Protein Engineering, Vol. 12, No. 3, 187,
March 1999
© 1999 Oxford University Press
Communication |
Comments on the Comments
1 Department of Biology, Johns Hopkins University, Baltimore,MD 2128-2685, USA and 2 Graduate School of Science and Technology, Kobe University, Rokkodai, Nada, Japan
Dear Colleagues
We are sorry that our experiment (see Tamura and Privalov, 1997
) has not confirmed your theoretical expectation for the entropy of association of two proteins. It is natural that you are looking for some flaws in the experiment, while we are looking for the same in the theory, suspecting that it is too simplistic for the quantitative description of such complex systems as proteins.
To analyze our experiment we suggest, instead of what you give in your Comments, to use the following thermodynamic cycle:
|
We measured
Sunfolding
cross-linked dimer and Sdimerunfold/dissoc, and found that the difference between these two entropies is small. As we said in our paper: `if we assume that the cross-linking of the native dimer does not lead to a significant change of its entropy' (i.e. that Sfolded dimercross-linking is small) then it follows from our results that the entropy of cross-linking of two unfolded polypeptide chains (i.e. S2 chainscross-linking) should be also small. How justified is the assumption that the entropy of cross-linking of the folded dimer is small? Unfortunately, there is no way to determine this entropy experimentally. It is difficult to imagine, however, that a single cross-link, which does not induce noticeable changes in the structure of a stable, rigid dimer, can result in a significant decrease of its entropy. It is clear also that the cross-linking of two unfolded polypeptide chains does not result in a change of their hydration, protonation, vibrational freedom or conformation. Therefore, the effect that we have estimated corresponds to the net translation/rotational entropy of cross-linking of two unfolded polypeptide chains. Moreover, in so far as cross-linking does not induce noticeable changes in protein structure, this effect can be identified with the translational/rotational entropy of dimerization of the native proteins.
You point out that there cannot be inconsistency between our experimental results and your theoretical estimates because we address different processes: while we estimate the association entropy of unfolded polypeptide chains, you are concerned with association of native proteins. This certainly is not true: we both study the association of folded proteins. You are right that the entropy of association of native proteins includes, above the translational/rotational effect, the effects arising from changes in hydration, protonation, conformation, vibrational freedom and counter-ion release. In our experiment all these effects, except the translational/rotational entropy, are canceled out upon comparison of the unfolding entropies of the noncross-linked and cross-linked dimers. What about theory: how could one take all these effects into account when analyzing the association of native proteins? This cannot be done using the Sackur–Tetrod equation (Finkelstein and Janine, 1989), or by normal mode calculations (Tidor and Karplus, 1993). So what do these two theoretical approaches give us for real proteins in aqueous solution, rather than abstract models in vacuum? It is noteworthy that Amzel (1997), analyzing the association process in aqueous solution, came to a value for the translational entropy which differs significantly from your values but is close to that found in our experiment. Does that mean that the translational entropy depends on the environment? If so, the concept of cratic entropy, which takes into consideration the presence of water, may be not so incredible. How realistic is it, one wonders, to apply gas phase statistical mechanics to large macromolecules in aqueous solution?
It thus appears that the problem of protein association, which is one of the most important in protein science, is far from clear, and this concerns first of all the theory: when the difference between the predicted and the measured values is more than five times the possible experimental error this is a clear indication that something is wrong with the current theory. Nevertheless, we are grateful for the suggestion to study a system with a flexible linker between subunits. However it would be helpful if you also advise us how to take into account the contribution of the long flexible linker into the measured entropic effect. Unfortunately, attractive ideas are not always easy in their practical realization.
References
Amzel, I.M. (1997) Proteins Struct. Funct. Genet., 28, 144–149.[Web of Science][Medline]
Finkelstein,A.V. and Janine,J. (1989) Protein Engng, 3, 1–3.
Tamura,A. and Privalov,P.L. (1997) J. Mol. Biol., 273, 1048–1060.[Web of Science][Medline]
Tidor,B. and Karplus,M. (1993) Proteins Struct. Funct. Genet., 28, 144–149.
Received November 10, 1998; revised December 8, 1998; accepted December 8, 1998.
CiteULike 
Connotea 
Del.icio.us What's this?
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||