The combinatorial multitude of fatty acids can be described by Fibonacci numbers

TL;DR

This paper demonstrates that the number of fatty acids with a given number of carbon atoms follows Fibonacci numbers, linking biological diversity to mathematical sequences and suggesting broader implications for lipidomics and evolutionary theory.

Contribution

It establishes a direct mathematical relationship between fatty acid counts and Fibonacci numbers, providing a novel combinatorial perspective in lipid biology.

Findings

Fatty acid counts follow Fibonacci numbers exactly.

Adding one carbon increases variability by approximately 1.618 times.

Results align with exponential growth patterns in biological complexity.

Abstract

The famous series of Fibonacci numbers is defined by a recursive equation saying that each number is the sum of its two predecessors, with the initial condition that the first two numbers are equal to unity. Here, we show that the numbers of fatty acids (straight-chain aliphatic monocarboxylic acids) with n carbon atoms is exactly given by the Fibonacci numbers. Thus, by investing one more carbon atom into extending a fatty acid, an organism can increase the variability of the fatty acids approximately by the factor of the Golden section, 1.618. As the Fibonacci series grows asymptotically exponentially, our results are in line with combinatorial complexity found generally in biology. We also outline potential extensions of the calculations to modified (e.g., hydroxylated) fatty acids. The presented enumeration method may be of interest for lipidomics, combinatorial chemistry, synthetic biology and the theory of evolution (including prebiotic evolution).