1. Genome Evolution. Amos Tanay 2012 Genome evolution Lecture 9: Mutations and variational inference

2. Genome Evolution. Amos Tanay 2012 Sources of mutations Mistakes –Replication errors (point mutations, tandem dups/deletions) –Recombination errors (mainly indels) Endogenous DNA Damage –Spontaneous base damage: Deaminations, depurinations –Byproducts of metabolism: Oxygen radicals that damage DNA Exogenous DNA Damage –UV –Chemicals All of these mechanisms cross talk with the surrounding sequence

3. Genome Evolution. Amos Tanay 2012 DNA polymerases replicating DNA A good polymerase domain has a misincorporation rate of 10 -5 (1/100,000) Any misincorps are clipped off with 99% efficiency by the “proofreading” activity of the polymerase Further mismatch repair that works in 99.9% of the case bring the fidelity of the main Polymerases to 10 -10 Some dedicated polymerases are not as accurate!

4. Genome Evolution. Amos Tanay 2012 Recombination errors A consequence of partial homology between different chromosomal loci Can introduce translocations if the matching sequences are on different chromosomes Can introduce inversion or deletion if the matching sequences are on the same chromosome Can generate duplication or deletions if the matching sequences are in tandem Replication slippage Processing a strand, disconnect and reconnect at the wrong place CACACACACACACACACACGACAGCGACAGTTACAAA

5. Genome Evolution. Amos Tanay 2012 Endogenous DNA damage: Deamination of Cytosines * Thymine has CH3 here NH H H H O N N 2 H* H H O N N O deNHn Cytosine Uracil H

6. Genome Evolution. Amos Tanay 2012 Deamination of Cytosine creates a G-U mismatch Easy to tell that U is wrong Deamination of Cytosine creates a G-T mismatch Not easy to tell which base is the mutation. About 50% of the time the G is “corrected” to A resulting in a mutation

7. Genome Evolution. Amos Tanay 2012 UV irradiation generate primarily Thymine dimers: Exogenous DNA damage Chemicals - Food Benzopyrene – smoke UV radiations (Sunlight) Ionizing raidation radon Cosmic rays X rays

8. Genome Evolution. Amos Tanay 2012 Direct repair Repairing DNA damage

9. Genome Evolution. Amos Tanay 2012 Thymine Dimers can be corrected by a direct repair mechanism Photon

10. Genome Evolution. Amos Tanay 2012 Deaminated bases are repaired by a base excision mechanism. BER

11. Genome Evolution. Amos Tanay 2012 Spontaneously occuring abasic sites are repaired by the same mechanism BER

12. Genome Evolution. Amos Tanay 2012 Dimeric bases and bulky lesions, e.g., large chemical adducts are repaired by Nucleotide excision repair NER

13. Genome Evolution. Amos Tanay 2012 Evolutionary consequences of the rich mutational process Cannot ignore dependencies among adjacent sites Mechanisms are evolutionary variable Lifestyle -> Environmental exposure Germline and male/female ratio Mechanisms are variable on the genomic scale – late vs. early replication

14. Genome Evolution. Amos Tanay 2012 Dynamic Bayesian Networks 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Synchronous discrete time process T=1 T=2T=3 T=4 T=5 Conditional probabilities

15. Genome Evolution. Amos Tanay 2012 Context dependent Markov Processes AAACAAGAA Context determines A markov process rate matrix Any dependency structure make sense, including loops AAA C When context is changing, computing probabilities is difficult. Think of the hidden variables as the trajectories Continuous time Bayesian Networks Koller-Noodleman 2002 1234

16. Genome Evolution. Amos Tanay 2012 Modeling simple context in the tree: PhyloHMM Siepel-Haussler 2003 h pai j h i j-1 hijhij h pai j h i j-1 hijhij h i j+! h pai j+! h pai j-1 h k j-1 hkjhkj h k j+1 Heuristically approximating the Markov process? Where exactly it fails?

17. Genome Evolution. Amos Tanay 2012 Log-likelihood to Free Energy We have so far worked on computing the likelihood: Better: when q a distribution, the free energy bounds the likelihood: Computing likelihood is hard. We can reformulate the problem by adding parameters and transforming it into an optimization problem. Given a trial function q, define the free energy of the model as: The free energy is exactly the likelihood when q is the posterior: D(q || p(h|s)) Likelihood

18. Genome Evolution. Amos Tanay 2012 Energy?? What energy? In statistical mechanics, a system at temperature T with states x and an energy function E(x) is characterized by Boltzman’s law: If we think of P(h|s,  ): Given a model p(h,s|T) (a BN), we can define the energy using Boltzman’s law Z is the partition function:

19. Genome Evolution. Amos Tanay 2012 Free Energy and Variational Free Energy The Helmoholtz free energy is defined in physics as: The average energy is: The variational transformation introduce trial functions q(h), and set the variational free energy (or Gibbs free energy) to: This free energy is important in statistical mechanics, but it is difficult to compute, as our probabilistic Z (= p(s)) The variational entropy is: And as before:

20. Genome Evolution. Amos Tanay 2012 Solving the variational optimization problem So instead of computing p(s), we can search for q that optimizes the free energy This is still hard as before, but we can simplify the problem by restricting q (this is where the additional degrees of freedom become important) Maxmizing U?Maxmizing H? Focus on max configurationsSpread out the distribution

21. Genome Evolution. Amos Tanay 2012 Simplest variational approximation: Mean Field Let’s assume complete independence among r.v.’s posteriors: Under this assumption we can try optimizing the q i – (looking for minimal energy!) Maxmizing U?Maxmizing H? Focus on max configurationsSpread out the distribution

22. Genome Evolution. Amos Tanay 2012 Mean Field Inference We optimize iteratively: Select i (sequentially, or using any method) Optimize q i to minimize F MF (q 1,..,q i,…,q n ) while fixing all other qs Terminate when F MF cannot be improved further Remember: F MF always bound the likelihood q i optimization can usually be done efficiently

23. Genome Evolution. Amos Tanay 2012 Adaptive mutations: Cairns et al. 88 Experimental system: lacz frameshift Luria-Delbruk’s observation The experiment suggests adaptive mutations

24. Genome Evolution. Amos Tanay 2012 The “Mutator” paradigm: Ability to switch to the mutator phenotype depends on particular DNA repair mechanisms (Double Strand Break repair in E. Coli) Mutator phenotype is suggested to be important in pathogenesis, antibiotic resistance, and in cancer Species occasionally change (adaptively or even by drift) their repair policy/efficiency The resulted substitution landscape must be very complex