Sphere exclusion algorithm

In dissimilarity-based compound selection the required subset of molecules is identified directly, using an appropriate measure of dissimilarity (often taken to be the complement of the similarity). This contrasts with the two-stage procedure in cluster analysis, where it is first necessary to group together the molecules and then decide which to select. Most methods for dissimilarity-based selection fall into one of two categories maximum dissimilarity algorithms and sphere exclusion algorithms [Snarey et al. 1997]. 

Sphere exclusion algorithms are closely related to DECS methods. The basic algorithm operates by selecting a compound and then excluding from... 

A diverse training set of 670 receptor binding pockets was selected from a modeling set of 800 complexes using the Sphere Exclusion Algorithm, as is typically done in our QSAR studies. This set was used by CoLiBRI to build models with the lowest PMR (Equation 10.3). The remaining 130 receptors... 

At each iteration of the sphere-exclusion algorithm [Hudson et at 1996], a compound is selected for inclusion in the subset and then all other molecules in the database which have a dissimilarity to this compound less than some threshold value are removed from further consideration. Variation is possible depending upon the way in which the first compound is selected, the threshold value, and the way in which the next compound is selected at each stage. It is typical to try to select this next compound so that it is least dissimilar to those already selected. Hudson et al. suggested the use of a MinMax method, where the molecule with the smallest maximum dissimilarity with the current subset is selected. However, it is also possible to select this next compound at random from those still remaining. 

Alternatively, the number of desired compounds can be predefined and a stochastic algorithm used to maximize the diversity of the selected set, although these methods are even slower than addition methods. Sphere-exclusion methods, which Pearlman calls "elimination" algorithms because the diverse subset is created by eliminating compounds from the superset, have been implemented in Diverse-Solutions (31) (see Section 2.2.1.1), providing a rapid distance-based diverse subset selection method. The minimum distance between nearest neighbors within the diverse subset is first defined a compound is chosen at... 

The first term in Eq. [429] is the hard-sphere exclusion volume term, which decreases the counterion concentration at the surface the second and third terms respectively represent the fluctuation potential and increase the surface concentration of ions. These terms can be included as an activity coefficient in a general-purpose algorithm through the exponential term in Eq. [378]. For ion distances Ar closer to the surface than three ion radii, Bratko and Vlachy multiply the ion concentrations in Eqs. [430] by an excluded volume correction factor B r) = (Ar- - a)j4a for distances Ar < a, ion concentrations are, of course, zero because of hard-sphere exclusion. 

The calculation of free volumes and free surface areas requires an efficient way of extending the cavity algorithm. To calculate the free volume of a particle i, the particle and its associated exclusion sphere are effectively removed from a snapshot of the particle configuration. The volume and surface area of the cavity that is produced in the absence of particle i are equal to the free volume and free surface area of particle i, respectively. 

Complete details about the method of construction of 3-D porous networks through Monte Carlo simulation can be found elsewhere [10] similarly, the precise algorithm employed to replicate sorption processes in porous networks has been reported somewhere else [11]. Here, we will only mention several key aspects regarding these porous network and sorption simulations. First, the critical conditions required for cavities (hollow spheres) and necks (hollow cylinders open at both ends) to be fully occupied by either condensate or vapor have been calculated by means of the Broekhoff-de Boer (BdB) equation [12], while the thickness of the adsorbed film has been approximated via the Harkins-Jura equation [13]. Some other important assumptions that are made in this work are (i) the pore volume is exclusively due to sites (ii) bonds are considered as volumeless windows that communicate neighboring sites (ili) bonds can merge into a site without suffering of any geometrical interference with adjacent throats. 

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