Lattice energy landscape

Computer simulation using lattice models and energy landscape theory using abstract models predict that the fastest folding of small proteins should occur without intermediates and by an extended nucleation process. Stable intermediates slow... 

The only allowed motion is the exchange of the vacancy with one of its neighboring atoms. The exchange rate depends on the local environment, i.e. on the relative position of the vacancy and the impurity atom. This takes into account the effect of the lattice stress induced by the tracer atom on the energy landscape observed by the vacancy. Each rate is simply proportional to the Boltzmann factor e-AE/kBT wjjere is the activation energy for the considered diffusional move and kBTis the thermal... 

We may list differences between the liquid water system and the FPU model the latter will be examined in the next section as a representative system in the study of many-dimensional Hamiltonian systems. The most important difference would be that the FPU model describes a lattice vibration around an equilibrium point and the potential energy function possesses a single minimum, whereas there are infinitely many local potential minima and the potential energy landscape generally becomes ragged in the case of the liquid water system. The reason why the character of the potential landscape could be so important is that the raggedness is considered as an origin of slow motions in liquid water or supercooled liquids. 

Fig. 5. Free energy landscape of a lattice model protein (see Sect. 2.2), as a function of two order parameters, the number of contacts C and the number of native contacts Qo (see Sect. 2.3). Unlike the energy landscape funnel picture, the free energy shows two stable states separated by a barrier (the transition state). Extended unfolded conformers quickly collapse to the molten globule, and have to overcome a barrier to folding to the native state. The funnel picture is thus reconciled with the two-state concept of a free energy barrier. Reprinted from Dinner et ah. Trends Biochem. Sci. 25, 331, (2000) with permission from Elsevier...

Abkevich, V. I., Gutin, A. M., and Shakhnovich, E. I., Free energy landscape for protein folding kinetics Intermediates, traps, and multiple pathways in theory and lattice model simulations. J. Chem. Phys. 101, 6052 (1994). 

The development of molecular simulations of a simple lattice-polymer model has allowed us to survey the topography of free-energy landscapes for singlechain melting and crystallization [43,44]. Thus, a quantitative thermodynamic description to the phase transitions of a single macromolecule can be verified [45]. 

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