Landscape energy

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].

Wolynes P G 1996 Symmetry and the energy landscape of biomolecules Proc. Natl Acad. Sci. (USA) 93 14 249-55... 

Bryngelson J D, Onuchic J N, Socci N D and Wolynes P G 1995 Funnels, pathways, and the energy landscape of protein folding a synthesis Profe/ns 21 167-95... 

We assume that the unbinding reaction takes place on a time scale long ( ompared to the relaxation times of all other degrees of freedom of the system, so that the friction coefficient can be considered independent of time. This condition is difficult to satisfy on the time scales achievable in MD simulations. It is, however, the most favorable case for the reconstruction of energy landscapes without the assumption of thermodynamic reversibility, which is central in the majority of established methods for calculating free energies from simulations (McCammon and Harvey, 1987 Elber, 1996) (for applications and discussion of free energy calculation methods see also the chapters by Helms and McCammon, Hermans et al., and Mark et al. in this volume). 

Figure 8 shows a one-dimensional sketch of a small fraction of that energy landscape (bold line) including one conformational substate (minimum) as well as, to the right, one out of the typically huge number of barriers separating this local minimum from other ones. Keeping this picture in mind the conformational dynamics of a protein can be characterized as jumps between these local minima. At the MD time scale below nanoseconds only very low barriers can be overcome, so that the studied protein remains in or close to its initial conformational substate and no predictions of slower conformational transitions can be made. 

Hans Prauenfelder, Sthephen G. Sligar, and Peter G. Wolynes. The energy landscape and motions of proteins. Science., 254 1598-1603, 1991. 

Fig. 5. The left hand side figure shows a contour plot of the potential energy landscape due to V4 with equipotential lines of the energies E = 1.5, 2, 3 (solid lines) and E = 7,8,12 (dashed lines). There are minima at the four points ( 1, 1) (named A to D), a local maximum at (0, 0), and saddle-points in between the minima. The right hand figure illustrates a solution of the corresponding Hamiltonian system with total energy E = 4.5 (positions qi and qs versus time t).

H and B J Berne 1999. Multicanonical Jump Walking A Method for Efficiently Sampling Rough Energy Landscapes. Journal of Chemical Physics 110 10299-10306. 

Fig. 10.27 Schematic representation of the energy landscape for protein folding. (Figure adapted from Onuchic ] N, Z Luthcy-Schulten and P Wolynes 1997. Theory of Protein Folding The Energy Landscape Perspective. Annual Reviews in Physical Chemistry 48 545-600.)...

Bryngelson J D, J N Onuchic, N D Socci and P G Wolynes 1995. Funnels, Pathways, and the Energy Landscape of Protein Folding A Synthesis. Proteins Structure, Function and Genetics 21 167-195. 

Figure 1 A schematic view of (a) a low temperature simulation that is confined by high energy baiTiers to a small region of the energy landscape and (b) a high temperature simulation that can overcome those barriers and sample a larger portion of conformational space.

Figure 1 (a) Schematic energy landscape for a random unfoldable heteropolymer. The roughness... 

---