Overlap sampling

Lu, N. Kofke, D. A. Woolf, T. B., Improving the efficiency and reliability of free energy perturbation calculations using overlap sampling methods, J. Comput. Chem. 2003, 25, 28-39... 

This approach is one of the oldest techniques for improving FEP calculations [36]. It is often called the simple overlap sampling (SOS) method and is usually markedly more accurate than simple averaging. It requires that one forward and one backward calculation be performed at every intermediate state. It is worth noting that no sampling is performed from the ensemble characterized by Xi+AX/2, so that the number of stages is the same as in the pure forward, or backward calculation. 

A detailed presentation of the overlap sampling approach will be given in Sect. 6.6 of Chap. 6. In the present chapter, we merely note that applying this scheme, or any other similar technique that will be discussed extensively later on in the book, almost always improves the quality of the results. It is, therefore, highly recommended that they be routinely used in FEP calculations, perhaps in combination with other techniques. 

Note that for the cases Fig. 6. lc, d, depending on the difference between the 0 and 1 systems, it may be better to go with higher-order stage calculations. For example, for case (d) one can construct an intermediate MB bridging r0 and r, so that the relationship of Tg and r B r are both described by case (c), and then perform overlap sampling calculations between 0 and MB as well as 1 and MB. 

As the initial and final states are set by the problem under study, their important phase space relationship could be any one of the cases illustrated in Fig. 6.1. For cases Fig. 6.1c, d, it is impossible to construct a funnel path from 0 to 1 directly. To satisfy the funnel requirement, similar to the MFEP calculation, a staged NEW calculation can be performed. For example, in the case Fig. 6.1c, one can first construct an intermediate in the common region of / ,[ and /), then perform two separate NEW calculations following the paths 0 —> M and 1 —> M, respectively. This NEW-overlap sampling (NEW-OS) technique will be discussed in detail in Sect. 6.6. 

However, it does have some disadvantages. The / and g histograms obtained from a finite-length simulation contain errors themselves. The histogramming and graphical analysis require additional steps in the calculation, and can introduce new sources of errors [54]. Better alternatives, such as Bennett s method and the overlap sampling method, will be discussed further in this chapter. 

We refer to (6.68) as the simple overlap sampling (SOS) method. The optimization feature is lost in the SOS method, but it usually produces a very good estimate of AA and can be used as a simple alternative to Bennett s form for those who do not like the small additional work of solving for C. However, we note that the application of the OS method with C = 0 in (6.64) is not recommended because its performance is uneven [35]. 

Fig. 6.10. Comparison of overlap sampling and FEP calculation results for the free energy change along the mutation of an adenosine in aqueous solution (between A = 0.05 and 0.45) in a molecular dynamics simulation. The results represent the average behavior of 14 independent runs. (MD time step.) The sampling interval is 0.75 ps. The upper half of the plot presents the standard deviation of the mean (with gives statistical error) for AA as a function of sample size N the lower half of the plot gives the estimate of A A - for comparison of the accuracy, the correct value of AA is indicated by the bold horizontal line...

Key dashed curve - forward FEP, dash-dotted curve - reverse FEP, solid curve - direct FEP averaging, solid curve with crosses - simple overlap sampling, solid curve with open circles -overlap sampling with the optimal Bennett s weights. Data have units of kcalmol-1... 

Figure 4.59. Class A (line) and Class B box overlap. Sample 2 is an unknown.

A typical application is the determination of position, size and orientation of an object together with the material information as control parameters for an automatic sorter. For clean, non-overlapping samples it is sufficient to determine the centre of each object and the approximate size to control the sorting unit. However, frequently these ideal conditions cannot be guaranteed, as samples overlap or surface adhesions may interfere with the classification, as shown in Fig. 7.4. Such artefacts will lead to (partially) false information about size and position of an object and hence to incomplete or erroneous sorting. 

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