Overview

If the R-loop is completely established, then the complex Cas9:gRNA stays bounded to the DNA strand and Cas9 will cut the DNA sequence. This will lead in the loss of some base pairs that the plant cell will repair via Non Homologous End Joining (NHEJ). This may cause a change in the reading frame (TS_OFF → TS_ON, and consequently in the proteins produced by the cell, performing what is known as knockout. Taking profit from this shift in the DNA reading frame, we included Luciferase after the genetic target.

Therefore, light signal emitted during Luciferase assays, will provide an output information about the whole process performed by CRISPR/Cas9 within the plant cells. As it relies on the target finding by the Cas9:gRNA complex, it is also a measure of the pair gRNA-target efficiency in order to knockout the undesired gene.

Knockouts estimation

While the Cas9:gRNA complex is produced, it produces knockouts among the host genome. In our case, these knockouts are expected to improve the desired plant trait. In this section of the modeling, we wanted to study in silico if the suggested pair target-gRNA would work in vivo, obtaining a predicted number of knockouts performed in the Testing System construction for the time at which the Luciferase assay is performed.

The number of knockouts produced at measurement time t _m will be:

Where:

• The concentration [Cas9:gRNA] (t) is the amount of complex produced at the time when the luciferase assay is performed. This can be estimated using the system of ODEs described in the previous section Cas9:gRNA complex formation.
• The term N_ON makes reference to the quantity of on-targets in the nucleus, i.e. the gene copy number of the Testing System construction which has been agroinfiltrated.
• The rate k_cleavage has information about the cleavage frequency in the Testing System construction. It has information about the complex diffusion, the rate of Cas9 cleavage, and the thermodynamic stability of the R-loop formed before the cleavage. It is:

The rates in last expression mean:

• The rate of collisions k_r, produced between the Cas9:gRNA complex and the DNA in the nucleus.
• The rate of cleavage k_c at which Cas9 cuts DNA strands.
• The occurrence of the Cas9:gRNA dissociation from a DNA region.
• The probability that the R-loop is formed between the complex and the target used in the Testing System construction. This parameter has also information about potential off targets.

Values for parameters k_r and P_{complex,target} are related to diffusion and thermodynamics, respectively.

ORFs probability distribution

From the moment that Cas9:gRNA complex is produced, it starts diffusing, colliding and binding to on-targets (ONs) and off-targets (OFFs). Those have known initial concentrations, since the number of on-targets is the gene copy number of the Testing System construction, and the number of off-targets has been obtained by our off-target search algorithm.

After the complex interacts with a target, it changes it sequence. The cut performed by Cas9 takes place in the PAM-proximal region, avoiding the possibility of a new zip-union with the gRNA to form the R-loop again. Therefore, knockouts cannot be represented as off targets or on targets anymore, as binding to the gRNA will not be thermodynamically feasible because of base pairs rearrangement.

In our Testing System strategy, we rely on the reading frame shift to let Luciferase be transcribed. However, this event will not always be likely to happen. There are three possible reading frames and the resulting one after the Cas9 cut, is unknown. This created the necessity of estimating the probability that the resulting frame after the Cas9 cleavage and NHEJ reparation, was the correct for Luciferase transcription.

Consulting bibliography about frequency of indels in Nicotiana benthamiana, we could gather information about this phenomenon. Results showed barely any difference between the three possible results (ORF+1, ORF+2 and ORF+3). Therefore, the probability that our Testing System would express Luciferase was P_ON≈1/3.

Figure. Estimation of probability associated to each one of the possible resulting reading frames after Cas9 knockout. Blue bars represent experiments performed only with Nicotiana, while orange bars depict results obtained working with various plants.

Main remarks

Analysis of bibliographic data determined that the probability that our Testing System would express Luciferase was P_ON≈1/3. Further experimental results in the future will allow to fully validate the model.