 We talked a little bit about energy landscapes, and I think it's instructive to consider that for proteins now. Assuming that I have something here that is energy and here I have some sort of are completely arbitrary coordinates and then I want to think at least about what happens if a protein is folding in a complicated free energy landscape. Well, for now we haven't even defined that the minimum should have low energy. That's going to be a key result that I come back to in lecture five. But if we believe that physics governs these processes, and I hope you do, you will have to assume that we want to get to a minimum of free energy because that's where all processes should not spontaneously. And it doesn't say free energy there though. It says energy. So as we go along the lower we are here, the more bonds we have and the tighter we're packed, that's good. But on the other hand there is some sort of freedom here, and I like to illustrate this by delta S, or S, whatever we call it. This is somehow, here we have a lot of freedom for the chain. A chain that stretched out is very mobile. While a chain that has curled up has started to form lots of structures quite restricted. So what happens here, as we are gaining interactions, energy, we are paying in entropy. And that's going to be a recurring theme for protein folding, just as it was for the balance when solvating hydrocarbons or forming hydrogen bonds in the proteins. In some cases, either in simulations or experiments, we can't even measure what the free energy is for a protein. There are too many degrees of freedom in a protein to plot this in 100,000 dimensions. But if you're lucky, you might have a special protein where it makes sense to have one or two degrees of freedom. Say, the size of the protein or the distance between two particular radius, radii, had two particular atoms forming a key interaction. I think this is a simulation result. So we had one degree of freedom here, one degree of freedom here, and then the color describes what the free energy is with the blue state here, being the native state of the protein. Occasionally it's even possible to do that in experiments. This is an experiment where you might be able to see the structure here, holding my hand behind it, that as we are forming more and more structure elements here, we are moving to the state here that is the lowest free energy one. So here they've determined intermediate states and eventually showed that the actual native state for which there is also a structure really corresponded to the lowest free energy. That's really cool, wouldn't have been available when I was a student. And in principle that's fine, but for some complicated proteins we could have some problems. What if there is not just one minimum, but many local minima? So if you start out here, you might need to get across this barrier, then you're stuck here, then there's a second barrier you need to get across. So this is just three dimensions, right? But in general we have 100,000 dimensions. So it's not quite as easy as I showed here. Going downhill is easy, but what happens when you get stuck here? Well, it's definitely better to be down here, but at some point you know the Boltzmann distribution, right? So that you should know how likely it is to be here versus how likely it is to be here. But you're going to need to get over that barrier. How likely is it to get over that barrier and when will that happen? To understand that we're going to need to be looking a little bit at the kinetics later today. But first, based on this, it turns out that the Boltzmann distribution is a key concept that we need to look a little bit closer at.