 Good, today we are going to have a slightly shorter lecture and talk about secondary structure and amino acid properties. This is to some extent a rehash of the very first lecture we gave for good reasons. You've been through a tough week of lots of statistical physics, we've been looking at entropy, free energy, enthalpy, and everything, and I'm not going to try to tie up the sack here a bit, refer back to lots of the things we talked about on Monday. And I'm also going to give a couple of summary things that we're going to cover after Easter. So that's what we'll gradually get into, I'll cover in a minute, but I would suggest that we start with these study questions that we've been doing the previous weeks, too, and go through them. 14, it's a bit shorter here, pick one of them each, and we can skip number three because that's going to take too long to go through. But pick one among the others and try to provide an answer to it, and then we'll see whether it's something we should discuss more. Any takers? Okay, difference between Helmholtz and Gibbs? It's almost the same, but Gibbs free energy has also the enthalpy. No, so, well, almost right. So the enthalpy, both of them have enthalpy. So the thing we previously called energy, we should always call enthalpy. The Gibbs free energy in the enthalpy, in Helmholtz, the enthalpy is exactly identical to the potential energy. In Gibbs, the enthalpy also includes this PV term from pressure. What I would suggest that you normally do, or rather, what I frequently do, what most of us frequently do, we talk about Gibbs, but we use Helmholtz and have a little bit bad conscience for it, because Gibbs is the one, Gibbs is what describes what happens in the lab. We need to include the work that we do when the pressure and volume can change, but then we know that in practice that term is so small that we typically ignore it. So that's why I say call it Gibbs. In practice, we use Helmholtz, and we should have just a little bad conscience that we should really have included the pressure, but we know that it's so small that we can't ignore it unless you're building nuclear devices. But I don't think, actually, I think we still have the export control, so we promise not to do that on our computers. Okay, some other questions? Yes, that's ballpark. And pretty much anything between two and five or so is perfectly fine. And it's starting to be at high, and it's not one because it's not vacuum. You have some electrons in here that can shield things. Right, so the point with 11 is that there are really, there are two components, right? At the very start, when you go from epsilon 1 to epsilon 2, that's mostly an effect of the electrons. The electrons are super fast. But beyond that, most of the effect of screening in water in particular is actually, it's not an electronic effect, but it's a molecular effect that the entire molecule is turning. But molecules do not turn instantly. So once you get up to megahertz or something, the molecules don't have time to follow it. And that is also, the reason I bring this up, but the book doesn't talk about this, but as you eventually go into simulation, it's going to sound really strange that we use epsilon 1 in simulations, but we still claim that water has epsilon 60 to 80. And the reason for that is simply that we actually, of course, in the simulation where things can move, we include the molecular polarizability, as you say, that the molecules can rotate. So it actually works really well. So this depends on whether you're looking at the world from an atomic perspective or whether you're looking at the world from a continuum perspective in mathematics. Both are fine. So they're not as incompatible as it might sound. And that kind of answers tend to that the role of epsilon is to provide some screening. Why is the water, why does water have such a higher value of this epsilon? This could actually be epsilon r, the relative epsilon. Why is the value for water so extremely high? Yes, strong charges and it's a small molecule that's very efficient to rotate. Other ones? Seven. Seven. Definition of temperature? Yes. And whether it's energy or enthalpy or something, that's a detail. And this is one of those definitions you can look it up when you need it. The point is that it's possible to define temperature from entropy. And then? From this experiment in which you used two solvents, one of them was very hydrophobic and the other one was just water or something, not so hydrophobic. So it's the grain here by which some molecule is shared between the two solvents. Exactly. So partition coefficient, the traditional way of defining partition coefficient would be how much is solvated in water compared to how much is solvated in oil. There's actually a reason why I brought this up. That's quite right, that is the traditional way of defining it. If you just look at experiments, we use partition coefficients all the time because in experiments the probability of A versus the probability of B. So you can actually extend this the second you're comparing two outcomes and that could be spectroscopy, it could be insertion of a membrane protein, it could be folding. Pretty much everything is that you use some relative probability of things to go from probabilities back to a difference in free energy. And that's, you're literally inverting the Boltzmann distribution. Okay, we have a couple of good ones remaining. How does the hydrophobic effect vary with temperature, any takers? Yes, and why? Exactly. Because it's a primarily an entropic effect and we don't really gain much in entropy but we keep destroying the energy parts. Had the hydrophobic effect been an energy effect, we would likely have reduces that the temperature goes up. And that relates to number four. What is the difference between hydrogen bonding in vacuum and water? Also then, it's always favorable. So just how it's bonded, it's free somehow. While in water, yeah, this, so the hydrogen bonding is actually, the hydrogen bond that you formed was actually present in the solvent. Exactly, and this is also part of a much wider concept that anytime, it's very easy to look at something and say that this is good. But you need to know what is the reference data that you're comparing to. And in this particular case, in vacuum, the reference data is not having a hydrogen bond and having a hydrogen bond is sure better than not having one. But in this case, in water, the only difference is where do we have the hydrogen bond? We will always have them. And this occurs in tons of other cases in biophysics and other things too. So you can never, to be a bit extreme, you can never say anything about one state. And whether this is one molecule or one absorbance or anything, one spectroscopic result, one microscopy image, it's always a matter of what are you comparing it to. Relative things are interesting, absolute things rarely say anything. With one exception. Remember yesterday that I realized right in the middle of the slide that I had, there was a strange thing that the delta in entropy, whether that would be negative or positive, I actually added a note in that in the lecture recording. And the reason why I kind of stumbled upon myself there is that in the previous slide, the reason why I said that an entropy is larger than zero is that I was talking about what is the entropy of, for instance, of a water that can rotate things like that one. And then entropy, in theory, an entropy is an arbitrary scale, right? But typically what would happen if I talk about not an entropy difference, but an absolute entropy, it would be very strange if they could be negative. Why? This is not an obvious question. How did you define entropy? You talked about that in the lab yesterday. Yes, but let's count, forget about the constant for a second, but not just counting microstates, the logarithm of the microstates. So what is the logarithm of one? Zero. So if something is smaller than zero, you would have less than one state. And you can't really have 0.9 states. That's kind of, it's non-logical, right? So when it comes to entropies, and that's why we typically say that absolute zero, the entropy is zero, then we have one state, nothing moves. But any other entropy has to be higher than that. So that's why you can talk about the negative difference in entropy, but an absolute entropy, we actually want them to be absolute in a sense. Other fun stuff. Yes, there are still some. So this gets really complicated because far beyond this course. Or actually, in a classical world, the answer would be yes. But there is something, there is a very deep theorem in quantum mechanics called the Heisenberg uncertainty principle. And that shows that the product of the uncertainty in position and the uncertainty in the velocity is always greater than or equal to a very small fundamental constant, which has related to Planck's constant. And the problem is that the better you know your position, the less accurate you know your velocity and vice versa. And this ends up being a problem at absolute zero, right? Because at absolute zero, if nothing moves, then by definition your error in velocity is zero. And then you no longer know exactly what your position is. So that very, and you can actually show this quantum mechanics with experiments, too. So very close to zero, you start having absolute zero, you start having these quantum effects. So in a classical world, the answer would be yes. In a quantum mechanics world, the answer is no. And there is a classical joke about that, that the police stops Heisenberg from having speed and I said, do you have any idea how fast you were going? No, but I know exactly where I were. Relevant and irrelevant energy barriers. That's an important one. Number two, at 300 Kelvin, mind you. This might sound stupid. Why should you know these things by heart? And it also gives you this, yes, but that you could look up. But the point, there are some things that you really need to have a gut feeling for. And there's a really good example for that. I'll show you that in a couple of minutes. Because my hope for you and your career in a couple of years, you're going to be the same voice in the room. When somebody says something that, no, but sorry, that's a really good idea, but I know that that can't be relevant in this case because that energy difference is far too small or far too large. So that can't be the reason. You don't need to spend an afternoon calculating it. You don't need to spend a week simulating it. It's impossible. And that's why if you know those things by heart, you can say that's straight off in two seconds. It's irrelevant. It can't be the case. So what energy barriers are relevant? And if you're really smart, you can cheat here. So what should you compare them to? KT. So if you're really smart, you're going to say what? KT. Which is, I'm going to ask you about this every single lecture until everyone of you says what it is immediately. 0.6 what? Per mole. So 0.6 kilocal per mole, roughly KT, that's a relevant and important region. Things that are substantially larger, substantially smaller than that, we don't care about because they're not going to, either they happen all the time or it doesn't happen at all. So the energy barriers that are in interest are in the range of KT. Within roughly one order of magnitude. Hi, I'm the morning partition coefficient. Why a free and asymptomatic couple of experiments that relates to the partition coefficients, right, that this is the interpretation of the experiment, this is pretty much always a free energy. Hydrophobic effect. And the reason why the hydrophobic effect is so well correlated with nonpolar area, that's kind of, I'm going to ask that this is kind of easy. I'll take these ones, the difficult ones. And the reason for that is that the amount of water that has to reorient, of course, it's an entropic effect in water and the amount of water that has to reorient is the first approximation proportional to this nonpolar areas. As I showed you in that plot yesterday and I might pick up some articles, don't knock down on these first order approximations. I would even argue that the first order approximations are far better than the fourth order approximations because the fourth order approximations, the really complicated advanced approximations, they might work really well in an advanced case, but suddenly you're forgetting something and that advanced model goes completely off the table. First order approximations are rarely perfect, but they're rarely completely wrong either. And in many cases they are surprisingly good. We have used a whole lot of them in papers we published. So try to stick to first order models. It helps you focus on what's relevant rather than the really complicated stuff. Number 13, why the book says, and I actually like that, electrostatics in waters originates not from energy but from entropy. It's a bit extreme because to some of course, electrostatics, the electrostatic interactions are related to entlepis, but what does it mean by that? Roughly as well. It's also that electrostatics in general is related to this concept of the hydrogen bonds, right? We're always interacting with something and the electrostatic interactions are so strong that you will do almost anything to find an interaction partner. For instance, water and hydrogen bonds and that at the end of the day means that the electrostatic enthalpy or energy is pretty much constant. And what rather happens is that to keep this constant the molecules will have to reorient, they will have to form another bond or something and that means that it manifests itself as entropy. I might not say that exactly, that it doesn't originate from energy because the electrostatics is energy but that it manifests itself as entropy and the way we show that is the temperature. This is not a theoretical argument. We can show that with the temperature dependence of the free energy, that is entropy. That's rateable, I mean, as we will talk about today too so I'll skip that a little bit. The idea with the rest of this course that I'm going to start today is that we're now gradually going to go back from the super simple systems in physics, water and everything and head more back to proteins. Even the labs after Easter, after we're going to have one week break but after that we're going to have one more lab when you start looking at kinetics that is not just whether things happen or off between these different states of how fast they happen. But then we will gradually start building real models first of liquids and everything, simulating real things at room temperature and then at some point you're going to be simulating proteins and start to looking at least some simple transitions in proteins. The one caveat here is simulations of real proteins can still be relatively expensive so that you can't complete an entire simulation and not the new. In some cases you will do simple ones and then we might provide you with some trajectories There's some pretty cool stuff you can do here and it's all based on the simple theories. You remember all those curves I had and I even managed to confuse myself yesterday which is not very difficult. Now we're going to have a bit of a practical here to see how smart you are. Forget about the entropy and the enthalpy parts for a second and let's look at one of the simplest systems we can imagine, pure water. So what this plot says is that as a function of temperature water can exist in three phases we have free energy here, Jesus Gibbs and the green one here is how the free energy of the liquid water roughly varies. The blue one is the solid and the red one is the gas. So what can you say from that one? This is not difficult. What does this say? The blue line is the solid one which gives you the minimum free energy when you see solid phase process. And right, and in between that we have water. So we have roughly 0°C here and roughly 100°C here, right? So that's where we have liquid water. Simple, plain and easy. This is an old, I wouldn't necessarily call it a scientific scandal but it's an important momentum, Mori. There are some links if you want to read more about this I put some links about that on the resources. In 1962, a Russian scientist called Nikolai Fidyakin who was far out in the countryside in Russia had some very strange experimental results that when he was pushing water through very, very thin capillaries under some conditions and he repeated this a number of times clean the capillaries and everything but under some conditions he kind of saw that water spontaneously underwent some condensation at room temperature and pressure so that's almost as if the water was polymerizing. So the water got a... thicker, changed in viscosity, changed diffusion, probably, and what's more, you even got a big change in melting and boiling temperature so that... I forgot what his original name for this was but eventually you had the Deryagin was a very famous big Russian scientist one of the most famous in the 1900s take this up and this led to a new field called polywater. And the argument was that under some conditions water would essentially polymerize into some complicated structure, small structures, so they would still be liquid and everything, but it would have very different properties from normal water. And this was picked up in particular by Lippingcott in the U.S. in 1969 and eventually there were a bunch of U.S. scientists that were very active in this too. The amazing thing is that this water would then have a freezing point in the ballpark of either... all the way down to almost this bit of 200 Kelvin and maybe up to 240 Kelvin. So a freezing point that was significantly lower and it would have a boiling point of this polywater that was like 500 Kelvin so up here. Now you obviously know that this is... well, the reason why you haven't heard about this this was of course wrong. You have no idea that there were like hundreds of papers published on this. It was also in the middle of the Cold War in the 1960s. A popular media picked up this and people in the U.S. were afraid that Russia were developing a polywater gap and if it wasn't so sad it would actually in hindsight it's pretty fun. There is something astronomically wrong with this. I'm not sure whether it was a coincidence but a year after this in 1963 Kurt Vonnegut published a book called Cat's Cradle where he talked about the hypothetical form of ice, ice-9, that would freeze already. The water would freeze at 45 degrees centigrade or something and the idea is that if this ice-9 came in contact with your body or anything this would catalyze the reaction and immediately cause your entire body to freeze. This is very close to polywater. But based on what you know now you should have been able to debunk this in a minute. How? It's simpler than that. So what I would suggest you do it's actually worth spending a couple of minutes because this helps occasionally we're so focused on knowledge and knowing facts right this helps you to think and thinking is the most important thing that we do. Try to imagine where what the curve for polywater would be in this diagram and then debunk it. I would suggest let's do let's spend ten minutes on this. So first talk to the neighbor right next to you or actually let's spend two minutes thinking about this yourself first. First two minutes yourself and then we're going to have you talking to your neighbor. Two minutes is not a lot. So let's start now. Think about this yourself with paper and pen first. And if you're watching this online you're going to have to wait. That's the advantage of showing up for the lectures. I think we almost have two minutes there. So now we just talk to your neighbor and see if you can either you already know this and then you just tell your neighbor what it is and otherwise try to reason together and it's still the same question. Try to explain this because ultimately you're all going to explain this to me. So the transition faces us. The transition points is where the green line crosses the blue one. Yeah and then so you kind of move it. So I imagine with the green line that works in the the cross points will be more on the left side. So at the same time it will be more on the right side. So higher than the left. But this is what it is. I think you're on the right track. It's about moving the green curve whatever pink curve. But then the idea compare the pink curve to the green curve. Compare poly water to normal water. Are you getting anywhere? I'll give you a clue. Do this in two steps. First you have the green curve. This is present water. Orange curve. The curve for poly water. What would the curve for poly water look like here? And then compare poly water to normal water. And that would lead to some pretty absurd effects. Well this was a clue. I didn't say that I would provide the answer. Spend another minute talking between the two of you and then you're all going to talk together. If you imagine that orange curve that is more downwards compared to the green curve you want to be farther to the right. Yeah because you imagine the green curve you move downwards and the intersection between the blue and the green line it is more to the left side. What that implies actually? So talk 20 more seconds. Try to say what you're going to try to tell the others or ask them. And then we'll have all of you talked. And then two minutes after that see if you can provide me with the answer. No so that's sorry. The temperature at Kelvin here. Remember that. Not centigrade. That looks really good. But what does it mean? What would it mean? What does it mean? What does it mean? What does it mean? What does it mean? What does it mean? What does it mean? What does it mean? But what does it mean? What would it mean if it was true? All your curves looks really good. But the question is what will it mean? That's usually the hardest part. Let's have all of you discuss this. Well pairs or a quartets or everybody around the table discuss them if you want. You have the curve. But what will this mean and why is that absurd? Should we do it together? So where would the curve be? Below liquid water. So you would have the curve roughly here right? What would that mean? So let's see. If you are at 50 degrees centigrade here what phase are you in? Why? I just didn't hear you. That's where it is on the curve. Why is it not red or blue? And you just said where would poly water be? So if you had poly water here where would you be at 50 degrees? Poly water. So you usually say that poly water should be the most stable state of water. You would never have liquid water. Now in theory you could of course have had this gigantic energy gaps you would never get to poly water or something. The probability that in 4.3 billion years nature would never have done this is starting to be pretty low right? There was a famous Richard Feynman in debunked this in like 10 seconds that if poly water existed it would have been an animal feeding of normal water and just excrementing poly water and then this animal would have an infinite amount of energy that it could live from. So here's the beauty that there were like a couple of hundred pretty good research groups who spent a decade on this just where it's pure crap. If you just think a little bit about free energies and everything you could have said it's impossible I'm not going to waste in this case it eventually turned out that there were impurities possibly some sweat or human amino acids and everything in this water eventually. Why it doesn't work is relevant just with some simple logics and thermodynamics are starting free and you can say that this is impossible there is no way this can happen and that's what's so useful with these gut feelings it doesn't matter you say there isn't even any Y scale here there isn't any X scale you have no idea what the exact free energy is you have no idea what the entropy is or where the enthalpy is it doesn't matter it's very simple principles and this is the cool part you can reason about things without knowing anything numerically about them and if you didn't follow this perfectly you're in pretty good company of some bunch of people who are close to the noble price and everything so but the point is that these things are very powerful if you do it right and if you want to read more about this there are some links on the web pages what I'm going to talk about today is polypeptide chains we're going to come back a little bit to structure turns and I might not spend that much of time on it originally I didn't have as much secondary structure in my first slides but since I have a bunch of different slides it's just stupid not to share these slides with you so I might jump through some slides here a bit quicker if you still would like to talk about them let me know and I'll pause there and spend more time on it but it might be useful for you when you look at this later so the first one we're going to come back to is the energy landscape and since I brought up energy landscapes I'm not going to talk about what they are but since you now know both enthalpy and entropy there are some things we can start thinking about here when you're exploring an energy landscape what is there are some barriers peaks here, there are some deep wells but what is preventing you from exploring the entire energy landscape what is the biggest difference here is it enthalpy or entropy well that's a difficult question in general you can't say it can be either or but it turns out that in different parts of the energy landscapes there are different things preventing you from this if you are here and would like to go up here what is it what is that preventing you from going there to going there enthalpy yes, you need and this is essentially the Boltzmann distribution you need to wait until you by chance have enough energy that you will somehow go up there and that might require very high temperature going in the other direction might well if you are there I'm going to go down there, that's going to happen automatically if you are here and need to go down there it depends on temperature the energy barrier is so high that it's significantly higher than kT it's going to take a while before you get there and eventually on the other hand if this energy barrier is smaller than kT you are going to jump over it fairly easy and be able to go down but at some point and in this case I'm not sure whether this is an ideal representative energy landscape but at some point you are going to be in these regions with hundreds of peaks hundreds of barriers and hundreds of small wells and then it's more about entropy and it's kind of a process where you need to search you need to try lots of different confirmations and it's not obvious that the next confirmation you are trying is significantly better from the previous ones and it's not until you've tried a very large number of this you will find the best ones what process here do you think is fastest? exploring things that are energy or entropy so that it takes time to search through entropy there are so many states to try out and that's going to be we will see later that's actually the main reason why protein folding takes time it's primarily an entropic search problem you need to explore phase space and that's why it's actually more useful than you think to think about the essential landscapes the Monday after Easter we are going to have a lab where we go back to your very simple systems we are going to look more in terms of kinetics that occasionally you need to visit intermediate states that has a much higher energy and you can't get to this state without crossing the intermediate states which is also very similar to the lecture we heard before the seminar we heard before the lecture today so we are going to go back to secondary structure now you probably know the secondary structure but we are going to try to think in slightly different ways we should try to identify the delta G components of these secondary structures we will try to think what happens during folding and why specific interactions or entropy are important what are the different properties of these secondary structures if you really love this the books will spend chapter after chapter after chapter on this in the intermediate half my idea is that I will probably not do that it's beautiful and if you're interested in physics and seeing the beautiful physics in structure it's certainly a couple of fun chapters to read but after Easter I think that it will be more useful for us to go more towards real systems so we are going to try to do some models and simulations of these things so if we start with the simplest one alpha helices we are kind of going to ignore the other helices for now the characteristic thing of an alpha helix that you should remember is that it's characterized by each residue hydrogen bonding a residue four units further down the chain so you have a hydrogen there to an oxygen there hydrogen there to an oxygen there etc and this continues round and round around the chain this is also the reason why proline breaks alpha helices because proline lacks that hydrogen on the peptide bond so suddenly it's going to be one of those hydrogen bonds you can't form if you look at the structure what is it that favors folding and what is that would disfavor folding because not every single amino acid in the world would form an alpha helix right so the reason why an alpha helix forms must somehow be that the delta G in some cases is good and delta G in some other cases is not as good or even positive and this delta G consists of two terms that you should know might now enthalpy and entropy so whether an alpha helix will form will apparently be a balance between enthalpy and entropy exactly when it's good or bad is complicated but already now you should be able to identify what, let's take the easy part first this is good and anybody can ask if they want to pick out, try to identify either the entropy or the enthalpy part when you have an alpha helix forming what is the effect on enthalpy and what is the effect on entropy the hydrogen bond and you see this is the enthalpy is the hydrogen bonds is good energy and this is the advantage of daring to answer quick because you just picked the easy one the next person will have to explain the entropy, yes and that effective means rather than having a chain that's completely free right, the entropy means that the first hydrogen bond will have to lock three residues in place so that previously you would have three residues at least if they were glycine they would be almost free to explore the Ramachandran diagram right the fine psi torsions could be anything they want in a helix we have locked in the fine psi torsion to an exact value they can't move at all anymore that's really bad from an entropy point of view so the only question is then do we gain more with the strong formation of these hydrogen bonds inside the helix than we lose by locking the entropy, by locking the helix in place so here's the problem the reason if this is a good structure and in many cases it is a good structure why would not, it still takes a finite time for an alpha helix to fold can you imagine why so let's, yes the fact that will happen in a particular, the reason I'm repeating some of these things I realize is that we have it in the recording otherwise people will just hear me speaking it's right but let's look at this from the start here residue zero first so residue zero is just one residue so what happens when you're going to add residue one to the alpha helix what parts will be good and what parts will be bad and I'll I won't draw it there but I'm going to have to draw that here so we have number of residues in helix and then let's draw some delta g here and I'll start with residue just one residue and then we are here completely arbitrary so what happens when I add one more residue to the helix and why does delta g go up exactly so the second residue I'm adding here I have to lock that in but I'm not getting a single hydrogen bond so I only get the bad components and I don't need anything good this is not looking good I just went up in free energy that's one of what where nature wants to go and then we start with the second residue well or second or third I'm a programmer originally that's why I like start counting at zero apologies what happens with the second residue we're adding to this it goes up again shit what happens to the third I'm going to count zero one two what happens to the third we're adding well no that's zero one two three the three is the third one and what happens with the fourth one we're adding so with fourth one now things start happening we will still get that penalty we will go up but now we gain an entire hydrogen bond so what likely happens is suddenly we're down here or something so we went up one bit but then down quite a bit and then the fifth one we're adding that's going to be even better because on average per residue the gain in hydrogen bond has to be better than the loss than the loss of the conformational freedom so then we keep going down and then we keep going down and we keep going down so what this leads to is something you're going to test in the lab next Monday so that you start apparently you have some you're not going to test it for an alpha helix but apparently you have some state here where you start you're going to have an end state that is really good but to get to your end state you have to pass a state in between here that's actually worse and that's what you call a transition state as you already saw in the lab right the Boltzmann distribution will fix that nature does not just go downhill in the angel landscape we occasionally can go uphill too so how quickly this happen will depend on how high this transition state is if this is 100k cal per mole we would never see any helix forming so how fast helix is forming whether they will form will depend on how high this transition state is in the middle without knowing anything and this is pure guess do you think that this transition state is really good or really bad for an alpha helix is it a high barrier you need to start go over to start an alpha helix well it's hard to say think about it for a second I'll come back to it when I talk about beta sheets we already talked a little bit about titratable amino acids and I will show you a quick move well no I'm going to talk a little bit before I show you the movie this is an example of a membrane protein which is the voltage sensor in all your voltage gated ion channels yesterday I said that in most cases if you put a titratable amino acid inside a protein it will usually lose its charge so that it becomes neutral so we can bury it but there are exceptions there are some really important charges and this is even a membrane protein if I said that there is a charged side chain that's right that's a titratable side chain in a membrane protein your first guess should be what that yes that's actually a very good answer because that's likely an incorrect prediction and you are in better company than you think so one of the first structures of this when it was attached to an entire membrane protein the group who determined that structure said that there is no way this can be true so this entire it's called S3 and this is a third segment and this is the fourth so it's called S3 and S4 so they actually argued this entire thing there is probably a paddle that sits in the membrane interface and then it must move through the entire membrane do you think that's a good or bad idea? why? it's not an entirely bad idea and there are many good things there so this person was Rod McKinnon who got a Nobel Prize for some of the structures so that Rod is an amazingly smart person and Rod of course realized that it's going to be very bad to have this side chain in the middle of the membrane then of course in Rod's defense too they also realized that this is a structure they saw in the X-ray crystal it does not necessarily mean that it's a biologically active structure there might be something stabilizing this on the way but yes, it is a bit of a challenge to move something charged through a membrane the only problem is that it's also right because if this one is responsible for all your heartbeats if you have it charged and subject that to an electric field it's going to move and if you don't have it charged there it's not going to move and then you would not have anything happening so if you want something opening every time you have the electrocardiogram there's a nerve signal and actually this is also what connects nerve signals in every single cell in your body having that charged there is pretty much important you could argue it's one of the most important protein parts in your body and for a long time we have debated this but the cool thing nowadays we can even do simulations so this is run on a gigantic special machine in New York, David Shaw so you see that the time scales here we can simulate things like a quarter of a millisecond and eventually we will see that this entire segment is moving down you don't see the rest of the channel here but this motion will push on the channel pore and actually close the channel so here we can simulate things exactly why these can exist in membrane proteins I will get back to but the point is that titratable amino acids occasionally they are super important and they can be very exceptionally functional and this was an entire alpha helical membrane protein too if you had looked really carefully you might have seen that there were some residues that were almost a bit twisted so that they were twisted so that they were almost thinner and that's actually partly a 3-10 helix but for all intents and purposes it's alpha helix that's the most important one forget about the pi helix forget about the 2-7 helix you can never have a helix where a residue binds to its next residue that would be too tight but this circle 3-10 helix so rather than binding 4 neighbors up you're twisting the helix so it's a bit tighter and that just moves the hydrogen bond one step further so rather than binding to 4 neighbors apart we bind to 3 neighbors apart and I will actually I'll skip that slide it's just another view of the helix forget, forget, forget, forget forget alpha helix here in the middle of the right-hand diagram and then the right-handed 3-10 helix is right next to the alpha helix you see that they're very close you virtually never see an entire 3-10 helix in a protein but you might see a couple of residues in the middle or at the end of an alpha helix that wound just slightly tighter those two you need to know and then you need to know about the beta sheets but the beta sheets are not part of a helix but it's own secondary structure so we've already talked about the beta strands the strand is the individual part the sheet are all 5 or how many they have so how about this the same way we thought about an alpha helix what is that favors folding and what is that disfavors folding of a beta sheet what happens when we fold the beta sheet hydrogen bonds here too so hydrogen bonds are kind of important in proteins as you probably realize now what is the bad part exactly the loss of entropy is the loss of entropy here better or worse than for an alpha helix think about what I said about physics first order approximations exactly well you can of course go into details I bet you can find arguments for or against if you don't know do you know exactly why it's worse or better okay the first order approximation is the same unless you know why it's more don't try to be too smart because when you try to be too smart that's when you go wrong to first again a beta sheet 2 just says the remachandran diagram this is also one region in the remachandran diagram ideal beta sheet is pretty much one point here just as an ideal alpha helix is one point yes you could argue that the region up there might be slightly larger or anything but just because this is stretched out we are pretty much looking every amino acid here exactly in place and that's the first order approximation so let's start to pick something here and fold it let's start down here what happens the first residue well let's ignore it the first residue has some sort of free energy delta G right and then we add the second residue to the beta sheet what happens what changes and in what direction you don't have the other 4 beta sheet you're gonna go up in free energy why you can't make any hydrogen bonds but we keep blocking this one in and then we add the second residue and what's gonna happen we keep going up in free energy and the third one I'll take the liberty of saying that we still go up and the fourth one roughly where we would be with an alpha helix by the fourth residue we would start going down what happens with the beta sheet we keep going up right and a beta sheet might be at least 10 if not 20 residues long here so we're gonna have a much higher initiation barrier to a beta sheet it will take much longer we're gonna need to look all these structures in before we can even start forming a hydrogen bond with the second chain or something so already here you don't know anything we haven't even talked about the specific energy of an hydrogen bond or anything but you can already hear say that it has to be a much higher initiation barrier to form a beta sheet so can you think which one of these structures will fold fastest alpha helix do you think that's right yes by several orders of magnitude and there are lots of other things to come into but I think that's enough really you see the point you don't need to we talked about a couple of lectures ago what is the volume or something the more stuff you add the more you confuse your mind we could of course have started to measure exactly what is the entropy here what is the number of microstates what is the specific energy of a hydrogen bond the more numbers you start to add the larger the risk that you make an error in a minus sign somewhere as I did yesterday and the more stuff you have the more likely you are to go wrong if you're just thinking of principles and first order approximations in real life is the beta sheet actually fold slower because of this initiation barrier yes but I would have guessed that it is more because you have to wait for all of the others to be synthesized but also if you had all the rest of the energy sort of let them go so now you're complicating something when you're saying that waiting for them to be synthesized you're adding the ribosome here and in principle there are some complications you can have when you add a biological system but you remember what Christian Anfinsen said so that you don't need the ribosome in general a protein exists in the global thermodynamic minimum and this is a much more important comment than we thought can the free energy depend on whether it was folded in a test tube or whether it was folded through a ribosome I would say that because it's not the same if you say you put it you lock in all the residues and you don't get any free energy that's fine we're talking about first order approximation but just for the recording the important thing that you get quite right here the free energy is what you call a state property the free energy only depends on the state not how you got there so by definition the free energy of a beta sheet compared to the free energy of the residue of water is not in any way affected how you fold the beta sheet now on the other hand the transition state on the way to beta sheet folding that could in principle vary between things but trust me the beta sheets fold much slower than alpha helix in particular in isolation in water there are some exceptions of course if you have two proteins that already have beta sheets if these beta sheets then get together and form a larger beta sheets then you already have them pre-existing but in general this is a much more complicated than tropic search problem than the alpha helix this is a local structure there are different ways of forming these beta sheets too they can be either parallel or anti-parallel these are the numbers of the residues and you might just be aware that there are slightly different hydrogen bond formation patterns here but this is probably something you can study yourself by looking at the lecture notes beta sheets will also have this property that they're pleated that's literally a property of the amino acid chain it's not something we're ever going to use we've never heard somebody talk about pleated sheets this is why they're pleated they also have a property because this might sound so amazing right it's kind of insane that the beta sheets are perfectly planar it's 180 degrees all the time why on earth would nature be so perfect that it just happened to have it's perfect upside down well I'll go back and show that to the ideal picture why would nature be so perfect that's saying that this exactly 180 degree turns all the time and they would be perfectly planar it's kind of amazing what a coincidence apart from the fact that it isn't their coincidence it isn't exactly 180 degrees the first approximation it's 180 degrees in practice it's like 178 or so and that will mean that beta sheets will have these slight twists if you see if you go from here to there it will twist some I think it's roughly 20 degrees per strand or so that's why you will see the simple instructions when you have very large streets it will start to turn another very special properties of beta sheets an alpha helix really has a start and an end and at the end of the alpha helix you have some residues in a coil shape or something before you can form the next alpha helix with beta sheets nature occasionally manages to do this that you go up let's see no we'll go up there no n c a it doesn't matter there we have the c you go up here and then you have this the last hydrogen bond there and they make a super type turn and then you go down again so here you don't really you don't have any free or flexible residues between the sheets and there are special names for these they can't be called type there are a bunch of different turn classifications but the point is that these turns are so tight that they are really part of the secondary structure and that's where occasionally you can have very nice and flexible beta sheets but they're much harder to form than alpha helices we're not going to go through that in detail and there's a reason that I will tell you in two slides the book goes through, in principle you can study the physics here, you can start to make predictions about when will different types of secondary structures form etc and some of the very first people who did this was Chao and Fassman and this led to the first implementations of programs that could predict secondary structure I'll leave it and I will leave their hanging because I know that you've been predicting secondary structure, guess whether you or they were better if you don't try to predict this but do it experimentally there are two simple ways, no there are two ways to determine secondary structure there's one very simple we call CD spectroscopy these machines are dirt cheap so this builds on the fact that amino acids are chiral so they will polarize, they will turn circular polarized light in slightly different ways so depending on the wavelength of the light you will get these very specific curves that corresponds to the red one is alpha helix, the blue one is beta sheet the green one is random coil and in principle you can just have a simple equation that says what is the fraction of alpha helix, the fraction of beta sheet and the remainder would be coil and then you could just fit your data to these curves the advantage is that you don't need a whole lot of sample, it's cheap it's very quick, the drawback is that you have absolutely no sequence resolution whatsoever, you can tell if a sample is almost entirely alpha helix and this is what was used in many of those very early trials that if you just want to study whether a protein folds or something, for instance the way Kristian Antin sent it, you can use for rations or you can use a simple method like this because if the entire alpha helix here unfolds you would see the curve fall down to the green one here right and if the protein refolds it would go up to the red again the only problems you can't say anything about the structure you can just say that okay now it's alpha helix and now it's not alpha helix it's used in very simple biophysical experiments, it's rarely used for large proteins for large proteins if you actually want some sequence resolution you can use NMR nuclear magnetic resonance do you know about NMR? NMR is kind of a fun method because it's a failed method in physics so in principle in physics the idea is you could study the spins and it actually came from solid state physics originally the only problem with NMR and the reason why it's problematic in physics is that this resonance frequencies will be influenced by their neighbor atoms which means that it's very hard to get things systematic and the funny thing that the so called failure in physics is what we use in chemistry because it's influenced by its neighbors these shifts in chemistry we're not necessarily interested in the absolute frequency but we're interested in how the resonance frequencies are changing based on the surrounding which in particular enables you to predict structure secondary structure is easy to predict for NMR predicting a structure of an entire protein is much harder but with secondary structure it works very well so what would you use? if I gave you a protein and say that we need to determine the secondary structure of this protein basically you would use the bioinformatics predictor do you have any idea do you remember what accuracy you got in your predictor? 75% okay do you have any idea of these early two fast man rules? not even like 40 or something so that you're I wouldn't say an order of magnitude it's hard to talk about these the further up you go the harder it gets getting the last few percent is insanely difficult and the problem with simple two fast man rules is that they only look at the local the next three or four neighbors while you have learned from billions of years of evolution you're looking at the entire protein background the two fast man word they're not even close and they pretty much this was the beginning of all the bioinformatics and it's just 40 years ago your accuracy is pretty much the same as NMR NMR good NMR spectroscopists would say I'm wrong that's perfectly fine but I would also say on average a computational predictor is likely going to do about as good as an average NMR experiment there are of course some exceptions there are some very special things that if it's something that's not really based on evolution some specific design you do that might be hard for the predictor to pick up but unless there is some very special reason to think that there might be that this structure might be strange or something it's hardly worth doing this experiment it's not expensive but it takes time and you need a collaborator just do the theoretical predictor and that's going to be perfectly fine so cryium is not an ideal method to determine a secondary structure cryium because cryium is cryium is in many ways the opposite of NMR although they both study so NMR works really well for these local features it's easy to find these shifts the larger a structure gets the more complicated it is to get right with NMR cryium comes from the other direction so with cryium the larger a protein is so here it is to find its overall shape and then the smaller structures you want to look at the harder it is to get things right with cryium we can get this with cryium too and of course at the end of the day you have the entire structure and then the cryium secondary structure might improve a bit on yours but the reason why it's in practice it's even hard to define secondary structure beyond 80% or so in a protein you always have a couple of loops those loops are flexible we can say that it's coil but it's frozen in the crystal it might be closer to a helix anytime you have a helix and I can move to the next slide any time you have a helix here the end and beginning of the helix will fluctuate a bit so that particular residue might sometimes be a helix and sometimes be coil you can't really get beyond 85% because it's not defined on that level well that depends why do you want the 3D structure in many cases yes in many cases it might be perfectly fine the goal is what you want to use the 3D structure for I would certainly agree it's great to have the 3D structure but in some cases you might have say 500 receptors you want to compare something and there might be some interesting transition between helix and coil or that one of them does not have a helix the cryium is much faster than x-ray we can do things with cryium in best case we can get a structure in a week if you have 100 structures that 2 years 100 structures in your predictor is likely almost a coffee break so that your predictor is not going to be as good but you have to compare that to the cost and effort of spending 2 years in the cryium lab the facility we have here at PsyLife lab our estimated running cost for that is a bit over 3,000 euros per day because the equipment cost people, consumables, lab space rent and everything multiply that by 2 years and that experiment is starting to be pretty costly so it all depends is it worth, yes it's better but is it worth it and I would argue that in 90% of the case your predictor is going to be more important so I think we already covered this here that helixes grow gradually but very fast because you can add to an alpha helix slowly the special property with beta sheets that I didn't talk about that we'll come back to they grow slower but it's also you either, it's like being pregnant you either have a beta sheet or don't it's very hard to gradually grow a beta sheet, one strand is no sheet when you have two strands you have your sheet so you, it's an all or nothing transition just like breaking a light bulb we're going to come back to that after Easter when we talk about phase transitions so this is a much more well-defined phase transition this one grows gradually I will very briefly cover the properties of amino acids too we've done that too so I'm going to skip through this a little bit quicker 3 letter code, 1 letter code the abundance, we've already covered this and as a reality check what determines the abundance? no it's a good it's a good guess the relative abundance is how frequent these amino acids are in nature and that's determined by and that reminds me of a very fun story a bunch of years ago a student in physics in Boltzmann you have this partition function which determines everything in your system do you remember what letter people occasionally use for that? capital Z and there was a question about this on our exam and the student was probably not the world's smartest student but in physics one nice thing about physics is not about learning things by heart you learn concepts and you're allowed to have this gigantic formula at the test this student probably didn't know what Z was so he kept looking this up in the formula until he found that Z was also used for the atomic number and then he used the atomic number in all these equations sorry the abundance here is determined by what? the number of codons the number of codons but your answer was not as stupid as you might think it was because this we keep talking about the fact that we have mutations in amino acids or something right? and that the mutations the amino acids might influence the free energy and what would determine if a mutation is good or bad? it would be very obvious to say the Boltzmann distribution, right? but the Boltzmann distribution depends on something you did in these labs the Boltzmann distribution depends on sampling all states that you go back and forth between them and realize that some are better or worse once you have created a protein in your ribosome, you don't change the sequence so the Boltzmann distribution does not explain why mutations happen or not and this comes down with this detailed balance you have a continuous flux between states if you do not have a flux between states they don't equilibrate so different mutations we can't explain those declarations if we look exactly that way it's very natural to think it is, but it's wrong and it's quite fun but this abundance is determined by the codons and now I'm adding a column here delta G solvation and there are some gigantic numbers here this is... no these are some very large ones there are some that are only marginally solid and there are even some ones that are positive if we look at the very some that are very large here glutamic acid, aspartic acid histidine lysine and arginine why are they so large and negative? they have charges and those charges are just going to be loved because the solvation we always measure what is the cost of having this in vacuum or oil compared to having it in water and it hates to be in vacuum or oil so that they want to be in water Proly and I already spoke a little bit about which is an amino acid and I know you probably know this but I'm also going to show it anyway normally this is an isolated amino acid in this twitter-ionic form and then we have the carboxyl grouper COO negative charge in a normal amino acid I would have an NH3 plus here but in Proly and I have an NH2 plus so Proly lacks one hydrogen compared to all the other amino acids when I put this in a peptide chain both of those hydrogens will disappear and then I don't have the hydrogen on the nitrogen there anymore and that's why it can't really participate in all these all the hydrogen bonds that I've been showing for both these secondary structures Proly is the odd one out there it doesn't have the hydrogen that enables it to participate in those hydrogen bonds so it's amazingly good at breaking helices you need the secondary structure and you see a prolin in the middle I don't even need a bioinformatics predictor it's at least going to be a kink in the helix it's pretty good if you want a kink in your helix and that's also it's not as stupid as it might sound the world proteins does not just consist of helices that are 100 or 200 residues long so in many cases in particular a membrane protein it's actually a membrane helix should be roughly 20 residues which is the thickness of a membrane on the other hand you want this helix to be very stable if this helix is a bit floppy so if you had a helix that was very strong helix and then you gradually started to have residues that are less and less favourable to be in helical form you would have a helix that had very weak and floppy ends it would not be entirely clear where the helix stopped and where the helix starts on the other hand you can have a helix that is 20 super strong alpha helical residues and boom then a prolin so then you would have a helix that is rigid it's clear, it's helical it's going to be super happy in the membrane and the second you're out on the membrane you break your helix and you have a small loop and then you form a new helix so that helices are good but occasionally you need a loop too and we frequently use that let's say glycine, glycine, prolin, glycine before or after a helix to make sure that it's only 20 residues of helix good question glycine is pretty much the opposite of prolin but it ends up having the same effect so glycine is, because of this lack of sighting glycine is so floppy so the glycine creates what I just said, glycine, glycine, prolin, glycine those glycines are also good because they don't really want to form helices either if we just have the glycines there we would get a helix that gradually became more and more flexible but glycine together with prolin is a great way of breaking a helix and then we have all these hydrophobic residues I'm not going to go through them in detail but there is a bit of nomenclature here that you might find out in your career that first carbon is called the alpha carbon in the amino acid and then as we go out the side chain we start enumerating this with Greek letters alpha, beta, gamma, delta, epsilon, z and in some cases you hear alpha and there is beta and then you have a branch here so after the beta you have one carbon there and one carbon there so the more in particular when you have these branches you get small and bulky residues that can be very important on the inside of protein this one is going to hate to face the water and then our last friend, cysteine I didn't bring this up cysteine is a pretty normal amino acid but it has a sulfur and normally you have a hydrogen bound to that sulfur too the special thing with this sulfur if you oxidize, if you have two of these close to each other and oxidize them you let go of those proteins and that's Java, I hate Java because it interrupts my presentation if you have two of these close to each other they can oxidize you let go of the two hydrogens and then you form not just an electrostatic interaction but a real cobalt and bond between the two sulfurs it's going to be super strong and that is a non-local interaction in the chain did you talk about this in the bioinformatics course? okay let's fix the structure in space which can occasionally be really useful I'll come back to that in a second and I'm going to show you a protein what do you think about this protein? it looks really floppy right? is this even a protein? is it more like a multi globular or something? you would be forgiven to think so I'll help you a little bit all the side chains does it become clearer? no, at least not to me there are side chains all over the place I just saw this I would say that yeah this is just a chain we had we put it in a computer it's been flexible, it's flopping around if I could turn this into a movie you would just see it moving around it would not really have any well-defined structure this could be a sequence that doesn't hold a protein but now you might start to see we have something there and it's yellow and you have something there and it's yellow disulfide bridges and it's even more you might not see it, but the chain here starts and goes from blue and through the color of the spectrum all the way to red and these disulfide bridges are actually so complicated that they literally form the knot of the structure so you can't unfold the structure without breaking those disulfide bridges so this is a super rigid structure it's even called a cysteine knot so what do you think this could be useful for? it's hard to unfold it's a toxin it's a spider toxin and the snakes frequently have similar toxins and because it's so hard to unfold if this one comes in and binds in particular to voltage sensors this will bind to the voltage sensor and influence and depending what sensor it is it will either close them or open them but it's very hard for your body to unfold them because they're so rigid and hard this particular one is actually even called HANA toxin which is a fun story behind it Kento Schwartz discovered it and named it after his daughter I have a 13 year old daughter and if you're 15 year old it's pretty cool to have a toxin named after you so the reason that what those disulfide bridges do they can lock in structures and they can lock in structures super hard it's frequently used in experiments for crosslinking or so it's a non-local interaction and they can be super hard to predict because you have no idea where they are in sequence but if you make a bioinformatics predictor and then suddenly you start having two cysteines close to each other you can of course test this you can test what happens if you oxidize them even if you just have one cysteine you can take another residue if you have a model and you think that this model would work you can mutate two residues to cysteine and see can I form a disulfide bridge here and the final residue here is tryptophan big bulky residue it's an extremely rare residue to have a normal protein might have one or two of them and that's simply because they're so large that they're hard to pack in anything there are two cool things with tryptophan first tryptophan is fluorescent actually so that you frequently and this is the reason I mentioned it you can occasionally use tryptophan in biochemistry experiments because this I think it absorbs around the emission at around 300 to 350 but the cool thing is that the emission depends on its surroundings so why is the emission wavelength around 300 to 350 why it absorbs at 270 or 280 that's a bit of physics no so that the wavelength is inversely proportional to the frequency so apparently it absorbs at higher frequency and releases energy at lower frequency going to quantum mechanics the frequency is proportional to the energy of the photons so if you can absorb you can never ever release photons of a higher energy than the ones you absorb so you absorb at a higher energy you lose some energy internally and then when you release the light as emission again it has to have lower energy so you always the wavelength always increases in fluorescence in the emission compared to where you absorb the reason why this works is because tryptophan is so rare if you only have one tryptophan in your protein you know what surrounding you're studying and if you then know that I don't remember exactly what the pattern in this fluorescence is but if you only have one tryptophan you can use this fluorescence to make predictions about does this tryptophan has say a polar or nonpolar surrounding and this has actually been used for a small protein to create a protocol TRP cage tryptophan cage it's an artificial protein and this is frequently cited as the world's smallest protein and the reason for that is that with the side chains and everything that tryptophan is actually completely buried so it's not exposed to the solvent at all we can see that with the tryptophan fluorescence and it's a protein that's like just under 20 residues long many would call it a polypeptide but the definition that we frequently use for a protein that you have some residues in this case one that is completely buried and not exposed to the solvent why is it useful to have a small protein you can certainly bind to many things and everything but one thing that can help is to learn about some processes right and a small protein we can even fold in a computer so this is the folding of the tryptophan cage and I should have started that automatically that colleagues of us run a bunch of years ago so you see can you imagine what the protein is doing here so you see that it collapsed very quickly right and that's this molten globular but then it has to keep exploring things it's searching here trying different things is not redefining anything good so here's the part where we're exploring entropy trying lots of different things and this is a fairly good state there appear to be lots of microstates related to this one and all this variations of the site here this is basically we're exploring different microstates but the overall state is that we had the tryptophan bound here in the middle and I don't forget whether this is the folded state where we're going to get one last transition at the end here but we're very close to the folded state no that was the folded state so this is something you can fold in a couple of microseconds in a small computer we can fold far larger proteins today but the important thing here is that we had this important discussion you brought up the argument that do we really reach the global minimum in free energy and at least for these small proteins it is true and we can kind of prove that that we can formulate the rules of physics and nature and we have still predict that the folded state is right but that's not particularly the experimentally determined states we have a bunch of polar or charged residues too I'm not going to go through and cover the residues again but I'm going to take this from a slightly different point of view remember that I said that the interior of proteins was typically uncharged because we don't want things exposed we want to take the hydrophobic things and turn them inside that typically means that the polar or charged residues tend to be in this turn loop region because if you have a membrane protein the loops are going to be outside the membrane we're going to come back to that the week after Easter so it's very favorable to put the charged parts outside the membrane the polar can hydrogen bonds to water and the polypeptide chain while and the charged ones the charged ones are similar but much stronger there is there is no rule in biology within and out than exceptions I would say that the rule is that these are always on the surface with those exceptions that occasionally you need them on the inside of the protein to create a binding site or a motion or something but there is one more fun effect in a helix do you remember that I spoke about the helix dipole the effect of the helix dipole is that you have all these peptide bonds which on the inside here is that you have okay so here you have an oxygen and then you have a carbon and then you see a little bit of blue there that's a nitrogen and then I've hidden the hydrogen behind that one and here is the opposite here we don't see the oxygen, carbon nitrogen, hydrogen the oxygen is strongly negatively charged and that hydrogen is strongly positively charged but the point is that all these dipoles point in the same direction so they keep adding up so the net effect of all these 20 or so dipoles here is that the equivalent having one gigantic dipole that goes from the oxygen terminus, the red to the nitrogen terminus the blue so it points against the direction of the helix but what is a dipole? a dipole we can kind of describe with the equivalent of having a small charge on one end and having a small charge of another sign at the other end so this is going to effectively going to be as if we had a big negative charge here and that's going to work really well if you combine that with a positively charged residue here just to finish off the dipole and conversely here, here we have a dipole that's point as if we had a positive charge here and then the helix is actually going to like a whole lot to put a negatively charged residue here so this is called helix capping that we frequently have positive charges at the end of the C terminus and frequently have negative charges at the N terminus the reason why I show you that is a funny result which relates to what I said before is as if amino acids seem to occur in places where they stabilize the structure now this might sound completely obvious but it's not obvious because this is no Boltzmann distribution they don't change we don't have this protein continuously swapping between the N and C terminus, the residues do not move around so the residues are there they are fixed, they are fixed by evolution and of course this is related to evolution but it's not just a simple Boltzmann distribution but there appears to be some connection here where where do residues occur where do proteins put residues and something that is looks very similar to free energies in Boltzmann distribution so this is of course based on the fact that evolutionary it will stabilize the structure and somehow it's good for nature to have stable structures those will somehow be better than non-stable structures and this in turn is very much related to the fact you remember that I said that a protein is only stabilized by a few hydrogen bonds if you make one or two minor disturbances into a protein you might very well completely kill the structure so it's very fragile but we can't quite put our finger on this yet it looks like the Boltzmann distribution but it's not the Boltzmann distribution it works like one and cracks like one the hydrophobic moment I'm not really going to talk too much about for beta sheets the point with beta sheets is that you have every second residue on the inside and outside and then create these layered structures where we have natural pockets or something the equivalent of a helix is something called this is a helical wheel and this might sound like complete a mess but it's not there should be a one somewhere, yes one so if you look at the helix from the top every residue it's 3.6 residues per turn in a helix and that corresponds to exactly 100 degrees of turning one, two, three, four five, six and then we keep going around like that if you take your residues and just put their names here do you see that there are lots of black ones up there isoleucine and leucine and then there might be a bunch of well at least a bunch of charts once here the charts are a bit different so this appears to be a helix that on average is kind of between hydrophobic and hydrophilic but it does so by being very hydrophobic on one side and very water-soluble on the other side so what do you think would happen to a helix like that it could be part of its channel and that's actually a good point I was initially thinking that this would actually be an interfacial helix that would lie in the membrane surface it would turn its hydrophobic side to the membrane its hydrophilic side to the water it's just as right to say that it could be part of a channel because this channel would need to turn the outside to the membrane right where it should be hydrophobic on the other side to be able to conduct ions or something, you would something that's polar so in that case that would be the membrane side and this side would face the pore in the membrane and the final part are these titratable amino acids we talked about those yesterday so I'm not going to cover it again you should be aware that histidine is really dangerous 6.5 way too close to 7 you can easily have this shift up or down so this can be pretty much anything and the complication with histidine is even when it's not charged it's still not nice there are two places where you can put a proton here either on the delta or epsilon nitrogen where do you typically have the proton? beats me it's 50-50 I don't even remember which one I think it's the delta one that's slightly better but now you're talking about the difference of 0.1 in pH units this is so close that you can't predict it it's going to depend entirely on the surrounding but this is hopeless if you have a pdb file or something can you see this in a pdb file? why can't you see it in a pdb file? so hydrogens are typically not present in pdb files because hydrogens don't scatter electrons well enough by definition because the hydrogens are usually slightly positive it has given up its electrons to the next higher atom and because it's the electrons scattering the x-ray if the electrons has left the hydrogen you're not going to see the hydrogen in x-ray today some x-ray structure actually starting to become so high resolution that you can't see faint hydrogens but in general you can't can you see it with cryoen? why? no, you can't there is a solution in cryoen it's too low the best theoretical resolution with today's sensors is roughly 1.7 there are no structures that are closer to that resolution in practice the best one are around 3 1 angstrom so that you can't see that that's a bit tough so what do we do in practice? we're going to need to model something there might be a difference between whether it's the delta or epsilon in theory you could use NMR but then you're starting to need to book in NMR if I give you a protein you will get a protein sometime after this you're going to start doing some models and quick simulations I don't think you want to start booking in NMR machine for that lab it's going to be a bit costly and complicated so first one you can guess that's what people frequently do it might not be the end of the world because we can rotate around that bond right so if you do it wrong the entire thing will rotate it's not symmetric but it's not extremely bad the other thing what you will frequently see in a PDB file is that you have a neighbor residue here you might have a residue say glutamic acid or something with an oxygen here where do you think the hydrogen is now? if you have another residue with an oxygen here then there is likely a hydrogen bond here right? so you don't see the hydrogen but you can see the hydrogen bonding partner because these are going to be polar hydrogens there is no way this is going to stick into a hydrophobic region so if you have normally you can see that there is an oxygen either in one or both places and if you see that oxygen you can use the position of that oxygen to determine where the hydrogen is that can certainly be the case and if you have a binding site but again the pKa value and everything it's not obvious because again both of these can exist right? and occasionally a case is better to have the protonated and in other cases it might be better to have the unprotonated state but there is the reason why these oxygens in particular are important there is no way you can have a negative nitrogen here right next to a negative oxygen and have them interact they would hate each other the only reason they would be close to each other is because there is a hydrogen between them and mediating that interaction so if you don't see the oxygens you don't know but if you do see an oxygen there you probably got it but there is one thing that can go wrong here this sounds really good right you can just take the pdb file and determine it but there is a caveat temperature here it's worse than that how do you think that they got that pdb structure so remember what is the experimental results from x-ray crystallography? no, structure factors structure factors how do you get from the structure factors to the pdb file model so somebody already put this in a computer somebody put it in a computer they might have guessed hopefully smart they guessed where they had their hydrogen so the funny thing that if you take this and put a hydrogen here somehow all the oxygen is really close that one is going to like you because that pdb file is already a model you think of it as an experimental result but the experimental result is only the raw structure factors in most cases this is right but you should be aware that somebody already modeled this before you started your model so if in doubt you might actually have to go back all the way to the original structure factors or crye and micrographs there are plenty of structures in the pdb that have been proven to be wrong the model is wrong the original experimental data was frequently right so that even the thing that we traditionally think of as experimental results rely much more on computer models than you might think so when it comes to these charges there are a bunch of these arginine for instance unless you have a very special reason to believe that that should be neutral it will require some pretty extreme ph's for this to change the thing that I showed you in that quick movie of the membrane protein actually turned out to be arginine residues and that was made in so amazing that this is one of the residues that we virtually never ever be uncharged and yet we had it in a membrane protein and not just one but one two, three, four arginines we will talk about that when we talk about membrane proteins it actually turns out that this is useful for nature not just that it's useful to have charges but there are a bunch of processes that actually turn out to be ph regulated so many of the channels that in your body are regulated by your nervous system by voltage in a simpler organism by a bacterium would you have a voltage gated channel in a bacterium because a bacterium doesn't have a nervous system so similar channels in a bacterium is typically ph regulated so that a bacterium can use ph to regulate things bacterium is actually smarter it's much more efficient and cheaper we get some things with the nervous system but our nervous system is pretty expensive to keep running in terms of energy there are a bunch of things we can use this with protein stability or salt bridges so depending on ph things will either bind or unbind DNA protein interactions all those big phosphates we talked about that when I talked about the DNA structure so depending on the ph DNA will undergo different transitions so charges are very useful the other thing that's cool that some of the ion channels this is not a potassium channel but a ligand gated channel so in a human it would be ligand gated and in some bacteria it turns out to be ph gated so this is a model of a channel that a talented French postdoc in my group built a bunch of years ago so Glick here is just a it's a Glarebacteria visual layers I think ligand gated ion channel so it's just an abbreviation of the name of the channel the colors here correspond to the five subunits you can only see three of them here the gray part here is the membrane and then we actually have all the water and ions and everything around it if I tried to show you the movie here you would not see anything so what Samuel then did is he's just showing the five central helices around the pore channel that either conduct ions or not and this is a channel where the x-ray structure is obtained at pH 4.6 where it's completely open but then we also know that this one should be closed at pH 7 and a couple of years later we even obtained a closed structure of pH 7 so initially I think we're going to start with the blue helices here and they will gradually move to the red helices in a simulation and the only thing we're doing in this simulation is that we have this entire system but we're changing the titration state of the residues and then let's see if this works so what you're going to see here is that normally I have lots of water going through this channel you have some hydrophobic residues but typically the electrostatic charges here are too large so they will repel each other and gradually the helices are closing in on each other and you will see that this one is eventually going to overlap with the blue ones and you see that the water thread is almost breaking up you see now there's a hydrophobic region here between these residues and eventually this is going to close more and more and more and more and by now we no longer have the water pour going through here so now this is a non-conducting channel and this by the time we're at two microseconds or so so this channel has now closed and this is simple and bifysical enough that you can get it in a reasonably fast simulation and although I'm only showing and now these helices overlap virtually perfectly it's a relatively small motion so that it's by no means a small system it's much more complicated than the simple stuff you started in the lab but it is exactly the same phenomenon that you have a system with two states you have one state that's more favorable at p86 4.6 the open one you have a second state that is more stable at p84.7 so depending on the external conditions nature can cause this system to move between two states this is how it would work in a bacterium in a human you would rather have something bind out here and when something binds out here this channel opens and this happens all the time in your nerve cells because these are the channels that are part of the synapse so the synaptic transmission when you move the nerve signal from one nerve cell to the next nerve signal the neuro transmitter is binding these channels and then they open this one so you know what this is a really good question I'll get back to that in a second I'm just going to tell you a little bit more you can start there so with the questions whether it was a histidine or something that closed this channel we and other groups have been searching for this for 10 years yes there are histidines but we can mutate away those histidines this still works we I think we have tried together with other groups we have tried some 40 or 50 mutants here we have this far we have found lots of mutations that influence this but this far we have not found one single residue that really explains there are some charged residues up here and in principle it sounds fairly reasonable right that if you have a charged residue say at the top of these helices if they are charged at pH 4.6 they would repel each other and then we remove the charge they would not repel each other so strongly and then they would close it's a really good model there's only one problem with that model what did I say at the beginning of this lecture it's wrong and no matter how we've calculated those pH the titration states with continuum electrostatics and everything and you can prove that they change titration state that is worth absolutely nothing because we can mutate away the residue and the channel still works so this is still an open debate we don't know exactly what residues in the bacteria is the reason for the pH sensitivity it could very well be that it's a collective effect you haven't asked me something else these channels these channels are important for a bunch of reasons they're some of the most important channels in your nervous system two of the more there are three important ones one of them is still the acetylcholine receptor and it's famous because it's blocked by cobra toxin so that when the cobra bites you this toxin blocks the acetylcholine receptor and then the nerve signal works great it goes to the end of one nerve cell and then the nerve signal can't pass on to the next nerve cell same thing here a toxin prevents the channel from working another very common channel is the gamma butyric acid channel and that builds a small amino acid actually, gamma butyric acid it's one of those amino acids it's an extra methyl group on the alpha carbon so it's not one of the 20 essential ones that one is very important in your brain and it's also the main target of fan aesthetics so when you want to sedate somebody in this fluorine we now know that these anesthetics bind to the channel and influence how quickly these channels open because these are situated between nerve cells they're really beautiful ways to start to modulate your nervous system it's Thursday even before the Easter weekend at least I'm going to have a glass of wine tonight when I have a glass of wine the alcohol will bind to lots of places but in particular the glycine receptor looks just like this one and this is the reason we get this intoxicating effects because it influences my nerve signals it's a pretty pleasant way it's purely for research reasons of course so what all these things have in common that they're part of your nervous system and they modulate your nervous system and now a friend of Forder would say something what was glyc? now glyc was a particular the G here was for gliobacter bisceolus which was what type of organism? bacterium do you see any problem with that? why would you have a channel like this in a bacterium? so what do you know about the nervous system of bacteria? so why would you have a channel like that in a bacterium? we don't know so in this case it definitely it's a pH regulator structure that conducts science right but in the grand scheme of evolution we don't know but this is very common and it actually turns out the same way we had some pH gated channels that are very similar to the voltage gated channels in human it's virtually almost every single complicated structure we have in human also exists in a bacteria usually in a much simpler form and it's not that advanced and that's likely because evolution obviously it's related to evolution they are like 25 to 30% identical in sequence it's no question they're evolutionary related but exactly why we don't know the reason why this is important is that it's much easier to determine the structure of bacterial proteins that is also an open question for some reason human proteins in particular membrane proteins tend to be much floppier, they're less stable they're harder to over express and everything we don't know why, that's just the case and you could argue that's not so bad we can just use the bacterial ones the problem is that the glyc channel if you give the glyc channel slightly longer chain alcohols or anesthetics behaves the opposite of human proteins I'll come back to that I'm going to talk a little bit about the research after Easter but it's not as all as obvious as we used to think 20 years ago that human and bacterial channels that are homologs behave the same way they can be very different and in this case it turns out I can swap one amino acid in this channel right in the middle here and I get it to behave like a human channel I have no idea whether these exist in archaea it's a very good question you can search it yourself in a sequence so you can see if you find it anywhere because this is also the problem it might seem obvious to search for this but what people have to do, you have to start to find a sequence, in particular a colleague of mine Eric Jacobsen at UIUC in a number of cases he's just taken a class of channels and then you spend a huge amount of time just digging through these database do you find something, is this interesting does it behave the same way I'm not sure have you looked at genome annotation in the bioinformatics course most things it was a potential protein but that's all we know about it somebody found a sequence at some point that might or might not be a protein and nobody has ever studied it and then you need to convince somebody to study this biochemically can we isolate it, is it an iron channel at that point you would have to show does it have similar properties to the human channels and that we can certainly do in experiments but it's no small amount of work and then what's happened the last 5-6 years now we actually have structures of the human channels too and I predict that this is going to be an explosion of individual neuro-pharmaceuticals because we have structures of a bunch of these in the human system and then we can of course start to target drug design to influence your nerve system which is going to be pretty cool that would actually first you might be able to design drugs that remove the alcohol toxicity you might be able to design drugs to combat alcoholism that's a very complicated disease but even anesthetics anesthetics is complicated let's say, simple field and it is to some extent but we have no idea of exactly molecular effects it also turns out that it's virtually all anesthetics have some side effects which is not a problem if anybody is going to sedate you because you're young and usually healthy if somebody is like 95-year-old obese and everything it gets to the point where a good anesthetist is going to say let's try to avoid anesthetics or let's at least try to avoid general anesthetics because there is like a 10,000 chance that you will die on the operating table so it's not can we design better anesthetics to control this better we could improve healthcare a lot we're starting to branch into science there I'm going to talk more about our science later because it's hard to stop me what I've mostly been covering here is chapter 7 and 10 there is a reason why I'm skipping one chapter 8 chapter 8 is full of beautiful heavy mathematics I'm going to come back to that after your Easter break but I figured to make sure that you actually show up for the course again after Easter is better to wait with that chapter and chapter 8 will likely be the last really heavy theoretical chapter we go through so what I'm going to do in chapter 8 then is then I'm going to tie up the sack from the other point of view I'm going to show that some of these things where I've argued for special cases they're actually universal phase transitions and everything we can classify phase transitions even in biological systems and after that later on in those two weeks I'm going to start I will actually put up these lectures already next week if you want to start studying them I will be around if you have questions but then we're going to branch out a little bit more into real proteins, modeling of real proteins and simulations that the book doesn't really cover in detail we will have some extra reading material for you there and then we're gradually going to start applying some of the things you learned in the lab to real systems important things to think about start thinking about things for the entire week and try to interpret the biological things that we now get back to in terms of what you learned with free energy, enthalpy and entropy it will help you a lot and it will give you these gut feelings I have a bunch of study questions here too the last few study questions here are related to the labs and we will go through that after Easter when you're all back and then I think I'll release you four minutes early today do you have any questions?