 We're mostly going to talk about amino acid properties and secondary structure, just as we did last Wednesday and Thursday. But now we're going to introduce free energy concepts in this. I don't have that many slides, I think 45 or so. And yes, I did hand out the slide hand out. So as always, I would suggest that we start going through the things we discussed last time, Friday. And then we spend whether it's the first 30 or 40 minutes or so on this. Only 40 questions, but some of these are a bit larger in scope than they were before. So who want to start? Helmholtz and Gibbs. Yep. And the difference between those two is, so what's this PV? What is PV? I think you all know what P is pressure and V is volume, right? But what does it really mean? It's work, but a particular type of work. Work or mechanical work. In mechanics, we frequently just call that work, right? But that you're somehow doing physical work on the outside. Either you're doing physical work on the outside or the outside is doing physical work on you. Is there another way to exchange stuff with the environment? Heat. And we haven't really talked about that. If you followed one of the deviations or one of the derivations that I have a link to there, what you typically do is that you're going to use W for work and Q for heat, if you ever see it in equations. So is there any other way to exchange energy with the surrounding? Sorry? Sorry, I didn't get that. No. So potential energy, I would say that goes into work, not necessarily PV term, but a work term that you're lifting something up. So basically there isn't. You could of course start to include complicated physical stuff such as the weak or the strong nuclear forces and everything, but for chemistry we don't really care about it. And this is kind of important because in some cases this allows you to actually solve for things. If the energy that we exchange must be either heat or work, and then we have entropy, free energy, there are only like probably five or so of these properties that you can take into account. I'll get back to that in a second. So number two then, give some examples of relevant versus irrelevant energy barriers at 300K. This is actually harder than you think in a way, at least. Let's start with the easy one first. What do I mean by relevant versus irrelevant here? And how do you decide what is significant? Yes, we need to compare this to kT. So what, give some examples then of energy barriers that are relevant. You had one example there, but conformational change, that's a bit fuzzy. I would like you to drill this down to a specific energy term. Torsional angle would be in the ballpark of a few kCals. And when it comes to irrelevant energy barriers, a small bond, but this is actually complicated because the small bond vibration, I would say bond vibrations are irrelevant, but for a slightly different reason, right? Normally the energies involved in bonds are actually very high. So that's not really the reason I was saying here. The energy bonds are so high that typically if you look at a bond, and as I mentioned before, in reality, if you're going to treat this very accurately, you should treat this with quantum mechanics. So you're going to have some sort of ground state here. And at 300K, a typical bond will hardly ever be excited from its ground state. So I would agree that it's irrelevant, for a slightly different reason. This barrier is so high that it's not really relevant. Again, if I want to go out in the corridor, right, the energy barrier that would be required if I were to go straight through the wall, it's irrelevant because it's so high that it's never going to happen. So at some point you get that it's so high that we're never ever going to see any processes crossing that barrier. And then you can start whether you call that that is very relevant or not matters less. But the point is, it's infinity. This is not infinity. Just now and then I would say you might see a bond go up the first excited state, but you're not going to see all the other ones. So the first approximation works great to treat a bond as a constant like in our case. But let's pick some other interaction, or at least an individual interaction that is much lower than kT. Bond angle, I would say, falls roughly in the same part of this. So remember that bond lengths and bond angles, they are fixed, right? And with they're fixed, that's essentially the same thing as saying, well, the first approximation they are fixed. And that's the same thing as saying, yeah, you can't go through the wall. So what is the weakest interactions we've spoken about this far? Hydrogens are in particular Lenna-Jones interactions, right? So individual Lenna-Jones interactions are so weak that they're not, they're going to be very weak compared to kT. So we can certainly violate an individual, we can tear two atoms apart or something. And again, this is why most noble gases and everything are gases at room temperature. But having a gut feeling for this whole spectrum of energy barriers is going to help you a lot, not just in this course, but in general. Because that is related to the third question here. How do you predict what processes will occur? How many of you looked at that length? Okay, good. I would recommend, normally I will try hard not to overload you with information. The things and articles I do link to, it's mostly for your sake, because it's stuff that's important that we likely will cover later. It's up to you to read it or not, but if you decide not to, it's at your peril. So how do you know what processes will occur? Yes. So processes that result in a drop in free energy will occur. Nature always strives to go to lower free energies. Well, yes, we'll come back to that in a second. But to first, let's ignore the barriers just for now. The nature would always like to be in a state of lower free energy. So locally, you will always go in the direction of negative slope in free energy. You can prove that. It's not very hard. That's actually what they do at this link. So how do you prove that? Well, some of you might have read the link, but even for the others, what would you start from? What are the things you know? So that's right, but rather than saying the flow of heat, there are some postulates in this area that you would eventually go back to, right? And they're the laws of thermodynamics. So to prove something in this area, you would eventually need to go back to the laws of thermodynamics. And the flow of heat is certainly related to the laws of thermodynamics, but the flow of heat, again, we don't always move to colder things, right? These heat packs I spoke about last week and everything. Occasionally, you can have a reaction that spontaneously results in heat because there is something else that's changing. So there is one thing that we always, always, always know about processes. And did you say enthalpy or? Entropy. Yes. So what do we know about the entropy for any process that happens? So delta S total is always larger than or equal to zero. And it can only be equal to zero for an infinitesimally small process. No real process can ever have delta S equals to zero. So that means that if you have a small system, this will consist of the change in entropy of your system and then the change of entropy in the rest of the world. And then it's pretty much just a matter of playing around with a couple of these. We know that how the entropy relates to energy and temperature, right? And all the work we do in our system, eventually at some point, we say that the total energy is work plus heat. And eventually you can solve for work and then you can actually show that the work you can do is related to the change in free energy. It's actually a pretty good exercise to go through, but you can prove pretty cool things about thermodynamics by just assuming the loss of thermodynamics and playing around a little bit with these handful of things, you know. And the math is not that hard. So if we move on to the hydrogen bonds, what is the... I spoke on Friday and you hopefully follow the hydrogen bonding in water versus vacuum. So what happens is it good to form a hydrogen bond? Why? The electron sharing and so the whole point is that you start before you had the hydrogen bond formed, you don't have the electron shared and when the hydrogen bond is formed, they are shared. I would argue that's right, but that's right in vacuum. What's the difference in water if you're forming a hydrogen bond with a solute in water? So the problem is that once you are in water, you already have the hydrogen bonds, right? You're just moving them around. So yes, you can certainly form for every hydrogen bond you're forming with a solute, you're breaking a hydrogen bond between two waters. So it's not in water, it's not at all as obvious that hydrogen bonds are good. This is going to matter. Do you gain or lose entropy by moving around your hydrogen bonds? If you gain an entropy, it's great. If you start to lose entropy, it's going to be bad. Partition coefficients are what? So partition coefficients are basically probabilities, right? What is the probability for a molecule being in solvated in water versus staying in, say, hexane or hexanol? Once you know partition coefficients, those are the probabilities in the Boltzmann distribution. And if we know those, we can take the logarithm of the ratio and then gain the free energies back from it. The reason why I should tell you that it's pretty much every single experiment you measure in the lab results in something that you can translate to a free energy. So the whole connection between theoretical and experimental research are really free energies. Sorry, I just answered question six for you, my bad. So what is the definition of temperature then? You don't necessarily need the formal definition, but what do we mean by temperature? So that the energy is really the scale of the Boltzmann distribution and everything to describe how things change in nature. And I realized that, as I think I mentioned last week, before this course, each and everyone understood what temperature was, but entropy was something difficult. And at this point, you would probably just reverse them, that this sounds very complicated. The beautiful thing is that this is something that comes out naturally of the equations. And it's also, as we're going to see a little bit later on in the course, this starts to explain a whole of things why various chemical processes are so sensitive to temperature and why we can really use temperature to control what happens or not. So one example of that is that by controlling temperature, we can adjust our scale, what energy barriers are relevant or not, right? There are tons of processes that you can speed up just by increasing the temperature. And that relates to eight. How does the hydrophobic effect vary with temperature and why? Yes. But what increases most? So that means that in general, the hydrophobic effect becomes worse when you increase temperature. And the most obvious way the hydrophobic effect manifests itself is that it's difficult to solve the hydrocarbons in water. And in contrast to salts and everything, it gets more difficult to solve the hydrocarbons in water the higher the temperature gets. So why is then hydrophobic free energy or the hydrophobic effect, they're really the same thing. So well correlated with non-polar area of molecules. Okay. You're actually right. It's not ideally formulated. So when I say hydrophobic delta geohydrophobic effect, this is really what we measure in the lab. How expensive is it to solve it various hydrocarbons? And again, the reason why I'm so obsessed with hydrocarbons is that this is going to be important for protein folding in general. These small side chains, the side chains typically correspond to various hydrocarbons. And if you start to measure all these and plot them in a diagram, there are, if you put delta g on the y-axis and various things on the x-axis, you're going to see some very clear trends here. And one of the trends is that the cost of solvating a small non-polar compound is pretty much proportional to the non-polar area. Right. So this is related to these clatterade structures I spoke about, right, that because the water, to maintain the hydrogen bonds in the water, the water molecules have to orient themselves around the molecules. And when the, again, to first approximation, the amount of sort, such ordering you need is going to be roughly proportional to the area of this shell. And again, that's why this is roughly proportional to the non-polar area of molecules. Now, another way of saying that is that it's roughly proportional to the number of atoms. In general, the area will grow, won't grow in exactly the same way as the heavy atoms. But if you put the number of heavy atoms, carbons, for instance, here, it would probably be roughly the same. And then we have two questions that are related. I spoke a little bit about this, but actually nothing exactly this way. So this epsilon, what is the epsilon I'm talking about first? Screening or the permittivity of free space. And that's, actually, I'm sorry, I asked what the role of it is. So the permittivity really describes how well any medium screens electrostatics. So why does water have such a high value? So that's part of the reason. Actually, I would say that there are two things you need. And you're quite right that waters have very, very strong dipoles, minus plus plus. So this creates a dipole that points that way. But there is something else that's important with water. Just having a strong dipole would not be enough. It's also a small molecule. And because the molecule is very small, and remember, the way a water really looks is that you have some sort of football and then two small hydrogen dots there. This means that the entire molecules can rotate very quickly. So if I now put a, say, positive charge down here, instead of positive ion, this entire water molecule would rotate in mere picoseconds, 180 degrees. And because all this water can rotate or rotate very quickly, they will be very, very efficient at screening. So what do you think is going to be more efficient at screening? Water or ice? Liquid water or ice? Why? And this is actually used in condensers and electronics and everything, not necessarily water, because they don't have other problems. But if you want condensers with very high capacity, you typically need some sort of liquid or at least gel-like medium because there is simply better at screening. And that leads to the next part, 11. Why does this permittivity or the screening effect go down for high frequency electric fields? Almost. Let's assume that we take this small dipole, but rather than having an ion, I'm going to make a condenser. So a condenser consists of one plate here with some charge and one plate here with some charge. And if you had a DC field, that could correspond to saying having plus charges here, right? And then minus charges here. And that's roughly what I had before. In this scenario, what would water do? It would realign, right? It would move. So let's change this field. Rather than having minus charges, and now I have plus charges there and minus charges here. And the water had just rotated, as you said it would. What does the water have to do now? Rotate back. What happens? So this works great if I do this once per second. If I start to do it with 1 megahertz, a million times per second, or a gigahertz, a billion times per second, what will eventually happen? The water doesn't have time to rotate it because by the time you're halfway rotated and pointing that direction, the field has just changed again. So that eventually, Epsilon will go down to roughly 2 for any molecule. And this is precise because once you get to the point, even water, as small as it is, doesn't have time to realign. So why doesn't Epsilon go down to 1? Why does it stay roughly at 2? Because of the electrons. Because all the electrons here, no matter how fast you change this field, the electrons inside each bond and everything will still have a bit of screening effect, and they move so much quicker than the molecule. It's basically, I'm not even sure whether it's possible to create fields that are fast enough so that the electrons can't keep up. So that was the electrostatic parts. We're going to come back to that in particular when we talk about membranes and membrane proteins. Because in membrane proteins, a normal protein is surrounded by water when we have all these electrostatic screening. That's not true for membrane proteins, and that's why we need to understand a little bit of electrostatics. So what is Epsilon roughly inside a normal, yes. So that depends a little bit on the electronic configuration of your atoms and everything. So I wouldn't say vacuum, but pretty much any gas. Any gas is going to be so, the concentration of atoms in any gas is so low, right? The whole point with the gas low is that we assume that atoms are so far away from each other that the first approximation, they don't interact. So this is only true for condensed matter, condensed phases. So what is Epsilon then roughly inside a protein? Three. So can you relate that to this factor two we just spoke about and the 80. So most of the things I mentioned are, most of these things I mentioned that at first sight might seem that it's not at all related to proteins. Why on earth should we talk about electrons and condensers? But it is related to protein. So why is it not one? That's the same explanation as we had. We have electrons in proteins, right? So that it's, you are going to have some sort of screening there. But why is it slightly larger than two, but not 80? Well, I wouldn't, if you look inside a protein, do you think can different groups rotate a whole lot? They can't really, right? So that's the main difference to water. Water is a small, very flexible molecule. The first approximations proteins are rigid. So what are the things inside a protein that could help you screen things? Charges, right? And in particular, different dipoles, say around peptide groups, different carbonyl, carboxyl groups inside chains. But of course, the second the protein has folded, you still have these groups. They're there, they're polar, they can screen, but you can't take a peptide group and rotate it 180 degrees without unfolding the protein. And this is what drops the electric screening by so much in proteins that they're simply not free to rotate anymore. So the book, and I think I last week mentioned this funny concept that electrostatics in water originates from energy. No, so it originates not from energy, but from entropy, which you can, I guess one could argue that it's not formally true because at the end of the day, all these things originate from interactions. But what does the book mean by it? Or conversely, I, but we just said that electrostatic, you said that first is quite correct, but you also said that hydrogen bonds are due to electrostatics. And we spent most of last week talking about how strong electrostatics is. Well, we just said it here too, right? So why is it not energy if electrostatics is so strong? Right, so that the point is that this is, there is so much energy and it would be such a great loss for the protein to start losing this energy. So the molecules would do virtually anything they need to in order to maintain the hydrogen bonds. And that relates to the thing we said up here too. The number of hydrogen bonds for most of these processes does not change. But of course, you're going to need to pay somewhere. And the place where we end up paying is that the molecules will reorient to maintain their hydrogen bonds. And that means that most of these changes will show up in entropy rather than energy. This is part of a very large concept, both in actually, this is not limited to biophysics, biochemistry, but chemistry in general. You probably have not thought and spoken that much about entropy and chemistry. I would argue that most chemical interactions, actually most interesting chemical interactions are more related to entropy than energy. As you will see later on in this course, there are some fundamental differences between interactions that are limited by energy versus ones that are limited by entropy. So if an interaction is limited by energy, could you imagine a way to speed it up? Heat. Just add more heat, then you have more energy, right? And then it's going to happen quicker. That's a very easy way to speed up interactions, but I will also argue those interactions are kind of boring, right? Because we understand exactly what happened. You just need to add energy. Whether that is because you're moving it to a higher energy state or because there's a very high barrier, we can come back to that later. But entropy, what does entropy mean if something is limited by entropy? So that it could be related to hydrogen bonds, but I'm thinking of a much more general, on a much more general level. I'm not thinking about any specific feature. So what do we mean when something is limited by entropy? That's an entropic barrier or is it the limiting rate of, sorry? So it's certainly limited to states and you're going to spend the afternoon in the lab talking about these states. So entropic problems are related to searching, searching and testing. Imagine solving a big puzzle with 10,000 pieces. That's an entropic problem. It's certainly going to be faster if you add two. Basically, well, of course, it will be faster if you try to solve it faster, but it's not really an energetic problem. But you're going to need to find the best possible ways of assembling all the pieces. Some of them are good. Well, in that case, there's only one way they work, right? You simply can test lots of different combinations. Occasionally, if you can speed up the testing or something, you can solve that problem faster. But in chemistry, that is usually a rate the molecules need to find each other. They need to test every single confirmation. In the case of a protein, they're going to need to test every single possible combination of packing their sidechains. There are lots of cases in chemistry where processes are slow simply because the molecules are so large and complicated that they will take almost forever before they find that particular pose. Could you imagine any way to speed up such a process? Yeah. Sorry? Exactly. One great example of this is when it comes to, for instance, splitting or forming peptide bonds. You have one amino acid here, right? And one amino acid here. Or in this case, you can forget whether there are amino acids or not. But two large molecules, and you want something to happen here so that they should form a dimer or something. But there could be a fairly high energy barrier for this to happen. This energy barrier could be so high that you would need to wait days on average. But if you now create a very large protein or some sort of molecule that tends to stabilize these in a conformation, where they're super happy together, so you bind molecule A and molecule B. And when both of them are bound, they're sitting right next to each other and you force the molecules to kiss basically. And if this happens, right, you see you're removing all these different degrees of freedom the molecules had. So just by binding these molecules right next to each other, they're now going to be, that solves the searching problem. And that's pretty much how most end times work. So the end time solves this problem because that this is not just a matter of adding energy. So once these are bound, they will now release again and the end time is free to do it in work. So end times work by reducing these energy barriers. And as you are all educated now, you know that a free energy has one energy term and one entropy term. So when it comes, and the energy barriers are what's going to limit all reactions. So if we want a reaction to happen faster, there are two ways. If it's an energetic process, we can solve it just by adding more energy, heating it up. If it's an energetic process, you're going to need to find some sort of way of fixing the cost of entropy, making sure that you don't have to search that much. For instance, with an end time. So an end time is just a catalyst. But it's a biological catalyst. We're going to come back to that. We're going to spend quite some time on that later on in the course. But my only reason for bringing this up now, all these fancy features at the end, they come down to this simple equation. In general, the simpler equations are, the more important they are and the harder they are to understand. I always found that the long and complicated equations, they are the easiest ones because they describe one very specific feature. The small equations, the apparently trivial equations, they're the ones that are hard because they frequently have so profound impact. And they're the ones you need to think more about what they really mean. Yes. How do you predict what processes will occur? Sorry. Free energy. Remember that I said that we are all sloppy and mix up energy with free energy? So you're quite right. It's free energy that determines what processes occur. The energy barrier is completely relevant. It's the free, only the free energy barrier that matters. And the way to think about that is again, these small, I love these heat packs because that's a great example for this. When you're starting the reaction that causes the heat pack there, you're not adding energy. You're just causing something to happen. When you're causing something to happen, you're releasing tons of energy. So you are getting energy back. And again, that would not, if you just got energy back, that would somewhat violate laws of thermodynamics and everything that, but energy itself is meaningless to describe what reactions will happen or not. There are tons of reactions that will release energy when they happen. There are no reactions that will spontaneously go against free energy. That does not happen. So when it comes, anytime you're talking about a barrier and deciding whether something happens or not, it's always a free energy barrier. And my point here is kind of understanding the energy part of this is trivial because that's just about adding more heat than it happens quicker. Understanding entropic energy barriers are going to be much more complicated. So what type of barriers do you think we have in proteins? So proteins correspond not to these 10,000-piece puzzles, right, but 100 billion-piece puzzles. And that's what makes them interesting and that's what makes proteins different from a whole lot of other chemistry. And not just, it's not just about understanding how normal proteins fall that occur in nature, but eventually if we're going to want to decide, design proteins or everything, we're going to need to understand what they do. So there was one last question about electrostatics here. What usually happens to titratable amino acids inside proteins? Yes, they have to lose their charge because either and it's exactly the same feature as this. It's so bad to embed an isolated charge in a hydrophobic environment that you will get a compensation effect, that they will lose its charge instead. But in that case, it shouldn't be so bad to embed a titratable amino acid in a protein because it doesn't have to be charged. Yes, but where does that energy cost show up? So if you take lysine, for instance, lysine would like to be charged at pH7. And you can actually calculate this from the, it's very trivial to calculate from the pKa value, but this is not an acid and base core, so I'm not going to do it. You're paying this cost when you're deprotonating your lysine. It costs a lot of energy to remove a proton from lysine at pH7 or conversely it costs a lot of energy to take up a protein and neutralize siglotamic or aspartic acid. You're just paying that when you're changing the titration state instead. So what we're going to do today is that we're going to try to move from one pair of water into slightly more complicated systems. We're not going to go through, Jesus, this is the trivial protein. It's super trivial protein. And you can probably still imagine, so this is a, let's see, just say, yes, this is the villain headpiece, I think. So even for a protein as trivial as this one, you can probably imagine there are going to be thousands of interactions here, right? But before doing that, I'm going to have you solve a small problem. So now you are all educated and understand free energies. If I, let me draw some sort of diagram here. And let's say we have temperature on the x-axis. And then I have two states or two forms of matter. This could be ice, for instance, or water. So on the y-axis, I have delta G or G, free energy. You will frequently see me ignoring the delta because this change is just an error. Since I haven't told you where my zero point is, right? It doesn't really matter whether I call it free energy. Free energy is always relative to some zero point. And if I now show you, say, one form of matter or my system might have a free energy that goes like this. And then I have some other phase or form, whatever you call it, that goes like this. So obviously there is something that happens here. So if you are to the left here, what form would you be in? What form is best to be in? Black. Black. And there is a billion dollar question. And if you are to the right, what form is best to be in? Green. Yes. So this was not a trick question. Good. You all understand this. So anytime you're looking at a system, say water, you can plot water, properties of water in different phases. So here I've essentially done this for water. There are three phases of not just water, but most matter. You can be in some sort of solid phase, ice, liquid phase, what we call water, or gas, which is water vapor. Does this make sense as a function of temperature that you have three curves like that? Yeah. So that at the very lowest temperatures, you're going to be solid ice. And then at some point you move over on the green curve. You are in liquid water and eventually it's going to be even better to be in gas. So technically, each of these phases can occur at any temperature. But if you're up here, it's going to be extremely unlikely that you're in the solid phase. You're virtually always going to be gas. In 1962, there was a very special experiment performed by Der Jaggen, who's actually famous for lots of other things in physical chemistry. So this was not a tier two or tier three scientist, one of the most famous physical chemists in the world, who together with Fedjakken published an amazing results. So they claimed that under very special conditions, water could spontaneously condense and essentially polymerize into small capillaries, very, very thin glass vials under special conditions. And they gave this a name. They call this phase for poly water. And lipping cart in the US was also one of the people who handed it. So the idea was that again under special conditions, you would get the water molecules to form very strong networks of hydrogen bonds. And these networks of hydrogen bonds, or well, even electron sharing here, they would cause the water molecules to not just move and have strong hydrogen bonds to each other, but they would literally polymerize. The water molecules would bind to each other. And they claimed that this water would then have a freezing point around, well, 210 to 240 Kelvin and a boiling point around 500 Kelvin. And this actually, this was even, to make it all, there was not just one paper on this. There ended up being a very large bruja about this in the world. At first they could only produce this in Russia. So there were some bunch of scientists, and I think lipping cart was among them. And people in the US argued that Russia was in the position of starting to develop a poly water gap that had all these new technologies that nobody in the US had. There is a famous novel by Kurt Vonnegut called The Cat's Cradle, where he talks about a new form of ice nine that would freeze at around 100 degrees Fahrenheit, so minus 50 degrees centigrade. And the idea with this ice nine was very much taken from the poly water. So the idea with ice nine was that basically what a phase that would expand as a horror story, that anything, if ice nine touched any other matter, that matter would also have its water freeze into ice nine. Based on what you know, there was something horribly wrong with this, that you should be able to debunk instantly. There is a much simpler way of debunking this. The person who debunked this, and nobody listened to him initially, but it was section Richard Feynman. There's a much, much easier way to debunk this. Forget about all the details about water and everything. Think about that diagram. So what is, sorry, somebody, so if if we for a second argue that Lippincott and the Fidyakin and the Ryagin were right, so that this is a correct phase. So under what conditions, what would be required for water to pour in poly water at room temperature? Go back to the simple formulas, you know, you have the diagram on the right, so what determines if something happens? Yes. So if this is to happen spontaneously at room temperature, what can you say about it relative to liquid water? It must have lower free energy. So sorry, I only, sorry, I don't have more colors here. Actually, I do have. So this phase would somehow need to be here, right? Lower in free energy. What would that imply? Yes, but again, what would it imply for normal water, all the water around us that we see? Exactly. If poly water really had lower free energy, all the water in the world would form poly water. You can decide, you can discuss how long it would take, but there is no way you can have, there is no way you can have a phase that's stable and has lower free energy, and that we would never have observed it for four billion years. And this is exactly how Richard Feynman debunked it. Do you see the beauty that because the second you start to make assumptions about how the polymerization happens or how the hydrogen bonds happens or the nature of the hydrogen bonds, then you're into the special cases. And the second you do that, people can certainly already know, well, there are special conditions here. But by only talking about free energy, it's universal. It doesn't matter what forms of water it is. This could be any molecule. The details do not matter because you've only assumed the most basic things from thermodynamics. Yes. So in the end, I'm not sure whether this was conclusively solved. There is a small presentation about this called debunking poly water that I uploaded on the Monda website. But one of the things that they managed to show eventually is that if you took this water and then just burned it, what happens when you burn water? Yes, you should burn the gas. But for some reason, there were some charred remains. So there was something in the water that's not water. And what they eventually were able to show is that the spectra you got from this water in spectroscopy were very similar to spectra you got from sweat and other things. I'm not saying it was body liquids, but there were a bunch of other ions and stuff present in it. So it could even have been that by pushing lots of water through very thin capillaries, you might very well have dissolved some silicates and stuff from the glass. And of course, 10 years later, everybody had forgotten about this. But right in the middle where this happened, I bet this was the coolest thing in science, because you discovered a new phase of water. So be careful when everybody says something at school, it might very well be completely wrong too. So today, we're going to head back to the polypeptide chains. And we're going to talk about secondary structure in terms and geometry topology and stabilization. But now we're going to try to formulate this more in terms of free energy. And we're going to speak a little bit more about amino acid properties and titration and what that means for protein folding. So we're going to start to look a little bit at energy landscapes and energy landscapes. And here's where here's where things are sloppy. We frequently speak about energy landscapes. What we typically mean is free energy landscapes. So if we just were to plot the energy of a protein related to some sort of arbitrary degree of freedom here. And this comes back. And this is where we introduced energy landscapes in the first place. We have no idea what this degree of freedom is. It's not important. But if you wanted to include all degrees of freedom in a protein, we would have 300,000 of them. And then we can't think about it. So you could imagine that this is just a simple bond length or a simple torsion. But in practice, it's just some sort of arbitrary way that you change your protein in one dimension. So what's going to happen when you fold the protein is that event, at the first part, we start with some sort of very high energy. This could be a completely stretched out protein chain. It's not interacting at all with itself. But you can also imagine if we somehow the white part here, if we think of this as the amount of available states, you have lots of available states for a stretched out chain, you can rotate pretty much any bond that it will still be stretched out. It's not going to bump into itself. And as we are moving down in the energy landscape, well, you're forming some sort of better energies here, these collapsed states might be the part where we turned all the hydrophobic parts to the inside or something. And as we're collapsing the protein more and more, you're gaining energy because you're gaining some useful interactions. But the entropy is also dropping, right? Because we now have less freedom because you're collapsed, you're not completely stretched out. This is complicated because gaining energy is good, but reducing entropy is bad. So whether this happens or not at the end of the day, it's going to be up to F equals E minus TS, right? If both of these go down, the question is which one goes down quicker? If the energy goes down very quickly, that's good. If the entropy starts going down too quick, we're not going to go there because that's bad. So the question at the end of that, can we get all the way down to some sort of folded states? Because this is what Amphins had predicted, that the global minimum here is some sort of, if the balance between energy and entropy is what's going to be the native state. And here's the point because this, in this case, I just plotted energy. What Amphins said is that we're going to have the minimum of the free energy, not necessarily the minimum of the energy. Because it could very well, in this case, we call it the folded state here, but it could very well be that the state that has the absolute lowest energy might not have the lowest free energy. So this is also something we're going to worry more and more about, the balance between entropy and entropy. And if you start to think in terms of a slightly more complicated protein, this is actually based on an experimental study. Here, we just try to plot something in two dimensions that you have some sort of completely unfolded state out here. And when we start folding, you move across some sort of energy barrier. But then you might have two states that are only one of these states would be native. But the other one might be pretty good, but not quite native, some sort of intermediate state here. So the red here, well, the purple down there would mean that it's super good. And the blue here means that it's good, but not quite as good. And this is quite common that you can capture experimentally too, particularly for large proteins, that you start unfolded, and then you get to some sort of intermediate, folding intermediate, and eventually you get to the native state. And once you're there, if you can only identify these states in the lab, and well, if you can identify them, you can likely measure their concentration as the probability or their occurrence as a function of time. And if you can do that, we can start to study how quickly the reactions happen. So a process like that with three states in terms of free energy, that would mean that you have some sort of unfolded states here that's worse. Then they have the intermediate states that's slightly better. And then we have the native state that is the best one. Between each of these, we would need some sort of energy barrier. And then we can calculate how quickly things move across that energy barrier. Why do we need energy barriers? Well, if we didn't, let's assume that we didn't have that energy barrier between the native and intermediate, what would then happen? I think you're right, but I'm just formulating it slightly different. Right. So the intermediate state, this comes down to what you mean by stability, whether something is stable. And if there were, if there was no local minimum and the free energy here, you would never observe a state. The fact that it's the fact that you call something intermediate in the lab, it doesn't read just mean that it happens on the way because then you could never identify it. It has to be stable at least for a small fraction of a second or something. You can't, you would not have an intermediate that just flies by while it happens. So whether, and the problem here is that the energy barriers here, it's not binary whether you have a barrier or not. This comes down to that you have different energy barriers. And the question is, are these energy barriers relevant or not? So if the energy barrier here was 0.1 kT, would you see the intermediate state? Why? If the energy barrier is a lot smaller than kT, in practice, we will just go right over it. And these processes on the molecular scale happens on fractions of picoseconds. So there is no experimental technique that would be able to identify it. But by the time the energy barrier starts to be in the ballpark of a few kT, then we might actually be able to identify that state. So here's also the problem that the whole concept of an intermediate state is a bit fuzzy. We say that there is an intermediate state if you can't identify it. Yes? Sure. That goes down to our friend, the Boltzmann distribution, right? E minus delta F divided by kT. The probability of being somewhere, or the, for instance, the probability of being at the top of an energy barrier relative to the state we are in, that's going to correspond to the difference in free energy divided by kT raised to E. If an energy barrier, if we are here and this energy barrier is significantly higher than kT, it's really going to be a perceivable barrier to us. You will not typically, you will be stuck where you are in the intermediate states until we have amassed enough energy that we really can go over this. And whether that is, if that is 5 or 10 kJ per mole, that's not going to be a problem. It will happen after a while, but it's not going to happen instantly. You might, you might try to go over the barrier 100 times and the 100th time you will succeed. And then you will likely be able to observe it experimentally. But conversely, if the energy barrier is 0.1 kT, it's going to be so low that on average you will go over it the first time you try. And then we will never, ever have any significant population in the state that you can measure. And the extreme case of that would be that we just remove the energy barriers. If we remove the energy barriers, the reaction will happen spontaneously, all the way from unfolded native. So this starts to touch upon the things we talked about last week about kinetics versus stability, right? It's not that simple. Stability, you can talk about stability in two ways. We can talk about stability in the sense that something is the best possible state, that it has the lowest free energy. That would be here. Or you can talk about something being stable on the timescale we study because the barriers around you are so high that you're not going to go over it on the timescales we study. If these barriers were 100 kT, we might very well feel that the I here is a stable state because on the timescales we study it, things will not move away from it. So that while the throws in free energy are important, the barriers are too. And this is, again, something we can measure experimentally. If you have a number of different states or, for instance, some simple reaction coordinates, you might have an EPR spectrum where you can measure the distance between two groups. Or you might have a spectrum where you can measure, say, the radius of gyration of the protein. Anytime you find a handful of different experimental observables, and you can measure this really quickly, you can define two arbitrary degrees of freedom or reaction coordinates, and then plot the free energy of the protein as a function of these. So in this case, the protein would like to be here. Here's where we have the highest population, but it's also possible for them to be at all these places. And today, even with NMR, you can measure this in for protein folding and everything. So this is not just a good idea. We know that proteins do behave this way. So if we then use this, and I'll try to go back to secondary structure that we talked about, but everything we do now, we're going to try to think in terms of delta G and what happens both during folding and interactions. And I think we're going to start with the lowest level with our friends, the helices again, the alpha helix. So the alpha helix is stabilized primarily by hydrogen bonds, the yellow dots here. And for each of these residues, they make a hydrogen bond to residue four units away. And the first hydrogen bond, if we start down, let's see, just no, I think it's going in that direction. The first hydrogen bond we make, that's going to lock residues one, two, and three in place. So the first hydrogen bond locks four residues, well, three residues in place. And then for each hydrogen bond, we're adding, we're stabilizing three residues. We're stabilizing the residues between the hydrogen bonds. But what does this really mean? Stabilize. So don't hand wave. Delta F for delta G equals delta E minus T delta S. What happens? What decreases? So if the alpha helix forms in the first place, I would agree, this should decrease. But if we look at, let's look at an individual hydrogen bond that forms. What happens to the energy? Why? Actually, so this is a bit complicated, and this comes back to this part in vacuum versus water. Let's cheat a bit here and say that we are in vacuum, so we don't have water around us. Which is not as bad as you might think, because in the inside of a protein, we might not have water. So we're just looking at the helix in isolation. Is the hydrogen bond energy itself good or bad? That's good, right? That is an interaction. So the delta E is good. But of course, if you had this in water, we would have the usual problem that we just stole the hydrogen bond from elsewhere. So what happens to the entropy? Decreases. Why? Right. So we had these three residues that, if we, apart from the fact that they can't bump into each other, they were free to move their torsions any way they wanted in this Ramos-Shandan diagram, right? And now we have locked them in and say that you can only be at one point in the Ramos-Shandan diagram. That's a much more ordered state. And we just did that for three residues. So what's going to happen here is that we're going to have a balance. On the one hand, we gain some energy, but we're going to lose some entropy when we form an alpha helix. And as I, I don't remember, I think I have that later today or tomorrow. But you can calculate this. What is, and again, you don't know exactly what the energy of a hydrogen bond is. So let's say that you have a particular energy for an hydrogen bond. We have a particular entropy that we're losing when we're forming an hydrogen bond. And then we can start to play around a little bit with these terms. But already now I'll wet your appetite a little bit. So why don't everything turn into alpha helixes instantly? Is there going to be some sort of energy barrier when you form an alpha helix? So that, but that kind of relates to the entropy, I said. What I'm going to argue, and again, we will prove this later on, when you form the very first hydrogen bond, you're starting to form one helix. You're not going to have a helix until you form one turn, right? But let's start from residue zero. I'm at residue zero here. And then I want to add residue one to my helix. What changes in energy to first approximation? Nothing, right? Because I can't form any hydrogen bond yet. What happens to the entropy? I lose entropy because I'm going to need to put the second residue in exactly the alpha helical conformation. So that was a pure loss. When I add the second residue to the alpha helix, well, hey, what can I say? I'm a programmer. I start calculating at zero. So zero was what I started with. One was a pure loss. What happens to two? Pure loss. Number three, pure loss. This is starting to be pretty bad, right? If this was a company, this is where you should sell the stock. But the point is once you get to number four, you actually start to gain something back because then you're also forming hydrogen bonds now. So the point is that initially we're going to lose free energy. And then at some point, we start to gain free energy back. So there will be some sort of energy barrier there. We'll go through that more properly later on. But what says that this was just my argument that we start to gain at some point? Couldn't it be the case that we keep losing? What says that the free energy has to go down? Because I said that this was a balance between the energy of the hydrogen bond and the entropy. What says that the energy is going to help us form them? So what would happen if all terms were positive? Yes, then we would never see an alpha helix. So the mere fact that we know that alpha helix can fold means that the free energy must be lower. Do you see again, just from the sign of things, you can learn a lot. So there are terms acting both four and against folding. These alpha helixes are super important in tons of places in nature. And let's see if I can play a show movie. Yes. So this is an alpha helix that occurs inside a membrane. But in this case, we have a titratable amino acids. So this is the a protein I'm going to tell you more about later. It's this small voltage sensor that occurs in all your nerve cells and your hearts. And they're responsible for gating channels as a function of voltage across your nerve cells. It's kind of important, you would all be dead if you didn't have this. So this allows something to happen when you change an electric field in a cell in a split second, a millisecond. And this is an example of a very long simulation that a company in the US ran about three years ago. I will tell you more about that later in the course too. But the point what happens here that you might not see it is that when this goes through and moves up or down, there are actually some small changes in the secondary structure. You're either folding or unfolding parts of the helix and parts of it even changes to a 310 helix. So there's a very delicate balance here of secondary structure as a function of where you are in the protein. That is related to overall. Normally the alpha helix has this that you're forming a hydrogen bond four units away. And the difference between all these helixes we spoke about that last week at that you get a different pattern for these hydrogen bonds forming. In the case of the simulation I just showed you, you move from the alpha helix to the 310 helix and then back. But what is the difference again? What determines when you have one of these helixes? What determines if you have a 2, 7 helix, 310 helix, alpha helix or pi helix? Speak up. Well partly the surrounding and partly the helix itself but go back to the equations. So again I like my equations. Let's use delta G just for fun. Delta E minus T delta S. To first approximation what is the difference in energy? Zero because you still have all the hydrogen bonds right? And each rest at least in an infinitely long helix you have the same number of hydrogen bonds. So we're not changing the number of hydrogen bonds. So the difference between all these four helixes must lie where? Entropy. So that the alpha helix is typically the most favorable entropy and the reason that both the pi helix and the 310 helix and in particular the 2, 7 helix they end up being fairly strained. So they're being more rigid and having less freedom. So there's mostly a difference in entropy. And let's see how much we're ahead in specific to say about that slide. No you know what. I'll skip it. You've seen enough alpha helixes. This is the typical right-handed helix. If we take that helix and put it in a ramachandran diagram you're there. And then there are all these other possible helixes that occur in slightly different places. Again this is just an average ramachandran diagram for a typical amino acid. But you see that this white spot is fairly large here right? Because the white spot here is fairly large that means that you have a reasonably high entropy. For most of these other places the white spot on the map is relatively small. And the pi helix there is very very tiny. And because you have a smaller part of the ramachandran diagram that is allowed for you that means that your entropy goes down the drain. And when your entropy goes down the drain your free energy goes up. Less favorable. So already just from looking at your ramachandran diagram you could start to say that alpha helical region that's going to be good and that is going to be good because there is quite some freedom around those areas. So let's try to make a similar rough reasoning about the beta sheets. So what is the main difference between a beta sheet and an alpha helix? If none of you can answer that I'm going to start getting a little bit worried. So there are lots of differences here. What is the main difference in the hydrogen bonding? That's of course related to shape. They're non-local. Very non-local even. So in general an alpha helix let's forget about the other helixes for now. So an alpha helix made a hydrogen bond from N to N plus 4 right? So what happens for a beta sheet? It can be pretty much anywhere and it will also depend on whether they are parallel or anti-parallel. I'll wait with side chains where they are pointing in a second. But let's try to make the same argument here. What is the drives folding and what is the works against folding? So you can start with one of them for instance this guy. What is that helps you to fold and what is that works against folding? You probably start to know this equation by now Right. So to first approximation that sounds exactly like an alpha helix but they're not quite like alpha helices. So let's start by looking at this chain. If you want a beta sheet to form here the point is before we can even start to form a beta sheet we're going to need to put this entire strand in a stretched out fashion. So rather than having any confirmation you allow for that you're going to need to take a chain as they stay at a completely stretched out fashion. When you only have that first chain you still have zero hydrogen bonds. So you're paying a whole lot more than for the alpha helix. It's even worse than that because you're going to need to take the entire second chain and put that in a stretched out form too right? But when you do that you get nirvana because suddenly you get like 10 hydrogen bonds. Not just one. So can you already now start to guess something what that's going to mean for the energy barriers? They're very high. Can you in turn say what that will make for the kinetics of folding alpha helices versus beta sheets? They will be much slower. They will actually be much more stable too in many cases. But already now without you don't know we haven't even started talking about individual amino acids. We haven't even started talking about specific energies and you can still draw conclusions about the kinetics how fast different structures can or must form. This is also partly related to the reason I think why we don't really have that many local structures. This gets to be a bit of chicken and egg problem because evolution has driven this for four billion years. But there aren't that many local structures where you simply have good stability and energy barriers that are high but not too high. So is it good to have these energy barriers or not? Why? Well you can still argue that as long as the free energy of the folded state is lower then it would be good right? Then it could form. But the problem is you would end up with a very fuzzy folded state because if you just started any if you went into a sauna your proteins would start to unfold because it's just an energetic sorry it's just an energy barrier. So having relatively sharp energy barriers helps us achieve stability so that you don't want proteins to unfold because of small disturbations. But on the other end you can't have too high energy barriers either because first the structures would never form and second you could not degrade them which means that you could not eat food. Overall the general feature of beta sheets is exactly this that they have a very high cooperativity when you fold so that you have an entire strand here an entire strand here and then you form pretty much all the hydrogen bonds at the same time and it's quite right that they're going to form much slower than alpha helices. But this also gives us some pretty cool features. We're going to come back I'm sure I might talk a little bit more about parallel versus anti-parallel sheets here but you can already hear you can show that there are some clear differences in how the hydrogen bonds form that's also going to influence the stability. So once you you start by moving from 130 and up here and then we make a turn and then we go back so in the case of being anti-parallel you're going to get a very nice regular pattern and the other alternative is that we are parallel you're going to get about as many hydrogen bonds but it's not going to be quite as good in terms of entropy. But beta sheets too will do virtually anything they have to maintain older hydrogen bonds. I'll do two or three more slides and then I think it's time for a break. So what this will mean to is that once you have many of these strands right next to each other because all the amino acids are forced to be stretched out virtually in a 180 degree conformation they're going to go up down up down they're going to be pleated back and forth and this will give the entire extended beta sheets this pleated structures up down up down up down. If you look at the atoms we typically don't look at the atoms why don't we look at the atoms? You can but imagine if this was part of a gigantic protein it gets complicated right? So I've even cheated here a bit what are all the yellow parts? So the yellow parts are the side chains so it's starting to take every single hydrogen bond and everything into account here we don't want the details. So we know the fundamental properties of beta sheets is that they can form large two-dimensional structures that's another key difference compared to alpha helices right? And alpha helix you can stretch out the alpha helix but alpha helices you can't really put them next to each other so you can form some sort of sheet light structure we call these beta sheets but once we know that we can form a sheet we might not want all the details about exactly how the bonding happens in the sheet we know that they can form a sheet so let's look at the slightly higher level. What if I take these side chains and you can start to place these in smart fashions? So what if I take all the ones pointing up here and give them some property A, A, A, A, A, A, A, A, A, A, A, A, A, A and then we take the ones pointing down and give them some other property B, B, B, B, B, B, B etc. Then you're going to have an A side of your sheet and a B side and apart from all the parallels to rock music and everything if you choose these properties wisely you have literally created a barrier where you have one property on that side and another property on that side. I'll come back to that shortly because that's going to be cool. Now in practice, yes this slide and the next one and then it's time for a break. In practice beta sheets are not exactly planar. Why? So this is a bit of a trick question. Why should they be planar? If you have the Ramachandran diagram right, the only scenario where they would be exactly planar is if we happen to place all the residues in a way that they would be, often two residues at least, you should be back in exactly the same orientation when you started. So that's going to be one infinitesimally small point in the Ramachandran diagram that would make them perfectly planar. And it's just a coincidence that beta sheets, well of course evolution it's not a pure coincidence, but the likelihood that we would be in exactly that point is basically zero. Beta sheets get the properties they have because they're very close to that point, but there is nothing that says that they have to be exactly there. Now of course in practice you're quite right that this will depend on the size of the groups and everything. So what's going to happen in practice is that you have a very, very weak twist. So these you see here too that instead of drawing every single atoms we try to draw this as some sort of model because at least I could not just looking at all the atoms here, I could not really say that it's twisting just so slightly here. But if we draw them this way with arrows instead it starts to get a whole lot more obvious that you're twisting a couple of degrees per residue. And when you start having large beta sheets you can see these twists because these twists will mean that the entire beta sheets start having slight twist too. So that's not an artifact of structures or anything that's fundamentally because beta sheets like to be in that conformation. But you could it's a bit of a check in and egg problem. It's based on the properties of the amino acids that they are close to planar but not perfectly planar. Can you see something else that's pretty cool up in B? This is a remarkably short turn right? Because here you have you have the residues and they are stretched out and pretty much you have one residue there making a hydrogen bond and then you have one nitrogen there one. So basically in two residues you turn 180 degrees and go back again. So normally we talk about proteins we talk about loops or we frequently draw them this way. This looks like that it's a bit of a floppy structure right? They're not floppy at all. So in terms of beta sheets we call these turns. So they're super tight turns and there are just a handful of there are just a handful of ways that you can have these turns so that they form a hydrogen bond as part of the turn and just go back. So we're basically losing one hydrogen bond compared to just continuing extending the beta sheet but at some point you have to turn otherwise we would never form a beta sheet. These turns are so close that you see them all the time in crystal structures and again there are only a handful of turns here that are really common and that you see everywhere and they are very well placed in the Bramashanla diagram too. I think this is it's 1020. I think this is a great place for a break. After the break we're going to talk a little bit more how we measure this in the first place. How do you determine secondary structure? And how do we know that our bioinformatics predictors and other things are correct? And then we're going to add a little bit more into protein folding I think. But I think we do pretty good on time so let's take 20 minutes and meet here at 2211. There were two or three questions here. Let's see if I remember all of them. The first one I got one mail about it yesterday and one question about here exam not entirely unimportant. So when it comes to your grades on this course there are going to be two parts. You need to pass all the labs and you need to pass the written exam. When it comes to the computer labs they are strictly pass or fail. You will not be graded A to F on the labs and the main reason for that is that programming is super important. I love programming but we also deliberately gave you a programming project on the programming course in bioinformatics so that's how we assess your programming abilities. In this case hey being a better programmer will help you a bit but in this case for this lab of course we want to assess your physical thinking about things. So that it's important that you won't pass the course unless you have all the labs approved but we're not going to grade them. And since there were a couple of you who didn't arrive first thing in the morning I will also say that Björn and Daria are going to force you to hand in very short lab reports. It should be less than one page and do that at the very write them during the lab and submit them by the end of the lab. Don't wait until next week or weekend or whatever to do it. It's not going to be a whole lot of work and because they are around you can check with them whether your answers are correct. If you do it that way you will likely just get them approved with returning email and you won't have five of them hanging after you. The second part then is the written exam. The written exam is going to consist of two parts where the first part is a couple of I forgot exactly how many questions I do but think of 20-25 questions that are going to be focused on small facts. Very similar to these study questions I give you at the end of each lecture and the idea here is that if you know these study questions you're going to pass the course. You're not going to necessarily going to ace the course but you will pass it and then at the end of the exam I have between two or three slightly longer essay style questions and the point is not that I want you to write essays but the point with a longer question is to force you to think and synthesize knowledge. So those are going to be parts where you have to well they're going to be related to the things we've talked about in the course for something where you should try to use knowledge for multiple areas possibly including some bioinformatics and everything and the idea is that if you want to really high grades you should do well on those last two three questions too. I will give you a trial exam or two if you want to towards the end of the course but for your sake the point is that you're learning for life not for the course so I don't want to give them and again they're also they're just examples I change them every year so I don't want to have them out too early and give you the impression that you should just learn that by heart. If there is something you should learn by heart it's the study questions. I will basically the first 25 questions I will basically pick from the study questions. I might not have exactly the same formulation but they're going to be the study questions. Depends what you mean by learn. I'm not interested in you learning to drive six formulas by heart. I'm completely uninterested in that because that's not how I would do it. I want you to be able to work a bit in mathematics and there could be probably not one of the simple questions but there could be so first you should know these formula because by far the easiest way to answer many of these questions short questions is just going to be to write down a formula saying because because delta E is the same the difference is going to have to be in delta S. Boom answer done. So that think of equations not that they're necessarily evil but something that helps you. When it comes to deriving things in particular in the longer questions yes there might be a part where I give you something but I would probably give you something completely new then so the point is not that you should learn to derive a couple of formulas by heart learn to work with equations. Having said that key thing here is about this is not mainly a physics course and it's not really a physical chemistry course either right. Our goal here is to understand proteins and what I am a strong believer in that any type of assessment should really measure the things that we want you to be good at. We use it's important to understand some physical concepts because they're going to be by using these physical concepts you will be able to make hard predictions that are correct rather than hand waving about say proteins and those are the things I want you to learn. I'm not really going to ask you that many questions about things that are not at all related to proteins. So we spoke about terms before the break the point here is that I didn't mention the year. They were proposed already in 1968 mainly from models and again 1968 we only had a handful of protein structures so do you see just as secondary structures were proposed by Pauling and other people very early on it's the same thing for turns people realize there are only a handful of ways these amino acids will form stable structures and this of course comes back to these 4.3 billion years of evolution nature has a whole lot of time for trial and error and the reason we have the structures we have are of course that they are the ones that we can form quickly and stably with proteins. Sorry with the amino acids we have. So how would we try to determine these structures experimentally? Yes are there more methods? If I gave you a protein and you it would be good I want to know whether there's a helical or a sheet protein. So there are a couple of different ways I'm very happy that you're not seeing NMR if my colleagues are going to kill me if she sees this I love NMR it's a really good method. The problem is yes or you can go down to Grenoble and where you have a synchrotron or max 4 in Lund you can book a session there at a couple of 10 000 euros or something travel spend six months you can of course determine the structure of the protein right then you're also going to get the secondary structure but the point is that secondary structure is a simple property that we want to get quickly and simply. So here it's all a matter of cost and if you're a new PhD student and you want to determine the structure the professor will just look at you and say yeah you have 500 proteins you're going to do this for and you would like to do this by determining the structure of each of them. You're not talking about a 20 million euro project or something sorry it's not going to happen. So the way we do this is with something called cd spectroscopy. Are you familiar with cd spectroscopy? Some of you are. So here is where what goes around comes around. Remember last week that I said that amino acids are chiral right and you all know what the chiral is and the stereocentric. So here is where we can rely on the fact that different chirality of amino acids will give rise to different physical properties but the chirality the handedness of amino acids also leads to handedness of structures. So because of this handedness even a structure say an alpha helix that's right handed by default an alpha helix is going to have different stereochemical properties. I'm well aware that's a bit fuzzy for now but because there is an built-in handedness in the structure you're going to have a different stereochemical physical property than you had from say a beta sheet and in physics by far the easiest and cheapest way is how you bend light. So normally light would be the polarization of light this has to do with how the electrical field is how the electromagnetic field is varying and normally this could be you can have a vertical polarization or horizontal polarization. It's a vertical polarization or horizontal polarization and if you combine this with a small filter you can also get light to be circular polarized which means that it basically goes around in a circle it's still normal light but it gives it's slightly different physical properties. If you have a circular polarized light and shine it on a sample that has a bit of handedness it's going to turn this light either slightly to the right or slightly to the left which will you will basically turn this circle into an ellipsoid depending on how you change the properties. The reason why this is nice is that you need a machine that's super expensive well I'm kidding it's like a couple of thousand dollars at most. You have to change the lamp like once per decade or so it's the the cheapest and simplest machine you can imagine. You just put your sample in the cuvette put it down and then you turn on the machine and you get a result dirt cheap there are like there are probably half a dozen of these machines in our department any lab that needs one can buy one and what you will then see as a function of the wavelength so what type of length you will get one pattern here for alpha helix roughly other pattern for beta sheet and then for the random coil that is neither helix or sheet you're going to get a third pad. This is sweet because it's cheap it's quick and it's super easy if you're not changing the temperature or something or denature the protein you would instantly as a function of sine see how the alpha helix shape goes to random coil shape and then reduce the temperature again and you will see that it would go back to alpha helix. What's the problem with it? Well sorry so you said something about temperature it depends on temperature but I can set the temperature to anything I want I can set the temperature to 37 degrees centigrade if I want to study how it works in a cell. So imagine if you have a gigantic protein that once you look that hopefully a bit in bioinformatics nuclear pore complex or something 60 different chains you have alpha helix's beta sheets you have everything what's this going to look like it's going to be a mess mixed right so you can certainly see if you're now denature your protein you can see that something happened but you can't see where it happened because you have absolutely no idea where the helix was or the sheet was so this works great if you have a small protein that's entirely alpha helix and you just want to see did it fold or unfold. So if you want the structure as a function of the sequence you're going to need to go into nanomar lab. So the spectrum the range of the wavelengths where you see this is the ballpark from 150 to 250 nanometers no this is this is very weak super weak light and this is a good question the reason why you see this are these wavelengths of course corresponds to wavelengths that are relevant for the protein structure now but that's not going to be a problem but the big problem is how limited it is it's a great way to see whether something happened but you can't see what happened but something happened. If you want to see what happened you're going to need to spend like a thousand times more money and a thousand times more work purify the sample you're going to need very high concentration and then you can use and in a nuclear magnetic resonance and this is not an nmr course either but the reason why nmr works is that the nuclear spin the shifts will sorry the nuclear spin in atoms will have a slight shift depending on its chemical environment and of course depending where you have a helix or a sheet it's going to lead to slight differences. Determine an entire protein structure with nmr is complicated but just determine the secondary structure works quite well so is that a good idea to use so what would you use both could you imagine something else so what did you do earlier this semester how good do you think well how good do you think bioinformatics is at predicting these things you probably mentioned it but I would say that bioinformatics is insanely good at predicting you have no idea how good it is you typically talk about 85 to 90 percent accuracy but what you don't do you know what the accuracy of nmr is it's probably at best 90 because at some point you start getting out in this loop right and it's is it helix or sheet or coil at some point it's going to be hard to say because it's just in between no method will have 100 percent accuracy not even the experimental ones and certainly well so the cd spectroscopy doesn't have any bioinformatics today is almost as good as nmr the difference is that then it's going to cost you roughly zero dollars to first approximation and it will take you one second just paste the sequence so nobody in their right minds today would go with nmr to determine the secondary structure for a normal protein then there are of course special cases something that is really pathological difficult to predict that the prediction is uncertain we don't know could it be a case where the secondary structure changes when you're moving from one state to another state so that can be a case where you have to go to nmr but if you just want to know the secondary structure of proteins this is one of the areas where theory is now so good that it's about as good as the best experiments so bioinformatics is no tier two solution here i would say that bioinformatics is tier zero the one you go to first and actually well you probably know that that so was not the case when i was your age this has happened the last 20 years when i was doing my psd studies and everything bioinformatics structure predictions they started to become really good but they were probably in the ballpark of 60 accuracy and today it's 85 which again is way better difference than you think so to sum up the helices versus sheets a bit is that they form well many of the features are similar but they also form opposing pairs in many ways so when it comes to helices not just the hydrogen bonds but virtually all interactions and helices are local so you have that sidechain can interact with that sidechain if you're going to see any patterns in the sidechains here what frequency will they have roughly three four five residues right because that residue is right next to a residue that's roughly three point six three point six residues further out so in theory you could have a positive residue here interacting with the negatively charged residue here but the point is it's local it's one or a couple of residues between them it grows gradually but very very fast i know that that kind of contradicts what i said before that there is an energy barrier there is an energy barrier but compared to the beta sheets it's almost non-existent it's a very low energy barrier and right now we're just hand waving about that but we will be more strict about it soon that if you have low energy barriers you can have very fast kinetics they will form fast beta sheets on the other hand are dominated by non-local interactions very far away and this in particular means that they end up being collective and in helices it's one good interaction and one good interaction in beta sheets it's all or nothing you need to have lots of good interactions along the entire beta strand this is also unfortunately something where the nomenclature for beta sheets is not entirely consistent i tried to call a single one of these arrows a beta strand many of them i call a beta sheet that would be great if everybody did it would actually be great if even i did that consistently i don't you typically call it the beta sheet even if it's just one but if you just have one you don't have any hydrogen bonds yet right so it's a bit unclear what you could even call that a beta sheet but this all or nothing means that you're gonna have a very high initiation barrier and you're gonna have very slow formation and as we will say i think it's later this week already this actually is intimately related to well protein folding certainly but also phase transitions similar when you move between water and ice there's going to be a very clear barrier yes so that's that's a good question it's let's try to let's try to answer it in the same way you had the alpha helix so when it came to the formation of the alpha helix the argument i made is that i looked at one residue at a time we're adding right for beta sheets i'm going to argue that we can think of adding one strand at a time so they i'm i'm going to draw these antiparallel now but that doesn't really matter here you have the first strand pure cost right second strand we're adding now well i'm paying a lot here but when i added the second one i get both the number of hydrogen bonds and i but i also get the entire second here now there are also going to be a lot of unpaired hydrogen bonds here and here right which is things we haven't gained yet by the time you're now starting to add the third or the fourth for each one you're adding we're getting lots of hydrogen bonds here we don't have any more we still have just two entire sets of unpaired hydrogen bonds so i'm paying one unit of entropy here but i'm gaining lots of hydrogen bonds back so this will have to be a negative free energy if this was positive free energy for adding one more you would never see beta sheets four so same for the helix i have no idea how large it is but we know that the change has to be negative and this of course means once you started to form a sheet it's downhill adding more and more so that probably answers your question exactly so once you will never see it one by the time you are two it's going to more advantageous to keep adding to it that's a super good question and that's not limited to beta sheets so let me repeat this for everybody i'm not gonna answer it comes later in the course if this is good why don't we have alpha helices that are 10 000 units long and if this is good why don't we have beta sheets that consist of at least 500 strands the larger the better right i won't answer it think about it we will answer it later this week it has to do with probabilities that much i can say so if we let's then head back and look a little bit about the amino acids that stabilize these different structures this is partly repetition but we also know that there are some very clear patterns of what amino acids occur in what shapes here and we will try to go through some of these and try to now formulate this more in terms of free energy both free energy and well both the entropy where it's advantageous to have them versus not and what parts of protein they a like to be in and b don't like to be in the fact that many of them are bad for secondary structures that's not necessarily bad in itself because some you don't necessarily want the entire protein to be alpha helix so sometimes it can actually be good to have some residues that are not alpha helix if we go back to the amino acid codes when i was your age that was roughly when we started moving over from the three letter codes to the one letter codes nobody in the right mind used three letter codes today apart from structure of biologists who want to emphasize what residue they are and for each of these we then have a natural abundance that tells you how frequent they are in proteins and this is now the salvation free energy small piece of repetition from last week what determines the abundance codons only codons it's so common here that people start to mix in evolution and protein stability and everything this is to first approximation at least perfectly proportional to the number of codons and not just the codons you have in particular genes but any we have 64 different codons right the codons that mix for it it's just throw them out completely randomly in nature the codons are the the distribution of ag c and t is roughly even so if you mix this up in triplets and then assign these for the amino acid they're coding for it's almost exactly the distribution going to get here don't mix evolution into it yes but we don't see if you if you have for each for each triplet you have the first approximation 164th of if you and we have four bases right there are 64 different triplets to first approximation all these triplets have roughly the same abundance so they have with nature has not selected for some triplets more than others they all occur now of course because some amino acids are coded for by more than one triplet that means some of them are going to be more common than others but nature does not seem to have discarded some codons for all of these we also have slightly different delta g of salvation and I should have units here but you see glutamic acid insanely negative very soluble in water some of them are well we have arginine somewhere never mind all the polar ones are going to be very soluble and then you have some large and valine it's not large but hydrophobic plus two so you have some months that are very soluble and other ones that are hardly soluble at all why are there two values for histidine yes it depends on the titration state how soluble it is the more charged it is the more these it's going to be it's isolated so if we start let's start looking at the worst one proline technically this is so something I'm not going to ask at the exam technically proline is not an amino acid but an amino acid don't fill your brain if you want it just for fun if you want to show your brilliance with friends something the reason for this is that you don't have the separate the full peptide group but the carbon ring here goes back and you have a carbon bound to the nitrogen too this makes it really horrible for alpha helices in particular why yeah so but what what is that it can't help for so there it can't form the hydrogen bonds that's correct and in particular this bulky part also means that you now normally the hydrogen bond is in a fairly narrow parts right between two layers of this one and here we're now forcing an extra full carbon to sit there instead so just a steric repulsion here that you're now going to fit the carbon will mean that anytime you put a proline inside a helix the helix will end up looking something like that you will have a kink in the helix because the proline would take so much space here this is such a strong effect that I think was Dave Eisenberg who showed a couple of years ago if you look at this evolutionary there are even proteins where some of the homologs have had a proline at some point in evolution and those helixes are still kinked even if the proline is gone but because of that this is so that this becomes so encoded in the structure you use a proline because you need to make a turn in the helix if you have more than one proline the helix will likely break so prolines are a great way for nature also to make sure that you no longer have a helix I will come back to that when we talk about membrane proteins but normally they're pretty bad normally protein prolines they're okay for beta sheets but they're not really good for beta sheets so where you really have them is in turn some sort of turns or loops when you don't have a well-defined secondary structure yes so this is how evolution happens right at some point one protein had proline there once you introduce proline this structure will now force to kink the helix again as you go through the billions of years of evolution here this will force the rest of the entire protein to adapt itself to this kinked helix it could of course be that the kinked helix is really good functionally that you needed that to fit the structure and then at some point again mutations happen randomly now when the entire rest of the protein stabilizes kinked formation of the helix you might actually mutate your proline to save alien so now you no longer have a proline there but because of evolution evolution will still have stabilized the kink in the helix so that suddenly you're going to have a kink even without the proline so Dave Eisenberg showed this for Jesus probably 15 years ago that when you go through and look at every single helix in particular membrane proteins and how kinked they are all the places where you have kinks you either have a proline or you have an evolutionary relationship that there was a proline and some other related protein at some point where you have kinks so proteins are intimately related to kinked helices yes yeah in in another couple of billion years what might very well happen is that that helix might straighten itself out again and depending on what that us to the functionality if that's really bad functionally that's likely going to lead that that organism won't survive but these are evolution is so very slow right right so that that's going to be bad for them but remember that let's see i need two more colors secondary structure is just one part of a protein so if i have my helix here and let's assume that we introduce a kink in this helix but the kink itself is not good you're losing at least one hydrogen bond so the way nature if i were nature over a couple of billion years of evolution i would likely try to stabilize that by having lots of other complicated structures in my protein here right now the problem is that when you now remove this proline you can't just straighten out the helix because you can't have the helix there so now you have other parts of the protein stabilizing this but the problem is of course if you now if you don't have a proline here you're now going to have a unfavorable stretch in the helix because you have a kink in the helix so i have no idea what would happen in evolution eventually if you wait long enough this helix might likely straighten itself out again but the point is at any time you see a kink in a helix either there is a proline there proline there now or it's very likely that there was a proline there at some point in evolution so what could what do you think nature could use that for so this has to do with the thing i said that it's hard to predict secondary structure because the whole definition of secondary structure is a bit fussy so typically you don't have a helix that's perfectly helix 100% helix and then 0% helix i know that's how we draw it but that's not how it happens so what you have you're gonna have a helix that goes around and eventually becomes weaker and weaker and then there are some residues here in particular if you simulate it you're gonna say that well there are two three residues here that are kind of 50 percent of the time in helicals confirmation and then they gradually unwind more and more but occasionally it's very important for nature to have a clearly defined helix and then not have a helix and one of those cases is transmembrane helices like membrane proteins that should be helix when it goes through the membrane and then you won't loop and then it's actually very convenient to put a helix breaker so you have helix helix helix helix and then boom you have a proline and you don't have a helix anymore the other two special residues are in particular glycine but also to some extent alanine they're small what is the main based on what we talked about today what would you guess is a main feature of these residues in terms of enthalpy and entropy glycine has lots of entropy right why so that's perfectly correct so when does but when does glycine has lots of entropy does it have lots of entropy in a helix does it have lots of entropy when it's unfolded so is it going to be good to take a glycine and put it in the helix why you're going to you're going you're the entropy the change in entropy becomes a lot more negative right and this was also a question I got during the break occasionally I and some other people one becomes sloppy if you start to gain or loss in entropy or positive or negative the way to avoid making mistakes is to go back to the definition and our definition is always delta g equals delta e minus t delta s so to avoid to be really careful here if something happens if the helix actually forms delta g should be negative for glycine well again the first approximation the energy of hydrogen bonds should not really depend on what residues we have apart from proline where we would lose here but for glycine this term is now going to be very important because there will be a very significant drop in free energy when I move a glycine into helix and that means that this is going to be more unfavorable and that's one of the reasons why we don't really see glycines in helices so this was an example of an entropic effect on the other hand glycine is going to be very good in terms because in turns we don't in particular those super tight turns where we just needed to turn the entire helix around in 180 degrees if you had a large side chain you would have things bumping into each other and suddenly you can use all that flexibility to form a really tight turn but you're of course you're losing the entropy goes down a lot alanine is not quite as bad as glycine because you have alanine starts to behave like a normal normal vanilla amino acid if you say so uh alanine is kind of the first approximation if we just want to study the properties of the backbone it's like a normal amino acid it is chiral and everything but it doesn't really have any specific side chain well I know it has a side chain of course it has this methyl group but the first approximation that if you want a normal amino acid but nothing special think alanine once you got up to larger and more hydrophobic residues then you basically take an alanine but building things upon this you have more and more hydrocarbons here you can have aromatic rings and everything the things that happen here typically they're hydrophobic and if you keep adding ethyl and methyl groups they're going to become more and more and more hydrophobic and that's what's going to drive these hydrophobic effect that we spoke about on Friday you're going to have a very strong driving force that again this is not just like hydrocarbon it is a pure hydrocarbon this is like solving uh propane in water it's not going to happen you have to turn this under the inside of the protein there are it's very common that you end up having multiple carbons here and the way you enumerate these carbons we start from the c alpha that one you've probably heard of these carbons are then enumerated just going away from the c alpha beta gamma delta epsilon etc and when you have a branch here you typically call them alpha beta gamma one gamma two and some of these are not entirely hydrophobic though this is one called cysteine so what type of atoms that sulfur we had I think with you had a comment about that last week when we talked about disulfide bridges or disulfide bonds so if you know your chemistry really well and I don't expect you to but if you have a group that is sh if you have two such groups and they are very close to each other sh you can turn that into a group where you have the two sulfurs covalently bound so this sulfur will let go with its hydrogen and will bind directly to a second sulfur in contrast to a hydrogen bond this is a really tight covalent bond so it's an oxidation and again this is not a course on inorganic chemistry so I'm not going to go through the oxidation formula but you're going to need something that air or hydrogen peroxide and then we can by adding the correct chemical we can make this happen you can of course also if you had a bond like this you can reduce it say with mercaptor ethanol or something I think again not something you should know so we can deliberately break that bond what is this good for why is it good for stability so this is a strong bond but it's also what type of if you compare helices versus sheets what type of bond is this it's a non-local bond right so you can have a connection very things that are very far away from each other in a protein these might not even be beta sheets so they could be long chains that are not interacting at all they would be super floppy and now we are creating a bond between them and unlocking them in place now that's a drastic reduction of entropy so for this to happen you also need to gain a lot of energy which we do in this reaction and whether this is good or bad for the protein that depends on the protein so when would when would you like something that's very stable because you said it was good for stability you would like something that's rigid or stable structurally yes when could you imagine that that's good or maybe bad the kind of it actually happens there too but what do you think this is this looks almost like a random coil right looks like an unfolded protein it's not an unfolded protein technically I think there are there are some parts of here this is probably almost a beta sheet down there but at first sight this looks very unstructured so this is a toxin and if I add all the side chains it's probably just looks even more unstructured right but inside this structure there are three disulfide bridges so we've locked there we have one lock and let's see here there we have one lock and there we have one lock so by creating these locks between three places in the structure you get a super rigid structure and this fold is even called a cysteine knot so these are small toxins that are very common in spiders for instance tarantula toxins and they tend to bind the reason we work quite a lot with them is that they tend to some of those voltage gated channels I showed at the beginning of this lecture they actually bind to these channels and force the channel either to open or close depending on what it is and this particular toxin actually I think I can show you the entire toxin so this is what the surface would look like so you now have something that's super rigid and small like a small football essentially and then you have a couple of areas here that are very electrostatically charged that's going to interact with those charged residues on the voltage sensor and then part of it that's quite hydrophobic that's going to stick down into the membrane and of course if you're a spider you want the toxin that should be very hard for the human or whoever you're stinging it should be hard for the immune defense or other parts to just break the toxin down right so most toxins fall in the side you want something small protein like so that the animal can produce it and then it should be very hard for the target for the prey breakdown so these class of toxins were discovered and explored by a guy called Kenton Schwartz and it's actually a bit of a fun story because they're named after his daughter Hannah so they're all called the this talk is called Hannah toxin and he told the story about this biophysicist society a couple of years later at first apparently when she was younger his wife was very upset and everything but apparently when you're an 18 year old girl it's pretty fun to have a toxin named after you but to sum up what they do is that you have two very potentially super flexible chains and by locking these down you're doing an astronomical reduction of the available conformational landscape for better or worse it's certain that you're paying with entropy hopefully you're gaining a lot of energy when doing it and this is one of the examples that I got when I say gain energy now I meant that it's going down right it's good for us and when I say losing entropy in this case that actually meant that the entropy went down too so gain or lose just means that whether it's good for me or not we're gonna see this a whole lot more in different parts of protein structure later on I think the final side chain I want to tell you about is tryptophan tryptophan is by far the largest and bulkiest side chain we have there are two rings one six and one five member ring let's say indole group in the five member ring which is so it's unnecessary knowledge for now but what this creates is a very large and very stiff side chain you can't really bend it anyway and in particular this side chain is going to be super difficult to pack because again if you just take a tryptophan and turn it around it's going to sort of take a tryptophan rotate the 90 degrees it's going to destroy any structure you had there for this reason not just tryptophan but all these proteins I've spoken about they're very common to use different types of scanning so when you use alanine scanning the whole idea is an alanine was just the vanilla amino acid that didn't do anything so when you do alanine scans that just means that you're systematically going through every residue in your protein and trying to remove the side the feature you had in that side chain by replacing it with alanine and then hoping that alanine itself didn't have any special features so whenever you get a strong functional effect for something that means that the side chain you just removed was likely very important for the function or could it have been important for something else the structure right we might have removed the side chain that caused the protein to unfold we don't know we just know that something happened when I changed that side chain same thing with tryptophan when you do a tryptophan scanning then we're taking one residue at a time and inserting tryptophan there why would you do that well for our ion channels for instance we frequently want to see if there is a small binding site or a small pocket or cavity erects or something and the idea then is that tryptophan would fill out that pocket but for all of these things that they have features and you can try to systematically scan through proteins to see whether this feature led to something and tryptophan in particular is a bit famous because it's part of something called the TRP cage the tryptophan cage which I would argue is the world's smallest protein what is a protein we haven't defined what a protein is right you just happily accepted last week that I talked about proteins you talked about proteins straight through the bioinformatics course so if I pick well times 20 is that a protein okay sorry yes but how would you sign of course you could imagine at some point a couple of heal a couple of things sorry any random collection of amino acid is just a polypeptide and this starts to touch upon something pretty important you say that they should be somehow important functionally I wouldn't necessarily disagree but you could of course also say that if we just have a protein that folds nicely if it has this large three-dimensional structure it has a well-defined state right that's kind of the same thing now in your body you would not have such a protein unless it had an important function but the physical process of folding into a large stable three-dimensional structure that's something I would say is enough to be a protein imagine that you have a protein but there was a new there is some sort of mutation in your protein so it kind of loses part of its function would you say that is less of a protein I would still say it's a protein right it's just that it doesn't work as well so somehow we want this to be large and specific functionally and here's the thing it depends this definition depends a bit on who you are if you're a chemist you would probably even say that functional having a functional role is important they should be large which as if you're again if you're a chemist you would probably say maybe 100 amino acids or something people on the physical side they might start to say well it has to fold in some sort of specific shape even taking say just polylucine or something oh this mixing alanine and lucine can get you an alpha helix a single alpha helix I would not say is a protein because it's just secondary structure but some sort of structure that's a bit more than just secondary structure and a definition that people have eventually agreed on most of them at least from a physical chemistry point of view is that you need to have one or more amino acids that are completely buried in the sense that they're no longer accessible by water remember what I said on Friday right that you have this collapse of a protein that you're turning hydrophobic parts to the inside and hydrophilic to the outside so what this is essentially saying there must be some sort of inside of a protein that is not exposed by water and some sort of outside that is and the TRP cage is the smallest protein this far that achieves that so the inside of the TRP cage is pretty much just one tryptophan and then you have a bunch of amino acids around it that form the environment and the reason why this is a bit cool is that you can actually simulate this so this is a simulation done by unfolding at home a few years ago so we're going to come back to what actually happens in the simulator but you see here how this goes pretty quick and I think it I forgot how long this takes probably a couple of microseconds but you see how quickly all the atoms are testing out and searching you're basically trying to assemble the puzzle here right you're searching searching searching and you actually have a complete set of water and everything around this that we're not showing but what eventually happens is that we are finding confirmations that are entropically a good balance between entropy and energy and in particular I think this is the folded state when we actually have the tryptophan molecule here buried on the inside and all the other side teams around it so this is a trivial example but it shows that the fact that we can do this in a computer shows that it's not merely hand waving and models when it comes to the book there is no way we can do computer simulations of protein this is less than 10 years old when the book was written first there was no way you could simulate this in a computer so then everything was based on just hand waving models but you can actually just taking the basic physical interactions into account predict what the folded state here should be and the reason why that works is because it's the lowest free energy state you don't you might not think this is cool when I was a PhD student actually just about become a postdoc there were several people in the world that saying that protein folding is going to be so complicated and it's so delicate balance between entropy and energy that there is no way we will ever be able to predict this with computers in general was something anytime somebody says that computers will never be able to do something you should bet against them because they typically can it took about five years and then we could do it on computers and this really goes to show that anphysen was right there is no magic thing there is no specific energy that works just take a stretched outside chain properly account for all the interactions and we can actually predict how it reaches the lowest free energy and we're going to come back to study how what whatever all these barriers and everything come from and what are the meanings of this but to 90 percent if not 99 computer simulations have confirmed our simple ideas yes so that's a good question I'll repeat for everybody your argument is that most peptide chains should assemble some sort of structure in the end well do you believe that if I take it random let's not limit it to 20 and I'll we can have some more amino acids than alanine you have 20 amino acids pick 100 random amino acids assemble them into a sequence will that fold the protein you have any other ideas so how many if you think that it will fold the protein in general they won't and you if you don't believe me you can basically go up you can do the experiment in the lab right synthesizing amino acids is super cheap in general they won't form proteins the question is does it form a protein in 50 percent of the cases one percent or one case of hundred billion so that's a good question we're going to come back to that in the course it's going to be way less likely than you think proteins are exceptionally rare and again when I was your age I think we people that you could do lots of changes in proteins but this comes back to start mutating proteins too much and they're no longer going to be they're no longer going to function as proteins usually because we destroy the fold so it's a much more delicate much much more delicate structure than you think yes so that's a lots of great questions I'm going to need to do further I think we're going to get back to the structure proteins tomorrow or so but what you're quite right is that they're going to be there are three different classes of proteins there are small water soluble so-called globular proteins like this one they're the easiest ones to understand you have large structural proteins such as hair skin and everything slightly different rules and then we have membrane proteins which are the hardest ones to understand but they fold in three different ways so it well so normally so it depends what you mean by a protein in the first place right so normally we start from sort of well-defined scaffold or a protein that we know that it will work or we're taking one protein and starting to deliberately introduce some changes into it uh but the the likelihood of saying again if I take my hundred first if I take my 150 residues what likely will happen is what we saw at the end of last week is that if you put this in water you're very rapidly going to get some sort of hydrophobic collapse that all the hydrophobic things turned into the inside you might very well have some parts of it that will form some small alpha helical segments and you could have some part that forms a small beta sheet segment but that's not necessarily enough because we also need this to be unique and well-defined right there's not if you pick something like hemoglobin that's going to carry oxygen in your blood you can't have a loosely defined superphylysis it has to be super rigid to have one specific function now in many case you might want to you can certainly do screening we can do a very sort of scanning to try to understand what happens with the function but getting a very rigid and stable function is basically never happens as we'll see later on in the course this is going to be so rare that if it was not for devolution it would never happen we're talking about probabilists of 10 to the minus 10 yeah but that's different because then you're talking about peptides right so peptides a small stretch you can certainly get a small alpha helix to form and in the case of these peptides you typically want the peptide to bind to a protein or create something else and that can certainly happen that's not a problem but for the peptide it's assuming that you would like this peptide to say carry oxygen in your blood that's a much more complicated and it's comes back to this definition what do we mean by a protein and I would say again based on this definition a protein should have some part that's completely buried but you can certainly have some sort of polypeptides with a bit of local structure in it lots of great questions but I'm just we're going to go through most of them in the next few lectures I'll defer a bit a bit of that polar and charged residues are both bad and very good they are bad in the sense that remember this hydrophobic collapse I spoke about right they're not going to be on the inside you don't want a charged residue on the inside of your protein because you would be paying to remove all the water from it and put it on the inside so you don't want polar residues right in the middle of your secondary structures on the other hand they are great to have on the surface to make your protein soluble otherwise the protein would precipitate so this means that typically we occasionally see polar residues inside secondary elements but in particular they occur in turns and loops at the end of secondary structure elements because those end of secondary structure elements should usually be exposed to the surface they're great for forming not just hydrogen bonds but so-called salt bridges to water so a well sorry there we have the charged ones they can form hydrogen bonds both to water and other parts of the polypeptide chain you can certainly have a hydrogen bond between a backbone the peptide bond on the chain and a polar group on the side chain charged residues are pretty much like polars but worse or better they're more extreme so a charged residue will never ever occur on the inside by default but they would be on the surface in some sort of active site frequently you would like to bind something or achieve something very special for instance in hemoglobin you're going to have this complicated setup where you want to bind the heme group and then iron and everything and then you're going to need some polar recharge groups right next to it there is also a feature where they can stabilize helices that I'll show you remember this dipole I mentioned for helices so that because there is a dipole in each of these peptide groups and if you have a long helix all these peptide groups the dipoles in the peptide will line up and point in the same direction so that goes from the first you have a co group here the oxygen has a negative charge to that side and then you have the nh group similar there negative charge to that side positive to that side when all these dipoles end up it's going to be a gigantic net dipole in the entire helix and having such a large net dipole that essentially corresponds by having a small negative charge here and a positive net charge here at the end of the helix it would be the same thing it's not really charged but it's caused by the added effect of all the dipoles so that the entire helix will appear as if it was a bit negatively charged here if you now put a positively charged residue here it's going to love it and same thing there if you put a negatively charged helix at the end terminus it's going to love it because it compensates for the positive charge so these are all patterns that you see in bioinformatics yes so first if it's not charged it's no longer charged right then you're then you're back in the polar one so the only case of well there well there will remain to be charged is if they are on the surface so that if you take an arginine but have removed it's they've deprotonated an arginine then it's neutral then it's back to be a polar residue even there so there are there are two parts of this question how do you know whether an arginine and a protein is protonated or not so in general this is not an easy question how do you see a proton you can't see a protein with x-rays actually with very high resolution structure you can occasionally see them but in general you can't see a protein with a proton with x-rays because there are too few electrons you can see them with neutron scattering and that's one of the reasons why people want neutron scattering but just predicting whether a particular residue is charged or not in a protein can be pretty difficult when it comes to the isoelectric points and everything the problem yes you can certainly titrate it and try to do but what frequently happens is that you're not unfolding the protein instead because the protein is at the particular pH right normally we only have them at neutral pH and this comes back to what i said before there no matter whether they're protonated or not arginine itself whether it's a charged arginine or a neutral arginine is going to be extremely rare inside a protein why if it's neutral it shouldn't be so bad right if it's neutral it's just polar so the point if it's neutral it's not horribly bad but it's not really great to have it buried and before that you guys will now have paid a very large penalty to deprotonate it because he doesn't like to be deprotonated at neutral pH and if you're now going to fold the protein where the folding of this protein depends on that you first have to pay a lot of energy to deprotonate an arginine well what evolution will likely do for you is what evolution would like at some point you're going to have a verse one species where this arginine has been mutated to something else right that species doesn't have to pay that penalty this is going to be great so suddenly you're now going to be disadvantaged because you have an arginine so evolution will get rid of that unless what well i showed the protein this morning this voltage sensor and i felt it had charged residues it's actually even arginines so why hasn't nature removed the arginines from those voltage sensors every time your nerve cells send a signal or your heart beats this one moves because when you change the field and you have a charge there is a force on the charge if you remove that charge there will no longer be a force and you would not have a nerve signal anymore that would be pretty bad you would die so that if it's functionally important we can tolerate things that are structurally bad because we don't have a choice so this is a long table from the book that i don't expect to read it but what this table says is that for each residue there are the plus or minus here depends as whether they can occur in the main chain and this basically plus everywhere except for proline so the plus means all of them like to be in the main chain except proline this then is whether the side chain what are the properties of the side sorry no this is not whether this is whether it has the nh group my bad this is whether they have a side chain this is whether they have dipoles and charges and here we have the good versus bad thing so the good versus bad thing is that do they occur before or in the middle or the c-terminus so n-terminal middle or c-terminal part of the helix do they occur in loops or in beta sheets or the core so the core is going to be that all the non-polar ones are good the charged and polar ones are not good etc this is of course not the table i expect you to know by heart but the point of this table is that amino acids occur in places with this stabilized structure that's probably not how you introduce it in bioinformatics so there's a bit of chicken and egg problem here do we get a structure because of the amino acid or do we get the amino acid because of the structure so in one case yes so if you stick to the central dogma of molecular biology it sequels the structure to function right so according to the central dogma of molecular biology this would be wrong you first pick the amino acids and then you get whatever structure the amino acids give you but then i also mentioned there is this feedback loop right that natural selection if you now just do random mutations here you're not going to get completely different proteins there are one of two things that will happen either this mutation is going to make your existing protein work even better because it fits in your structure and it's good for your function and then you will likely have more offspring eventually or it doesn't fit and then the organism will likely die so here's the problem it and just as the chicken and egg they are interrelated you tend to the mutations that tend to survive are the ones that work well with our structures yes right so in general the answer is yes there is a very clear and there are there are some great examples of this i think i even have that in a coming lecture so you can look at this over the course of billions of years of evolution different types of hemoglobins for instance whales have one type of hemoglobin humans have another one animals that live at very high altitude have a third type of hemoglobin the fetal hemoglobin is different from the human one so that all these have been optimized to get a specific function but the other part is when some specific change and particularly cause your disadvantage and the disadvantage could be that your function is worse and if your function is worse you will likely have fewer offspring in some cases many of the genetic disease that tends to survive are genetic disease that only manifests themselves after we've had kids so if i get some genetics disease that only influenced me when i'm 50 or 60 years old right it's likely not going to influence my ability to produce offspring and that will survive so it's basically natural evolution has to be intimately related to offspring and then there are a few cases where you actually have treats that are bad but because they're surprisingly good in another way they tend to survive because depending on where the population is and depending you might suddenly know that for 90% of the population is good but for a very small set of the population it's very good i will come back to that later no in general that's bad things that need to be things here need to be balanced there is a really cool example with cod in the Hudson river it's a Hudson river is one of the most polluted places on earth and there has actually been an example that they showed that these this cod has developed resistance to PCB in just 10 or 20 years because i guess if you're gonna if you're living in the Hudson river being resistant to PCB helps i think it was PCB at least i'll i'll look it up i have a paper on it for you later but i this evolutionary part in a particular how structural and evolution is how structure and sequence are interrelated in revolution we're going to come back to that tons of time in the course so i have five more slides here that we're going to take it down i like by the way i love these questions please interrupt me as much as you want the worst thing that happens is that we don't finish the slides and then i just move them to the next lecture remember that i told you about these a versus b sides of the records or the sheets so if you now pick these groups carefully such as if this is my sheet if you take the entire underside here and make those hydrophobic and the entire oversight and make those hydrophilic so the sequence that would mean that every second residue should be hydrophobic and every second should be hydrophilic hydrophobic hydrophilic hydrophobic hydrophilic and then you have to match that up so that they occur in the right place in the next chain because beta sheets form these natural slightly extended charts if you now take what that would mean is that you would have a beta sheet that would have one side likes to be in water and the other side likes to be in oil this is something that's very difficult to create with the helix but with a beta sheet you can do it easily so you now have one fat soluble side and one water soluble side if you take a small a pair of these sheets and they make them outside here water soluble and the inside fat soluble what you've now created is a fat soluble pocket so you now can take something like a lipid or a fatty acid that i once used in membrane the fatty acid will happily bind here on the inside of your protein the fatty acid itself would have an extremely low solubility in blood or anything but once you bound it to this protein you can transport fatty acids in blood fabp stands for fatty acid binding protein and that's exactly what the small protein does isn't a hydrophobic inside hydrophobic or water soluble outside most of this part is just the beta sheets and then you see or how you use the loops to pretty much just try to tie up and create some sort of pocket beta sheets are much more efficient than helix is that creating a pocket but you're still gonna need to put something on the short sides when you see a structure like this with lots of bands what type of structure is this nmr technically it could be a simulation too but this is an nmr structure so in an x-ray structure we typically show proteins as completely rigid that there is just one state but what you can see in nmr you really have an whole ensemble of states just as the movie side been showing you protease move even when they reach their folded state so what you see here is that the core part of the secondary structure such as the healer such as the sheets here they're super rigid right they hardly move at all but in particular these loops the further out you are in the structure the more motions we have but they're still fairly rigid but the point is that this is not the crystal in water and in room temperature protease move and they move all the time but they're still stay close enough that they maintain the rigidity of the structure so say that you would like to create something similar for an alpha helix what could we do with an alpha helix if we wanted two sides of it so let's look at the helix from a slightly different point well the reason here that this became mobius is that we looked from the beta helix from the side right and it's from the side that you really wanted one property here and another property there if you want to look at a helix and have one property on one side of the helix and now we should look straight down on the helix from the top and this is called a helical wheel the way you draw them and if we start with one here that's the first residue and then we go to the second one we turn 100 degrees between two residues and then we get number three and number four and number five and number six and then we keep drawing that way if you now place these residues in a smart way let's assume that you only place hydrophobic residues in this part and only hydrophilic in this part you are now going to create a helix that has one hydrophobic side and one hydrophilic side where do you think this helix would end up actually before we take this helix if we only had hydrophilic residues what type of helix would it be where would the helix like to be solid well yes in water right or inside a plasm and if we only had hydrophobic residues in a helix where would the helix likely end up in a membrane so what do you think happens to helix that has half one side hydrophobic and the other side hydrophilic so it would like it would likely lie in the surface of the membrane so we turn the hydrophobic part to the hydrophobic the hydrophobic side to the hydrophobic part of the membrane and then all the charges on the surface nature actually does that sometimes it's it's not that common to have these interfacial helices but if you want one this is how nature creates it the other thing you can do this way you could probably get a bundle of three or four helices to stick together right so that they could all turn the hydrophobic parts right next to each other and the hydrophilic part on the surface and at that point we're essentially starting to build lego with a couple of helix I only have three pens here but then you can start to build some sort of very small miniature structure with a handful of helices that form some sort of rigid protein people have done this this is basically the first type of simple protein engineering so what's different from bioinformatics here well protein engineering you don't necessarily need to stick to the proteins we know in nature right you can try to design something ground up using the laws of chemistry to create a structure that we know will be stable and hopefully have a very specific binding site on the inside and there are a few cases like that that we're going to come back to in the course and here and at that point of course it's get super important that we understand this because no matter how good evolution and bioinformatics is you're never going to be able to predict a structure that nature has never created because the prediction relies on evolution and if evolution has never explored this part of chemistry evolution won't predict it yes they can occur in lots of places I'm deliberately not going to tell you the details of it the cool thing is that you can use them if you have one of these four helical bundles you can create a binding site right on the inside of the bundle and then you're having a small completely artificial protein that can bind a very specific group on the inside of it I will talk more about that in the coming lectures but they're super stable and they're great for protein engineering so to come back to this titratable residues we've talked about these quite a few times before so I will just mention it very briefly most of these are trivial glutamate and as glutamic acid aspartic acid arginine lysine they're trivial they're always positively and negatively charged respectively histidine as I mentioned is hopeless because it has a pka relatively close to seven and for all of these if you're the hardest part of this you're actually going to do this in a simulation because all these things are based on statistics this relates to the Boltzmann distribution it's never ever that things are 100 percent charts or zero percent charts but what these pka values basically describe what is the probability that an individual amino acid is charged and if you measure these in the lab you're essentially going to get different curves at very low pH so remember you also have the backbone of the amino acid right you have the NH group and the CO group that can either release or take up a charge so depending on what pH to push these things on there are another two charges in each amino acid that you can get to either release or take up a proton initially this is not really going to matter this is a major headache in simulations because just predicting what specific titration state you should use is one of the big answer problems in biophysics we hope to solve it more with neutrons but we're so not there yet histidine is a particular horrible because you have these two sites delta and epsilon how do you think you predict that in an x-ray structure or something how do you predict where the proton is in a few rare cases sorry histidine is completely in few rare cases you actually have his plus right so that you can have one proton here and one proton here the normal case is histidine is neutral and then you have one proton but that proton can be either on the delta atom or the epsilon atom so which one is it it can be shared but typically it isn't so the way you find this out is that you determine the structure of it and of course you're not going to see that proton in the structure so why in this case did we put a proton there well in this structure this is just a nice I would bet that there was a big oxygen there and then a double bond and the carbon and the fact when you have a nitrogen closed in oxygen the only case that would happen is that there is a proton right between them so we deduce the location of these protons based on hydrogen bonds even if you can't see the proton itself but five years from now on you might we'll all be doing neutron scattering experiments and finding out exactly where they're located so just to sum up on the charges the charges here are painful the reason why we still bother about the charges is that they're super important there is so much important functional things the voltage gated channels I just spoke to you about is one case binding of any type of small charged molecules DNA protein interactions DNA is supercharged lots of these those phosphates so anything that's going to interact with DNA typically needs to have lots of charges there are lots of iron channels that are pH gated in particular bacteria and we look at many of these let's see is that a movie yes it's a movie so this is actually a small channel that's pH gated so you start out with the red molecules sorry the red states of the helices here and then when you change the PA of a couple of key residues here you will eventually see this channel close and you're going to see the water here goes through you see that we're breaking up the water here so over the course of roughly one to two microsecond here the channel is dehydrated and yes now it's been closed there and these red helices now almost overlap the blue states that's the closed one so just by making a jump in the pH here we can force a channel to move over move over from one state to another why does this happen why would a protein move from one state to another sorry actually in a bit in particular free energy right so in this case without knowing any details we know that whether things happen or don't happen or related to free energy so in this case this this particular model this particular channel happens to be open at low pH pH 4 so what we do know is that pH 4 the open state has lower free energy and then something happens when we change the pH so when you move to pH 7 suddenly the closed state must have lower free energy these occur this particular channel is extra bacterial one but this type of channels occur throughout your nervous system and this is something we normally do not see in the structure that you think you mostly think of structure as one state right because that that's the conditions under which you determine the x-ray structure but what we're more and more going to see that most proteins occur in more than one state and the transitions between these states happen when you change surrounding factors you're altering the free energy and suddenly there's going to be a different state that has lower free energy and then they will gradually move over to that state in the course of a microsecond to a millisecond or so that's all I had for today sorry I ran over by one minute here there are a bunch of study questions to go through and most important we will see all of you at 1 p.m. in the computer room this afternoon and if there are any of you right late who don't know where the computer room is let me know but otherwise I'll see you all there at 1 p.m.