Kazuhito Itoh

A statistical mechanical model of allosteric transition of proteins is developed by extending the structure-based model of protein folding to cases that a protein has two different native conformations. Partition function is calculated exactly within the model and free-energy surfaces associated with allostery are derived. In this paper, the model of allosteric transition proposed in a previous paper [Proc. Natl. Acad. Sci. U.S.A 134, 7775 (2010)] is reformulated to describe both fluctuation in side-chain configurations and that in backbone structures in a balanced way. The model is applied to example proteins, Ras, calmodulin, and CheY: Ras undergoes the allosteric transition between guanosine diphosphate (GDP)-bound and guanosine triphosphate (GTP)-bound forms, and the model results show that the GDP-bound form is stabilized enough to prevent unnecessary signal transmission, but the conformation in the GTP-bound state bears large fluctuation in side-chain configurations, which may help to bind multiple target proteins for multiple pathways of signaling. The calculated results of calmodulin show the scenario of sequential ordering in Ca2 + binding and the associated allosteric conformational change, which are realized though the sequential appearing of pre-existing structural fluctuations, i.e., fluctuations to show structures suitable to bind Ca2 + before its binding. Here, the pre-existing fluctuations to accept the second and third Ca2 + ions are dominated by the side-chain fluctuation. In CheY, the calculated side-chain fluctuation of Tyr106 is coordinated with the backbone structural change in the β4–α4 loop, which explains the pre-existing Y–T coupling process in this protein. Ability of the model to explain allosteric transitions of example proteins supports the view that the large entropic effects lower the free-energy barrier of allosteric transition.

A statistical mechanical model of allosteric transitions in proteins is developed by extending the structure-based model of protein folding to cases of multiple native conformations. The partition function is calculated exactly within the model and the free-energy surface reflecting allostery is derived. This approach is applied to an example protein, the receiver domain of the bacterial enhancer-binding protein NtrC. The model predicts the large entropy associated with a combinatorial number of preexisting transition routes. This large entropy lowers the free-energy barrier of the allosteric transition, which explains the large structural fluctuation observed in the NMR data of NtrC. The global allosteric transformation of NtrC is explained by the shift of preexisting distribution of conformations upon phosphorylation, but the local structural adjustment around the phosphorylation site is explained by the complementary induced-fit mechanism. Structural disordering accompanied by fluctuating interactions specific to two allosteric conformations underlies a large number of routes of allosteric transition.

Theory of multidimensional representation of free energy surface of protein folding is developed by adopting structural order parameters of multiple regions in protein as multiple coordinates. Various scenarios of folding are classified in terms of cooperativity within individual regions and interactions among multiple regions and thus obtained classification is used to analyze the folding process of several example proteins. Ribosomal protein S6, src-SH3 domain, CheY, barnase, and BBL domain are analyzed with the two-dimensional representation by using a structure-based Hamiltonian model. The extension to the higher dimensional representation leads to the finer description of the folding process. Barnase, NtrC, and an ankyrin repeat protein are examined with the three-dimensional representation. The multidimensional representation allows us to directly address questions on folding pathways, intermediates, and transition states.

Multidomain proteins are ubiquitous in both prokaryotic and eukaryotic proteomes. Study on protein folding, however, has concentrated more on the isolated single domains of proteins, and there have been relatively few systematic studies on the effects of domain–domain interactions on folding. We here discuss this issue by examining human γD-crystallin, spore coat protein S, and a tandem array of the R16 and R17 domains of spectrin as example proteins by using a structure-based model of folding. The calculated results consistently explain the experimental data on folding pathways and effects of mutational perturbations, supporting the view that the connectivity of two domains and the distribution of domain–domain interactions in the native conformation are factors to determine kinetic and equilibrium properties of cooperative folding.

The folding pathway of the B domain of protein A is the pathway most intensively studied by computer simulations. Recent systematic measurement of Φ values by Sato et al. [Sato, S., Religa, T. L., Daggett, V., & Fersht, A. R. (2004) Proc. Natl. Acad. Sci. USA 101, 6952–6956], however, has shown that none of the published computational predictions is consistent with the detailed features of the experimentally observed folding mechanism. In this article we use a statistical mechanical model of folding to show that sensitive dependence of multiple transition state ensembles on temperature and the denaturant concentration is the key to resolving the inconsistency among simulations and the experiment. Such sensitivity in multiple transition state ensembles is a natural consequence of symmetry-breaking in a nearly symmetrical protein.