4 research outputs found
Enumeration of saturated and unsaturated substituted N-heterocycles
Mathematical and computational approaches in chemistry and biochemistry fill
a gap in respect to the analysis of the physicochemical features of compounds
and their functionality and provide an overview of known as well as yet
unknown, but hypothetically possible structures. Nitrogen containing
heterocycles such as aziridine, azetidine and pyrrolidine bear a high potential
in pharmacology, biotechnology and synthetic biology. Here, we present a
mathematical enumeration procedure for all possible azaheterocycles with at
least one substituent depending on the number of atoms in the ring, in the
sense of saturated and unsaturated congeners. One subgroup belonging to that
substance class is constituted by ring-shaped amino acids with a secondary
amino group such as proline. A recursion formula is derived, which results in a
modified Lucas number series. Moreover, an explicit formula for determining the
number of such substances based on the Golden Ratio is given and a second one,
based on binomial coefficients, is newly derived. This enumeration is a helpful
tool for construction or complementation of virtual compound databases and for
computer-assisted chemical synthesis route planning.Comment: 11 pages, 4 figure