Two transition state model

The determination of the thermodynamic parameters from equilibrium studies is based on a two-state transition model. Free energy variation, AGd, can be deduced directly from the transition curves ... 

Two different tests can be applied to check whether the denaturation of a given protein can be described with the two-state transition model, namely, the population test and the Vant Hoff test. The population fractions of native and denatured state, fN(/) and fi)(7), are independently evaluated [154,184] (see Figure A3) ... 

The Pink model is found to exhibit a gel-fluid transition for lipids with sufficiently long chains, which is weakly first order. The transition disappears in bilayers of shorter lipids, but it leaves a signature in that one observes strong lateral density fluctuations in a narrow temperature region [200,201]. In later studies, the model has been extended in many ways in order to explore various aspects of gel-fluid transitions [202]. For example, Mouritsen et al. [203] have investigated the interplay between chain melting and chain crystallization by coupling a two-state Doniach model or a ten-state Pink model to a Potts model. (The use of Potts models as models for... 

Both the denaturation process in proteins and the melting transition (also referred to as the helix-to-coil transition) in nucleic acids have been modeled as a two-state transition, often referred to as the all-or-none or cooperative model. That is, the protein exists either in a completely folded or completely unfolded state, and the nucleic acid exists either as a fully ordered duplex or a fully dissociated monoplex. In both systems, the conformational flexibility, particularly in the high-temperature form, is great, so that numerous microstates associated with different conformers of the biopolymer are expected. However, the distinctions between the microstates are ignored and only the macrostates described earlier are considered. For small globular proteins and for some nucleic acid dissociation processes,11 the equilibrium between the two states can be represented as... 

As seen in Fig. 10, the model accurately predicts the presence, location, and area of the cold and heat denaturation peaks. Under these conditions, the hierarchical partition function predicts a heat denaturation peak centered at 58°C and a cold denaturation peak centered at 4°C. The enthalpy change for the heat denaturation peak is 59 kcal mol-1 and the ACp is equal to 2.45 kcal K-1 mol-1. The experimental values reported by Privalov et al. (1986) are 57.5 and 3°C for the heat and cold denaturation transition temperatures, 53 kcal mol-1 for the enthalpy change, and 2.5 kcal K-1 mol-1 for ACp. Analysis of the theoretical curve indicates that it corresponds to a two-state transition, in agreement with the experimental data. The population of partially folded intermediates is never greater than 10-5 during the heat denaturation transition. 

Thus the temperature-dependent transition of polypeptide chains can be modeled by the statistical mechanics treatment of the two-state zipper model. 

Both the coil-to-helix and hehx-to-coil transitions are cooperative and can be described by the two-state zipper model. 

Figure 1 Simulated plots of the mole fraction of the native state, X, versus perturbation axis for a two-state transition described by the following thermodynamic parameters. The circles indicate the anticipated range of data that is usable for calculating the unfolding equilibrium constant (or AGJn). The curves were simulated for a two-state model using the following parameters and equations 3-9 and 11. AHSun = -20000 cal/mol at To = 0°C, ASJ oo = -90 cal/mol K, ACp = 200 oal/mol-K, m = 4.0 kcal/mol M, pKa,u = 4.5,pKa,N = 2.5, and n = 4.

For two-state transitions, the AH parameters obtained by both methods are equally reliable, so it is best to report the average of parameters from the 1/Tm versus InCx plot and fitrm the fits of the shapes of curves (41, 74). Obtaining AH from melting curves measured at different wavelengths can be used to check the two-state approximation (6). Importantly, agreement between enthalpy changes determined by different methods is a necessary, but not a sufficient criterion to establish two tate behaviour (16, 27, 38). Additional methods for validation of the two-state model are described in Section 2. 

How can experiments determine whether a transition is one-state or two-state Both models can give sigmoidal curves of /n(T), or of an order parameter mix) as a function of an externally controlled variable x. So a sigmoidal... 

---