 Okay, good morning everybody. Now we shall start and today lectures will be the part of the school physics of life and a little bit attention will be paid on the biological oscillators. I am Angelica Hedrick from Mathematical Institute of Serbian Academy of Sciences and Arts and today I will talk about biological oscillators and exactly, especially two examples of it because it's a really wide area of research and you can really find a lot of papers regarding each sector of human or any kind of biological system as an oscillator. Okay, I'm my background, I'm a medical doctor, but I got a PhD in biomedical engineering and technologies so that means that I pass through some steps like cooperation with scientists from different fields and with the multidisciplinary and interdisciplinary cooperation and interaction so I would like to share some of my experience regarding that multidisciplinary. Okay, but before that, what is also very interesting and important for you as a theoretical physicist is to make the mathematical models of biological systems if you want to feel work in the field of biology. And there are some problems regarding working in this field. The first problem is, as I say, multidisciplinary and yesterday we have some questions about is it really possible to understand each other if you are from the different educational background and from different completely different areas of science, like for example, who's the one physicist, medical doctor and electrical engineering and for example, physical chemists or biologists understand each other if they want to do some together research on any kind of biological system. Well, it is possible, but it's not so easy. And it's not easy in a way to find people who will are willing to cooperate so the first thing is to find people who are open for experience, who wants to cooperate. And then, after you pass that step. All other things are much, much easier. First thing that you can understand it's that we are all let's say focus to our approach of the same problem. For example, if we have a cell. We can look at it as a biological object that is alive that could be killed that could be seen through the microscope that you can reproduce it in the cell culture, multiply and so on. Physical chemists, for example, will be interested for the same system of chemical reactions and their how they are connected and what is the input to the first product and the end of the products after the system of different chemical reactions. He will deal with the same system, but on a different way. And, for example, electric engineering will see the cell as a conductor or as electrical. For example, if you connect many cells you can you can treat it as a connected capacitors or, or, for example, if you have a muscle cell of the neurons you will treat it like electrical wire or electrical circuit yes electrical circuit so it's a different approach. And let's say the medical doctor will also think about if he's from the area of genetics, what are the genetic basis of that is this health cell healthy or it has some kind of chromosomes aberrations or numerical doesn't matter so this is all the different aspects of the same system. And what is also important that the biological systems are very complex system so the complexity is one thing that it's really interesting and fascinating to explore, but also in order to understand the system we have to divide it to many. In many aspects actually, but in the end to understand the system, you have to connect all the knowledge together again. So that is why very important actually bikes so much trendy let's say that kind of multidisciplinarity and interdisciplinarity. And what is also, but in the, if you want to model certain aspect of the system. You need to do the simplifications and approximations of your model. And in that kind, as a physicist, you will use equations and some. Phenomenons already exist in the physics in any in the whole field of physics so what is the point of physics physics is very interesting field of science because it can cover everything. So, in the period of phenomenological mapping, you can use the same equations to explain different processes, especially different processes in the biological systems, but what is important to use the right one. And that these equations have some kind of biological meaning so it is not just the math that you can do in a virtual space, but also these equations have to represent the, the, the, let's say natural the force of the nature, the law of the system that will be applicable for most of the time. And in that case, I would like to, I remember one, one joke regarding mathematical biologists because it's like that, like this. So, there was a pharmacologist on the some mountain and he saw a shepherd taking care of the ships and he said to him. If I, yes, how many, how many ships you have on this medal, you will give me one of your, your ships. And he said, okay, it's okay and he said you have 20,000 ships. Wow, he was completely astonished exactly because every shepherd have to count its sheep and to return it to the home and the mathematical biologist take one of the animal and put it on his neck and go away. And the shepherd then told him, you are, you must be mathematical biologists. And then he was really surprised how one simple stupid shepherd could guess what is, what is he by his education. And he asked him, how do you know that it's impossible. Well, you're carrying my dog. So, I want to tell you that in many cases, mathematical biologists are completely have no clue what are their model. So what are their, their modeling so they know the equations, they know the boundary conditions, the results, the limitations and everything, but they know what are their models. I would like to, let's say, pay, pay attention to you not to do that. So, because it's not a good way to understand the science. So you have to make an effort to at least 10% understand what you're modeling. And that means that you have to cooperate with the, let's say, biological part of your team. And at the first to know what are the terms you're using for the same thing. So that is the crucial to have the keywords, the different keywords for the same thing and then you will understand each other. So, also, when as the model is simplification of some biological system or the process, no matter if it's healthy system or system in disease. It has its limitations. And when you write the papers and describe your system, you have to tell the readers what is the limitation of your system and what will be, for example, the future. So how you can overcome those limitations in the next step. So nobody can create in one moment the best, the perfect model. So there is a time that you, let's say, improve your model step by step, and it's okay. So nobody will blame you because your model is not perfect. Regarding the accuracy of the model, I would like to mention some papers, which are, let's say, they're good in a way they did everything methodologically correct. So this is one example regarding but what is the problem I will tell you at the end just you see pictures. This is a matrix where you put your tissue that you could use in the lab is very dense tissue and it is you produce actually artificially the cancer tissue of some kind. But you make it too dense and then you do the research on the dense tissue regarding the perfusion of some drugs and how this issue will react regarding the concentration of the drug you put in. Is it going to be destroyed on what places and to find the equations for the diffusion in the modeling part, but what is not correct in this so tomorrow on a chip also is one of. Okay, so what is not correct in this experiment, although many money was in this and many effort was put also in this for all the researchers. You've got the nice photos and nice pictures and this, let's say, is good for someone who is financing your project and to go to the ground, but those were, let's say, evaluated this money are mostly most in most cases are not people who are doing science. They don't understand this and understand that you can call pictures, you do something, wow, and you can postpone and bought more money for to continue your research. But the basic problem about this research is because if you have such a dense issue. First, first of all, no tumors have such a kind of dense tissue because tumors firstly have a need a very good nutrition supply, very good vascularization and very. They don't have blood vessels inside they would the tumor tissue die so making tissues so dense would not firstly corresponds to the real situation. Secondly, it won't, what is the point to make perfusion in a dense environment. The nutrition and the drugs won't come inside. So, at the first time you are the main parts of the experiment are wrong at the beginning. You do not mimic the natural thing you create artificial something which will serve for nothing so all the conclusions you will get from this research won't be applicable in the future, or for the medical doctors for the biologist to do the part to find the pharmaceutical solution for certain humans. And also the same very interesting research. So what is the point, the point is you can do that. But the conclusions are valid only for these experimental treatment, not, you cannot conclude, you could not transfer the same conclusions to the biological system. And this thing in this paper, there is a, let's say tumor in a chip project that you completely artificially in the lab or the tumor tissue. And then you do the experiments on the issue you are using the lab. Also, you have the same conclusions only for your experimental set. Humors in the biological systems are uncontrollable in most cases, and they adapt very quickly. They can escape the effect of different drugs very quickly. You have one through three cycles, and patient is not responding to the drug, like you do not need any kind of medicine, any kind of drugs, but you have the side effects of drugs on the healthy tissues, you know. So this is also the question, should this model be the right, the right model for the cancer therapy and the cancer research. And of course, you can do the modeling theoretical one for this experimental setup. And that will be, let's say, valid for this and similar conditions. This is also the same story about the printed printing of different type of issues and experiments on them. Actually, this was made to escape complicated procedure of getting alive or cancer tissue from the logical center or from the surgery, because you have to. In some cases, for example, in Serbia, you do not need to ask for the patient informed consent if you use the material is already in the protocol of the treatment. So from the pathological department, you can take everything you want, but from the surgery, from the surgery before it comes goes to the pathological department, you need the informed consent of the patient and it's time consuming and sometimes patients from different reasons not want to give their issue or their are extract from their bodies. So this is somehow alternative of the research, but the accuracy and the validity of the conclusions are very important. One very interesting problem. Okay, it's also the problem but the example is interesting at least for me. So, you got the results and they're negative, they're not what you expected to have in the experiment, but you claim it's good and it's okay and you somehow put all the results you got in your research, but in the conclusion, because it's negative, you know, you somehow say it's good and it's promiseable and so on. And there was, when I start my PhD, one of the idea for the PhD thesis was the sperm encapsulation in order to let's say improve the IVF treatment for infertility. So the point was then to put the sperm cells when they are fresh in the beads made of alginate and then to apply as artificial insemination and the point was that the alginate will melt in the certain time points, you can actually program how the tick will be and how long it needs to melt to have the exact time of ovulation and then you can then have increased let's say the percentage of successful in vitro fertilization. If I've mentioned some strange words, please ask me to explain, so because I do not have knowledge if it's strange to use it's familiar or what. Okay, so, and the point is what was that you got the sperm cells from the human population I actually did not have from the population. They have from peat from cow, and yeah, vegan cow and of course was these three species that were experiments were carried on that sperm, and the point was, you put that in syringe and you have, let's say, the alginate is also met and you mix them and you have the electrical extrusion and you make the small drops of the encapsulated cells. But the point is because you use natural marginate and in the solution it was a calcium, calcium ions and then when they react there. The point is that that calcium, not harm the sperm but it does not prolong its life in in the in the beat, because calcium are important for this firm. Let's say maturation process, and if you put calcium, they will speed up their maturation process and they will be, and the point is they could not live forever, they have limited the lifetime and if you do not if the fertilization does not happen in that time they will die, and you have nothing so. So, the experimentally, it was not correct. And for the other thing, in order to check their vitality, you have to actually melt the, the alginate beat. And the point was you have to steer that and they have to wait so you actually expose the cells to the forces and actually harm them so they leave less than in the solution that was already commercially available or you can mix it in the lab. So the incubation in that case was not the right solution for the purposes they, it was intended to, let's say, escape that calcium. They want to get some of the researchers use barium ions, but actually the barium ions are toxic for any kind of cells, especially for the sperm cells. So, in that series of very promising papers in the end you have just a break and nothing after that. So, it is very important to carefully read the papers. And especially if you have to model the biological system, you need at least some basic knowledge about how it, about the anatomy about its function and to ask for the parameters that are important for your equations. Are there, is it possible to measure some of them experimentally so that you can have the right model. So the sperm incubation fails and okay. Yeah, this is what I want to emphasize so purpose of the research. Is it useful the outcome of the research for the doctors and clinicians that kind of models does it save money does it predict something that is still not found. And the most important is it bring the new value to the science. So, there are many, as we spoke yesterday on in cance in session, is it bring new value to the science. So, publishing, publishing, publishing, but in some point all that knowledge have to be synthesized in some conclusion, and to make the further step. So, in that moment that you have so many papers that does not bring new value to the science, you have to change the paradigm of that problem. You have to think on a different way, outside the box. And that's why it's very important to be open for experience to hear how someone is seeing the same problem. You're here from the different countries from the different cultural background and different, maybe not so different educational background that that means that all of you have something that is different. That will bring the new value to the team and new value in the in the end. Okay. Yeah, publishing negative results. This is maybe in theoretical physics, not so typical, but in medicine and biology is typical. So, it's very important not to go that way, because we know it's negative so find another solution. Okay, biological oscillators finally. Well, there are many examples. As I said, the biological systems are very complex, and because they are non linear. And, as I said, you can use the same equations to explain different processes, and we have many. Let's say, we consider one human being is consist of many cells many systems and they all have to work together. Like, for example, the bio rhythm of our sleeping, the level of the hormones, the, our heartbeat. They're all the same that the circulation of the blood, the muscle contraction, the neuronal neuronal activity, they're all actually examples of the biological. So they have their phases, their amplitudes, their frequencies. And, of course, here we have the dumping effect. As Edgar yesterday mentioned, you have to put the energy in the system so the human system is an open system, it's not perfect mobile mobile. You need energy of any kind of source is going through the food through. And it's influence and what is the point it's in equilibrium, but it's dynamical. So you have the oscillations and you have certain values when the system function functioning it normally. So, if that value is down or up system is not in the equilibrium and it brings you to the disease. So, what you can use. Typically, the oscillators that are used in modeling is a simple harmonic oscillator, the equation, you already knew, and the solution, and we have the frequencies for the angular frequency and ease the string constant. You can also use the damp harmonic oscillator. And this is the equation in this form for this form. And dumping ratio, of course, driven harmonic oscillators also can be used their equations in different forms. Okay, the solution. The most used one is duffing cost later, which can actually cover the dumb harmonic and the driven morning. So, and this form is really typically used. What you have to find you have to find more water delta alpha and beta in this, in this context. And so it could be undamped. And this form or damped and has this one. What is also important when you have the biological oscillators and not just biological it is synchronization. So how they work together, do they have a delay. Do they synchronize fully. What are the, the, the examples for the synchronization as I mentioned already it's a heart rate respiration frequency, and then muscle contraction and neuronal potential. And then hormones typical is the typical example for the hormones is the master cycle and you have to synchronize very smoothly very precisely. Different kind of hormones like astro genes like a chemical stimulating hormone like hormones of the hypothesis. And you have the outcome on many different organs in the system. So, if you do not synchronize then you could not predict the moment of the ovulation which is very important for fertilization for the future and so on. And yeah, the also examples is the cell division. We've heard in Monday, you've acknowledged was talking about the methotic spindle, but it is just very complex structure that is very important for the cell division cycle so without methotic spindle there is no cell division, but also without nucleus, it's not, we don't have, we do not have cell division. And maybe at this point I would like to emphasize that all these steps, all these phases, you know, here, here, here, here and finally here when we have methotic spindle, it means that chromosomes and genetic material and the organelles inside have some kind of nerve and some kind of positions. I mentioned that now because I will tell you about our model of methotic spindle and importance why we model it in this way. It's not perfect, but the point is the way you are here. You know, you are sitting more or less the same as the first day. This is going to happen the same story with the chromosomes are going to move on the same, exactly same on the same way to align to have the same neighbors during these processes. We do not know that. So, the arrangement of chromosomes for now it's stochastic. And what governs these movements on this specific way, we do not know. Also, what needs precise synchronization is environmental development. So, and the crucial thing in this process of development is, okay, we have the DNA and some kind of program that governs all the steps precisely what will be, what will be done in certain phases of the development exactly. And this is, let's say, the area of research of bioinformatics, bioinformatics or genetic informatics, but still we do not have a code what governs this. So, what we know, until now, it's that that alignment of cells, the microenvironment of each cell actually governs that kind of differentiation. In this, what forces are important, not just the mechanical forces that are happening during the alignment and changing the position of certain cells but also the electrical forces, the chemical reactions not just in the cell between interaction between many cells. So, we have many events. We have many events, but the same event is covered by many, many fields. So, that's why, in some part of the modeling you are talking about coupled fields, coupled electrical mechanical and chemical field, at least to explain the same process. So, I'm now going to talk about two examples of the oscillators, one is from the area of reproductive biology and interaction between both sides, the female reproductive cell and the sperm cells, the male reproductive cells. And to, let's say, explain how the dynamics between their interaction could be treated as an oscillatory phenomenon. Okay, here what you can see is the outer surface of the oocyte, and yeah, what's also important before I start to explain. In the natural system, oocyte is covered with the, each cell has the membrane and oocyte is covered up above the membrane, there is one ocellular structure that is called zona pellucida, the pale zona, and it is some kind of a gel. And above the zona pellucida in the natural system, you have other cells that are forming corona radiata and they help somehow in the process of fertilization. But in the lab, usually in the process of in vitro fertilization you remove the cells to increase the, you know, to increase the chance for in vitro fertilization. Okay, but they're also important they have some immune roles and so on. So, the, the experiments are done on all side, which are, in which are removed the cells. And so, the story will be in this case, and there are many papers that are discovered the mechanical experimentally and theoretically, of course, the, they discover the mechanical properties of oocyte pellucida, their 3D structure and their chemical components and so on. So, what is the conclusion regarding all these elements, it's the structure, it's not like structure, it's not like structure. No matter if it's oocyte of the cow, of the pig, of the human, of the mouse, of the horse, it has more or less structure like this. And it has, let me see, you see the mouse that calls like this. So that means that the sperm cell, here is, this is the mouse sperm. So it has like this little hook, and it can attach to this net, and it can back the net. But, so what is also the structure changes its mechanical properties during the process of maturation of the oocyte. And after the fertilization, in a way, it is one. In a way that it is first soft, it is first hard, and in the moment of fertilization, it is soft, and after the fertilization, it again gets hard. And at the moment when the oocyte, the fertilize oocyte, the zygote have to attach to the uterus, it vanishes. So it escapes, some kind of catching outside. So the group of scientists use the, that's changed in a mechanical properties to attach a chip on the surface of the oocyte. It's a microchip, you see, and it is also on the embryo. And the chip is made of silk. During what is also fascinating, regarding the different levels of events on this structure. So the changing of the mechanical properties is actually followed by the chemical reactions there that are occur in order to collect molecules and synthesize them and put them in this structure. Actually, connexious has a lot of sulfatized bones, sulfur bones inside and so on. So, these are some of the curves that represents the elastical properties of zonapelucida. This is in, I think in the horse. So before and after fertilization. And, okay, the values of different methods of probing the mechanical properties are also different and so on. But the conclusions are like this. So, no matter of the value of the parameters. So, that's why for my PhD thesis, I came to the conclusion that it will be nice, let's say to model this structure as a net structure, because it resembles like a net, as we saw on scanning microscopes. And that we can use the chain systems with the molecules attached with the masses to, let's say, theoretically and numerically discover what will be some, let's say parameters nice to explore like, like a number, how will the system oscillate the net, how will net oscillate. If it's one layer, of course, the approximations are you will hear the approximations or that it's one layer net and it is very good and connections and the arrangement of molecules keep the molar ratio of the structure elements of the zonapelucida they have in mouse they have three different type of that kind of molecules. And the point was how the system will oscillate if you put the external force, and you think you are approximated external forces, the impact of the sperm cells and you then can vary the number of the sperm cells, the their frequency and the movement, would these parameters influence the oscillatory state and the way of oscillations of the structure, because the, we want to propose that actually the fertilization process will be considered as an oscillatory process and that the fertilization occurs in the moment when one of the sperm cells has the same frequency as one of the eigen frequencies of the zonapelucida molecule or one area one part of the structure. Okay, these are already existing models. So half space model layered model shell model and so on. They are based on their experimental results of the micro pipette probing. And here is also the Hertz model shadow model. If you want, I will, I will send the papers regarding these models together with the abstract of this. Also, yeah, what was so you see that this is from scanning electron microscopy and this big one is a whole site, and it is much, much bigger it's it behaves like inert mass in this system. It doesn't move and it is assess cell. So this big compare it is the biggest cell actually despite neurons but in humans it's 100 micrometers, the metro site, and the sperm cells are very small and very tiny. As you can see, like this, their dots, these dots are actually attached to the surface of the whole site, but only one will pass in physical conditions. In natural conditions, you could not actually, in reality, have the fertilize act just once. So it's not possible. It's possible in the lab when you put in the needle once firm and then inject directly to the outside and put in this. But in that case, when you do not have nothing, just one. The natural selection is off. You do not know what is the quality of the genes inside the sperm cell you put into the egg. If it's good if you look the first and the second division by looking at the microscope are there the embryo is healthy. You transfer that so the biologists will decide if this embryo looking at it for the microscope, the number of the cells they are shaped they are how they look like in between. So this embryo is healthy we can transfer it and expect to have the healthy offspring. But in the nature to have normal, you need the minimal quantity of the sperm cells for the event. So some parameters, as I remember, were 20,000 per millilitre. So less of that their problems in humans. And what is also interesting that that number of the normal sperm. cells in in in a collage is decreasing as the development of the world increase. So it is a negative in negative correlation. Why is it so way of living food of eating. It's not clear. So it's just the speculations what is what causes this but for the, let's say, average human in 21st century it is 28,000 per millilitre. And why is this important, because if you have also in a petri dish you need certain amount. We do not know what is the way, as Rafael yesterday said, which one she choose, we do not know. What are the parameters. Is the outside chooses the best the the fastest one. It should be because it have come. It's not speed enough. Others will come, but also there is a theory that you need to move the mess to change the, not just the electrical charge of the outside because it's involved in the process of utilization, but also to have some kind of cover all the receptors on the outside surface, and also from the physical point of view. To have enough genetic energy transferred to the outside to change its conformational structure of the of the envelope. So that's why probably the amount of the sperm cells are important. So they all contribute it's, according to my opinion that all the all of them contribute to the specific oscillatory state of the whole site that is necessary for the fertilization, but only one will come which one we do not know what is the kind of selection that would not know if for now it's the history, but is it also important, the, the, the structure and the weak spots on it. And what are the parameters that we can use to determine to determine the determine what is the weak spot, how to find the weak spot. This is, this is to represent that equal distribution and non equal distribution, and each of the sperm cell will have specific impact to the outside. So, there are one or two or many possibilities for this modeling and for this outcome. Of course, if you use symmetrical one you make yourself easy for the calculation, not too many complexity in the system. So these are the approximations model. So chains cross sect. This orange should be the zp one molecule and blue and green are zp two and zp three. The arrangement. Yeah, they're connected like chains and they are can oscillate in meridian and equatorial direction so in both axes and in a radial direction, because they are attached to the surface of the surface of the outside. So, I will just mention that we got the different during the modeling. Actually, the results were that the sperm number will give you different different different outcomes of the reverse of the molecules that are oscillating in the simple quadrant of the simple one segment of the net. So, if you have four of them, if you have three of them on the knots acting on the knots on the zp one molecules or just two. It is also important of their symmetry but it is due to the model is due to the model, and if it's one. Also, you can use a different approach to this problem. So, to model this on a polluter not like a net but like an empty shell and to have the symmetrical distribution and then to calculate the not the forces but the the formation work of the structure and then you can have the different values if the zp structure is thicker or is thinner because it is also important for the process of fertilization. So, if it's thicker, then you got infertility if it's the right. It's usually happens with the in in the biological system it's not thinner than it's usually frequent more frequently happen that it's thicker for example if you're the women smokes and it has thicker or side zp is on a polluter and it could be one of the reasons for the it's not causal but it's somehow related and the years. These are the graphs of how the the thickness of the zp can be related with the with the deformation work of the structure. Also, this work was was done with my colleague mechanical engineering during very good in answers simulations and so on. And we did this modeling in his lab. It was to model the contact of the one sperm cell to the whole side. And we model it to be the friction contact so it happens in the liquid in the water. I mean liquid that liquid has has parameters like water and what will be if we change the angle. So, what is the because there was one paper very nice that asked the question. There were models that test what is the force that one sperm cells will transfer to the whole site but they all use that it is a perpendicular. So, but the experimental results when you can see it's not perpendicular in the when you see through the microscope it's like with our so if you have, for example, this is the whole site and it has oblique back. And we want to explain this so it's not corresponding the theoretical and the the experimental results and I think it's for the bishop I also send if you are interested in that paper it's very interesting. He was explaining the story why it's oblique back because the sperm cell we're trying to not to have because when it passes it doesn't makes a call is not formed so it passes and everything is then healthy covered there is no hope from that so it passes really smoothly and what is the reason and through this modeling we actually found that that if the angle is smaller so the force is less and somehow the sperm cell is using and and the the formation and the the formation of the structure is less and the force that the force that all side is making as a reaction of the penetration is less so somehow you know the sperm cell have to sneak inside if it's too hard it will make the outside to resist and this is what is confirmed by the probing experiments so if you press it so hard then you got the harder response if it touches gently and it's softer so it somehow yeah like you are dealing with with women so if you are you know pressing too much she will just kick you out if you are no find the ways to find the right way to her heart then she will let you to forgive you the opportunity I'm joking but it is really corresponding you know and yeah the it's not just the receptors but it's also that the force the resistant force of the it's not be so we then change the angles and and what is also important it's honest from my side to tell that that effect on the surf it's really on the surf superficial so it's not impacting the set of pleasant we use the parameters from the experimental results we use the model the shape exact shape from the anatomical articles where you have the anatomical numbers of the sperm and so on and when you from the articles that measure the speed of the sperm cells so the speed is also connecting with the quality of the sperm and also a lot of questions arise from this because we do not know if those who swim faster have that kind of angle we do not know that still so is this correlated if they have some kind of better attachment we do not know that and since the data we obtained also the angle was related in this simulation with the time of decreasing the speed of the sperm cell so if the angle is lower it's for the 10 degree it decreases but at the end it could last longer it loses its speed not earlier but before it after it the sperm cell need more time to lose its speed and its quality the angle is lower and if the angle is 90 degree you see very fast it goes to zero and this graph represents the zippy stress equivalent zippy stress and during the time regarding the sperm impact angle so the shapes of the curves are more or less the same but for 90 degree you see it's not that we got the results they are black and white so certain combination of the parameters of the angle and the speed can give the positive outcome but it's not strictly this or nothing okay yeah and you can use the relaxation we then propose that the mechanism of penetration could be the oscillations of relaxation so come and go and then make that oblique path smoothly as I have yeah so what's also the point I would like to show a short movie super polysperm block I could not I mean it's really short time in one hour so when the one past then the changes in the structure first electrically in the first place electrical change in the zippy structure and the change its stiffness and make a block that any other sperm cell will be repelled so this is very important it is study mostly on the sea or him and it is important because the quantity of genetic material stays the same in each generation so there is no polysperm once one complete of the genes from the mother and one from the father and that that's important it's made this is first record in 2012 by the Japanese group of scientists and they so this one the leading sperm will penetrate but this will stays outside and you can see here there are much there are a lot of them it's penetrating but it will be moved apart so it is electrical event that goes in fast and slow and so on it's also a very very big story and as I do not have time I will then just mention okay you can then study to synchronize you can use a different approach to studies on a polluted up you can consider it as a mechanical responsive polymer since it has such kind of a structure like an analogy with other mechanical responsive polymers and we did not make such a model so if you're interested we could do that together also it will be interesting to to study the terminal effects and the whole thing from the point of thermodynamics so it's neglected in the research of this structure but is very important I planned to speak about an oscillatory model of the topic spindle but yeah the time is short okay yeah we speed up so arrangement of the chromosomes is it stochastic or not how they arrange is the frequency of the centrosomes the structures that organize all these topics are same or not they're very important it's one organelle that divides before the process starts make its position in the cell the opposite on the poles it's not always symmetric on the poles if it moves that will govern the that alignment and differentiation of the cells actually and also the chromosomes do not have they are different size they carry different quantity of genetic materials and that genetic material it's not active equally on each of them actually the genes that are active in the process of mitosis are only related to the mitotic apparatus so the other genes are not active they're packed in chromosomes and they are inactive in order to be transferred to the new cell but genes which are active in that process are related to the mitotic and there are many many many proteins not just microtubules not that just centrosomes which are discovered by the molecular biologist by the genetics and it is not always clear what are their functions so what we have we have separate research for different molecules and it's hard to model the whole structure and their models can explain how the steps are made how the microtubules are extend how they are elongated how they are shortened what are their mechanical properties and that their mechanical properties differs regarding the phase of the cell cycle so they're not elastic equally in each phase okay so that's why we want to make one one okay I would just mention so the model consists of it is imagined as a system of popular oscillators these are centrosomes considered as aerodynamic centers of oscillations so they generate the oscillations we don't know how but we make the model so these are oscillation stars here and each this is the pair the sister chromatids they are going to connect with the spring that represents the chromatid fiber and this one are also strings that represents the microtubules connected to the chromosomes and then this one can be modeled not just the spring but as a viscoelastic elements and you always consider it as a max model depends what you want but you can model this as a viscoelastic elements because they change their elasticity during the process of models and the point is well this can divide and how this can elongate and what we I would just mention this and maybe we can stop and if you're interested during the break the point was to calculate the energy of oscillations and to find in which conditions this will bring this will break and that we consider that the resonance is the condition for breaking but if something can be right here and then we have the chromosomes aberrations also in this model we change the places of chromosomes in the center put the most heavy and then to put the others the lighter on the periphery of the methotic spindle and this is model that is valid only in the metaphase only when the chromosomes are aligned like here and we go to different results and we go different results when we have equal frequencies of and they're different so the oscillate the energy of oscillations are not the same so I will just skip this yeah so you have curves like this it's separate for let's say first 10 were in the middle if if the center zones oscillate with the same frequency so it's oscillatory but the amplitudes of each the maximum amplitude is the same but if the center zones are are not oscillating with the same frequency you have energy is more or less the same pattern for potential and kinetic energy and for the total energy and what is also important that potential energy contributes according to the model more than the kinetic energy to the system and what is also important when you put the heavier one in the center you go to the lower amplitude so the energy consumption is lower and we believe that the system is governing by the minimum of energy spending but we do not know that so we need experimental tool so for now it's a fair deal that is based on the experimental data and of our modeling but I have to be honest this have to be proven okay this is improvement of the model because one of the reviewers mentioned okay your system is in vacuum that's impossible where is the friction forces so we add the friction force and we consider that the set of boson is highly viscous fluid with a little slow manual number and yeah we have to prepare this it's new the numerics but what is also important what we want to to prove so it is also the hypothesis that if the chromosomes have to move in such a dense environment that will last forever so probably there is some kind of a trick maybe also oscillations of relaxation or another kind of trick the state of the because the cytoplasm is a net there are other many models inside it's changed it's probably it changes its structure during the cell division otherwise you could not move you imagine that you're moving through the air and you have to go to the swimming pool like this and you have to move so your your speed will be less it's also for the chromosomes right yeah and we want to find a way how to measure the energy does the energy of the whole cell change so like you have in the room so each of one is in each position and have some kind of energy if I make a photo you will be like this so I have some kind of thermal print of your positions and if you change places and I mark it the question huh okay okay which kind of coupling between us is generally considered to study me don't explain in this case in this case the coupling is by the center zones so it's not it's not you know parallel connections like in the circuits or or or along so they're coupled by the by the renomic centers that's the coupling sheen scheme I skipped them they were in the in the okay so then may I just show the slide where are the installations the equations of oscillation I'll stop right just a minute okay okay I will close this okay so I skip this because of the time but these are the equations that this is for the velocity of the upper and the chromosome the system that is down and this is the equation that describes the elongation of the the chromatin fiber that interconnects the two sister chromatids and when you put this in the kinetic energy you some actually the whole canal of each of the oscillator in the system and this was done for their 20 because they're 20 in the mouse cell and the data was used the masses of the chromosomes were used for the mouse cells from the from the testicles because there will be only data available in the literature that we found for the mass of the chromosomes and then you then you some the kinetic energy and the potential energy of each one plus the each chromosome sister chromatids plus the potential energy of the interconnected chromatic fiber so these are the equations of motions if one isn't I skip them because of the time I believe we had one question okay okay one more question and then we can continue during the break is it okay yeah please ask now I mean we include that in the met through them so chromosomes are treated like masses with the spheres so you yes we do not count their shape because the shape will also be important if we have a model where we treat the city pleasant as a as a viscous fluid so then the shape moving in the fluid will will will have the impact on on the energy and the oscillations and on the friction force also so in this case we do not treat that the chromosome itself is oscillating so it's oscillating through the whole system like a mess that is moving along the mic microtubule fiber so yeah that was the approximation also that will complicate the model that could be a stochastic model if if they are assumed to be stochastically aligned in the yes in the core okay I'm really sorry because okay thanks for your nice presentation well mechanical party I would love to have this light okay I will send yes yes yes yes okay okay thanks for suggestion okay okay I will send the presentation thank you thank you everyone for listening I hope can you repeat again please graphs the same pattern but it is the sum of it it's for each of the oscillator in the system it's not for the total so each of the so each pair of sister chromatids they are connected in the metaphase and through the microtubules and the renomic centers the center zones so the graphs you are shown is for each of these of these 20 for the mouse chromosomes and yes they show the same because you know mass does not contribute much because it's really slight difference between masses of the chromosomes what contributes to the difference is the angle the position of the chromosome in the structure according to the model and we assume that that angle is not changing during the metaphase and analyze of the cell division so when it takes the position in the metaphase plate it's keeps the position in a way that it goes to the one or to another centers impact we saw that Eva Tollege show some animations that in a 3D so this is the planner model that assumes that the position of the center zone does not change that is not rotating during from when they start from the metaphase plate to one of us when they separate they do not change that position in in a plane could you louder a little bit no no no just be louder I did not hear the question okay they have the same pattern yes in the way the amplitude such as different that means in general sense it means that the pattern of oscillations and the type of oscillator does not change during this process so but I could not tell you in the way for this for example this will change if the if the central zones do not oscillate with the same frequency so it's some kind of nonlinear pattern and what will in the biological system different week frequency will mean that that the cell division exactly won't won't be exact in a way okay let me find the right words so if if you have such kind of a pattern compared to this one this difference in frequency will change the position of the cleavage plane it could affect the differentiation process so that alignment of the cell the smooth positioning also we believe that the array if arrangement is different so if you put the heavier chromosomes in the center you will have the different energetical the amplitudes are different the pattern is the same you're right the amplitudes are different in the way compared to this situation when you put the heavier at the at the side so that kind of difference the positioning of the chromosomes can change the energy pattern of the cell but what really happened what governs the different position of chromosomes in the cell during cell division you will not know because you have some kind of 27 percentage of the same same alignment of same chromosomes but not in the hundred percent so for example I'm going with Bogdan five times we are going out five times per week but two times I'm going with someone else why we do not know I mean that's similar with the chromosomes why it's not always this way there's some law that is still not discovered which governs all the process and at this moment we do not have the equipment to measure the energy of the subcellular structures to let's say validate the model or just the theory correct the model so let's say this is what we what we obtained through the model through the equations and through let's say the theory of elasticity theory of mechanics on the macro scale yes on the surface of your side actually they put with a tiny not a needle but the FM yes this was not the FM I have to check I have to check is it imaged by the FM but I think no it was by the scanning microscope FM does not give you such kind of high 3D structures density I can send you the article just yes not in each case if you if you do the probes in the water in the liquid you keep a cell alive but if you put the cell on the microscopic plate you kill the cell actually but how to put the chip chip is measuring the mechanical property of the cell and chip is detached after certain moments so it was you know to see if the surface is rough enough to catch the chip and the chip to stay and it's roughness change as it changes maturity or the fertilization and this was the embryo and this was the embryo so they put it with a tiny inset through the microscope and just lay down I can send you the article it's not an FM it's not an FM it's not the FM I think it's a scanning probe microscope I would I am not sure because it was not going to go so I will check now send okay I know for messages and I would call it you thank you very nice work it's okay thank you very much very much also