**Joint seminar of the Matthias Schleiden Institute and JCB**

**Tuesday, 09. May 2023, 4.15 p.m.**** **

**Lecture Hall – Am Planetarium 1 **

**The Golden Ratio in botany and biochemistry**

Prof. Dr. Stefan Schuster

(Dept. of Bioinformatics, Matthias Schleiden Institute, Friedrich Schiller University Jena)

One of many definitions of the Golden Ratio (a.k.a. Golden Section) says that the ratio between the smaller and larger parts is the same as the ratio between the larger part and the whole. This ratio, 1.618…, is widely used in architecture, painting, photography etc. It can also frequently be found in biology. For example, flowers in the form of a five-pointed star and five-membered ring-shaped biomolecules such as pyrrolidine have the property that the diagonal and edge length are in the golden ratio. For regular pentagons, that was known already to Euclid in the 3^{rd} century BC.

The Golden Ratio can also be observed in phyllotaxis: If leaves are arranged at the stem in that ratio, they shade each other as little as possible. A less widely known number is the Silver Ratio, which is related to the Pell numbers (a.k.a. 2-Fibonacci numbers). Some plants appear to follow that ratio.

A biochemical application is the enumeration of fatty acids (or analogous aliphatic amino acids). Their number increases with their chain length according to the famous Fibonacci numbers when cis/trans isomerism is neglected. The ratio of two consecutive Fibonacci numbers tends to the Golden Section. Under consideration of modification by hydroxy or oxo groups, diversity can be described by the Pell numbers. Finally, recent results on ring-shaped amino acids (analogs of proline) are reported. Their enumeration also leads to a number series related to the Golden Ratio.