Double-wide sampling

Double wide sampling enables two free energies to be accumulated from a single simulation. 

In order to check the self-consistency, the simulations can be run in both directions, i.e., Xi — Ai+i and A,+i —> X, except at the two end points. This is known as double-ended sampling [50]. It is facilitated by using double wide sampling, i.e., the free energy... 

MC-FEP simulations were performed in 21 windows where charges were gradually annealed using the double-wide sampling technique. For each window the system was equilibrated over at least 10 million configurations, and the average was done for 10 million configurations. In all cases the hysteresis and the standard deviations were small, which lends confidence to the protocol of the simulation. 

The number of windows can be significantly reduced when a double-wide sampling [248] is adopted a molecular simulation is carried out for each hybrid state A, and the free energy variations to the previous A,./ and to the next A,+/ states are evaluated using the sam.e produced trajectory. AF is then calculated as ... 

For a typical proton transfer, O-H- -O > O- -H-O, it was found that the O- O distance remains relatively constant and that r(0-H)-r(H-0 ) can be used to compute a 1-D PMF. Normally, these calculations are split into a series of 30 windows with increments spanning 0.04 A for the proton transfer over the O- -O distance the resolution is half of the window size due to the use of double-wide sampling. In our study of the FAAH catalytic mechanism, it was shown that the change in AG (i.e., AAG) for the individual FEP windows could be fit almost perfectly by a cubic polynomial, as shown in Figure la [24]. Typically, the sum of all AAG values relative to a reference AG = 0 value in the reaction would yield a... 

Figure 1 Schematic illustration of the forward, reverse, and double-wide sampling thermodynamic perturbation methods.

The ability to evaluate forward and reverse perturbations simultaneously can be used to decrease the perturbation from one intermediate step to the next in multiple-step thermodynamic perturbations using the method of double wide sampling. In this method, free energy differences are evaluated from each ensemble for half a step in X forward and a half a step in X in reverse direction and taking the sum of all contributions as the final free energy difference,... 

Using this technique, the perturbations are made smaller, resulting in more accurate final free energy differences. The difference between forward, reverse, and double-wide sampling perturbations is illustrated in Figure 1. 

Another measure of error that is applicable to FEP simulations can be obtained from so-called double wide sampling . At each point (other than the endpoints) in the windowing chain during FEP, one can actually calculate two free energy differences one in the A. A. -F 5A direction, and one in the A A — 5A direction. The respective delta free energies are given by... 

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