Parallel tempering

Many additional search methods have been devised in addition to the basic three just discussed. A few of them are outhned below. Note that whereas some methods, such as parallel tempering and J-walking, are improved or speciahzed versions of the basic tech-... 

Thus far, we have been discussing the crystallization of a multichain system. However, under suitable conditions, crystallization can even occur in a single-chain system. Using a combination of biased sampling, multihistogram techniques, and parallel tempering [ 125], we can directly compute the... 

Fig. 23 Parallel tempering of the free-energy curves in the overlapping windows as a function of the number of molten units for a single 1024-mer at a temperature of 2.967 p/A b. The y-axis is not for the absolute value of the free energy but for the relative distribution of the free energy (Hu and Frenkel, unpublished results)...

Hansmann, U. H. E., Parallel tempering algorithm for conformational studies of biological molecules, Chem. Phys. Lett. 1997, 281, 140-150... 

Hamiltonian hopping, as any other version of parallel tempering, is highly efficient if it is implemented on parallel computer architectures. In a stratified FEP calculation involving N states of the system, the simulations of the different A states are carried out in parallel on separate processors. After a predefined number of steps, A ampie, N/2 swaps between two randomly chosen simulation cells are attempted [38]. This procedure is illustrated in Fig. 2.11. Acceptance of the proposed exchange between cells i and j is ruled by the following probability [39] ... 

Fig. 2.11. Schematic representation of a parallel tempering simulation, in which the N states of a stratified FEP calculation are run concurrently. After a predefined number of steps, iVSampie, the cells are swapped randomly across the different processors. A Metropolis-based acceptance criterion is used to determine which of the N / 2 exchanged A-states should be accepted. Pairs of boxes that fail the test are swapped back. Then additional sampling is performed until the next exchange of the replicas...

One of the most popular such techniques is parallel tempering in the canonical ensemble, for which the index parameter is temperature [13-15], While parallel tempering (or replica exchange) strategies had been independently proposed on multiple occasions in various scientific areas, perhaps the earliest seed of the idea can be found in early work by Swendsen and Wang [37]. 

For clarity, let us present the details of the swap process in a temperature-based parallel tempering algorithm. Generally, parallel tempering involves the implementation of the following iterative steps ... 

Molecular dynamics has also been used to replace the MC moves for conformational advancement [43]. In the molecular dynamics version of parallel tempering, often referred to as replica exchange molecular dynamics, momenta are used in the propagation scheme such that a constant temperature is maintained between the swaps. After the swap in conformational space (with the same acceptance criterion as in the MC implementation), a readjustment in momentum space is also needed. This is done by renewing the momenta for replica i by the transformation... 

Other exciting applications involved using parallel tempering in connection with available experimental data. For example, Falcioni and Deem [57] used X-ray data to refine structures of zeolites, and Haliloglu et al. [58] refined NMR structural data for proteins (in particular using residual dipolar coupling constraints). 

Another practical limitation in complex applications lies in the fact that, if temperature is used as a control parameter, one needs to worry about the integrity of a system that is heated too much (e.g., water-membrane systems or a protein heated above its denaturation temperature). When issues such as those mentioned above are addressed, parallel tempering can be turned into a powerful and effective means of enhanced conformational sampling for free energies over a range of temperatures for various systems. 

For an excellent overview of several other applications of parallel tempering, as well as for details on the pertinent questions to be addressed in practical implementations, the reader is referred to a recent review by Earl and Deem [59]. 

Predescu, C. Predescu, M. Ciobanu, C.V., On the efficiency of exchange in parallel tempering Monte Carlo simulations, J. Phys. Chem. B 2005,109, 4189-4196... 

Schug, A. Herges, T. Wenzel, W., All-atom folding of the three-helix HIV accessory protein with an adaptive parallel tempering method, Proteins-Struct. Funct. Bioinform. 2004, 57, 792-798... 

Rathore, N. Chopra, M. de Pablo, J.J., Optimal allocation of replicas in parallel tempering simulations, J. Chem. Phys. 2005,122... 

Calvo, F. Neirotti, J.P. Freeman, D.L. Doll, J.D., Phase changes in 38-atom Lennard-Jones clusters. II. A parallel tempering study of equilibrium and dynamic properties in the molecular dynamics and microcanonical ensembles, J. Chem. Phys. 2000, 112, 10350-10357... 

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