms MaCS PSMC coalHMM Kim Tree Data
  • 65. PhD defense Paula Tataru AARHUS UNIVERSITY Bioinformatics Research Centre Population genetics: Methods vs Data 32 Beta with spikes diCal-IBD diCal ARGWeaver MSMC ms MaCS PSMC coalHMM Kim Tree Data dimension reduction