Bacteriophage Qbeta (Qubevirus durum), widely considered a second modern structural proxy for the Earth’s oldest evolutionary RNA viruses, single-stranded RNA genome length of 4,217 nt converges with the 19th Fibonacci number = 4,181 at a remarkable precision of 99.15% by Stefan Geier et al., ISTS Simssee

Bacteriophage Qbeta (Qubevirus durum), widely considered a second modern structural proxy for the Earth’s oldest evolutionary RNA viruses, single-stranded RNA genome length of 4,217nt converges with the 19th Fibonacci number  4,181 at a remarkable precision of 99.15%

by Stefan Geier et al., ISTS Simssee, Gerhart-Hauptmann-Straße 6, Haidholzen, Germany

We analyze the genomic architecture of Bacteriophage Qbeta (Qubevirus durum), widely considered a second modern structural proxy for the Earth’s oldest evolutionary RNA viruses. We demonstrate that Bacteriophage Qbeta (Qubevirus durum), widely considered a second modern structural proxy for the Earth’s oldest evolutionary RNA viruses, single-stranded RNA genome length of 4,217 nt* converges with the 19th Fibonacci number = 4,181 at a remarkable precision of 99.15%. Building upon the morphogenetic framework proposed by Stefan Geier et al.** we will later discuss how this numeric harmony reflects electrodynamic, gravitational (quantum gravitation effects in a long run setting: natural experiment) and thermodynamic constraints and maximum data-packing efficiency in early and recent (todays) evolutionary history. We assume and hypothesize that this nearly perfect fit is associated with the extremly long evolutionary pressure of (bio-)physics described by GEIER's equations on Qbeta (Qubevirus durum, Leviviridae).

Addita:
a) Other characteristics (four genes: 3rd Lucas number) fit GEIER's programme, too.
b) Consider the role of Lucas- and Fibonacci-numbers, please, as described earlier by us***.
c) The icosahedral structure of bacteriophage Qbeta (Qubevirus durum) fits GEIER's programme, too: April 2025 DOI: 10.13140/RG.2.2.19806.14403. ... .
d) With https://humanistischebetrachtungen1.blogspot.com/2026/06/ms2-leviviridae-widely-considered.html this result allows in the context of GEIER's programme to introduce the theory that speciation (Charles DARWIN ... ; genus grouping by the genome nt-count here: Qubevirus in distinction to Emesvirus genera) is causally corelated (not only correlated) to GEIER's equations and differentiation according to every near FIBONACCI- and LUCAS-numbers. (This is an unexpected new finding.)
e) (i) SPIEGELMAN's monster based on Qβ with 218 nt fits (L11 + F13)/2=216 with 99.1%; in the GEIER programme another hint for consistence (Spiegelman, S., Haruna, I., Holland, I.B., Beaudreau, G. & Mills, D. (1965). "The Synthesis of a Self-propagating and Infectious Nucleic Acid with a Purified Enzyme". Proc. Natl. Acad. Sci. USA. 54 (3): 919–927; Stefan Geier, 7. October 2024, Facebook****).
e) (ii) Frank OEHLENSCHLÄGER and Manfred EIGEN demonstrated in 1996 48 and 54 nucleotide long RNAs using T7-RNA-polymerase and HIV-1-reverse-transcriptase; 47 is the 8th LUCAS-number (97.9% fit), 55 is the 10th FIBONACCI-number (98.2 % fit); this underlines the consistency furthermore (30 Years Later – a New Approach to Sol Spiegelman's and Leslie Orgel's in vitro Evolutionary Studies, DOI: 10.1023/A:1006501326129).
e) (iii) Table Fibonacci-Lucas percentage fits for reported RNA replication systems.

Observation	System	Length	Target	Fit (%)	Source / note
Bacteriophage Qbeta genome	Natural ssRNA phage genome	4217 nt	F19 = 4181	99.15	Qbeta structural/genome literature; GEIER note
Spiegelman/Kacian MDV-1-type RNA	Qbeta replicase extracellular evolution	218 nt	G216 = 216	99.08	Kacian et al. 1972; GEIER composite target
Biebricher-Orgel selected RNA	E. coli DNA-dependent RNA polymerase	125 nt	L10 = 123	98.40	Biebricher and Orgel 1973; central estimate approx. 125 +/- 25 nt
Oehlenschlaeger-Eigen EP2	3SR, HIV-1 RT plus T7 RNA polymerase	54 nt	F10 = 55	98.18	Oehlenschlaeger and Eigen 1997
Oehlenschlaeger-Eigen EP1	3SR, HIV-1 RT plus T7 RNA polymerase	48 nt	L8 = 47	97.92	Oehlenschlaeger and Eigen 1997
Schaffner nanovariant RNA	Qbeta replicase short replicator	91 nt	F11 = 89	97.80	Schaffner/Ruegg/Weissmann 1977; UZH note
MNV-11	Qbeta replicase short RNA	87 nt	F11 = 89	97.75	Biebricher and Luce 1992
QT45 polymerase ribozyme	RNA-only polymerase ribozyme	45 nt	L8 = 47	95.74	Gianni et al. 2026
SV-11	Qbeta replicase recombinant short RNA	115 nt	L10 = 123	93.50	Biebricher and Luce 1992
Microvariant RNA	Qbeta replicase short self-replicating molecule	114 nt	L10 = 123	92.68	Mills et al. 1975

Notes: G216 is the GEIER programme-specific F-L-mean 216 nt target used for the 218 nt Spiegelman/Kacian case. With standard Fibonacci/Lucas numbers only, the 218 nt case is closest to F13 = 233 at 93.56%.The mean was the authors first look's intuition, additionally with the above sums are meaningful, too: 216= (L11 + F13)/2 = F12+F10+F7+F4 = L10+L9+L5+L1.

Spiegelman, S., Haruna, I., Holland, I. B., Beaudreau, G. & Mills, D. The synthesis of a self-propagating and infectious nucleic acid with a purified enzyme. Proc. Natl Acad. Sci. USA 54, 919-927 (1965). doi:10.1073/pnas.54.3.919.

Mills, D. R., Peterson, R. L. & Spiegelman, S. An extracellular Darwinian experiment with a self-duplicating nucleic acid molecule. Proc. Natl Acad. Sci. USA 58, 217-224 (1967). doi:10.1073/pnas.58.1.217.
Kacian, D. L., Mills, D. R., Kramer, F. R. & Spiegelman, S. A replicating RNA molecule suitable for a detailed analysis of extracellular evolution and replication. Proc. Natl Acad. Sci. USA 69, 3038-3042 (1972). doi:10.1073/pnas.69.10.3038.

Mills, D. R., Kramer, F. R. & Spiegelman, S. Complete nucleotide sequence of a replicating RNA molecule. Science 180, 916-927 (1973). doi:10.1126/science.180.4089.916.

Biebricher, C. K. & Orgel, L. E. An RNA that multiplies indefinitely with DNA-dependent RNA polymerase: selection from a random copolymer. Proc. Natl Acad. Sci. USA 70, 934-938 (1973). doi:10.1073/pnas.70.3.934.

Oehlenschlaeger, F. & Eigen, M. 30 years later - a new approach to Sol Spiegelman's and Leslie Orgel's in vitro evolutionary studies. Origins Life Evol. Biosph. 27, 437-457 (1997). doi:10.1023/A:1006501326129.

Biebricher, C. K. & Luce, R. In vitro recombination and terminal elongation of RNA by Q beta replicase. EMBO J. 11, 5129-5135 (1992). doi:10.1002/j.1460-2075.1992.tb05620.x.

Schaffner, W., Ruegg, K. J. & Weissmann, C. Nanovariant RNAs: nucleotide sequence and interaction with bacteriophage Qbeta replicase. J. Mol. Biol. 117, 877-907 (1977). doi:10.1016/S0022-2836(77)80004-1.

Mills, D. R., Kramer, F. R., Dobkin, C., Nishihara, T. & Spiegelman, S. Nucleotide sequence of microvariant RNA: another small replicating molecule. Proc. Natl Acad. Sci. USA 72, 4252-4256 (1975). doi:10.1073/pnas.72.11.4252.

Brown, D. & Gold, L. RNA replication by Q beta replicase: a working model. Proc. Natl Acad. Sci. USA 93, 11558-11562 (1996). doi:10.1073/pnas.93.21.11558.

Gianni, E. et al. A small polymerase ribozyme that can synthesize itself and its complementary strand. Science (2026). doi:10.1126/science.adt2760.

Biebricher, C. K., Eigen, M. & Gardiner, W. C. Kinetics of RNA replication: competition and selection among self-replicating RNA species. Biochemistry 24, 6550-6560 (1985).

Biebricher, C. K. & Luce, R. Template-free generation of RNA species that replicate with bacteriophage T7 RNA polymerase. EMBO J. 15, 3458-3465 (1996). doi:10.1002/j.1460-2075.1996.tb00712.x.

(Difference in nucleotide count: 36 nt; distance: 0.854%)

References:
*K.V. Gorzelnik, Z. Cui, C.A. Reed, J. Jakana, R. Young, & J. Zhang, Asymmetric cryo-EM structure of the canonical Allolevivirus Qβ reveals a single maturation protein and the genomic ssRNA in situ, Proc. Natl. Acad. Sci. U.S.A. 113 (41) 11519-11524, https://doi.org/10.1073/pnas.1609482113 (2016).
**St. Geier et al. "GEIER's Equations" and "GEIER's Φ(e) ↔ Φ(α) Equilibrium Programme" with FIBONACCI/LUCAS extensions (GEIER's Equations Part 2.1). ResearchGate, February 2026, DOI:
10.13140/RG.2.2.33185.67689.
***St. Geier et al., https://humanistischebetrachtungen1.blogspot.com/2026/06/ms2-leviviridae-widely-considered.html (2026).
****It's noteworthy that the lin-4 microRNA is 21 nucleotides (bases, „base pairs“) long and 21 is a FIBONACCI number (F8) and thus the microRNA concept is (strictly) consistent with our considerations below.
Please, note that with the LUCAS numbers 18 and 29 we get {F(8) + [L(7) + L(8)]/2}/2 = {21 + [18 +29]/2}/2 = {21 + 23.5}/2 =
= 22.25 (nucleotides)
a good approximation for the microRNA length of more advanced organisms.
A good fit to our considerations below, too.
Yours Stefan Geier, Haidholzen
#NobelPrize #NobelPrize2024 #NobelPrizePhysiology #microRNA

Wikipedia, today: Bacteriophage Qbeta. Transmission electron micrograph of the bacteriophage Qβ attached to sex pilus of the bacterium Escherichia coli

By Dr Graham Beards - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=22482145

Wikipedia, 27.062026: Genome of enterobacteria phage Qβ, an example of an Qubevirus (formerly Allolevivirus) (here: 4215 bp, closer to F19): MA2: maturation protein A2 , CP: coat protein, MCPA1: minor-CP A1, RdRp: RNA-dependent RNA polymerase. By Julie Callanan, Stephen R. Stockdale, Andrey Shkoporov, Lorraine A. Draper, Paul Ross, and Colin Hill - https://www.mdpi.com/1999-4915/10/7/386/htm, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=93760346