 Alright, so I'm a mathematician, and I feel comfortable talking about biology to physicists and physics to biologists, but I'm really scared to say physics in front of physicists and bio in front of biologists, and I'm going to do all of that today. So some of what I tell you is not exactly right, but it's the way that I think about it, alright, and we'll go with that, alright. So the majority of the time I think we're going to end up talking about the action of these type 2 topoisomerase, topo4, and then I hope to talk a little bit about glubol and glubol decay later in the talk. So alright, so here's the problem, I don't know if any of you have children, but Despicable Me, beautiful movie with these little minions here, and I want you to imagine you're the minion, alright, and you're given this little piece of rope and what you're supposed to do is get the knot out of it, alright. So first of all you're supposed to see that there's a knot, and then you're supposed to get it out, and the way that you do this is you can take kind of one spot that looks like this and you can cut one of them and pass it through and do like one little crossing change, does that make sense? So you get to do that somewhere here and in doing so you have to make this thing into just something that's equivalent to a circle, so you might look a little bit more like this because you get the little scissors, alright. The problem is that you're actually not that big, you're much smaller, alright, you're like that size, and also you can't see, alright, so you're this tiny thing and you have to find somehow the right place to act on this, alright, and so that's kind of what these type 2 top-wise summaries do, alright, and what we want to do is figure out how they could possibly find the right spot to act, alright, so I'm going to give you this is, alright, so now this is where I'm afraid to talk in front of you, Lynn, but anyway, so top-wise summaries are these enzymes, they regulate tangling sort of stuff and supercoiling in DNA, there are type 1 top-wise summaries which cut one strand in type 2 that cut two strands, Dushan was talking about this yesterday, so it cuts both strands of the double-stranded DNA, it works a little bit like this, I mean this is something I stole off the web, but the idea is that it grabs one piece, the G segment, kind of traps that part, you get another segment that goes down, it clips the blue piece, passes the red piece through, reattaches the blue piece and it goes through, so it changes something that looks like this, cuts it and changes it to look like that, alright, alright, so this is what I found out that I was just lying to you, but anyway, so the great thing about these type 2 top-wise summaries is that they're used as chemotherapy drugs and also as antibiotics and so this is great for grant writing because the congressman don't want to go after your grants because it says that you're trying to save humanity a little bit, one of the wonderful things here, alright, so the idea is that these top-wise summaries, if you give them these chemotherapy drugs, it signals to the cell that it wants to die, is that fair? It's a suicide signal, so anyway that's the way these things work, but they're important because they deal with this top or with this supercoiling and we want to understand kind of how they work, alright, so here's more pictures, I think this is one, I think you showed ones like this yesterday, Duchenne, alright, so we're dealing with something called topo 4 which is a type 2 top-wise summaries and it mostly does kind of unlinking here, it also relaxes some supercoiling but we're kind of dealing with unnotting and unlinking and people have found that it's very good at unlinking stuff, much better than kind of random sort of action, so it's going to do something like this, right, that's you sitting right there, alright, so you wonder how the thing figures out where to act, right, Andre always tells me that these enzymes don't think, right, they're mechanical things, they just do something, right, I still like to think of them as thinking but they don't really, alright, so where do they know how to act? Well one thing is that maybe they just attach when things are close together and they do one of these actions, it's basically like random sort of thing, but that doesn't seem to be the case, alright, and there are a couple problems at least with this, one is that every time topo 4 or these type 2 top-wise summaries is act, they use energy, so this is a huge waste if they were just to continue to use energy and then basically have to undo what was just done, the other problem is in anyone who's like untied cords knows that if you kind of pass the wrong piece of string, the wrong place, you create a gigantic mess, right, when you undo your shoelaces and you're not paying attention, all of a sudden you're like how could this be so awful when it normally just pulls out, right, so the point is that you can easily by doing the wrong sort of movement increase the amount of entanglement instead of decrease it, alright, and that doesn't seem to be the case, so in particular we're thinking of this as being our molecule here, our DNA, and in this situation it doesn't seem to act in these twisty regions, alright, which wouldn't create a problem so much as just be a waste of energy, it seems to know to act in these regions where you're actually simplifying the entanglement, alright, so then the question is how do they find this right place to act, alright, and so now this is my very lean background, so Cosrely's lab had this stuff that said that top of four basically is very efficient and unnotting DNA, Greg Buck and Lynn had this this model that it was these hook juxtaposition so somehow maybe it acts where these two pieces are coming together like this like what we see right here, and then Hussan did some stuff with Lynn as well with some simulations, you also have a has a poster out there which is a little bit along the same lines, trying to see if acting at these hook juxtapositions does simplify the knotting, basically found that that is the case, Andre Stasiak did some work in chrysodoris as well, I think I have everyone that worked on it, and then and then from Giovanni's lab with Andre and his I guess which was a PhD student at the time, right, they found that by super that supercoiling been basically tighten the knot and the idea is that if you've got supercoiling and you tighten the knot then you might be more likely to create situations that look like this which then maybe the top of four can find and then do the action there so we wanted to see if kind of putting all that stuff together would create some sort of geometry that the that the top of four could could find right could isolate all right and so that's what we're trying to do all right so the basic idea is we're gonna create some simulated DNA chains and we're gonna take places that look like this these hooked juxtapositions we're gonna pass it through itself we're gonna do like a we're gonna do our little computer version of a top of four and then see what happens right this is us some other things to keep in mind which will tell us a little bit about which motivates why we looked at some of the quantities that we looked at one thing is that it appears at top of four either likes DNA that's bent or likes to bend DNA I think that's not exactly known which of the two it is but anyway it prefers to have the one segment be bent and that it seems that it prefers certain sort of angles all right of one of them next to the other all right so this is what we actually did then so we're gonna simulate we have worm like chains we're doing this all on a computer all right and we generate some chains and this red thing right here is our G segment so it's the thing that the top or two attaches to and the blue curve is the one that's supposed to simulate is passing through the red one all right so we're gonna have something like this and we're gonna basically move that blue one down to here all right we're gonna pass it through and some technical stuff we actually don't use this you know we actually replace three segments by a straight line so it's a little easier to keep track of angles and stuff like that but I'm not sure you really care about that and we looked at juxtapositions that are within kind of like two edge links that's how close they have to be together so if they're like this but they're far away from each other then we don't do it they have to be close and kind of next to each other all right and then the sort of things that we measured were well we measured other stuff but the sort of things that actually mattered in the end were how much this one was bent the G segment all right so that bending angle right there and the other thing was the angle with respect to each other so if you could kind of look down on the red one to see that angle at which the blue one lies over and it's going to be right this is going to be a like an oriented angle right so this is a I forget if we call this positive or negative I guess this is positive and then the other way is is negative all right so that's what we're doing okay so we generated these worm like chains these were done by Julian who's in Andre Stasiak's lab with Dushan we generated negative trefoil knots and then link chains this is like one of the trefoil knots this is one of the links or catnames and we're simulating you know three KB chains so just 334 edges and we used a delta LK of 16 and that's just measures how much supercoiling that we have in it all right and so this is what they look like all right this is an example all right so now I just want to rehash where we are so far in case you didn't understand anything that I said so far this is a re re entry point to the talk if you care to listen any further all right so the point is that DNA gets tangled during replication there are these enzymes these topo 4 that do the unnotting and unlinking and they have to figure out where to act all right they have to be smart about it to some extent and we want to figure out if the supercoiling basically tells us some or spots some highlights some spots where you could act and preferably simplified either the knot or the link all right did I say everything here yes all right and I had to put the guy down here is I like to have at least one picture on every slide right otherwise I just feel wrong so okay so first we're gonna start with the knots all right so we're starting with a knotted configuration and we're trying to see what we can find out here so some observations there's just two examples of this so the knots tend to get localized because of the supercoiling this is kind of what Giovanni found earlier and usually what happens is the knots end up at one of the two ends all right so the knot tends to isolate down to the end the same way Duchamp had the simulation where they were open remember and he was twisting the thing and the knot just kind of flew off the end right and so it's the same sort of idea here and the other point is that you get lots of places where the knot is kind of close to itself right so you get a lot of kind of potential places where they're close enough together that the top-oil summaries could act all right and has to decide whether that's a good spot or not we so we usually saw it look like this but sometimes we would have the knot move you know in between the thing which made us think that the Monte Carlo stuff was actually working yeah yeah I you know Julian dealt with that part of it but I think it's crankshafts and maybe some reputation sort of stuff yeah I think he actually does he figures out how big of a crankshaft you can do to guarantee that the knot stays the same that you're not passing anything through itself and it ends up for long kind of you have to run this thing a really long time to get a sample you know but but when you do you know when you see samples where that knot is actually moving its way through your heartened with the fact that it's working right somehow if it's always down at that end then you're it's not so great all right so this is so this is what happened all right this is the data right here all right so this is alpha one remember alpha one is how much the the the first segment is bending all right the one that the top is supposed to attach to all right the because of the way that the angle is measured a low alpha means that it's really tight bending and a high alpha means that it's like straight okay because it's an interior angle not an exterior angle so this means that it's here very highly bent and this means that it's not bent at all all right so this is a stacked histogram the green part so okay so this is this tells us the distribution of angles that we saw at juxtapositions by by this bending angle and then the green part of it tells you how many of the juxtapositions if you do the topo to action or topo for action how many of them keep the same knot type and the blue ones are the number ones where you actually simplify the knot type okay so the total height of this thing is the total number of is the histogram for this thing and then it's colored by how many of them actually change so you can see that there are lots of bending angles up here in the 140 to 160 range but a low percentage of them actually change the knot type right now on the other hand if you look down here you see that there aren't as many of these but there's a higher percentage of them where doing that topo for action would change the knot type so up here is a is the renormalized basically version of this and so you can see that that when you have more bending it is more likely that your that your action is going to change the knot type all right so this is kind of consistent with what we see here all right does that make sense any questions yes no well it does kind of right if it's in the supercoil part I guess it would not be bending as much as it would in the in the like the trefoil region but you know these things are also just vibrating so every once in a while you see some low bending in the knotted region some high bending in the supercoil region and so I think that's part of it yeah Luca no because we made sure that the edges never pass through each other at any of the steps so the trefoil was always there it started with it there and then it always stayed there what's that part of the code yeah all right so this is so this is again the same one I just made it bigger that was fun wasn't it all right so so again alpha one's the bending angle and what we're seeing is that higher bending angle does improve the chances that it's going to simplify the knot all right if you were to choose those the ones that have higher bending angle you have a higher probability of changing the knot type now theta is this angle right looking at one of the the t-segment over the g-segment I guess alright and here you can see the effect is much larger right most of the you know you're more likely to see angles on the order of 40 to you know 70 degrees here but almost none of those change the knot type because those are all kind of in that supercoiled region right on the other hand if you look down here in the negative region negative theta values then nearly all of them will change the knot type so there aren't many of them but if you act there you're almost always going to be successful all right why is it not symmetric because it's yeah yeah all right and so that it looks this minus 45 degree angle looks like roughly like that that's the whole point so then so the I guess okay there's the combined effect all right can you now can you look at out at alpha one so this bending angle and this you know is it like a coupled quantity and so here we get like a heat graph and you can see that there's more of an effect you know when I look at this thing I I kind of see a diagonally sort of vision of this thing which suggests that that theta is more of a well that theta you know clearly this thing has a verticalness to it but it's slightly kind of horizontal so so clearly like theta is the major player here but alpha one has it seems to have a little bit of an effect as well all right and so red here means that if it has that alpha one and theta value then essentially all of the passages at that point simplify the knot type and the blue means that that none of them do essentially all right so then we want to go to links and see if the same thing works for links all right for knots it looks like it works pretty well all right that there is some geometric information there that that would you know point you to the simplifying spots for links so just in general we have the same sort of situation where the linking part of it seems to be isolated right they the supercoiling seems to push it into regions what we see more often is that they tend to leave in kind of the same direction not in opposite directions like this they tend to like each other all right which I think is sweet all right and the other thing that we see again is that there are lots of places where the thing you know where the two edges are close enough together that it could act all right so if we do this for links again now we're looking at the bending angle of that g-segment and we again see that there is an effect of alpha one that more tight bending does improve your likelihood of simplifying the knot acting at those juxtapositions but it's much milder than what we see for knots all right yeah I mean it's they're all this link you know I forget what it is maybe there's six crossings in it or something like that I can't remember maybe it's five I don't know I don't want to count in public it's a little embarrassing of trouble above four so anyway if we go to theta right this is the angle at which one goes over the other one you can see that again there's a more of an effect than what we see for the bending angle but it's but it still doesn't explain everything right I mean here you see kind of much more many more situations where you could be in that kind of sweet spot for theta but still not be able to simplify the knot or simplify the link I guess it is but the point is that actually you know what we saw before was this region was very good for links and it's very good for knots as well and so that seems to be kind of a sweet spot here for both of them which is encouraging and here's our heat map for links again you know alpha being further this way makes you more likely so in other words having more bending makes it more likely that you're gonna that this juxtaposition will simplify the linking but clearly having a this certain negative theta values in general makes you more likely or that's the as a bigger effect I guess than the bending angle right so it's a similar sort of thing to knots and here they are together with knots and links with the alpha ones so again you can see the effect for the knots with the bending is bigger than for the links and for theta again you can see that for knots it's a bigger effect than for links but again there's this region kind of say from minus 60 to minus 20 where in both situations a great majority of those juxtapositions do simplify the sort of knotting or the entanglement that you have here all right now so stone had a paper in PNAS in 2003 that suggested that the theta angle for topo two is between minus 60 and minus 30 right which is cool because it's right in the range that we were looking at and then Newman had one where he thought it was that theta should be minus five now I mean Andre's the biologist I'm a simple man all right and Andre says that that maybe this minus five isn't right that the experimental setup made it so that that's not quite what we have I guess from my perspective like you know even if it's like this grabbing it at the at the like it's gonna make some mistakes right it's not gonna be perfect they're gonna be sometimes that it acts and it's at the wrong spot but it just at some point it can happen too often right and I don't know if you know working 85 percent of the time is enough or if you need 95 percent of the time or only 50 percent of the time would work and I'm not sure that anyone really knows anything about this and so so it could be that minus five is the right angle and you know only working you know 60 percent of the time is enough but we would argue that that we think that probably the state of angles between minus 60 and minus 20 would be our guess all right and again from our perspective here I hate to claim that we're actually doing any biology here right the point is that I think what we found is that if you had a machine that were to act at these certain spots with these certain angle preferences that it would simplify the thing preferably and conceivably nature would figure this out somehow and that's maybe why it would be that way right so that's our proposal all right and here's the combined effect of the heat maps again you can see it seems to work with knots better than links but so it goes so then the question is okay we have these sweet spots here right kind of in this region or down here where we're very likely if we have these theta and alpha angles to simplify the knot or the or the link so where do these things actually happen right so then we went back and we took these spots where did this and we went back to the supercoiled chain to try to figure out where they were and what we found was that it tended to happen so this is an example of one of the links where the two linked parts are together and just when they separate all right so just when they come apart there's this spot right here where you get this kind of negative angle and that seems to be the spot where acting would simplify the thing so it it appears to not be working out here ideally it would work at that spot and since there's kind of only one you know that's why we don't see a lot of them kind of and kind of not right I mean they're not colored in the cell as far as I understand is that right Lynn yes okay first thing it has to do is get the glasses on to get the color right but it's the our idea here is that it's attaching to the red one right and looking for blue spots I guess so it was so it would so it's just so it's colored in this sense and that that didn't make any sense okay so but yeah the angles that do that it but the point is that we're yes I think the point here is that that our model is that it's grabbing on to the red one and then it has a groove right it has a groove that that has basically if you're a happen to be at this other angle then it can fit in there and it can do the action right and so it wouldn't if it attached to the blue one the red one wouldn't be aligned with it in that way and so it wouldn't do the action in the other direction I think is the point it could but yeah well but the point is on the links we never saw I guess the point is that this this coupling of angles we never saw that happen on a common link or on when we were doing linking we never saw a red red one or a blue one we sampled enough no it's I mean yes but I guess the point is that you know we're just we're taking a snapshot and just looking at what happened at this time right so we have a number of snapshots we have a number of places on each of those snapshots where it could happen but we certainly we're not doing any dynamics where who's son saying well it could go there and maybe it could swing around and do something well we're not dealing with that right we're saying okay well it would have to be in the snapshot exactly like this right so it's a little different right well no but but we search for all we look at all of these juxtapositions and see so this one for example we analyzed but it was in one of those situations where the theta angle wasn't in the sweet range right and the not type stayed the same or the link type stayed the same right so that is the end of my of that part so in particular the point is that I guess the supercoiling localizes is not in linking if the topo could somehow kind of recognize maybe these certain theta values that that could be enough to simplify the nodding enough to kind of explain how it can be so efficient at nodding and unlinking things and also stronger bending will help a little bit as well all right so that's my biology stuff now I'm getting into my physics stuff that I don't know about all right and so I'm going to talk about glue walls all right so so this thing is wildly out of scale that the quarks and anti-quarks are this size so that I could write quark and anti-quark on them all right that's the scale of them anyway there are these things called mesons mesons mesons okay mesons are quark anti-quark pairs they're held together by the strong force and I guess this strong force can be thought of as it as a exchange of gluons through like a tube all right this is all right so that's our model and the idea is that these things are cruising around in space this quark anti-quark can come together and in doing so they kind of destructs and creates can create a sort of circle thing like this and it makes the sound boom all right it's not in the literature but I'm pretty sure that it's true okay and so so this is called a glue ball that's just purely a tube of these gluons being cut and exchanged around and these glue balls exist for like 10 to the minus 21 seconds they don't have a long life by our but by their skill they live very rich lives all right okay and so Kepp Hart who's an actual physicist right says that that these things for energy considerations if they create this when they actually come together and create this tube then the tube shrinks all right and you get into what's called a tight knot state all right so this is it without a thick tube around it that's it with like a maximally thick tube around it and this is a image I got from some paper that was out I think last year of what a glue ball might look like but the point is that it's a long tube all right and so if you have a long tube and the two ends come together then there's a chance that it's knotted all right okay so the other thing I should say is Jason and I with others but have been trying to create these tight knots for many many years right for what's really a frightening number of years at this point like 20 or something and so we have computer programs and stuff to simulate what these things look like when they're tight all right and so what I want to talk about here is the decay of these glue balls so you have a glue ball that we assume is in some tight and state and we want to know what would it decay to right over time over its course of its short life it's going to decay maybe down to just a linear thing and then fall apart so the two ways that it can decay is via at least two of the ways that it can decay is quantum tunneling which is a word that at least Renzo used yesterday I was heartened by that all right so there's quantum tunneling and the idea is that you just you kind of pass one edge through another edge which is exactly the sort of thing that we were doing with top or two right one piece of software two different areas that's the beauty of it all right and the other thing that you can do is reconnection all right so you could reconnect these things as well using this orientation preserving I guess is a orientation preserving reconnection so this gets into this reconnection stuff that Dewitt's been talking about for a while Mariel talked about as well yesterday and Renzo as well right so this quantum tunneling is like top of four and so that's what I basically just want to show you some pretty pictures all right so here's a tight trefoil knot and now every time so our model is that every time the tube runs into itself that's what these yellow things are all right there's whenever the tube touches itself there's one of these one of these tubes goes from the middle of one piece to the middle of the other piece all right so those are like tube contacts and now I want to color them by doing a quantum tunneling event at that spot right so I'm going to take it's like this then I'm going to pass it through itself and see what type of knot that we get see how it would decay in that situation and so if you start with a trefoil what you see is that all of them turn into unknots so if you pass any of these edges through any of the other edges goes to an unknot but the question is what do we see for other knots so here's the figure eight knot all right so again the figure eight knot only has one knot that it decays to and that's to the unknot all right but if we get up to the five one knot for example it decays mostly to a trefoil basically all these ones on the outside but a couple of spots it decays to the five two knots so if you pass that edge through that edge and of course this thing would be thickened right I just made it thin so it would be easier to see it can pass to the five two knot and the five two knot can turn into the unknot if you hit one part of it to the trefoil if you had another part of it and then there's something that's actually kind of back here where it can also turn into a five one right so there seem to be some like in most of the spots the thing simplifies the knotting and in some spots it it will kind of make the knotting either kind of equivalent or more complicated but they tend to be isolated spots right and Jason will someday I'll talk to you about this as well because we've got this compression thing that we can put into this model as well but the also well so one thing is just like I created these pictures and then I just sat in my office and I looked at them because I found them very beautiful all right but the other thing is see how it kind of it kind of divides the knot into a couple pieces right kind of there's this one twisted version over here and then there's another version of or there's a diff kind of a different area over here which I think is kind of interesting and might tell us something about the knots in general as well to get to some more complicated ones so here's the seven one knot which is which I guess that's a twist knot right and so that has areas where you can pass if you act at that clasp all right then it goes directly to the unknot if you start acting in other regions where the twisting happens then you can simplify to other knots the the tight knot the ideal not depending upon oh this is a six to I meant right here oh so that doesn't go all the way to the unknot it goes to the five one okay so the point is that these ideal knots are tight knots don't always get into a super symmetric position all right so what's that very symmetric excellent point right I can say that in a math crowd and they won't it was not as problem problematic right so anyway these these are a function of the you know of the configurations right if you change the configuration you'd see different places where it would act but these are the Titan ones so for most of the seven one they pass down to the five one so it basically just gets rid of one of the twists I guess oh the six two is six two must be what's right okay so here's the six well six two which passes to several different types of knots again here's one that's more complicated or two that's more complicated but they're just kind of these isolated spots 817 I now I just started grabbing ones that I thought looked cool 818 was probably my favorite right it has kind of one side of it that all passes to a positive truffle and then it has another side of it that passes all to the minus truffle and here again you have for the 817 you have a couple of spots where the it passes to more complicated ones but again those are kind of isolated in the middle if we go up to 10 crossings 935 I don't remember is there anything special about 935 I guess I kind of remember it before what's what's special about it can okay it's a pain in the heck so 935 has a bad attitude super bad attitude but that's okay right okay so so yeah 935 like almost has everything switching to the 7 4 not which I didn't see very many times going up to 10 crossings this is I think one of the only ones with just a few isolated spots that got more complicated you know here's a 10 8 not which again isolates into kind of these three regions 1032 which isolated into a number of different regions which are kind of all their own thing which I thought was cool I don't know what I liked about this one it's 1041 why not all right and then some other ones this was a situation there are a couple ones right here where you end up in a straight so one of the things that these tight knots can have is these straight regions and in the straight regions you can have just kind of spots that do have one more okay I do have it I'll we'll see that better on the next one so 10123 is kind of related to the 818 not and it has the same sort of behavior right kind of half of it goes to one thing half it goes to another and what else here okay and here we see some of these kind of strange regions here's a straight region right there in straight regions you don't have to have these tube contacts which is like what you see there and right there and a little bit right here you have ones that are not that are kind of just barely you know in in most of these tight knots they're trying to tighten down right and so it's you get these like clasp situations where they're kind of tightening down on each other but occasionally you have things that are kind of riding side by side right and in those situations you don't have as much of you know you don't have as many of those struts you have just kind of enough to keep them from falling down on each other so anyway I don't really have anything to to conclude about these glue balls except that I think this is really cool and I want to do the reconnection events and then I'm going to talk to anyone who said reconnection that I remember in the last five years and show you what the pictures look like and we'll go from there all right so that's where we are so I would just like to end by thanking our organizers and I see TP for having us it's always fun to come here and I have a number of collaborators from different parts of these things who are right here and thank you very much