Simulating replica exchange

Key Words Force field Molecular dynamics simulations replica exchange GROMACS GROMOS96 folding secondary structure... 

Simple Continuous and Discrete Models for Simulating 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. 

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... 

Mitsutake, A. Okamoto, Y., Replica-exchange simulated tempering method for simulations of frustrated systems, Chem. Phys. Lett. 2000, 332, 131-138... 

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). 

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.

Zuckerman, D.M., Lyman, E. A second look at canonical sampling of biomolecules using replica exchange simulation. J. Chem. Theory Comput. 2006, 2, 1200-2. 

The common multicanonical techniques such as replica-exchange or simulated tempering have been described and reviewed extensively in different contexts [124], They interface naturally with MC simulations as they are cast as (biased or unbiased) random walks in terms of a control parameter — usually temperature. They work by exchanging information between the different conditions, thereby allowing increased barrier crossing and quicker convergence of sampling at all conditions of interest. 

Without loss of generality, we can assume Tj < T2 < < Tm- A simulation of the replica-exchange method (REM) is then realized by alternately... 

After a long production run of a replica-exchange simulation, the canonical expectation value of a physical quantity A at temperature Tm (m = 1,..., M) can be calculated by the usual arithmetic mean as follows ... 

We now present an example of MREM. We consider an isobaric-isothermal ensemble and exchange not only the temperature but also the pressure values of pairs of replicas during a MC or MD simulation [94]. Namely, suppose we have M replicas with M different values of temperature and pressure (Tm,Vm). We are setting Eo = E, V = V, and Am = Vm in (4.58). We exchange replicas i and j which are at (Tm,Vm) and (Tn,Vn), respectively. The transition probability of this replica-exchange process is then given by (4.48), where (4.60) now reads [3,80,96]... 

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