 So I stopped here yesterday and I will do a recap of the last life where I was showing you a movie and then it was supposed to be a movie of a particle which is being driven by a external field. As I said, the particle is small but not that small because it's bigger than the molecules of the environment and because of the interaction of this column or particle between the molecules of the environment, this particle sometimes works backwards, backwards mean against the strength of the field. It's putting the particle sometimes there are red events in which the particle moves against the Earth's tendency. And this, as I explained yesterday, happens also in molecular motors or small biological machines, which is the image that the support is going to appear on the right. So I have some issues with the recording and with the presentation and the presentation. All right, I see it in my screen. No, you don't see it. Okay. Okay, I'm really sorry. This is totally out of my control. Ah, yes, okay. So you see here, I was showing you here an example of an experimental trace of a molecular motor that sometimes moves against the chemical drift induced by the chemical reaction. Okay, so today I will try to go one step further and introduce you to the minimal models used in biophysics. I will be very descriptive. I won't give many equations but at least I will give you references and where can you find more information about this topic. Molecular motors and beyond because just keep in mind what I said yesterday, biophysics is a very broad field and there are many systems that are studied in this discipline. Molecular motors are just a very small part of this big field. So okay, if you want more details, I have a full course in YouTube, you can search it like this, QLS Bio where I give a lot of details and models and exactly solvable models. I solve analytically many models of biophysics. You can find the lectures online for free in YouTube. This is part of the STP diploma program. So most of the things I'm going to tell you come from this course which you can find online and here are some classic references of biophysics and also related topics. For example, the ones I can start with you later, the names of these books. The ones that show here in the bottom are the ones I follow in my course. They go from basics. This is a very good book, cell biology by the numbers. You get a great idea on scales, the forces of space and distances, the energies of biophysics. Very good for introduction. I use also a lot of basics in the stochastic process, in particular these two books that Rafael and I we know very well and really they contain the basis for physicists on stochastic process. And this one is like a mixture of ideas in biology and ideas in stochastic process together. And this book I follow quite a lot in my course. It's a bit advanced but it's quite nice if you want to do biophysics because it shows a lot of stochastic models that you can solve. So you can go to the blackboard and find exact solutions for many properties that then you can use it in an experiment to extract useful information from biology. Okay, so I will present some of the models that I discussed. They are very, very simple biological systems. One paradigm is an ion channel. So an ion channel is like a gate that cells have in their membrane. Here we have a gate of the door in this room. And we also have gates in ourselves which open and close to allow this selective entrance or escape of molecules. And instead of cell, it takes food from the environment or it doesn't take science, ions are electrical charges. These electrical charges, for example, are important in the transmission of information, for example in neurons. So this is a very simple object if you look at it from far, which you can describe as a gate that is open or closed. And this gate opens and closes stochastically because it has a very, very small gate. It's not that someone comes and opens this gate. It is so small that opens and closes stochastically due to flat faces. And this you can model it as a Markov process in the same way of what Andrek was explaining yesterday. You have two states, open and close, and you can jump from this state to this state at a random time. So there is a rate of opening, but this is a rate of closing. This is a rate of opening, which are two numbers to that gate. And you can do an analysis of what is the probability to be here and the probability to be here. That would depend on the values of these rates. They typically depend also on biological values. So here below I'm showing you a decent experiment. So experimentally, you could see the current through a channel. So you can put an perimeter and measure how much electrical current passes through a channel. Electrical current means there are ions that are passing by the channel. And these ions generate electricity and a current. And something very important is to see that there are, in this channel, they have like two values. Okay, this is, okay, they remove the offset. So it's either zero or this one. It's like jumping. Someone is jumping between two values. Okay, so it seems like an object that is going from this state to this state at random times. And you see another thing that's very important is the value. So the current here is five picohamper. You design an electrical circuit, a map scoping, you will have an ampere. An ampere is one coulomb per second. Here we have picohamper. So there are 10 to the minus 12 ampere per second. It's very tiny, tiny, tiny current. And still it can be identified and measured experimentally. Okay, so this is an experimental motivation to show you that these type of models that we explained in this course and in this school make sense. Okay, because they are really real defenders. Yes, another thing just to emphasize is that the time that the channel spends in one site and in the other, it's a random variable. It's not always the same. It's not like a clock. It's not something that is takes some time and this time is a distribution. Okay, so if someone is here, spend some time and then jump at the random time. Okay, and the residence time, residence time we call how much time you spend on average here for here depends on the value of the rates. You see here in this time series, it's more time in the close than the open state. This will mean that it's more time here. So it means that this k minus will be smaller than the k plus. If you want to do a good model, it should be a model that to describe this experimental time series, k minus should be smaller than k. It's one example, but there are many other things you can explain in this example. Yesterday you saw in the movie by movies of Ibatoli, these polymers that were forming, creating and destroying. It's a fact of times. They are dynamical objects. It's not that motors move in the tracks that are fixed. It's not like a highway that is just given, not from me. It's a highway that is being created from one side all the time and destroyed from the other side. It's a dynamical object and you can do also stochastic models to describe this state of phenomenon. It's more complicated than the Ion Sanity 01. It's a model that will describe the length of the polymer that will be changing at random times, but it's also a classic model. This was the idea, this was basically what Iba was explaining yesterday, that micro two volts, which is the place where chromosomes are segregated, are continuously being polymerized in these polymers. It's a dynamical object. About motors. Yesterday some of you asked me how do you model the motor, etc. This is a more precise description of a molecular motor in which we have the machine that is being filled by ATP. There's a chemical reaction that gives energy to this motor, but this energy typically is used to move the motor in one direction. Whereas on the other side, the motor is connected to a cargo that can be trapped with a laser. You can design an experiment where a laser is being strapped in and this colloid is being pulled by the motor. If you do this, it's like you have someone who is putting your big backpack and the backpack is pressing you backwards, so it's opposing the next motion of the motor. So here there's like a tug of war. We have one side the chemistry pushing in one direction and the other one the mechanics pushing in the other direction. So typically what we do when we model this motion would be a random walk, so it will be a motor that is a particle in a lattice that is jumping between sites. And these sites are different monomers of a polymer. Polymer has like units and the motor is jumping between these units. And a very simple model would be this one. So it would be a random walk in which you have a rate k plus to jump to the next. So you go from zero to one or from one to two and a rate k minus to jump backwards. Of course you would tell them okay this is fine but this why does this need to be a motor. Typically this can be a particle. This could be whatever. But then you can find in my courses that typically we relate these two via hidden balance condition what André explained yesterday. But this k plus and k minus are related to the free energy change in this chemical reaction and also to the external force. So the k plus and k minus should have to be functions of these parameters. The external force and the chemical potential of the chemical reaction. They should appear in k plus and k minus. Otherwise you don't do biophysics, you are doing just mathematical. You can do random walks or I can do brand new motion without having this in the end. Biophysics is about using physics models that you have to input here functions. So k plus would be a function of the different forces the chemical and the chemical. If you are curious later I can show you how it is with equations but I'm just it is not supposed to be an introduction. So I'm just trying to give you the ideas. Moreover it's not all about a single model. Just we don't want to understand the single model moving. It's not the only important thing in biophysics. I told you yesterday that collecting effects are important. So to move a muscle fiber you need the action of many, many of these movements. Like they are rowing. So to model this you can do like a more complicated version of what I show here in which instead of having only one motor you do a model where there are many of these motors. Here what I show below it is called flashing ratchet to be very precise and what I show below are it's a model of many motors that are connected to a backbone. So the backbone will be practically this thing and in which each of the particles is the position of a single motor. So you can do a model of many motors connected to a backbone like here in which the motors can be attached or detached at random times. So you see the motor can be here free or it can be attached to the fiber. And how do you model this is by doing this type of dynamics in which you have the motors which are these balls here that are connected with the spring to the backbone here and then they can attach and detach in between two different potentials. These are potential energies that can be the potential energy of the motor when it's free which is this one or the potential energy of the motor when it's bound to the polymer which is this one. You see this energy is periodic. So if you repeat every monomer what is periodic is asymmetric. It's asymmetric because you are not just these structures are roughly asymmetric they are not perfectly symmetric in space. So when you have this type of model and you do switches so these spheres here are switching at random times you generate so just by having these these dynamics you generate a current so you can make this object to move in a given direction. It's something quite non-trivial and I explain this in my course with math but it's just to tell you that you can generate net motion by switching particles between potentials. Basically if you want to generate motion you need an external force you need someone pushing. Here there's no one pushing it's just things that are being switched on and off. You're like shining a light and shining a light is stochastic for each of the motors. You're changing the energy of the time and this generates motion. It can generate movement the fiber in this direction. This was really 20 years ago on my FD6. This was really one of the main issues to solve. So we were seeing motion but we don't have in cells we don't have heat engines like the energy of a car. The energy of a car moves because it's a heat engine so it's a system that is in contact with two thermal baths the fuel which is hot and the air which is cold. When you have this type of machine it's very easy to generate power to move things but here they are not there's not a fuel on the air it's everything is in the same temperature so for people working in thermodynamics it was really fascinating to say okay there is a machine that is moving in one direction but it's not a it's not a heat engine. No okay but I wonder how. You can have better factories but not enough you may need more in one direction. But how big a difference would you need at this scale in order to do this? I can I can send you a reference where it's discussed. It's much higher than what you would be happy. There are several reasons but they are super small. It's less than a Kelvin in a cell. You see a cell you put a thermometer. When you see a one Kelvin in a machine that is in contact with the single thermal bath and yet moves and this is because okay two things is broken in the balance and second is because there is this asymmetric for the cell. So having an asymmetric there means motion in one direction. If you want more details I can tell you a reference or the lecture where I explain this but I just wanted to introduce models or present models for the motion of a single motor we use this type of random walks which can be in discreet like a particle jumping in a lattice between sites or it can be also continuous sometimes we use that this moves in the real line depending on the cases it's a good approximation and that to describe collective effects we use similar models but in of many particles many particles please. Is that when you propose the random walk for the single motor then why would you propose that in particular I mean is this the simplest model you have or you have some distribution for the times and you say okay this is the distribution of a random motion for. Yeah so this is the simplest actually this is this is to start okay the simplest you can imagine you have a machine moving in a line and I can think about this but then it comes in fact what you say exactly you can look at the waiting time distribution in each of the sites and maybe the waiting time distribution is not described by a random walk this would be because here I'm assuming that in every jump I'm consuming ATP but it could be that the motor makes a step because of a fluctuation it could be that the ATP molecule didn't bind to the motor so in that case this description will not be enough will not because we will have two variables we will have one side the position of the motor this will be x and on the other will be the ATP consumption this will be one we will have a random walk in two dimensions okay okay maybe can I take a can I draw something because it's frustrating that I can anywhere I'm fine yeah so the simplest mode you can think of is a random walk but in many few others the simplest mode I can think of is a directed motion but it could be that this mode is not enough to explain the experiment because if you are okay this will be a mark of process like the one André explained this a mark of process in a mark of process the waiting time distribution is exponential so you spend a random time in space even said exponential is the same exponential is true but sometimes you go to an experiment you look at the waiting times and they are not exponential it can happen then this mode is not enough so you need to build a more precise one okay so the random walk can be used instead of one exponential waiting time could be because after all you see only one dimension you can have a two dimensional random walk in which you don't see the second dimension and this is very common so okay so so Elgas the way you add another dimension is like you are adding like the hidden information that you're not considering exactly the hidden information so here I'm saying every time I'm doing a job I'm using ATP but you could do a more different model in which the variable x which will be the position and the variable y which will be the number of ATPs that are consumed in this model I'm saying every time I do a job I spend ATP so if I go from 0 to 1 I will also spend 180p so I will do like this okay then when I'm here okay I can go back we can make a reaction in the step as it could be in the space so I'm doing something like this this is ATP this is position but I'm not okay I'm not losing any information if I'm doing a random walk in this one you see if I look at x in the same as I'm looking at it but there are models that do not work with this the more complicated there are something like this so they can do the following so I am in this state and they can move without using ATP this could be a plot twist so this is again y the ATP and this is x which is the position so you could they could do like this and go back but they can also do the same jump using ATP like this okay and you could also say okay there are events where there is like a chemical reaction happening but the motor doesn't move you could have something like this in particle so in this case you will have a random walk in two events if you maybe you would like this then like this and like this and like this and like this please okay something like this so now in the experiment there's one second in the experiment you cannot see the ATP you can only see the projection of this trajectory in X so then the model that I presented now was accurate and the waiting time distribution in each of these states okay the waiting time distribution in the coarse-grained state in which I don't see the one will not be exponential okay that you are doing very careful somehow it's what Eva was saying yesterday if you have an experiment you can embody this model you may have this experiment okay this theory and then this theory predicts that the time spent in one state is exponential distribution of that time versus time exponential period but then maybe in the experiment this happens a lot you know the distribution of this then you have to do nothing more yeah but then you wouldn't you couldn't describe this experiment in the left with a different k sometimes no sometimes no there are features that are common to all random books all random all models that have k plus k minus yeah they have some common features and one of them is exponential waiting time yeah and that there are many approaches you could do a macobi approach into dimensions or you could do another model in which you have a learning work or you are you have a random work with non-exponential distribution as you can also do in one dimension there are many possibilities there are many possibilities but typically by physics we try to find a macovian dynamics which in this case would be okay you add in x go to x plus one with some rate and go backward it is with y or you can go like this or you can go like this this would be this model okay this is the typical approach very nice that i have but i'm just waiting for now i have a question about the graph like when the when the motor goes back you like obtain yeah yeah you're doing the reverse reaction okay and this in there are motors in which this is very very unlikely but there are motors where this is happening a lot you synthesize it instead of burning it you can have them the reaction but without yeah it can happen i mean you don't cross the threshold for me no i mean it could be that if we are neglecting a lot of details in the motor we are not adding the structure of the movie so maybe this is what you put into it exactly exactly there was one question here yeah it was sort of related it's just that so the specificity of the motor without these empty steps that is due to the mining of the heat and then the specificity of the water surrounding the motor is the empty steps okay for this i need an equation that is typically typically what you do here let me let me take that simple one let me take a simple one and assume that i'm here so in this type of parameters where every step as a as a standard you use this the typical relation between the rates is written like this k plus over k minus remember k plus here is k of x going to x plus one please i'll come forward and k minus is the rate of calling from x to x minus one okay this is jump backwards typically the relation we use is called local interval which i'm going to explain you yesterday which we write here the exponential of a beta times f m so local interval and you will see this a lot in the address force is exponential of something beta is related to the thermonucleosus is one over kvp okay here is the temperature delta mu is the um free energy change so how much energy one hydrolysis of ATP gives you so delta mu is the free energy change in the chemical reaction so the new this is energy this is the force exerted by the motor and this is l is the step size okay so you recognize here this is work first time displacement and this also is energy and this also energy and they are different sign okay this is a way of putting chemistry and mechanics together this mode so now you say k minus is one something to say one second minus one and k plus will be one second minus one times this so when the chemistry is strong k plus will be much larger than k minus typically this is what we do but this is when you say in every step you have both you have more complicated models like i say in uh this okay this this you have something like this but you can jump like this like this or like this there are more rates it's not just they're not only two rates forward backwards there are also these ones and these ones and here each of them is different so okay so the diagonal will be written like this so this is in a paper with alexander but he was doing master review yeah this but you can also have this step in which you don't spend ATP just for three seconds okay and these two let me call it k plus x and k minus x is related in a different way so there chemistry doesn't play in your role so you have something like this k plus x divided by k minus x is different itself of minus beta effect just this because in that step there's no ATP consumption okay get my point i'm being a little no i understand this i just wondered where the king came from like you didn't include a couple of water in this space no but beta beta is one of the thermo energy the kicks are here hidden so i thought you were going to be terrible but doesn't but but the kicks are here because it seemed better okay the water is everywhere and it's generating fluctuations included here then there are external forces so we say there is an environment which is made of water and then there are external forces one is chemical and one is mechanical this is typically in physical mechanics the thermal bath appears so one single parameter how do you generate stochastic trajectories is another thing how do you do it but i can explain this i can explain i can explain but short answer is you generate trajectories as in any mark of process okay which is called using the gillespie algorithm but using the gillespie algorithm with these rates which are biological parameters i think i you must understand people we don't have to take it here okay we'll go with this okay but it's going to ask me questions because then i see if we understand or not and we can have separations from this formula now if a problem does me right okay so i mean wait a minute i don't know if the locals can help me there are also questions yes but yeah sorry i go to the end of the end i think we need to okay so i hope the people online just don't worry so okay as i said there are more complicated dynamics the one i was telling you is just a random walking line which is the simplest but there are other molecular motors that have more complex dynamics where we are psychos and we include what i said before was just saying the chemical reaction happens all of them and we cannot see intermediate steps during the chemical reaction but there are cases where we can see we can see structural changes during the hydrolysis cycle if we can see it in the microscope with optical tweezers techniques then we must do a model which has all these states here for example the you have ATP binding the ATP is hydrolyzed when it's bounded then it's released so there are hydrolyzations when when it's bound and unbound so you have more complicated dynamics that sometimes are a sense of to describe the dynamics of the motors for example by the way you asked me about ATP synthesis and ATP synthesis is essential because i tell you we we get ATP we get ATP from food but there are several plants producing ATP from from energy of the sun i mean they need to do this reaction but the reaction has to be also buffers and the molecular motor that is responsible for that is called F1 ATPase it's quite famous quite very important in nature and the model that that is used typically is a three-state or six-state model so you as a physicist can do quite a lot but here it's clear that ATP synthesis happens not that there's only one direction okay so i'm talking about the topics that i talk i dealing with in my course and another one is self-sensing an important problem is how a cell is in the environment so sometimes the cell has to take the seasons divide or it has to differentiate etc it has to be able to sense what is happening in the surroundings and there are beautiful models of how a cell can sense or for example how a cell can count molecules and how precisely with with models which is like an antenna that is measuring the number of particles in a sphere surrounding the antenna and i discuss it is a classic classic paper a book and i can give you a reference later where which discusses what is the precision of the perfection is a physical model for a sphere that counts molecules what is the accuracy of a cell counting the molecules surrounding the surface and it's really nice paper i will share with you the reference later because it has an analogy also between biology and electrostatics they use models of electrical it's a spherical capacitor with charges which is used to solve counting problem itself this is just to give you a smell of we can use solved problems in physics to study biophysics okay now i will go to further applications biophysics of something more modern that they learned in my last years as researcher going to conference or knowing in school etc beyond models so this is way out of classics the model is really classic one example is the development here i put an example of c-elegance embryo c-elegance is a worm that you can see the almost naked eye looks like this and is used quite a lot by biologists mainly because it's transparent so you can see you can see the anatomy of the c-elegance without requiring very complicated you can see for instance the development you can see how a new worm is born inside this one you can see how eggs are formed in the c-elegance and they are developed and over the last year there's been an incredible progress in this field and for example this is a nature paper 2010 where they measure the forces that are acting when in the x of this c-elegance embryo they can measure velocity fields because of forces so something that I cannot see here is that there are very useful tools from physics that are used to model the x here in the c-elegance the development of the growth of the difference in and if they are fluid dynamics and differential geometry so here they use differential geometry to describe this process because this is an elixoid which has forces that are tangential to the elixir so it's really really advanced and you can see that the highly theoretical concept of physics can be used in biology so it's not just random works now for example I'm showing that that is really an extremely growing field in biology is phase evasion so phase evasion for a fish this is like water and ice very very classic problem but now biologists have found that in this embryo that I was talking about there is a phase evasion liquid liquid phase evasion so all of a sudden there is during development the creation you see these are cell division they are to look like here there are droplets that form in one side of the egg only in one side okay what is this and it turns out this is related to where the tail of the head of the animal there these are molecules that will have information about creating an asymmetric animal we need to create asymmetries otherwise we don't have head and tail so and and this is really fascinating and there's a lot of research on this topic which uses classical algorithm dynamics and phase transitions to try to explain quite this phenomenon because here what you see is that there is the creation of organelles which are the droplets the droplets of water created here and they are separated from the reference so it's another example quite modern another one I know a bit better are is endocytosis in human cells which is here I'm showing you an example of a cell with big nucleus where you see different colors different colors typically well this used to see different proteins okay you can fluorescence proteins so moreover some of these proteins are like indicators of the fact okay they are like um labels of smaller vesicles that are called endosomes as a cell cells can send environment they are challenged but they are also formation of vesicles so this is like an imagination of the membrane that creates a a vesicle called endosomes so endocytosis takes in material and in the late years there were many quantitative analyses here it's just biology is really exploding in terms of producing data right now there's so many labs that can do so precise measurements that is really big opportunity and they can count how many of these endosomes are in the cell and how many molecules they have inside so they can have an ideal how many and how how fat they are and in physics there have been approaches to describe this phenomenon of endocytosis and endocytic network like if it were the formation of of clusters containing molecules so it is like they use population dynamics models to say for example two endosomes can fuse together and make a bigger endosome all those endosomes can split into different parts or they can transform into a different type of vesicle etc you can use this type of statistical physics or population dynamics models to describe what happens in the future so it's really fascinating and quite exciting because equations you see that are quite complicated to they're called integral differential equations so it's not just random walks this is my my main message I want to give today and another topic that I like a lot and I do a lot of research is on the hearing in particular in bullfrogs there are fascinating experiments where researchers are able to see what happens in the inner ears of the bullfrogs the inner ear of the bullfrogs surprising it very similar to the human at the inner part okay and there are cells that okay I will talk about them later in more detail where in the surface of the cell you have an antenna it's antenna which is called a hair cell bundle and it moves in a stochastic manner like I show here so this will be the motion of the top of the antenna and there has been a lot of data extracted from these animals during hearing and I'm missing something but there is 40 years of modeling for this cell and people use the plastic process quite a lot and also dynamic assistance and now we are even doing the thermodynamics so how much heat is dissipated by a single cell you can kill and several years later I'll try to give you more more information for this okay something else I want to say is I see the interaction in physics and biology like a two-way journey there are different subfields trying to say biophysics for me is a very broad thing but there are other fields that are related such as bioinformatics or mathematical biology or ecology which what they do some way some way is to ask questions interested interesting for biologists and use physics concepts to answer these questions for example how can a molecular motor move such big loads or how do birds fly in blocks it is something that biologists will be interested to know and then we can give physics answers to this but it's a two-way journey one can also say I am a physicist and I have physics questions and I want to use a full bag or a biological system to answer physics questions this is taken care of by a physical active matter or stochastic thermodynamics which I work or a biology and others example here one question is you can't read that is what is the heat capacity of our heat capacity is a physics quantity so how much heat a system absorbs when I change the temperature in the environment it's called heat capacity what is the heat capacity for heat this is a physics question because we say I know what is the heat capacity of water I know what is the weight okay but I don't know for me the biological system is another system that I can study so we do also this way and this is a typically physicist to this trip sometimes in the street it's very tiny because you have to enter a lab learn biology and be able to identify important questions in biology this is harder than this but it's also exciting and it has many very relevant for science okay just to tell you that there are different disciplines and they are different questions for instance this is a very growing thing active matter where you can see models of the particles that swim like this like bacteria but typically then you read a paper about that and see all the parameters are equal to one okay this you won't see in biophysics because in biophysics numbers matter so if it's important what is the rate the rate is one per second or it's not the same a motor moves and makes one step per second but it makes 100 steps per second okay so different directions different techniques and different methods and I will give you a little bit on about active matter I don't know how much time we have 15 minutes okay very good and recent experiments are insights and techniques in this field of active matter I just briefly introduced so first of all let me talk about classic physics problem which is called fine entratis I don't know who in this world knows what is fine entratis so fine ent in his book lectures in physics he he proposed this type of experiment just right possibility in which what you do is the following you have two thermal pads two boxes that are disconnected and these boxes can be had at different temperatures one is hot one is cold or vice versa inside the boxes you are on one side this which is called pain totally symmetric object and on the on the left side you have this type of ratchet wheel which is connected to a pole okay this is kind of constraining the motion of the box so the question is if we attach an object to the axis to the axis connecting the two thermal pads can we make this ball and we raise this ball another trigger question that Feynman found that if two thermal pads at different temperatures you can lift away by putting in contact to some of us and an object you can lift this object this may seem to you quite strange but it is somehow related to what a heat engine does heat engines contact with two thermal pads and as a result you can move a car it's a transfer of energy from here to here but not all the energy is transferred to this motion but part of it makes the ball move so the weight can be lifted this was Feynman's conclusion if the two temperatures are different so without okay without the second temperature the wheel does not move on us because unless okay you have someone who is rotating this here okay but we are assuming there's no one doing a torque in this machine so if we have this in a thermal pad this will not move will not have a net rotation in one that's something that I want to emphasize as well is that this is motion generated by fluctuations these are small objects in thermal pads and fluctuations are generated so this is converting fluctuations into motion so this was Feynman's conclusion that if you put a wheel like I take a glass of water and I put a small wheel there you don't expect that it will rotate right I mean why should it should be rotating unless if I do like this of course but I'm not going to exert a torque okay so some people some researchers um 15 years ago they said okay what if we put a wheel in a bacterial bath so we put it in water but the water is a dirty water so it's filled of bacteria so this is what happened this is the wheel the microscopic wheel is millimeters and happened to the for symmetric wheel in a bacterial bath the wheel rotates autonomously so you are using a biological system move things generate power okay now it's my question to the audience why this is happening why we have bacteria it rotates but if you put the same wheel in water yeah but I can put a laser and heat the water it's out of the equilibrium because it's dissipating out of the heat bacteria profound themselves forward and then someone gets stuck in these sharp angles and push the wheel forward yeah the other if they don't get stuck in the other directions of the same so you can see yes that's that's exactly one the bacteria are self-prepared so they we get stuck you said that they get stuck in this angle and because of the symmetry they generate rotation it's we are so generated by the self-proposal bacteria are not as small as water self-proposal they get stick here they self-prepared and then they press in this direction whereas in the other direction they escape free but the symmetry of the wheel together with the self-proposal of bacteria generates motion just to tell you that we can use biotic assistance to extract power to extract energy and of course this was really the the perfect science when the last year they they did something more advanced in which here's like a parking of I don't know 12 from 16 different bacterial enter and move this wheel and they could generate this in a you know larger scale these are a 3d printed ratchet wheel and they could do something much more spectacular which is a series of these wheels connected to each other that around you but it's it's only this is scaling and something that is quite interesting for for physicists and they can have even engineering applications it's not just that we burn the bacteria and we extract energy from this but then we can protein move things and that power so it's quite spectacular but it's one of many things so and I can as I was saying I've been studying quite a lot hearing hearing in the end is the following is the sound that enters the ear and this sound is transformed into an electrical current of course the auditory nerve and the brain we are studying this quite a lot we have a lot of insides but what is not so common this happens again this happens in the deep what we study is what happens the cochlear where there are this this tissue a field of hair cells this antenna I was talking about is this part of the large body cell ear cell and these are the final responsibles of transducing the sound into an electrical signal that then goes to the nerve that is connected here so this process is known quite well they are 40 years old it's the same but something it could be a big crisis what is instead of sound we shine light to one cell in the ear maybe it can stimulate a part of the cell and enter from this light in electricity like in photorethric fact may sound crazy but a little bit of this but there were recent experiments where they did this actually I know that the authors of the of this article and they told me it was just by chance so they started to see a cell vibrating on its own when they left the window open Saturday working in the lab so straight discovery but later on they did this experiment where they shine one of these cells with ultraviolet light and they can shine it in different regions so you can shine it in a small region of the cell like this purple or orange but you can shine it in a bigger region this and let's see what is the motion of the tip of the cell under this illumination and they saw that when you illuminate for a larger region the vibration gets amplified simple to amplify motion but it just shines light to the ear the ear it's not designed to use light sound but it's very fascinating and then they also started what they say that this is a process happening is exciting the mitochondria cell is generating electrical cuts and they also measure the displacement of the cell as a function of the frequency of the light and see that it's more sensitive to ultraviolet light so these are opportunities for PCPs and still many things to do and to study and I don't know how much I have five minutes okay I'm trying my best you're the boss so I'll give you five minutes let me see how many slides they have because to be honest I'm not I don't remember okay I think okay I think maybe 10 minutes so I'll give an appetizer about applications of stochastic thermodynamics in biophysics this is really a extremely growing thing so in five minutes I'll do my best and one of the first things that is going interesting for me is to find the non-equilibrium signatures of light so on the left I see an object that is back to it and on the right I see another object that is back to it and one can ask the question okay do you see any difference in the muscle of these two objects we have something special that's the same but what I'm showing on the left is a dead object so it's a colloidal particle it's a plastic particle in the water it's a passive equilibrium dynamics and the analysis is reversible on the right I'm showing a red blood cell like a disc okay red blood cells look like this and it fluctuates but it looks there's random motion as well but we know that actually we didn't know if red blood cells are equilibrium non-equilibrium no idea but we would like to use physics concepts from physics to to say things about is this alive or not and how much alive is this so it's not a real question you see now that here it becomes something and it's hit dissipation if it's not okay but we don't have a calorimeter which is so small and we don't have an ATP counter so we have to do what we can with this information let's see and sometimes things are quite complicated like this is the red blood cell fluctuating but in other cases you could look at a biological system that is clearly out of equilibrium this is a claming of mono which is a micro swimming which is using its arms to to swim and here you see clearly this is clearly a non-equilibrium system because it has a direction it has a current and in the motion of the arms it's dissipating and what is the difference between irreversibility and strong irreversibility okay here you don't see this weak irreversibility because difficult to see by eye okay it's not apparent okay here is seen by us you see you see it moving but I mean particle will never do this it's not moving in any way that actually but this could be the swimming in a burning particle but creating so this is not a find it is it's hard but hard problems usually are more interesting so um what is really an appetizer what people did and some research a good research group did was to trap one single red blood cell what they do they is to trap okay in reality they don't trap they trap four particles with laser that are attached to this red blood cell and then they look at how these particles vibrate in that so here there are two curves and in five minutes I'm not able to explain these two curves but one is related to the fluctuations so how these molecules vibrate what is the energy of the molecules during the equilibrium by okay the spontaneous vibration and the other curve is what happens if you take one of these molecules and you sorry one of these particles and you drive it you know for example a sinusoidal force then you look at the response of the red blood cell when you do this forcing and what what the researchers found is that the response and the spontaneous fluctuations are different this is a signature of non-equilibrium it's called the fluctuation response equation the fluctuations which is the spontaneous motion of the red blood cell and the response the external force do not coincide I'm not giving formulas but if you are interested we can talk later yeah after some time the red blood cell the activity it's spent on ATP and after some time so here is after two days they get the same fluctuation response and this is a dead so this dead in the sense not responsive okay in response because the there is a response but it's the same as the fluctuation response to a fluctuation when these two curves coincide it means the response to a force is the same as the response to a fluctuation and this happens after two days and here we classify the red blood cell activity is dead you see you can use thermodynamics to even 125 life so how a life is a cell it's a life cycle please okay in the y-axis it's the okay and when do we have it technical but this is the when you transform the correlation function it's called the power spectrum density okay and the other one is the imaginary part of the response function so you have a trajectory here it's pretty with work you have a trajectory in time and then you do the the power spectrum the trajectory so you go to the Fourier space in the Fourier space it's broken but this dissipation is broken but they are not the same when it's alive and it's recovered when the cell is dead so what you are plotting is the PSB of the movement of the SNC particle of the red blood cell is the PSB of the power spectrum density yes of the of the motion of the red blood cell of the red blood cell this phenomenon is called flickering of the membrane but you can notice type of technique in many systems for example in the headband there's one variable x and this was done and it was shown also that it's broken when it's alive and when the cell is dead you see this so this is really a way to classify if a system is non-equilibrium or like this and this was not known so it was not known that the flickering of the red blood cell was non-equilibrium until this experiment 2016 okay this is very recent six years ago there was the bench it's just a flat equilibrium pattern but it's non-equilibrium okay moreover these are data points experimental and this is a line that comes from a physical model you can use these experimental measurements to design and to try to improve models just for fun but you're kind of poking it to see the dead right you're kind of poking it to see the dead I know some is better meaning that they in the experiment you're kind of protruding it to see if it's dead or not yeah okay thank you thank you so much yes good point but just to say in the headband is we could do that without poking okay this is what I'm going to explain in two minutes like that I think it's hard you say I work on this for nine years okay I'm trying to be quick so this is our friend Lota question is station and it's the type of bullfrog from where we extract cells and we put the bullfrog inside the fight I don't know explain it I'm going to explain how they do different the bullfrog is sacrificed then a piece of the ear is cut and this piece of the ear of the cochlea which is very small it's put in a solution and it's put in the fix and then after some time you take this solution and you apply and you put in ions and being very serious and another instrument and the set starts to do like this so this is right after the animal is killed yeah but still cells are oscillating because inside the cells there are motors that consume ATP so still it gives ATP to that cell it's vibrate on it's own and one can measure with a fiber a glass fiber the motion of this top of the set will be X and okay as your colleague was saying you could be forcing the cell or you could be just looking at how the fiber is moved like this this would be not not poking right in your language okay and just I got this done then express so you may do a non poking experiment but you just look at the vibration of this spots of time and look at these threads this X versus time and you may think maybe we can see irreversibility here there is some directs on some irreversibility this is a bit difficult because if you look at the time reverse signal it looks very similar to the real one this is the real experiment and the other one is I'm taking and flipping in the out of time trying to see if there are differences and yeah right oh okay if there is no difference no it is dissipated yeah in thermodynamics we will say for example you have a sinusoidal signal then reverse is the same okay this is but that is reversible and I cannot see cannot predict dissipation dissipation is associated with irreversibility and when you see the signal to see they are quite similar it's hard so you have to fine-tune and do a very fine statistical analysis took us several years but we found a way I'm really not going to give the algorithm and it's related to pullback liner divergence course in the second week so we compared so we designed an algorithm that quantifies how irreversible is the signal and we compare different okay these are different cells it's a lot of money but this is just name for friends but these are different if we look at 182 cells 182 different quantities and compared to equilibrium fluctuation so you can have a negative control where you have a double one and a particle jumping in a clue this you can do in a computer tomorrow if you want it's very simple so you will have a signal going like this up and down up and down okay quite similar to this what we expect you're going to be okay it's not that the bullfrogs will have a double well this could come from a different potential typically the models do not use the well use something else but I would like to compare equilibrium with this algorithm and this algorithm showed that this pullback liner or measure of irreversibility when you take longer and longer information or longer and longer parts of the time series it goes to zero and here there's a signal in the equilibrium case and in the bullfrogs it goes saturates the value that is possible so you can really see irreversibility even if you don't perturb with an external force system not only that it's not only just no equilibrium but also you can quantify some of them are more far from equilibrium than others so these tools in non-equilibrium are useful not only to say respond to a binary question but to quantify and again over the last year there's been a big challenge of research program on estimating the energy dissipation at the beginning we had this simple algorithm we still ask okay we are out of equilibrium but it's very very little compared to the real heat dissipation which we can estimate from models but now when you have more than one variable so now we are looking at just the tip but what if you can also see the current the transduction current generated by the abandoned then you have two variables and instead of looking at signal in one dimension it's a signal in two dimensions where you can see like cycles this cycle is much more easy to see than this one I'm being very brief but when you have two variables you capture much more in the reproduction of much more specific assessment being very brief I'm just just to say that in the reproduction heat is the concept that we can afford to biology and it has useful information we are trying to to go into this topic in different systems okay and this was it by now of course you'll have questions you can discuss more thanks for your attention I don't know what to say but okay so yes thanks a lot and yeah I hope we can discuss in more detail about new stuff I have one information ah it's now after the break okay but let's make the break brief because all heads are engaged maybe I can reply to the question the motor the motor is typically I guess the short question to this short answer to this question typically the motor is sliding the roll is I don't I'm not aware of many motors that roll but typically they have legs and they they're sliding the frictional force is relevant yes and yes it's relevant as far as you know yes and typically the motors are over time over time dynamics but fixed that's it thank you