CRISPR Cas13

Number of Cas13 molecules in a typical detection environment: ???

Dissociation Constant = 29 ± 7.0 nM

Number of reporter molecules produced: couldn't find any.

CRISPR Cas12a

Dissociation Constant = 54 ± 4 fM.

Other articles found Cas12a to have a dissociation constant of 0.1 nM. The reason why the above is a thousand fold different from other articles is because "the previous studies used direct measurements of the fraction of DNA target bound rather than kinetics measurements, and they did not provide the >32-hr incubation required to reach equilibrium (i.e., at least one half-life of the bound complex), which would lead to apparently weaker binding of Cas12a."

Number of reporter molecules produced: couldn't find any.

Theory on Binding affinity and dissociation constant

Assume you have A and B to form a complex AB. i.e. an enzyme and its corresponding ligand coming together to form a complex.

Applying this idea to how enzymes work, the ability for the ligand to bind to the enzyme is reversible. Meaning, the reaction described above is in equilibrium and will give us two rate constants: one in the forward reaction and one in the reverse reaction. With that in mind, the dissociation constant can be calculated via the rate constant of the reverse reaction divided by the rate constant of the forward reaction (kr/kf). The binding affinity is the inverse of the dissociation constant. So, the lower the dissociation constant, the higher binding affinity we have between our enzyme and ligand. Conversely, the higher the dissociation constant, the lower binding affinity.

Reporting Molecules Calculation

Taken from last year's iGEM project, 1µl of 50µM FQ quencher was used. To be able to calculate the number of reporter molecules, one would need the mass of a single FQ quencher. The figure below are the reporters used, including its sequence along with the attached fluorophores.

For the sake of simplicity, we will only take the first example and calculate the number of reporting molecules in a solution based on that.

Mass Calculation

Name	Molecular Weight (g/mol)	Link
56-FAM	537.5	https://www.idtdna.com/site/Catalog/Modifications/Product/1108
TTATT	1632.8
3' Iowa Black FQ (3IABkFQ)	442.4	https://www.idtdna.com/site/Catalog/Modifications/Product/3463

Note: The average molecular mass of a single nucleotide is 326.56 g/mol ⇒ 5 nucleotides would weight

Mass of a single reporting molecule: 2612.7 g/mol

C=\frac{n}{v} => n=Cv

$C = 50µM$

$v = 1 µL$

n=(50\times 10^{-6})(1\times10^{-6})=5\times10^{-11} moles

number of reporting molecules = n \times N_{A} = (5\times10^{-11} moles)(6.022\times10^{23} molecules)= 3.011\times10^{13} reporting molecules

Assuming a reaction will take place with 1 μl of 50 μM FQ reporter, then we will have $3.011\times10^{13}$  reporting molecules.

References

(Author, year)	Link
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Team:NYU Abu Dhabi/Documentation/DOCS 20ee279bfcdc46b09c4fb108851b2757/Biology 93d1eff7b0cd4d6ca8529879e773d615/BioNumbers cb92527fa8f34aebac2e8ebe1add3543