Monte Carlo sampling protein modeling

Lattice models have proved to be extremely useful in studies of simple, exact models and somewhat more complex models of protein-like systems. Similarly, the conformational space of a real protein could be discretized and explored in a very efficient way by various versions of Monte Carlo sampling techniques. Depending on the assumed level of discretization and model of force field, various levels of accuracy can be achieved. For example, simple lattice models of real proteins were studied by Ueda et al. 

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]. 

Monte Carlo method, 210, 21 propagation, 210, 28] Gauss-Newton method, 210, 11 Marquardt method, 210, 16 Nelder-Mead simplex method, 210, 18 performance methods, 210, 9 sample analysis, 210, 29 steepest descent method, 210, 15) simultaneous [free energy of site-specific DNA-protein interactions, 210, 471 for model testing, 210, 463 for parameter estimation, 210, 463 separate analysis of individual experiments, 210, 475 for testing linear extrapolation model for protein unfolding, 210, 465. 

Sampling of the biomolecular conformations is usually performed using MD simulations or Monte Carlo methods (61, 62). The protonation state of titrateable amino acids can be treated with constant pH dynamics, QM/MM calculations, or continuum electrostatics methods (61, 62). Formation of a protein-protein encounter complex is often studied using Brownian dynamics (63). Studies of protein-protein docking involve electrostatic potential analysis and, more recently, protein flexibility models, for example normal mode analysis (64). 

A novel approach to protein conformation is the entropy-sampling Monte Carlo method (ESMC), which is described in detail in another contribution to this volume. The method provides a complete thermodynamic description of protein models, but it is computationally quite expensive. However, because of the underlying data-parallel structure of ESMC algorithms, computations could be done on massively parallel computers essentially without the communication overhead typical for the majority of other simulation techniques. This technique will undoubtedly be applied to numerous systems in the near future. 

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