 So now we fast forward five years. Here's Alberto Dinelli. He was in the court 2019-21 During Covid Yes, and well now he's in Paris and he's working on bacterial ecosystems and He will tell us something. Thank you So thank you so much for inviting me here. It's a real pleasure also because it's basically my first spring college live so happy to be here and Yeah, I'm now working. I'm a PhD student now working at University of Paris. I I'm working under the supervision of Professor Julien Tailleur and I met him during my my PCS master actually was a professor at my second year in France and so I decided to continue working with him for my PhD thesis and now I'm today I'm going to discuss one work that we have been doing about the self-organization of bacterial ecosystems from the microscopic to the macroscopic skill So the field that I'm working on is active matter and I don't know if you are familiar with that So I'll try to give the grounds on on this subject So by active matter we define those systems whose microscopic units Dissipate energy to exert some non-conservative propulsion forces and these are ubiquitous in biology at all scales So basically you can you can go to the microscopic scale and look at the bacteria Well bacteria they use the energy coming from their metabolism to move their phlegelum and thus to self-propelled If you go to the scale to the animal scale Birds are a good example of an active system because they use the energy to move their wings So fly and we are active particles in a way because we walk So that's another way in which we we can be defined as active particles And what I'm particularly interested in is the emergence of collective phenomena in active systems So here I'm showing three different examples Drone from the from the three previous Biological examples that I was making so here on the left you can see the emergence of ring patterns in Excadica coli, and I will go into these in the next slide. So Don't worry about that for the moment. I just think it's a nice picture Then the second example is way more clear. I think it's the flocking of birds So you see the emergence of of a collective behavior by the fact that all these particles align to their neighbors And so they get these collective motion But also another example is at the human scale the emergence of collective oscillations in crowd And that's something that has been studied for example by the group of the Ney Bartolindia So the key element here is the fact that there is a feedback control over mobility So I look at the agents around me and based on that I decide how to update my motion rules And as I was telling you I want to look at the case of bacteria So here on the left you can see a single trajectory for E. Coli. That's something that has been tracked Back in 1972 And here you can see the motion of one single E. Coli bacterium So I want to start from the scale the micrometrics scale and go up to the one of the petri dish So something around 10 centimeters and how to do that Well as a statistical physicist I'll try to model the trajectory of these bacterium as a run-and-tumble motion The idea is that these particles self-propell with a given self-propulsion speed V along an orientation vector That's dictated by this theta angle in 2d and then at stochastic times They abruptly change their orientation which gives rise to these fragmented trajectory here So the idea is what we would like to do is to go from microscopic to macroscopic So first of all I need to define the microscopic interactions are at play in this system And then coarse-grain the microscopic dynamics into a macroscopic field here And once we have that what we would like to achieve is an understanding and possibly a control of the self-organization of a system of interacting bacteria So here's the outline for today First of all I will give you and will give you some details on the interactions at play in this system Which are a quorum sensing interactions I will then move into the physics of what's going on Just giving you some details about multi-duty induced phase separation phenomena and finally I will move on my actual PhD work, which is the generalization of these concepts to ecosystems of bacteria So systems that are made up of many different species living together So let me start by quorum sensing So by quorum sensing we define Particular type of interactions by which the cell density is modulating some biological function and this is a mediated interaction occurring bacteria meaning that Each bacterium is exchanging with the other some chemicals and these chemicals in turn can trigger these interactions So let me give you some concrete examples One that you can find in nature is bioluminescence in these libero fishery bacteria When these bacterium is swimming alone or at very low cell densities, nothing happens But then you start to increase the density of these bacteria and at that point They start to exchange with one another these small molecules like signaling molecules that are called auto-inducers and these auto-inducers in turn can Regulate the genetic expression of some particular proteins And the proteins that they regulate are responsible for bioluminescence, which means that here we have a mechanism that's density-based Beyond which beyond a certain threshold We observe the appearance of some biological phenomenon. So in this case bioluminescence Now what we would like to do is to use these quorum sensing mechanism to control another biological function Which is motility for example, and so the question is whether we can use quorum sensing as a pathway for self-organization in active systems Short answer is yes. This has been engineered in bacterial strains work mostly around 10 years ago The key idea is the following You have these engineered bacteria that exchange these signaling molecules A H L I mean, it's not important the name It's just these signaling molecules and these signaling molecules in turn They regulate the genetic expression of some protein GZ which favors swimming over tumbling so All in all what happens is that at high cell density these bacteria eventually tend to stop at low cell density instead they tend to move freely and This is observed when you change the cell density of your Petri dish you look at the relative the diffusion coefficient of these bacteria and what they observe is indeed a drop at High cell density meaning that actually these mechanism is working. So these A H L auto-inducers They are a proxy for the cell density And they give rise to a self inhibition of mutility Meaning that the density itself is inhibiting the motility of the pie So what good what happens in this system? Well, what they do is that they put in a central inoculum in a Petri dish their bacteria They let them grow over one day and they observe the formation the spontaneous formation of these rings So you see how from these central inoculum over the scale So these are how we're passing by and you see how the system forms these concentric rings and Importantly, you must notice that these rings are alternate between dilute regions and dense regions of bacteria so This is indeed a phase separation phenomenon between a dense region and a dilute region and we would like to understand it with the physics of phase separation but The question that now we would like to answer is why motility inhibition favors these kind of self-organization So these brings me to the second point motility induced phase separation But before speaking of out this kind of out of equilibrium phase separation I want to just refresh some notions of equilibrium phase separation so at equilibrium liquid gas phase separation occurs because of a competition between energy and energy you have energy that is basically cohesion attraction that brings particles together you have Entropy that tends to Homogenize the system and the competition between the two leads to if you are at sufficiently low temperature Leads to a liquid gas coexistence. That's standard equilibrium physics Now on top of that we add activity. So these self propelling Okay, now we start what I want to show you now is a system of Particles with Lenard-Johnson interactions. So at very short scales repulsive, but at an intermediate scale attractive interactions at the beginning there is no self-propulsion. So this is perfectly at equilibrium and You see that the system basically is phase separated between a very dilute gas and a liquid cluster liquid bubble in the middle and Then we start to increase the self-propulsion You see this V parameter is the self-propulsion speed of the particles I increase it Again and now what you see here is that the liquid gas the liquid phase as completely evaporated and we have a fully homogeneous gas But then if I increase it even more We start to observe again the formation of of a liquid But now we're completely out of equilibrium and this phenomenon is just dominated by the self-propulsion speed So what happened can be to put here on a phase diagram on the y-axis You have the self-propulsion speed here You have the density and I have fixed the temperature of my particles So first of all here, that's the equilibrium regime very low self-propulsion speeds The first thing that you go do if you increase your speed is that you've upperized the liquid phase and Then you end up into these the entrant transition, which is called Motidity induced phase separation and that's the one that we have seen in the movie And what's striking about it is that you can also observe it in the absence of attractive forces So you just take repulsive forces self-propulsion and you observe these motility induced phase separation And now I would like to understand how this happens So let's take I think the simplest scenario to understand the physics behind MIPS Which is quorum sensing active particles So the dynamics is the following one you have this particle whose velocity is proportional to an orientation vector u Times a self-propulsion speed and then these particles they change their orientation abruptly with a typical rate that's the tumbling rate and These self-propulsion speed is Regulated by the local density around yourself and this is what I call quorum sensing in this particular Then what we have what I would like to convince you about is that Motility inhibition so the fact that your speed decreases with the density can lead to MIPS So there are two elements that we have to take in mind The first one is that active particles accumulate where I go where they goes lower now I'll try now to give you an experimental reason why so imagine there are regions in space where it moves lower and Others where I move faster imagine here. I'm faster here. I'm slower What happens is that it's more likely for you to find me here where I'm slower And I'm passing more time than finding me there. So that's the intuitive explanation of what's written here But coupled to that you also have the fact that There is mobility inhibition so you move slower where you're denser And now if you take these two effects combined together You will have a positive feedback loop that amplifies density fluctuations and thus leads to mobility induced phase separation And this is as regards quorum sensing interactions, but something very similar can be understood if you think of repulsive interactions Because what happens is that your self-propassions to yours? Sorry, your velocity can be split between a bear's a propulsion and the interaction bits You put everything together In a fieldish way if you want in a effective speed along your orientation you and These effective speed will take into account the bear's a propulsion and the effect the projection of the total of all of all the forces onto your orientation and As you can imagine repulsive interactions will act in such a way as to reduce your effective speed and thus Steric repulsion actually behaves in a way as a mobility inhibition and can thus by the same reasoning above lead to mobility induced phase separation sorry Is this Notility induced phase separation Independent of dimension do you have it in all dimension or do you have a lower critical dimension an upper critical dimension? so No, it can be it is found at all dimensions Actually in one dimension even in one dimensions both also you can see that in simulations, but also with with full theory What can change this is the presence of disorder? So if you have for example if you imagine that your particles are moving on a on a rough surface that can be modeled as a Say as a disordered potential in that case that has been shown that it can lead to To having a lower critical dimension that's three if I remember correctly so that's something very recent But yeah in general in these very simple scenario you have it in all dimensions. All right So I want to give you Okay, some more quantitative insight on these multi-induced phase separation So what we do Is to coarse-grain the microscopic theory so the dynamics that I showed you before into a large-scale hydrodynamics and Eventually I won't show you how you do that. It's quite long But the key message here is that eventually you end up with a mean field theory hydrodynamics that's basically a transport dynamics for your density field and The mass current is given by the gradient of some chemical potential. So that's basically a thick transport load if you want And now if you look at the detail of these chemical potential It can be written as the derivative of a free energy functional of an effective free energy functional Which in terms can be expressed as the integral of a free energy density over space and Now let's give a look at these free energy density So there are two terms competing with one another there is one which is very resembling to an entropic term So we call it an entropy in quotes These roll-on-roll part and then you have this part here which we interpret as an effective energy for our model I'm saying effective because of course these model is out of equilibrium. So there is no actual attraction between the particles But from a formal point of view, we can call it an energy and an entropy and so the competition between these two gives rise to Non-convex free energy, which can then be Which on which one can use than standard equilibrium methods like common tangent construction and the term in the gas density and the liquid density So these energy These effective energy entropy competition is what explains multi-induced phase separation at the large scale So now let's put these into simulations. We simulate this system for example in 2d and That's not yet what we want because you see that the system fully coarsens into us into a Single bubble so you if you remember the movies that I showed you before about the bacteria You had these concentric rings of finite size and the physics of these things so far doesn't give you any finite size selection You just have things That take there are that scale with a system size these are bubble scales with the system size so there is still something missing and Maybe for biologists it will be more intuitive for It's population dynamics, so of course bacteria live and die and reproduce And if you add to your MIPS theory these logistic growth term These will stabilize finite wavelength, and I'll try now to justify what's going on But maybe just to make sure we are we all agree on this So the first lambda row part is basically an exponential growth of the density These second part here is such that it saturates the growth to a carrying capacity row not So that's basically a logistic term So why does it stabilize a finite wavelength because now you have two competing mechanisms For the formation of a of the liquid so first of all you have the mass the mass flux So all the particles come in inside a liquid droplet for example And these flux is proportional to the surface of the droplets So if you're in 2d that will be proportional to the radius But at the same time inside the droplet you have mass variation So you have loss of particles due to these terms here And this will be proportional to the volume of the droplet So the competition between these two terms is what stabilizes a finite size And in particular it will fix a ratio between the surface of a droplet and a volume And so it will fix a particular a particular size So this let's make a recap so far We have seen that motility induced phase separation plus population dynamics Leads to a selection of patterns of finite size So this is what we have seen so far So quantum sensing interactions are interactions that make the motility density dependent And can lead to MIPS motility induced phase separation Population dynamics meaning a finite carrying capacity can lead to wavelength selection And these can give you a qualitative explanation of the experiments For example in the simulations that you had here on top Is the simulation of this model And you see pretty quite well reproduces the experimental results But what about complex ecosystems? So that's the same Sorry I missed one point So this density dependent motility is also due to steric interactions Because essentially what is also due to say the crowding effects It can be if you if you include steric interactions it can be So for but it's not necessary So for all the models that I will show you also in the following I will just speak of quantum sensing interactions Neglecting completely steric interactions I will neglect the steric repulsion But you can effectively account for that So you can effectively account for steric repulsion as an effective motility inhibition No because that in one dimension is quite important Three dimension maybe is much less important No, yeah in one dimension Yeah, so Yeah, okay, I have I'm not sure Because okay with quantum sensing interactions you do get motility use phase separation in 1D Now that I think about it I'm not sure about what happens with a steric interaction so that I would check For sure you get it in from to the on but I'm not sure about If you just have steric interactions For purely quantum sensing you can so with particles that can interpret each other you can All right So now I would like to tell you something about what happens when you have multiple species living together So complex ecosystems and that has been the focus on of my PhD work So I would like to discuss the self-organization of active mixtures So we'll start with a very similar basically the same model as before So run and tumble particles In 2D for instance, but this time we have two strains that are labeled with an index alpha and beta The dynamics of a single particle is the same as before So you have a run phase with a self proportional speed V and then you tumble and you change your orientation Now we have these additional specification of the species I belong to but that's Yeah, so yes in our models. Yes, that's what we I would guess so I'm not even sure how so for the coarse-graining for example I don't know how this would affect it and that's something that would be worth checking also because in There is a work by Eric Clemont in ESPCI They're They're experimental group. They have studied the the motion of E. Coli bacteria and I've actually shown that The distribution of tumbling times is not exactly A Poissonian distribution, but there are actually some important corrections to that And I think yes, it would be nice to incorporate these effects, but So far we just keep it a simple Poissonian process Okay, so here we just have these These standard dynamics then on top of that we now consider a quorum sensing Which means that the self proportional speed this time now depends on the two different density fields. So I'll find rho beta I will speak of motility inhibition in the case in which V decreases with rho. Otherwise, it will be motility enhancement And now in this scenario here, there are way more complicated Possible interactions because you may you may have self interactions meaning that my speed is regulated by particles of my same type Cross interactions between different strains or global interactions by which the speed of one particle is dictated by the overall density around it Okay, so what we start by doing is to simulate these model these dynamics here and see what happens So we start by considering self inhibition a couple to global enhancement of motility meaning these basically And what you see here on the right is the phase diagram that we obtain from this system And the axis correspond to the density to the homogeneous densities at which we initialize our simulation for the two species So there are quite different colors. I'll go into that in a moment Let's start by the white regions. Those are the boring ones in which you scatter your particles around you look at the system It remains homogeneous. So white regions are the boring ones. Yep So if you want, yes, I mean You can also it's very analogous to what you would see if you have self inhibition and cross enhancement the nice bit of this of the physics here is the Interplay between the two species But so I don't I'm not sure if I understand what you mean by redundant You mean by the fact that you account in a way the effect of one species is taken into account in the two parts Both in the self in the total part. Yeah Yeah, I think okay. Yeah, I think the phase diagram will maybe clarify this point and then we can discuss it later Um, so yeah, the the first part here of the phase diagram is quite boring So it's just a one species phase separation So imagine you initialize your system here at the start Then you follow this dashed line which is called tie line of phase separation And you end up at two points the extremes of the segment these two points that give you The phases in which the system has phase separated. So you see that here there is The tie line is vertical So it means that the density of alpha particles in the two phases is basically the same and these you can see here The the density is homogeneous for alpha But beta has a Beta poor phase and a beta rich phase. So you see actually These multi induced phase separation, but just for one string If you go in the middle And follow these tie lines you will see that you have two demixed phase which you have an alpha rich Phase and a beta rich phase and these again you can just look at the extremes of the tie line And that's informative on the kind of phases that you have Finally you also get a triple phase coexistence We with alpha rich patches beta rich patches and well mixed regions So here the static phenomenology is very rich At least it's quite rich and we want to understand it starting from the microscopic theory. That's our goal So same as before we start from the microscopics We do the coarse graining which corresponds to taking a diffusive limit and doing some ito calculus And we end up with a stochastic field theory that has this form here There is a mass transport term as before the gradient of some chemical potential and there are fluctuations And this effective chemical potential takes into account the log of the self proportional speed and the log of the density Right, so now that we have this field theory We would like to squeeze something out of that. So one thing that we have tried was to say whether In some particular cases it could be time reversible So what we do is that we compute the entropy production rate for these field theory Meaning that we compute the average over all realizations of the field Of the log of the ratio between the probability of a forward going trajectory and a backward going trajectory So i'm I'm not sure if everyone is familiar with the concept But one thing that you can keep in mind is that if the forward and the backward trajectory are equally likely This ratio goes is equal to one The log is equal to zero and this entry production rate is zero Otherwise if you have some time irreversibility this quantity will be positive Um, all right. So okay, we ask ourselves. What's this quantity in this model? And Whether it can ever be equal to zero and the answer is yes There are some cases in which this sigma this entry production is equal to zero If that is so then these Equally these dynamics here is it effectively an equilibrium dynamics with an With an effective free energy f And a probability a stationary probability for the density fields that goes as the exponential of these Of minus these effective free energy. So what are these cases? Well, uh, we look for the for the condition for equilibrium and we find this relation Which at first sight might look unintuitive it was for us to So the the derivative of the log separation speed of alpha particles with respect to the density of beta Is equal to the derivative of log separation speed of beta particles with respect to density of alpha So the intuitive idea that we grasp is that the way in which beta particles affect the motility of of beta Sorry, beta particles affect the motility of alpha must be reciprocated By the way in which alpha particles affect the motility of beta when these holds We get an effective what we have called a generalized action reaction principle at this field level But in all in all this means that we have an effective macroscopic free energy And once we have a free energy you can build analytically your phase diagram using common tangent construction And what you now see on the right is the comparison between the colored regions obtained from our analytics And the black lines corresponding to the simulations So there is a very good match which tells us that our theory from micro to macro is effective in describing the emergence of static patterns in the system But of course this only is valid when we have this condition here So to sum up we have started from an out of equilibrium dynamics at microscopic scale And when this condition holds we ended up with an equilibrium field here Now the question of course is what happens in all the other cases So this brings me to the last part of the talk We ask ourselves what happens when this condition is violated We take self inhibition coupled to no reciprocal cross regulation of motility Meaning that we violated the condition before And what we observe are Dynamical patterns in the case in which we have opposite cross interactions meaning that alpha Enhances the motility of beta but beta inhibits the motility of alpha So we start with our our homogeneous system with particles scattered around And eventually we observe the formation the spontaneous formation of a self propelling band Where the red particles are chasing after the blue ones We have a variety of Dynamical patterns for example these Okay, or another one that I like that's hopefully going to be the last move. So here you see the two the two strains And after a while red tries to invade blue And so these sets on a basically an intermittent dynamics between the two strains chasing after one another My supervisor said it looks like my cat's playing Okay, so Yeah, we have tried to Get some quantitative understanding of how this happens and we have done basically a linearization of the field theory I will not into the go into the detail of that I will just try to give you an insight of why this happens So again, what I told you before active particles accumulate where they go slower But on top of that we have motility regulation between the two strains So motility inhibition means that I will slow you down We will spend more time together. And so this means that motility inhibition plays the role of an effective attraction At the same time motility activation plays the opposite role. I activate your motility. I speed you up We spend less time together So effectively motility activation plays the role of a repulsion But now if we take the two of them together, this creates a sort of frustration Because alpha which is inhibited by beta will accumulate in beta rich regions So it will slow down But beta will be activated by alpha. So it will speed up and run away Now alpha is activated by the lack of beta particles So it will chase after them and these will set on the run and chase dynamics Which is the microscopic origin of the patterns that I was showing to you before And finally, I'd like to conclude by going a little bit beyond these theoretical fantasies and going to another Experimental realizations that has been done with two bacterial strains And this time we have orthogonal quorum sensing secrets Meaning that you have two strains A and B And A produces a particular chemical signal these blue dots here That binds to a receptor in B and regulates the expression of some gene in B On the other hand B produces some chemical signal the yellow one which binds to receptors in A and has an effect On regulating the genetic genetic expression in A So you have two pathways of genetic regulation that are not interfering with each other If now you engineer the system and then put the bacteria essentially inoculum let them grow That's what you observe This is the same petri dish, but three different fields of view You have the one one strain of bacteria that's marked green the other strain that's marked in red And the two of them together and you see that they form these demixed Rings So you see that It's the same petri dish again, but three different visualizations And you see that spontaneously It forms these concentric rings So this is if you want is a realization of the demixed phase of an active mixture in an actual bacterial system Finally one just last remark is that again here we see some finite size patterns So these rings and this is because on top of the theory that I've shown you before on for MIPS one has to add population dynamics So these brings me to the conclusions Well, I have shown you that quorum sensing interactions Can lead to self-organization in bacterial systems Using core screening methods one can draw a direct connection between the microscopic and macroscopic dynamics of the systems and the joint The joint phenomena of multiple induced phase separation and population dynamics can lead to finite size patterns In the final part I have shown I've talked about active mixtures as a model as a possible model for a bacterial ecosystem of many species interacting together And as a new direction that we're now exploring for example We're trying to study a very large ecosystem that is made up of many different species And trying to model that using a random matrix theory and that's a collaboration that we're now doing with adult hearing pairs I thank you all for the attention and i'm glad to take any question Thanks And you showed Different examples of engineered strains where In the lab the people were able to reproduce These these patterns and these mechanisms and and this is not like this is just curious. This is not provocative, but are you aware of Like situation Where you actually observe this without the need of engineering like it's nice to to engineer it and see that everything is consistent but either either those patterns are present or something like this plays some role of biological relevance in the sense of like Yeah Yeah, that's actually a very good point and The short answer is no not that i'm aware of For wild type bacteria The point is that there are very complex ecosystems. I'm thinking of the gut microbiota or the Or for example The rhizosphere so the all the bacteria that are living at the roots of of plants and trees And those are very difficult to I mean it's very difficult to pinpoint exactly which interactions they have which chemicals they exchange So it's very difficult to say all these interactions can actually be there in In a real bacteria in wild type bacteria. That's not been observed. That's for sure What I think is cool about these experiments Is the fact that we have some control of self-organizing Biological systems that are quite complex and we have some understanding of that Maybe it can be used in a way to to produce self-organizing patterns in a intelligent way that's The long run, but yeah, the short answer is no um Well, this question is the question that shows that I didn't understand anything Can you come back to the to the part of the entropy where you write the sigma, please? Yeah, yeah, so For what I understand of the active particles that you have to feed them constantly with some chemical potential or well an agent and molecule and In principle these are processed out of equilibrium So you are taking the entropy or that sigma is a measure of entropy So that's I think a very good point that you're that you're making We're hiding something under the rug. That's the point when you do the coarse-graining You forget about some degrees of freedom that are the orientation of the particles And the fact that you have microscopically, it's true. It's an out of it's always an out of equilibrium process Even when these sigma whatever that is is equal to zero Microscopically you always have an out of equilibrium process because this particle always fueled with some energy that they need to self propel So for sure the full dynamics if you could also keep track of the Of the orientation of the particles for sure you would have a positive entropy production When we look at this theory, however, we have coarse-grained out the orientation degrees of freedom So you're looking at less degrees of freedom and this theory can be actually something that's time reversible So that's what's going on But the problem is that you cannot relate these entry production rate to some production of heat in the system It has no say thermodynamic interpretation because you're forgetting The sources of of energy of energy inside your system. So I don't know if that makes things. Yeah, it may Yeah, it makes kind of sense because and then when you define The distribution like the exponential of the This free energy that is because Okay, it is out of equilibrium You have this measure of entropy equal to zero because you are forgetting about the microscopic Details or I'm just taking it like some out But then it is still not clear what you can take the like an equilibrium distribution for them So, okay, if I just started if I didn't tell you all the story before And I give you these equation up here. Yeah, okay If these you can be written as the derivative of some free energy functional, that's an equilibrium theory. Yeah, okay We're doing the reverse. We have the chemical potential and we ask ourselves When and whether it can be written as the derivative of some free energy When that is That occurs you can show that the stationary distribution is a Boltzmann one And one way to show it if you want is to write a Fokker Planck equation for this density It's a functional Fokker Planck equation in this case You look for a stationary solution And that will be an exponential of minus It was my mistake because I was thinking acolytum, but this is stationary then it makes sense Thanks Any other question? so if not, then uh Thanks, uh, thanks again Alberto and um, we'll see you tomorrow at 9