A Biophysical Model of CRISPR/Cas9 Activity for Rational Design of Genome Editing and Gene Regulation
(A) Each crRNA strand is expressed with rate rcrRNA. The active crRNA is formed by either hybridization of an expressed tracrRNA with an expressed precrRNA or by direct expression of a single guide RNA (sgRNA). The Cas9 endonuclease is expressed with rate rCas9. (B) Cas9 binds to the mature crRNA with a forward kinetic association constant kf. After loading the crRNA, the structure of the Cas9:crRNA undergoes an isomerization with forward kinetic constant kI to create an active complex. NcrRNA, NCas9, Nintermediate, and NCas9:crRNA are their numbers of molecules. (C) The resulting active complex performs a 3D random walk with molar flow rate rRW. The probability that it binds to a DNA site is determined by the site sequence, including the presence of a protospacer adjacent motif (PAM), the number of same-sequence DNA sites (Ntarget, j), and their binding free energy (ΔGtarget, j). (D) The formation of a stable Cas9:crRNA:DNA complex occurs in several steps: Cas9:crRNA recognizes the PAM site, unwinds the DNA duplex, and sequentially replaces DNA:DNA base pairings with RNA:DNA bases pairings in an exchange reaction to form a DNA:RNA:DNA complex, called an R-loop. The DNA target site's binding free energy to Cas9:crRNA (ΔGtarget) sums together its PAM interaction energy (ΔGPAM), the energy needed to unwind the supercoiled DNA (ΔΔGsupercoiling), and the crRNA:DNA exchange energy during R-loop formation (ΔΔGexchange). During these steps, the Cas9:crRNA:DNA complex may dissociate with first order kinetic constant kd or it may be cleave the bound DNA site with pseudo first order kinetic constant kC. (E) After cleavage, the Cas9:crRNA:DNA complex remains bound to the cleaved DNA, and is considered a no-turnover enzyme. Additional model parameters include the DNA replication rate (μ) and the degradation or dilution rates of Cas9 (δCas9), crRNA (δcrRNA), and Cas9:crRNA complex (δCas9:crRNA).