 to solitons and nerve signals. We're looking forward to that. OK. Thank you very much for the invitation. I got a mail about two years ago from Irio to Sati about the tribology conference. I had never heard about that term before in my life. So I didn't know what it is. No, I know it after a few days being here. But I still don't work with friction so much. But I work with thin layers. You see a thin layer in my brain. It's only about five nanometers thick. And I somehow believe that the processes that I'm going to describe are more or less frictionless. And maybe you can tell me why that might be so, because most people would expect friction there. But in some sense, I'm a black sheep in a herd of white sheep that know what proper science is. And I have refused to include friction in my talk so far. Another part of my topic is nerves. What you see here is a nerve cell. You see these long cables in the nerve cell. And these little blobs here, the white lights, they seemingly represent nerve pulses. You see if you find hundreds of drawings like that on the internet with nerve pulses that are extremely small. However, a typical velocity of a nerve pulse is about 100 meters per second in a motor neuron. It lasts a millisecond. And you can easily calculate how long a nerve pulse would be then. So 100 meters per second times one millisecond gives you 10 centimeters. So that means a nerve pulse is actually big. It's macroscopic. And these drawings are all wrong. And another thing that's important is that this layer is very thin. The membrane is made out of lipids. Lipids have polar head groups and A-polar chains. That means they have a thin layer with an insulator in the middle. And they, therefore, form very good capacitors. So that means every kind of deformation that I described in the following will also affect capacitance of the system and cause electrical phenomena in these systems. OK. About a few simple facts about nerve pulses, because I assume that most of you are not familiar with it. First of all, the most commonly known signal in the nerve is a voltage pulse. So that means that the reason is that most people use electrodes to measure nerve pulse. They don't use thermometers or AFMs to measure that because it's more difficult. And that's why there is this unjustified assumption that a nerve pulse is something electrical. But it is something else that happens as well. If you put a nerve under an AFM, atomic force microscope, without scanning it, just leaving the cantilever on the nerve, and then you let it fire, then you see a dislocation of the order of a few angstrom up to a nanometer. So if you really get in good contact with a neuron, it's a nanometer. A nanometer doesn't sound like very much, but if the membrane is only 5 nanometers thick, it's 20% change in thickness of the membrane, which is actually a significant signal. One of the more puzzling results is that there are temperature changes in there. This has been known since Helmholtz 200 years ago that it is impossible to measure any heat that's dissipated in the nerves during a nerve pulse. So what is measured is temperature goes up and goes back down in exact, in phase with a voltage change in the system. And if you integrate over the whole heat release over the complete nerve pulse, you get a heat release at a 0. That means you would conclude that it is an entropy conserving process. So that means that the nerve pulse, seemingly, is an adiabatic phenomenon and not a dissipative phenomenon. I could talk for a long time about these heats. That is this absent of a heat over the nerve pulse has puzzled people for more than 100 years. And there are many studies that have investigated that. The nerves we work with are partially from lobster. So this is part of the brain of the lobster. That is the first ganglion. There are big strands between those which are called the central nerve. If you cut the central nerve open with a small pair of scissors, actually a lot of small neurons pop out. And these are what we typically consider as nerves. So this thing is rather a nerve bundle. And most nerves in our body, like the median nerve or the ulnar nerve or so, they are nerve bundles. The single neuron is a part of a nerve bundle. So we made the AFM experiment that I showed you earlier on this single neuron here. It's very nice for a physicist to have such a neuron because it's big enough that you can see it with your pure eye. It's about a 10th of a millimeter big. So you see here the scale of the whole thing. So summarizing about the property of nerve, you have a pulse length of about a few millimeters to a few centimeters. You have a pulse duration of 1 to 2 milliseconds. Sorry, that is a mistake in my writing. It has a pulse velocity of the order of a few meters, 200 meters per second. And it has a diameter ranging from a few micrometer to, let's say, a 1 millimeter in the biggest nerve that I have seen. So you would expect, let's say, our pulses going along the nerve. And in this pulse, a number of thermodynamic features of this nerve change, not only voltage, but also, but also, well, it's good to have some music in between. So this pulse represents thermodynamic changes in the membrane and a pulse that is overall adiabatic. So we have a diameter, we expect curvature in there. And people have, for a long time, described curvature by an elastic theory made by Wolfgang Kelfrich in the 1970s. It's one of the most famous works in the membrane biophysics where you say that free energy density of a membrane has a quadratic dependence on curvature. It's basically Hooke law. And there is a Gaussian curvature term in there. And you can also stretch the term, the membrane, and you get a quadratic dependence on area in there. This is also just a Hooke and spring, basically. And people assume that these things here, the KB, can bending modulus or the KG, the Gaussian modulus, or here's the KTA, as a thermal compression modulus, that these are constants, they are called the elastic constants. And you would assume that constants are constant. And this works fine as long as nothing happens. So people have successfully used this kind of theory to describe vesicle shapes. This is a red blood cell. These are vesicles, these are, one of those is vesicle from synapse. So you can find from elastic theory shapes of organelles that are very similar to the calculation, to the experimentally found shapes. But the problem is, and that is the central part, is the central idea of my talk, that in biology, elastic constants are not constant. So they are variables, functions. So in order to explain to you why they are not constant, but they depend on some dynamic variables, I have to go a little bit into what a membrane is and how membranes behave. What's very important is the main component of a membrane is the lipid. That's how a lipid looks like. So it's a hydrocarbon tail. This is hydrophilic head. And all these things in the membrane here are lipids. And the big blobs in here are some proteins. And you have many different lipids in this membrane and what the composition is is not really important for me. But the important thing is that they have an order transition from an ordered state at low temperature to a disordered state at high temperature. So you get something like a transition. I don't want to call it a phase transition in the presence of so many theoreticians. But it's an order transition, which you could call a higher order transition from an order to a disordered state. And you can measure that by measuring the heat capacity. And heat capacity is basically as you heat it up and you measure how much heat and you need to increase the temperature by a certain amount. Heat capacities are very, very simple to measure and it's very easy to obtain them. So you also find, and what I just showed you in the previous slide was a transition of an artificial lipid. But you also find these transitions in biological membranes that's practically unknown. Hardly anybody has and considers this effect. This is a melting, the heat capacity profile in nervous membranes from the spine of pigs. This here is from lungs effectant of pigs. I could show you many, many pictures of different bacteria, cancer cells and so on. They all show transitions. It's other blue pigs in here. And then this here is body temperature and then you see some other pigs that's unfolding of proteins. But the melting of the membranes in the biological system happens always slightly below body temperature. Such that body temperature is at the upper end of this transition. Now, a little bit thermodynamics. The heat capacity is a change of the enthalpy when you change the temperature. So it's DH, DT. The average enthalpy in an ensemble can be just, it's just a weighted average of the microstate states. And this is a normal way of averaging a thermodynamic extensive variable. And if you now take this average and you make the temperature derivative of it and you calculate a little bit, then you find out that the heat capacity is actually equal to the mean square deviation of the enthalpy from the average. So that means it's proportion to the fluctuations. This is called a fluctuations relation. Every single susceptibility is related to a fluctuation relation. And capacitance, for example, volume expansion coefficient, compressibility, dielectric constants, they are also susceptibilities that you get when you change an extensive variable upon changing an intensive variable. So the heat capacity is related to fluctuations in enthalpy. So to give you a kind of more lead direct picture of what that means, I show you what fluctuations are. I mean, you are familiar with fluctuations when you have Brownian motion. This is basically thermal collisions of particles with the solvent. And this just moves around. But in membranes, when they are close to transitions, you also get something like that. On the left-hand side, you see a membrane close to a transition point. And on the right-hand side, you see the transition of this particular lipid. This is an AFM experiment. And then underneath, you see a simulation that's an easy kind simulation. And if you run it over time, you see the fluctuations in state. So the dark colors are the ordered state of the lipids. The bright colors are the disordered state of the lipids. You see fluctuation in the system. And if fluctuations, then if you just count the number of liquid disordered lipids, you would see that this fluctuates around an average. And the mean squared deviation of that noise, that is the heat capacity. So the interesting thing is, you get the same thing for other susceptibilities. For example, compressibility. The volume compressibility is given as the derivative of the volume with respect to pressure. Now, since the enthalpy here in the exponential term, the Boltzmann term, depends on pressure. You can make the same calculations as before and you find out that the volume compressibility is proportioned to the fluctuations in volume. The same you can do. And what you can also do by using Maxwell relations is to calculate the adiabatic compressibility when you know the isothermal one. You can do the same trick for area compressibility. That is proportional to the fluctuations in area. And capacitance is proportional to fluctuations of charges and so on. Every single susceptibility is proportioned to a fluctuation in some quantity, some extensive quantity. Okay, now we have made an experiment on membranes where we measured how the volume changes as a function of temperature. So you see two curves here. One of them is the heat capacity. That is a solid line. And the more dashed curve in here is the change of volume with temperature. You're measured by a densitometer. And what you see is that these two curves are completely superimposable. So that means volume and enthalpy change in an absolutely proportional relation with each other. And you can infer some similar things also for the area. So what you get is that the volume change is proportional to the enthalpy change and with a kind of coefficient in there which happens to have a number that is very similar to many, many systems that I've investigated. So that means if I know that number, I can calculate certain things. And I will show that on the next slide. So what you see here is, again, the fluctuation relation for the heat capacity, the fluctuation relation for the compressibility, the one for the area compressibility. We know that the volume change is proportion to the enthalpy, the area change is proportion to the enthalpy. And that if we just insert that into this equation, then we see that the compressibility would be proportion to the fluctuations in enthalpy. And that means I can relate the compressibility, the volume compressibility to the fluctuations in enthalpy. And that means that the compressibility is proportional to the heat capacity. So that means I can calculate elastic constants from heat capacities in our system. The same thing for the area compressibility. So I can calculate those from the heat capacity. Now I told you already that I can also determine the adiabatic compressibility. That's important because it is part of the sound velocity. If you try to measure sound propagation in a system, the sound velocity would be equal to the square root of 1 over the compressibility times the density. And now I told you I can calculate all of these things from the heat capacity. I've done that here. That would be the sound velocity as a function of temperature. And the dots are experimental points that people have measured in getting with an ultrasonic resonator. So that means you can successfully predict the compressibility and the sound velocity in experimental systems. Another thing that one can do that has also something to do with the fluctuations is that you can determine the lifetime of the fluctuations. The lifetime of the fluctuation is the same as the relaxation lifetime. And you can prove that the lifetime of fluctuations is proportional to the amplitude of the fluctuations and will yield something which is known as critical slowing down. That means if you are in it in the transition, the process is slow. And it turns out in just this is experimental data and the other curve is the heat capacity profile that you can calculate the relaxation time scale by, well, you find that it's proportional with an experimental accuracy to the heat capacity. So you can also determine the lifetimes from that. That is because we have a system here that has basically only one single order parameter. And all fluctuations turn out to be proportional to each other. That has, so in the following, we take it as an experimental fact that the elastic constants are proportioned to the heat capacity. The relaxation lifetime is proportioned to the heat capacity. And everything that changes the heat capacity will change the elastic constants and the lifetime. So that means I can manipulate all these properties by changing the thermodynamic variables. For example, pressure or temperature or something like that. Now, I want to present you this set of data that I had before in a slightly different way. Rather than plotting the sound velocity as a function of temperature, I want to plot the square of the sound velocity as a function of density. And what you see, but these are basically the same data. It's just presented in a different way. So that means here, this would be the temperature in which a biological moment is slightly above a transition. It's with the lowest density. And then when you go up in density, that means you compress the membrane and you make it more solid. Then the sound velocity goes down because the compressibility goes up. It's a very strange kind of spring. We have a spring that when we compress it becomes softer because we move the spring into a regime where the fluctuations are high. And so, and now I can make a statement about sound propagation in the system. The wave equation for propagating of sound is given here that is just standard hydrodynamics. That the second derivative of the density with respect to time is proportional to the derivative with respect to space. And the sound velocity is in the bracket term here. And we can sort of try to approximate this density depends of the sound velocity with the Taylor expansion. So we have a constant term, a linear term, a quadratic term, and so on. And I will use that and insert that into the wave equation. And that's what you see here. Then the wave equation looks like this. So you have instead of sound velocity squared, you have a constant term, a linear term, a quadratic term as a function of density. We have added a second term in there, which is called the dispersion term that takes into account that density is also frequency dependent. Sorry, the sound velocity is also frequency dependent. The interesting thing is this equation has analytical solutions which are solitonic. It's a soliton. It's in contrast to the talks this morning. It's not a topological soliton, but just a normal one like in water. I show you that in the moment, but it's remarkable that this soliton, that is the solution of this equation, has, is very, very similar to the nerve parts. So it has a maximum amplitude of about one nanometer. It has a velocity that is about two thirds of the sound velocity in a membrane, which is approximately 100 meters per second, like in motor neurons. It has, since it's an adiabatic process, it has a, it first releases heat and reabsorbs it in the second phase. And there are many, many other things that are remarkable effects. So these things are experimental profiles. This is a soliton which is a solution to this equation. So I said these things already. We have nerve parts approximately speed of sound in certain terms are associated with sickness changes in the moment. They are adiabatic, and this is all remarkably similar to the nerve parts. To show you what a soliton is, I show you this video from the internet. This is the famous John Scott Russell's soliton from 1834. It's basically a propagating water pulse. You get these solutions to the propagation equation when you have shallow water. In deep water, you get just silent or soiled waves as usual, but in shallow water, you get a single pulse that makes elastic collisions. It is reflected from walls. And so it propagates without much dissipation. So when did I start? I started approximately. Okay, so now this equation that I just showed you has four parameters. That is these three which come from the experimentally measured sound velocity and the dispersion term which is just a constant that determines how broad the paw peak is. And it's a little bit ugly that one is that we have not explained the dispersion term so far. But that I do here. I've shown you that the relaxation time in membranes is proportion to the heat capacity. And we also find that the heat capacity is frequency dependent. That has something to do with the relaxation process in the system. And by using linear response theory, we can actually find out that the dispersion coefficient is also a function of density and we can calculate it from the thermodynamic properties of the membrane. So we can then get a dispersion coefficient which is not a constant, but it's a profile like this as a function of density. And you get solitons that look like that and the different shapes that you see there depend on how fast they travel and how much energy they have. But we have now a theory for the propagation of sound in biological membranes which can be found without any free parameter. All the information is the thermodynamic information about the phase transition of that system. Good. So these solitons, so we basically claim that these solitons are the nerve pulse. Everything that can move the membranes through a transition would be able to excite a soliton. Everything that moves the transition away from physiological temperature would inhibit the excitation of a nerve pulse. So the things that can excite a nerve pulse would be voltage increase in pressure, a local temperature decrease and so on. Inhibition could be a temperature increase and aesthetics but also changes in pH and things like that. Good. So now what is that good for? We have here, I show here the transition in the biological membrane again. Here is the melting point of the membrane. This is physiological temperature. So now the claim is everything that moves the transition to the right side would make the nerve more excitable. Everything that moves it to the left side makes it less excitable. So we can by controlling the transition we can control the physiological function of the nerve and we can now check whether that is true. One remarkable thing about anesthesia is that all anesthetics at critical dose of anesthesia have exactly the same concentration in the membrane. So it's completely unspecific, doesn't depend on chemistry whatsoever. And one can explain that by a simple law from Funtoft, that's the freezing point depression law that basically says that the depression of a melting point by dissolving a substance in the liquid phase is exactly proportion to the amount of substance and that is exactly found in the experiment. So if you add anesthetics, I added here octanol but I can and here Lidocaine which is a local anesthetic. If you add that to, I'm nearly finished. And if you add that to membranes then you lower the melting point and this here is calculated by assuming the melting point depression law. This here is the experiment. The interesting thing is that there are other variables that shift transitions in the opposite direction like pressure. So if anesthetics shifted downwards and pressure shifts it up but what happens if you do both things at the same time? Do, can you wake up somebody who's anesthetized by applying pressure? And that people have actually measured that in tadpoles. And if you apply pressure on anesthetized tadpoles they in fact wake up at pressures that can be predicted from the numbers that I've shown you before. There are other phenomena that makes sense in that sense. For example, if you stretch enough, that means you have a tension in the membrane that would move transitions to lower temperatures and that would make the action potentials smaller because you need a larger energy to excite them. And that is what the calculation says. This is what you find in an experiment. You stretch a nerve and action potential in fact gets smaller. Another effect is tremor. If you shake and you assume that shaking is nerves shake, they are overexcitable meaning that the transition is at a slightly too high temperature. Then anesthetics should work against tremor and that's actually something where you find a lot of literature about that people with essential tremor basically stop shaking when they drink a glass of wine. And I had a student in one course who explained that to me and I found that very interesting. And another student in one of my courses actually had bipolar disorder treated by Lysium. Lysium is a very strong binder to charges nearly like calcium but much stronger than potassium or sodium. And that increases transition temperatures. So an overdose of Lysium also causes tremor and that can be counteracted by anesthetics. So I come to my summary slide. I could talk for hours about phenomena like that. But it's a powerful approach, right? It has a lot of predictive power and some of the phenomena can be predicted in numbers. So the nerve pulse can be understood as an electromechanical soliton. You find the right velocity and amplitude. This is a consequence of the nonlinear elastic properties close to melting transitions. This is consistent with reversible heat production and the adiabatic nature of the pulse and there are absolutely no free parameters in there. And there exist numerous medical conditions that can be associated to the shift in the melting transition and that makes a lot of sense. Thank you very much. Thank you very much indeed for this physical view into biological membranes. Very fascinating. Erio has some questions. What about the electrical signal and the depolarization wave and the whole classical story? Yeah, well I talked in my talk mainly about volume and area changes. But of course you also have membrane polarization. You have the capacity of the membrane. Of course if you have it, the soliton consists of a region where the membrane becomes thicker because you move it through the transition. That changes the capacitance by 20% and you get capacitive currents, for example. You also get a change in voltage. You get a reduction in voltage when you do that. Do you get a side effect? No, I wouldn't call it a side effect. In thermodynamics, all effects are true effects that are coupled with each other. But when I discuss with people from the neuroscience field, they often call the mechanical effect side effects, which is also wrong. These are all effects that are equally important. I'm wondering, what is the role of ion channels in all of that? So would these nerve passes propagate even without ion channels? Yes. Is there a role of ion channels at all? Or are they useless? I don't know, but the thing is I don't have that on my slide here. But I could show that to you in the coffee break. In the regime where the membrane fluctuates a lot and when you then make a patch clamp experiment and you measure the current through the membrane, you get events which are fluctuations in the permeability which look exactly like ion channels. So all these phenomena like ion channel opening and closing is also a consequence of the thermodynamics. Can you open the chat? Who's the host? There was a question online. And whoever put the hand up, can you unmute yourself? Yes, yes. So it's a related question. I'm definitely not an expert on this subject, but is there an explanation here for the refractory period? Why after a pulse has passed, there would be a time before which it can generate and transmit a pulse? Well, at least there's something that is similar to a refractory period because in order to get a soliton, you must accumulate material from the side. So that means two solitons that are close to each other compete for material. And there is a kind of minimum distance that you get between two solitons in order to have mass conservation in the system. Okay, so because we have to do our schedule today for the next post-assessment in time, thank you very much indeed. So yeah, applause for our speaker. We are meeting again at 4.40, yeah, 20 before the hour. And please come back a little bit earlier and meet our...