First, the probability function. Reading carefully shows that the function that was given at the beginning of this thread is not a probability density function (PDF), it is the probability of obtaining a structure with an RMSD less than or equal to X. Therefor, taking the derivative of this function will give the PDF (it's really too complicated to write in text format). However, the mean value of the PDF is 15.5A, which means that one would expect the most frequently occuring RMSDs to be around this value. This is obviously not true; the most frequently occurring is 99.9999999. One thing that this PDF doesn't take into account is that structures with RMSD of more than 100A are rounded down to 100, I think. But the function given says that ALL structures will have 100A or less RMSD. In actuality, there is a big jump from the probability of getting a 100 to the probability of getting a 99, which is not reflected in the PDF.

Next, there was a question about the energy. All matter in the universe is subject to four basic forces (depending how you count). They are the strong force, the weak force, the electromagnetic force, and gravity. In intermolecular interactions, only three of these matter, because one of them has to do with interactions inside the nuclei of atoms. The gravitational interactions, when taken on the molecular scale, are known as Van der Waals forces, and they depend on the masses of the interacting particles. The electromagnetic interactions depend on the charges of the particles (a proton having a +1 charge, and an electron having a -1 charge). I always get the strong and weak forces mixed up, so I'll skip them.

There are two types of energy to be mindful of: kinetic and potential. Potential energy is when a particle (or any massive object), has forces acting on it that can accelerate it. When the particle is allowed to accelerate, the potential energy is changed into kinetic energy. The potential enery, both in gravity and electromagnetism, follows an inverse-square law, which basically means that the closer a particle gets to another particle, the less potential energy the particles will have. (To note, the particles can't accelerate forever, so the kinetic energy, which depends on a particle's velocity, gets changed into other types of energy when two particles get close enough together, such as sound energy, light energy, heat energy, chemical energy, etc.)

Now, in chemistry, molecules are known to be more stable when they have less potential energy. To apply this to folding, the proteins will jiggle and bobble around until they find a setup which is stable enough to maintain. If it is not stable enough, the external forces from water molecules and such will force the protein to unfold and start over.

So, when they say that proteins with lower energies are scored better, it is because they are more stable, and more accurately represent a molecule that will occur in nature.

Furthurmore, there was mention of calculated proteins that have lower energies than the actual things. This is because, in the real world, if a protein finds a setup that is stable enough to withstand the external forces, it won't unfold and try to find an even more stable setup, simply because it doesn't need to. Say the external forces are 5 (example units), the protein will need to be able to withstand 5 units of external force. Now imagine that the most stable setup of the protein that is computationally possible can withstand 4 units of external force. But, in it's bobbling and jangling, the protein finds a setup that can withstand 4.8 units. This setup will stick, because the external forces won't pull it apart. However, it is not the most stable setup possible, it just works.

I hope this helps at least somebody.

Ciao