 That concept of kind of cheating, the reaching time scales or processes that physics would otherwise not let go is going to be very powerful. Here we're back at one of these simple ion channels that Johan and my team worked with and what if I would like to calculate how fast or slow an ion goes through this channel? Well, if it is an ion that passes through the channel quickly, I can just calculate how frequently it goes through. But if I would now like to compare that to an ion that I don't expect to go through the channel, I would have to wait almost forever before it goes through spontaneously. That's not going to work. But what if I instead grab the channel, the ion at least, by the horns and force it, I pull it through the channel and then try to measure the force I have to apply for that to happen? Well, if I do that carefully, I can actually get the potential from that. How? Well, remember that the force was really minus the gradient of the potential, right? And if I invert that, if I just calculate the average force to even out all the noise along some sort of variable that I'm going to call lambda, if I integrate that from zero to X, that's really going to be minus my potential. So I can get the potential from the average force along a specific reaction coordinate. This even has a name. It's called PMF or potential of mean force, very efficient. And when I do that, I get a free energy along a reaction coordinate. In this case, the reaction coordinate is just a Z value inside the channel. And you see here how the free energy varies. And here we have the barrier that the ions will have to go through. This is exceptionally useful if I'm now comparing this between two different types of ions. And then the relative heights of these free energy barriers should correspond to the relative conductance of the two ions. If you weren't yet convinced that it's useful to be able to violate physics now again, here's one last example before I do it slightly more advanced. Anna Johansson and studying those proteins inside membranes. Well, remember when I said earlier that the only thing that really differs between amino acids is the side chains, right, the backbone part of the same. So if we were anyway cheating, get rid of the backbone, just take the side chain, the amino acid analog, and study how expensive is it to put amino acid analogs at different depths in a bilayer. I can do that by forcing it to a particular depth and then just applying enough force to make it stay there. But since I know this force, I can measure it because I'm applying it, right? I take that force, I average it, and I integrate it, and I get the potential of mean force of the cost of inserting amino acid side chains in bilayers. And if I now want to get the cost of a total helix, I just add up all the contributions from the individual amino acids. And this worked. And it generated some beautiful publication. I'll share one final example from my group here. Those skin formation things I talked about. Christian has a colleague Magnus Lundborg who has worked extensively on this. So the reason why they created the models of skin was not just that it was fun. They're actually working on a startup called ERCO where they have used cryo-EM data to obtain and gradually refine very good models of this horny layer of skin. So their goal is that they want to use this to be able to predict what properties of molecules make them good to apply as drugs to skin patches. And after quite a few trial and error iterations, they ended up with these admittedly approximate models of skin. But using these models, they can then calculate first the free energy of putting a molecule at an arbitrary depth here, and second the diffusion rates through these layers. So in addition to knowing how expensive it is to insert, they then effectively get the permeability that is the number of molecules per time that are expected to go straight through this layer. And that will still not be perfect, but it's going to be a surprisingly good model to predict if a compound will go through the skin when I apply it as a patch. Most compounds don't. And their idea in this case for commercializing this is to help companies design better compounds or maybe add or remove a small group on the drug to improve the drug's permeability through skin, or maybe mix in some other molecules to increase the permeability. Also an example of very applied work on simulations, but using the first principles that you know now in this class.