 Welcome to lecture four in the molecular biophysics class. Last time we learned what free energy was, entropy, enthalpy, and we used these terms to examine what happens when a hydrogen bond formed between two waters in vacuum. I'm going to extend that slightly now. So let's start with doing exactly the same thing for a hydrogen bond forming in a protein. Now, we haven't gone through all the residues in a protein yet. That's coming in lecture five. So let's do this schematically. Here is some chain. Exactly what it contains is important. And then I have some sort of residue here that can be a hydrogen bond donor and one that can be an acceptor, but the hydrogen bond hasn't formed yet. And then after, because we're always going to be looking at differences, right? We have the same chain, but then the donor and acceptor have formed a nice hydrogen bond there. What will this do to the various changes? Well, let's just write them down. What is delta H? We're going to be chemists this lecture. Well, that was the energy of a hydrogen bond. If we use the same nomenclature as we did last time, that's going to be negative because it's good that it formed. What is the entropy or T-delta as if you want? Well, that's going to be hard to define, but if you forgive me, I'm going to grossly oversimplify this. It's a great ability to have. We don't have any effect of the entire proteins, rotations being hindered here or anything. So I will just bluntly say that that's roughly zero. First approximation at least. And that means that the net difference in free energy is going to correspond to the difference in enthalpy, EH. So this is caused just by the case in water because we're forming a bond that has negative enthalpy. Great. Proteins don't exist in vacuum though. They exist in water. So let's make this slightly more realistic. Here we have the same protein and we have a donor and an acceptor. I'll get back to that in a second. We have the same thing here. We have the donor and the acceptor. And in this case, I definitely have a hydrogen bond, right? And we might want to say we don't have an hydrogen bond. Well, that's true, but that just means that we don't have one between the donor and acceptor. This is in water now. This donor is not gonna be dangling around and the same thing for the acceptor. But what's gonna happen in this case is that the donor which donates a proton is happily gonna donate that proton to somebody in need such as a water. And the acceptor will happily accept from somebody who has too much here, a water. So here we actually have two hydrogen bonds but they are formed with waters. And after the case here, these two waters, if I draw them in some sort of simplified fashion here, will have been able to form one new hydrogen bond between themselves. Again, there could be other water molecules involved here too, right? But the net effect is that I free up the ability of these two water molecules to form one hydrogen bond in the rest of the system. But wait a second. This is gonna lead to something different. Let's draw the same thing again. Delta H is now one two hydrogen bonds here and one two hydrogen bonds here. So delta H is zero. Delta S, on the other hand, that corresponds to a difference in entropy here that is the same thing that I went through in last slide. I have the net effect of two times half of water rotation because these waters couldn't rotate and now we have a pair of water at least that can rotate. So the big difference here is that it shows up at entropy instead. And that's gonna mean that delta G equals minus T delta S. And this is gonna be something that keeps coming back in the class. Things are different in vacuum versus in water and all those things that appear simple in vacuum are more complicated in water. We always end up having balances and in general, you will never break nor form hydrogen bonds. The hydrogen bonds are roughly gonna be constant and the effects show up as entropy instead. We're gonna be looking at that in slightly more detail but that requires us to start examining some other molecules first.