 In Genova, v Pizdiči, u kvaliti, u Vrlča na taj vzivosti. I del neko vse v Vrlči, v Kultu, v Kultu, in v Kultu v Vrlči, z kvaliti, kaj mislilaš v sebeku. Vziv nama, da se začeli, kako, tako, z jaz naprej tento vso vzivosti, kaj se sebev začeli. z vsem progrom, da je tukaj izgleda. Zato sem pačila tukaj tukaj. Tukaj sem tukaj vse. Zato sem pačila tukaj vse, kaj je tukaj z Dr. Eleni Vazilaki, Sr. lektur na Universtju Sheffield, kaj je tukaj tukaj izgleda. Tukaj je tukaj vse, rojvsovsocija in vsev, kaj je tukaj tukaj izgleda. Tukaj sem tukaj vse, kaj je tukaj vse, kaj je tukaj vse, poš Dakle, jo je občasitva na uponodnih tretljih, več in uponodnih tretljih, vi prezentacijenja. Prosti taj upodnih tretljih je so zaznačiti zapravo za tretljih, zanim sem vso vodvalo, ta začala vlastnje konek Tomix. Ne bo na putri da majli tudi poprošanj domovina biological attempts at the brute force reconstruction of the wiring diagram of the brain. How will focus, however, on a different, on a slightly different approach stemming from technological opportunities and also coming from the fact that at the microcircuit level there might be individual differences and these wiring diagram is likely to change over time. So, something that was proposed and made and shown to be accessible technologically in the recent literature is the so-called few nodes wiring diagram dissections or the dissection of the connectivity motif at the level of small microcircuit. So, not thousands of neurons, not definitely billions, but few, two, three, four. And I will, I hope to convince you that this is enough and it gives some initial interesting feature among them that several non-trivial random, non-random features have been revealed. So, particularly connectivity is non-random. And therefore, this technology is related to establishing conventional slice work. I'm sorry, this is not good. So, is coming from an addition to neuronatomical methods to conventional patch clamp recording in acute cortical slices, for instance, in which people by multi electrode, by multi patch recording set up, pioneered among the others by Henry Markram and by Jesper Schostrom, from which this work is taken, could detect connections in a functional way. They could elicit action potential firing in a pre-synaptic neuron and they could look for the echo, the excitatory post-synaptic potential, in this case, in the post-synaptic cells. And whenever they observe a connection, they could actually draw the connectivity diagram. There is also another information about the weight of this connection, but I will not talk about that now. So, the non-random feature that's where shown and that are quite interesting is the over expression of some connectivity motif, particularly the over expression of B directional connection, so neuron A is projecting to neuron B, and higher than the chance than what you would expect by random connectivity, neuron B is also projecting back to neuron A. And there is also evidence, although the numbers are very low, so the statistics is very poor in a way, despite attempts to compensate at the level of triplets. And as you can see also, there is an over expression of motif in which there is this B directional reciprocal connectivity. So, the question came in the literature recently also in the community of computational neuroscientists, where is this asymmetry coming from? And maybe this comes from conventional long-term plasticity and the fact that in some forms of this long-term potential and long-term depression, there is an asymmetry that is asymmetry is in time, particularly in the time difference between the pre-synaptic and the post-synaptic action potential firing, this could maybe explain why you observe sometimes an over expression in some area of the cortex. So, here I'm referring to the glutamatergic system, particularly pyramidal to pyramidal cell synapses. So, modeling allows to explore specific hypothesis and one hypothesis that was considered, particularly by the group of Wolfgang Gersner and by Michael Leake, Eleni Vasilaki, was whether this non-random connectivity could indeed emerge from this spike timing and frequency and firing rate dependent plasticity. And what they did in a natural neuroscience paper, they consider a toy network model where individual neurons were extremely simple, no bifysical details other than in their excitability modeled by an integrated fire model, and also featuring a specific type of spike timing dependent plasticity, they tried to relate and they convincingly show that this could be related to the emergence of connectivity motifs, external activity and the external activity could have reflected the way inputs are represented, how information is represented, whether or not this is represented in a rate code by elevation of the number of spikes per second in one neuron instead of a neighboring neuron or whether it's the precise order, the sequence of activation, whether this is leading to the connectivity motifs. And indeed they show that external activity could explain the emergence of those over expression of connectivity motifs, particularly they related to the possible information coding. Very briefly what they did, they assumed in a very simple model that the information could be encoded in the rate levels or in the sequence of activation as I said, and because of the spike timing dependent plasticity and its asymmetries and another ingredient which is the firing rate dependence they could show that in one case the reciprocal motifs were overexpress and in the other case it was instead the temporal causality of the action potentials and the sequence of activation of the neurons that were indeed instead generating or potentiating synapses and leading to instead unidirectional. And this feature that I mentioned already in addition to the spike timing dependency is the fact that in precise models of STDP as you increase the firing, the frequency of the pairing between the pre and the post-anaptic neuron, LTD, regardless of this causality pre before post before pre, is reversing into an LTP like in the Hebbian conventional plasticity. However synapses are more than plugs and here is where I'm grateful to the previous speaker to show that these are physical systems and as all physical systems they undergo transient fatigue for instance synaptic vesicles are going to be exhausted or because of accumulation of calcium in the pre synaptic buton, there can be a facilitation and this has been already described and mentioned and reported for the first time in the neuromuscular junction and then later kind of rediscovered in the cortical, the central nervous system in the cortical synapses for instance among pyramidal cells and here are examples of this progressive non-stationary activity dependent transmission of individual pre synaptic action potentials in a depressing fashion or in a facilitation, facilitating fashion. How is synaptic dynamics related to connectivity motifs? This has been reported in the literature recently and perhaps not considered particularly interesting but it struck our attention, our interest because at the glutomatergic system synapses of the prefrontal cortex of the ferret, the visual cortex of the ferret as well as in another glutomatergic system in the mitral cell to mitral cell connection in de facto rebalt, what has been reported is an overexpression of facilitating synapses in reciprocal motif and an overexpression of depressing synapses when the connectivity motif is only unidirectional. This is by no means exclude the other case but this is more often associated facilitation with reciprocal and depressing with non-reciprocal and this is the quantification obtained by friends and colleague Michele Pignatelli in his PhD thesis in the olfactory bulb in which you actually see that, indeed once more reds is facilitating associated to bidirectional and blue depressing associated to unidirectional motifs. So the question is natural, how is this emerging? And once more modeling could allow us to explore specific hypotheses and the hypothesis that we formulated is that maybe synaptic, short-term dynamics and long-term plasticities, the two components that I introduced in a moment ago are determining or contributing to the emergence of these motifs and because the model allows ones to perform experiments that would not be possible in vitro or in vivo, one could also ask how, which are the ingredients, the essential ingredients for this. So we build a similar, philosophy of the previous paper by the group of Wolfgang Gersner, a toy model, rather toy model, we don't explain the connectivity of the entire cortex, of course, and we added the fact that synapses were also showing and displaying synaptic dynamics by means of the very well-known sodic marker model. And what we focus instead of the externally imposed activity, we focus on the endogenously, so the internally generated activity, we consider neurons connected only by facilitating synapses or by depressing synapses and I will relax this hypothesis in a moment. And what we found if you want to shut down your brain because of the lack of glucose is that indeed this co-occurence of facilitation on bidirectional motif, depression on unidirectional motif, could be explained by the interaction between short-term dynamics and long-term plasticities. The interesting thing is that this is reflecting not the external, or in addition, complementing the previous case, is not reflecting the external activity, but instead the recurrent, internally generated activity and I will show you in a moment how. This is just to show that we consider conventional, exponential, integrated and flyer units with adaptation and the marker and sodics model for facilitating as well as for depressing synapses, these are clearly simulated traces and on the top of this, we actually consider post-synaptic long-term potentiation in the form of spike-time-independent as well as firing rate dependent. And for those of you who are familiar with this, we, in other words, accounted for the so-called triplet effect in which at high pairing frequency LTD is switching to LTP regardless of the causality of the pre- and post-synaptic firing. So we consider a very simple model for this slide made of 10 neurons and at the beginning the connectivity was random and it was exposed to the same background activity, it was a noisy background activity mimicking what cortical neurons could experience in vivo during nonselective activity and we had, in addition, and it would become clear why we did that, also a kind of cycling, repeating deterministic component. This doesn't really need to be cycling but it needs to be deterministic component that we had, we added as a background activity. So what we observe is that when you have neurons connected by depressing synapses, you have that all the connections that are formed after a while, that letting the network to evolve its weight, and this is by the way, it's a double dynamics, we don't freeze synaptic weight, it's neuronal dynamics influence synaptic dynamics and synaptic dynamics is also influencing the neuronal dynamics so the system is stable in a way and here I'm using the convention that whenever the connection is dashed it means it's unidirectional. Vice versa, when the connection is indicated by a continuous line, it means that it's bidirectional. Depression led to mostly or in all unidirectional connections and facilitation led to most bidirectional connections so here you see more continuous lines. And because it's a model, we could plug basically all the electrodes where we wanted and you notice that here the number of action potentials are less, they are more sparse than in this case. Facilitating networks as intuitively you would expect contain more action potentials and I will get back to this to give you an intuitive flavor of an explanation that we observed this. So this was one simulation we wanted to get the statistics so we repeated this 2,000 times generating a measure, a very simple measure just one number between zero and one zero unidirectional connections prevail one, all the connections in the network are instead bidirectional and we repeated this over and over and we could initialize the network randomly in terms of connectivity, in terms of topology and as the time in arbitrary unit is passing you actually see that with depression most of the network will all converge to low values of this synaptic symmetry matrix index as I said I will not enter into the details but zero means all unidirectional and one means all bidirectional. Vice versa, with facilitating synapses there was a convergence towards higher values of this symmetry index and what is interesting is that not all the simulations converge to a network with a larger number of bidirectional synapses so here you actually see a small fraction of the simulations that led to networks that were not with more bidirectional motifs possibly suggesting a role for heterogeneity in the experiment or an explanation for heterogeneity in the experimental data. So because it's a model we could open the black box and we could see and we could identify the minimal, the essential feature the first is heterogeneity in the firing rate distributions and I tried to give you an intuition I will give you another one and then I will show you a more quantitative analysis based on mean field analysis and again I'm in depth with the previous speaker for mentioning it so if you have neurons connected by depressing synapses after a while in case of recurrent activity or externally generated activity doesn't matter the synapses are going to get fatigued and effectively neurons are going to decoupled vice versa, if neurons are connected by facilitating synapses the more activity there is the more the synapses are getting stronger and so the more activity will be produced internally because connections are in general recurrent so it's a kind of positive feedback and you can analyze this quantitatively by mean field analysis so you can resort to numerical simulation of integrated and firing models as well as equivalent mean field extended mean field analysis for homogeneous network of facilitating synapses of neurons connected by facilitating synapses or depressing synapses in this particular case with only feed forward inhibition but also with feedback inhibition the result don't change you can prove that in the analysis of the attractor states in this case both in the case of unbalance or balance external inputs the facilitating network is always going to fire at higher firing rates than the depressing network it seems trivial it can be also appreciated analytically because of the simplicity of the mean field version of the Markram-Sodix model and this is also the case for balance external inputs in which you might have multiple equilibrium points should be the intersection of this gray and black curves with the unitary slope line and the intersection of the facilitating network are always higher so you always have higher frequencies and you remember that I mentioned in the beginning that this is the second ingredient that the spike time independent plasticity is going to switch and to become an associative plasticity rule as soon as the firing rate is higher than some kind of frequency some pairing frequency which I will call a critical frequency which is not that high it's of the order of 30, 40 spikes per second with the numbers with the parameters identified for cortical synapses so this is the second ingredient and in order to show that this inversion and the temporal and the temporal sample feature of the plasticity are the key ingredient we could alter the plasticity rule we could use in this case is the pair based STDP rule the first that was proposed in the literature it will not change if you increase well it will but it will not reverse LTP into LTP in the way the triplet rule is performing and when you do so regardless whether the network is made of synapses that are short term depressing this networks are going to evolve to always a relatively low synaptic matrix symmetry index so the main ingredient is not the temporal window but it's the frequency dependence here it's broken and the physiological connectivity motifs are not emerging anymore you can change and alter the temporal window for instance proposing a kind of potential anti STDP that is by the way reported in the literature but retaining the frequency dependency and you recover the same phenomenon so facilitating leads to higher value of symmetry that means bidirectional motifs are overexpressed and depression leads to low values unidirections are overexpressed concluding I would like to relax the hypothesis that I made at the beginning about the homogeneous character of this population what happens if you consider heterogeneous population composed of both facilitating and depressing synapses here are once more indicated in the framework by the notation of the mean field approach and I will get very fast here it turns out that as a consequence of the Hebbian character the associative Hebbian character of this STDP triplet based rule the configuration that is depicted here by synaptic lines between the two population is stable and to show microscopic simulations that this is indeed the case I show here the firing rate distribution and here the fraction I will count the number of synapse of synaptic motif for a network of only depressing synapses and here you see that all the neurons all the integrated and firing neurons are firing this is a much larger network of 1,000 neurons and they all largely fire at relatively low firing rates and unidirectional depressing motifs are over expressed if the network is composed by facilitating synapses neurons are firing at higher firing rate indeed matching what the intuition and the mean field analysis and reciprocal motifs are over expressed and when you consider the heterogeneous population so everything in the same network you actually have that you have a split between a group of neurons that are connected by depressing synapses that will fire less although some of them will fire more and the neurons connected by facilitating synapses will fire at higher frequency higher than this critical value and once more you will have reciprocal facilitating more expressed than unidirectional facilitating and unidirectional depressing more than reciprocal depressing concluding there is evidence for non-random feature and I welcome and I am extremely interested in these new recent data where connectivity is also contained by synaptic physiology in terms of synaptic dynamics and the co-currents of connectivity motifs and specific properties have been found in distinct area I believe it might be a property of a large variety of glutamatergic synapses and existing biological mechanism here combine as a kind of elementary system approach STDP and the zodix marker model are sufficient to explain the observation of the experiments and the interplay between synaptic dynamics and neuronal dynamics leads in this specific example so in silico in this very simple model to a stable configuration and it might lead might propose specific experiments to test this hypothesis and I conclude thanking you for your attention Thanks again for this very interesting talk Are there questions? Does your model include homeocytic resistivity mechanisms or a weight scale? No, it doesn't so the way this is implicitly accounted for in the model is by these hard boundaries of the synaptic weight so the synaptic weights are going to hit these boundaries The next step is indeed including homeostatic plasticity mechanism or perhaps more interesting a recent proposal by the group of Larry Abbott for the so-called time-shifted STDP that apparently is intrinsically stable without boundaries and without the need of homeostatic plasticity mechanism Thank you Are there questions? I would like to thank all the speakers for coming.