Dept. of Bioinformatics, Friedrich Schiller University, Ernst-Abbe-Platz 2, 07743 Jena, Germany.
Institute of General Botany and Plant Physiology, Friedrich Schiller University, Dornburger Str. 159, 07743 Jena, Germany.
Sci Rep. 2017 Jan 10;7:39821. doi: 10.1038/srep39821.
In lipid biochemistry, a fundamental question is how the potential number of fatty acids increases with their chain length. Here, we show that it grows according to the famous Fibonacci numbers when cis/trans isomerism is neglected. Since the ratio of two consecutive Fibonacci numbers tends to the Golden section, 1.618, organisms can increase fatty acid variability approximately by that factor per carbon atom invested. Moreover, we show that, under consideration of cis/trans isomerism and/or of modification by hydroxy and/or oxo groups, diversity can be described by generalized Fibonacci numbers (e.g. Pell numbers). For the sake of easy comprehension, we deliberately build the proof on the recursive definitions of these number series. Our results should be of interest for mass spectrometry, combinatorial chemistry, synthetic biology, patent applications, use of fatty acids as biomarkers and the theory of evolution. The recursive definition of Fibonacci numbers paves the way to construct all structural formulas of fatty acids in an automated way.
在脂类生物化学中，一个基本问题是脂肪酸的潜在数量如何随其链长而增加。在这里，我们表明，当忽略顺反异构时，根据著名的斐波那契数列增长。由于两个连续斐波那契数的比例趋于黄金分割率 1.618，生物体可以通过每投入一个碳原子来增加大约那个因子的脂肪酸可变性。此外，我们表明，在考虑顺反异构和/或羟基和/或氧基团的修饰时，多样性可以用广义斐波那契数列（例如佩尔数）来描述。为了便于理解，我们故意在这些数列的递归定义的基础上构建证明。我们的结果应该对质谱、组合化学、合成生物学、专利申请、脂肪酸作为生物标志物的使用以及进化理论感兴趣。斐波那契数列的递归定义为以自动化方式构建脂肪酸的所有结构公式铺平了道路。
