"Channelrhodopsin geometry and Fibonacci–Lucas targets: testing Geier’s programme motivated by the Nobel Prize in Physiology or Medcine 2026" by Stefan A. Geier et al.

Channelrhodopsin geometry and Fibonacci–Lucas targets: testing Geier’s programme motivated by the Nobel Prize in Physiology or Medicine 2026:
A coordinate-based case study of the native-sequence CrChR2 transmembrane domain  

by Stefan A. Geier*, Caroline Geier, Stephanie Geier, Constantin Geier, Katharina Geier,

Nora Blättermann-Goldstein, and Michèle Geier-Noehl**

Institute for Structuralistic Theory of Sciences Simssee (ISTS), Gerhart-Hauptmann-Straße 6, 83071 Haidholzen, Germany; and Ludwig-Maximilians-Universität Munich, Germany.
**Dermatologische Klinik der Landeshauptstadt und der Ludwig-Maximilians-Universität LMU München, Thalkirchner Straße 48, 80337 Munich, Germany.
*Correspondence: Stefan A. Geier; wissenschaftstheorie.simssee.1@gmail.com

Abstract 

Channelrhodopsins provide a tractable test of proposed connections between protein architecture, Fibonacci and Lucas numbers, and the golden ratio. We analysed the experimentally determined Cα coordinates of Chlamydomonas reinhardtii channelrhodopsin-2 (CrChR2; PDB 6EID, chain A), distinguishing the originally characterized 737-residue protein, its 315-residue experimental construct and 247 modelled residues. Seven transmembrane-associated helical spans contain 33, 22, 21, 24, 32, 28 and 39 residues. Their exploratory sum is 199, a Lucas number. Four lengths fall within 5% of a Fibonacci or Lucas target; adding nonrecursive adjacent midpoints increases this to seven. However, the expanded grid already covers 23 of 31 integers between 15 and 45. Circular-helix fits give 3.610–3.736 residues per turn and winding descriptors g = √(2πR/P) of 1.564–1.651. The unweighted mean, 1.61887, is close to Φ = 1.61803, although local geometry and boundary changes show appreciable heterogeneity. A conventional ideal α-helix gives g = 1.63590 and also passes the 5% criterion. The observations provide a reproducible numerical characterization compatible with a restricted structural reading of Geier’s programme. They do not establish enrichment under a biological null model, exact golden-ratio organization or a causal design law. Source annotations, coordinate data, sensitivity analyses and executable code are included. One-sentence abstract CrChR2 exhibits Fibonacci–Lucas length matches and near-golden helical geometry, but target density, boundary dependence and an ordinary α-helix control prevent proximity from establishing a specific biological mechanism. 

Keywords Channelrhodopsin-2; optogenetics; Fibonacci numbers; Lucas numbers; golden ratio; Geier’s programme; α-helix; winding geometry; protein structure; target-density control; reproducibility.

Figures:

Sources:
1. Advanced information. NobelPrize.org. Nobel Prize Outreach 2026. Tue. 6 Oct 2026. <https://www.nobelprize.org/prizes/medicine/2026/advanced-information/>

2.1. Our posts on the topic on this Blogger Blog.
2.2. The complete paper will be published on ResearchGate soon. (07.10.2026: Channelrhodopsin geometry and Fibonacci-Lucas targets: testing Geier's programme - A coordinate-based case study of the native-sequence CrChR2 transmembrane domain

• October 2026; 
• DOI:
• 10.13140/RG.2.2.28596.62080 )

3. Congratulations!

Hi, channelrhodopsin has 7 transmembrane domains and thus follows "Geier's equations" by a LUCAS number. Very nice!

Yours Stefan Geier, Haidholzen

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Announcement of the 2026 Nobel Prize in Physiology or Medicine