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Modeling the Evolutionary Dynamics of CRISPR spacers

Presented by: 
A Kupczok [IST Austria]
Tuesday 21st June 2011 - 16:10 to 16:30
INI Seminar Room 1
We present a phylogenetic insertion- and deletion-model for CRISPR spacer turnover. CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) is an adaptive heritable immune system found in Eubacteria and Archaea. The system consists of a number of CRISPR associated (CAS) proteins and an array of repeats and spacers - the later represent the viral/plasmid targeting sequences and the system functions in an analogous way to the eukaryotic siRNA system. The length and content of the spacer array varies considerably among individuals within species (suggesting a rapid arms race) and it has been suggested that there is a selective cost, in the absence of parasites, associated with maintaining these arrays. At one point in time and space spacers can be beneficial, if a parasite with the corresponding sequence exists in the community, or they can be useless and thus neutral or slightly deleterious.

The rate at which spacers are gained and lost from these arrays provides insight into the evolutionary dynamics of host-parasite interactions. To this end we model spacer insertion and deletion as a continuous-time two-state Markov process. The model parameters are then estimated by maximum likelihood along the phylogeny. We assume different dynamics, modeled by different two-state Q-matrices, for beneficial and neutral spacers. An underlying switching process allows for changes between these Q-matrices. The information whether a spacer is beneficial or neutral is not known, thus we use ambiguous states. Using known spacer annotation we can also apply a partition model allowing the evolutionary rates to differ between spacers of different sources. We evaluate the switching model by simulation and also analyse bacterial data sets.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons