Free-Energy Landscapes

Figure B3.3.10. Contour plots of the free energy landscape associated with crystal niicleation for spherical particles with short-range attractions. The axes represent the number of atoms identifiable as belonging to a high-density cluster, and as being in a crystalline environment, respectively, (a) State point significantly below the metastable critical temperature. The niicleation pathway involves simple growth of a crystalline nucleus, (b) State point at the metastable critical temperature. The niicleation pathway is significantly curved, and the initial nucleus is liqiiidlike rather than crystalline. Thanks are due to D Frenkel and P R ten Wolde for this figure. For fiirther details see [189].

Bursulaya, B. D., and Brooks, C. L. (2000). Comparative study of the folding free energy landscape of a three-stranded /i-sheet protein with explicit and implicit solvent models./. Phys. Chem. B 104, 12378-12383. 

In what follows, we use simple mean-field theories to predict polymer phase diagrams and then use numerical simulations to study the kinetics of polymer crystallization behaviors and the morphologies of the resulting polymer crystals. More specifically, in the molecular driving forces for the crystallization of statistical copolymers, the distinction of comonomer sequences from monomer sequences can be represented by the absence (presence) of parallel attractions. We also devote considerable attention to the study of the free-energy landscape of single-chain homopolymer crystallites. For readers interested in the computational techniques that we used, we provide a detailed description in the Appendix. ... 

Substitution of Eq. 22 into Eq. 17 gives the free-energy landscape in terms of the lamellar thickness ( m) and width ( // ) per chain for a given choice of e, a, and lc. The remarkable consequence of the entropic part of Fm>/X is that Fm,ii has a global minimum for a finite value of m. 

Chipot, C. H6nin, J., Exploring the free energy landscape of a short peptide using an average force, J. Chem. Phys. 2005,123, 244906... 

Braun, O. Hanke, A. Seifert, U., Probing molecular free energy landscapes by periodic loading, Phys. Rev. Lett. 2004, 93... 

US studies can produce informative free energy landscapes but assume that degrees of freedom orthogonal to the surface equilibrate quickly. The MD time needed for significant chain or backbone movement could exceed the length of typical US simulations (which are each typically on the nanosecond timescale). However, in spite of this caveat, US approaches have been very successful. One explanation for this success lies in the choice of initial conditions US simulations employ initial coordinates provided by high-temperature unfolding trajectories, which themselves have been found to yield predictive information about the nature of the relevant conformational space. 

Zhou, F. X. Berne, B. J. Germain, R., The free energy landscape of f) hairpin folding in explicit water, Proc. Natl Acad. Sci. USA 2001,98, 14931-14936. 

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