Talk:Conformational entropy

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I corrected a few minor errors. We need more references here. Biophys 03:37, 4 November 2006 (UTC)

Thank you! It is better now. However conformational entropy represents only one of energetic contributions that affect stability of protein mutants. In this regard, text seems to be a little bit misleading. Biophys 06:06, 4 November 2006 (UTC)

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This discussion was previously in article Talk:Molecular mechanics

I like the new formulation. It is actually a strange state of affairs, to ignore entropy completely. Actually the formula you find in the article on conformational entropy for side chain rotameric entropy is problematic. It assumes that the side chains' entropy is uncoupled among side chains and uncoupled to the backbone. Statistically, the coordinate distribution of each independent side chain is a marginal probability distribution. A marginal probability distribution is guaranteed to have (equal or) higher entropy than a distribution considering all correlations. It is only equal in the case of no correlation, which will only happen for atoms belonging to non-interacting, distant molecules. In MM, commonly the normal mode analysis entropy (vibrational entropy of the harmonic oscillator) is used. This entropy contains correlation between all solute atoms, and is in this sense a better choice than the former equation. However, it is very local in phase space and takes care only of linear pairwise correlations. Jorgenumata 17:00, 3 November 2006 (UTC)

Yes, authors of the paper cited in conformational entropy article assumed that backbone and side-chain entropies are uncoupled. That was a valid approximation in their case, since the backbone was fixed. But the equation in conformational entropy article is simply a general definition of entropy (not necessarily conformational). Note that p(i) can be a probaility of any state of any system. I do not think this equation is problematic. The problematic can be only definition of states, which is often indeed the case. Biophys 22:35, 4 November 2006 (UTC)

You're right about that equation not being problematic in general, as it's simply the definition of the (classical) entropy of a discrete probability distribution. But if you isolate the side chains (without fixing the backbone), you will certainly overestimate the entropy. If you do fix the backbone, you arrest collective motions [3] in the molecule in which side chains also participate and which contribute much more to entropy than localized motions. So in effect, the entropy they are measuring has limited significance. [1] In other words, I think entropy estimation from group contributions would be nice if it existed, but unfortunately is a misled idea [2]. I recommend the following articles for more information:

[1] Mark, A.E. and W.F.v. Gunsteren, Decomposition of the Free Energy of a System in Terms of Specific Interactions: Implications for Theoretical and Experimental Studies. J Mol Biol, 1994. 240(2): p. 167-176.

[2] Dill, K., Additivity principles in biochemistry. J Biol Chem, 1997. 1997(272): p. 701-704.

[3] Hammes-Schiffer, S. and S.J. Benkovic, Relating protein motion to catalysis. Annual Review of Biochemistry, 2006. 75: p. 519-541.

I want to reformulate the whole article to reflect these papers. The most problematic sentence in the current article is <<These characteristics [such as side chain rotamers and backbone dihedral angles] are used to define the degrees of freedom (in the statistical mechanics sense of a possible "microstate").>> Microstates are formally non-linear correlated combinations of degrees of freedom. Even if the Hamiltonian (total "enthalpy") of the system can be expressed as additive functions of the degrees of freedom, the free energy and entropy depend on the correlations. [1] The microstates of the system are thus not locally defined. In the most strict definition of entropy, correlations between a protein and every atom in its environment have to be taken into account. What do you think? Jorgenumata 14:51, 5 November 2006 (UTC)

I basically agree. Authors of the cited papers are right that decomposition of entropy may be problematic - srictly speaking. But this is not to say that authors of the paper in JBM are wrong. One can estimate approximately certain entropic contributions and compare them with experimental data. Main question here is what precision do you really need, and how a certain approximation works in a certain special case. For example, the discrete conformer appoximation is crude. But it seems to work with a reasonable precision (say ± 0.5 kcal/mol at 300K) for evaluaton of side-chain conformational entropy. What I do not like in the current version of this article is this: "conformational entropy of the amino acid side chains in a protein is thought to be a major contributor to the energetic stabilization of the denatured state". This is also not wrong, but it is entropy of the entire polypeptide chain, not only the side chain contribution, that stabilizes the unfolded state. Biophys 18:41, 6 November 2006 (UTC)