 So this type of small defect cost penalty explains a ton of things. For instance, why we virtually always see the strands in a beta sheet making the same type of crossover. An individual crossover in the right wrong direction does not look to be too costly, but it does a couple of k-cals and those k-cals will show up exactly the same way as the solvation-free energy of an amino acid in the probability. We're going to look more at the quasi Boltzmann statistics in next lecture when we talk about folding. But armed with that I can study something else. Do you remember the Rosman fold? We had helices on the outside and then some beta strands. I'm going to draw six of them because remember from earlier today that each beta strand was roughly half the length of a helix. But why do the beta strands always occur on the inside? Couldn't I have helix helix helix helix helix helix helix helix helix helix? Nice and regular pattern. Well, this corresponds to a long chain here, right? And then I would have to ask myself what is the probability of having a helix versus what is the probability of having two beta sheet segments? And again, if I say that this is length m and the probability of having a helix, the probability here we're just, oh sorry, I can't use p everywhere. This would be p raised to the power of m. I'm going to be blunt and say that it's 50-50, so the probability of being in a sheet is also p. But the length here is only m half. On the other hand, I have two of them. So I'm going to have p raised to m half multiplied by, sorry, multiplied by p raised to m half, right? And that's equal to p raised to m. So those probabilities are the same. But how many ways can I place the helix? Well, I can place that in roughly n ways, right? If that's the total length of the sequence. Might small two strands, on the other hand? Well, the first I can place in roughly n ways and the second one I can also place in roughly n ways. Maybe I should say that it comes before the first or so, but that's just a factor of two. So there are many more ways I can place two short segments than one log segments. So based on this, we're saying that entropy makes it much more likely to have the short beta strands on the inside of a structure than a single long alpha helix, even though it's just a factor of two difference in their lengths. But in biology, there is always an exception to every rule and they're usually very interesting examples.