Phase Space Invaders (ψ)

Episode 25 - Ivet Bahar: Elastic network models, targeting hinges for drug discovery, persistence and alertness

• Miłosz Wieczór • Season 4 • Episode 25

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In episode 25, Ivet and me start with a general overview of the elastic network theory and its applications to biology, as well as its strengths and limitations. Ivet then tells us about the specific takeaways from the different lines of her research, talking about evolutionary dynamics signatures, mode excitations in allosteric effects, as well as her recent research on the relevance of hinge regions for drug discovery. We talk about the relevance of the proteins-as-graphs picture for machine learning, and end up with a few general reflections about the complementary roles of persistence and alertness in scientific careers.

Milosz:

Welcome to the Phase Space Invaders podcast. We're coming back after break with season four. Two quick advertisements before we jump into the episode. Firstly, you can now support the podcast on buymeacoffee.com/phacespaceinvaders, all written as a single word. So I've been covering all the subscription fees for the editing and hosting tools out of my pocket, and I will continue doing so, but if you value what I'm doing here, I will very much appreciate even your smallest support. Secondly, with the help of Tamar Schlick we got a commentary published in Biophysical Reviews about this very podcast. So in case you ever need a scholarly reference for the podcast itself, feel free to use it. But now to the episode number 25, where my today's guest is Ivet Bahar. Ivet is a director of the Laufer Center for Physical and Quantitative Biology at Stony Brook University or State University of New York. She's mostly renowned for the development of theory and applications of elastic network models in biophysical research across scales from individual proteins to entire chromosomes. With a foundation in this conceptual framework. She successfully explored research programs in evolutionary biology, a lost theory and drug design, genetic pathology, and many more recently earning a seat in the National Academy of Sciences of the us. So we started the conversation with a general overview of the Elastic Network theory and its applications to biology, as well as its strengths and limitations. Ivet then tells us about the specific takeaways from the different lines of her research, talking about evolutionary dynamics, signatures, mode, excitations in effects, as well as recent research on the relevance of hinge regions for drug discovery. We talk about the relevance of the proteins as graphs picture for machine learning, and end up with a few general reflections about the complementary roles of persistence and alertness in scientific careers. But then enough of me talking, you should hear all that directly from my guest. Ready? So, Ivet Bahar, welcome to the podcast.

Ivet Bahar:

Thank you.

Milosz:

So, Ivet, you made innumerable contributions to the computational biophysics of proteins, coming from many different angles, from, you know, evolution to drug design, to what can now be called dynomics, but most of them have a common denominator, and that's your, I dare to say, favorite computational tool, namely elastic network models. And I have to say, thinking about this, this simple concept really gives you access to such a broad and universal set of insights that in hindsight, I can't really say I'm surprised by the impact your work has had on the field, but how did you decide to make it the cornerstone of your research toolkit in the first place?

Ivet Bahar:

that's true. You know, network models that we've been using have been very useful for, for a quite broad variety of applications. usually, you know, I, I'm more driven by specific biological questions. for example, when there were, let's say, hi-C data for, uh, determining the chromosomal organization, uh, contacts, gene gene contacts, or contacts between gene loci. I immediately realized that, you know, this is a field we could easily explore with our network models. that's what we did. And that helped us gain a new Uh, so we were able to relate, those contacts to gene gene correlations, co uh, data. and to me it was fascinating because, you know, you've been, we've been always thinking of, the DNA is an alphabet of four different, types of letters. now we are talking about, a three dimensional structure that's also moving and, uh, you know, it's totally physics based after all, or mathematically driven, our, approach. And we are able to interpret lots of, data on this type of network models. So that was an example. But I think there are lots of different ways of also thinking. Another classical example I have been broadly using, you know, is the allosteric communication. So when it comes to signaling any signal, actually, any type of conformational change that propagates, I think, network models are extremely useful. Obviously, you know, the Kirchhoff matrix that we use or adjacency matrix, they have been used in electric circuitry as well. So it is a natural, tool if you wish to try to understand phenomena or biological interests. So first, I'm intrigued by a biological question, and then I try to see what would be the best tools to deal with it. So elastic network models have been very useful. Of course, we do molecular simulations and learning models. In recent years, we've shown that to combine them is even better.

Milosz:

Right. In the end, we all are sort of generalists with some minor specialization, right? In one subfield of the whole landscape of methods, but to, to go back to the basics, do you care to elaborate for our listeners? You know, what is the most basic notion of, of the network model and how it applies to, let's say, protein structure on protein research broadly.

Ivet Bahar:

So the network models are a good representation of the geometry, actually, or the structure. So if you think about it, we are taking a complex system, and now we are representing it in terms of nodes and springs. So it is, a huge simplification to, represent a material or a biomolecule or a system of interactions by such a simple model. Now, uh, we the most commonly used a network model, an isotropic network model uses, alpha carbons of individual residues as the nodes, and then, uh, harmonic springs of uniform force constant for all amino acid pairs whose alpha carbons are within an interaction range, let's say 10 Angstrom. And then we just use the PDB coordinates. We used to use PDB coordinates. Now we are also using alpha fold database. just use a known structural information on the residue coordinates build The network model for the protein or the complex. It's equally applicable to proteins or DNA molecules, RNA, etc. So once you build this network, now you have a platform, if you wish, for doing lots of analysis. One of them is, as you know, the mode decomposition. We try to see this Equilibrium structure, because by definition what we're using is the equilibrium structure. Whether this equilibrium structure has certain modes of relaxation, and we, hypothesize that those modes of relaxations are, you know, the accessible movements, the structure actually uses in response to stress, in response to, whatever necessary functional requirements are. Okay. So that's one thing, mode decomposition, understanding the spectrum of modes. The other type of analysis that we do is we try to analyze based on that what are the critical sites, nodes of the network. And it, we try to see whether those critical nodes have been indeed observed to be evolutionary conserved have been targeted, by drugs, et cetera. So, the model is very simple. What is unique and what makes it work is that you have a unique analytical solution. It's not simulations. You have one unique analytical solution for every given structure dependent on all the 3N coordinates. You know, if you have N residues, let's say it is, we are Not considering local interactions, but we are considering the coupling of the entire network, and we're having a unique solution for the spectrum of motions. think the mathematical rigor, uh, mathematical precision of the theory is helping to kind of offset the physical approximations, because it is purely based on geometry. And if you would like to talk, in terms of energetics, This is purely entropic. There is no specific interaction. we know the limitations that, in some cases, especially in drug discovery, The local interactions are important. we complement it, you know, we design hybrid models, we complement with other methodologies. But the essence of it, this framework, this graph theoretical approach, is actually very powerful. It just gives a good description of the entropic effect.

Milosz:

Right. So you never bump into computational resource problems with, with this method, at least, but,

Ivet Bahar:

absolutely true. We have, you know, we don't run into computational resource problems. The only thing is the size. Sometimes we are, we like it

Milosz:

mm hmm, mm hmm.

Ivet Bahar:

larger systems, because the approximation of this type of harmonic potentials or Gaussian distribution of inter region distances, it is strictly discrete. true in the limit of an infinitely large network. And when it comes to smaller systems, not specificities, unharmonicities, all those things matter. when it comes to the global dynamics, which is the collective motion of the entire big network for systems that are not typically resolved by cryo EM, I think that is where those network models are most useful. And, uh, we have been, developing, you know, we're now using directly electron density maps to build the network models. we can, you know, at many hierarchical levels, different levels of resolution. What is beautiful me is the fact that the most, cooperative low frequency, or what we call the softest modes of motions, are very robust. They are maintained across, different levels of representation. So that's the essence.

Milosz:

Right. And while we are at it, well, there are certainly patterns that you can find if you look across the proteome, right, or across evolutionary timescales. What kinds of patterns have you been able to pinpoint in, in proteins looking at exactly this kind of conserved modes or these robust modes that are preserved across eight classes of proteins?

Ivet Bahar:

Yeah, yeah, that is, you know, in biology, uh, bioinformatics actually started with analyzing sequences, right? Sequence motifs, there are signature sequences that are known to perform certain functions. And then there are signature sequences. Structural motifs, that would be, accomplishing a certain function. And they have been recruited by nature in many different proteins, not only one. Now, then we recently came up with this concept of signature dynamics, which means there are certain movements. let's say in the simplest case, if it's a domain enzyme, there's a cleft in between and there is this opening closing. This type of movement is, so, useful for, you know, enabling the binding of a substrate or then, uh, surrounding the substrate. nature has been using the same mechanism of motion, some torsion, some bending, etc., in many different, proteins. So, um, yeah. That's it. now, uh, it is possible to understand what is the repertoire of all motions that are accessible. And, then we went a little bit further, we went deeper a bit. We considered families of proteins that share the same structure. Of course, in our model, structure dictates the network model, which in turn determines the dynamics which relates to function. That's the, you know, the way everything connects. Then when we analyzed families of proteins, also, we could see that many of them share the same global dynamics. So this is like the signature dynamics of this family, which It makes them perhaps members of the same family, but then we can see subgroups that their own specific variations in their dynamics, and that's how the function has been, specialized, if you wish, to accomplish, uh, different, requirements So, it is possible to approach the universe of proteins or protein families from this dynamic perspective to understand, you know, their mechanism of function, how this type of function has been, differentiated or became more specialized, and that brought us to many, many evolutionary stages. arguments. So it is not only the sequence or structure, but the dynamics that needs to be conserved in the first place. But now you can have many variations to increase specificity.

Milosz:

All right. So it makes you think of this kind of convergent evolution, right? That evolution comes up with the same, well, through different means comes up with the same solution to,

Ivet Bahar:

Yes,

Milosz:

several different problems, right?

Ivet Bahar:

some kind of convergence. Many systems chose even though their function might be different, they chose the same mechanism. And however, there's also divergent evolution because that point, if you would like something to be more specific to a certain environment or species, there is also divergence. Yeah.

Milosz:

You can evolve allosteric pathways or, or modes as you probably prefer to, to think about them, right? I mean, you, you mentioned this two ways of thinking about allostery.

Ivet Bahar:

yeah, that is, that's an interesting topic. You know, allostery, there are so many definitions in the literature and what my understanding is that it's a cooperative response to some kind of perturbation at a given location of the molecule, which is not necessarily the active site. then affects the activity, and mostly it affects the interaction with other proteins. So that is, my broad view of allostery. And these cooperative events are actually things that we can predict by, network models, elastic network. Now there have been another group of studies. And we have even, uh, our group has been publishing like that, trying to see the network as a, you know, a platform where you have a framework, let's say, where you have propagation of signals through Markovian dynamics. So,

Milosz:

It's more like time dynamics, yeah, time series. Right.

Ivet Bahar:

transition rates to go from one node to another, first passage times, et cetera, and you try to understand when you perturb a given region. which we call the sensor, is this signal propagated through what we call effectors. So we try to dissect the structure in terms of sensors, effectors, where, what are the spots where you can, you know, alter dynamics significantly, et cetera. So that has been, this type of based on connectivity, essentially, and some kind of propagation of signals, also broadly used for understanding allosteric responses. My is the first, where we have some intrinsic cooperative movements already, now when you change the cooperative move, it is not because there is a progression from one point to another, but things are moving together. now when things are moving together, if you really one end of the structure, now that particular movement, especially if you perturb the hinge site, that movement will be, uh, you know, collectively, affected and impaired or, um, you know, accelerated. To me, that's the way I was theorizing mechanisms. This is more an all or none approach that, Mono, Wiemann, and Changeux introduced, than a sequential event. Now, of course, this is a long discussion, and we've seen in many applications, in single, uh, simple systems, early organisms, let's say. This all or none mechanism really works well. the organisms get more complicated, you know, we approach humans. Now, everything gets more sophisticated because we compared the chaperonin for bacteria, GroEL GroES versus those for mammalians that were more recently resolved. and we can see that, uh, In the case of GroEL and other non works, when you go to higher organism to mammalians, now you have a combination of sequential and other non mechanisms. It is more complicated. So we need all those theories actually to perhaps make better sense of observations.

Milosz:

It's a common pattern that when we try to figure something out for humans, it becomes intractable.

Ivet Bahar:

It

Milosz:

Right.

Ivet Bahar:

but we learn a lot for simpler, simpler organisms, which form a basis. But, uh, we need to, biology, unfortunately, in contrast to physics, uh, biology has, uh, lots of exceptions or peculiarities. So, but still the basic rules of physics, they help us a lot.

Milosz:

That's true. I often, I often thought about all those, for example, old kinetic models that were essentially based on excitations of molecular, normal mode frequencies and so on. And very often it was so hard to apply this to biological problem, like to, to see how this excitation exists in an, like in an enzyme environment rather than in a diatomic molecule, right? Or something like this. But it's actually a quite a useful concept once it's applicable. I agree. But you mentioned hinges and, uh,

Ivet Bahar:

Yeah.

Milosz:

you, you recently went into exploring the hinge motion as related to the drug design. Right,

Ivet Bahar:

groups also have demonstrated, interfaces, et cetera, to identify hinges. intuitively we say, okay, since hinges play such an important mechanical role, hinge sites, if you target those sites, there. ought to have some kind of effect on the function of the protein. So we have been always, assuming that, but there was no rigorous systematic examination of all existing, you know, drugs, where they bind. Do they really bind any of them? Do they bind hinge sites, et cetera? So we, uh, since we always make this assumption, I thought maybe it is worth exploring rigorously now that we have access to tons of data. So we, looked at, FDA approved drugs, their interactions with, target proteins and try to understand Whether hinges have been indeed targeted, by those drugs that turn out to be approved. now we know that most of the drugs have been, uh, the structures that have been resolved show the binding at the active site, like the catalytic site of enzymes, which we call also the orthosteric site. Then, uh, more recently, Uh, we know that, in some cases, you know, you have drug resistance mutations, et cetera. Allosteric have been targeted. You know, this, uh, a typical example is the ABL kinase. You know, there are now new, allosteric drugs that target, this, uh, myristoidation site, if you are familiar with. And now there are even drug resistance mutations that arise there. Now we, I thought, uh, the first one is more like a chemically important site. You know, it's where the chemistry takes place. The ortho steric the, uh, allosteric sites are physically important. They modulate the interactions, Then I was thinking hinges could be also important as mechanically important sites. After all, you know, we have people saying enzymes are mechanochemical entities. There is the mechanics and there is the chemistry and they are together. mechanically important sites, uh, would be hinges. And, It is very interesting. In this paper that now we published a few months ago in PNAS with a PhD student of mine, that actually many drugs, existing drugs, do target allosteric, uh, hinge sites. in many cases, what happens also is that hinge sites and orthosteric site, they may, overlap. They may be co localized. So, At least, uh, 40 percent of the drugs, you know, the popu the probability of hinge sites is way above, uh, random probability. This has not been a strategy that has been, you know, explicitly used in drug design, but it has apparently worked without, you know, without, uh, to do that. So what we're proposing is from now on, why don't we just plan this way and try to target really the hinge sites, which already doing that in many applications.

Milosz:

I guess historically a lot of drugs that were supposed to be rationally designed eventually bound to places that just happened to be good binding sites, right? So we don't always. know where the old drugs supposed to be binding. That's a fair point.

Ivet Bahar:

So everything started, you know, as trial and error, and we, we still, uh, you know, we are very glad when we have anything rationally designed that works. But

Milosz:

That's true.

Ivet Bahar:

with the explosion of, now and data, accessibility of data. We're gonna see increasingly more, rational design.

Milosz:

Well, that's the promise of it all. Yes.

Ivet Bahar:

an example. You know, uh, again, many repurposable drugs have been just discovered by coincidence. But, we have really powerful tools to understand what are the side effects, which particular drugs actually target those. off target proteins. And, uh, yeah.

Milosz:

Also for technical reference, how do you define hinges in proteins? Because that might be not that obvious for someone who doesn't see a protein as a bunch of, you know, blobs that move in a hinge like manner.

Ivet Bahar:

You know, conceptually, the simplest thing is you have, two domains, connected and there is a region that allows for the relative movement of the two domains. So this is like the intersection between two structural regions that undergo opposite motion. So one is moving like that, the other is moving and the hinges in, you know, in between.

Milosz:

So it's very easy to detect in a,

Ivet Bahar:

Yeah.

Milosz:

model, right?

Ivet Bahar:

But, you know, now, you know, well, if we look at the structure, we can say, oh, this is likely to be a hinge allowing for that particular subdomain to swing. But you can do also mathematically, you, if you plot the movement in a long, principle axis along a mode axis. There are regions that undergo positive movements and others that undergo negative, and then there is a crossover region. It is very interesting. If you look at the crossover regions, even though they may be sequentially separate, on the structure they all co localize in the same hinge that governs that particular motion.

Milosz:

Right. That looks like a good hint. And then that also helps you, I assume, understand the action of a given drug, right? Because not all drugs have the same biological effects. Some are activators, some are inhibitors. Uh,

Ivet Bahar:

And it's not only drugs. Uh, it is also mutations. for

Milosz:

yes.

Ivet Bahar:

we have been now using dynamics information for determining whether a given mutation is neutral or pathogenic. so most of the mutations would be neutral, but there are certain, especially, of course, a sequentially evolutionarily conserved sites or very tightly packed regions in the structure, but also regions that play an important dynamic role. So we have been, able to use this type of, uh, you know, information on the motions, mechanisms of motion, even, you know, the type of allosteric communication sensors, effectors that I just mentioned. If a given, uh, residue plays an important role as an effector of allosteric signals, its perturbation might be damaging. So we have many, many features that add up, you know, in it. algorithm, machine learning algorithm. feature is assigned a weight learning from existing data. we're able to make a very accurate predictions, depending on the data set, but it is certainly in the 90 percent accuracy levels the consequence of point mutations. Now we're trying to extend these things to or insertions, deletions, these are less explored. the same arguments that hold for identifying critical sites also hold for identifying sites that can't tolerate mutations. And you might ask now, if you use just elastic network model, you don't, you identify a site, but you don't know the consequence of a specific substitution. that's true, we don't. that's why, you know, we're using, the network models in combination with, uh, sequence, analysis as well as, uh, structural. you know, analysis. So it is, part of the information, but it is nicely complementing others, uh, something that has been not enough explored.

Milosz:

I see. Yes, we have very good or increasingly improving tools for studying point mutations, missense mutations, but as you pointed out, there is no easy way to see the impact of, say, insertions, deletions in something like alchemical simulations, right? So I assume this might be a really, really interesting resource to study.

Ivet Bahar:

is less studied Of course, the other thing that we can't do, talking about what we can't do, uh, network models are, by definition, elasticity is a solid like property, right? So they apply to solid materials. Uh, and proteins, to the extent that they are solid like, we can apply, elastic network models. On the other hand, Now there is a huge literature about IDPs, intrinsically disordered proteins. know, we can't use elastic network models for understanding the behavior of IDPs IDP segments in general. And also, you know, when we, for example, when there is a new protein and we look at the alpha fold database, are certain regions that are structured. But others that are completely disordered, you know, and these are regions where we can't apply our tools. And that's where we start also to use other, you know, classical molecular simulations or some polymer network, polymer theories also work for this type of disordered regions.

Milosz:

I see. I have a guest scheduled for this season who is an expert in IDP. So we'll talk about it more. I don't want to give it away yet, but there will be an entire episode dedicated to that.

Ivet Bahar:

Yeah.

Milosz:

regime, uh, still, yeah, but it's interesting that, this question of proteins viewed as graphs nicely extends to the recent, um, Graph neural networks and machine learning approaches, right? So like you're at this interesting interface that has a lot of opportunities, a lot of insights that also have a nice future outlook.

Ivet Bahar:

the reason for that, Miloš, is that they are very efficient. You can serially apply the methodology to thousands of proteins, and now extract amounts of protein. data. can't do, uh, on, you know, very collective events, et cetera. So that the efficiency, the ability to generate, you know, outputs very efficiently makes it possible to plug these as, uh, modules in other machine learning software.

Milosz:

And so I assume there are also, many cases where this protein mechanics is actually important for protein function, not just as like an enzyme or as allosteric communication, but in real life. biomechanics, right? So what about systems where the actual mechanics is part of the function? Sure,

Ivet Bahar:

That's right, that's right, of course. We have mechanosensitive channels, you know, the name already tells it all. actin, tubulin, these are systems where the mechanics really matters. so that others have been, you know, generating lots of interesting results mechanically important systems.

Milosz:

sure, sure.

Ivet Bahar:

focusing on membrane proteins a little bit, membrane proteins are good targets for drug discovery, obviously. And like everyone else, you know, we like big machines also, multi meric, multi protein. systems. but yes, there are tons of

Milosz:

What are the largest systems you have applied these methods to?

Ivet Bahar:

You know, we applied to the, Nucleosomal pores, you know, nucleosome, we, uh, we apply to viruses, big viruses, uh, and it's not only the capsid, but also the interior, the RNA or DNA,

Milosz:

Oh yes,

Ivet Bahar:

the virus. yeah, there are of, big supramolecular machines like the ribosome, so we have been. a broad variety. You're testing the limits or trying to understand to what extent our theory and methods can explain observations or generate new information.

Milosz:

right. In case of viruses, I imagine these are disassembly processes, right? Where, where the most sensitive part is and if mutations actually, I imagine correlate with that.

Ivet Bahar:

Yes.

Milosz:

I see, I asked you about, what you think are important features in a scientist. And, uh, you mentioned persistence as one of the, main topics. And I can see how exactly persisting in one, um, fruitful approach can yield a lot of interesting results over the years. So what is,

Ivet Bahar:

there is also, is also important is to be a little bit, uh, some kind of awareness to be alert.

Milosz:

Oh, yes. All

Ivet Bahar:

from advances in experimental technology. Now there is cryo EM, we have big structures. Or as I mentioned, there is Hi-C technology. Now we're using machine learning, artificial intelligence. This is another technology we're using. So, it is important to be persistent in general. But also, one other thing I would mention is to be Alert just have a good understanding of you know, what are the new opportunities the new, areas we could further expand and not to be shy, not to be reluctant to, move from one topic to another, after all, you know, this is like, uh, Exploration that we do all the time. will. It is. It gets more exciting when we explore new areas. that's what I usually tell my students. Your PhD thesis or your master's thesis is not going to be, know, the topic that's going to define your career, you will be exposed to new problems and you will need to come up with new solutions. to where you have a very solid foundation in the first place, and secondly, the persistence and the strong desire to pursue to dig deeper. There is no way you are not gonna, uh, succeed.

Milosz:

right.

Ivet Bahar:

succeed for sure. is one thing I try to emphasize. the fact that You know, the topics, important topics are changing all the time, and this is a really exciting time, and we just need to, be, able to use our knowledge, our tools to, address new questions.

Milosz:

All right. This is comfort that comes with staying within your favorite field. But as you say, the most interesting things come out of really, really jumping onto the new thing of the era, right? that can be a different topic every, well, every half a decade. I wouldn't say every year, maybe because that's probably too, too flexible.

Ivet Bahar:

That's right. The other thing I also, sometime, try to say is, in our field, at least, we need a lot of patience. It takes, sometime a long time, uh, to, find something of interest or to solve a problem that's really difficult, but it pays off. So it is worth, uh, pursuing, you know, being persistent again and patient.

Milosz:

Well, at least if you, if you use network models, you don't need to be patient running the simulations, but if you run atomistic simulations, you need even more.

Ivet Bahar:

that's true for the network model, you don't need to be patient, but there are some tedious problems that require,

Milosz:

Oh yes.

Ivet Bahar:

to solve it, to come up with a good solution. Now we are trying to understand, for example, the connectome. How does the brain work? is tedious. It is more complicated. You know, just a simple description based on the, location of brain regions using network models. It's not sufficient. So there are, uh, there is this issue. important issue of memory. For example, if you think of a Markovian propagation of signals, it doesn't work because Markovian processes just know the instantaneous state, right? Brain, you know, we know that brain has memory and the way it is being processed is much more complex than a simple linear process. So it is, uh, Then this requires some new formulation, adaptation to the specific system, at first to see that our simple models don't work, uh, Kind of, let's say frustrating at first, but then when you start to dig deeper, you try to understand what's et cetera. So persistence is very important.

Milosz:

Absolutely. I think, what comes out of the research in artificial intelligence is that graphs or those networks have information embedded in them in a very non trivial way, right? Like ChatGPT actually remembers things just through connections.

Ivet Bahar:

That's

Milosz:

can you can you generalize that to biological networks? Do they remember things in this way off, you know, encoding evolutionary information in a way that we cannot really access? And maybe there's a code to access this information. I think that's a part of that is what you have been doing for many years. But perhaps there are new ways of approaching this, this question.

Ivet Bahar:

So, uh, It has been a pleasure to

Milosz:

Okay, so, yeah, Ivet Bahar. Thank you so much for,

Ivet Bahar:

You're welcome.

Milosz:

for your knowledge, for sharing with us what you have learned and explored.

Ivet Bahar:

it's very useful to have a dialogue. This is part of what we're doing. Thank

Milosz:

I hope so. I hope people get inspired off your research and look into that and find applications to their own interesting questions. And, you know, that becomes a fruitful exchange in the long run. again for coming here and talking to me.

Ivet Bahar:

Have a nice

Milosz:

Have a great day.

Thank you for listening. See you in the next episode of Face Space Invaders.