Replica exchange

Figure 10-5. Representative conformations of the (5 amyloid peptide (10-42) under different pH conditions. The conformations were obtained as centroids of the most populated clusters from the replica-exchange CPHMD folding simulations [43, 44]. The N-terminal residues 10-28 are shown in blue the C-terminal residues 29-42 are shown in red. In the most aggregation-prone state (pH 6), the side chains of the central hydrophobic cluster Leu-17, Val-18, Phe-19, Phe-20 and Ala-21 are shown as van der Waals spheres in pink, grey, cyan, purple and green, respectively...

Nymeyer H, Gnanakaran S, Garcfa AE (2004) Atomic simulations of protein folding using the replica exchange algorithm. Methods Enzymol 383 119-149. 

Sugita Y, Okamoto Y (1999) Replica-exchange molecular dynamics method for protein folding. Chem Phys Lett 314 141—151. 

Fukunishi, O. Watanabe Takada, S., On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems application to protein structure prediction, J. Chem. Phys. 2002,116, 9058-9067... 

Fenwick, M. K. Escobedo, F. A., Expanded ensemble and replica exchange methods for simulation of protein-like systems, J. Chem. Phys. 2003,119, 11998-12010... 

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]. 

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... 

Jang, S.M. Shin, S. Pak, Y., Replica-exchange method using the generalized effective potential, Phys. Rev. Lett. 2003, 91... 

Sugita, Y. Kitao, A. Okamoto, Y., Multidimensional replica-exchange method for free-energy calculations, J. Chem. Phys. 2000,113, 6042-6051... 

Sayano et al. [97] generated the potential of mean force for interactions between amino acids and base pairs. Okamoto and coworkers [98, 99] have also developed replica-exchange multicanonical methods for proteins. Numerous additional biological examples can be found among the references within [94]. 

Sanbonmatsu, K. Y. Garcia, A. E., Structure of Met-enkephalin in explicit aqueous solution using replica exchange molecular dynamics, Prot. Struct. Function Genetics Feb 2002, 46, 225-234. 

Rhee, Y. M. Pande, V. S., Multiplexed-replica exchange molecular dynamics method for protein folding simulation, Biophys. J. 2003, 84, 775-786. 

One increasingly popular method which lead to non-dynamical trajectories is replica-exchange MC or MD [11-13], which employs parallel simulations at a ladder of temperatures. The "trajectory" at any given temperature includes repeated visits from a number of (physically continuous) trajectories wandering in temperature space. Because the continuous trajectories are correlated in the usual sequential way, their intermittent — that is, non-sequential — visits to the various specific temperatures produce non-sequential correlations when one of those temperatures is considered as a separate ensemble or "trajectory" [14]. Less prominent examples of non-dynamical simulations occur in a broad class of polymer-growth algorithms (e.g., refs. 15-17). 

Both the correlation-time analysis and the block-averaging scheme described below assume that a dynamical trajectory is being analyzed. Again, by "dynamical" we only mean that correlations are "transmitted" via sequential configurations — which is not true in a method like replica exchange. 

Analyzing non-standard simulations — for example, replica exchange... 

Replica-exchange simulations, because of their growing popularity, merit special attention. While their efficacy has been questioned recently [19,39], our purpose here is solely to describe appropriate analyses. To this end, a clear distinction must be drawn between "mixing" (accepted exchanges) and true... 

Figure 9 A cartoon of two states differing only in entropy. Generally, in any simulation, energetic effects are much easier to handle than entropic. The text describes the challenge of analyzing errors in replica-exchange simulations when only entropy distinguishes two energetically equal states.

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