 And thanks to the organizers of the LynxNIST webinar on antibodies in solution for giving me a chance to talk about my favorite pet project, antibodies, and how to understand them using colloid models. We have actually been interested in concentrated proteins for a long time, initially driven by our interest in understanding the islands, and in particular also understanding protein condensation diseases around this like cataract formation, for example, or impaired vision like Presbyopia, but also more in more general terms, understanding protein crowding and the stability of the cytosol. And accordingly also the our prime interest initially was mainly on protein aggregation protein phase separation stability of protein solutions and mixtures and so forth. But then later on moved very much towards dynamics. In particular also of a more newer interest and that has to do with the formulation of biologics involving high concentration protein solutions. Now this is in particular this is of course also the focus of today's webinar this has come from from the fact that when once to formulate antibodies, one actually faces a few problems. And this is has to do with the fact that antibodies are very large proteins, typically around 150,000 molecular weight, but they only only a small fraction of this protein is really the active site that is targeting then sort of the, the structure of interest for the pharmacological treatment. And so we need relatively large doses of antibodies to administer something like a milligram of antibody kilogram of patient. And, obviously, currently, I mean we all know how important antibodies have become in pharmaceutical industry. They're primarily administered. In the hospital. I, I, I be into witness. And what would however be preferred is of course you fund if the patients could self administer these drugs, for example through containers injection. Now given the fact that we only can inject a limited volume. This means that we have to have high concentration for relations typically above 100 millimeter per milliliter antibody concentration. And that of course then again raises problems because of something that one often finds that that is the increase of viscosity in protein solutions if one increases the concentration. Now, there is something like a window of opportunity here if the if the relative viscosity the ratio between the seership viscosity and the viscosity of the solvent goes above something like the factor of 10 injection becomes very difficult and painful and so one needs to create formulations with antibodies that that the viscosity even at the high concentration formulation is below this critical threshold. And as you can see in this particular example of an antibody that can for example then strongly depend on parameter such as for example the ionic strings with a pH. We really need to understand and better even predict the viscosity of concentrated antibody solutions as a function of the molecular structure of the antibody and the other formulation conditions and physical parameters. Now there is obviously a link between the molecular structure and the interaction potential between antibodies in solution. There is also presumably a link between a tendency of antibodies to self assemble and the resulting viscosity then of the antibody in solution that higher concentrations which we need to understand. So, there are of course ideas about around drawing analogies from colloids why the viscosity increases with antibody concentration if we typically look into colloidal systems say heart sphere particles in in in a solvent. We see that with increasing volume fraction. Initially, the particles are able to undergo freedom fusion. Once the volume fraction increases particles around a particular particle or target particle then form sort of form something like a cage. There, the particle now is no longer to diffuse freely but will initially bounce around within the cage until it's opens and the particle can escape. Once the concentration and the volume fraction is too high and for heart sphere colloids this is close to random close backing so close to about 64% volume fraction typically with lower such cage openings no longer can happen. And, and basically the solution or the suspension arrests. We assume that for proteins similar mechanisms hold, and indeed if we grow or compact globular proteins that interact primarily via excluding volume interactions. Indeed we find exactly the kind of behavior quantitatively reproduced by the relationship between the relative viscosity at the volume fraction as found for heart spheres and predicted through so called no carbon theory. However, the situation for proteins is actually more complicated because proteins are and this is something we will come back to in a minute are not really like billiard balls and and so when we then look into the different types of proteins, we realize and here I just show information from a related type of experiment. And that is, Newton spin echo experiments that allows us to measure the collective diffusion coefficient and relatively local distances in the nearest neighbor distance between proteins at high concentrations. And it's the short time collective diffusion coefficient in this case we indeed see dramatic differences between the diffuse safe behavior of different proteins. And also when you look at the dashed lines here that indicate the rest transition as a function of the given volume fraction here, you see that this actually shifts down to very low values below point three or so for certain types of proteins. These are in effect proteins that are known to interact, not only through typical colloidal centrosimetic simple interaction potentials but are known to also have attractive patches that result then in the cluster formation in transient cluster formations. And the idea then that allows us to qualitatively at least understand what's going on here is that clusters open fractal clusters as they typically form up to these conditions, take up much more volume than the monomers themselves and so you can still have these kinds of teaching effects and the rest transition, but now the clusters these open clusters play the role of the color it's initially. And so what is important in is that when we now go for different types of proteins and in particular and we need to understand what the relative mechanisms are that determine the viscosity for concentrated, for example, antibody solutions. Before going into this we need to think about how we characterize the structural and dynamic properties of these antibody solutions and what we typically do is a combination of different techniques. That's dynamic light scattering static light scattering small angle x-ray scattering and my choreography. So we want to derive models to understand the behavior of these proteins and analyze these experimental results that come from these from these techniques it's of course first of all important that we really understand what we measure. In the case of dynamic light scattering what we really look at is the dynamics of density fluctuations or concentration fluctuations of wavelength given by 2 pi over the scattering mixture which we do this dynamic light scattering experiment. And so the number of fluctuations or the decay of concentration fluctuations is governed by a quantity. That is called the gradient diffusion coefficient and it's really this quantity that in the limit of small angles, small scattering victories and small protein dimensions is what we measure in light scattering. In the dynamic light scattering side what we what we look at is the magnitude of these density fluctuations at the same wavelength. And this is expressed or governed by the multi-compressibility. When we then go to SACs instead of light scattering static light scattering. Of course now we go to much larger Q vectors so smaller structure link scales that we can investigate. We look at the scattering intensity as coming from a combination of influence from the particle structures so in this case for example the antibody structure or the protein structure more general and into particle correlations that become more prominent at higher concentrations. And finally in the microbiology experiment which we prefer for protein solutions compared to a classical rheometry measurement. And what we really measure here is the self diffusion or mean square displacement of large trace of particles well and I say large they're a couple of hundred nanometers in diameter so much larger than the characteristic length scale in the solution given by the proteins and their distribution in the particle distances. And so, we can then look at the protein solution as some sort of a bulk solvent, and the trace of self diffusion then basically gives us access to the searshift is considered you have this bulk solvent. Now, as I said we now need to create models that allow us to interpret these data based on for some of the molecular structure of the protein. However, can also self assemble and so, and, you know, apologize for the density of formula here, but we have to understand then that in this case we have to consider a system where we might see actually a polydispersed solution of clusters that also in that that also interact with different interaction forces and and also indirect interactions caused by high dynamic interactions. And so what we then measure in the dynamic light scattering experiment is so called Z or intensity average parent gradient diffusion coefficient that is given by the two diffusion coefficient and and then for you know spherical high dynamic function H of Q and the direct structure factor S of Q, which is also measured in the sex experiment. And in the static light scattering we can measure something like an apparent weight average molecular weight. And the problem here is that we need models that allow us to consistently incorporate both self assembly so particle size distributions, as well as interactions that are also influenced by the self assembly in order to then arrive at a consistent analysis and interpretation of this data. And so this is really here. The important thing to consider and this is what we need to keep in mind. So how do we do this well in general, or, you know compact global proteins, the use of colloid models has as a long tradition, and actually been successively used in order to describe and also even predict base behavior of protein solutions base separation aggregation rest transitions And typically, what one does is instead of, of using, you know, the full molecular structure of the protein or here also seen as the as the as the full shape of the hair. We go to something like a spherical here in the extreme case of a spherical colloid that interacts via spherical isotropic interaction potential. Now for some proteins, these may not be good enough so we may have to incorporate some particle shape and I saw to be or also the include the possibility for directed interactions patchy interactions, cause for example by high default patches or non homogeneous distribution of charges. But we never try to use the full atomistic structure because for example, doing computer simulations of highly concentrated protein solutions using an optimistic description of the protein which has to be absolutely impossible, because it's it's way too costly in terms of the medical effort that needs to be taken care of. And so the key questions when when trying to attempt to use colloid models, in order to analyze experimental data then is what is the right level of course training that is capable of reproducing the concentration dependent properties. So this. And the importance of direct interactions and shape and interaction and I saw to be do we have to take this into account or can we get around with simple spherical models and interaction potentials. Now, for antibodies it's becoming even a bit more complicated because of this open widely shaped structure of the antibody. And we have to see whether we need to use the full here, or whether we can get away with the spherical here. And so there are different levels of course training this criteria on this, on this slide, where we start from the two molecular structure of the antibody that we can then for example, use in something like in the simulations or so to gain information about the most chemical confirmation of the antibody and gain insight into the flexibility of the antibody and so forth. Typically we will then make a course training step and, and for example, model each amino acid as a small sphere. And then we can then use this using for example Monte Carlo simulations to gain insight into the charge as a function of pH ionic strengths and so forth. And it's still highly demanding. And so we might need to make further course screening steps and they to go to a smaller number of beats, but still maintaining the why shaped structure of the antibody or go to a full spherical antibody description so the analog of the spherical here here. And this kind of model that is typically used by many of the researchers interested in antibody solutions and their characterization and description. And it's used to interpret, for example, theta potential measurements or a sketching experiments both dynamic and static sketching experiments. Let's start with this very simple color with approach and see how far we get. For this, we take a first example of an antibody. It's a so called IGG one. A typical molecular weight of about 148,000 Dalton. It comes with the high dynamic radius of about five and a half nanometers, radius of charge for five nanometers. And it's, it's strongly positively charged with a charge net charge of about plus 30. So if we make such a spherical void model we take a particle that would then be modeled like a non conducting sphere with a given radius or say call it the heart sphere radius. And the interaction potential of that would then be a combination of the heart sphere potential. The screen cool on potential and some short range attractive potential. That is typically then taking into account things like fundamental attractions and possibly also some hydrophobic attraction. And that's really the kind of classic color potential that people then use also in the protein business. Now, there is one thing that is often forgotten about and not taken into account and that is, when we look at the screen cool on potential that describes the effect of the charges in the presence of ions counter ions. It often forgets to take into account the dissociated counter ions from the charged amino acid residues that also contribute to the screening. And so, in effect, we then actually get a interaction potential that in particular at low ionic strength so no added salt for example, then makes the potential fairly strongly dependent on concentration. Here, the example of the kind of colored potential that we then use for the analysis of the data here. And the dashed line here is without the additional attraction and the solid line is then the full potential that also takes into account the short range attraction. And a low ionic strengths coming just from the buffer itself and no added salt and the higher ionic strengths with an additional 50 million dollars sodium chloride added. Now, the question then is, is this type of potential capable of reproducing the experimental data that we then get from the four techniques that I have mentioned. Lots of lines and lots of data here. Let's just walk through this. So let's start with the static light scattering results here the the solid black points are the measured data set from the low ionic strength sample. So, looking at the S of C or the osmotic compressibility as a function of concentration, all the way up to very high concentrations of close to 200 mixed per mil. The blue solid symbols are the same data at 50 millimolar added sodium chloride. So, all together 57 millimolar ionic strengths. And the solid black and blue lines are the corresponding results from colloid theory where we calculate the static structure factor and the compressibility to liquid state here using what is called a Rochester's young closure that is known to be particularly accurate also at high concentrations. And we see that indeed our data is almost quantitatively reproduced over the entire Q range. The dashed line here is the is the same calculation for potential that only includes excluded volume effects and screen coolant repulsion but no attraction. This dotted red line here is for pure heart sphere system here so you see indeed we need some attraction in order to cover all concentrations measured. And here on the right upper corner you see the results from the dynamic light scattering experiment. Again, the lines mean the same and the data points and colors also mean the same. So black is low ionic strength is high ionic strength. And the solid line is a full calculation where we use the percolation function as we get it from the Rochester's young closure relation calculation and then calculate the hydrodynamic function. And again, here, we cannot do this up to very high concentrations because of the fact that this approximation that we use here is not valid at concentrations higher than about 50 mixed per mill. And so again, things look good. The full structure factors are also nicely reproduced by the Rochester's young closure for these two concentrations shown here at low ionic strength 2050 mixed per mill. And what I have to say here is we use a colloid model with an effective charge of plus 20. And then finally, the even the relative is causing and its concentration dependence is more or less quantitative reproduced at the lower ionic strength sample through a relationship phenological relationship that is known to reproduce heart sphere data quite well. Things look pretty good. Well, there is, there is a problem here. And, you know, if this were a standard talk I would stop here, but I tried to show not only the benefits but also the problems with this colloid model. And, you know, there is more to say here because at the end of the day what you will see is that we can indeed use this simple spherical colloid model to reproduce the data. But we cannot predict it we cannot predict the parameters of the model that we need to use to reproduce the data based on the molecular structure of the antibody. Let's for example look at the charges that get out that we get out from from the theoretical treatment of the data. There are three ways on how we determine charges on the antibody other than also chemical titration, which has its own problems. One is of course, the theoreticians or simulators way by by by really, you know, calculating amino acid charges using Monte Carlo simulations of the antibody where the protonation state of the amino acids are allowed to fluctuate to go for minimum free energy of the system, and then if you unexpected theoretical charge net charge of the system, but also the charge distribution positive and negative charges along the surface of the antibody. The standard way protein biochemists chemists. The trick is that they measure electrophoretic mobility or, you know, they normally call it seat the potential measurement, even though one doesn't measure the seat the potential but the electrophoretic mobility of a charge particle in an in an external electric field and then use a colloid model to deduce the charge. And results then together with the hydrodynamic properties of of of the of the particle in this mobility. And then finally the way a colloid scientist often deduce charges on their systems is by doing sex measurements calculate the structure factor then use the liquid state series in order to reproduce the structure factor based on an effective charge, that they introduced, what are the values for this particular antibody if we do these three different types of of calculations or predictions as well. The theoretical charge as we get it out from from the molecular structure and the Monte Carlo simulations is plus 31. And the kind of of charge distribution as it shown here on the inside of the picture. If we do the electrophoretic mobility measurement analyze it with a spherical colloid model we get an effective charge of plus 13. And if we analyze the structure factors we need to use an effective charge of plus 20. So obviously, you know, they all differ wildly. And it's clear that we really have to be aware of the fact that all of these is model dependent and and the question then remains how we, how can we obtain and predict charges and their effects on on antibodies stability. Well, there is another problem in the in the simple colloid model and that is in the way we actually look at the structure factor. At higher concentrations we see that we no longer reproduce it with with the colloid model. The local part is finding is not the compressibility comes out right, but the peak the nearest neighbor peak is vastly enhanced in in the technical prediction, but it's not present in the measurement. So clearly, we have some deficiency in this in this simple spherical model and we need to look at effects of course grading on the effective charge and on the effective structure factor so we then made a systematic investigation starting from the amino acid representation, and then going through successive course grading steps to come up with why shape models and finally with the spherical colloid. We started with the full amino acid representation. And we also did then many antibody simulations. We now introduce an effective beat beat potential between beats on different antibodies given again by a screen cooler potential and the liner Jones to take care of hardcore and short range attraction from the most attraction. The idea is that indeed at both ionic strengths we can we can more or less quantitatively reproduce the measured structure factor from sex and all the different concentrations using the theoretical charge of plus 32 variation that we that we tested in the in the strengths of the, not the attractive interaction this epsilon term that we vary the round values that are known to work well for for the other types of proteins on this, I mean, acid representation. So what is then happening when we six, you know, in steps reduce then the number of beats and so we consider here 1296 and one beat models. Let's first compare the six and the one beat model you see that already for the six feet model, the structure factor at both low and high concentration for the low ionic strength is very well reproduced by the six feet model. A higher charge so we need for the six feet model we need to use an effective charge total net charge of about 26 compared to the 24 the one beat model. And you also see that at low protein concentration, the level of course creating doesn't really matter, but at high concentrations it does. If you then go to the nine beat model, things really become quantitative we can reproduce all measured structure factors with a new yet still a bit higher net positive charge. And you can see here that indeed the charge that we need to use the effective total charge on on the model depends on the level of course creating and it sort of approaches the net charge that we get from the initial single molecule simulation on amino acid level. And so clearly the take a message from here is that charges obtained are indeed effective charges that depend on the model that is used to interpret the data. Moreover, it's the anisotropy that is crucial also for calculating the correct measure structure factor. Why does the nine beat model work reasonably well and why is the charges lower that we use the effective charge lower on the one beat model then on the safe for example nine beat model. You have looked at this by sort of measuring an effective potential of mean force in simulations between two antibodies on the left bottom you see a movie on not on an antibody but on a more compact protein that I got from one of our polymini. And so one basically looks at the percolation function between these two particles that are allowed to move around and rotate and and and based on this we can then estimate the potential of mean force. And what you see here is that in particular at low on the string so that's the upper right hand graph. You see that the long range tail of the potential for the one beat and the nine beat model using these different types of effective charges actually more or less overlap. So you see at shorter distances when the potential start to deviate. And obviously, for the one beat model, antibodies cannot come closer than the heart speed diameter of the one beat system, whereas for the true antibody and also for the nine beat models they can of course come much closer. The, the minimum distance that they can have is basically something like the heart speed diameter of a single beat. And, and so, since in the low ionic strength system, the potential is fairly long range and fairly repulsive antibodies hardly ever approach very closely. And so, in that sense, what we then see is that we have to choose an effective charge in the one beat model that results in the same long distance tail of the screen cool on potential and that is of course a much lower charge. Since the charges in this case are all smeared on on the surface of these non conducting sphere. On the other hand, there is still the need of some attraction also in particular at higher concentrations where distances are shorter, because we need to compensate for the two large excluded volume that the one beat model has. And, and so, again, what one needs to realize is that the charges that one gets when analyzing structure factors or compressibility using these one beat colloid models these are effective charges that very much depend on the model to interpret the data. And the attraction needed in the one beat model is also not really directly linked to the fundamentals attraction, but it sort of is there to compensate for the two large excluded volume. And so, the values in the attractive part only become meaningful for antibodies once we go to a much less coarse grain model. And this is, of course, in contrast to the much more compact, typical proteins like Lysos, Gamma crystalline and so forth that people have used, where we indeed have the charges on the surface and the structure is not so open. And finally, anisotropy is really crucial for calculating the measured structure factors. There is one final thing to add here and that is, even for this antibody that is highly charged, and with a relatively homogeneous charge distribution, still at high ionic strengths, we suddenly start to see a dramatic increase of the viscosity at high concentrations. And this presumably comes from the fact that now at high concentrations, at high ionic strengths, the range of the repulsive interaction between like charged spots on the antibodies become much shorter. And so, patches start to develop and eventually we can also start to see cluster formation that then leads to higher viscosity. So the homogeneous charge distribution stabilizes initially the map against aggregation and cluster formation and once we give enough salt, patches develop and attractions take over and clusters form and the viscosity shoots up. So that was this and you have already seen a bit about pros and cons of such colloid models that we can use to interpret data for antibody solutions. Now let's switch to another map. And this other map is again positively charged. It's still a reasonable charge of plus 13. But you see now when we compare the so-called electrostatic iso surface. Whereas this is fairly homogeneous and normal, you know, sort of globular spherical for the first map that we looked at. For the second map it looks different and there are actually clear, positively charged and negatively charged regions in this particular antibody. And that actually has consequences when we look at the resulting relative viscosity as a function of concentration. And back here are the data taken for the first antibody that we looked at, map one, and blue are the data taken for the second antibody map two. The open symbols are the ones with high ionic strings, the solid symbols are the ones at low ionic strings and you see that for the first antibody charge is stabilized the antibody against aggregation and high viscosity. At salt, we start to see a much more increased viscosity and high concentrations, whereas the opposite is true for the second antibody, where adding salt to a high concentration antibody solution decreases the viscosity quite a lot. And so, in one case, ionic strength, increased ionic strength seems to destabilize whereas in the other it seems to stabilize. So this made us rethink again our approach to colloidal modeling for this type of antibody. You see this actually when you compare data from static dynamic light scattering and my choreography as a function of concentration for this antibody. With ionic strength we have a clear indication of a concentration in use self assembly with both the apparent molecular weight and the apparent dynamic radius increasing, but then at higher concentrations interactions take over. And so obviously we need to now include also a possibility for self assembly when we model this particular antibody. Given the heterogeneous charge distribution and the fact that charges seems to destabilize the antibody against self assembly and clustering, we designed a three patch model here. Either in a by shape computer model. In this case it was a six speed model where we had then patches be and a type to be and one a type there a attractive interaction was then happening between a and b and b and a and a were repulsive. And the rest was just excluded volume. And we also used a patchy sphere models to which we then applied analytical bedtime series so called bedtime theory that allows us to look at this simple numerical calculation. The approach in this course training modeling is then that we start with patchy monomers use their time theory that allows us to calculate as a function of a of two key parameters the the heart sphere diameter and the strength of the attractive patch patch interaction. allows us then to calculate the bonding probability as a function of concentration. This can then be plugged in into another polymer theory so called hyper branch polymer theory that then gives us the cluster size distribution. So the next course training step in order to calculate also dynamic properties such as the diffusion coefficient and the viscosity, we then treat clusters again as in the heart or attractive heart sphere collides. So how well is that time theory able to reproduce the mission compressibility. Almost quantitatively you see here is three patch model. The bond strength here and and and the S of zero or the apparent weight navigation weight average aggregation number is is is almost quantitatively reproduced. We can then use the bond probability as these come as he comes out of their time theory as a function of concentration. We can then use the so called hyper branch polymer theory to calculate now the cluster size. At each of these concentrations, there's no additional free parameter there. And when we compare the analytical cluster size distributions with the ones that come out from patchy why computer simulations they quantitatively agree. So we're confident that the cluster size distribution shape of the cluster size distribution makes sense. And we can then use this and now again calculate compressibility and and through the sort of a heart sphere relationship where we treat the clusters as as an attractive or attractive sticky heart spheres with the radius given by the cluster size. And we see that now indeed. Once we have fixed the parameters in the bedtime model. These resulting cluster size distributions are then capable of reproducing both static light scattering data for both ionic strength as well as the microbiology almost quantitatively. And also if you use a simple cluster model to calculate the mission structure factors they also reproduce the structure factors quite well. So indeed, when we beef up our our colloid model course great colloid models with patchy interactions is again works beautifully. I think it's time to conclude and let me just run you so some of them. The major take home messages that I would like to convey to you when we talk about the use of colloid models to deal with complex antibody solutions. First of all, I think it has become clear from what I said that individual techniques such as dynamic light scattering or static light scattering or rheology or saxa sense alone don't provide conclusive data or assessing aggregation propensity or predict the nearest transition. I think this it's fair to say that this is not enough. And we really need complimentary techniques. These two colloids and using the existing theoretical framework from colloid physics allows us in principle to understand model and predict the onset of aggregation and the location of the rest transition in an asset in principle. The problem here is that we have to be aware of the fact that the predict is difficult because since these since the parameters that we then need in this colloid description are effective parameters and we cannot just take the molecular structure and then predict the parameters that are the effective charge. And so we have to include shape and isotropy and patch interactions. If you really want to go from the molecular structure to all the measured quantities. So really the combination of stacks or sense SLS and deal is my theology and compute the simulations that we believe is vital to understand concentration effects on diffusion and rheology of different antibodies. I would like to particularly point out since charge is a very important parameters determining the stability of antibodies in solution. And charge distribution is essential for stabilizing monomers in many cases and preventing cluster formation and face separation. But it has to be clear that simple colloid models together with the experimental tools that one uses to determine charges like electrophoretic mobility measurements or structure factor measurements. These are the yield effective charges. They are different from the actual net charge as it would come out of a titration experiment or in particular from computer simulations based on the fluid molecular structure of the antibody. Colloid models are great, but we need to design them appropriately by first looking indeed at the molecular structure, looking at possible charge heterogeneity is that determined in the repulsive or attractive charge charge interactions. We need to look at the presence of possible hydrophobic patches that will not be covered by long range repulsive interactions between antibodies. And so we need to combine molecular and colloid viewpoint. And it's only the link between the molecular structure and the resulting stability and dynamics on all relevant links and timescales that can come out of this if we really make this marriage between the molecular and the colloid viewpoint. With this I'm through. And I would like to thank those that did all the work. There are a couple of experimental postdocs, Alessandro Glover assembly and Nicholas Cargislinghe, as well as our simulation friends Marco Polimani here in London, but also the more senior PIs Mikhail Lund Anna Stratner. And there were collaborators from Rome around Emmanuel Lattacarelli, and we had industrial scientists from no one or this concern of that we're also participating in some of the studies that I presented here. And with that, I'd like to thank you for your attention and I'm happy to answer questions. Thank you.