will tend to tie knots... There is a theorem, due to De Witt Sumners & Yuanan Diao that says

that the knotting probability goes to 1 as the length of the chain goes to infinity, in r 3.

So if you have a very long cable - it doesn't need to be a complicated knot, but eventually - it will knot itself.

So 'you have such long molecules in so such small environment, it is to be expected that these molecules

will have some topological complexity. Now, we do not know if there is spontaneous knotting...

We can anticipate there is. And we do not know - if there is spontaneous knotting - is it important

for the cell? We don't know that. We know that the cell typically does not like topological entanglement.

So the cell has an army of enzymes that, the moment they see a knot, they'll come here...

they say 'Oh, look there is a knot here. Ok, we need to break it. ',

They open, they break, they transport, one strand through the break, and they reseal the break.

And when they do that, they unknot the knot. So these are little pacmans that go around the cell,

they're called 'Type-2-Topoisomerases', and they will just break the chain, transport another strand,

reseal the chain, and remove the topological complexity.

Type-2-topoisomerases are enzymes that are ubiquitous; they have been found in every possible organism;

I mean from archaea to humans, and they are essential to life.

meaning: if the Type-2-topoisomerase in the cell doesn't work, the cell dies.

So they are wonderful targets for antibiotic drugs, for example... So there's uh...

a big family of drugs called 'Fluoroquinolones', ...

you may have heard of 'Cyprofloxacin', ...

used for... to treat bacterial... uh, like urinary tract infections, or sometimes * infections,...

What that drug will do is it will target the Type-2-topoisomerase in the bacterium that is making you sick.

In all those bacteria, when the T-2-TopoIsomerase stops working, these bacteria will have an accumulation of

interlinked DNA - not knotted, but interlinked DNA - and that accumulation of topology will kill the bacteria.

So let's assume this is a DNA molecule that is not helical yet.

Okay? So now let's make it into a helix.

It has to be a right-handed helix, and I need to twist this an even number of times, because otherwise

when I close it, I would get a Möbius band; And that's not what I want.

So, now, I'm going to close this chain right here...

- So this is not human DNA then, or...? - No, let's assume this is either one of those loops

or is a circular DNA molecule that could be a bacterial genome, or it could be just a naturally-occuring plasmin.

And this coil is just a natural coil from the double helix.

And here I just put two of those turns to make it simpler.

But there's many more turns...

- Now, what 'you doing? - And now, these scissors are the enzymes that

are going to start DNA replication. So the circle - if we assume that this is a bacterial DNA -

there will be an origin of replication; replication will go by directionally; there will be first enzymes called helicases

that will unwind the DNA. So they will break the hydrogen bonds and open up the two strands.

So.. unwind DNA, and we can mimic that by just cutting.

And you can imagine another pair of scissors going in the other direction.

Okay, replication is done.

Now we went from one circle - one circular DNA molecule - to two circular DNA molecules.

Well, look what the problem is... We have a topological problem right here...

- What's going on there? They're knotted together, they're linked...!

- They're interlinked. So they are two independent circles. Each one of them has exactly the same genetic code.

But these two circles are interlinked. So, now, if each new cell wants to inherit one circle,

they will pull. If they pull, they will break... If DNA breaks, that's a very bad... that's very bad news for your cell.

Or, very gently, an enzyme called Type-2-Topoisomerase - your old friend - will come here,

will break very gently, will transport one chain through the break, and reseal the break,

and then assess 'Am I done?' 'Oh, I'm not done!' 'Okay, then I need to break again!'

'Okay, I'm going to break again, transport, reseal...' 'Okay, now I'm done..!' 'Now I'm done.'

Now each one of those chromosomes can segregate to a new daughter cell, and cell division can happen.

So this is a problem: when Type-2-Topoisomerases don't work, then the newly-replicated chromosomes are

interlinked. And there is nothing you can do about that.

And that interlinking will eventually kill the bacterial cells.

And this happen every time the DNA is replicated. Every time you go through replication,

the DNA is interlinked. Why? Because DNA is a helix. That's the reason.

It's a very simple mathematical reason: DNA is a helix, so when you cut it through the center

- if it's circular and you cut it through the center -

these crossings will become linked - interlinks between two chains.

Chromosomes look like notes but the occupy distinct territories within the cell nucleus.

And then you're looking here.

Well, the question is, is there an organisation here?