 We're not gonna look at an entire protein. At least I wanna introduce you to the concept of what the torsion bonds mean and why they are important. So we wanna pick something that is as simple as possible but still has kind of some properties that are protein-like. And scientists have a toy molecule that we've used for years to study something. One of the simplest possible amino acids is alanine. We're gonna look more in that next week. And if you wanna take something that is just a tad more complicated than that, let's pick two alanines. Actually, this is not even two alanines. So I pick one alanine amino acid in the middle here and then I'm just essentially picking the parts without the side chains. So this is a molecule that has in principle four bonds along this long chain here that we could rotate around. But I'm gonna argue that we do not have four bonds. You remember that I spoke about the amino acids yesterday or last lecture that we had the C-alpha and then we had the nitrogen and then we had a carbon, oxygen here. Then we had a second nitrogen and then we had a second C-alpha here and then we had a second carbon there. You also had those R-groups and then I'm not drawing any hydrogens that all to save a little bit of time. This part was this peptide bond that I spoke about in lecture one, how it formed and by two amino acids merging together. And I already mentioned that this is gonna be a very stiff bond with a resonance of electrons all the way from the oxygen to the carbon to the nitrogen to the hydrogen there. So there's gonna be a net shift that all the electrons have moved down a bit here towards the oxygen. And that's effectively gonna give this central bond a property as if it was a completely rigid bond. This bond will never rotate. If we look up here on the right, it turns out that two of those bonds involved in this molecules, that's gonna correspond exactly of this carbon that is not the alpha carbon to nitrogen. So we can kind of scratch those out. Let's forget about both those T-tests for now. That means that we just have those other two bonds that we call phi and psi. They are by far the most important bonds, rotations in amino acids and you're gonna need to remember them and you're gonna need to know which one they are. They're called the torsional angles or the Ramachandran angles. I'll get back to Ramachandran angles in a second. And we would somehow like to describe how this molecule is changing as we're moving those. So if I start rotating around those two bonds, the very first and the very last part of the molecule here is gonna rotate and under some conditions, the atoms might be clashing a bit. So it's bad contact and in other combinations of these two bonds, we're likely gonna have very good contacts. So essentially I have a, this is an equation that I'm gonna measure a potential energy that is a function of two variables and these variables would be the angle phi and the angle psi. For now, we're not gonna worry about the bonds and the torsions and everything. I will just assume that those will take the best possible positions. And you could of course draw that in MATLAB or something. And a very simple representation would just be a two-dimensional diagram here. And in this case, blue means good, low energy and red means bad, high energy. So it turns out that you have at least two areas here that are quite good where the molecule is likely to spend time and at least one area because this diagram is periodic. So if you go out on the top, you're gonna re-enter on the bottom here. Remember, the angles are periodic. The red area here is gonna be a bad part where things are clashing and you do not wanna spend time there. And it turns out that this was calculated from a simple molecular simulation. But if we now take this blue area up here, one local minimum and the other local minimum on the other corner there, we know what the phi and the psi angle is at the center of each of those minimum. And then we can take those conformations and draw them. And those are actually the names that we say here in white. So we have, in the case, even of something as simple as the Allen 9 dipeptide, it's a single amino acid that just happened to have two of these, two of the peptide bonds so that we have both a phi and a psi angle. Even something as simple as that ends up having two local minima where the structure is fairly happy. And you're gonna need to trust me for now when I say that you would actually see both of these as room temperature. Which is a bit strange because one of them will have lower energy than the other. So why do we see both? We'll talk more about that next week.