Two state kinetics

For these sequences the value of Gj, is less than a certain small value g. For such sequences the folding occurs directly from the ensemble of unfolded states to the NBA. The free energy surface is dominated by the NBA (or a funnel) and the volume associated with NBA is very large. The partition factor <6 is near unify so that these sequences reach the native state by two-state kinetics. The amplitudes in (C2.5.7) are nearly zero. There are no intennediates in the pathways from the denatured state to the native state. Fast folders reach the native state by a nucleation-collapse mechanism which means that once a certain number of contacts (folding nuclei) are fonned then the native state is reached very rapidly [25, 26]. The time scale for reaching the native state for fast folders (which are nonnally associated with those sequences for which topological fmstration is minimal) is found to be... 

Ritort, F. Bustamante, C. Tinoco Ir., I., A two-state kinetic model for the unfolding of single molecules by mechanical force, Proc. Natl Acad. Sci. USA 2002, 99, 13544-13548... 

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. 

Very small proteins, such as 02, can have a very expanded Dphys (see Chapter 19, section B4). The IgG binding domain of streptococcal protein L (62 residues) is of similar size to 02 and also folds by two-state kinetics (see Tables... 

Chyraotrypsin inhibitor 2 (CI2) folds rapidly by simple two-state kinetics that is, D N, with a r1/2of 13 ms.18,19 CI2 is a small 64-residue protein that has all its peptidyl-proline bonds in the favorable trans conformation.20 (There are, of course, additional slow cis —> trans peptidyl-prolyl isomerization events, which account for about 20-30% of the refolding amplitudes.) The occurrence of two-state kinetics does not prove that there are no intermediates on the folding pathway there could be intermediates that are present at high energy and are kineti-cally undetectable (see section B4). Two-state behavior has subsequently been found for many other small proteins. The simplicity of two-state folding kinetics provides the ideal starting point for the analysis and illumination of the basic principles of folding. 

In conclusion it is to be mentioned that the kinetics of real ion channels is much more complicated than the two-state kinetics discussed in this chapter. Further analysis is necessary in order to assess the effect of more sophisticated kinetics on the rate of exocytosis. 

The rcCPMG approach relies on a series of experiments with different rcp delays between the 180° pulses in the CPMG pulse trains used to measure R2 relaxation rates. For two-state kinetics in the fast exchange limit, the dependence of R2 on Tcp can be formulated as78 ... 

The G-Peptide has Apparent Two-State Kinetics After a Small Temperature Jump Perturbation... 

Equations (3.5), (3.6), and (3.7) enable us to compute the dehydronic field, that is, the mechanical equivalent of the dehydration propensity of hydrogen bonds made along the folding process. This computation requires the evaluation of the gradient (R) = — Vr [4tt (R)]-1 qcf/t of the electrostatic energy with respect to the position vector R of the test hydrophobe (in the simulations we adopted methane as test hydrophobe). This analysis is motivated by the need to support the two-state kinetic picture outlined in Fig. 3.1. To normalize for the number of hydrogen bonds formed at any given time, we computed the dehydronic field per... 

Two state kinetics does not necessarily obey the van t Hoff-Arrhenius law, which presumes a linear relation between the logarithm of the rate constant and the inverse temperature. As for proteins both energetic and entropic contributions are important a more general applicable expression for the rate constant is given by transition state theory (TST)... 

Here, <... > denotes an average over the equilibrium ensemble of initial conditions. C t) is the conditional probability to find the system in state B at time t provided it was in state A at time 0. According to the fluctuation-dissipation theorem [63], dynamics of equilibrium fluctuations are equivalent to the relaxation from a nonequilibrium state in which only state A is populated. At long timescales, these nonequilibrium dynamics are described by the phenomenology of macroscopic kinetics. Thus, the asymptotic behavior of C(t) is determined by rate constants and kg. At long times, and provided that a single dynamical bottleneck separating A from B causes simple two-state kinetics. 

The kinetic mechanism described above bears some resemblance to the framework and to the nucleation-condensation models." " In fact, the compact structure formed immediately after the early process of condensation is very similar to the molten globule concept proposed by Ptitsyn " in the case of all a and mainly a proteins, the molten globule does not suffer any other drastic changes, thus essentially following the two-state kinetics of many small proteins, " but in the case of a/jS and mainly jS proteins, the molten globule continues to evolve into a different shape as proposed in the... 

The sequence, whose native state is shown in Fig. 4, displays two-state kinetics for the temperatures T > 0.87 that is, P (t) exp(— ), where Xf is the folding time. To probe the sequence of events en route to the native conformation, we computed Rg t)), which reveals two stages in collapse. Initial rapid burst phase is followed by a gradual chain compaction (Fig. 5). The overall collapse time Xc is associated with the second characteristic time. From the approach to the native conformation we draw the following general conclusions regarding two-state folders ... 

Sams et al. [61] proposed a two-state kinetic model which assumed a monomeric state and an associated state consisting of aggregates in various sizes larger than the monomer. The model describes only the fast process and assumes that the rate constants for association and dissociation are independent of the micelle size. A revised version of the two-state model [62,63] assumed micelle formation to be an adsorption phenomenon, with micelles at equilibrium with monomers adsorbing and escaping from the surface of micelles. 

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