Speaker
Description
In metabolomics, a fundamental question is how the potential number of molecular homologues (congeners) increases with their size. Here, we show that the number of unbranched fatty acids and unbranched aliphatic amino acids grows according to the famous Fibonacci numbers when cis/trans isomerism is neglected and adjacent double bonds are excluded \cite{schuster2017,fichtner2017}. This number series had been known in ancient India from Sanskrit prosody as Matrameru numbers. There is a striking mathematical correspondence between the verse structures of poems and bond structures in biomolecules. Moreover, we show that, under consideration of cis/trans isomerism, hydroxy and/or oxo groups, or triple bonds, diversity can be described by generalized Fibonacci (Matrameru) numbers, for example, Pell numbers \cite{schuster2017}. Finally, an enumeration procedure is presented for all possible cyclic secondary α-amino and imino acids (proline and its homologues), depending on ring size. A recursion formula is derived that results in a modified Lucas series \cite{schuster2023}. Our results should be of interest for mass spectrometry, combinatorial chemistry, synthetic biology, patent applications, and the theory of evolution.
Bibliography
@article{schuster2017,
title = {Use of {Fibonacci} numbers in lipidomics–{Enumerating} various classes of fatty acids},
volume = {7},
number = {1},
journal = {Scientific reports},
author = {Schuster, S. and Fichtner, M. and Sasso, S.},
year = {2017},
pages = {39821},
}
@article{fichtner2017,
title = {The tip and hidden part of the iceberg: {Proteinogenic} and non-proteinogenic aliphatic amino acids},
volume = {1861},
number = {1},
journal = {Biochimica et Biophysica Acta (BBA)-General Subjects},
author = {Fichtner, M. and Voigt, K. and Schuster, S.},
year = {2017},
pages = {3258--3269},
}
@article{schuster2023,
title = {Enumeration of saturated and unsaturated substituted {N}-heterocycles},
journal = {arXiv preprint arXiv:2309.02343},
author = {Schuster, S. and Malycheva, T.},
year = {2023},
}
