Okay, so I want to remind you again, that not only we have an anatomy here, of many cell types and of many layers and of many synapses connections, but eventually each cell has its own characteristics electrical property. So for example, this cell may fire spikes regularly, very regular. [SOUND], it's a non in, non accommodating cell, it fires regularly. Another cell, let's say from lay four, may be a burster. It fires [SOUND], stop. [SOUND], stop. So, this is another cell type, electrical cell type. And we discussed the different cell types. Of course, I have to take into account not only the anatomy of the network, the connectivity within the network, but also the electrical characters within the network. So what I need to do when I'm modeling a system like this, is to get a particular cell type anatomically, reconstruct it anatomically. This cell is also reconstructed anatomically. This cell is also reconstructed anatomically, but at the same time ,this cell is firing this way, and this other cell fires like this. You can see it is accommodating and this cell is burster. So, I need to find mathematical rules, mathematical ways to write the equations, to replicate the firing properties, not only the individual spike, but the firing properties of, of different cell types. And again, we use the classical equations of Hodgkin Huxley, but now refining these equations, making it more sophisticated, the equations, because these equations do not capture firing properties, they just capture the single spike but not the firing properties, the whole firing repair to, [COUGH] of cells. So we need to use the Hodgkin, Huxley, extended Hodgkin Huxley equation to capture the spike and the repetitiveness, the different types of spike in properties, the repertoire of firing. We also should use another mathematics that we just went through in the last eh, lecture, The Passive Cable equation, and now the active cable equations that we did not discuss to characterize what happens between the synaptic input to the sum of this particular cell, so we need both. And eventually, we can today, without going into details, there are methods, some of them developed by myself, there are methods, to find ways, to extend Hodgkin-Huxley, almost automatically to model a particular firing part, type. So, look at this, this is an experimental, recorded spikes, the brown spikes here, one, two, three. And the model, extended Hodgkin-Huxley model, which we wrote here with students, capture the green spikes that are the mathematical solution of the equations. And you can see the great similarity between the actual firing, [SOUND], the brown spikes to the green spikes in the model. So this is what we mean by saying that I'm modeling the spiking repertoire of many neuron types. We also need to model the synaptic interaction. And not only the transmission between a spike in the axon and the EPSP or IPSP, the synaptic response in the, in the dendrite, the post synaptic dendrite. This we know to do, we also need to mathematically write down the plasticity rules because eventually, we want to teach this generic column to perform something. So, we need to write equations like this that we already wrote before. This is equation describing spike timing dependent plasticity. So, when the network will work, will be active, the simulated network and you implement this rule of plasticity, the network will change automatically due to the implementation of this Plasticity rule. So, one of the challenge is to model mathematically the connection between neurons, this we know to do and it actually done. We model several types of synapses, inhibitory, excitatory, with different dynamics, some of synapses depresses fast, some of them facilitate, and so we know through modern synapses and connect neurons. Now plasticity is more difficult because there are many plastic rules, not easy to implement in a network like this, but we are now ongoing, trying to embed the plasticity into the cortical network. And also, of course, eventually we want to connect the network correctly and we don't fully have all the anatomy as yet, but we have a lot of the anatomy and we may now predict what would be the connection between pairs of cells that we did not record from. We take all this information and we put it into this huge, big, supercomputer. We have now a bigger one than before, we can simulate now 100,000 to real detailed neurons and look at the activity of the network. So this is the Blue Brain Project in the blue brain machine. So here we take one cell, schematically after another cell, each one represented by a processor, and this processor solves the mathematical equations, associated with this neuron, and with the connection between them, and eventually we get a simulated network that is supposed to replicate closely, what we know about the cortical column. We can simulate a single cell, with the ion channels in the, in the membrane and the axon with the synaptic inputs, excitatory, inhibitory. We can simulate a single cell in details using this, simulator, the Blue Brain simulator. We can also simulate a whole network, both anatomically, just to check whether this cell is connected, correctly statistically to this other cell. You can see the jungle of axons. So you see the axons, the thin wire, you can see the dendrites, the thicker wires. You can see the jungle, within this, cortical column, about 10,000 cells connected in a particular way, and you can also see, the synapses. So you see, the red synapses are the excitatory synapses, you can see the blue synapses are the inhibitory synapses. You can see all the synapses within this column. Each one simulated mathematically, using what we know about how to simulate synapses. So, you can see the activity now of all these hundred million of synapses in a column, active in a particular, for a particular input. And you can look now at the activities. So, red means spike, blue means no spike. And you can see this electrical activity now within a piece of simulated cortical network. Simulated, now coded in color. So you don't see the spikes, but I can tell you this fire, this fire, this now fire, now the network tend not to fire. So there is some waves of activity following a particular input, you can also look at the active column, receiving an input, let's say from that thalamus, and then this column, the simulated column, is active. It's active here, this now fires, there is a wave of activity, and so on. So, you can really get a very, very beautiful, simulated activity and of course the question is, and that's the big question, now how do you relate this particular activity to a particular behavior? Whether seeing angles, visual angles, whether being sick with Parkinson or some other autistic disease or something of this being autistic. What in the network goes wrong when suddenly a road activity emerges from this building block? This is exactly where we are, we are trying to simulate diseases based on the generic general kind, of a column. So this is the mission, and of course this column, is a column, composed, from many, many neurons, coming from different, in this case, rats. So this neuron comes from one road, rat and this another, and we model each neuron separately, we glue them together, put them integrate them together into a simulation, that hopefully will lead us to an understanding of a normal or diseased behavior. This is of a rat. Can we do it also to human?