Simulated annealing Monte Carlo sampling

Simulated annealing, ESMC [108,109,161], Monte Carlo with minimization [162], genetic algorithms [64,163-165], and the combination of genetic algorithms with Monte Carlo sampling have been successfully used in the past to find the near-native conformations of reduced models of small proteins [68]. 

This problem is NP-complete, and the cardinality of that space is enormous even for the most conservative cases encountered in combinatorial design. This has prompted Agrafiotis and Hassan et al. independently to propose an alternative solution based on Monte Carlo sampling. Their idea was to define an objective function that measures the diversity of any conceivable subset of compounds, and then use simulated annealing to identify the optimal set. 

Monte Carlo/simulated annealing (MC/SA) algorithm for sequential assignment in uniformly 13C, 15N-labeled proteins [137]. The two-dimensional (2D) NCACX and NCOCX spectra measured for the fibril samples of full-length Syrian hamster prion protein (residues 23-231) have been analyzed by the MC/SA protocol, from which it has been concluded that the fibril core is formed primarily in the region of residues 173-224 [54]. 

The literature is full of examples of many types of conformational sampling algorithms [17-20]. Some of the principal ones are the model building approach [21], genetic algorithms [22, 23], the Monte Carlo (MC) [24] and simulated annealing [25] protocols. 

Simulated annealing provides a more efficient application of Monte Carlo methods. To apply simulated anneahng to conformation sampling, we implemented the following process [2]. A random walk in the conformation space of a molecule is implemented. 

Use parametrized interatomic potentials to sample the geometry, using classical Molecular Dynamics (MD) or Monte Carlo/Generalized Simulated Annealing (MC/GSA). 

An alternative to molecular dynamics based simulated annealing is provided by Metropolis importance sampling Monte Carlo (Metropolis et al., 1953) which has been widely exploited in the evaluation of configurational integrals (Ciccotti et al., 1987) and in simulations of the physical properties of liquids and solids (Allen and Tildesley, 1987). Here, as outlined in Chapters 1 and 2, a particle or variable is selected at random and displaced both the direction and magnitude of the applied displacement within standard bounds are randomly selected. The energy of this new state, new, is evaluated and the state accepted if it satisfies either of the following criteria ... 

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