Alien Technology 101: From Cells to Neutron Stars ▸ KITP Chalk Talk by Greg Huber

Thank You Lars I'm here to tell you that there is alien technology and that you shouldn't be too worried about it but it is every bit as mysterious as the phrase sounds now I have to define what I mean by alien technology very carefully so I do not mean I know it's cute but but I don't mean green visitors who come in their souped-up spacecraft or like that to visit our planet even if they're friendly well meaning what I do mean is something that you might say at first glance is a little more pedestrian and I'll give you an example the humble pinecone I just picked one example out of probably millions of things around us that you think is an everyday object or everyday piece of your life but in fact if you really think about it there's a degree of design here which has nothing to do with anything human that these were these structures evolved eons before our ancestors evolved and in fact they're all around you if you only have eyes to see them and this has given rise I think to it's not an original thought and it's given rise to a whole field called biomimetics where people design technologies or architecture around the biological organism solutions to different problems in some cases we don't even know what the quote-unquote problem is but we do see the biological design around us so I found this online it's a to me it looks kind of alien but in fact it has basically the same architecture as the pinecone if you look you might know about the arrangements of the buds well the the incipient buds on a pinecone called primordia in fact they form a kind of Fibonacci structure if you look at the spirals created and in fact that's what this architect was trying to capture in this pod building right it's always been my dream to live in a pod building I like this one now the most striking examples of this are not at the level of pinecones and things that are macroscopic like us it's actually the structures inside your cells structures in your side your cells have nothing to do with any human design whatsoever they're truly alien in the sense that we don't really understand them and not only do we not understand them we had nothing to do with them at all they go back to the most primitive cells these structures go back billions of years I think the latest estimate for bacterial origin is 4 billion years something like that and already a huge amount of structure and biochemistry was invented by bacteria only refined by eukaryotes which are our type of cell ok so before I go any further I'm going to show with the aid of some Hollywood special effects artists who actually work not far from where I used to live near West Hartford they were commissioned by Harvard University to work with some Harvard scientists Harvard biologists to create an animation this was 10 years ago but it's so spectacular I want to show it to you and it comes with some music to get it to play oops and I stopped it [Music] so just oops oh wait sorry that's not right this is the right one alright we'll discuss afterward okay that's going to let you view it [Music] blew things this is membrane to feature in my talk later these are stiff filaments in the cell called the cytoskeleton these are basically polymers formed out of proteins laughter Greg oh yeah sorry you guys should turn this down [Music] another part of the cytoskeleton this is an interesting cytoskeleton carrying a big membrane bag this is all going on inside your cells this is slowed down I'm scales here at milliseconds but it's been slowed down so milliseconds become second space [Music] this is a structure called a mitochondrion your cells have hundreds of those maybe thousand that membrane membranes the circulation meaning membranes pinch-off spheres this is called the Golgi apparatus you may have heard of that [Music] and we're outside of the cell the cells rolling along other cells and this rolling behavior this is supposed to be a leukocyte leukocytes are your white blood cells slipped out of the vasculature in between two other cells to fight an infection okay that's what's going on in your body all the time non-stop if that's not alien technology I don't know what it is so what does physics have to say about that it's an interesting question so first of all when I saw this I was very impressed that the tools of Hollywood were being applied to science that was a great thing but I was also concerned about some basic physics going on first of all even if you could have a camera that would be able to take pictures of all these things of course you can't have it using visible light because visible lights wavelength is just too big it's bigger than almost all of those structures so but let's put that aside there there's something missing here it's the degree of crowding you see these big vistas where there's nothing and then you see the molecular machine off in the distance that would all be filled with other stuff all doing its thing simultaneously and so you'd never be able to take a picture of it because you'd have to look through everything else of course that doesn't make a very interesting movie but the other thing is Brownian motion you may know that at these scales everything is in thermal motion it's all kind of a random jitter to everything and whether that's important to the process depends on the energy scales involved in the processes but it's there nonetheless in every one of those structures so I think someone it wasn't me must have pointed these same things out to the filmmaker so a few years later they said oh we're gonna fix it we're gonna put in crowding and we're going to put in the random jitter so let me show you what they did [Laughter] I may have just played the same one over again no this is it so now they tried to fix it now they couldn't quite put in all the protein packing but they did a lot better now they're zooming in on a neuron you might know neurons have these extensions called dendrites and they have a big fat part of their body called the soma so now we're going through the soma through an ion channel okay okay it goes like ah it goes like this for three minutes I can't take it it's it's unwatchable so there's a lesson there sometimes the schematics like I'm going to show here actually are better than if you had a movie of the real thing quote-unquote but none of that was the real thing of course but it's the best we could do with the scientific knowledge that we had ten years ago and then more recently that one was made I think about five years ago so so let's go back to schematics because the other one was giving me a headache it might have sparked an epileptic fit so I'm gonna focus my talk not on the whole panoply of things that you saw in that movie all those molecular machines I'm gonna focus on this thing that was recently discovered called Terasaki ramps and it's just a little reflection of the complexity that we see inside of cells that wasn't known these Terasaki ramps were just first published in 2013 so four years old it's it's really quite new and and I think it's the tip of the iceberg in terms of looking at cellular structures we're going to keep discovering new things that those filmmakers didn't know about because the scientists didn't know about them to tell them about it so Terasaki ramps are a structure in something called the endoplasmic reticulum I'm not going to say that word anymore I'm just gonna say er because the bio does themselves avoid saying it they just say er for endoplasmic reticulum it's something that connected to the nucleus which is here in purple and it's indicated in this red kind of I don't know what you'd call it pinkish membrane structure it's a membrane structure it's very convoluted topologically it's very complex it's not very well characterized in fact I try to work on it years ago and I just gave up I thought it's too complicated for physics but that's where some progress was recently made and that's what I'll describe there's a lot of membrane structures in the cell I mentioned the Golgi apparatus there's other things called lysosomes and there's there's peroxisomes there's things that aren't even mentioned here this is the nuclear envelope itself and then there's the plasma membrane what separates the outside of the cell from the inside of the cell that's here those membranes all have the same architecture exactly the same and I'm gonna tell you about it right now it's a bilayer it's really two molecules thick the molecules are called phospholipids lipid is like fat and phospho means there's a phosphorus atom in part of it and I made a model here which is hiding here's my own phospholipid I created you can see in this model black is oxidized carbon black is carbon that makes sense white is hydrogen so these are called hydrocarbon chains so the basic structure of a lipid a phospholipid is there's a phosphorus atom up in the head group that's this purple thing and then there's two hydrocarbon chains these are really chains that is from the thermodynamics point of view they don't mix well with water well and the chains they don't like each other the chains would much rather be in an environment with other chains nearby and with no water and the water would much rather be with other water molecules so I'm kind of answer from Worf sizing it but but but all of that has to do with something called free energy in thermodynamics it's a it's a shorthand for talking about systems that have a huge number of microscopic States and so it just happens that when you have these molecules in the conditions that you find inside of cells that is pressure and temperature in a certain region they like to form big sheets and the sheets have the structure that I'm gonna pass this around the sheets have the structure that the oily chains to get away from the water all in a sandwich they're the meat of the sandwich and the bread of the sandwich are the head groups that contain the phosphorus so these are called amphiphilic molecules because amphiphilic and greek means they like both that is the head groups like water and the oily tails like themselves but they're kind of welded together so it's a funny arrangement where you can form these the sandwich over gigantic scales compared to the scale of the molecule the thickness here is only five nanometers okay if you know what five nanometers means it's five times ten to the minus nine meters that's five over a billion of a meter okay it's very thin but yet the scales at which you can extend can be thousands of times greater than that so thousands of times greater than a nanometer is called a micron that's only a millionth of a meter okay but in biology that's a big difference right a micron by Cron's you're beginning to measure the sizes of cells when you're in tens of microns 20 microns 100 microns you're measuring the sizes of some of our large cells okay so I already described lipid molecules I'm not gonna go through this is my cartoon of the lipid bilayer so these are the my cartoon of the lipid I'm just gonna compress that to make it look like this and this is the structure of what's called a sheet in an endoplasmic reticulum sheet this is not just a bilayer this is the bilayer and this is a bilayer but this is another fluid layer and what's interesting about that is that this arrangement allows the cell to have shapes which aren't possible if you just had the bilayer so for instance as I said the middle of the bilayer doesn't like water if you break it you would expose the meat of the sandwich to the water and that thermodynamically is a big no-no however look here I can have a kind of edge imagine this is a cross-section through a sheet that's going in and out of the board this is a kind of edge at least on a greater scale it's curved in this cross-section but it's coming in and out of the board this is a way for the cell to have an edge to end the bilayer so now it's not a bilayer it's a bilayer plus another bilayer Plus this layer it's like a penta layer because it's five layers thick it's a weight for the cell to have shapes that it couldn't have just with that so in one sense this added degree of complexity is necessary for the cell to make more complicated structures and more complicated machinery so all I did in this case that's not really a word that's just a lumen I just reflected this about this mirror axis or I rotated it like that so this is you could say a figure of rotation just a cross-section so if you want to rotate this around you'd see I have a wormhole now a wormhole that connects this region with this region and this is still separate from it so it's funny the cell seems to know about the topology of inside from out in a sense but what do I mean by what's inside and out this for instance could be the cytoplasm of a cell that's where all the action you saw in that movie was happening over here for instance this could be inside the nucleus because this is exactly what you find in the nuclear envelope the nuclear envelope isn't one of these it's one of these doubled structures with the width with its own lumen so in fact in this funny view there's a topological and by that I just mean things are connected to other things between the cytoplasm and the nucleoplasm so from the cells point of view the cytoplasm and the nuclear plasm are connected the inside of the nucleus is connected to the stuff inside the cell but it's disconnected from this thing called the lumen very interesting because that's the same space inside the endoplasmic reticulum also so that the cell which keeps this topologically pure it's kind of an invariant it's very interesting and you can see this in this schematic I like this one because it shows two different shapes the endoplasmic reticulum can assume one of the sheets which look like flat layers that are parallel and the other is a tubular network which is much more complicated in this schematic but what's in the pink region is that lumen I described so the lumen here is connected to the lumen there which is connected to the lumen there it's it's all one continuous space but I'm looking at it from the cytoplasm so you can do things in the lumen that don't have to happen in the cytoplasm it's a way for the cell to keep compartments separate these are actual micrographs that I'm going to talk about in more depth these these were taken very recently and the way to read this is down you look at this and then this and this imagine slicing through a cell physically slicing through a cell and then doing an electron micrograph on each separate slice that's what you see here and what do you seeing this is the endoplasmic particulars sheets caught in cross-section and you can see there you can see the lumen the lumen is that little space between the two black lines there so that's a bilayer than the lumen and the bilayer and there's another sheet and there's another sheet and so on it was this quality of data which allowed scientists including I was part of that group to understand how the sheets were connected to each other before this it was actually a mystery how the sheets were connected because no one could ever see a connection they couldn't see tubes or any other structure actually connecting them but they knew from biochemistry that you release something in the lumen of one and it goes all over the lumen of the whole structure so it was a mystery another mystery was why this more or less constant spacing between the sheets okay show actual data because I think it's really instructive I'm gonna show hundreds of micrographs all in sequence and I have to tell you these are very thin slices these are 30 nanometers thick this is imagine taking something and slicing it so it's only 30 durian of a meter thick you can't even see those slices because it's so so far below the wavelength of light so collecting something you can't see is really an art and I'll describe a little bit about it but I'm gonna step through a hundred of 20 of these so this is this is the neuron of a mouse this is a neuronal cell and one thing you notice is there's a lot going on there but in fact you you have no Isis this is just the membrane structures all the proteins all those filaments all the small molecules the DNA off none of that is being imaged here this is a very particular technique that only stains membrane so you're only looking at a fraction of what's going on but you can see membrane is everywhere in this neuron in fact here's the Golgi apparatus when you see this you get a whole different appreciation for it this is part of the same golgi but because you're slicing it you know it looks disconnected it actually is connected in a funny way these are the endoplasmic reticula sheets that I was describing and if you go through this you can actually see if you look at carefully how sheets are connected to other sheets and I'll just show you an example of it it turns out to be topological weird I used already but I'm going to tell you what it means in this context okay there all over the place but I just found one with my little eye if I look here this is a sheet here's a parallel sheet oops and I don't know how to work the program there we go and what you'll see is there's a disconnection here that edge so that's the edge of a sheet comes over to the other one makes the junction and then the opposite side disconnects and now that one will bend to the next sheet or no actually it did something a little more complicated in that case but it bent to another sheet and there was another disconnection and so on so this data revealed that there was something topologically really interesting about how sheets were connected to each other by the way I could talk for an hour on this one image these were mitochondria those are those sausage shaped things you saw in the movie but here of course they just appear as ovals because you're slicing them turns out they're not just sausages these these are all connected to each other and kind of a network so they don't have to be sausages though they it can be please please ask questions because I spend a lot of work doing that and I can describe some of that and I'll show some results of that but I have to say if you if you just do this to the whole structure you get an unbelievable complicated mess you really have to focus in on these regions where you think something interesting is happening and look only at those regions and then find many examples of it and I'll show the results of that any other questions yeah I'll get to it that's gonna be a whole topic all right okay so let me go back to the presentation okay so I'm gonna answer that right now actually how do we know what we know like how do we know how to do that what what is that you know so I'm gonna start my story back in the 30s this guy Aaron's true ska he was a PhD student and his advisers name was max Canole and they worked in Germany so while the world was falling apart around them and things were terrible things not unlike her own time's right they were creating these incredible images because ruscus thesis was he wanted to do for light for photons what well he want to do for electrons what had been done for light in microscopy that is he wanted a lens that could lens electrons of course you need magnetic fields but that was the overall idea can we use electrons which have much smaller wavelength instead of photons and this is one of their successful images I think it was taken in the late 30s but wasn't published until 1941 I love this image it shows a bacterium this is like an e coli it's about a micron across and these are bacteria phages these are viruses that attack bacteria this might be the first image of a bacteriophage so this is about a micron but you can see this is pretty unresolved it's not you can't really tell what's going on with the bacteria oh you can tell a lot about what's going on with the bacteria phage and that's maybe you know tens of tens of nanometers right compared to this micron so this technique was really good for things that were tens of nanometers and less good for really big things like micron on Zoom ahead to the 1950s or late 40s early 50s keith porter working at Rockefeller University took these tools and really put them into the service of cell biology that is he made some of the pivotal breakthroughs that we're all relying on now and one of them well in fact they coined this word endoplasmic reticulum which is marked already at I'm er and this is a mitochondrion in the image this is the nucleus you see the new place is big can't really tell what's going on with the nucleus but if you look carefully there's this gray structure very lacy in the background let me zoom in that was maybe the first image of the endoplasmic reticulum this gigantic membrane structure everywhere hiding out kind of lacy in the background by the Kandra they're very dark because again they're staining for membrane and membrane is very rich in mitochondria it turns out very convoluted internal membrane structures there this is what's called the bloom Porter microtome the basic design is unchanged to this day there's a very sharp blade diamond blade or sapphire and then the tissue is held there and then this is repeatedly brought against the blade and you physically slice the tissue as fine as you can blades are very expensive they wear out very quickly so that's a major expense let me show you the modern version it's basically the same tissue holder blade you can't see it this is a whole device to capture the slices this is the real innovation this was developed in Jeff's Littman's lab and by the way I put a list of people who I should thank but I won't have time to thank them wrath over there on there on the board but Jeff Lippman's lab at Harvard had this idea what if we collect the slices that are coming off here's the tissue there's the blade they're coming off on this on what if we collect them on a rolling adhesive tape this was a new idea the rolling adhesive tape offers incredible advantages to the usual method the usual method was a liquid film collect the slices on a liquid film that has some advantages if you want to do cryo-electron work but this has a great advantage because if it's rolling at a constant velocity and you're slicing at a constant velocity you in advance where every slice is going to fall and you can put them in registry much easier this way then if you have something uncontrolled like a fluid right the big disadvantage here is if these slices are 30 nanometers thick well what's the thickness of an adhesive tape it's like a human hair it's like a hundred microns or 60 microns at most so what's the ratio between you know if this is the slice 30 nanometers I would need 2,000 of those slices to equal the thickness of the adhesive tape big difference that means you can't do transmission electron microscopy the question was what kind of microscopy you're doing well the gold standard was always transmission electron microscopy so what was Lichtman solution you do scanning you do scattering off the surface and you hope and pray that you're not missing too much in the next 30 nanometers because you're going to get that next slice for sure if everything works out so you kind of cross your fingers we're not going to miss too much by going to the next 30 nanometers so we could just image on the surface of that slice we don't care about the electrons going through it that would be transmission we only looking at the backscatter basic okay so that's like I described that gave rise first to these images this would these were done in mice neurons already there so tell us aki saw something no one else saw in those images and that was this first indication that there was a topological connection between the sheets and so we first called it sheet like endoplasmic reticula junctions that didn't that didn't take off but but but you can see it's not a tube at all it's that what I want in blue here so this is actually what you're asking about three-dimensional reconstruction is in the sense what's blue here is the edge of the sheet so it turns out the sheets are actually connected at their edges but the edge is doing something funny it's curving and it's twisting in space it's very interesting because there are a couple things that curve and twist in space I'm going to talk about it in a second here's a little movie of one of the first of these I would say Terasaki first Junction Terasaki ramps as we call them now in biology but I'll just run that again but all these edges are fake the only edge that's counts is the one in the middle there it's only because I didn't have a lot of clay that I had these other edges the only real edge is that thing winding through the center it looks like that's what's connecting the sheets based on that data this so Terasaki had a great idea he's an expert on ER and the nucleus he said why don't we image why don't I take all those techniques I move them to my lab and we imaged all kinds of cells that are called secretory cells secretory cells are so called because they secrete what are they secreting mostly proteins where the proteins made turns out the endoplasmic reticulum these cells have a job their job is to secrete molecules out of the cell to do that they need to have amazing endoplasmic reticulum it in the neurons we were seeing like maybe four levels in this you can see 20 more 30 something like that it's a big difference so let me I'm going to show you so these are actual slices with that same technique this is the endoplasmic reticulum that's a mitochondrion sneaking in I'm going to image in 3d what's going on in this right box and then also what's happening in the left box and I'll show that here so that's the left box and that's the right box three-dimensional image like you asked it's a helix in this case it's a left-handed helix and in this case it's a right-handed helix and in fact when you look across the whole cell across the whole er it turns out you seem to get 50% left handed and 50% right handed within the errors that we can so that doesn't seem to be a fundamental helix in the sense of DNA or what's called the Alpha helix and proteins which always comes in one handedness these seem to come in both chirality z' as we say in physics so whatever is causing these can allow them to to not break the symmetry in a sense in the physicists language so so the symmetry doesn't seem to be broken we get 50% left-handed 50% right-handed they're all over the structure it actually allows you to think in a kind of physicists way now you think hmm what about some of these mysteries about the structure well is this the only way that sheets are connected to each other it seems to be the only way that's really prominent in the data it also explains why the sheets come in the kind of a wave length why are they more or less equally spaced because that's what's called the pitch of a helix so you know I have something that's helical here helix this is not quite a helix this is something called a helicoid but I'll get to it in a second this has a periodicity in the Z direction and that's mapped onto the spacing between the sheets in a stack of sheets in the endoplasmic reticulum so this was this ended up making a little bit of a splash in this journal called cell physicists don't know about this journal but biologists think it's really nifty the they made the cover as you can see this is one of those three-dimensional reconstructions and the journal even commissioned this picture and called it the parking garage model in fact they even put little cars on it these are not cars these are ribosomes because it turns out I haven't described it but ribosomes are covering parts of the ER ribosomes are where the proteins are synthesized so all the proteins that I showed you doing crazy things in the movie they're all made somewhere where are they made they're made in these machines called ribosomes and that's what's coding parts of the ER so the ER is enormous ly important I didn't tell you how important it is but it's it's it's it's a central thing and and some cell biologists named Sidney Tam decided to make a cartoon about this because he I think he liked that picture and he actually made the ribosomes into cars entering a parking garage and I think it's very funny but in fact it's not crazy parking garages are the idea of a helical parking garage turns out it goes back to the 1920s or so I looked it up on this website oh yeah sorry that's a good question it doesn't matter let me just say why I mean it may matter but if you have let's say a right-handed helix you turn it upside down it's still a right-handed helix so there's no way for me to tell which which direction the nucleus was in but it's correct yes so so you you've identified an important thing these sheets are locally flat but when you look at the whole cell it that that local direction seems to change depending on what part of the cell you're in so you could always say if I followed this long enough I would hit the edge of the cell right hit the nucleus and that's absolutely right yes these are breaking off from others and reconnecting to others the dynamics of these things is really interesting we don't know because when you do electron micrograph not only is the cell dead you know the animals dead the tissue step everything has been changed to to prepare it for these electrons right so the dynamics of these things is still a mystery and so we need some new methods of observing very tiny things in cells and these are coming on board in cell biology but I don't think there we know yet what the dynamics of these are it's a great question okay yeah so that's an interesting thing that actually wasn't a movie that was going through the Z direction as if it were a movie that was that was a snapshot a three-dimensional snapshot but because my limitations three-dimensional snapshots have to be processed in slices first right so that was a frozen structure that the electron micrograph was imaging but it didn't represent time right but it could be exactly what you're saying that there's a huge kind of complicated reconnection of HeLa sees you know when you're talking about making a movie now you have to imagine a helix is involved not just the slices so what's the helix doing in three-dimensional space plus time it's a great question yeah absolutely yeah so you take this funny helical structure well let's go back to the data yeah you take this funny helical structure and you slice it in any direction whatsoever you're gonna see those reconnections that you saw in the data okay so let me so what about what can physics do for this problem you know if to a physicists who study soft condensed matter or even hard condensed matter these structures seem very familiar there's things called screw dislocations that you study in crystal planes they're mathematically they looked very similar so you might think the mathematics you can just import over and basically that's correct in soft matter liquid crystals also have these defects so so in physics we use the word defect it doesn't mean anything's wrong with it it just means that there's a different kind of order which isn't quite as perfect as it could be but it's it's interesting and perfect in its own right in a different in a different way and that's what a defect means in physics so I would call these topological defects in an otherwise parallel set of stacks so there is an attractive model but to explain it I have to go a little into what's called differential geometry of surfaces so let me let me just make an attempt to do that there is a thing called a helicoid here's a helicoid which i'll pass around and i've got another one here which i'll pass around this one's a little bigger this one I got on Etsy those do hang it and let the wind rotate it and have deep thoughts but I'm gonna make the helicoid here too this is a business person's desk toy there we go okay so there's a helicoid also you can get a helicoid very simply almost too simply you take a stick like my pointer you rotate it constantly at a constant rate while you also translate it in the z direction while you rotate it that sweeps out a surface in three-dimensional space that surface is called the helicoid now what's special about the helicoid it doesn't sound terribly complicated but it has an interesting property it's mean curvature is zero everywhere and what does that mean that sounds complicated so I'm going to going to give a lightning introduction to the geometry of surfaces and curvatures imagine I'm sitting in a surface and I look at it I sit at a point and I look in Direction D in Direction d2 I can fit a circle that best fits the curve that's the intersection of surface in that direction and I can fit another circle in the direction 90 degrees from that original direction and so I'll have two different circles that are the best fits for those two directions those two circles have radii let's call it r1 and r2 okay so I'm going to define a curvature in each of those two directions c1 will be 1 over the radius 1 and C 2 will be 1 over radius 2 so a curvature in my language this I'm going to getting toward mean curvature is always going to be 1 over length there's another curvature let's call Gaussian curvature I'll get to in a second so every curvature that I measure no matter what direction obviously has to lie between the minimum curvature and the maximum curvature that's just the tautology if they're all right minimum and maximum you could have a plane for instance then it doesn't matter which direction you take it's flat everywhere so flat I'm going to call this a circle infinite radius okay so 1 over infinity is 0 so this has 0 curvature this straight line and in a plane of course no matter what direction you pick to choose you choose it's always going to be that line so you're always going to get 0 curvature so plane I can tell you right off the top the mean curvature if I average is always 0 but what about other shapes well to look at all the other shapes mathematicians realize going back to Euler this is before mathematics and physics split apart so I don't know why I called him a mathematician should I call him a physicist but boy was and Gauss also were instrumental in using these curvatures to describe all kind of surfaces basically all smooth surfaces so the mean curvature is just the average of those two curvatures and the Gaussian curvature is the product of those two curvatures so I said this curvature had units of 1 over length this curvature is a little different it's got units of one over length square okay so that's the introduction so now let's make a table I already said a flat surface has zero curvature and zero curvature in the two direction so therefore it's mean is zero and its product is zero all right maybe I should stand over here something a sphere let me show you a sphere well a sphere also has this property that it doesn't matter so here's part of a sphere I bought it today and Michael's this time of year is great for buying different shapes that Michael's ah so let's here's my point here so it doesn't matter what point I pick on a sphere because all the points are equivalent right let's just pick this one if I measure what the maximum curvature is well it's going to be like that now I remember 90 degrees oops this is harder than I thought hey those circles are equal they are the great circles so I just get them equal when I average I get the same thing and the product is just that okay how about a cylinder I'll skip the cylinder I didn't bring it saddle okay I've got something hyperbolic oh it turns out the helicoid is the perfect hyperbolic surface for this it's actually curved in a funny way if you go across the region of even though I generated it from a straight line it's actually highly curved so if I go this way the circle bends one way if I go this way the circle bends the other way so I give those two different signs one is going to be positive and one is negative so it's quite possible and in fact it's the case that when you take the two curvatures the principal curvatures for something like the helicoid they add exactly to zero and the product will be negative in that case so if you hear the phrase this is that in everyday phrase but negatively negative surfaces of negative Gaussian curvature that's exactly what we're talking about here so you can go home tonight and say all surfaces of negative Gaussian curvature I got that covered I know everything about that so this is the surface of negative Gaussian curvature and in fact what's interesting look at the surfaces that are have zero mean curvature there's only two on this table but there's plenty more plenty plenty plenty I've got some examples here you can come up afterward this is a surface where every single point has zero mean curvature exact cancellation at every single point the only problem with this one is that if I were to extended its intersects itself that's not very good for a biological model here's another one this one you might know it's called a cat annoyed at every point of this surface you get that exact cancellation also and here's another one it's called an upper surface and so on and so forth and here's another one the helicoid that you're passing around now it turns out it turns out that this is actually goes back quite a ways why these surfaces are interesting for physics and the first inkling the first time it appeared in the literature as it were was back in the time of Sophie Scherman and Sophie Sherman was interested in the elastic properties of lamina which meant sheets and she wrote a whole essay for a prize in Paris on this she proposed that the energy should a way to describe these surfaces in terms of a kind of elastic energy she proposed that it should have this form I'm not going to go into great detail but this is basically what we believe today with some slight refinements the refinements are complicated and I just flashed them here to show you how complicated they can get but but it's not really that different from what she said back in the early 1800s yeah there was a question oh yeah it's a very interesting story so she she grew up if you look when she was in her teens the French Revolution was happening Paris was not a safe place to go out at night her parents said you are staying home and her father had an incredible library he was a doctor so she devoured every single book in his library including all the math and physics books she self-educated herself and in fact she started corresponding with all the Great's of that era Gauss Laplace was younger than small so forth the only problem was she realized they wouldn't take her seriously because her gender coming back to modern times right she disguised herself as Monsieur Dubois okay so she would write all these letters discussing deep issues in mathematics and physics but always as Monsieur Dubois okay so that was the time of Napoleonic Wars and things and they were France was invading Germany she was a great fan of Gauss she thought Gauss was the modern Archimedes that's quite a statement if you know who Archimedes was she also read in her books how Archimedes died not a good story he was he was too concerned with his geometric figures and the Roman soldier who invaded his town said listen to me you're coming with me so don't disturb my circles okay that was it that was the end of Archimedes she didn't want that to happen to Gauss so she was highly connected with people and the army or father was and they said by all means when you invade Braunschweig where the Gauss live take care of mr. gauss do not harm him you know treat him very nicely so the general did exactly that send a special contingent to Gauss's house that hey Harry gasps are you okay okay you know do you need some snack in you know whatever and and in fact that worked Gauss was completely safe and the general said well you know you have a great friend and so future men and he's got Sophie who he'd never heard the name so future man because she was always material of law that's so you know Mel Blanc Meshugga Blanc that's why Sophie German basically was right on you can make a kind of energy you can make a kind of energy out of these geometric properties of curvatures I'm not going to go into it but I do want to know this is for a soap film situation which is not exactly a membrane but it's similar and note this equation get rid of the constant it's just saying mean curvature equals zero mean curvature equals zero it's amazing to me how much physicists and mathematicians can obsess on an equation like this and get incredible insights but all these surfaces I showed you are solutions of that equation H equals zero every single point of these surfaces has mean curvature zero and it turns out if I went back a slide this is a solution of all of those elastic equations so if a membrane can take a shape in a cell this is a possible description of the shapes it can take and that's why it's very interesting to apply this gyroid this is called a gyroid to the Terasaki ramps this makes an excellent model for a Terasaki room all I have to do is take out the center of it when I take out the center of it I intersect that surface on a helix so I have an infinite surface this is not infinite but that stick could keep going up if I make it infinite and take out the center I have an infinite surface that ends on a helix and it's a minimal surface so it's a solution of those elastic equations so that's a huge advantage from the point of view of physics because now I have a candidate that can describe those things so what if I take a left-handed helix our I'd handed helicoid prepared in this way of taking out the Centers and I bring them together can I make a surface that spans disband it's infinite but it ends on to Ulysses and here's an example so I'll pass this around but this is 3d printed mathematical model of the left-handed Terasaki ramp or this is the model for one and a right-handed one and you can see the endoplasmic reticulum sheets how they go off and become very very flat okay I'm going to show this image because it leads me to a slightly different topic which is a little bit related to the question about dynamics which so this was made by my colleague Jamel güven who was an expert at working on these architectural CAD programs where you can make beautiful three-dimensional images you know does our architects use these a lot and also designers for machinery but this is showing something interesting you could split a left-handed and right-handed Terasaki ramp off of some other structure and that structure looks almost like a 3-way Junction a 3-way Junction maybe maybe in fact one could have other kinds of geometries that aren't quite as simple as the thing I'm handing out by bringing different ramps together in different symmetries so I call this ER origami after the origami of course but I'm getting ahead of myself but this this opens up a new area I think which is can you make kind of design or make structures and membranes that have the properties that are like the endoplasmic reticulum but in fact you get to choose where these Terasaki ramps are and okay so I'm gonna make in my last minutes here I'm gonna make a right angle and talk about an interesting connection that popped up in the last year which is can you find these ramps in nuclear astrophysics and this takes on special urgency now that we've observed the merger of two neutron stars I won't have anything to say about that directly in my talk but but uh maybe lawyers have some speculations about that because now I'm intruding in larsa's sandbox so I noticed a certain article involving the work of a group of Indiana University and and so we started corresponding by email sending each other images there's from simulations of dense nuclear matter and on my side I was sending images that were electron micrographs from so and what we discovered was a commonality so let me go a little bit into the nuclear astrophysics story so in the mid 80s there are two famous papers one of them is represented here by this Japanese group the other was a group at Illinois I think Petach Wilson and Raven Hall or some permutation of that they both were arguing an idea and they made it a little more precise the idea had been around since at least Hans betas time that when you have dense nuclear matter nuclei are no longer but as little spherical type things are no longer the preferred shape that the collection of neutrons and protons wants to assume in fact as the matter gets denser you move from something that looks like a nucleus maybe it's a big one and a heavy one but to something that could look more like a tube and then when the tubes get dense and close together it looks like a slab or a layer and then when those get so dense maybe you get an anti tube and then finally maybe an ant nucleus that is a everything here is nuclear matter except for that empty spot so this took on later the name nuclear pasta because they call this nuclear spaghetti nuclear lasagna I don't know what they call this but anyway maybe nuclear no key and so on where do you find it was already evident in those early papers where you would find this state of matter if you go through a neutron star so as you know a neutron star is what you get when you take neutrons and protons and smoosh it to a very high density basically the protons and electrons will combine to make neutrons and then you'll be left with some admixture of neutrons and protons with the sea of electrons around it you go through a neutron star that's about ten kilometers in radius typically then this is not to scale but in the first kilometer or so that's termed the crust based on what we know about the nuclear state of matter for dense for dense for high densities this is not very heavy compared to the rest of the star until you get in this little slice which is about 100 meters before the end of that crust then then this is called the core and that's believed to be a fluid a uniform fluid of nuclear matter so this is kind of boring and this is kind of boring out here because it's just the lattice of collection of nuclei but what's really happy what's really interesting is this dense structure in what's called the inner crust okay so I've done a lot of damage to all the people studying neutron stars but from my point of view it's kind of boring boring really interesting right around here okay but no this is ten kilometers and this interesting zone that I'm pointing out there's only a hundred meters so it's one percent of sorry it's one percent because it's a tenth of the tenth right so so it's a very thin region but it's actually very massive compared to the rest of the crust here not compared to the star but it's it's it's about about maybe at least 40 percent or 50 percent of the mass of the crust because the densities jumped up here by a factor of a thousand or so but that translates it's not dense compared to this but it translates into about two or three percent of the total mass of the neutron star that's significant here's another artist rendition the nuclei are beginning to get closer they're interesting they're getting bigger spaghetti lasagna than the anti phases so here's a simulation from that Indiana group see if I can run this this is actually a simulation of dense nuclear matter done in a certain way that I don't have time to describe but the way they do it is they make the Box bigger and bigger slowly so that's decreasing the density so imagine this is nuclear matter going out from the edge of the crust out to the to the well for the inner edge to the outer edge something interesting happens right when these lasagne sheets you missed it right there [Applause] the lasagne sheets were kind of parallel and then all sudden they developed all these connections is that what are the connections between those layers is it like the is it like the Terasaki ramps it turns out so this is just a snapshot of what I showed you this is from a cell this is from the nuclear data it's an exact correspondence the same geometrical structure is found in down inside ourselves and also presumably in the crust of neutron stars nuclear matter compared to our matter you know it's it's it's more exotic because we don't live there but in a sense the equations are simpler because it's just neutrons and protons doesn't you know it's in a sense there's a way in which there has to be something like this in the crust of neutron stars because we know the density changes so we know that there's a zone there where you're in a sweet spot you can't avoid it ok so here's some snapshots showing in fact very detailed pictures zooming in on the left-handed and right-handed Terasaki ramps and they form arrays so like I was saying a origami you might have to come together or four come together they're finding entire streets of left-handed and right-handed so you could you could take a little box around here and say it goes left right left right left right so the basic unit it's what's called a quadrupole in physics because it has four of these defects but for theoretical reasons we believe this is maybe the unit in which these things are organized but okay I want to end on this last I'm almost good I want to end on this very last speculation there was a book by Robert forward many years ago which was about very speculative science fiction of course about life on the surface of a neutron star now on a neutron star you have to know the scales are so different it's incredibly dense and length scales are measured in tens of femtometers that's ten to the minus fourteen meters time is measured in femtoseconds so you could have entire civilizations come and go in the blink of an eye on the surface of a neutron star what Freud thought was maybe you could have maybe on the crust of a neutron star there'd be some interesting things going on he called it nuclear chemistry well that means something else completely to nuclear physicist nuclear chemistry is not what's going on in the crust of a neutron star but what if he knew about nuclear pasta you didn't really know about nuclear pasta that's where the most interesting shapes are that's where all that activity was happening could it be that that activity could support complicated structures kind of analogous to what we have on on the earth it's complete speculation but I think it's a funny thing to think about because that zone for sure my point of view has the most interesting structure okay so I'm gonna end my talk there you can read these I don't have to read them but it looks like the cell with it's complicated technology really uses some basic physics to construct the things that has there that is yes they're complicated but in fact there's fundamental physical laws underlying at least the one I've focused on in this talk and not only does it take place in the cell we might also find that physical law doesn't isn't restricted to things that are made of lipid molecules and water and things like that but in fact that same motif may appear in other forms of matter the physics is very different in this fundamental but maybe at a larger scale there's a common description of these two phenomena thank you [Applause] wouldn't be valid to reverse the sense that last statement it's absolutely true yeah that the geometry does result from the detailed equations right but I've reversed it to make a point here and that's that the geometry is so amazingly similar does this give us a new way to think about let's say one or the other of the systems so in nuclear physics they're they use something to call the semi empirical mass formula the ideas I showed involving curvature they're nowhere to be found in that subject so the nuclear physicists are very interested in this connection because it may give them a new way to make effective theories effective theories are very useful in physics because often you can solve the quantum mechanical problem exactly you need to step back and smear things out of it and that's smearing out may give you different equations and one question is is those equations have anything to do with the equations in the biophysics and that's a that's something being worked on now do they buy they maintained through these transformations or do they actually have different Betty numbers okay so yeah so I'll just translate your question for everyone so a Betty number is a way to talk about the connectivity of a surface and the kind of holes it can have basically you can combine the Betty numbers and something called the Euler characteristic back to Euler again so the Euler characteristic is what tells you the difference between something like this and a sphere like this has a hole but the surface of a sphere doesn't so the question is are these topological invariants actually invariant in the biological system and to first-order I'd say yes but we don't but there are examples where proteins specialized proteins embedded in membranes can actually change the topology so you saw that there was a that was pictured in the animation when you had a sheet which represented the endoplasmic reticula sheet and then all of a sudden a little sphere butted up out of that like a little disk something like this and then it detached that's a topological change and that's created not usually naturally but through the agency of proteins so proteins which are burning ATP's the energy unit in cells they can actually change the topology of membranes so I'd say we don't know precisely if the Terasaki ramps work in that particular way with machines changing topologies but if left on their own devices topology would be invariant yeah you know yes yeah you know okay I mean let me make a comment I I think it's actually interesting what you're proposing so so these layers that are parallel they they don't carry net charge that's not they may have a slight charge but it's screened by the aqueous environment around them so as a screening length which is quite short so it so that doesn't mean that there's no Electress that electrostatic interactions between neighboring sheets it just means it's highly reduced from what you would expect naively now these high the frequencies you're talking about they would actually be observable in cell so in fact one could test your hypothesis that these radio frequencies or other frequencies would actually oscillate the layers of the endoplasmic reticulum I haven't seen literature on that but it's not absolutely crazy and in fact it's known that cancer often is associated with weird membrane structures so so I don't know the answer off the top but I think it's not unreasonable to think there could be some connection there okay [Applause]

Channel: Kavli Institute for Theoretical Physics

Views: 1,187

Rating: 5 out of 5

Keywords: kitp, kavli institute for theoretical physics, ucsb, uc santa barbara, alien technology, eukaryotic cells, nuclear matter, neutron stars, physics, terasaki ramps, space, biology, greg huber

Id: _jQOHC9ACv4

Length: 70min 27sec (4227 seconds)

Published: Fri Dec 22 2017