 You can see the title on the screen and and as Tina said, we're looking forward to having a discussion in the end, but I would also like to emphasize. If there is any reason you would want to interrupt me at some point, midway through the talk. Feel free to do so. Obviously, presentations given by zoom, sort of slightly difficult in terms of connecting to the audience and connecting with the audience so if there is a question please just unmute your microphone and and shout. Okay. So, this is about protein dynamics studied by scattering. And I will, I will briefly introduce later what exactly I mean by that and why this is relevant before I do so let me just mention before let's get sort of forgotten in the end. As you can see, this is a group effort. There is a number of people who contributed to this, both in tubing and as well as in particular in Zeke in this case in a collaboration with the same good. And also elsewhere you can see all the names on the screen and probably I've forgotten one or two. I'm not going to read all of them. And indeed, most of what we do is with scattering and I tried to connect also to the mutual scattering world as well as to the extra scattering world. The, the schematics you see on the bottom are different projects we're working on all in the context of soft molecular and biological matter. The focus on today is this. These are projects where we're basically talking about proteins proteins in the bulk in an aqueous solution. And effects of the of interfaces or other things are neglected in this context but I'm certainly happy to to comment on this if you wish. Okay. So, by way of introduction, the question I mean why why do we study proteins in a way it's actually quite simple proteins are considered the machinery of life and just what everything we. We understand about proteins helps us understanding the miracle of life better. And, however, it's a rather complex system and there is various components involved. We're not convinced why they're important basically everywhere you look in your body or other as we're in nature if you want. They're involved whether it's for structural purposes or they serve a specific purpose in terms of transporting or other contributions so from from your skin to your muscles. Everywhere and including of course also even the food you're eating. The typical scenario is that people look at a protein as you can see on the on the screen here and consider the structure and then look at the structure, and then they come go back to this famous sort of mantra that says if you want to understand the function. You have to understand the structure. So in order to understand the function in your body in terms of whatever it may be, you have to understand where all the atoms sit in, in the protein and that's certainly not wrong. So basically, you see pictures like these, which you have on the screen in the biochemistry book, for instance, and then the protein has a certain shape and it fulfills a certain function, and in order to understand the function. You have to understand where the atoms are. They're fine and and again it's not wrong. The point is just, it's not necessarily everything so at some point people said well you have to understand structure, but also dynamics because basically whatever you look at in in biology, or in related subjects and indeed if you want also in conventional solid state physics. So there's always something moving and that certainly makes it more interesting still. And so what you see now on the screen is basically the same protein as before, just moving, obviously, and in this specific case. This is the center of mass motion so it's sort of diffusion. And it may not be everything so there's actually a whole range of aspects to the dynamics, which are relevant, and you might want to look at this in this form, where from the bottom left to the top right. There are different types of motions or structural elements of the, of the protein. And if, if things go well, it actually starts moving now in some form. So, on the very short length scale you see individual atoms or small groups of atoms moving such as the methyl groups. You may look at side chains. This is the second. The second part that is displayed here in a slightly different way of representing it. We're just seeing this this helix moving in some form, or it may be the entire protein that is moving and some in some form and rotating and changing it shape slightly. And of course, above all, you can look at the center of mass motion that is indicated as I said before on the top right. So, we have dynamics in these systems that really include a huge range of length states from from let's say angstroms for the individual atoms if you will, all the way to the length states of diffusion of the entire object which is several nanometers or more than that if you will. And with all these length scales are associated also different time scales, and that makes it a bit more complicated of course but it makes it is necessary to understand this. And in a way it's also wonderful area for scattering because we know that in scattering we are not just addressing length scales in some form, why the queue vector but we can also address time scales and we can connect the time scales with the length scales. Okay. So, if I look at this whole host of dynamics in various forms. I will, in a scattering experiment typically look at sort of certain ranges of length scales and time states and not all of the not all of these but I emphasize all of them are potentially relevant of course. Here's one example. And here's an example of of diffusion that was basically your, your schematic in the top right corner this animation of the protein bouncing around in terms of center of mass. But here, we're looking at a situation that is actually a bit more realistic because we're not looking just at one protein. We need many of them as you can see and we're having a rather crowded situation which is still more realistic, of course in biology so in addition to the things I've said already. We also consider that the proteins are typically in a crowded environment where crowding means. We're looking at at a significant percentage of the solution being covered and occupied with with the proteins. And let's say that goes all the way up to 30% or so 2030% is not unrealistic actually in the biological context. And what that means is, we're not looking at just individual proteins and can look at their diffusion in water which is essentially determined by the size of the protein and the the viscosity of water, but we have to consider that they're constantly banging into each other and and so things in this crowded solution will be slowed down typically. And we will look at where we're looking at some form of let's call them collective effects. And one example where this is this is demonstrated it's a it's a work now slightly more than 10 years ago, in this case done with quasi less of neutron sketching looking at the short time self diffusion, where you can see that the diffusion which is plotted in on the right hand side obviously normalized by the diffusion at infinite dilution that is zero concentration if you will, goes down from some value which is determined as I said by the size of the protein and and the viscosity of the solvent of the water around it goes down to substantially lower values of something like 20% or less of the initial value if you go to concentrations which are here on the bottom right corner of the diagram around let's say 30%. Okay, so it's a significant effect. And this will influence various issues related to reaction equilibria and and basically everything that's that that is related to movement movement and motion and dynamics in the cell. It's quite interesting from from a moral, let's say, physics biophysics or physical chemistry point of view that you can actually model these things quite successfully, as has been done by Felix was longer at the time by mapping this onto models that are basically borrowed and inspired by by color physics. So, this is reasonably right under control one might might say and it just has to be born in mind that dynamics changes upon changing concentration. And here I should say, I don't make interactions may become important, of course, the slower the slowing down is due to the higher concentration you can even do with neutrons targeted to duration and then look at specific proteins so you, you project a certain set of proteins out of these crowded solution as we have also done in a sort of related study, but that's not going to be the focus. Today I just want to remind you that things that complex of course with increasing concentration. If we look at the broader picture from a scattering perspective so x-rays and neutrons with those there is, there's this famous diagram of looking at time scales and length scales over range, several orders of magnitude quite obviously, and then I tend to call this sort of the world met of spectroscopy but there's different entries depending on who draws the world map, then typically for short length scales and short length scales, there's various neutron techniques such as backscattering and spin echo. And if you go towards longer time scales, typically, you're somewhere in the range of x-ray photon correlation spectroscopy so this big yellow block you see on the screen. And there is a bit of a gap between synchrotron based techniques and the neutron based techniques and in between drawn in a mildly optimistic way I admit there is, there is the x-ray laser that might cover it and if time permits I will comment on this later. And if you put all of this together basically you're looking at the local and small length scale motions potentially in the bottom left corner, and you're moving somehow towards macroscopic effects might even be way above the individual like here in terms of concentration fluctuations, liquid liquid phase separation for the experts is very interesting in this context, so larger length scales, so maybe up to microns if you will. And then, from an experimental perspective, you're of course challenged by looking at this over something like 10 orders of magnitude easily. So all the way from the local motion to something like domain motions and that's actually not so easy to do. Ideally, we apply all of these techniques, probably a bit too much for one talk and it's a longer subject of discussion but we actually attempted to do this and to some degree, we were able to do this. For what follows, I will mostly concentrate on XPCS so that what's on the top right corner in this diagram. And what we can do there in the context of proteins and I will later comment a little bit of time permits on also work done at the XFEL and you've seen some of the neutron results already and how we can connect. Of course, we also tried to do. Okay. Let me show you one more example because this becomes important for for whatever follows which is related to the dynamics of proteins when you actually heat them up and finally drives them into denaturation. So, then this is a neutral example and we will connect to the x-rays in a minute. The typical scenario you might have is you first look at the situation at low temperature that is below denaturation temperature which for the present example is somewhere around 340 Kelvin. So if you have your proteins exactly in the shape you would want them to be initially, I assume you can see my mouse slightly weak. So if they are temperatures, then the the backgrounds and chains are starting to modify their unfolding to some degree, and then they start to connect to each other and form a network and then of course you have a completely different network of all these chains. And if you cool down again it's still a network and you don't get back to this. This is sort of like you're boiling an egg. And things are starting to connect and once the egg is at room temperature again of course it remains a network of some description. Okay, there is no unboiling of the egg. And the dynamics will behave sort of accordingly initially the dynamics will just go up in terms of diffusion increasing with temperature, but then actually once the network forms dynamics change completely and the network has completely different dynamics of course and the individual proteins. This here is on the nanosecond timescale for the neutral experiment and roughly also on the angstrom timescale. And this is what we want to understand a little more in detail. Looking at this with x-rays so we're looking at it at a collective behavior of this gel like network where the length states roughly are sort of the mesh size, the mesh, which I show you in a second and we're interested in the length of the egg, which goes to something like a boiled egg. Sunny side up if you prefer that expression, and we're focusing on the egg white after going up to about 80 degrees C. And then we expect this type of network to be formed of the chains, and we're looking at the dynamics of the network. The mesh size will turns out to be roughly 400 nanometers, which of course comes out of a scattering experiment. And now if we're looking at the kinetics of the network formation. So, when we run up, we will find out what the timescales are we're looking at the dynamics of the network, which is a different piece of course. So we're looking at the network and this whole arrangement in terms of its aging so if you, if, if, if, if you look at things over slightly longer timescale things will still change, although you think you just have your, your final product. And all this done with coherent x-rays so x-ray photo correlation spectroscopy. So, the experiment looks as follows the box with all the details, as certainly interesting but you don't have to read all this. Just, you might want to look at just the animation which Anita Jireli has produced at some point which is, it might be quite nice. And we're looking at our sample by opening the shuttle for the x-rays for a very short moment of time. We get some scattering pattern, which is a small angle scattering pattern, however, with this typical grainy structure of our coherent beam. And we do this once we do this a second time. Let's see what happens. We get a second scattering pattern, a second image on the detector, and we may do this a third time if we want. And then we get a series of these scattering patterns, and we can compare how these scattering patterns evolve, and we can correlate them. That's the essence of it. And if we look at one of these, for instance, we might look at a certain range of cues between these two red circles, and then calculate our correlation function which contains the time which is the correlation of the time and one moment in time correlated with the scattering at another moment in time at a time t later than this t zero. Okay, so connecting different patterns with small distances in time helps us and gives us a tool to understand the kinetics and the dynamics, the evolution of the scattering pattern as a function of time that's the whole idea. And this dynamics is what we're interested in. Okay, you can rewrite the scattering function if you want, as something like one plus this intermediate scattering function. And the key point is this will give us a time scale, as you will see in a second by which we characterize the dynamics. Before we do this, I don't want to pretend we're just looking at the dynamics we also look at the structure, of course, so it's obviously essentially a small angle setup, or the mode we're looking at with a key range might call this ultra small scattering. And we can look at the scattering pattern. First of all, is sort of as a time series which would probably call more like kinetics. So, and the, the left figure and shows the evolution of our scattering pattern as a function of time. And from the early stages after a few seconds to something like 160 seconds, and you see there is quite a serious evolution of the scattering pattern, which is due to the fact that we have, in this case, the virtual or proteins, they starting to connect and the network is forming and that that takes about under these conditions roughly 160 seconds. And if you go further than that, beyond this point of about one 160 seconds. There isn't really much happening if you look at the central set of curves and then also on the right hand side, the static pattern is not changing anymore on any substantial level. So, the statics is as basically converged after some 160 seconds, and you have your network formed. And this is, this is your denatured protein network. However, that doesn't mean there is nothing happening anymore and there is, there is quite a bit of dynamics as we will see. First, before we, before we go there, we can try to quantify the raw data a bit more. This is one way to do this we can can calculate the scattering invariant which is the left figure a, and we see that there is there is a nice well behaved growth curve of this scattering invariant which basically converges after a little after a little more than 100 seconds which is what I just described. And if you look at sort of this power law dependence in the central figure, you see that this is also converging after two one or 200 seconds to an exponent of about minus two. In the length scale you extract from this small angle scattering in this context is, is roughly of the order of 400 nanometers. After the time we can extract sensibly this length scale at all so once the network has formed which is after or let's say one 160 seconds which you see in figure three. So this is our, let's call it more or less static characterization so it's small angle scattering as a function of time but in a static sense of every given scattering pattern. So we have characterized the network, which is our foreign nanometers and and the parameters which I just described. And then we can look at what happens in terms of dynamics so this thing will move. Most definitely it will not be a static object only. And you can also by the way do this as a function of time and sorry as a function of temperature and solve change conditions and extract parameters from this, such as sort of barriers for insulation. If you want if you do the time states as a function of temperature this is still in a rather static mode and and you can see some of the values on the right hand side figure as in the form of an Arrhenius plot. Okay. Now, all this requires things to move in a dynamic sense and and that's what we're going to address now this is dynamics via the two time correlation function. We have the central plots in this experiment if you if you use coherent x-rays to look at this network network. And what you're going to see is always in this color representation, this correlation function which is given in this plot in blue, which is our correlation function as we discussed before. As a function of t1 and t2 so two times we're collating two times. And then you can extract more than just sort of a one dimensional thing which is sort of on your on one axis of this, but actually look in a bit more detail into this. And if we take these, these pictures you will see that following this this arrow this broken line arrow is sort of the time, which, which our system is progressing. This is sort of the central diagonal, and then we expect that from the early stages where you have proteins shown in this schematic after zero seconds if you were, you will in a natural state, they somehow turn into the network. After about 160 seconds. Then the nature and also cross link. The different certain self assault for bonds which are then formed and so you have a cross link network. And then if you look at these correlation functions in time, you will find that initially it's it's a very narrow line on the central ridge. But this then broadens. And you're getting pictures, as you can see on the screen now so the dynamics initially is completely different from what you see later. Okay. And this is what we're going to analyze now in a bit more detail. So, first of all, you can look at these these correlation functions which are indicated before. And the time correlation functions that give you a sort of a character characteristic time tau, as well as if it follows the functional form that is indicated on the bottom right of the slide. This is the exponent gamma, and these are basically the two key quantities. If you can fit this consistent with this expression for the G to that describe the dynamics the tau and the gamma so the characteristic time and this exponent. And we're going to look at this now as time progresses during this denaturation and and cross linking process. And, first of all, the relaxation time towel. So the images you see on the top of this, this panel. Basically what you've seen before just tilted by 45 degrees so that the waiting time or the boiling time if you want is now on the horizontal axis. This is along the main diagonal of the previous plot. And the, the time constant that we can extract which is our towel is given in seconds then in this plot, and you see initially this, this slightly sort of whatever the color is that comes out at your end I call this sort of faint pink or faint red. For the first few hundred seconds, the time constant changes still substantially and goes up and go things go slower and slower. And, and at some point it sort of saturates and and reaches a certain plateau value. And so, and there is still a change in the dynamics, even after the structure has essentially established in terms of a static sense, static in quotation marks. And actually, until about 500 seconds under these conditions. And one way to interpret this is sort of it suggests that there is some sort of a slowing down after the network formation, due to increasing a sulfur sulfur cross linking. Okay. And then at some point, we come to this later. We will use the term aging of the gel, but we will not get there. If you go further than that you can look at the gamma which was your exponent and the expression you see on the screen here. So people call this equal harsh Williams was exponent. And this sheet connects to the type of motion we're seeing this is the other results for this gamma. It's not simple to extract this reliably but you will probably appreciate that initially, it's closer to one whereas at later stages is more or less close to two with some substantial error bar. If you want to interpret that actually the gamma equal to to one is some form of a diffusive motion. And if it goes above one at some sort of hyper diffusive motion, which in this network is not so easy to interpret and I will get back to that later. Okay, so the question is actually what is behind this type of dynamics. After we formed the network and there is this network of cross linked chains of our proteins. But it's still moving in some form so what is the motion behind this. But one way to look at this is inspired by some of the earlier works, which were different types of networks but nevertheless some form of a network on in these references given, given below. So you look at this network and at some point, there may be actually a rearrangement. So the system has been brought into the work state there has been cross linking, but that's not necessarily in some form of a sort of ideal state in terms of close to equilibrium if that's the word you want to use. It's rather strained presumably the somehow the network has been formed. But this may not be necessarily comfortable for the entire system so may run into a situation where this this blue connection on the left has been broke with is broken up, and the chains may rearrange in this network, and that would lead to some form of dynamics along these red arrows of the components you see. And that's actually rather typical situation for these systems. And the questions you might ask are about. Let's call them activation barriers, the length scale so which regions which size ranges are involved which time states are involved, and this is something you can address with these experiments. So if you analyze this in more detail. If you look at one of these two time correlation functions again. This is one of the several TTCs which I've shown you before. One of one of them and specifically the one around the 500 600 seconds. Notice that there is actually quite a bit of fluctuation around the central rich. And that's not necessarily just statistics you can look at those carefully and you find out it's not only counting statistics there is some something beyond counting statistics if you look, look at it, and sort of this rich is changing. And people have analyzed these things, these things, there are some predecessor papers quoted on the bottom for, I would say slightly simpler systems. And you can extract from this information on the intermediate scattering function. The point here is that, if this thing changes if the chains are moving. It can see this as sort of a series of decorrelation events of the gel network. And so there are these these events that are spontaneous, more or less spontaneously happening, and the decorrelate the chains and then you have a change in the correlation function obviously, which you see on the time axis there. There has been a model being produced in these references which are given. And in essence, what you learn from that, you can extract sizes regions sizes of these regions where these decorrelations happen. This is the parameter sigma in this in this expression. And you can determine sort of the typical size range where things are happening. Okay, there's a bit more to this model but I would probably want to leave it at that and show you the results in the interest of time. And, and you find that as a function of the let's call it waiting time so as a function of the time of your system. It changes slightly but then approaches values that are rather low and and more or less constant as you can see in this plot. So the, the decorrelation events happen rather locally that's that's the message. You can quantify this further and if the data are good enough. He can actually calculate what is known as the fourth order correlation function, which is a way to quantify further the heterogeneity if you want. And people some people use the term dynamics susceptibility in this in this context. And if you calculate this quantity this guy for from the data that I've shown you before. So basically, it's using these as a correlation function as an input here. You find a characteristic behave here with this with a peak of the fourth or correlation function at at some point which is around, let's say 10 seconds. And this peak is actually moving as a function of Q. So what does that tell us. The peak position which we call T star decreases while the height of this guy starts from the peak height increases with Q and it basically means there is less heterogeneity for large length scales. So if you sort of look at larger length case, if you want average over larger length stays. There is less heterogeneity so it's really a local thing. That's one way to phrase it in simple terms, and importantly, and there is less heterogeneity with increasing time with increasing waiting time. Okay, because the network sort of reduces the internal buildup of stress. You can push this a bit further and actually plot these quantities and then you can see this very nicely. The peak parameters to T star and the chi star change rather systematically with Q. So that is your length scale. Okay. I just want to add you can do all these experience of course also for different heating times that is not just 80 degrees as as as we've used all the way up to here. But if you do this for for different times, you see similar behavior, and with just basically one parameter to scale the characteristic time. So our towel which I've shown you before, and we use as a scaling factor is new. And you can basically plot all the curves more or less on top of each other so they collapse onto one more or less universal curve. And basically that tells you it's it's a relatively universal type of behavior with these two step dynamics if you want to use that word, which I think is quite a nice result as a, as a generalized final final. Now, what I would want to do is I would want to wrap up everything I've shown you up to now and then, if time permits, I will show a few more examples of what you can do with photon correlation spectroscopy. So here's sort of the tentative and preliminary summary. So the dynamics is key for the understanding I think I emphasized that point quite a bit. If we look at this denituration network formation, and under the conditions I've shown you it's about finished after one 60 seconds, and then rather the same dynamics set in, which are certainly not just a characteristic of static object but something that is still changing and you could call this some form of aging, if you will. This has I've characterized this a bit more. You can see it down and then the hyper diffusive motion, as you could see. Importantly, if the data are good enough you can even characterize the heterogeneity with this guy for expression. And that allows me to I will give you a bit of an outlook into what else you can do with the same technique essentially but not in the context of the nature proteins but actually proteins kept alive near room temperature. Yeah. So this connects to the picture you see on the bottom of the screen now, and that is actually face separation so completely different type of phenomenon. So from an originally essentially a homogeneous solution, the separation into different regions of high and low concentration. So, where do we find this. So if we have a face diagram. I'm not going to go too much into this but if you if you're interested. This is this was done with. IGG so some form of a protein but slightly more complicated complex shape and antibody with pack polyethylene glycol to increase attractions through depletion and you find a face diagram which is indicated here on on the screen where you have a certain range you have your homogeneous phase, if you quench down into a region you have face separation into these two regions, rather general phenomenon in terms of face separation which you can also have in many other areas of science, maybe, maybe metals, binary, binary alloys, it may be other systems so important here is, it's a system that shows face separation. So, initially, initially clear and then turbid, and, and here's again your, your illustration of that. So, we expect a concentration profile of a sample that is homogeneous initially, and then separates into regions of low and high concentration of proteins. Another question is, what drives that, and how is the dynamics behaving the driving force is given by the thermodynamics essentially, but within these systems there's, there is dynamics, and without the dynamics things will move obviously and you wouldn't also have this. This type of change of the phases. Typical thing for for scattering experiment. So, and it will be described by the carnaval equation. So you will have your your initially homogeneous state and then later after certain waiting time you have the face separated state and how to get there in the kinetic sense is given by the carnaval equation. You don't have to go too much into this if this is not your daily business. But if you bear in mind, you somehow have to change your system and some heads has to get that there. And for this you need mobility mobility parameters is the new in this equation, and it directly connects to the diffusion parameter. If there was no diffusion things wouldn't happen. Okay, and that exactly is what we're trying to characterize. To understand what we're expecting. We just free it from the simulations on the on the on the right. Actually, by the way, this has been done by Anita g rally in her PhD. Now working in Sweden by the way. And we get these patterns and these patterns are scattering patterns. So, intensity of the function of Q but there will also be a time component. We cut the short, we dive right into it, and we will find in order to reproduce the data we have to assume a mobility parameter that is not constant but has a certain concentration dependence. And that actually connects back to what I've shown you very in the very beginning the mobility, the diffusion is of course concentration dependent. And that's consistent with what we're finding. We can, we can record the scattering patterns we can record the time constants of these scattering patterns. And finally, find that they're consistent with the carnival simulations. If we introduce a mobility parameter that is concentration dependent. And of course there's a bit more to that but I use that as a sort of as a bonus track and and and outlook to what we can do. And just as an indication. We have one at the X fell. In a rather involved experiment. In order to cover these length gates which are indicated initially which are somehow a gap between the nutrient experiments and the synchrotron based XPCS. And this is an indication of what we can do connecting spin echo with the X fell in order to have one common. The scattering function that tells us something about the decay of the correlations, and that's particularly relevant if one technique cannot cover all this. So that's the idea of connecting 10 orders of magnitude. And with that, I would probably want to come back to my initial conclusion slide. So I hope I've convinced you that you can study the mix with XPCS I hope I've convinced you it's important to do so, and you can do this for various systems on a very broad range of time and then states. Thank you so much.