Reversible Two-State Model

Figure 4.2 Protein transformations in reversed-phase chromatography for a two-state model. The native folded state can exist in either the mobile phase (Fm) or the stationary phase (Fs), as can the unfolded state (Um, Us). The equilibrium constants (k) for interconversions of the four species are indicated. (Reproduced from X.M. Lu, K. Benedek, and B.L. Karger, J. Chromatogr., 359 19 [1986]. With permission from Elsevier Science.)...

A good example of application is given by the protein structural changes of bovine ribonuclease A in the course of its denaturation by pressure. The UV spectrum of RNase is dominated by the absorbance of tyrosine - this RNase does not contain tryptophan. As shown in Figure 6, an increase of pressure from 1 to 500 MPa results in a blue-shift of the 4th derivative maximum from 285.7 0.05 to 283.5 0.05 nm. This shift of 2.2 nm corresponds to an increase of the mean dielectric constant from 25 to 59. It is characteristic of the exposure to the aqueous solvent of part of the 6 tyrosines, as it is expected for a partly denaturation. The transition is fully reversible with clear isosbestic points. The pressure effect can therefore be described by a simple two-state model between the native (e,. = 25) and the partially denatured (e,. = 59) state. A simulation on the basis of this model permitted us to determine the thermodynamic parameters of this transition AG° = 10.3 kJ/mol and AV = - 52 ml/mol. A comparison with results obtained by other methods indicates that the (e,. = 59) state corresponds to an intermediate in the defolding process which has molten globule like characteristics [12]. It thus appears that fourth derivative... 

Observations have also been made on the properties of the bound and bulk water molecules. Thus, a two-state model [142, 143] has been proposed for the water molecules in the core of the reverse micelle a very viscous water which is close to the interface, and water in the center of the pool which has properties similar to those of bulk water. This is specially evident when the [H20]/[A0T] ratio is increased beyond a threshold value [143], leading to the formation of a bulky structured water plus bulk-like water variation in dielectric constant is also noted in such cases. It has been noted [143] that the effective dielectric constant at the AOT/n-heptane interface increased with w 2.3 at w = 0, increasing to 9 at w 10, finally reaching a plateau at w 12. In case of AOT reverse micelles, a discontinuity of some physical properties has been noted at a w value of about 12. It has further been indicated that at low values of w, hydration of AOT head-groups and the counterions is important, so a bulky structured water can be visualized on the other hand, at high values of w, the aqueous core becomes bulklike [143]. 

The classical and perhaps the most widely accepted picture of RMs seems to be that of Zensli who describes the water in the interior water-pool of microemulsions using a two-state model.A very viscous water, close to the interface, would be in equilibrium with that in the center of the pool, which exhibits properties similar to bulk water. FTIR and H NMR studies of the AOT reversed micellar-solubilization of pure and aqueous 1,2-ethanediol (ED and ED-W) as well as 1,2,3-propanetriol (PT and PT-W) show that the reversed-micellar-solubilized ED or ED-W as well as PT or PT-W molecules do not seem to coexist in layers of different structures as suggested by the multistate water solubilization micellar model. 

Alexa488 bound to IFABP monitored by steady-state fluorescence was fitted to a two-state reversible unfolding model. This modified protein is slightly less stable (midpoint of 4.5 M compared to 4.7 M for wild-type IFABP). 

Here, we present a formulation suitable for reversible binding of a Ugand and a protein to form a binary complex. The two-state kinetic model involves the interacting molecular species L and P under equilibrium conditions, exchanging between their respective free states and the bound state L P according to Scheme 1. 

AEq = 0.37 for the LS (1A1) state (relative to natural ion at 298 K). Debye-Waller factors were determined for the two states. The values -lnf(sT2) and -lnfi A,) follow the Debye model between 175 and 250 K with 0D (ST2) = 126 K and between 105 and 225 K with 0D (J Aj) = 150 K, respectively. Deviations encountered outside these regions were considered as evidence for the formation of cooperative domains as suggested by Sorai and Seki34,87T The difference between the Debye temperatures 0d(5T2) and 0d( Ai) may well be understood in terms of more rigidity in the lattice of the 2A state as compared to that of the ST2 state. A study of the magnetic hyper-fine interaction at 4.2K yielded VZZ( A1) < O. VZZ(5T2) > O, however, was concluded from the spin reversal of the texture-induced asymmetry of the Mossbauer line intensities. 

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