CRISPR-Cas, a particular type of microbial immune response system, has in recent years been modified to make precise changes to an organisms DNA. In the early 2000s scientists discovered through the study of Streptococcus pyogenes, that a unique CRISPR locus (Cas9) exhibited specific RNA-guided cleavage near short trinucleotide motifs (PAMs). Further research on Cas9 eventually led researchers to create methods that actively edit genomes through Cas9-dependent cleavage and to manipulate transcription of genes through engineered nuclease-deficient Cas9 (dCas9). These techniques have enabled new avenues for analyzing existing gene functions or engineering new ones, manipulating gene expression, gene therapy, and much more.

While great strides have been made over the last decade, CRISPR is still prone to inaccuracies which often generate sub-optimal editing efficiency or off-target effects. The primary interest of this thesis is the investigation of targeting efficiency concerning changes in the guide RNA (gRNA) composition. While many different factors affect the ability with which a given gRNA can target a DNA sequence, we have focused our research primarily on the formation of the R-loop: the hybrid structure formed when the Cas9/dCas9:gRNA complex binds to a host DNA site.

In our investigation, we have attempted to account for several experimental findings reported in the literature as influential for binding efficiency. These include position dependence, base pair composition dependence, and the effects of runs of consecutive mismatches. Using a Gambler's Ruin Markov model to mimic the process of R-loop formation, we fit our model to experimental data and show that the match/mismatch configuration between the gRNA and the DNA target allows for accurate predictions of R-loop formation in bacteria.