 I'm excited to tell you about the work that we've been doing, which is really what I'm going to show you is kind of our latest milestone in trying to understand how synapses work. And I'm very, very happy with where we're at at the moment with this and the promise that the future holds for where we're going to go. So our motivation behind our work is, ever since I was a little boy, I wanted to know how the brain works, and especially how synapses work in the brain, since I think that's where the rubber meets the road in understanding how the brain computes. And in order to understand how synaptic structure and function are related, we need to know the topology of synaptic structure and the perisynaptic space around synapses. Because they're not bottled up little compartments, they're actually open through the extracellular space to the other neurons in the brain. That means we need to understand neuropill. And I put three excumulation points after neuropill, you'll see why in a minute. I'm sure a lot of you already have a fear of neuropill, as I do. We need to know the organization of the pre- and post-synaptic cytoplasmic organelles and the distributions of receptors, ion channels, enzymes, and transporters, et cetera, throughout these structures, because the biochemical reaction networks and their dynamics are occurring in space that is not well mixed. And the numbers of molecules can be very small. In synapses, as Avrama told you earlier, the number of molecules in a spine head can be very, very small. And so the reactions occur stochastically. And so we have to understand how they interact with each other stochastically. And so the simulators that we use to simulate these things have to be able to not shy away from these things, but embrace these things and tackle them head-on. So I have a little cartoon here that shows how influx of pre-synaptic calcium causes release of neurotransmitter into the synaptic space, activating receptors, and then all the post-synaptic downstream biochemical cascades that Kim told you about occur. And also there's spillover of neurotransmitter into the auxiliary space to possibly activate synapses on adjacent dendrites, or synapses of the same dendrite, and reuptake of neurotransmitter by astrocyte possible activation of other biochemical processes in the astrocyte itself, and of course in the target dendrites. And this little cartoon gives you an idea of the spatial arrangement and numbers of different types of molecules that we'll be talking about in the simulations that I'm going to show you. I'm going to show you the construction of a realistic model of synapses in hippocampal neuro pill. The simulation is going to include all of these different molecules, their locations in space and their correct densities and biochemical reaction interaction networks. And I'm going to walk you through one by one each of these as we put the model together. To construct a model like this we need constraints. You'll hear tomorrow in one of the workshops the topic model what you can measure. So that's precisely what we're attempting to do here, but at the molecular and reaction pathway level at tiny structures. So we were able to obtain through our collaboration with Kristen Harris a 3D reconstruction of a 6x6x5 micron chunk of hippocampal CA1 neuro pill from an adult rat in stratum radiotum. This little chunk here was chosen by Kristen to be centered on a part of a primary apical dendrite. There were 100 slices, 50 nanometers thick in the reconstruction to give us the five microns in total in Z and we have 6x6 microns in X and Y. And here's the entire structure reconstructed, viewed from the outside in. The yellow represent dendrites, the green represent axons and the blue is an astrocytic glial process. It's all a big tangled mess. I have an animation that I won't have time to show you, but it's available on YouTube. If you go on YouTube and type in waltz and hippocampus, it should be the top hit and you can watch a movie that our postdoc student Justin Kinney put together as part of his thesis project to study spillover of glutamate, and he has a paper that recently came out in Journal of Comparative Neurology on this topic. But I do have a shorter movie showing the dynamics in that structure coming up in a moment that will give you some appreciation for the internal structure of that. But part of the challenge that Justin faced in putting this together was the fact that it's well known that there are shrinkage artifacts that occur during tissue fixation in preparation of samples for TEM. And also there are numerous sampling aliasing artifacts that occur during the reconstruction process itself of trying to go from slices where a human being or a machine learning algorithm draws a contour. Human learning algorithms aren't nearly up to the task of fully automating this, so a human being needs to assist and the machine assists and the human finishes the job of tracing all the structures. But because of the limited Z resolution, when you reconstruct, if we take this and cut it in the XZ plane, so now the Z axis is going downward through, and if we look at this little box here and magnify it on the screen, this is the raw reconstruction that results. You'll see places where the extracellular space is very narrow or even occluded, places where structures actually touch and overlap with each other. This is not a problem with the traces that were drawn. This is a problem that occurred because of aliasing of sampling in the Z direction, sampling at a limited step-wise resolution results, inevitably, unavoidably results in these artifacts. So Justin was able to write an algorithm that corrected these errors and got back to an extracellular space volume fraction that is thought to be the same as what occurs in vivo of about 22% ECS fluid. Here in the raw reconstruction, not counting the overlaps which obviously are completely wrong, the extracellular space volume fraction here was only 8%. Having made those corrections, we now have a proper geometry for performing our simulations in. We then need the constraints of all the reaction pathways and chemical kinetics for all the different molecules that I showed you on previous slides. We have gluR1 type amper receptors, N2RA and B type NDA receptors, LRPQ type voltage dependent calcium channels, GLT1 and GLAST glutamate transporters, PMCA, NCX and circo pumps, endogenous calcium binding proteins of some unknown generic type, and specific calcium binding proteins such as Kalbinden D28K. We also have a chemical kinetics scheme and kinetic rate constants for the calcium sensor in this near complex that results in release of neurotransmitter. This diagram has 36 different states in it, a release enabled state and a release disabled state for the entire active zone and each dock vesicle in the active zone, which on average is maybe seven dock vesicles at a hippocampal presynaptic terminal. Each dock vesicle has a molecule that behaves like this in it, but they're coupled together through an interesting mechanism. The release disabled states of all the dock vesicles in a single active zone are coupled together through this state so that the state of the entire active zone behaves like one macromolecular complex. Each individual dock vesicle is in one of 36 different states and if there's seven dock vesicles then we have 36 to the seventh power different states that the entire active zone can be in at any one time. This is one example of combinatorial explosion of which ChemKinase 2 is an even more extreme example. The other molecule, important molecule that I'm going to show you in this simulation is molecules are Calmodulin and ChemKinase 2 which Calmodulin binds calcium and when it does it can bind to ChemKinase 2. Calcium binding to the ChemKinase 2 undergoes these state changes to be in any one of these nine different states and when the ChemKinase 2 is bound calcium it can bind kinase K represented as K here to form a complex with ChemKinase 2 monomer is shown here. Of course the holoenzyme consists of 12 subunits in a complex and so now take this to the 12th power and then not counting the phosphorylation states that it can be and if we count all those the ChemKinase 2 holoenzyme can be in any one of say 10 to the 16th different possible states possibly more. And so traditional modeling methods using differential equations and even the Gillespie algorithm where it's required that you calculate a propensity function require that you map out a matrix say in an ODE or PDE method you have to map out a matrix that represents your your system of simultaneous differential equations and then diagonalize that to find the eigenvalues in order and you have to do that on every time step to move forward in time in order to get the how the concentrations or numbers of particles update on each time. Simulating a molecule like ChemKinase 2 or the active zone is prohibitive prohibitively expensive and even intractable. Fortunately we use MCEL which is a particle-based method that tracks individual molecules through space and time and each molecule is in only is only in one state at any one moment in time. And it models 3D reaction diffusion systems. It uses rigorously validated and highly optimized stochastic Monte Carlo methods to track the Brownian dynamics of individual particles in 3D volumes and 2D surfaces embedded in 3D. We as you have seen of the 3D reconstruction that we've made we can handle arbitrarily complex 3D geometry. We don't create volumetric meshes we make triangulated surface meshes because we track the particles where in in 3D space each particle knows where it is in 3D space. We don't need to voxelize space which is a can have a large advantage in simulating complex geometries and as I've alluded to we can handle arbitrarily complex reaction networks. We do this by using either a Markov or a rule-based specification method. A Markov method would require you to write down all the all the states and all the all the pathways that would be prohibitively expensive with a something like the active zone or ChemKarnes 2 but with a rule-based specification method you just write down the rules that govern how the state transitions occur and those rules are evaluated on the fly as the simulation runs particle by particle so each particle only needs to know what state it's in and what rule applies for its transitions to its adjacent states and you only evaluate those rules on a particle by particle basis which is very efficient and this is all possible with a highly flexible model description language at MSOL employees and we have a new model building and visualization and analysis analysis environment that allows the user to create all these things visually in a 3D modeling environment based on blender and it's a Python plug-in for blender called cell blender and now I'm going to show you an animation that represents many many many years of effort of many many many people working together and I'm very proud of when I'm of this I think you'll enjoy it too so what you're looking at is a that large apical dendrite a single axon making contact a snap to contact here and there with this dendrite the blue represents the astrocytic glial process of a single astrocyte embedded in this volume the axon has been made transparent so that you can see inside of it you can see it has an applied reticulum going through here's a here's a mitochondrion in one of that bercocities we're going to zoom in on this particular one the red patch is on the dendrite represent synaptic contact areas all the other dendrites and axons that you saw earlier are made invisible here so that we can see what's going on the little yellow particles moving around our calcium this is what hundred nanomolar calcium looks like at rest these are synaptic vesicles we have ample and NMDA receptors on the post-synaptic side this is a small patch of voltage gated calcium channels on the pre-synaptic side the little gray particles on the surface of the membrane here are PMCA pumps the little green particles on the endoplasmic reticulum are circo pumps we're now stimulating the axon with an actual potential it turns a brighter shade of green as we do and the voltage gated calcium channels open and allow calcium to flow in when the calcium flows in it starts to build up I want you to notice how how tightly contained and how focused the calcium micro domain is nano domain is these little red objects here represent this the snare complex release mechanism that in a moment is going to find enough calcium to cause release of neurotransmitter and right about now right there we released about 2,000 molecules of glutamate that diffuses through the extracellular space and when it does it spreads out very quickly but also activates ample and NMDA receptors within the post-synaptic patch on the spine head but the glutamate also diffuses outward and binds to glutamate transporters on the astro site which are invisible until in this visualization until they bind glutamate and which time they turn red and the glutamate gets quite far and persists for quite a quite a large amount of time oh this is the wrong this is the wrong animation this is the wrong animation I'm going to no it's not it's not good no oh how did that happen anyway it didn't show it didn't it was the wrong one I apologize and in closing the one I wanted to show you then also shows activation of the NMDA receptors and then flux of calcium into the post-synaptic spine head and activation of Chem Kines II and Cal Modulin going out to 100 milliseconds of time and somehow I put the wrong one in there but I want to thank all our collaborators who have worked with us over the years on putting this together especially friends no longer with us thank you