Superposition algorithms

Bultinck, P., Kuppens, T, Girones, X. and Carbo-Dorca, R. (2003) Quantum similarity superposition algorithm (QSSA) a consistent scheme for molecular alignment and molecular similarity based on quantum chemistry. J. Chem. Inf. Comput. Sci., 43, 1143-1150. 

Molecular quantum similarity measures, as formulated in integral (1), are dependent on the relative position of both studied molecules in space. Consequently, a procedure capable of arranging the molecular coordinates needs to be established. Two methodologies have been implemented to deal with this question the maximal similarity rule (MSR) [71], which considers that the optimal orientation corresponds to the one that maximizes the value of integral (1) and the topo-geometrical superposition algorithm... 

From a mathematical point of view, we can propose maximization of the MQSM as a function of a set of molecular alignment parameters in such a way as to obtain a superposition procedure with a general scope. Several algorithms aimed directly at maximizing the MQSM have been published. The first example is the MaxiSim algorithm developed by Constans et al. A second one is the quantum similarity superposition algorithm (QSSA) by Bultinck et al. An algorithm developed by Stefanov and Cioslowski is similar to the MaxiSim and QSSA ideas, and it will therefore not be described explicitly because it invokes similar points of view. 

Figure 4 Deterministic and interval modal superposition algorithm.

Our superposition algorithm consists of a sequence of MC loops carried out at linearly decreasing acceptance rates. First of all, the structure to be aligned on the reference molecule is translated to locate the two centres of mass at the same position. At each step of a MC loop, the structure to be aligned is displaced by random translation and rotation steps. The maximal translation and rotation displacements were set equal to 0.5 A and 0.5 rad, respectively. The new alignment is evaluated using Sab and is accepted only if it is probable enough, that is ... 

In the present work, a Monte Carlo/Simulated Annealing rigid superposition algorithm was applied to six families of drug molecules, that is, elastase inhibitors, and ligands of endothiapepsins, trypsins, thermolysins, p38 MAP kinases, and rhinovirus, for which various alignment problems were reported in the literature. 

Carbo-Dorca R, Besalii E, Mercado LD (2011) Communications on quantum similarity. Part 3 a geometric-quantum similarity molecular superposition algorithm. J Comput Chem 32 582-599... 

A quantum algorithm can be seen as the controlled time evolution of a physical system obeying the laws of quantum mechanics. It is therefore of utmost importance that each qubit may be coherently manipulated, between arbitrary superpositions, via the application of external stimuli. Furthermore, all these manipulations must take place well before its quantum wave function, thus the information it encodes, is corrupted by the interaction with external perturbations. The need to properly isolate qubits but, at the same time, to rapidly... 

Sippl, M.J. and Stegebuchner, H. Superposition of three dimensional objects a fast and numerically stable algorithm for the calculation of the matrix of optimal rotation. Comput. Chem. 1991, 35, 73-78. 

Diederichs, K. Structural superposition of proteins with unknown alignment and detection of topological similarity using a six-dimensional search algorithm. Proteins Struc., Func., Genet. 1995, 23, 187-195. 

Special attention has been dedicated to the study of the basis set superposition error (BSSE). The SCF-Ml algorithm which excludes the BSSE from the SCF function was employed. A multi configuration version of it, particularly suited to study proton transfer effects, has been formulated. The use of these techniques has led to binding energy values which show a better stability against variation of the basis set, when compared with standard SCF results. For a more complete evaluation of the advantages of the a priori strategy to avoid BSSE see references [47-50], where applications to the study of the water properties are reported, and reference [51], where the Spin Coupled Valence Bond calculations for the He-LiH system are presented. 

Fig. 5. Structural superposition of binding sites using Med-Sumo . The Surface Chemical Features (SCF) are used to superimpose the protein binding sites (toppanel).The SCF are represented in color code bar (bottom panel) and the SUMO score measure the quality of the 3D structural superimposition that is calculated using a bit-wise matching algorithm of the color code-bar fingerprint (bottom panel).

Equations 1-4 constitute an algorithm for determining from atomic coordinates and some property assigned to the atoms whether the molecule is achiral, and, if not, quantitatively how chiral. Compared to other methods, it is fast and simple because it avoids finding the globally optimal superposition of two... 

For each modulation parameters pair, [(p,r, one experimentally measure the average decoherence rate of the qubit, R(t) (either decay of an initially excited state, or dephasing of an initial superposition of ground and excited states). Then one runs a simple numerical algorithm that finds the coupling spectrum, G( ), that best fits the observed results. 

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