Molecular enumeration

Historically, molecular enumeration has brought a fertile groimd of research among chemistry, mathematics, and computer science. Still today new concepts and techniques are being developed at the interstice of these fields. ... 

The purpose of the final section of this chapter is to review the practical applications of molecular enumeration and to give the reader interested in any of these applications pointers to relevant codes and techniques. In particular, the numbers of isomers for a specific molecular series are given, popular structure elucidation codes are reviewed, computed-aided structure elucidation successes are surveyed, and the connections between structure enumeration and combinatorial library design are established. The field of molecular design with inverse quantitative structure activity relationship is also reviewed. We conclude the chapter outlining future research directions. 

Pander J W and F M Richards 1987. Tertiary Templates for Proteins. Use of Packing Criteria in Enumeration of Allowed Sequences for Different Structural Classes. Journal of Molecular Bio 193 775-791. 

To overcome the limitations of the database search methods, conformational search methods were developed [95,96,109]. There are many such methods, exploiting different protein representations, objective function tenns, and optimization or enumeration algorithms. The search algorithms include the minimum perturbation method [97], molecular dynamics simulations [92,110,111], genetic algorithms [112], Monte Carlo and simulated annealing [113,114], multiple copy simultaneous search [115-117], self-consistent field optimization [118], and an enumeration based on the graph theory [119]. 

A.T. Balaban, ed.. Chemical Applications of Graph Theory, Academic Press, London, 1976. V. Kvasnicka and J. Pospichal, An improved version of the constructive enumeration of molecular graphs with described sequence of valence states. Chemom. Intell. Lab. Systems, 18 (1993) 171-181. 

The main obstacles to increasing our knowledge in this field are methodological (103). Microbial cell enumeration techniques and identification procedures are often difficult or tedious, and the collection of relevant samples or the simulation of natural conditions in the laboratory can be problematical. However, the development of molecular approaches for the study of microbial populations can contribute to solving these problems. Considering the vast array of techniques used and presented in the literature, only a selection of these methods is discussed in this review. 

It was found [9,49] that all the postulates enumerated above are satisfied by the autoclave method for the reduction of technetious acid in concentrated hydrogen halide solutions by molecular hydrogen under a pressure of 3-5 MPa at 140-220 °C. A series of experiments showed that the final product of the reduction of H [TcOJ under these conditions is a mixture of outwardly similar crystalline substances with similar physico-chemical properties. The composition of the mixture can be described by the general overall formula [TcXi,s o.3 m(H20, OH , H30+)] , where X = I or Br and n > 2.8... 

In this case, systematic methods for generation of feasible molecular and mixture candidates have been reported for the design of functional chemical products [see Achenie et al (2003)]. Methods based on database search, total enumeration of feasible candidates (rule-based techniques that avoid a combinatorial explosion), mathematical programming, genetic algorithm, and,... 

The dissection of a molecular model into those components that are deemed to be essential for the understanding of the stereochemistry of the whole may be termed factorization (9). The first and most important step toward this goal was taken by van t Hoff and Le Bel when they introduced the concept of the asymmetric carbon atom (10a, 1 la) and discussed the achiral stereoisomerism of the olefins (10b,lib). We need such factorization not only for the enumeration and description of possible stereoisomers, important as these objectives are, but also, as we have seen, for the understanding of stereoselective reactions. More subtle differences also giving rise to differences in reactivity with chiral reagents, but referable to products of a different factorization, will be taken up in Sect. IX. 

Faulon J-L, Carla J (2003) Churchwell the signature molecular descriptor. 2. Enumerating molecules from their extended valence sequences. J. Chem. Inf. Comput. Sci. 43 721-734. 

Virtual screening applications based on superposition or docking usually contain difficult-to-solve optimization problems with a mixed combinatorial and numerical flavor. The combinatorial aspect results from discrete models of conformational flexibility and molecular interactions. The numerical aspect results from describing the relative orientation of two objects, either two superimposed molecules or a ligand with respect to a protein in docking calculations. Problems of this kind are in most cases hard to solve optimally with reasonable compute resources. Sometimes, the combinatorial and the numerical part of such a problem can be separated and independently solved. For example, several virtual screening tools enumerate the conformational space of a molecule in order to address a major combinatorial part of the problem independently (see for example [199]). Alternatively, heuristic search techniques are used to tackle the problem as a whole. Some of them will be covered in this section. 

Fig. 2.4. Product enumerations of a combinatorial library. For reaction-based enumeration, individual groups of —N(R1)(R2) and —(C0)-R3 are replaced by corresponding molecular fragments from reactants A and B. For template-based enumeration, the R-groups R1, R2, and R3 are replaced by independent lists of molecular fragments. Note that some combinations of R1 and R2 may not exist in component A for reaction-based enumerations. The template-based product structure with R-groups is also called Markush structure and its enumeration is called Markush enumeration or Markush exemplification.

Computational library design process begins with reagent selections, followed by diversity analysis and virtual library enumeration, and ends with selection of a final set of molecular structures to be synthesized (Fig. 9.4). Two databases, Available Chemical Database (ACD) (2) and Chemicals Available for... 

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