 So now we're almost done, right? Now we just need to wrap things up and understand how hydrogen bonds describe protein structure and then we can finish this entire class after two lectures. I'll deliberately run a little bit ahead of ourselves and imagine if we have a protein and we talked about proteins having these long sequences of amino acids that I described in the first lecture. There is some sort of sequence, for now I'm going to forget about what it is. These green part is the backbone and that's, as I already drawn in a couple of cases, that is this nitrogen C-alpha carbon, nitrogen C-alpha C, nitrogen C-alpha C, that's the backbone or main chain of the protein structure. And then connected to each alpha carbon C-alpha, we have a side chain which I called R. Those side chains, as we will see later, are going to have slightly different properties but some of them are going to like water, so called hydrophilic ones. Other ones are not going to like water, hydrophobic or fearing water. What I've drawn here is a highly schematic part where the yellow part here corresponds to some sort of side chains that would be hydrophobic. And I deliberately, I think it might even be Finkelstein's illustration, that we've deliberately drawn some water right next to this. Now waters are not going to like to be right next to something that's hydrophobic. Why? We will have to wait until next lecture or two to show. But you can probably guess that already on the previous small snippets here, right? Those water molecules, they want to participate in the hydrogen bonds. And if you now have something that's a pure carbon here, there are no lone pairs, there are no hydrogens, that molecule is not going to be able to participate in a hydrogen bond. So the waters here right next to the hydrophobic molecules will not be able to participate in hydrogen bonds. So why, what might happen if we now take this protein and throw it inside a cell? In a split second, what if this protein somehow curls up? So it can take these yellow parts and put them together so that the hydrophobic or oil-like parts will now be next to each other. We already know that's what happens if you throw oil and water, right? And then all the waters will somehow be out here free to interact with each other. In principle, that's not entirely wrong. That's partly how things actually do work. And there are a couple of things here that we're going to need to understand. And that's why there will be a few more lectures before we can do this for real. First, we're going to need to understand what are the different amino acids we have involved in a typical protein? And why do they have different properties? And what are those properties? That's going to come up in two lectures, I think. We're also going to need to understand what is this concept of state? I talk here about some sort of unfolded state and some sort of folded state. So first, what is a state? Is that specific XYZ coordinates or something? Or is it some sort of larger things? Well, to be honest, we haven't even defined what a state is. This is just random drawings. We're going to need to understand a little bit what actually happens with these waters and hydrogen bonds under different conditions. When will waters form hydrogen bonds and will they break hydrogen bonds? I've already hinted to you actually even explained twice that the reason why water has its properties and in particular such a high boiling point is that those water molecules will do almost anything it takes to maintain their hydrogen bonds. So it's not going to be a CCS breaking hydrogen bonds and then you can go to another state. So we're going to need to understand the torsional degrees of freedom, how these chains will rotate. We're going to need to understand what that means that it happens when this moves over to another state. Do we get more or less hydrogen bonds? And then things might get really complicated because you might have a water here that forms a hydrogen bond with the protein. But in this case, the same water might be forming a hydrogen bond with another water molecule. So all we've done in some cases will be that we have just moved around the hydrogen bond. So we still have the same number of hydrogen bonds but they're suddenly formed with different molecules. And that is also something that we're going to need to start covering with physics. And it turns out that a unifying concept here that's going to come back, this has to do with arrangements. Different ways of arranging molecules and then trying to decide is this arrangement good or bad? And this far I've just glossed over that. I've just told you and you just believed me when I said a negative energy is good, a positive one is bad. We're going to need to derive that a bit. And you might, you've probably seen this in physics, I don't think you've derived it, which is quite fun because it's some of the most basic concepts in physics. If we're going to do this proper, I would be throwing a ton of equations at you. Caveat, I am going to throw a ton of equations at you. But if I do that tomorrow, I would only have one fifth of the class remaining for lecture four, which would be a bit of a bummer because I kind of like these things and I want to introduce you to it. So we're going to follow Finkelstein here and I'm first going to introduce this with a bit of hand waving in the third lecture without going to too much gory details about physics. And then later on when we've had a chance to go back to biology, we're going to show this in a more universal way where we don't make as many assumptions. But this will arm you with the arms you need to understand models in very generic systems. We're going to be able to start drawing conclusions about what processes happen, when will, for instance, a protein fold, when will it not fold? You will be able to explain the hydrophobic effects. You will be able to explain what happens in phase transitions and a bunch of things that are borderline pure statistical physics. But they are super important and I would argue that long term it's probably the things in my education that I've had most use of. The most complicated equations are not necessarily going to be the one that look most difficult. The hardest equations are frequently the easiest ones. But that is probably all we're going to say about the different conformations today. There is one final concept I want to leave you with. Assuming that for each of these conformations I can calculate what the energy is, whether that involves hydrogen bonds and everything, I might have a gigantic computer. We could do this for the all-in-line dipeptide, right? Remember, just two degrees of freedom, I change the phi and the psi torsions, the so-called Ramachandran torsions and then I plot it in a Ramachandran diagram and I get the energy as a function of those two torsions. In practice, when it's the all-in-line dipeptide is such a common molecule, we all know what these angles are so we tend to draw that in two dimensions. But of course we could draw this in three dimensions. This is also another study on the all-in-line dipeptide. And here too, red is bad, blue is good. It contains pretty much the same information apart from the fact that it's a slightly different study. But most of the molecules I've showed you contain way more than two degrees of freedom. Many of the computer simulations we do contain a few millions of degrees of freedom. And I'm not sure about you, but I find it somewhat difficult to imagine one million dimensional spaces. So we're going to need to simplify this some way. And what we typically do is that we think of some sort of rugged landscape and we say that it's high dimensional, but it's not really high dimensional. This is still just a two-dimensional landscape. It's just that I have lots of minima and maxima here. And the reason for those lots of minima and maxima, again, if I imagine my one million atoms, there are going to be lots of places where they are very happy and interact closely, all the blue parts here. And there are likely going to be lots of places where they bump into each other and are not so happy and that would be the green parts of this particular energy landscape. And somehow the only thing I have to decide to determine where a protein is, is what is the best point in this energy landscape? I think. Or is it that simple? Because now we also, if there was one molecule, you could imagine that it's that simple. But assuming that this is water, and we might have avogados number, water molecules in a glass, every single water molecule can't be at the same time at once. So in particular, it might very well be that a particular bond is really good to form. But if we would take a very large molecule and stick that so it can't move at all, it has to be in the very lowest position here. That might be bad for other reasons. And for now, that will just have to be hand waving. This corresponds closely to a concept that you have touched before, entropy. You think entropy is going to be difficult. If there's one thing I promise you is that after this class, you will hopefully not think that entropy is difficult. But we're going to need to find tools that describe what do we mean about the distribution in this energy landscape? What do we mean by moving in the energy landscape? In principle, it's bad to be at the peaks here, but sometimes you might have to move across a peak to get from a low, but not really low as well, and to find the really lowest well here in the middle. And right now I can't say, when will that happen? When will it not happen? I just hand waved and claimed to you that, well, when we have intermediate energies, that's good enough. But intermediate energy has to be intermediate relative to something else. So there has to be an energy scale that we're not aware of yet. That covers what we're going to talk about for molecular interactions today.