How do you calculate or experimentally determine the entropy of enzymes or protein? In particular, I am interested in Boltzmann and conformational entropy, and Gibbs free energy. Any references are welcome.
In practice, like Energy calculations, Entropy is a relative numbers and difficult to get. Computational chem and bio have been working on this problem with mixed success. The summary of what I'm going to say here is that when you try to calculate the differences in entropy (or energy for that matter), the Gibbs Free Energy differences in most biological processes such as enzyme/substrate binding, protein/protein or protein/DNA interactions or protein folding etc is so small compared to the errors in these calculations that the computations are hard to believe.
Entropy is ultimately a term one would use in calculating the Gibb's free energy which will tell whether a given chemical or molecular process will occur. So it's a valuable number to have. Gibbs Free Energy (G) equals Enthalpy (heat) minus the temperature (T) times the change in entropy.
G = H - T$\Delta$S
The Entropic term, $\Delta$S is described in chemical systems often as a change in the combinatorial change of the system and the change in the heat capacity of the system. The first of these could broadly described as a 'mixing' term. When more than one solvents or a solvent and a solute diffuse into each other mix completely, the number of possible states is maximized.
The heat capacity of the system is a more often the focus of entropy calculations for proteins and biological molecules. This is because the conformations of the biological molecules, especially how free they are to move around are thought to contribute to the entropic part of G.
So attempts have been made to estimate from NMR and crystallography as well as molecular dynamics how much domains and side chains are free to move. Unfortunately this is only an insufficient proxy for biological entropy. A substantial if not dominant contribution to the T$\Delta$S term comes from solvent.
How is this so? Water molecules form structures around proteins which are not static, but do involve many water molecules residing there on the average to see them in crystal structures and NMR experiments. While the individual waters are exchanging rapidly, they are not in the same entropic state in water solution as they are when they form a hydration shell around an aromatic or charged side chain.
Attempts have been made to parametrize the solvent entropy by looking at the buried nonpolar surface in a folded protein, looking at the mobility of sidechains before and after folding/binding, but these metrics appear to be configuration dependent to the point that they can't calculate the protein entropy via these efforts, at least heretofore.
Conventionally, molecular dynamics tries to calculate this by surrounding the proteins or other molecules with water molecules and some approximation of the overall entropy is calculated on the entire system. It turns out that small differences between the water molecular models and the simplifications in ball and stick/Hooke potential water models we make are also problematic approximations when there are hundreds or thousands of water molecules in the simulation.