## Knots were the wrong math

**The Knot Math** was eventually understood to be the wrong kind of math to model our problem on.

Knots take the form of a circle that has been broken and rejoined at a point on its circumference after being wrapped about itself an arbitrary number of times. What we’re working on doesn’t utilize any function that twists loops of DNA the same way. The knot maths provide a way to real-value-vectorize these shapes, but do not provide an easy way to insert our own data. There are two properties that relate to the incompatibility. The first is that knot maths consider two knots equal if their topology with respect to the number of twists they have are identical. Our problem does not consider these two knots equal, as distance and sequence specificity (imagine each particle on the rope circle was labeled) are required. Second, what we produce overlaps arbitrarily by lying a circle segment on top of another circle segment whereas the knot maths produce overlaps with twists. While I think there could be a clever way to identify our problem with the knot math, I don’t think there is a feasible or cost (time) effective way to do this.

Brain continues to storm.

I did managed to uncover some very exciting papers however. One of them was on a piece of software called TangleSolve— which does do site specific recombination and visualization of DNA knots– reading on this software was actually instrumental in understanding why our problem was not identifiable here. Side note– topoisomerase — is an enzyme involved with DNA knot formation and super coiling relaxation.