# CRISPR as a Diagnostic Tool

### What is CRISPR?

CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) refers to a family of DNA sequences originating from bacteria and archaea. CRISPRs are the basis of systems such as CRISPR-Cas9, CRISPR-CPF1, etc. which tools for editing genomes and diagnoses.

CRISPRs were discovered in archaea as a defense mechanism against viruses. They consist of repeating sequences of genetic code interrupted by “spacer” sequences which remain from previous invaders (Broad Institute 2018). CRISPRs aid the cell in detecting bacteriophage in subsequent invasions. The system works by transcribing the “spacer” sequences into short RNA sequences (called crRNAs) which guide the system towards matching DNA sequences - in this case, that of the bacteriophage. When the target DNA is found, CRISPR produces an enzyme which binds and cuts the DNA. Cas13a is an enzyme which goes beyond gene deactivation by indiscriminately cutting surrounding RNA (Gootenberg et al 2017). SHERLOCK is a diagnostic tool which relies on additional strands of RNA which release signals after being cleaved (Zusi 2018).

## Modeling Collateral Cleavage Activity of CRISPR-Cas13a

We wanted to create a model to better understand the relationship between the amount of target DNA, amount of RNA, and the resulting collateral cleavage activity. We based our ODE’s and parameter values on the work done by the 2017 Munich iGEM team. For parameter values which could not be easily be found, we arbitrarily determined the values by inspecting various solutions to the set of ODEs. This inspection is demonstrated below. We also used a “general” degradation factor for each protein, mRNA, and RNA. Since proteins have a significantly higher half-life than mRNA, further experimentation/literature review should be done to determine exact values in order to produce reliable results with this model.

1. $$\frac{d[Cas13a_{M}]}{dt} = k_1 - \beta \cdot [Cas13a_{M}]-k_2 \cdot [Cas13a_{M}]$$
2. $$\frac{d[crRNA]}{dt} = k_1- \beta \cdot [crRNA] - k_3 \cdot [crRNA]$$
3. $$\frac{d[Cas13a]}{dt} = k_2 \cdot [Cas13a_{M}] - \beta \cdot [Cas13a] - k_2 \cdot [Cas13a] [crRNA]$$
4. $$\frac{d[Cas13a_{crRNA}]}{dt} = k_3 \cdot [Cas13a][crRNA] - k_4 \cdot [Target][Cas13a_{crRNA}]$$
5. $$\frac{d[Target]}{dt} = -k_4 \cdot [Target][Cas13a_{crRNA}] - \beta \cdot [Target]$$
6. $$\frac{d[Cas13a_{crRNA/Target}]}{dt} = k_4 \cdot [Target][Cas13a_{crRNA}]$$
7. $$\frac{d[RNA]}{dt} = -k_{col} \cdot \frac{[Cas13a_{crRNA/Target}][RNA]}{k_M+[RNA]}-\beta \cdot [RNA]$$
Constant/Parameter Value Description
$$k_{col}$$ $$10 \frac{1}{min}$$
$$k_M$$ $$500 nM$$
$$k_1$$ Determined by speculation Constitutive expression of $$Cas13a_M$$, crRNA (coupled)
$$k_2$$ Determined by speculation Transcription of $$Cas13a_M$$
$$k_3$$ $$1 \frac{1}{min}$$ Equivalent to $$k_{cr}$$ in Munich 2017's model
$$k_4$$ $$0.001 \frac{1}{min}$$ Equivalent to $$k_{t}$$ in Munich 2017's model
$$\beta$$ Determined by speculation Degradation factor