"Ephaptic-axonal interference and neuronal development" by Daniel Rebbin

[00:00:00]Yeah, let's get started. Um, so ific interference and neuronal development, that's the title of my talk today and a flashy trippy gift to start with, but I just wanted to ask the question, who am I actually for those that haven't seen me? I finished my masters in Amsterdam, University of Amsterdam recently, um, where I already worked with Wes and Mike on this project. And um yeah, it's our honor to be to be part of this lab before I continue with uh my PhD at the University of Cambridge uh in October.

[00:00:36]And uh it's funny, I already said to to Wes that I I had presented a year ago.

[00:00:40]Don't worry, I'll recapitulate everything, all the essentials. Um it was literally tomorrow a year ago so to say but we have completely reworked uh the the paper since and uh yeah now it's really leave I need us a bit of time for uh the discussion at the end because we want to submit this very soon. Okay. So, effectic coupling um what is that and why is it relevant? Um so I think what's over overarching the overarching paradigm in in cognitive science certainly is connectionism. idea that you know we can just model the cognitive networks as like effectively like connected connected graphs where spike time dependent plasticity plays a role where we have synaptic weights and wires so to say modeled after the good old uh molic pits neuron. Um but that stands a bit in contrast to the actual physical reality um in which neurons really live um that uh that is illustrated here.

[00:01:42]Namely, they also send um yeah signals through bioelectric fields. So ion fluxes that are that are caused um by them. They drop off or they have quite a steep uh drop off or decay length um short decay length and that's why they're often like ignored. If you look at the effect one to one basically coupling it's it seems kind of negligible um because of its short range um but at the global scale it actually can make a difference. I'll get back to that in a in a second on the next on the next slides. Um but uh an important point is that what you see here where they applied like an external field um to to LFP uh to to to neuronal cultures. Um you can see that if it's off they kind of burst pretty randomly but the spike timing is the one that's influenced not so much the spiking rate. Um so it's a relatively subtle effect you you could say. Um, next slide. Exactly. So that's that much for for functions. So it's really important for synchrony on a functional level, but it's also really important for structural um development.

[00:02:52]So yeah, there's this nice experiment here by um Yaoal 2011. You see if you have like some single neuron and don't have any fields uh applied, no electrical field cues, they will kind of grow in all kinds of directions. Um but once you switch on um a field apply to it they will you know axons will tend to align themselves with the with the field lines. So they enforce uh directed directed growth from isotropic one together with other chemical cues. Um of of course um what is really important for um effective effective coupling is that we also get rid of this just neuros neuronentric uh view and also take into account the gllio cells that are not just glue um as we know um by now um there's this interesting experiment where they applied some electrical stimulation um to to neurons um on electro array and look at look at the before and after and if only if you have astroytes which you see here, you really get this clustering um of neuron [snorts] bodies and axons pointing away from it um which is blocked. Then again though if you do apply TTX a um blocker of synaptic activity. So what that means effectively is um you do need the the aststerytes which are heavily implicated in in the transmission of epoptic signals and but also the recurrent amplification of this effect through um network activity. Um the first ones to notice that okay these two things tend should belong together um is to my knowledge an estio in 2011 who who wrote quoting here to the extent electrical fields can alter spiking of neurons um correlation and spiking between two synaptically connected neurons can affect the synaptic strength of their connection this would constitute an indirect impact of ephaptic coupling and synaptic function.

[00:04:49]So we need to take into account both of those together and this is what really inspired our project.

[00:04:58]So we know that these yeah immediate voltage effects are quite quite localized. So how can it be that we can talk about millimeter scale um effectic uh effects which previous research um has shown there are two ways either that this can happen. either there are really large synchronous field potentials um a lot of neurons like sometimes hundred thousands or like millions at once then you can measure it three four millimeters away there's another kind of overlooked mechanism as well in in in the literature that can that can allow for this um at least overlooked with respect to coupling um here is a paper braid that looked at just promotal oscillator networks and there's no contradiction between having a spatial kernel that's quite localized and a a phase coherence across large distances um with that coupling. I think that's a really crucial kind of distinction um that was tried to illustrate here now from our paper, one of the first figures. We have the local voltage effect um that drops off and decays relatively steeply and um you can have though it's no contradiction to have at at a large distance still um a high degree of um of face clearance. And the experiments have shown that it's in at least in mostly in rap hypoc campus preparations that have mostly been tested uh that this effect not of course the field itself um but um that this effect uh spreads at about 0.1 m/s roughly. There's a bit of variation there but much lower than unminated um exonal um conduction would allow for. So that's also important for us because we want to look at this together when neuron one is spiking through axons and sinapses. We have a many to many kind of coupling together with this much lower conduction speed um of the of the phase advance that is caused through these um ifoptic effects. And our idea is basically what does this emergent interaction between those two um contribute to neuronal self-organization.

[00:07:17]So there is um a little illustration of like what what it is that we were expecting to observe. So uh again we're looking at uh endogenous development and symmetry breaking that occurs um during it. So in the beginning we have a relatively homogeneous spatial distribution. Each dot is here supposed to be like illustrate like one neuron and in the beginning quite weak coupling um especially in the in the gamma phase where there's not that much activity yet but as um isolated neurons start firing um at a at a gamma frequency frequency um we should have a particular distance which is here character as the inter patch distance also illustrated down here um that our model predicts where different clusters um start to form with not many um neurons in between. And so it turns out that if you enter that into kind of like this the two speeds and this the speed difference together with here like an exemplary frequency low gamma frequency of like 34 hertz you end up in the 2 to 3 millimeter range. Keep that number in mind. Um that's going to pop up uh again and again. Um an important step here is that this differentiation process is mediated through um yeah a synchrony. So there's some experiments that show that only synchronously active clusters um survive um as the free energy of the network is is minimized. Um so yeah we have maximally efficient heterogeneous networks at at the end of it that kind of for free exploit those those gradients um electrical field gradients that are already there.

[00:09:07]So our setup of the experiment are um dissociated neurons on a high density multi-elerode long word so HDMA dimensions are roughly 4 * 2 mm roughly.

[00:09:21]Um so these are all dissociated and plated homogeneously um sitting on top of this. So basically measuring this just in 2D and here's a little simulation. I'll get back to that um later. Um how we arrive at at these kind of um results or this kind of sim simulation. Um but the main point is that we hypothesize that these two vertical bands effectively that we also do observe already taken some of the results already up up front here. um that along the two um um short edges the these like vertical bands um that are going to come and like a little road map for the upcoming slides. Basically, we're we're going to try to link synchrony function here to the geometry the literally the uklitian distance um that that um we see as the anotropy of the the neuronal structure emerges. So we'll start with looking at how gamma bursts um emerge in our cultures uh just indogenously long range synchrony at these large millimeter scale distances and then look at how a generative model could reproduce a spatial structure that we that we observe.

[00:10:35]So this is basically the gamma uh main figure that we have um in in a in a preprint soon going to be up as a as a preprint. So I'll guide you a little bit through it. So we have here um activity of the network at day in vitro that's the AV at 12. So our first recording day we measured from a thousand electrodes that are ranked here by activity. It's like one out of six wells that we have that is representatively shown here. And this is here over the time course of 10 minutes shown. And then if we would average it at each time point, we get population instantaneous firing rate um which is here colorcoded. So brighter color means more spiking activity effectively shorter intervals between successive spikes.

[00:11:26]And um if we now zoom in, we take a little time slice here. Um we can see that there's quite a bit of additional structure here. Um so at DV12 we have quite long periods of what we designated classified as um high activity periods um where the population activity was elevated above a certain threshold. And within those we also look at the participation proportion that means the number of um electrodes that recorded a spike within a short interval.

[00:11:57]We do see that especially in the beginning um we have these network-wise bursts um that we want to distinguish um from the background activity. Um why do we want to do that? um because that's where we expect strong field effects and wavelike behavior in which you'll see um later more. And if we separate these two um and plot histograms of the instantaneous firing rates, how often do we see um yeah spikes with a certain interval, the spike interval? Um we see that during those bursts, gamma is during this early burst here V12 gamma here in this case for this culture 44 hertz um usually around 40 Hz um being being dominant. Um so that's that's really important. Why? Because we look at the whole thing at the IV 12. Some things have changed, but this theta gamma structure is now moved into the high activity periods being led by really high frequency burst. A lot of multi-unit activity that will be mixed in there.

[00:13:04]Um and uh yeah, we see the scaffolding of like the theta gamma kind of coupling that I'll show you a bit more um about on the on the next slide. Um but yeah we have many more many more bursts um but shorter the bursts are shorter but also the intervals between um these bursts as you can see here um becomes um shorter.

[00:13:25]So yeah the there's some more stereo there what's very important is that we're very stereotyped um yeah burst sequences um across wells and across the which was quite interesting um to see.

[00:13:41]So here's an example talking about theta gamma nesting. Um um we can look at individual events. So if we just go back like one slide if we look we can look at each this for example would be where we have these diamond shaped things. This would be like one burst peak um event that we use as an anchor uh temporal anchor for events which is would be here the red line.

[00:14:04]Um so um these are milliseconds here by the way on the on the x-axis and again the instantaneous firing rates um huge spike in the in the beginning and that is then followed this is at d21 separated by one theta sometimes two theta faces afterwards um we have gamma firing here you can see it pretty well here as well um at theta peak so yeah this is quite interesting that it recapitulates what others have found um mostly in vivo and that our cultures endogenously um self-organize to to to this attractor state. Um where we can see also here if we look at the instantaneous firing rate profile we always have this these like triple peak the super high frequencies leading a lot of electrodes implicated and then some kind of hub like nodes um that yeah show this theta gamma nesting effectively and if we resolve this in time um I promised you waves and here are waves so what are you seeing here focus like leave out about the the colors the color coding right now. Just look at the um individual like white circles that you see. So this is like what you see is from top down effectively our HDMA and um all of the active sites on it.

[00:15:27]And if you see a white circle around not that's um a spike being recorded at that um at that time. And um here at the top you can also see like the like um what what time we're at with respect to the burst peak that was recorded and can see 150 milliseconds later after the first b we see these this idea 12 um mind you where was often believed that there is not that much [snorts] structure even yet um these left to right um waves here. So, um, they kind of whiz across the across the array. Um, and yeah, it's kind of back and forth going one way and now you'll see it going the other way um afterwards. So, that's that's already interesting. Um, let's look at it a bit later. Um, this is the same dish at a at a more mature state. And what you would also noticed likely is that we have here we already see as well where the active sites are the most active sites that we're recording from automatically are located on the on the left and and right. But uh yeah, I'll get back to that again later. Um, and what is really noticeable um here then is that we have these super fast um spiking waves um that that yeah quickly right now fly across the array and then afterwards we have these reverberations and now we do pay attention at like the colors actually which is the gamma phase. So we apply a hilbert transform in the 30 to 50 Hz range and uh see that there's a separation of of time scale. So this exactly corresponds to what we would expect mostly exonally conducted super threshold events going from left to right and then sub threshold much slower oscillations accompanying them.

[00:17:25]Um yeah, here is basically the same point that I already just made in the in the headline or in the title. Um so we stay with the spikes here for now. Um yeah, we'll you will see this give um over and over just to remind you of like I think this is the you know the best uh spatial temporal visualization of of what we're what we're talking about here. So um yeah, we often see this left to right propagation of spikes from one band to the other band on the other side. Um what we do now um to um estimate their speed is that we detect um on which side of the dish the burst here for example was on the right moving to the left um a it emerges and um then can plot across events. This is now average. You see here colorcoded in the background time on the y-axis progressing in time like this. Um we can see um how peak population activity progresses from the origin side which would be this one here. Um towards the other horizontal site and can then fit a slope to the delay um over of the distance that it covers. And we can see that this is if we look here at the this this blue line.

[00:18:44]Um I'll tell you about this here about the black one in a second. Um we can see that this is pretty consistently just under 1 millm per millisecond a median of 0.62 mm per per mill. This is average many events. um quite reliable and um yeah this corresponds pretty well to to exonal um microscopically estimated exonal conduction speeds in similar or yeah basically the same kind of preparation that that we were looking at. Um so strong indicator that these super threshold events um that we see here is like spike peaks travel at exonal conduction speeds um and over days we have the 12 14 21 that we were investigating overall synchrony is also increasing so synchronies here at the the black line. So that is the conditional probability that an a node J is firing if a node I is is firing within it's very important two plus minus 2 milliseconds after one spike was recorded at a given given site. So that increases over over time they overall become more synchronous and um we also see an interesting finding that will actually go in the supplementary but anyways worth mentioning it's it's quite interesting that it's stereotype it becomes more stereotyped the um which um which direction they travel towards. So in the beginning it's like we have this index here effectively um the this like imbalance index at zero is like 50/50 effectively or trouble trouble as often to the left from the left to the right as vice versa and at one it's always the same direction um within within a well each dot represents one well and there's already a shift there between 12 DV2 a slight bias at DV12 it goes higher um at at 14 and stays stays relatively high um also at DV 21. So um speaks for increasing degree of self organization over days in vitro and I had mentioned before that you know we have the separation of time time scales and as we're now connecting super threshold traveling speeds to external signals um when we investigated also and estimated from our data um the local velocity vector of the um the at which the phase the gamma phase advances over face. So, we can ignore now these uh white dots that you see here. Um but I'll walk you through the methods of like kind of like what what we did here and how we arrived at our um sub threshold conduction speeds. Um so here's an illustrative example, right?

[00:21:26]Where we have some wave traveling across a um array and from a local neighborhood with a given radius can estimate at um at what speed. velocity it it it travels. Um we before band passed this um so we look at bursting periods which are shaded here in in blue um with the burst with the anchor of maximum population activity signaled here with this dotted line and um yeah can see in this way gamma sub threshold fluctuations that if optic effects will be particularly relevant for um we can see that um yeah there's a preferred phase um during which spike ing actually occurs. So if we look at coupling between it's relative is relatively weak. It's a statistically significant. That's exactly kind of what we would expect from these effectic biases. Um that there's a preferred phase gamma phase during which a spike is recorded. And um if we now do a lot of fits to a lot of events um then we can estimate if there's a sufficient sufficiently good um um fit of the the the um the phase plane.

[00:22:40]We can estimate at which the speed at which it bounces. That's in our case um 0.08 millimeter per millisecond. crucial parameter for a model to estimate the distances at which these at which these um bands are likely um to to emerge. And this is very much consistent with um previous literature that measured between 007 uh to.1 mm per milliseconds oftic propagation speed. And this is very clearly a lot slower almost by an order of magnitude um than the super threshold spiking waves.

[00:23:19]And here we can see now the spatial distribution um over in in in one of our example dishes over diavs it just becomes a bit more differentiated but the overall pattern is already there looks almost like a bit more pixelated bit comes so to say quotequote a bit clearer um over days what's colorcoded here is the average um activity at a given site and uh we see higher activity where we predicted right remember that this is like roughly 3 mm meters um distance between these two bumps as we al call call them. But crucial question is like do we see synchrony above that baseline firing rate? So for control for if we were to randomize location phases um would we still see um an increased likelihood that a neuron for example this side fires synchronously with a neuron um two to three millimeters away. Um little example of like how we again like arrived at these arrived at this distance. So there are three crucial parameters that fit in there that can go in there. So we estimated the aonal velocities and ifoptic velocities that I talked about on the previous slides. And what you see here is if we look at the um the instantaneous firing rates um over over days and fit and look at where the peaks are as we did on on one of the first slides um they are consistently in the low gamma um like around for around 40 Hz as I mentioned.

[00:24:55]So that enters as well our models to give us a particular distance at which we are expecting to see deviations from a Q exponential which an exonal only model here indicated in light blue um would predict we would not expect um there to be within the dimensions of our array at least a um a significant deviation there but we would have we make a very specific prediction about where with first of all that there would be this period this cosine like periodicity um in our synchrony data and also what its wavelength um would be. Um so here we again have um the the synchrony conditional firing probability corrected for baseline um they do increase um or it does increase over over diabs overall as we can see here. um but also the magnitude of the periodicity becomes a lot clearer significant for for all of the days but here if you look at the residual structure from this so you see the dotted line is just a pure exponential fit which yeah especially for later days it's it's quite poor um and uh shows this clear periodicity and um yeah this is clear evidence kind of that yeah our model something that the um yeah external only um explanation just count. Um and um despite having these extra parameters inputs um we still have overall a lower um yeah basian information criterion value and but this is only from spiking data and also at DV12 it's it's it's quite a subtle effect. So we asked ourselves okay can we get something clearer from looking at uh LFPS directly. Um so um it turns out yes I'll take that away up front. Um this is now TIV12 gamma phase data filtered in a way that that I explained um already before and um yeah this is what it basically emerges if we resolve this over over time. So if we look at coherence which is like cosine between phase angles um over distance so time progressing here on the x- axis um coherence being colorcoded here in this case um around this burst anchor here time zero um we see close to at sides close to the reference uh side we loop this over all of all sides um and weighted also by the amplitude that's also really important um a stronger clearance and then a drop and a rise again uh around two to three mm on the next slide that will come out I will take this cross cut here and show it to you even more clearly. What's important for this slide here is that we have overall um high [snorts] coherence in the low gamma and the beta range. So instead of just filtering as we did here for like the low gamma band, we can do the same and look at coherence over distance um for all kinds of frequencies block scaled here. Um and what also first of all stands out that there's some yeah um volume conduction artifacts. So that's exactly this kind of immediate onetoone effect that if you were to take the reductionist perspective and not look at the emerging network effects um does often stand out to people when they talk about optic coupling. But what we see as well is that for beta and low gamma um we have also at a rise and not just exponential decay of clearance with distance here is distances on the x-axis um at distance sides but if you look closely at where these peaks kind of occur and that is happening on the next slide um they both have strong periodicity cosine like pericity as we predict but um they differ in wavelength um in a way that is consistent with with our model. So um gamma here is the low gamma in the 30-50 Hz range um here is shown in yellow and beta filter 15 between 15 and 25 htz um in purple and um yeah what is what our model just to remind you again what our model actually predicts is that the lower the frequencies are um the further away you would have these um the coherence rising uh Right. And um that is um what we observe. If we plot here the again the residuals from an exponential um fit um we have a wavelength of about 2.9 um for which is consistent with what I've shown in the previous slide um but it was like 2.8 roughly um for the gamma spiking but then also beta is basically reaching the extremities of our um of our array. Um so dropping lower um as uh our public excel interference function predicts. Um if we compare our whole coherence data I mean gearish implants have have done something before quite quite similar in in spirit. They have also looked at invivo though looked at um coherence again always between here zero and one um slightly different method but effectively quite comparable over time across the whole um frequency spectrum and really saw significant rises as well in around 20 htz and 40 htz and again if I go one side back that is where we see this as well. Unfortunately, they kept the coherence over distance. Here we have for the different bands coherence over distance. They kept it at 1.6 millimeters. So possibly we would have hypothesized that there would be a rise a non-molotonic rise like we do have it here um hidden. So it's as if it's if as if we were to cut off our uh plot right here at 1.6 six millimeters effectively where this whole structure effectively would would stay hidden. Um yeah, that would be very interesting as well to um investigate in uh in vivo of course this this this effect but I'll talk more about possible future directions also later. Um yeah they have uh also a gamma peak very very close to what what we have measured around 37 hertz. Um so now we get to the structure or like how does the all this talk of coherence and um conditional fing probability synchrony over distance relate to structure? How could um an an an isotropy of the spatial distribution emerge from the synchrony? Um so and can the exonal only model with only exponentials here. Um where we vary the the wavelength of the exponential um can even a double the exponential. Um so one that that accounts for local clustering um one term that we that we pass into both models um plus a second exponential for long range uh connections. Can that somehow recover um the structure that we that we do observe spatially? So let me explain to you like how we simulated this. Right now there's still you know definitely important biohysical um parameters missing. It's more of a phenological model at this point. It has to be said but it's still um directly relates to um yeah activity or synchrony dependent apoptosis um that I talked about earlier. So we have a homogeneous seeding like we do um now here in silico um with some gshian noise in it. Um each dot here on this yeah simulated HDMA um is supposed to represent one neuron you can imagine. And now um if we take a reference neuron here for example and now um look at okay what is according to our external model where we have this this curve we would have a negative contribution at like 1.6 six mm here, but a positive on for long distances.

[00:33:05]And if we now start pruning those um nodes, letting them die so to say um based on their synchrony score um then and and stop when the count um of leftover neurons matches the one um of of the matches the number of electrodes that we record from our last recording day. um what kind of patterns u microscopic kind of distribution of neurons um would we would we get and that can be measured by the um KS statistic um the two dimensional version of it. So we basically look at the dissimilarity in distributions between here's an example distribution blue um yeah superimposed on the empirical uh one with the with the two two bands here um and and a lower score effectively means means a better better fit here and that's next slide um yeah the result is um that exponentials alone even the double exponential cannot reproduce this spatial anisotropy that we um observe.

[00:34:13]So here is the fit landscape for both models. We'll start with the external only um grid search that we've done in the fit for it. Brighter colors here indicate lower case statistics so better fit. Um so for the external only model um the local clustering strength by this super short range like a DK expansion decay length of only 100 micro meters um that seems to be important. So better fits for higher values here. Um if we look at one of those examples um that would be this one here like this um the rectangle where we see some this is but this is the best fit here the the star um where we see um some local clustering that we also observe in our data um but other than that a homogeneous um distribution.

[00:35:04]If we increase the external decay length like here over distance um what we would get then is just one big bunch um in in the middle which looks very much unlike kind of like the exact inverse of what we uh observe empirically.

[00:35:20]In contrast, um the epoptic exonal uh model has instead of like a d varying the decay length of the exponential, it has our cosine um that results whose wavelengths whose wavelength um results from the frequency at which we see oscillations. So that means again to to recapitulate um a higher frequency leading to a shorter wavelength. So that would correspond here to multiple of these patches kind of emerging. Um we simulate this for a bunch of values and what is remarkable is that the best fit here again the star see it here and compare it to empirical um recovers the 35 hertz at uh that we measured independently at DI 12 and um yeah that's yeah quite a again despite the simplicity of the model um there still a remarkable result I would say and um yeah important takeaway is that we're not going to get this at least at the spatial scales that we investigated in our um HDMA we're not going to get this from exponentials alone and now we already go into the kind of dive into the discussion part and like try to relate this to existing literature and um yeah existing findings on the bump core code around 3 mm um so there are three example examples here. The first one I'll start with is Usaki and Wang's uh seminal 2012 PA paper on theta gamma coupling um particular gamma firing um so they also um analyzed some red cortex data just like us uh like um but did that in vivo and um yeah there's a small number of cells that you see here everything that's orange in all these figures is what I superimposed on this um where mind you this is the maximum um spike LFP coherence. So there are some um sides that or some pairs that have a maximum coherence three 3 mm away um and a clear deviation and again from a monotonic decay over distance and the same data set showed again this 30 around 30 to 40 Hz um yeah um yeah modulation like increase in in modulation of the spiking rate. So that's yeah that's that that's the the first example um that was not further discussed in the paper how that bump exactly um kind of emerges. Another one of these examples here it's interesting that is um this seems to be really shows this is a frequency dependent um effect or like they looked at different gamma frequencies. So um distances here on the x-axis and this is in the rat hypoc campus where a lot of stuff a lot of studies about the coupling have have been conducted and looked at the gamma coherence over distance and specifically for the 30 to 50 Hz band that we also um found similar results for um that we see a rise in coherence um that is also not further discussed in in in the paper And um it would be very interesting to investigate as well because this corresponds in the red cortex also to important anatomical um boundaries functional and anatomical boundaries.

[00:38:56]Again this overlap between function and structure here that our paradigm um is um yeah supposed to explain. And um one last um example um is actually an HDMA plating as well that was done where they analyzed the functional connectivity by by polyatal 2015. And um yeah they they refined the functional connectivity this uh yeah pruned a lot of edges based on the structural connectivity and what you can see again is different dimensions of the of the array. And this is exactly what we would expect if our var grid was actually rectangular. And would be interesting to also test that in the future. Of course, different physical constraints of the array and how they would because our model again even under the phenomenological generative model makes specific predictions about where these clusters would um would emerge um and and be synchronous or have a higher likelihood at least of showing face coherence and spiking synchrony.

[00:40:00]And yeah, um quite quite interesting to see the consistency between those different results. Um also just like some yeah things that we haven't uh yeah investigated observed in our models and and limitations. Uh now two main limitations are first of all that it is uh endogenous activity only um that we investigated and um yeah inducing which turned out a while ago to be more difficult uh than expected. Uh inducing reliably firing in a certain frequency band and seeing how that changes structural outcomes is a is a is a major goal um down the line.

[00:40:48]Um but yeah again we have only indigenous activity here and we only observed the B12 12 plus what's important here is that um for exit couple really good papers on this stuff around the 2000s that were published on on um self-organization on electrode arrays um is that we have here for this line which is like dense plating of a culture. we would expect strong epoptic um effects. Um already a lot of apoptosis happening. So here's the cell density per square millimeter and that drops already a lot before we start um start recording and um yeah what how they re research by short for example showed that already at an early early time point um small biases in like sender receiver dynamics um are amplified recurrently and drive the results in computational structure in the long run.

[00:41:44]Um really important point that speaks to the unobserved mechanisms that um pedal on here um is the role that inhibitory um neurons actually play and um we know that they are really important um for uh gamma oscillations and um they already mature before we we start recording around DV8 um and drive burst um activity synchronous dispersed which are plotted here by for example a later paper 2001 um really show that large gurgurgic inhibitory cells the density of them determines um yeah beyond a certain threshold um we get a lot of um synchronous burst activity as we also see it in our recordings and specifically um smato starting inter neurons they are likely responsible for this they mature earlier than p inter neurons and are um really cool paper recently by by Leadal 2024 showed that specifically in the 30 to 40 hertz range that they are sensitive to optic and training. So another pointer in that direction and with that I come to my last slide the conclusion.

[00:43:01]So what what have what have we done to to to summarize uh once more? Um so our paradigm just connect function to structure in spontaneous development self organization often cultures electro arrays and our model predicts the wave periodicity and its associated wavelength and like radial biases um and connecting in that way synchrony to to to structural outcomes. Um what's really important about electrical fields is that um there's a yeah birectional causality um spikes cause electrical fields which again feedback and change especially as we see saw the timing um of of um of spikes which again has an effect on um spike time dependent plasticity and and and so on.

[00:43:53]So it's not just like in a neural network where we feed forward activity through synaptic weights and update those um but electrical fields of coupling um seems to be an important determine of um uh of structural outcomes and and synchrony and this is immediately connected to uh the situical coupling hypothesis by ponisel one of Demetrius Ponis one of our co authors on the paper um I'll just quote me where he says uh electrical fields are the link between information the brain is processing and a stable organized cytokeleton so again building building this building this bridge um yeah maybe coupling seems might be a missing link recently these debates here between vortex and pongadel where yeah one side was effectively fighting hard for the wires in the brain the connecttome's like no we can leave out all the wires ing and and just look at um I molds from from geometry um treating the brain like homogeneous tissue in a similar fashion as we kind of did um and um yeah maybe well they not really discussing coupling in their in their debate but um interesting last visual I'll leave you with uh is that if we would naively fit a model basically to these exponential fits uh there are these clear deviations in this case this would correspond this is kind of like a wavelength around 30 millimeter with our models. Again, I'm not saying that this certainly explains it, but there's still these this ongoing this yeah persistent puzzle of like what um how deviations from the exponential wiring rule rule can be explained and um also if we look at the autocorrelation.

[00:45:40]So it was me who added here these it was not from the paper originally should have indicated that more clearly. uh these clear deviations at certain distances um this periodicity that requires an explanation which for which we propose um one this is all just starting to be exploit the computational benefits of of like harnessing this analog um back plane of neuronal activity is only starting to be um exploited in some recent neuromorphic architectures and there's a lot to be done also in in modeling this further in more detail and with that I would like to thank you for your attention and a huge huge thanks for Wes to Wes and Mike for um yeah having been so crazy trusting Casper and me. Casper [clears throat] wrote the original commentary of a paper on energy minimization during embryogenesis that that inspired all this uh and in actually on investigating this and also fellow co-authors and I'm happy to take any questions you have.

[00:46:44]Uh great talk. Um do you do you mind going back to the slide where you compare the axonal only decay length and the effectic >> where where there isn't like an Yeah.

[00:46:58]This one right here.

[00:46:59]>> Yeah.

[00:47:00]>> Um so the the the DK curve in the middle which is the fabic axonal combined model it it sort of resembles a Mexican hat.

[00:47:10]And there are models um in you know theories of pattern formation and I think computation neuroscience as well >> where um a short range activation and longrange inhibition models can actually produce this sort of uh Mexican hatike function. So, so the question is um I I think uh a reviewer might ask is is evapic external model the only model that can produce this thing or could it be external only but a combination of short short range activation long range inhibition could also >> a possible hypothesis.

[00:47:48]>> Absolutely. And that was actually one of the main um yeah concerns on like the the paper that that Casper was originally commenting on. they um had assumed kind of two different different cell types with different DK length. The motivation for our proposal is to not having to assume two different cell types with different exponentials effectively um DK length that in our case under our constraints um can cannot reproduce this this this structure but explain that with a joint um mechanism with this inter interference effect and but of course this is like this is an important question I mean for further tests also down down the road um especially improving it started out as more of like a sketch at first but then refined this phological model but more to include more biohysical parameters also including cell types and so on and really look at yeah kind of the solution space behind this um even more even more closely. I mean what we could only establish now is that you know a combination of two exponentials um could as they had a their paper could not um could not reproduce this um effect effect that we see but good point yeah >> yeah that's very cool thanks Daniel that's great >> awesome >> really interesting Uh I don't have a question because I was I was with the paper but um we will probably send the preprint out to the computational crew in the next coming weeks. So if this is interesting at all to you um I'd appreciate any kind of feedback. Uh we'll go through the normal this kind of partially counted because all the figures that you saw today are the ones that'll be in the paper but um yeah would love to discuss more. Um Daniel's unfortunately going do his PhD so you know we have to send him away at some point but he's done some phenomenal [clears throat] work up to this point.

[00:49:53]>> Thanks. Yeah I'm sure it can the project can live on.

[00:49:58]>> Yeah. And uh Hana asked a question about gap junctions. Um Han, I don't know if you can jump on voice, but um I'm not sure how to measure it functionally um in a meaningful way. I mean, you could go back and stain things and try to guess, but um I have no idea. I mean, one thing that people do is uh they'll um put Lucifer yellow in the medium and then scratch up some neurons, wash it out, and see what else it enters that you didn't scratch. Right? So, so you rip up the cell membrane, the lucifer yellow. So, lucifer yellow is a small fluorescent molecule that only goes through um you know, it's it's it will only get through the abductions, right?

[00:50:43]It can't it can't just get in from >> can't pass the membrane. So uh you rip up some cells and Lucifer yellow gets in there. If they have gap junctions, it will it will sort of float it into the diffuse to the whatever it's connected to. So if you then wash it and you ask and so there's a so you do a control by also throwing in some large like rotine dextrand die which will label the things you've scratched but not actually pass gap junctions. And so anything that's yellow but not red, those are the things that were gap junction connected. It's a bit of a pain but but it done.

[00:51:17]That's cool.

[00:51:19]>> The other thing uh Daniel wanted me to try but there was other issues that didn't come from his but one thing that would be very interesting for us is to see if we can um you know create this artificially. So the the CMOS MEAs have stimulator electrodes as well. Um and and right now the only validated version of interaction is with voltage stimulations, but we could in theory >> try to keep a culture in in the incubator under some kind of stimulation for an extremely long period of time like these first couple very critical divs that Daniel was showing to see if we can make uh eaptic patterns essentially. So, can you imagine shrinking the Mexican hat that's there in the middle of the slide, you know, >> by half?

[00:52:06]>> Yeah, that's is is intervening basically here in this this >> Exactly. Yeah. Um would be would be super cool. Um technically a little challenging though.

[00:52:16]>> Yeah.