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From what I've been reading, it seems that entropy (rather than enthalpy) is the biggest driver of protein folding (especially the burying of hydrophobic residues). However, popular energy functions like AMBER, Charmm, etc. don't model entropy. They are however able to identify the native fold within a few angstroms (i.e. the minimum energy structure per the force fields is not more than a few angstroms away from the native structure) (http://onlinelibrary.wiley.com/wol1/doi/10.1002/jcc.20720/full).

If entropic changes are the primary driver of folding, then how is it that energy functions that don't even model entropy are still able to get close in terms of identifying the native structure (in particular, the burying of hydrophobic residues as well)? Is the entropic information incorporated in the solvent models?

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  • $\begingroup$ Entropy is indirectly related to energy through probabilities. So it's not a separate term in the energy function. Basic explanation of entropy: youtu.be/P9eksvw2e6w. Calculation of entropy from MD simulations: compchemhighlights.org/2013/03/… $\endgroup$ – Jan Jensen Dec 4 '17 at 8:23
  • $\begingroup$ @JanJensen I'm not referring to MD but the ability of the energy function + solvent model to identify the native structure as the energy minimum. You can minimize energy even without MD (and softwares like Rosetta and Tasser do so). $\endgroup$ – Opt Dec 4 '17 at 16:39
  • $\begingroup$ Well, if you only want structure, you just need appropriate scoring function. It doesn't even need to explicitly involve energy. $\endgroup$ – Mithoron Dec 4 '17 at 17:37
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I am sure that a more definitive answer could be provided by someone more familiar with the field, but here are a couple of observations.

First, I think it is a bit of an exaggeration to say that protein folding is almost entirely the result of entropy because the protein will have larger entropy in the unfolded state than in the folded state. The main entropic increase on protein folding will be the entropy of the solvent (and the system solvent + protein is what matters thermodynamically). This is the so-called hydrophobic effect which is what you're referring to by saying folding buries the hydrophobic residues.

Notice, however, that an energy function which contains solvent-solvent, solvent-residue, and residue-residue interactions implicitly contains this entropic effect. This comes by maximizing solvent-solvent and solvent-residue interactions. In order for this to happen, the hydrophobic residues will naturally become buried because this will increase the average number of hydrogen bonds between solvent molecules (I'm assuming the solvent is water) and strengthen the solvent-residue interactions at the exterior of the protein.

Second, the reason an energy-only model of protein folding might get "lucky" by ignoring entropy is that even if the net enthalpy change for protein folding is roughly zero, this does not mean that energy did not play a significant role in the folding process. People often talk about how proteins cannot simply be randomly walking the conformation space because it would take an endless amount of time to find the energy minimum by doing this. This is exactly why intermolecular interactions between residues get discussed so frequently.

So, an energy-only approach will very likely identify the residue-residue interactions which are important structural features of the final folded state. It is entirely possible that there are steps which are energetically destabilizing, but when these steps take place (if they are to take place in the real world), there must be a very constrained conformation space for the step to take place by randomly sampling states. Nonetheless, each step in the protein folding process must hit an energy minimum at some point, so just searching the energetics is a perfectly reasonable first approach. Furthermore, when this approach fails, it tells you that whatever is going on must be quite sensitive to the entropy of the system, so it is not like you are flying blind.

Third, it could easily be the case that energy-only approaches sometimes arrive at the correct structures completely accidentally. That is, there is more than one path from the unfolded state (which unfolded state?) to the folded state. The "real" path, if there is a single path that proteins take, might be quite different from the one that a model like this will take. In fact, if the protein is being sort of randomly perturbed and energy minima are being sought out, the pathway is likely complete nonsense, but this doesn't really matter as long the as protein is folding. It would be interesting to see how models like this do with proteins that have very energetically similar but distinct folded states. If what I'm saying in this part is true, one would expect the model randomly ends up in either state when you run the simulation. This would indicate that in the real world, there is a kinetic effect which forces the folding to follow a certain path and the model does not capture this.

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