Energy, surface free

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... 

The CFTI method extends the standard TI to an arbitrary number of dimensions [2, 8]. Analogously to Eqs. (1) and (2) the free energy surface is defined as... 

Y. Wang and K. Kuczera. Exploration of conformational free energy surface of helical Ala and Aibn peptides. J. Phys. Chem. B, 101 5205-5213, 1997. 

Y. Wang and K. Kuczera. Conformational free energy surface of the linear DPDPE peptide Cost of pre-organization for disulfide bond formation. J. Am. Chem. Soc., submitted, 1997. 

Surface free energy Surface lubricants Surface modification... 

Z Guo, EM Boczko, CL Brooks III. Exploring the folding free energy surface of a three-hehx bundle protein. Proc Natl Acad Sci USA 94 10161-10166, 1997. 

This section contains a brief review of the molecular version of Marcus theory, as developed by Warshel [81]. The free energy surface for an electron transfer reaction is shown schematically in Eigure 1, where R represents the reactants and A, P represents the products D and A , and the reaction coordinate X is the degree of polarization of the solvent. The subscript o for R and P denotes the equilibrium values of R and P, while P is the Eranck-Condon state on the P-surface. The activation free energy, AG, can be calculated from Marcus theory by Eq. (4). This relation is based on the assumption that the free energy is a parabolic function of the polarization coordinate. Eor self-exchange transfer reactions, we need only X to calculate AG, because AG° = 0. Moreover, we can write... 

More generally, the connection between the free energy surface and the simulation data can be made by the relation [81 ]... 

Figure 4 Free energy surfaces of triiodide ion in various solutions. Contours correspond to isoenergy lines of IkgT, Ik T, and 3kgT, respectively.

Computed free energy surfaces of the triiodide ion in its ground state in acetonitrile, methanol, and aqueous solution are presented in Figure 4, in which the two I—I bond... 

Figure 5 Free energy surface at l l(Fig. 5a) [22, 24, 28] and 1 3 (Fig. 5b) [23, 24, 33] stoichiometries in the vicinity of disordered state ( f=0.0) at T—. 7Q and 1.6, respectively. The solid line in left-hand (right-hand) figure indicates the kinetic path evolving towards the L q LI2 ordered phase when the system is quenched from T—2.5 (3.0) down to 1.70 (1.60), while the broken lines are devolving towards disordered phase. The open arrows on the contour surface designate the direction of the decrease of free energy, and the arrows on the kinetic path indicate the direction of time evolution or devolution.

The consideration of

potential diagrams, that of yjr to the free energy surface,... 

The approach presented above is referred to as the empirical valence bond (EVB) method (Ref. 6). This approach exploits the simple physical picture of the VB model which allows for a convenient representation of the diagonal matrix elements by classical force fields and convenient incorporation of realistic solvent models in the solute Hamiltonian. A key point about the EVB method is its unique calibration using well-defined experimental information. That is, after evaluating the free-energy surface with the initial parameter a , we can use conveniently the fact that the free energy of the proton transfer reaction is given by... 

Since a significant part of our discussion will involve comparison of reactions in solutions and in proteins it is important to establish a link between experimental kinetic measurements in such systems and the corresponding free-energy surfaces. 

In order to construct free-energy surfaces for this system we start by defining the diagonal matrix elements, or the force fields , for each resonance structure ... 

FIGURE 7.5. Calculated free-energy surface for the 2 > 3 step in solution. Forcing this surface to reproduce the observed value of (Agj 3) is used to determine H23. 

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