 We covered angles, we covered torsions and we also covered these ramachandran diagrams that was the two-dimensional landscape that showed roughly how the energy would vary as the phi and psi angle change. And that's also why we call those ramachandran torsions occasionally. I already talked when I spoke about interactions, I already mentioned another type of interaction, right, electrostatics and these so-called van der Waals interactions, and that's pretty much the rest. So if we take a molecule and just dive in, no matter where we are in space, you're going to have a ton of atoms either in the protein or in the water around the protein. Basically we would never ever have vacuum at room temperature and normal conditions in a test tube. There is always an atom right next to you interacting with something. And that gets complicated because they're not necessarily, a water molecule is not bound to another water molecule or the protein. So we need some sort of way of describing this. There are two parts to this, I already covered them a little bit. One of them has to do with steric interactions that atoms cannot overlap, Pauli exclusion principle. The other part that is related to that, actually it's not really the same process, that's these induced dipole-dipole interactions I spoke about. The reason why we say that they are related is that if we for a second pretend that all these atoms didn't have charge. Even if they don't have charge, they would still interact so that they can't overlap. You would still have the repulsion. And even if they don't have charge, such as noble gases, they would still have these dipole-dipole interactions at very long distances. So there is one repulsive component when they get very close and there is one attractive component at very large distances. The second type of normal interaction has to do with electrostatics, and that you know, since you're undergraduate studies or even upper secondary school. A positively charged atom, iron, will attract a negatively charged ion. So in one way, the electrostatics is very simple. The problem with this, if we're now going to start modeling this, is that every single, if I pick one atom here in the middle, that atom might have two or three bonds. It might have three or four angles and it might have five torsions, I don't know. But if you pick the atom in the middle, how many atoms, other atoms is it interacting with in terms of electrostatics and non-bodied interactions? Hundreds, maybe even thousands. So it gets computationally very complicated and expensive to handle this, which is a bit difficult. Let's have a look at how these interactions look like and how strong they are relative to each other. So I spoke about normal interactions in terms of electrostatics and van der Waals interactions. You already heard in a previous slide that the van der Waals interactions are quite weak. Remember, noble gases, they don't condense until very low temperature. So can't we just ignore those? Well, if I draw lots of atoms here, here's one atom and another one, third, fourth, fifth, etc. I'll let you imagine the remaining 5000 ones. This one might have a plus sign, minus sign, plus, plus, minus, minus. If you now imagine having 500 atoms here, sure, these interactions are strong. But most things if I look around me in this room, there are pretty much, there are no free charges. Even inside a battery, the positive and negative charges are paired up as ions in the electrolytes. So on average, if I look at a few nanometers around an atom, on average there's pretty much exactly the same amount of positive and negative charge. So while each individual interaction here is very strong, they tend to cancel each other. The problem is that they don't cancel each other exactly. So there might be hundreds of K-cals per interaction, but plus to minus, that's attractive. Minus sign in potential, plus to plus, that's repulsive, bad. That's a plus sign in potential. So when these cancel out, it's going to be very noisy based on the exact positions of all these atoms. And at the end of the day, that's going to tell us whether it's a good or bad conformation. Remember, good low energy, bad high energy. But if we imagine exactly the same molecules, but forget about those charges. So we just look at the repulsion and dispersion part of this. Again, if we push these atoms very close together, they are not going to want to overlap. That's exactly the same between all atoms. And if you push them close enough, imagine a nuclear device or something, eventually that repulsion is going to be even stronger than the electrostatics, even if they have different charge signs. But at very long distance, well, I already said that is weak. So come on, why can't we just start ignoring that? If you look at that one atom and look at 5,000 neighbors, what's the sign of the interaction with that atom? It's attractive. That one is also attractive. That one is attractive. That wasn't attractive. And that one's attractive. So the attraction or dispersion at long distance has the peculiar effect that all the signs are negative. They all attract each other. So eventually, if I just, well, when I add up another of these, the energy will always be negative. And that's why you get these effects that if you just reduce the temperature far enough so that you overcome the thermal energy, we're going to come back to that later on in the class, eventually that small sign will start to dominate. And that's why even noble gas is condensed at some point. So we can't ignore this. It's much weaker than the electrostatics, but where the electrostatics fluctuate with different signs, the attraction will always have the same sign. And that's why we need to consider both of them.