What I'd like to do is to provide brief background for Ellen Crummy for her thesis defense today. Today, the longest day of the year is filled with uncertainty. I don't think we yet know whether the U.S. government will be open tomorrow or not. So I thought we'd spend the next hour on a topic of greater certainty, biochemistry and protein-protein interactions. And Ellen will tell you about a novel protein-protein interaction that she developed that she characterized. Ellen was born in Hershey, Pennsylvania, and I'm tempted to guess that that's where she learned her baking skills. We've been the happy recipients of her baking skills, and I've always associated ability to bake with ability to do biochemistry and vice versa. I don't know if that's false or not. But anyway, we've been the recipient of Ellen's baking skills. She's been progressively going west from Hershey, Pennsylvania. Her first stop as an undergraduate student being at Case Western Reserve University, where she was a major in biochemistry. She was quite busy there. She was on the swimming team, and I noticed from a website that her times in the backstroke progressively decreased over the four-year undergraduate period of time. However, and maybe more importantly, she also conducted research. She conducted research in the laboratory of Ruth Siegel in the Pharmacology Department for about a year and a half, something like that. And the topic of interest was studies of the GABA ion channel receptor. They were interested in studying the GABA receptor for its potential role in the adaptive response to hypoxia in terms of affecting the respiratory system. Ellen conducted a fair amount of PCR work as well as mouse husbandry work, and it turned out that the project was then published in Brain and Behavior with the following sort of bottom lines. The mouse knockout that had the particular GABA subunit knocked out didn't really show very much modulation of respiratory control. However, Ellen found that other subunits were adaptively upregulated in this mouse. The neat finding was that the mouse experienced increased anxiety. So when Ellen came to Madison further west, she joined my laboratory presumably because of some interest in neurobiology and also to not have to work with mice or anxiety. However, there was a fair amount of anxiety associated with her project, I have to say. Basically, she undertook an ambitious project of defining a protein-protein interaction for CAPS. CAPS, as she'll tell you, is a protein we discovered many years ago in my laboratory. And in my laboratory, we consider it to be the center of the universe in terms of function of dense core secretory granules and their fusion and other activities of the dense core vesicle. So Ellen was able to take some initial findings in the lab and bring them to a point of completion in defining a novel CAPS protein interaction. I noted in her graduate school application she saw an analogy between swimming and conducting research in the laboratory that both require a substantial amount of patience in order to get good at it. And I have to say that Ellen has been remarkably patient in what turned out to be a fairly long-term project. So with that, that's the title of her work. Thank you, Tom, for that kind introduction and thank you all for coming today or for listening online. Today I'm going to be talking about my work on this protein CAPS and its role in the regulated exocytic pathway. I'm going to tell you a story about how CAPS interacts with this protein, RAB Connecton 3 beta or WDR7, and how both of these proteins are involved in modulating the acidity of dense core vesicles. However, before I begin talking about CAPS, we'll take a couple steps back and start by talking about the regulated secretory pathway and an overview of it. Why is it important? What cell types have it? We'll then talk about the discovery of CAPS, which, as Tom mentioned, was discovered in his lab a number of years ago. That will lead into background information about the protein CAPS and what was known about it when we began this project and what inspired this work. I'll then talk about my research, of course, and show you my data, and we'll wrap up with some future directions and ways that this project can be taken forward even further. So as I mentioned, today we're going to be talking about the regulated exocytic pathway. But I think it's important to know that all of the cells in your body have a pathway by which they can secrete molecules, such as extracellular matrix proteins and growth factors. This pathway is called constitutive secretion, and in it, cargo proteins cluster together in the Golgi, butt off of the Golgi, and immediately and rapidly fuse with the plasma membrane. This process is extremely rapid, and it's happening in all of your cells all of the time. It was actually years after they discovered regulated exocytosis that constitutive secretory vesicles were purified because of how rapid the turnover is. You might imagine that certain cells in your body secrete important signaling molecules that you wouldn't want to be released at this kind of rapid unregulated manner. These cell types include, say, pancreatic beta cells that secrete insulin, they include neurons that secrete neurotransmitters, and neuroendocrine cells that secrete hormones. These cells have an additional pathway that's called the regulated exocytic pathway. And after vesicles bud from the Golgi containing their cargo, they traffic to the plasma membrane, but instead of immediately fusing, they pause there and wait for a physiological signal. There's a number of cell types that contain this regulated exocytic pathway, and I'm showing you two of them here. These are electron micrographs of neurons and a neuroendocrine cell. In it, you can see the membrane-enclosed compartments. So in this neuron, you can see a number of these synaptic vesicles. These synaptic vesicles are clustered around this active zone, and upon a calcium influx, they will fuse here and secrete their neurotransmitter contents into the synapse to allow for neurotransmission to take place. We know a lot about the process of synaptic vesicle exocytosis, and a lot of what we know about the secretion of neurotransmitters has been extrapolated into other systems, such as the secretion of contents from dense core vesicles. So our lab is interested in secretion for these dense core vesicles, and you can see one of them in this neuron and a number of them in this neuroendocrine cell. So it's hard to tell from this picture, they're actually significantly larger than synaptic vesicles, and they contain different kinds of signaling molecules, such as hormones and catecholamines. The pathway for dense core vesicle exocytosis looks something like this. Cargo gets clustered together in the Golgi, and an immature secretory vesicle buds from there. This clustering of cargo is actually important for the formation of the immature secretory granule, and is reliant upon properties of these proteins, as well as the slight acidic pH of the trans Golgi. After budding from the Golgi, this immature vesicle will undergo a number of maturation steps before it's ready to fuse with the plasma membrane. These maturation steps include exchanging the proteins from the plasma membrane, taking the Golgi proteins off and putting on proteins that are relevant for plasma membrane fusion. The vesicle will become larger, and it will become more dense as additional cargo proteins are pumped in. But importantly for what we're going to talk about today, these vesicles are actually acidified. So this acidification process takes place via this proton pump called VATPase, which hydrolyzes ATP in exchange for pumping protons against their gradient into the lumen of the dense core vesicle. This process is important for these immature secretory granules because an acidic lumen is required for the pumping in of certain signaling molecules, such as catecholamines, and this transporter relies on the acidic pH, as well as for the processing of hormones. So in order for a pro-hormone to be converted to its active state, enzymes need to cleave it, and they require, again, this acidic pH. So when a vesicle buds from the Golgi, its pH will be around 6.4, and by the time it's ready to fuse with the plasma membrane, it will be around 5.5. After it has trafficked to the plasma membrane, it will sit and wait for this physiological calcium signal upon which time it will fuse with the plasma membrane. This final step in regulated exocytosis has been of a lot of interest for researchers for a number of years, and that's because the fusion of two lipid bilayers together is an extremely energetically unfavorable process, and so it follows that there would be certain proteins that would need to catalyze this opening of a fusion pore, and scientists were, of course, interested what these proteins were. In the early 90s, the snare proteins were discovered to be these molecular machines that are required for fusion. There are three snare proteins involved in this system. There's one on the vesicle, and then two on the plasma membrane. The snare proteins begin by interacting at their end terminus, and upon a calcium influx, they zipper up from their end to their transmembrane C terminus, and in the process, pull the two membranes together so tightly that the lipids begin to mix and a fusion pore opens through which the contents can be released. Prior to this fusion step, I'm notating this docking and priming step. Docking and priming describes a state in which the snare proteins have begun to interact with each other and the vesicle is held close to the plasma membrane, but the snare proteins have not begun to zipper up. It's thought to be important that the vesicle is near the plasma membrane and that the snare proteins are partially formed, such that upon a calcium signal, the vesicle confused with the plasma membrane very rapidly. So it was around this time that scientists were interested in learning more about these snare proteins that my lab was also interested in learning about what was happening around the fusion pore. And so they developed this permeabilized neuroendocrine cell assay in which they took cells and pushed them through a homogenizer. This homogenization tore a single hole in the plasma membrane of these cells through which all of the cytoplasmic components could be washed out, leaving only this ghost cell that contained vesicles and organelles, but no cytosol. They then stimulated these cells to see if they could secrete these dense-core vesicle contents. But as it turned out, there was a very modest response. There was very little secretion. However, when they added back those cytosolic components that they had emptied out of the cell, they saw that there was this large recovery of secretion, this robust secretory response. And this said that in addition to those three snare proteins I showed you on the last slide, that there are additional soluble factors that are also required for dense-core vesicle exocytosis. Of course, they were interested in what these soluble factors were, and so they used size exclusion chromatography, testing all of the eluids in this secretion assays to see which one reconstituted this secretory phenotype. They were able to purify these eluids down to homogeneity and found that a single protein was able to reconstitute this secretion. And of course, that protein is the topic of my talk today called caps. So over the years, a number of different fusion assays have been done with this protein caps, and I'm just showing you one of them here. So in a normal neuroendocrine cell, after you stimulate it, there will be a certain number of fusion events over a period of time. But if you knock down caps, the ability of these dense-core vesicles to fuse goes down significantly. There's barely any fusion events at all. This has been shown in not only this cell type, but additional cell types. Homologs, endrosophila, and C. elegans also require caps in order to secrete dense-core vesicles. If you knock caps out of mice, the mice die at birth. And all of these facts say that caps is a vital protein for the secretion of dense-core vesicle contents. A significant amount of work over the past 26 years has gone into trying to figure out exactly what caps is doing and why it's so necessary for dense-core vesicle exocytosis. It's been found to be a so-called priming factor. And priming factors are soluble components that interact with the vesicle, or the snares, or the plasma membrane, and kind of set the stage such that upon a calcium influx, the snare proteins can zipper up in a way that's conducive to fusion. Without priming factors, the snare proteins form non-productive complexes, and the vesicles are not able to fuse with the plasma membrane. We know a lot about this protein caps. We know that via this monchromology domain that it binds all three of the snare proteins. We know that via its pH domain it interacts with the plasma membrane. And again, we know that it is a vital priming factor for dense-core vesicle exocytosis. However, at the time that I started in this lab, there were a couple papers in the literature that suggested that maybe caps plays additional roles. Upstream of its role is a priming factor. And I'm showing you two of these papers here. This first paper shows that when you knock down caps in this neuroendocrine cell line, that there is some kind of defect in the formation of immature granules. So here is a normal cell, and you can see that this fluorescent dense-core vesicle cargo is packaged and shipped out to the cell periphery. Whereas in caps' knock-down cells, the cargo seems to be trapped in the transcolgy, suggesting that there is a defect in the formation of immature granules. This second paper demonstrates that if you knock down caps, there is a defect in loading catecholamines into granules. So here I'm showing you in caps' knock-down cells that they are unable to load as much serotonin as wild-type cells. All of these assays suggested that caps had this additional function upstream of its priming role. However, there was no real mechanistic reason as far as how caps could be performing these other functions. It kind of reminded us, though, of something that we've known in our lab for quite a number of years now. I'm showing you this really nice SIM image that was done by Declan and Aaron in our lab. And you can see if you antibody stain caps and you antibody stain a vesicle marker that caps localizes to vesicles extremely well. And you can see that in this merge image where the localization is depicted in yellow. So this is kind of weird, though, because caps is a soluble protein. And further, it's performing its action at the plasma membrane. So why would caps be interacting with these vesicles? And further, what is it bound to? Again, it's soluble, so it must have an interaction partner on these vesicles in order for it to localize there. We thought that if we learned more about what factors caps was interacting with on dense vesicles, that we could learn more about these functions that it had upstream of its priming role. Therefore, in order to address this question, I performed covenoprecipitations from rat brains that were enriched in membrane. Brains have a lot of caps in them, but the issue is that about 60% of it is soluble. I wanted to have my input material be very enriched in membranes because it would also be enriched in the last binding partner that tethered it to membranes. So I made these synaptosomal fractions, which are just pinched off nerve endings that contain vesicles, mitochondria, as well as plasma membrane. I broke open these synaptosomes using detergent, and I bound a caps antibody to beads, and I used this antibody to fish out endogenous caps and see what proteins it was interacting with. I ran my eluids from the beads on a gel which I kumasi stained. And as you can see, along with caps, I get a number of other proteins. I also see a number of proteins that I get in control conditions, where I bound a non-immune rabid IgDs to beads and saw what stuck non-specifically. I was, of course, curious what these other proteins were, and so in order to analyze putative interaction partners, I submitted my sample for mass spec analysis. When I got my data back, I sorted it using spectral counting, which is a label-free method to measure protein abundance. Here I'm graphing the spectral counts in caps immunoprecipitation conditions and control conditions. Therefore, the proteins that we're interested in lie along this x-axis, and things that were maybe there for non-specific reasons lie along this middle line or down here towards the control condition. You can see I got a lot of caps, so that was good. And you can also see this protein Rabconnectin3-alpha, and its subunit is buried a little bit further down here, Rabconnectin3-beta. And these proteins were very robust. Each time I did this assay, these two proteins kept coming up, Rabconnectin3-alpha, Rabconnectin3-beta. And so I wanted to know a little bit more about maybe the stoichiometry between caps and these two putative binding partners. So instead of running my entire LUits on mass spec, instead I ran the LUits on an SDS page gel, stained the gel with kumasi, and cut out bands that I could see in my caps IP but not in my control IPs. I then had these bands analyzed with mass spec, and again I saw this Rabconnectin3-alpha protein and Rabconnectin3-beta protein and found them corresponding to distinct bands. I measured the intensity of these bands and compared it to the intensity of this caps band and found the stoichiometry to be six molecules of caps per one molecule of Rabconnectin3, which seemed like a pretty promising ratio for an interaction partner stoichiometry. I also got a number of these VATPA subunits, as well as this verified caps interaction partner, SNAP-25. I was still very curious about this Rabconnectin3 complex, and before I further pursued it, I really wanted to make sure that these proteins were not present in control conditions, that they weren't there for nonspecific reasons. So I obtained antibodies for Rabconnectin3-alpha for Rabconnectin3-beta, and I performed caps immunoprecipitations and saw that when I IP caps, I was able to get both proteins, as well as components of VATPAs complex, but not in control conditions, indicating that these proteins are interacting with caps and not with the beads. Finally, I wanted to make sure that there was nothing kind of strange going on with my caps antibody, and so I obtained an antibody for Rabconnectin3 that immunoprecipitated the alpha subunit. I was able to see that when I immunoprecipitated Rabconnectin3-alpha, that I was also able to pull down caps, showing that the CoIP goes in the opposite direction. So together, all of this data says that the Rabconnectin3 complex robustly and reproducibly immunoprecipitates with caps, and that the alternate is true, that caps immunoprecipitates with the Rabconnectin3 complex. And so these are the protein complexes that I further pursued, but before I jump into all of that data, let's take a moment and talk about what exactly Rabconnectin3 is. So the Rabconnectin3 complex is composed of two proteins that exist at a one-to-one stoichiometry. There's the alpha subunit, which is also called DMXL2, as well as the beta subunit, which is also called WDR7. Both of these proteins contain a number of WD-40 repeat domains, and each of these repeats forms this beta sheet, and when there are five to seven of these repeats in a row or near each other, they form this plate-like structure. These plate structures are thought to be important protein-protein interaction hubs, because there's so much surface area for many proteins to interact on. And so I was excited by this. I thought, okay, this makes sense that caps is interacting with this protein interaction hub, because there's a lot of proteins that are coming onto and off of vesicles as it's maturing and going towards the plasma membrane. However, I got even more excited about this domain called the RAV domain, because the RAV domain is thought to be involved in interacting with VATPase and mediating proton pumping. I talked about VATPase in some of my intro slides. VATPase is a large protein complex that hydrolyzes ATP in exchange for pumping protons into the lumen of vesicles. VATPase is present on not only dense core vesicles, but also endosomes and Golgi and lysosomes, and other acidic compartments. So, because it's pretty abundant and because it can use up a lot of cellular ATP, you can imagine that it's important that this complex is regulated, that it's not just always using up ATP or pumping protons into, say, a compartment that was already acidic enough. Therefore, this complex can be regulated, and it can be regulated by the dissociation of this V1 domain. So, in conditions in which it's not favorable for the VATPase to pump protons anymore, the V1 domain will come off the membrane-bound V0 domain. And in this confirmation, protons cannot be pumped, and ATP cannot be hydrolyzed. The issue, though, is that while it's pretty easy for VATPase to fall apart, it's a little bit harder for it to get back together. And the reason for that is thought to be these side domains, E and G, which need to be bent into place in order to fit securely on top of this V0 domain. Therefore, studies in yeast have shown that there's a protein complex that's needed in order to guide this V1 back onto the V0 to form a stable complex and allow proton pumping. This complex is called the rave complex, and its central subunit is this RAV1P protein, which looks a lot like DMXL2 slash RAVConnectin3-alpha, in that it contains both a RAV domain as well as a number of WD40 repeats. So due to its homology to this yeast protein, a lot of studies on this RAVConnectin3-alpha, RAVConnectin3-beta proteins were undertaking trying to look to see if it also mediates VATPase proton pumping. It was found that both of these proteins interact with VATPase subunits. That knockdown of both of these proteins cause defects in vesicle acidification in various organisms, and that the presumed function of these two proteins is conserved from yeast, that they positively regulate VATPase assembly and therefore positively regulate proton pumping. The reason that this finding was so exciting to us is because both of these papers on caps in the literature could be explained by a defect in acidification. So the formation of immature secretory granules is reliant upon the slight acidity of the trans-golgy. The pumping of serotonin into dense-core vesicles is reliant upon the acidity of the dense-core vesicle in order for the transporter to pump in the catecholamines. Therefore, our idea was that caps interacted with RAVConnectin3 complex and that through this interaction mediated the VATPase acidification of dense-core vesicles. When I was a couple of years into this project, somebody actually came out to say that, indeed, caps does influence the pH gradient of vesicles. So this paper shows these hippocampal neurons and when they knocked out caps using SHRNA, they found that the pH of the dense-core vesicles in these hippocampal neurons was increased from about 5.8 to about 6.8. And so this demonstrates that caps is somehow involved in the acidification of dense-core vesicles. However, these authors were unable to propose any kind of mechanism as far as how it could be performing this role. Therefore, my project became a way to try and explain how caps could influence the VATPase proton pumping as well as potentially the loading of catecholamines into vesicles. The first step into trying to show this hypothesis was to see whether RAVConnectin3 was actually on dense-core vesicles in the first place. So I used this neuroendocrine cell line that was expressing this dense-core vesicle marker that was tagged with a GFP protein. I then stained these cells with antibodies using RAV-against RAVConnectin3 alpha and RAVConnectin3 beta and found that these proteins localized pretty well to dense-core vesicles. You can see areas where RAVConnectin3 alpha and beta are not localized to vesicles just because they are also found on endosomes. And so these areas where they're not co-localizing are likely endosomes. Of course, the whole reason that we started this project was because we were interested in the protein that was tethering caps to dense-core vesicles. And so we wanted to know if RAVConnectin3 was responsible for caps localization to dense-core vesicles. In order to test this, I worked with a postdoc in our lab, Manny, and did these assays in which we had these cells that were stably expressing this NPYGFP dense-core vesicle cargo protein, as well as this fluorescent caps molecule, CapsMK. Under control conditions in which we transfected the cells with non-targeting SIRNA, you can see really good co-localization between caps and the NPYGFP vesicles. However, if you knock out RAVConnectin3 alpha or RAVConnectin3 beta using SIRNA, you can see a significant redistribution of caps from the dense-core vesicles into the cytoplasm. And this can be quantitated using Pearson's coefficient by measuring... which tells you about the localization between two fluorescent constructs. So here in non-targeting conditions, you can see the Pearson's coefficient is quite high, but upon knocking out RAVConnectin3 alpha and beta, there is a significant decrease in the amount of caps that's localizing two dense-core vesicles. Another way of looking at this data is asking whether caps is in a punctate confirmation or whether it's cytoplasmic. In non-targeting conditions, 80% of caps is punctate, presumably on the dense-core vesicles. However, in RAVConnectin3 beta knockdown conditions, only about 45% of caps is actually localized to vesicles. And this data says that when you knock out RAVConnectin3 beta, that there's a significant redistribution of caps from dense-core vesicles into the cytoplasm, suggesting that it's important that RAVConnectin3 beta expression is important for proper caps localization. This assay kind of showed the negative that knocking out RAVConnectin3 beta also took caps off of vesicles. But we were also interested in kind of going the other way of seeing if RAVConnectin3 beta could recruit caps onto vesicles. And so in order to look at that, we used these cost-cell lines. And cost cells don't contain any dense-core vesicles. And so if you express caps in them, it's totally soluble. We expressed RAVConnectin3 alpha in these cells and found it also to be soluble. However, RAVConnectin3 beta formed all these punctate structures. And we were curious if we co-expressed RAVConnectin3 beta with caps, whether caps would redistribute onto these RAVConnectin3 beta-positive structures. And indeed, co-expression of both of these proteins together, caps in RAVConnectin3 beta, redistributed caps from the cytoplasm onto these RAVConnectin3 structures, indicating that RAVConnectin3 beta may be able to recruit caps onto vesicles. All of this data was highly suggestive that RAVConnectin3 beta is involved in caps localization with vesicles. However, this did not necessarily say that these proteins were directly interacting. And so in order to figure out if these proteins made a direct interaction, I purified both caps and RAVConnectin3 beta for direct binding assays. I purified caps using this streptactin system that Ducklin from my lab developed. And you can see I get a really nice band at the correct molecular weight. RAVConnectin3 beta is a little bit more unstable. This is the correct molecular weight for RAVConnectin3 beta. And although there are additional bands that you can see in this gel, there are other effects and not other protein interactions. In order to see whether these two proteins could interact with one another, I purified caps on these streptactin beads and eluded it with a biotin derivative. I then incubated caps with these beads that were bound to either RAVConnectin3 beta or that were just control beads that were not bound to RAVConnectin3 beta. And looked to see if caps would bind these RAVConnectin3 beta positive beads but not be there in control conditions. And, indeed, that's what happened. When RAVConnectin3 beta was present, I was able to pull out caps but not in control conditions, suggesting that these two proteins form a direct interaction. We know a lot about the functional domains of caps, and so we were curious where on caps RAVConnectin3 beta interacts. In order to ask this question, I used a number of fragments that Masaki from our lab designed. There's an N terminal fragment that's a little bit shorter, this longer N terminal fragment that contains a dimerization domain as well as this plasma membrane binding domain, and then a C terminal fragment that contains this snare binding domain. In order to see which of these domains interacted with caps, I co-expressed caps or the various fragments with RAVConnectin3 beta. I then laced the cells and used an anti-HAB to pull out caps or fragments and looked to see if RAVConnectin3 beta was also pulled out of the cells. When I did this, unsurprisingly, when I pulled out full length caps, I was able to see RAVConnectin3 beta. However, interestingly, when I pulled out N terminal fragments of caps, the shorter N terminal fragment as well as the longer N terminal fragment, I seemed to get even more RAVConnectin3 beta, suggesting that it was preferentially interacting with the N terminus of caps. This is in contrast to a C terminal fragment as well as control conditions in which I did not pull out any RAVConnectin3 beta. Together, all of this data says that caps directly interacts with RAVConnectin3 beta via its N terminus. We were very curious what these two proteins were doing together in the cells, and we were very inspired by all of the assays that were suggesting that both caps and RAVConnectin3 were involved in vesicle acidification. In order to see whether that was true, we used knockdown cell lines in which we knocked out caps or RAVConnectin3, and we looked at the vesicles acidity in a couple different ways. One way was using this fluorescent probe called Mini202, which could be loaded specifically into vesicles, and whose fluorescence depended upon the pH of those vesicles. The second way was using this expression construct, NPYGFP, NPY is a dense-core vesicle cargo protein that's specifically in dense-core vesicles, and GFP is our pH sensitive probe, and I'll go through each of these assays briefly. So for my first assay, again, I used this probe called Mini202, and Mini202 looks a lot like dopamine, in that it's loaded specifically into dense-core vesicles via this VMAT transporter. The nice thing about this chemical is that it's actually fluorescent, and further, its fluorescence is dependent upon the pH of its surroundings. So if it's loaded into a very neutral vesicle, it will fluoresce brightly if you excite it at 370 nanometers. However, if it's loaded into a very acidic vesicle, it will fluoresce more brightly at 335 nanometers. Therefore, I could look at cells that had been in which I had knocked out caps and looked at control cells and compare the ratio of the fluorescence at these two wavelengths in order to make statements about whether or not the pH of the vesicles was impacted by the knock-down condition. The first thing I did was make sure that this probe was actually loaded into dense-core vesicles as it was supposed to, and so I loaded a neuroendocrine cell line with Mini202, and I looked at it under the microscope, and you can see all of these punctate structures. I was hoping those were dense-core vesicles, but I made sure I performed another experiment in which I pre-incubated the cells with this drug called reserpene. Reserpene actually blocks this BMAT transporter, which is only present on dense-core vesicles. If I block this transporter and this probe is only loaded into dense-core vesicles, I shouldn't be able to see a signal of Mini202, and that's what happened. This told me that this probe was being loaded into dense-core vesicles, and any information I got about acidity with the pH of dense-core vesicles and not, say, endosomes or other acidic compartments. The other thing I needed to make sure of is that the plate reader would be able to see differences in the pH. So what I did was I incubated this Mini202 compound with buffers at different pHs ranging from 4 to 8. I then read the fluorescence at 370 and 335 nanometers and took that ratio to see how it changed as I increased the buffer pH. I was able to see that as you exposed Mini202 to buffers of increasing pH, that the 370 to 335 nanometer ratio increased. And this told me that I would be able to look at this ratio in cells, and if the ratio was higher, that would mean the vesicles that the compound was loaded in were less acidic. So in order to do this acid, I should say I worked with a very talented undergrad named Connor, who helped me very significantly with these assays. And so we would load cells into a 96 well plate and transfect them with SIRNA. We would then add Mini202 and wash the cells and read the fluorescence at 370 and 335 nanometers. We did this for control cells as well as cells in which we had knocked down caps, RAB Connect and 3alpha, and RAB Connect and 3beta, and much to our disappointment there was actually no statistical difference in cells that had been in control cells versus cells that had been knocked down, that versus cells in which we had knocked down these proteins. And this was pretty disappointing to us and also pretty confusing because the literature had really said that these proteins were involved in the acidification of dense core vesicles. And so in order to reconcile this data and try and figure out what was going on, we went back to the literature to try and kind of figure out what we were missing. So we know VATPase fluctuates between an assembled and a disassembled state. And when it's assembled it pumps protons and when it's disassembled it does not pump protons. We assume that there are stabilizing factors for VATPase such as the RAB Connect and 3 complex and caps. We also assumed that if we knock out some of these stabilizing factors that we would drive the VATPase complex to this disassembled state such that all of the vesicles in the cell would deacidify because there would be no more proton pump on them promoting their acidity. However, it's possible that we are not completely obliterating this assembled state of VATPase when we're knocking down these stabilizing factors. This phenotype might be a little more subtle. It might drive it towards this disassembled state but there might be some VATPase complexes that are able to assemble and able to pump protons and maybe this would be enough in order to acidify the vesicle at a steady state condition. We wanted to look and see maybe if there was a more subtle phenotype, a more subtle pH phenotype. And so to do this we basically wanted to deacidify all of the vesicles inside of a cell and see how quickly they could reacidify, see if there was a defect in the reacidification process upon knocking down these proteins. And so we did this by incubating the cells with this drug called Bathlamycin. Bathlamycin binds the V-naught domain of VATPase and it deacidifies the vesicles by inhibiting proton pumping and tearing apart this complex. The nice thing about Bathlamycin is that it's reversible and so you can wash out this drug and then see if the vesicles are able to reacidify. So this is the scheme that we went forward with then. We added this incubation with Bathlamycin prior to adding Mini-202 to the cells. So we basically deacidified them and gave them about 90 minutes to recover their pH gradient. We did this with control cells and we compared the untreated cells versus cells that had been treated with Bathlamycin and given a period of time to recover. We could see there was a slight increase in the pH of control cells. However it was not significantly different than cells that had not been treated with Bathlamycin, suggesting cells were able to recover their pH gradient to some extent. However, when we knocked out caps as well as the RAB Connect-in-3 complex, there was a significant deficiency in their ability to recover their pH gradient as indicated by these bar graphs which are much higher than the untreated condition. Therefore we can say that RAB Connect-in-3 alpha-beta as well as caps are involved in modulating the VATPase-mediated acidification of dense core vesicles. There were a couple drawbacks to this particular assay, mainly that I had to load that probe into the cells each time I did that experiment. I wanted to do a different assay in which I didn't have to load any kind of material into the vesicles. And so to do this I used an expression construct NPYGFP which I expressed in a neuroendocrine cell line. NPY is a dense core vesicle cargo protein so this would only localize two vesicles and GFP is a pH sensitive probe. If you image cells at a low magnification their NPYGFP is actually very dim because it's inside of those vesicles that are about a pH of 5.5. However, if you add this neutralization agent, ammonium chloride at a pH 7.4 you can see that these vesicles get brighter and therefore the whole cell gets brighter. And that's because the GFP goes from being exposed to a pH of 5.5 to a pH of 7.4 which increases its brightness. You might imagine that if I pre-incubated my cells with a drug like Baflamycin that the cells would be much brighter in the beginning and that adding ammonium chloride to them, adding this neutralization agent would not increase their brightness anymore because they're already at a neutral pH. I wanted to kind of use this scheme to look at how much the vesicles increase their brightness in order to make a statement about whether or not caps is involved in acidifying dense core vesicles. So I did these assays by capturing movies of cells before and after neutralizing them. I then identified regions of interest the cells and I measured the fluorescence intensity per cell before and after ammonium chloride neutralization. I could then calculate the ratio of GFP fluorescence and I found that in normal cells this ratio was about 0.4 which corresponds to the approximate 3-fold brightening that's happening going from a pH of 5.5 to a pH of 7.4. However in cells that I have already deacidified I would, the ratio is closer to 1 corresponding to the fact that there is no additional increase in neutralization and in fluorescence intensity. When I did this assay with cells that had been knocked out from caps I could not see any statistical difference between caps knocked down and control cells and because I had already done the plate assay this wasn't so surprising to me. However if I pre-incubated the cells with bathlamycin and then asked them to recover over a period of 30, 60 and 90 minutes and looked at whether they could regain their pH gradient I could see that in control cells while they were able to reacidify within 60 and 90 minutes that caps knocked down cells were unable to reacidify to the same extent and even by 90 minutes they were not at the level of control cells nor at the same pH as when I did not add bathlamycin and again this demonstrates that caps is involved in modulating the pH of dense corpuscles and so this data brings me to my model in which caps interacts directly with Rabconnectin3-beta via its end terminus expression of Rabconnectin3-beta is necessary for caps proper localization to vesicles and Rabconnectin3-beta is able to recruit caps onto membrane structures this whole complex Rabconnectin3-alpha-beta and caps are involved in modulating the pH of dense corpuscles likely by promoting the assembly of VATPAs into a proton pumping state there's a lot of ways to continue forward with these studies and they kind of fall in two categories we can learn more about caps interaction with vesicles and we can learn more about its involvement in pH in dense corpuscle pH so I'll talk about how we could further define caps interaction with vesicles first this is actually a project being undertaken by Stephanie in my lab and she has identified I should say first, we know that in addition to interacting with dense corpuscles via its end terminal domain with Rabconnectin3-beta we also know that caps makes a C-terminal interaction with dense corpuscles and we can see that in control cells caps is punctate but if you knock out the last 135 amino acid of caps it becomes soluble, suggesting that this C-terminus also mediates an association with vesicles Stephanie is currently undertaking work to identify a minimal dense corpuscle targeting domain. She can then purify this recombinant fragment and do immunoprecipitations with the fragment as bait to identify what other interaction partners caps has on vesicles. Additional work could address what domains of caps interact with Rabconnectin3-beta we would also of course because we're very interested in the priming and exocytosis of dense corpuscles we could learn how caps interaction with Rabconnectin3-beta protects its priming function and then finally we know that at the time of regulated exocytosis at the time of vesicle fusion caps actually dissociates off of the vesicles it would be interesting to know what the Rabconnectin3 complex was doing at this time as well there are also another a number of additional studies we could undertake to learn more about the acidification of dense corpuscles and how caps and Rabconnectin3 are involved in it one study would be to really kind of nail down this mechanism to really test to see whether caps and Rabconnectin3-beta knockdown impair VATPase assembly and so you could do this by making knockdown cell lines and then lysing the cells and pelleting their membrane fraction you would assume that in knockdown conditions when Rabconnectin3-beta and caps are knocked down from these cells that if VATPase were stabilized that the V1 domain would be in the supernatant whereas if the complex were able to assemble just fine that V1 would be in the membrane fraction another way you could perform these studies would be to make these cell lines and then you do a microscopy assay in which you transfected them with a V1 subunit tagged with GFP and quantified whether this was able to localize to membrane or whether it was soluble and this would again tell you something about the ability of the complex additionally I showed you those two papers at the beginning of my talk how caps was involved in dense corvestical, potentially caps was involved in dense corvestical biogenesis as well as how caps was also maybe involved in catecholamine uptake you could measure you could knockdown caps in the Rabconnectin3 complex and see if this impacted either dense corvestical biogenesis or catecholamine loading to try and understand the importance of these proteins in maintaining the pH gradient and so with that I would like to extend some acknowledgments I first want to thank my advisor Tom Martin for the opportunity to work in his lab over the past several years I've learned a lot from Tom over the years, I think probably the most important things that I'll carry with me throughout my scientific career are the importance of patience in experimental design in running the experiments and analyzing the data the importance of thinking before you start talking how you need if you can explain something well you only have to explain it once so you should choose your words carefully and then finally the importance of being optimistic that knowing that if you have a good hypothesis and you do good science that you will eventually happen upon something that will be good and people will care about and so I do try and keep those things in mind I thank my lab mates both past and present I thank Manny and Connor who directly contributed to the work that I showed you today I also thank Declan, Stephanie and Masaki for their contributions to the second chapter of my thesis which I didn't have time to talk about but it was really kind of fun to try and put all of our data together and form a nice story about again CAPS interaction with vesicles I thank all of my lab mates for providing this supportive environment for helping me with protocols and giving me cells and plasmids but also just being very kind and encouraging and just helping me figure out what I should be doing I thank the core facilities the microscopy core, Elle was actually initially my lab mate I think that she showed me how to turn on this very simple confocal microscope like 10 times my very first year in graduate school but I've certainly graduated on to more complicated techniques and I'm grateful for all of her help throughout all of it I also thank Greg and Greg from the MassSpec facility that MassSpec experiment was my first big experiment in grad school and I was very nervous about it I didn't really know how to analyze the data or how to work up the materials they were extremely helpful and I'm very grateful, thank you I thank my thesis committee I particularly thank John, Sebastian and Belle for being here today and I thank my whole committee for helping me throughout this process and for helping me push this project forward particularly in the last year because I'm really proud of the strides that I've been able to make I of course thank then my funding sources and I did want to take a moment to offer a couple more personal thank yous I wanted to thank my friends I came to Wisconsin because it had a really good reputation for science but when I met all the scientists here I thought they were really nice people and people that I could be friends with really wonderful people and I picked up a lot of really random hobbies too I learned how to bike and how to play frisbee, play really nerdy board games and I can drink just a lot of beer and make a lot of comments about it that sounds snobby so all of these things I'm grateful for my friends for being supportive when things were hard and for celebrating with me when things were good and then finally my family so my parents came today they're from Philadelphia area so it was kind of a long trek but I'm really happy they were able to come and I hope that presentation made sense I appreciate your support throughout my graduate school career and of course throughout my entire life I'm so grateful and I thank my partner Ben who has kind of seen me through each step of graduate school from joining this lab all the way through preparing this presentation it's not just about Ben but the first time any of my friends meet him they always comment on how calm he is and it's really true because I feel like I would always come home from work and I would be all frazzled and not sure I wanted to go back the next day and I would talk to Ben for like five minutes and I'd be like alright you know what I got this I'll go back tomorrow so thank you for all of your support and with that I also thank all of you for I would be happy to take any questions where on the N-terminus no I haven't tried to parse down that interaction region is that your question I haven't no just that assay that I showed I mean the that longer N-terminal piece seem to interact better than the shorter N-terminal piece and so it's possible that it might be kind of like you know in the middle of that of that long N-terminal piece but yeah I haven't tried to parse it down any further yes that is a great question as far as like how many protons are in that dense crevessicle I'm not sure if anyone knows that particular information but definitely there are free protons within the dense crevessicle as well as protons that are kind of accumulated within that dense core sorry what was your other question what forms the dense core are there metals I honestly am not sure about whether or not there are metals good question I'm sorry can you say that again upon knock down is that what you mean well there's certainly so for example caps is only really expressed in neurons and as well as a number of other cell types so that's certainly a very particular protein to certain cell types and the wrap connectin 3 alpha protein is also kind of specifically in brain and insulin secreting cells I'm not I'm not sure about the beta some unit but I would assume that it would be expressed in the same sorts of cell lines that's a good question I know that there is a system on endosomes it's called Arno this protein Arno R6 and those proteins apparently can respond to some kind of change in the structure of VATPase once the endosome is fully acidified and it's known that their binding to endosomes is dependent upon the pH gradient that's the only protein that I know that's really been tested as far as that so wrap connectin 3 alpha and beta are thought to also localize to synaptic vesicles our lab does not tend to think that caps localizes to synaptic vesicles although that's some people do think that as far as what the synaptic version of as far as how wrap connectin 3 alpha and beta are regulating the acidity of synaptic vesicles I don't think that's ever really been looked at I don't think I don't think the involvement of these proteins in acidifying synaptic vesicles has been really looked at at all actually yeah I looked yeah I looked for that really hard in the literature but you know I couldn't if there is I could not find that paper I also really want to know that how how deacidified do these things need to get before everything messes up I'm not sure of the answer to that oh thank you very much thank you thank you thank you


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Hello and welcome to Mojave here in the high desert of California on this incredible day. Now you are going to witness history in the making. All of 368,000 views!


Okay, so let's get to what we're announcing here today. So we held back some things that we've been working on for announcing today because we thought this is a great audience to talk about some of the new things we're doing. The first thing we're doing is sort of a business model thing. So obviously Oracle Databases and all of the Oracle products for years have been sold via what we call perpetual licenses. You pay us money for the license up front, okay? You get the use of that software for the lifetime of your business, basically. And then you pay us an annual fee for support, right? In the open source space, people have been using a slightly different business model, which says, okay, you don't pay us up front, but you do pay us annual support fees for getting support for our products. Or we're just open source, you can just download the software from the web and play with it for free. So what we're announcing today is we are going to add to our existing perpetual licensing business model for Oracle NoSQL Database, a more open source friendly kind of model where we now have a version of Oracle NoSQL Database called the Community Edition. That edition of the product is available for download by anybody on Oracle's website. You go to OTN, which is what we call our technology network.  And then if you decide, hey, this is a pretty cool product, I want to get support. What we're announcing here today is now you can get support. And you can get it in a very simple fashion. You can just go to the Oracle store on the web, shop.oracle.com. You can give us your credit card number. And for $2,000 per server per year, which is actually a very good deal. You get full support, the full enterprise class support that Oracle provides for all of its other products are now available for the Community Edition of our NoSQL Database product. And I know a lot of you, maybe, from startups. Startups, of course, don't want to spend any money at all. This is great for them. They can just start using the software. And then when they finally become real, go live. They can get support and get the full benefits of Oracle's support organization. So that's the first announcement. Number two, we want to talk about appliances. So over the last few years, Oracle, since we bought Sun, is now not only a software vendor, but we're a hardware vendor too. And what we've been doing is something we call engineered systems. Other people call appliances or converge solutions. What we do is we take our software and we take the hardware, we integrate it together. We're basically like a systems integrator in my group. And we deliver appliances to customers. So that customers don't have to be in the business of engineering complex, clustered computer systems anymore. The first one we delivered for my group is called Exadata. Exadata is sort of a play on the Teradata name. And Exadata is this database machine for running massively parallel, clustered, scale out, database technologies, database systems for big data warehouses. We have customers running over multiple petabytes of information on the Exadata systems for data warehouses. They're also used for big transaction processing systems as well. After that, we added something called the Oracle Database Appliance, which is, again, an engineered system for the Oracle Database for more low-end use cases. And what we're announcing today is our big data appliance for Oracle NoSQL Database is our latest engineered system. So if you want to go and start playing with Oracle's NoSQL technology, you can buy our big data appliance. You can start with a six-node cluster of two-socket commodity Intel servers. That's what we call the starter rack. And we will have a whole set of scripts to pre-install your software for you on that machine so that you can be up and running in a matter of hours.  So it's something we found our customers really like, this whole notion that they don't have to design complex clustered computer systems anymore. Of course, all the technologies I mentioned earlier work in this environment. Enterprise Manager works. We give you full support. The big data appliance also is an engineered system for Hadoop, so you can also run Hadoop on the same hardware as you run Oracle NoSQL. You can have some of the nodes on the big data appliance running Oracle NoSQL Database. Some of the nodes can be running Hadoop if you want to integrate the two together. We support that as well. And just the last note, if you want to go to this link, this hardware is very competitive in price. And if you do the math, we think you'll find in a lot of cases this is actually cheaper than going out and buying hardware yourself and integrating it together. And then the last thing I wanted to mention is that in order to get people playing around with our product, we welcome you to go to this website. nosequelcontest.com. And play around with the product. Come up with some interesting app, send it into us.  The contest ends October 18th, so download the software today and start playing. And with that, I'd like to welcome you all to go to our website, get more information. At the conference this week, this afternoon, I think we have a panel session from some of our developers who are going to be here to talk about Oracle NoSQL Database. I think we have another session tomorrow as well, so where you can learn about the technology in a lot more depth. And with that, I think we have a couple minutes. I'll be happy to answer a couple questions if we've got any questions from the audience.


Thank you, Jessica. Thanks very much for the invitation to speak. Can't be there in person. Let me know if you have any trouble hearing me and also first let me know if you have any questions. So, here's a drawing provided by my daughters. If you zoom in you can see some equations. So here's a plan for the these lectures. In the beginning, I'll be discussing the general concept of symplectic resolutions. This plan roughly corresponds to the days of the talks but maybe not precise. Then I'll talk about symplectic duality. Then I'll speak about the government. Then I'll speak about the special case of number three generalize. And then time permitting. Cool own branches and in particular of these generalized African grass mania slices. So which goes into the name of truncated shift to the unions. So there's a plan. And as I said, we'll roughly correspond to the lectures but maybe not precisely. And there'll be two question answers. The first one on Wednesday, we hosted by Michael McRee. And the topic of that. And the second one on Thursday will be hosted by eHow. Sorry, if I misspelling it last name you have. And the topic of this session will be on connections with physics. And specifically also about these generalized African grass mania slices. So let's begin today with the synthetic resolution. So, there's a famous quote from a kunkab from about 10 years ago and he said something like symplectic resolutions are the le algebra of the 21st century. And hopefully I'll convince you today that there are very interesting objects of study. They have been quite extensively studied in the 21st century. So, let me begin the definition of first glance looks a little complicated, a lot of structures. So what is a symplectic resolution. So in fact, we're going to play the restricted class called chronicles. It's a first of all, morphism of two complex algebraic varieties X and Y. There's something there's some feedback. I did hear also a little bit of echo is it. Maybe now people have muted themselves and it's better sounds better to me now so okay great. Okay, so the conical symplectic resolution is a morphism of algebraic varieties. This map pies is a resolution of algebraic variety so it should be irrational and projective. And why is smooth and usually I'll work over the complex numbers all over algebraic varieties over the complex. Why is smooth and carries the algebraic symplectic structure. Okay, and now echo seems to be gone. Okay. Okay, well, let me know if anyone has any questions. Okay, great. So let's go again. So kind of a symplectic resolution we have it's a by ration. It's a two algebraic varieties over the complex numbers map between them which is a resolution of singularities so it's by rational and projective. The space Y is smooth and symplectic. And the space X is a fine. Poisson. So maybe I just remind you that this particular this means that the coordinate ring of X is a plus on algebra. That means in addition to multiplication, it carries a plus on bracket, which which is something which satisfies Jacobi identity, and also the liveness identity with respect to the multiplication. Okay. And more structure. This is okay so that up till now that's what it means to be conical. I mean a symplectic resolution now I'm going to add the adjective conical. That means I have an action of C star on Y and on X so it acts on both varieties and the morphism is compatible with the action. And the, the, this action of C star and X gives rise to a grading z grading on that algebra functions. And I demand that the nth graded piece is zero. If n is less than zero, and is C if n equals zero. So it's strictly not it's not negatively graded with C and degree zero. So this, this fact is equivalent to the geometric fact that the fixed points for this C star action is just a single point. And that the action of C star contracts X to this fixed point. So that's another piece of structure. And now yet one more piece of structure where somehow is not quite mentioned in the adjective sometimes people might impose a different word but let me just say, I'll put another piece of structure without giving it a name exactly. I want another action of a Taurus. So a Taurus another algebraic Taurus, which will also act on the morphism X and Y. I should have mentioned here before that this scales the symplectic form. In terms of this plus on bracket, it means that this plus on bracket has degree one or degree two. So we can consider conical actions of weight one or conical actions weight two. I'm not going to be too specific about. Okay, but now I have another action of a Taurus, which is now preserves the symplectic form. In fact, it's a Hamiltonian action. And I'll demand, not that this, not that this contracts the space to a point that wouldn't be possible for action which preserves the symplectic form. But I will ask is that there's finding the many fixed points for this Taurus action on Y. So this is a condition, which is not always true, but often is true. Okay, so that's a lot of structure. The definition took a whole page. So let's see some examples. So even though it seems like a long list of structures these things which satisfy this list of axioms is are quite common and very interesting in doing major representation there. So here's the first example is we take the cotangent bundle of P1 mapping to the nilpone and cone of SL2. So what is that well in pictures it looks like this nuclear reactor in this ice cream cone. So this morphism collapses the P1 sitting in here. In matrices, so I think of the nilpone and cone of SL2 as two by two matrices of trace zero and determinant zero. Two by two matrices trace a zero and determinant a zero. In terms of equations, those matrices look like w u v negative w. Already we get trace zero and determinant zero. We get w squared equals u v.  And this is the same as the as an algebraic variety to the quotient of C2 by the action of Z mod two. And we think of T star P1 as a pair consisting of a matrix like this and a line. So LA is a matrix and L is a line point in P1. And the condition is that A of C2 is contained inside of L and A of L is zero. That's just a way of describing this cotangent bundle. And so the fiber of this map. Well, if a is a non zero matrix, there's a unique such L just it's kernel. And if a is a zero matrix that's here, this is a zero matrix sitting here. So it is zero matrix. Well, there's no any L will work. So we get this P1 fiber here. That's our Y. That's our X. We have this C star action, the conical action. Joella. Yeah, we have a question. The question of the torus and the C star should be compatible or not. Yeah, they commute. Any other question. Okay, so we have in this case the conical C star action just comes from scaling of the matrix. Or equivalently scales and cotangent fibers. And, and we have this Hamiltonian. Torus T which, well, you could say it's C star squared or you could just say it's C star because part of the C star square will actually anyway this Hamiltonian C star squared action this. It acts just by acting on C2. Therefore on P1 and on the, and on the no one con. That's our first example. So this example of course admits many generalizations. So the first one maybe they'll be like really relevant for us will be the cotangent bundle of a project of space to PN minus one, which maps to the square zero. And by an matrices of rank less than or equal to one. So that's our X. That's our why it's resolution. And again we have conical C star action Hamiltonian torus action. That's before. Of course this is itself admits many generalizations. We could put here cotangent bundle of some flag variety. This is all under number two years we could put here some G mod P. And it would resolve P of G here we need semi simple group or the complex numbers and P parable example. And this would resolve a no put an orbit closure. I won't actually talk so much about this kind of thing so I'm not going to go into much detail about it so let me just put it in a bracket. Something that will be a bit more special case of this is more relevant for us is the cotangent bundle of the flag variety of SLN. So right that in more detail, which resolves the no potent cone of SLN. And here we have all n by n no potent matrices. And here the resolution is by a pair of no potent matrix and a flag. In the n dimensional vector space. So the flag in a n dimensional vector space. And this matrix and the flag are compatible in this way. So that's one. And once again we have, maybe it's worth saying here we have C star conical, which is given by scaling, and Hamiltonian tourist action, well in this case like the tourists or whatever group we had or in this case he started this C star n minus one, this acts on the, on the ambient CN. Another way this first example generalizes. So I pointed out that it was that this affine algebraic variety W square plus UV equals zero can be thought of as C2 mods Z mod two. So another way we could generalize that is we can consider C2 mod gamma as our X. Take gamma to be a finite subgroup of SL2. And then we have this client in singularity C2 mod gamma. That's our X, and has a well known resolution C2 mod gamma. That's our Y. So if we take, if we take the zero point here. This, this, this map is well it's by rational. And it's in fact an isomorphism away from this zero point, and over the zero point is a chain of P ones. And these finite subgroups of SL2 C are classified by simply lays thinking diagrams. And so the, and the, the thinking diagram tells you the pattern of this P one so this, this example here I'm trying to show a pattern of P ones, like, well I know how many drew seven or something. So this is a six connected together in a chain. So this is of course one to the basics thinking diagram, according to the graph. And actually, if you look at my, the conditions that I wanted to satisfy, the only way to get the Hamiltonian tourist action as if gammas is the group Z mod in so to get some kind of tourists acting here with finding many fixed points. So it would not satisfy the last condition that I impose the vision, if we didn't have, if we didn't take some of it. So mostly we'll consider the case of C2 mod Z mod n type a singular. Another way to generalize the cotangent bundle of P one, and the cotangent bundle of other projector spaces is the theory of hyper toric varieties. So this is a beautiful combinatorial way of constructing many solutions. And it's a main source of like intuition in the in the subject. So I'll explain a little bit about this, but for more detail. This will be the topic of Michael session on Wednesday. So, how many hyper toric varieties work. So I'm going to take a picture of a tourist acting on a vector space. CN. This is just some other big tourist of rank, like less, less than or equal to n. I assume it acts effectively this purpose. And then we formed the cotangent bundle of CN, which is the same as CN, plus a dual copy of CN. It has a moment map to the dual of the the algebra of our tourists. So, in coordinates. If this, we can say that this choose coordinates on CN. Well, it has natural coordinates. So this action is given by say some weights kind of one. So it's torus T. And then you can use that we can write down this, this moment. And then we take the, this will be a moment. Then we take the zero pre image of the moment map. And we can take a GT quotient for the action of the tourists. And in fact, we can take two different kind of GT quotient we can take a affine GT quotient or a project of the IQ quotient. So, if we take the affine GT quotient, we'll get the, the space X. And if we take the kind of project of GT quotient. Then, sorry, maybe I'll call this one Kai. I shouldn't have put these kinds. Some weights. That's not worry about them. And then, and then I'll get the space Y. That's our X, and that's our Y. Let's, so let's see an example of this. So, so sub example of these hyper dark writers. So the first example I want to take, as I take C star acting on CN. So just a tourist just one dimensional, and this action just by scaling. So then here, I have T star CN. Again, it's like CN plus CN. And here the action will be like scaling of weight one, and here scaling of weight minus once my tourists will act in opposite ways in the two copies. And I have this moment map which is just given by taking the A, B to summation of a IVI. And then if I take the zero level of this movement. And I divide by this project of GT quotient, well as Kai is just like the identity map. Maybe I should have pointed out. I want to find this project of GT quotient, but it depends on Kai, which is a character of the tourist morphism from the tourists to see star. If I don't get any map, then I will get the cotention bundle of projectors. And no map to the affine GT quotient, which will be this rank square zero rank, square zero rank less than one matrices. In fact this matrix A is made from these two vectors and it's like the, the product of a and B in the opposite order. So that's, that's, that's one example. And then the dual example. So this is our first appearance of symplectic duality. So what would be dual to see star acting on CN by scaling. Well, I mean, you'd never heard of this duality might not, might not be obvious but here's the dual is you instead of taking. Again acting on CN, but rather than just see star you take a big tourist like this set of T1, TN such that the product is one. So rank and minus one towards here at a rank one towards here I have a co-dimension one towards I take this big towards acting on CN. So I do the same construction, I formed the cotention bundle of CN, and it's have its moment map so it's moment map. This time will land again in the dual to the algebra here so not right. But I have a moment here to the algebra, and then I take this Hamiltonian direction. And that is our old friend C2 mod Z mod n results this resolution of the financing. So here we see a way of producing the cotention bundle of PN, and the resolution of the client is singularity using Hamiltonian reductions of an affine space by tourist action. And that's so hyper torque variety is just the generalization of this so you start with any tourist action on your vector space, take the cotention bundle, and take the Hamiltonian reduction. And sort of the ways of doing I mean, not always when you get a smooth space, but the classification of these actions the classification which ones give you smooth things, and the study of the resulting things. So places those that's all can be done combinatorially in this theory of hyper torque rights. So that's the next, that's the end. And even if you don't know what this duality means yet, which you shouldn't because I haven't explained yet, you can sort of see there's something dual about these two things here have a rank one tourists and here I have a rank and minus one to us. So one more major class of examples, which will be important there's two more major class of examples but I'm going to pause on introducing the, the last class of examples, which are the affine gross money and slices and go right here to the equipment varieties. So, for varieties here, I was taking reductions of actions of Tori. Now instead of just Tori I'm going to generalize it to products of GLN so Tori are products of C stars. Now I'm going to consider products of GLNs. And how am I going to do that, I'm going to start with a framed graph. So what is that, and draw this picture. It looks a little like this. So it's a graph, a directed graph. Some of the vertices are circles, some of the vertices are squares important, and all the vertices have numbers. So what I do with this graph, this quiver, I associate first a group, and my group is the product of the GLs of the circled vertices. So these are circles, and vi refers to the number in the vertex so it's just, just think of these numbers as being vector space of those dimensions. So in this case I have GL3, GL4 and GL5. And then I build a big vector space which I call M for some reason. So this vector space is just the direct sum of all arms along all edges in this graph. So which we could split in terms of Vs and Ws. And my convention is that there's only arrows from squared ones to circle ones. So it ends up looking like this. So that's my end. And then I do something like what I did a few minutes ago with the hyper torque varieties, I double the vector space I take its cotangent bundle. So again it's just a vector space so it's just n plus n dual. And you can think of and the dual lens is thinking of, you could think of it as doubling the graph, but arrows in both directions. And then this thing admits a moment map to the algebra this tourist. If you think about this as being doubling the arrows, this moment map is just about composing all possible, following one arrow and falling opposite arrow back. So if I put in this here, and maybe give this guy some names maybe I'll call a this will be. So if this map is just the bias bias. I j j or something, then this map is something like the sum over j of a i j b i b j i plus a j i. I mean, no. It's just the sum over always are going out and back from your vertex so either you follow this one out and back you go.  So just some boiling all the ways out and back. Okay, so that's the moment map. So we construct this Nakajima program writing. So this construction is due to Nakajima. We take the zero level of this moment map. And we take the project of g i g quotient by this product of gels, and here Kai, again it's a map from G to see stars given by the product of determines. So that's a special case. There are a couple of facts about what one general fact when they know, yeah, one general fact and then it's a special case I just got us. So, these w vertices, they didn't participate. They were just sitting on the sidelines, but they sort of come into play right now that this guy will retain an action of the general linear group of those w vertices in particular, we can consider the action of the tourists inside there. This tourist flag, and that's the that's going to be our Hamiltonian Taurus that acts on this question. Sorry, is there a question. What is the notation w I for so I should maybe should emphasize that these dimension vectors are called w eyes. These ones are called the eyes. It's just a convention. I mean, this is just the integers I wrote over there and the integers are so in this case, these are three four and five and W's is to maybe zero and seven. Here's a special case, which is very nice. So if we just take the following quiver. One, two, one, two, three and so on up till in minus one, and then put it in dimensional framing over there is that quiver, the quiver variety produced by this construction is actually just our old friend the cotangent bundle of the flag. And how does it work. Well, it seems at first glance, like a miracle like here I had some matrices how did I get this flag. Well, you just compose everything up into up into this framing vector space. So, maybe, maybe I'll do it in a shorter example, then you'll see exactly it works. In fact, let me just think slightly. Let me do it slightly. So that's my example. I want to explain that one. But I explained this one works pretty much the same way. So I put just K, and then frame the vertex. So then I have matrix a. So my end here just on CK to CN. So just a K by matrix. Then when I double it. I have two matrices. Another one matrix going backwards be. And if I take this Hamiltonian reduction. Then I then my momo map condition is just the product. So, G, okay, takes a B. In the right order. So first I want to use major A and then the matrix B to get back to CK. And then if I take the zero level. So then I'll be studying matrices like that with product zero in this order. And then when I take this project of GIT quotient by GLK, so G here is just GLK, because I only have one circle of the vertex. If I take in my notation before V would be K and W would be N is only one of each of them. If I take the, this Hamiltonian reduction. Sorry, if I take this project of GIT quotient, then it's the same as restricting to Paris AB, like this. Such that a is injected. This may be not very obvious fact, but it's a true back. And then mining out by the action of GLK. So if I restrict to the locus AB or is injected, then the image of a will be a K dimensional subspace of CN. And I also remember the AB and I'll be my animal. So this base here is is more to the potential bundle of a grass mining. So, and again I think of this potential bundle of grass mining as a pair, W, C, so W is a subspace of CN and degree K, I mean dimension K, and C is this matrix. CN, W, C, zero CN. So, backwards. There is a question in the Q&A. Great. One second, C, W, zero and C of CN is contained in W. And this, to go from this pair AB to this W, CN, this W is the image of a, and this C is the composition of A and B this way around. So that's first B and then A. Go ahead, no question. Oh, I mean, I guess I need to read it. Sorry. This is the direction from square N to circle N. So I was maybe a little like imprecise. It actually doesn't really matter what directions you put there on the arrows. In the sense it matters for the construction of this vector space N. So the definition of this vector space. The definition of this vector space N, that depends on the direction of the arrow. But once you go to this cotangent bundle, you double the arrows anyway. So it doesn't actually matter the direction of the arrow. Well, sometimes people usually fix on convention and stick to it, but I don't seem to be doing that. So it doesn't, it doesn't matter too much, maybe usually better to write from Bs to Ws, but it doesn't really matter which direction. So here I wrote from B to W. Here again I guess I wrote from B to W. Any other questions? So, that's it. I mean, it's not even the talk, but that's it for the examples of simplified resolution. So let me just remind you that there's a long list of examples. So, so again, I'll just summarize this example so things to always keep in mind so cotangent bundle of P1 that's like the basic example. And this generalizes to cotangent bundle of flag varieties. It generalizes to C2 mud gammas. So, I need resolution planning. So it generalizes to hypertorics. And it generalizes to. Joel, there's a big problem here. Your screen is completely messed up. So you should just wait a few minutes. Sorry. It just got better. Is it okay now? No, no, it didn't stay better for very long. Wait, what's the writing is messed up? There's a local problem on our side. Just a screen projector is messed up. I turned on the microphone in the room so you can stop. We are very sorry. The story is that our video is messed up so nobody in the room can see what you're writing because you know the mathematical symbols. So this is the right time to ask questions. You know, in order to avoid more awkwardness. The people in Zoom, can they see if everything is fine? Yeah, they can see. Yes. So give us the microphone, it's on the right. No one wants to ask a question also here. Okay, now maybe, no, now it's started. No, but if it moves, I think it's going to mess up. Can you please scroll? No, it's completely frozen. Yeah, you see it's frozen. Oh, it's for the one that's the same. Someone else at the distance, it's the same on your computer? Yeah, but my computer is perfect. Yeah, right here. Oh, so you may see Bonjour, but but there is another question. Let's see. Yeah, no, this was. Can you, yeah, but I can transfer, can you share? Maybe we found a solution. So join me. That's, that's all for that. Can I ask a question? Yes, please go ahead. So what is the relationship between the synthetic reality and maybe it's murals? Are there any relationships between them? Like homology? Sorry, between synthetic reality and what? You know, for example, for the synthetic reality. The relationship between, for example, homology between the space and its mural. Oh, well, that's going to be the subject of like the next few hours. So many, many, the short answer is there's many, many relationships, but we'll see some soon, although I don't think I'll talk about synthetic reality until next time. But yeah, we'll see lots of relationships. So there was a question, what does this tilde mean here? So we're just a shorthand. So there's this client in singularity C2 my gamma.  So there was a question, what is this C2 my gamma tilde. So it just means that there's this client in singularity C2 my gamma. Well, just to find as the affine GAT quotient of C2 my gamma. In other words, C2 my gamma is by definition spec of invariant functions. And then it's a singular variety and it has a kind of unique minimal resolution, which is very well studied. So I just call it C2 my gamma tilde. It can be constructed in other ways. For example, I mean, can be constructed sort of. Yeah, more representation theoretically, let's say. And for example, in C2 my Z money and it's constructed as this hyper torque right here. C2 my Z money until this. There is also another question. And then you can start because now we solve our problem. Right. And then the last question is, you may see the Q and F. Oh yeah, the circles and squares I think exactly come from the physicists. Yes. My last point was going to be there's one more class of examples which I'm not going to talk about just yet, which are called affine gross money and slices. And maybe I should mention any. I didn't emphasize it so much but there's also these cotangent bundles of other flag rights which I'm in general not really going to talk about much in this series of stocks. Okay, so. So we define this general notion of conical synthetic resolutions. I give you lots of examples. By the way, I don't know if it's exactly considered a problem to try classify them but maybe it's not believed that there's very many examples besides the ones I've listed. There's some kind of complete list of examples as a big statement but I don't know of any precise statement like that. One thing you might you might ask what about this way off topic but people have tried to like classify all possible. There's a few specific resolutions which are of this form so CN mud or T star CN or something my gamma gamma is fine it so that that's something. That's something people have studied tried to classify and I think I think the classification of those those ones is complete. Okay, there's a few besides these two markets. So there's a few more things like that which don't fit on this. So definitely does not a complete list but maybe that's close to a complete list. Okay, so these are some examples so what are the general properties why is this interesting things to study these like resolution so. So I'm going to try to explain some general theorems about on a person like the resolutions. And basically these results are due to collated. And then the color from roughly speaking, the early 2000s, 2000 to 2010, maybe some of the results were in a bit early. Okay, so the first result is that X has a partition into finite finite partition. And these. Okay, so over some pieces x alpha right. So this is finite. What it what it what's, what's good. These x alphas are all simplected. So there's a plus on structure on x, and these x alphas are the symphonic leaves of that plus on structure. And they're also smooth, which is that before I said there was somebody. And also this map pie from y to X is. Maybe they're very least. But it's like locally trivial over x alpha. That's exactly true, but they're very least the push forward of the constant shape is constant over each other. Let me not write this let me write something more precise. Okay, so if we can check the push forward of this constant sheet. It will decompose in the following way. Well it's going to be. Let me ignore this. Let me come back to this slowly. Number two. The map from y to X is semi small. So semi small what does it mean. It means that the dimension of the fiber product, why was why over X is equal to the dimension with Y or X. So that means that the fibers are not too big. In particular, the dimension of the fiber over some point x alpha, little x that's supposed to be a little x alpha and big x alpha. And that fiber is equal to one half the co dimension of the stratum. I think in most cases, it's actually. And together what one and two will mean is that if I take it that I can take the push forward of the constant sheet on why. And this is the complex of constructible sheaves on X, which captures the information of the cosmology of the fibers of the map from my next. And this will decompose into a direct sum over the alphas of the IC sheaf of X alpha. The topology of the fiber alpha. Your alpha is fine. And I should say one thing here I'm assuming really I should be right a bit more complicated statement but just to make my notation simpler. And since it's true in the most examples I'm interested in. I'm assuming that actually X alpha is simply connected. And this is, for example, not true for the cotangent bundle of the flag variety outside of typing, but it is true for the potential model of flag variety in type. So we have a decomposition of the push forward of this. And I'm sorry to be a bit more precise expositions for the homological shift. Excuse me. Can you take the closure when you take IC? Well by the IC sheaf of some stratum I mean the intermediate extension of its constant sheet. So yes, you could say it's the same as the closure. It's just, yeah. Yeah, you, you, you asked for I saw for to be smooth. That's why I asked. Yeah, so I really mean the, we could put a bar here. I'm just simplifying the notation of it but yeah I mean the intermediate extension of constant sheet on the X. Okay, so. So we'll come back to this decomposition shortly. But when I'm done, but you should take away from the part that has beautiful properties that's not from what. Okay. Next point is the existence of a deformation. So our original map Y to X. So it's a family. Script the X. How does it work so this script II Y maps to the vector space, which is, which is identified with H two of Y second called module Y with complex coefficients. So script the X maps to H two of Y modular the action of a finite group W which is called the Nami color while group in such a way that the fibers of these maps over zero give you X and Y. This seems a little weird but let me explain an example will become clear. So here we take the cotangent bundle of five variety. Mapping to no bone and cone. And as I mentioned before, these are pairs. Such that a of the eye is contained in the I minus one is no potent. And then I can construct, I can embed this in a bigger space and this will become my scripty Y which is in this case usually called g tilde. And in this case this deformation is called the growth in the simultaneous resolution usually. So here I put pairs a V, where a is not necessarily no potent, and I just have the condition a of vi is contained in the eye. So then I can just remember the matrix a. Sorry, then I can management. Yeah, that's this here. And this no point of course is contained inside the whole the algebra GLM. So all matrices. So this map takes a V to a, and the space of matrices maps to the T my W, which is just taking the characteristic polynomial matrix. And this thing maps to T, which is Cm, which is just recording the eigenvalues of a but we get to actually record them in order, because we can just take the action of a on each portion. So I have a flag, which is invariant under a. So able act by a scalar on each quotient vi over vi minus one. So that's this growth in the simultaneous resolution. And that's what happens in general so my original symplectic resolution is here. And it extends to this family. And if I put, take the fiber, if I take post zero, zero polynomial, of course I get back no potent comb. And that's the general picture. So why, when you see this you might ask where did this come from seems a little surprising. But he here's an explanation. So if we pick. If we take theta in each to why. And we have a good name, but we just temporarily I'll call it C or something. And then we take C inverses. Why theta so the fiber over this data. So essentially why theta is isomorphic to why, well, not as algebraic variety, but as a, as a smooth manifold, not as an algebraic variety. In fact, in fact, for most, for most values of theta why theta is actually affine is an algebraic right. But in any case, it is a smart because a smooth manifold. And we can use that to identify the second homology of why theta with the second homology of why. And inside the second homology of why theta, we have we can consider the symplectic form of why theta, and thereby, we can map it to a class in each to a why. The, like, compatibility of this diagram is that this class of the second homology of this, the class of this effective form is actually there. So for example, if we took theta to be zero, the class of the symplectic form on why is zero, which is not surprising because I didn't say it's above but this this why only its homology is only in that it only has KK homology only down the center of the high diamonds. So this symplectic form automatically would be in the two zero part of the homology. So that's somehow this that's somehow the reason for this appearance of this H2 of y. So for this reason, this map is sort of a period map, maybe precisely a period. I don't know much about the period maps that is mentioned. So this is another beautiful feature of symplectic resolutions they always come with this deformation of the big varieties. And the another feature that they come with is that they always come with. How much. I guess there was a couple of interruptions so maybe I go another five minutes or something is that is that good Francesco. Maybe also 10 minutes. Yeah, you can do it even more. Yeah, I mean we interrupt you so many times. I guess 10 minutes is a side to know. Yeah, 10 minutes. Okay, I think. Great. So the next feature is the existence of the universal quantization. So I think this will be the last thing I'll talk about, but it will probably take attendance. Okay, so what does it mean quantization. So I mentioned before that this, let's start just algebra purely algebraically. So this coordinate ring of X, I mentioned before this is a question algebra. So a quantization of X is over a polynomial ring and some variable usually called each bar quantization parameter. And sometimes this would be the power series in each bar, but one slight advantage of this adding this axiom of it being a conical symplectic resolution is that we can, it's quantization will actually live over polynomials in CH, but it's not a very big deal. So quantization of X is a CH bar algebra a such that if I take the quotient of I specialize each bar to zero to aim on each bar a. This will be isomorphic to see a X as a person algebra. To make this precise, I need to tell you why the left hand side is a person algebra. So it's an algebra just from this algebra structure. Now this a is going to be a non-community of algebra, and this the plus instruction left side is going to represent the first order non-community of algebra. So the plus and bracket of a bar B bar. So here in the elements in a bar and B bar elements in a mod H a. This is by definition, we form the commutator of a and B in a, and then because divide by each bar. Okay. Another way of saying this is like, sorry, this thing is this this commutator is necessarily divisible by H bar, because AB minus BA are equal. So, so this in C since CX is commutative, and the products are equal in CX. So the first order of non-community activity is divisible by H bar. And then, then we take the class of that and we get this plus on bracket. So that's the definition of the plus on bracket. And I would like that this, and that this plus on bracket agrees with my original plus on back and CX. Okay, so that's the notion of quantization guy. And then we could, this could be a quantization of why we would define a similar way but just in the sheath of algebras. Why. In this sense that this is is more of a structure. So then, so then I would like to say that there exists a unique universal quantization, just like our universal deformation. So this again will be parameterized by the again, parameterized by this H2. Or if we work, maybe I'll just write the statement for X is slightly simpler. So it's used for quantization of X parameterized by the same age to Y mod this W. So this is it. So this can be an algebra a and not too many different kinds of script. Okay, this will be another script. It will contain the coordinate ring of this H2 of Y mod W. So as a center is the center they and for any respect of the center which is the same as H2 of Y mod W. I can take the reduction by this ideal journey by this data. And this is a quantization of X. And more over every quantization of X horizons way. So I guess to be a little bit more precise. I should say every quantization of X that extends to a sheet of quantizations on Y horizons. So that's like an example again. And we'll take again this potential bundle the five varieties are our example. So, so X is this no quote and cone. Why is the potential bundle of this library. So then let's say G is the algebra GLN or SLN. SLN for simplicity. Then this universal quantization a will be the H bar version or the resalgebra of the universal envelope the algebra SLN. This is like the resalgebra of the usual universal envelope the algebra SLN, or if you like, it's the resalgebra generated by X by elements of SLN and then relations X, Y, Y, X is equal to H bar. So if we in this thing contains the center of the universal envelope in the SLN, which can be identified with the team with the carton model. So, so in particular, if we specialize to the Anyway, you can see if you set H bar to zero, then, then a will become this universal commutative deformation. The coordinate ring will become this same aspect of the symmetric algebra SLN, which is just this universal coordinate, which is just SLN itself, which is the universal commutative deformation SLN. Okay, so this I could have said that here as well that for this universal quantization a, if we take the any fiber of it, if we specialize data, we get a quantization of X and if we specialize if we don't specialize data and just take amod HA for the whole a, then it's the coordinate ring of this X tilde that I wrote about. Now, the last point I just want to make before we stop is that so there's like two kind of notions of quantization this thing here which called a formal quantization. So this CH bar version. But that's called usually a formal quantization. And then there's also a filtered quantization. So the first thing we specialize H bar to be one, so we take a what H bar minus one, then we get the filtered quantization. So we get instead of filtered algebra. It was associated graded is our original personal. So for example. In the example, we could take this you G and you H bar G and then we take this one.  So oftentimes we'll study these filter quantizations instead of these formal quantizations but usually you can pass back and forth between the two things. Yeah, I'll stop there. Any questions from the audience or from the people over zoom. Yes, I have a question. When you define Nakajima with a varieties, you took some kind, which was a product of determinants. So if you choose another guy, another character for the group. Yeah. So, it's a good question. It's actually sort of a good general question. Okay, so let me let me actually answer the question sort of more generally and then come to this because I think so. So I started with X. Why is my like starting data. What's the solution. One interesting thing one can do is to start with just X. And then, and then try to find all possible wise. Maybe multiple different symbolic resolutions of X. One reason why you might want to do this is because we'll see soon that this data of these different symbolic resolutions has a sort of meaning on the symbolic dual side. For that reason, it's kind of interesting. And so in the case of an X expected as a Nakajima quiver variety. Or more generally as any kind of Hamiltonian reduction. So I'll write, I didn't actually introduce this location, but let me write it here for the first time. All right, three lines that I mean that this symplectic reduction. So what I mean by that is I take the in the mode map image and then take the, the genetic portion. That means and actually this zero in fact. When I write this notation, it's maybe helpful to write two pieces of notation here maybe. Hi, which could be well which would be this zero. It's just zero zeros. Don't need to invent some new letter. So I just take this. And then as you, as you said, we could take and change the, the this guy so this would be take the zero level the moment still, but then take the different character guy so so as I mentioned before usually this would be the product of determinants, but you could do something and yeah, if you do that in the case of Nakajima for writers are more generally for these symbiotic reductions like this. Yes, you could obtain other synthetic resolutions. And certainly there's some examples where you get interesting spaces. This way I'm not I mean, I know the people in the audience much more expert than me. But for example, in the case where you are considering Hilbert schemes, maybe Hilbert schemes of points on on on C2 my gammas, you can get these different versions of the Hilbert scheme this way is by varying this, this guy. And this brings up a different point which maybe I should have mentioned earlier, you can also vary that this parameter, the level of the movement, so which I'm writing here, here, here, you can vary that thing. So this is going to be responsible for this deformation that I explained earlier. So this deformation of the cover variety this universal deformation from the theorem of Kaleida and Amakawa. That's going to come from very bad that that that zero to other to other. So thanks for the question, but yes this study of different possible synthetic resolutions of a given synthetic singularity. This exit called a synthetic singularity. We have also a question and a window. So if you can check it or I can read it for you. Yeah, does the deformation in part three is a theorem carry a personal structure with the leaves given by the various white seated. Yeah, I think so yes. These are global plus on structure on the whole thing. Because I was, but yeah, I think so, yes. Any other question or comment. And no one is also. Okay, so maybe we can thank. You can join again.