Comment on: `The entropy cost of protein association'

M. Karplus1,2 and J. Janin3

1 Laboratoire de Chimie Biophysique, ISIS, Institut le Bel, Universite Louis Pasteur, 67000 Strasbourg, France, 2 Department of Chemistry, Harvard University, Cambridge, MA 02138, USA and 3 Laboratoire d'Enzymologie et Biochimie Structurales, CNRS, Université d'Orsay, 91198 Gif-sur-Yvette, France

An understanding of the origin of the entropy loss involved in association processes (protein–protein or protein–ligand) is important for an interpretation of the many equilibria that play a role in biology. Although the total entropy change on association can be determined by measuring the transition temperature and associated enthalpy change (Privalov et al., 1995Go), interpretation of the results is hindered by the fact that there are several partially cancelling contributions [Tidor and Karplus, 1993 (TK)]. The loss of three translations and three (two for a linear molecule) rotations is entropically unfavorable. This can be offset by favorable entropic contributions, including those that arise from the hydrophobic effect, changes in the protonation states, solvent and counter ion release, as well as the presence of six (five for a linear molecule) new vibrational degrees of freedom. Because the translational and rotational contributions to the entropy of binding appear to be very simple to calculate, they have often been discussed. However, there are no direct measurements of their contribution to binding and theoretical estimates vary by more than an order of magnitude.

A recent paper by Tamura and Privalov (TP) (1997) purports to make a direct measurement of the translational/rotational entropy contribution to the formation of a dimer of the Streptomyces subtilisin inhibitor (SSI). TP studied the temperature-induced unfolding of the wild-type dimer and of a mutant (D83C), with a disulfide cross-link between the subunits, by differential scanning calorimetry; the measurements were made as a function of concentration. When normalized to the same temperature, the entropy of unfolding of the native SSI dimer adjusted to a 1 M standard state was found to be approximately the same as that of the cross-linked mutant dimer; the measured difference was –5 ± 4 cal/mol·K. This result is very different from that obtained in an earlier calorimetric study of the same system by Tamura et al. (1994), who found a value of about –100 cal/mol·K for the difference of the entropies of unfolding of the two systems. Although the difference between the two sets of results is of some concern, TP have given cogent argument to support their measurements (TP, 1997; Privalov, private communication). We do not feel we have the expertise to comment on this question and consider only the interpretation of the TP result in what follows.

TP infer from their measurements that the translational/rotational contribution to the entropy of binding of two native SSI monomers to form the native dimer is very small. They state that their result is inconsistent with estimates of the translational/rotational contribution to the entropy of association published by Finkelstein and Janin (1989, FJ) and by TK (1993), as well as by others; the FJ and TK values are in the range –30 to –60 cal/mol·K. We wish to point out here that there cannot be an inconsistency because TP, on the one hand, and FJ and TK, on the other, address different processes. The TP experiment attempts to measure the translational/rotational entropy of associating two unfolded polypeptide chains to form a native dimer, while FJ and TK were concerned with native proteins; i.e. the formation of a native dimer from two native monomers (the insulin dimer in the work of TK, and the trypsin–BPTI complex in that of FJ). FJ based their estimates on data for whole molecule movements in protein crystals and the TK results were obtained from normal mode calculations. Neither method is applicable to the unfolded state.

To make clear what the TP measurements determine, we consider a set of thermodynamic cycles in Scheme I (asterisks indicate cross-linked species).



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The calorimetric experiment of TP on wild-type SSI yields (2{Delta}Sfold,mono + {Delta}Sass,native) and that on the mutant yields {Delta}Sfold,di*. The difference, which TP found to be small for the 1M standard state, is equal to ({Delta}Sass,native + 2{Delta}Sfold,mono{Delta}Sfold,di*) and provides no direct information on ({Delta}Sass,native + {Delta}Scross,native), the quantity that could be related to that estimated by FJ and KT; i.e. there is no reason why the difference between two (large) entropies of folding, (2{Delta}Sfold,mono{Delta}Sfold,di*), should be equal to the (small) entropy change of introducing a cross-link in a native dimer. This makes clear the essential difference between the measurements, which deal with the effect of the cross-link on association of an unfolded state to form a native dimer, and the calculations, which treat the association of the folded subunits. Various other relationships can be obtained from Scheme I, but none of them avoid this problem.

Certainly the problem that TP are trying to approach is of great interest. In that regard, it may be useful to study a system with a flexible linker between subunits for a protein (e.g. hemoglobin) where the dimer, monomer equilibrium can be studied with both species in the native state. Such a linker has, in fact, been constructed by Sauer and co-workers for the Arc repressor, but that protein also dissociates into denatured monomers (Robinson and Sauer, 1996Go).

References

Finkelstein,A.V. and Janin,J. (1989) Protein Engng, 3, 1–3.[ISI][Medline]

Privalov,G.P., Kavina,V., Freire,E. and Privalov,P.L. (1995) Annal. Biochem., 232, 79–85.[ISI][Medline]

Robinson,C.R. and Sauer,R.T. (1996) Biochemistry 35, 13878–13884.[ISI][Medline]

Tamura,A., Kojima,S., Miura,K. and Sturtevant,J.M. (1994) Biochemistry, 33, 14512–14520.[ISI][Medline]

Tamura,A. and Privalov,P.L. (1997) J. Mol. Biol., 273, 1048–1060.[ISI][Medline]

Tidor,B. and Karplus,M. (1993) Proteins Struct. Funct. Genet., 15, 71–79.[ISI][Medline]

Received September 10, 1998; revised October 27, 1998; accepted October 27, 1998.