 So, I have chosen here to talk about less unknown protein protein interactions and this is of course, a little bit where you're coming from, what is less unknown. But I think that what I picked is really less unknown, but let's see. So the first slide here is also the motivational slide. I think that many of you who are here today have already have an interesting protein interactions. So if we look first here in the living cell we have actually a lot of proteins and it's a very dense environment we have up to 40% of the volume is occupied by things other than water. So there, there will be a lot of interactions between proteins and of course also other matter. And this is important in this setting also when we are talking about antibodies and solution. For example formulation of vaccines you want to have a high dose of antibodies, and there will be strong protein personal interactions. And how to describe them how to control them is very important for example the stability the viscosity of the samples and so on. And also important in, for example, food formulation where you can use proteins to control taste texture and mouse feel and so on. And lastly I'd like to to mention that as a background we have actually a very complicated matrix of ions so we have water and electrolytes, and that also plays a very important role on the protein protein interactions. I think a very good example is the pH that we often use as a handle to control protein interactions, and it's part of this background, but we'll talk a lot more about that today. So, let's think about when we say protein protein interactions. What do we actually mean. So here I have two proteins and we are obviously interested in how they interact with each other. And here we have to remember that it's not just proteins that we have to talk about, because around the protein, we actually have water. So we also need to consider the protein water interaction. Because there are now waters we also need to consider how waters interact with each other. This is a very important feature of any aqueous solution the water water interaction is very dominant on how the, the solutes they behave. We could even start to add co solutes. So this could be small molecules or salt. And they will of course also interact with the protein with themselves and with the water. And as I just described the solution we need to take into account all of these interactions we cannot skip any of them. So it's really an effect of all of them. At the same time we have to remember that often the systems we are interested in, we have a temperature in the system so they are not static they move around they rotate the diffusion so on and we need to capture that as well we need to be able to describe all of that simultaneously. So, if we consider non covalent inter atomic interactions if we really go back to basics and think about how can two atoms interact with each other, and it turns out that they're not so many ways we can think about. And basically, I would say an important part here is that all atoms they have an excluded volume and that can be some electric interactions on top of that. And by electric interactions I mean two things, I mean that I can be dispersion interactions and that can be cool on big interactions for example if we have an iron. And that's, that's about it. So we have very few interactions to, to actually take into account. And all of this, then builds up a lot of more intricate interactions we could say. So, now we have our two proteins over here and we consider the interaction between two proteins to two atoms. And we consider that we embed this into some background here of typically an equal solution. So, let's see what happens now. So, from these fairly basic interactions over here we can now describe and talk about a lot of more complicated interactions that I'm sure that many of you will have heard of before. We have hydrogen bonds hydrophobic interactions. That's very much related to for example what I mentioned earlier the water water interaction. We can have crowding, which is an entropic effect we can have screening due to ions. And sometimes if we have multivitamins we can have iron condensation over charging and so on. And now we come to three parts that I've marked in green down here and that's actually the ones that I want to talk about today. I'm going to talk about charge regression, Hofmeister effects and van der Waals interactions. I think that the, the last one van der Waals interactions I don't think this is really belongs to less unknown protein protein interactions because it's something you will find in any biophysical textbook. But I'd like to just highlight a few things that I think could be less unknown, but we'll get back to that in the in the end of the talk. That's the outline. I cannot really talk about all of this because it would be a very, very long lecture then. The idea is that these three parts they are fairly separate so I'll just try to explain what what these different effects what they are and how we can describe them. And I've tried to do this in an kind of an educational in an educational way it's not going to be much research that it's going to be a little bit about what we've done in the past. And I have a little bit of on published results but most of it is just descriptions about these mechanisms and how they could affect protein protein interactions in solution. So, when we have the possibility to describe all these effects. We can do that with, for example, computer simulations and this is what I do normally. So that's why I'm just highlighting it here. So here we have a box of proteins. And by taking into account interactions between individual particles we can then capture all of these, all of these effects that we have here. And once we describe them in simulation we can then start to calculate properties, and many of these properties that you could go out and measure in experimentally could be there's multi pressure view coefficient structure factors and so on. So, we can get information from the simulations from microscopic picture and relate that to the experimental data. So we're trying to talk, not to talk too much about simulations today but mostly about mechanisms. So, with that short introduction I think we can get started with the first topic. And that's going to be charge regulation. And I start off a little bit morbid here because these are the you see to really very highly influential physical chemists, John gamble Kirkwood and last on saga here buried next to each other and you can see here that Kirkwood was a very he made a lot of contributions including charge regulation that's why I mentioned, mentioned him here and of course last on saga a bit, a little bit more modest. It's just noble or it, and then asterisks, etc. here. And they were contemporary these two. Kirk would never got the noble price but I think it could be because he, he passed away, very relatively young I would say. And he was the, he was one of the first to describe the charge regulation mechanism and let's just try and go go through what, what that means. So, this is an effect that arises due to protein fluctuations. And what we have here is a is a molecule and it can with with some titratable sites and we have for example, an acidic acid and an amine, and what they will do that they will be in equilibrium now with the protons and the solution. So that there will be a fluctuation of their chart state. So at any given time we can come and have observed the site, and we will either find the proton or it will be free. And I think that, for example, up here the decide will will estimate between being in a being an anion or be neutral this one from neutral and being a cat ion. So, the charge distribution is not static does fluctuating. And that's the origin of the charge regulation mechanism. And to see this, we can see what happens when we take two particles, two molecules and put them next to each other. And this means that when we do that the judge distributions they can now become correlated. And that means that the will have a lowering of the free energy. For example, let's say that this side down here could be a carboxylic acid. And this one up here could be an amine. So this one can alternate between zero and plus one and this one zero and minus one. There will be a correlation between these so more frequently would find that there would be a minus and plus combination because that would lower the electrostatic energy. So all of this in total lowers the free energy. And this means that a new intermolecular interaction arises due to that. So, this was discovered a long time ago by Kirkwood and Schumacher. This paper from the early fifties, but actually turns out that the charge regulation mechanism was discovered, actually a lot earlier, 30 years earlier at my Kyle Linnaston long. The interesting thing about this is that comes from the Casper laboratories. And at that time they were very interested in describing proteins and the physical chemistry of proteins. Kyle Linnaston's boss. So he was the one that determined this that is the pH concept. So all of this in sort of an in trying to understand enzymes and proteins for production. So, if we continue a little bit, I'll try and keep the equations a little bit down in this presentation to what I have a little bit here and I think it's important to understand the charge regulation mechanism. And here we have a multiple expansion so here we have to imagine that this is one child's distribution is could be a protein and we have another protein macromolecule over here. And we can now express the electrostatic energy between these as a function of the mass sensor separation here. And this, this, this is a fairly easy to do. And if you do that you get something that looks like this multiple expansion, where we can express here the free energy of interaction as a series of terms and the first term is something that we all know quite well. And that is the iron iron or monopole monopole interaction. So what we have here is just the net charge of one of the distributions times net charge of the other one divided by the distance. So that's like a coulomb interaction, but from macroscopic bodies. This is the reason why we say that if we have to like charge proteins they will probably repel, and you could predict that using a multiple expansion like this. But there will be higher order terms and they are coming up down here. So for example, if the charge distribution is uneven there will be a contribution from the iron with a dipole with a dipole and dipole and iron quadrupole and so on we can continue this expansion out here. And you can see for the iron dipole it decays as one over R4. I should mention that the results here they are actually angularly or average so we have allowed the charge distributions to rotate as well. And you can see that the case as one over R4, this one as one over R6 and so on. Normally when we do these multiple expansions we keep the charge distribution fixed, we assume that there are no fluctuations but we've just argued that there are fluctuations if you have titratable groups, like capoxyl acid acid and amines and so on. Performing this multiple expansion and not normally if the charge distribution is constant these terms they cancel out, but if not, then we actually get extra contributions, and you see that they come in here right after the iron iron terms so we have an induced iron induced iron induced iron. And we see here that they decay as one over R squared so they are relatively long range. And we can see that they depend here on the charge on one side times what we call the capacitance C on the other proteins and so on. So, even in the case when the proteins are completely neutral, we can still have an electrostatic attraction between them as we see here so if this term with net charge is neutral. We can still have this term coming up here and that's simply just due to the fluctuations of the of the protonation states. To to use this, I think it's important that we try to describe what the capacitance is the C, and then this I'll do in the next slide here. So here we have the iron induced terms in the multiple expansion and they contribute to the protein protein interaction and you also see that it's always a negative contributions this means it's always attractive. The capacitance here, you see that this measures the fluctuation in the net charge, and that's always going to be a positive number. So the contribution to the protein protein interaction is always attractive. And it turns out that the fluctuation in the net charge here. It's actually very easy to obtain experimentally because it corresponds to the derivative of the pH titration curve. So if you have measured the protein charge as a function of pH, we can take the derivative of that function, and we get the capacitance. So with this we can obtain from both experiment but also from from theories and simulations it's quite easy to obtain this property. If we do that. Sorry for the very monochrome image here I hope we can, we can read it. So we have here we start with the pH titration curve. So charge versus pH, we take the derivative and then we end up with curves that look like this. So here we have it for NMR that's the circles, and then we have a null model an ideal model where we just consider the sequence of the protein so we can predict okay we have, we have a lysine here and we as we have pk value and we can then take the derivative of that and getting the capacitance like this. And the thirdly, fully drawn lines that from our Monte Carlo simulation. And we don't need to go into too much details about this other than know that we have here at low pH and at high pH we have peaks. And this corresponds to that we have a lot of titratable sites which are in their pH is close to their pk value. And this means that they can fluctuate a lot. And this is very typical for most proteins they will have peaks here on pH for corresponding to aspartate and glutamates and then up here in the high region we have license arguments and so on. In the middle, we typically have lower capacitance, except if you have a lot of histidines, then we can have higher capacitance up here. We see also that we can use this kind of information to judge whether the charge fluctuation attraction is at play or not. Because if we have a very low capacitance, this means that these pre factors here are the, if they're small then this is going to be a small contribution. So, we can use the concept here to determine if this is important or not. So, here I'd like to show how how the fluctuation force can influence the interaction between two proteins so here we have Lysosine interacting with calbinding so this is done using computer simulations. And we can do that with is the with static charges so it means that we just assume that we have a constant charge distribution which is, which I would say is common to do in computer simulations. And we can include a fluctuating charge. This is this we can do in Monte Carlo simulations by simply alternating the charge state. You just have to do it in the, you know, in the right way. So we keep a constant pH. So comparing these two here we have the mass and separation. And here we have the angularly averaged interaction free energy so the potential of mean force. And we can see that we start to we go from a purely repulsive system to something where we start to see a retraction. And this is due to the fluctuations of the charge. We can study this a little bit further and have a look at what happens here with the charge of the two proteins. So here again we have the mass center separation and here we have the charge of Lysosine charge of galbinding. We see that Lysosine doesn't change much. And there are two reasons for that. One is that it has this condition it has a very low capacitance. And secondly, the charge of Calbindian is fairly low so it doesn't induce as much charge in Lysosine. The other way around though this has a Lysosine has a high charge and Calbindian has a high capacitance so here we get a big response in the charge distribution so we go from 1.5 But at far separations into actually shifting a sign when we are close separations. And that's the charge is simply because we can, we can release protons as the two proteins they approach each other. And this is not just something that happens between proteins and proteins it could also be approaching a surface could be a membrane could be could be DNA or something like that. A mineral surface and you can have these effects. It could also be a small iron phosphate for example could approach protein and you could imagine that phosphate would also see fluctuations in its charge because it has PK values close to pH seven. So, that's, that's the charge regulation mechanism and just to empty section we can talk about the capacitance. So, what that is and I would say that it's an intrinsic molecular property, and it's very similar to how you would talk about the net charge and the dipole moment it enters the multiple expansion. It's a property that you can calculate for a single protein and then use that to say something about how, how proteins interact together. It measures the fluctuations in the charge. And this is in a way, how easy this to distort the proton equilibria of the touch radical groups. And it's something that's since in proteins we have a lot of touch radical groups is something that can easily occur in proteins. And it's strongly dependent on pH and the PK values of the touch, touch radical groups at pH seven we often have only small effects and that's because we have no groups tight trading there except for the histidines. So, so they can become important contributor contributors to charge regulation at pH seven. Other than that we have to go to either more acidic or more alkaline pH to see the effect. We can obtain it either experimentally or from calculations, just the derivative of the proton titration curve. And we can see that it answers the free energy between macro molecules. So, that's a little bit about the charge fluctuation mechanism. And I think this definitely belongs to the lesser known mechanisms it's a, if you if you go back in time you can see that this has come up. You know, maybe a 20 year interval so sometimes it's get some attention and then it kind of dies out again. So it's a it's a little bit. I would say in the obscure in but I wouldn't say that it's unimportant. And we can. There are now more and more methods in molecular dynamic simulations methods where you start to include fluctuating charges and there I suspect that we will start to see these mechanisms again. So let's move on to the part two, and then this is about iron specific effects, and then also sometimes known as Hofmeister effects but I would say more generally and specific effects Hofmeister series is a, is a, is an early discovery about irons. And it's a limited effect I would say. And the, the very nice picture here is done by Stephen Hansen as a former student and we are trying to use this for journal cover we don't know if they will accept it yet, but what this is about this is a cup of coffee. And what you see here in the phone. That's actually a caffeine molecule that we are investigating, we're investigating how the thermodynamics is affected by these. Let's call it ionic candy lying around here on the, on the plate so these are different ions, and they will affect the caffeine molecule and the caffeine caffeine interactions significantly. And we're trying to study that using experimental computer simulations. We're trying and go through the iron specific effects and I'll try to, I'll try to outline the sort of the major effects that's behind these observations. And this is something that has been, I would say fairly recently has been unraveled. This has been a puzzle for a very long time. But I think we know now, pretty much what's going on, but I will try and explain it. This is a series here was discovered by Franz Hofmeister. And what he did was to take different proteins and look at their solubility as you add different sorts. And what he observed was that the depending on what sold you added, you would have a different solubility is basically. And here we have a list of anions and cations and they are ranked according to how well they, they sold in or sold out the proteins. But it's important to note that when he did these discoveries, it was not at all clear that souls would dissolve into dissociate into distinct ions. This was highly controversial at the time. So this is something this is a newer formulation of his series. But back then when he did it he, he just took sorts he didn't know that they actually dissociate. And to show you what happens, I will show you some experimental data that we illustrates that this is a very strong effect. And here we have a osmotic second vehicle coefficient data measured using light scattering. And down here we have the salt concentration and here we have the video coefficient that's it's presented like this one minus the video coefficient. And then this is done in our different potassium salts. So from chloride bromide nitrate iodide and thiosynate up here and we see that side sign it here means that this induces a very strong protein protein interactions, whereas much less interaction is induced using a potassium chloride. And that, what is even more puzzling is that if we cross the isoelectric point of the protein, then these half master series they reverses. And the molecular level explanations for this, they have really puzzled us for a very long time but as I said, I think that most of it is known by now. And I would say that there are two main mechanisms that control this and I'll try and go through them. So, the mechanism behind the specific effects. One of them is that we can have ions that can bind to the macro molecule. Here we have this is this is a model we made now quite some time ago and we use molecular dynamics to do this but you can do the exact same experiment on proteins and you would see basically the same what I'm about to, to tell you now. So the green ions they are small and ions and the red ones they are big and this could be for example, fluoride and this could be iodide, let's say. And now we have macro molecule here, where we have put some cat ionic patches on the surface. So, these are plus one out here and then this part here is has no charge so it's a polar. And we embed this in explicit solvent so everything the solvent molecules are there. And we now just look where do these iron distribute on the surface of this artificial macro ion that we have constructed. And it looks something like this. And that there is a really a distinct absorption of the small lines they go to the charts patches, and then the big iodide sized ions, they sit here in between in the much more a polar regions. You could talk about that these are more they have a more a polar character these big irons and make sense because they are, they are much less solvated than the small fluoride ions here that would be really highly solvated they will sit the water molecules would sit very tight. And if we, if we transfer this to protein surfaces, of course gets much more complicated because the salvation, if you, if you scan the surface of the protein you will find that the salvation of the protein surface varies a lot. We can have cat ionic and an ionic groups, and then we can have polar groups we can have a polar groups, and all of that will have a special affinity to differently sized ions. So, the binding of ions is really an important. Driving force for the for the half master or I'm specific effects as a rule of thumb, we can, we can use this principle called the law of matching water affinity is not sure it here. Here we can see that ions of like sized. So like sized ions cat ions and anions they tend to pair together they form strong iron pairs, whereas similarly sized ions. They tend to stay away from each other, you can see this in electrolyte solutions in the activity coefficient you will find this kind of behavior. And we can translate that to the surface of macro molecules like proteins. And this is the reason why the small, the small ions they sit to the attracted to these blue patches here because they have similarly similar size. So that's the reason why they accumulate like this, whereas the big red anions they sit here in between they're not so so happy and and all of this is due to the salvation properties of the ions versus where they bind. So that's one mechanism behind the, the half master series. And the next one is the opposite. And that's exclusion of ions. And a typical example of this would be sulfate. So what we have here is we have for example, highly solvated. I am like sulfate. We, in order for it to approach this poorly solvated macro molecule I have over here, then they would have to let go of some of the salvation layer in order to get into here. So that's, that's an unfavorable process so in order to reduce this excluded volume that we have around this molecule and here, one way to exclude that and gain more entropy for these ions is that we can see simply push them together. So this is a sorting, sorting out effect. So the salt is pushing the particles together like this. Another way to view this is that you could say that there is an assault effect on the hydrofluoric interaction. And that effect is so specific. More weekly charged ions, like these ones we have up here, they are quite happy to enter this region we can see that up here so they can actually be absorbed on this a polar surface, especially if we have some charged patches as well. So it's really iron specific effects, both of these binding and exclusion of ions. So from a theoretical point of view, if we want to make models where we can treat, for example, hundreds of particles of macro molecules, this is really quite difficult to capture these effects because it's so it's so connected to the to the salvation of the iron and of the macro molecule. And if, for example, we have implicit solvent models, and we lose all this information simply just isn't there. So we have been working on ways to incorporate that into into our models, even in systems where we don't even have explicit ions, and I'll try and show you how that can be done now. So, one model we have and we are working on at the moment is is one where we're using solvent solvent accessible surface area approach. And here we have two proteins, they're close together and what we can do during a simulation is that we can. We can for that particular configuration we can now measure the solvent accessible surface area per residue. And this is a quite expensive calculation but it's, we can do it it's part of the we can have it as part of the Hamiltonian. So we are on every step in our simulation we calculate this sasa for each residue. And what we do is that we let this change in the in the area we let that be part of the Hamiltonian in what in what I've written here we have a parameter here that is sold specific and it's amino acid specific. And we then multiply that with the salt concentration over here. So, what this means is that, depending on the sign of this epsilon, we can either favor or penalize the creation of area in the between the proteins. So, we could, we could introduce attraction between the proteins or actually keep them apart. And if we keep them apart that would correspond to an iron binding to the surface, or if we push them together that can be an iron exclusion to the surface. I should say that we have other ways to include iron binding, but I will not talk about it today. So, this method here is mainly for treating exclusion of irons and how they can push the particles together. But it's a fairly expensive methods as of now. What we've done is we've tried to apply this on a small molecule caffeine. And this is what I've illustrated here. So, here we have a caffeine molecule and it has some distinct motifs, and we have coarse grained it like this. And now we can simulate many of these caffeine molecules together using our many body assessor Hamiltonian that has described. So by assigning. I go back once, sorry. Watch that once more. So, if we assign these epsilon values to some of these motifs, we have some idea about based on all that molecular dynamics we have some idea about how we wear the ions bind how they excluded. We can construct a model that can take into account on specific effects on caffeine. And really the reason why we're looking at caffeine is that it's, it's a proxy for a small amino acid, and we would like to extend this so that we can describe peptides and proteins as well. So, first, if we look at here we have calculated the osmotic coefficient of just caffeine in pure water as a function of caffeine concentration. So, caffeine very quickly starts to, to interact with itself and it can form, can form stacked configurations so it's, we cannot go to very high, high concentrations of caffeine because it's simply not soluble. So this is just to test our model in a in pure water and using the Hamiltonian here where we use sasa to describe the ion specific specific effects. We can then look at the change in the excess chemical potential as we now increase the salt concentration. And here we have some experimental data and we try to, to compare that with our Monte Carlo results. So, so that's, that's ongoing work I would say in trying to incorporate these effects and see how molecules are being affected by different sorts. Right. So, that's a little bit about ion specific or Hofmeister effects and then now we come to the, to the last part where I would like to talk about some a few things about fundamental interactions that I think is perhaps not so well known in the protein field. It's very well known in the colloidal field. And if some of you are from coming from there then then you will probably have heard about this before. So the image we have here is is actually painted by one of our collaborators Cliff Woodward from Australia and I just realized it looks like I put an earring on on one of us but it's actually because it's taking from a book cover. And then there are some some atoms, atoms on the side. But, nevertheless, let's continue with this topic. So the Van der Waals interaction is actually exactly a sum of different mechanisms, and we have three different mechanisms called dispersion interactions we have dipole dipole interactions between, if you have for example small polar molecules, and we can also have dipole induced dipole interactions, if you have something that's internally polarizable. Common to all of these making these interaction mechanisms is that they, they vary as one over six. So the decay, the interaction energy decays quite quickly with the distance. And because of this, it's, it's common that you will see them in models and in computer simulations they have just been lumped together to one term. So for example in a Jones potential you will have the, the Van der Waals term comes in here. And a few notes here. So, a and B in simulations and theories they are often used just in as an empirical fitting parameter. And I think this can sometimes be a little bit problematic but it's well, maybe not problematic but I think it's important to just realize that they are actually three different mechanisms. So if we talk about explicit solvent models, and then the key some part dipole dipole part is explicitly included. But only if we have polarizable simulations which I would say is not that common because they're very expensive. And then the Dubai into a Dubai part is also included, but normally it isn't. So this means that if you take a standard or Latin molecular dynamic simulation, it would be the key some and London interaction. That's, that's part of the constant up here. Right. So if we go to implicit solvent models, and then then be in principle, can be negative it includes all of these terms but it's an excess polarization that we have. And this means that it can in principle be negative I've never seen that done but I think it, maybe sometimes it could make sense it could be that it would correspond that you have something of a very high dielectric that you approach something of a very low dielectric. So that's just a comment about this and something that I think it's not talked about so much when we talk about one of us interactions in these implicit solvent models, at least not in the protein field. Finally, I would like to talk about another aspect of the Van der Waals interactions that comes from the colloidal field that I never see mentioned in the protein field. And that is that the Van der Waals or these are six one over our six potentials they decay very rapidly so they're quite short range. But I tried to illustrate this with the ants up here that when there are many of them together, they can actually reach further. And just to show you this so we have the potential here one or six, but then we have to remember that they are not alone. They sit, we have to evaluate this over all the atoms in the macro molecule. So it looks something like this and we have to, in order to calculate the total energy we have to sum up between all of these different particles here. And we can do that in computer simulations for any kind of shape we want. No problem. I think it can be interesting to do this also for more idealized shapes. So for example if we do this for two spheres. And it looks something like this, we have to integrate this one over six potential over these two volumes. And doing that, we end up with something that goes one over D, where D is the distance between the surfaces of these two spheres. So what this means is that the interaction here has gone from being one over six potential to be something that the case as one over D so much more long ranged. And this is important because this can be have very strong effects on the, on the thermodynamic properties. So a long range interaction, long especially long range attractive interactions will have a big impact when you start to calculate thermodynamic properties. Right. We have now reached the end of the talk. Yes. I would like to mention here in the end that we have, if you're interested in simulating many party protein systems we have software available for this. And we do a lot of protein simulations I would say and many of the effects we've talked about charge regulation in terms of specific effects. They are we're trying to include that in these in these models. So with that. Thank you for your teaching.