First Look: FIBONACCI-Numbers and LUCAS-Numbers and Andes Virus (Hanta Virus): A Reasonable Fit

First Look: FIBONACCI-Numbers and LUCAS-Numbers and Andes Virus (Hanta Virus): A Reasonable Fit

by Stefan Geier

Starting Structure of the Andes virus (ANDV) Nucleoprotein (N) N-terminal domain (residues 1–74)

Helix 1	1–35	Forms the initial hydrophobic interface for trimerization. 34 is a FIBONACCI-number F(9)
Linker	36–43	Flexible loop connecting the two main helices. 8 is a FIBONACCI-number F(6)
Helix 2	44–74	Provides the second "arm" of the coiled-coil to stabilize the trimer. 31 - 2 = 29; 29 is a LUCAS-number L(7), difference=2

The experimentally studied ANDV nucleoprotein N-terminal domain is N1–74. 76 is s a LUCAS-number L(9), difference=2.

The Heptad Repeats fit L(4)=7**. 

The first Fibonacci-numbers and Lucas-numbers:

Fibonacci F(n): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

Lucas L(n): 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ...

The above provides an at least reasonable association of the Andes virus (ANDV) Nucleoprotein (N) N-terminal domain with the GEIER programme based on GEIER's Equations and FIBOBACCI-Numbers and LUCAS-Numbers.
Improvement is possible. +/- 1 or 2 residues should be considered.

(Two hours later: Please, note that the count 3 of trisegmented viral RNAs, the count 3 of mRNAs, the count 5 = F(5) of proteins - NSs, N, Gn, Gc and RdRp -, and the structure and unique 90°-symmetry of the 4xGn + 4xGx spike - compare with floral fornulae* - also fit FIBONACCI- or LUCAS-numbers, 4=L(3) and 8=F(6)=2xL(3); see 2nd Vaheri, A., Strandin, T., Hepojoki, J. et al. Uncovering the mysteries of hantavirus infections. Nat Rev Microbiol 11, 539–550, 2013.)

Yours sincerely,

Stefan Geier

Gerhart-Hauptmann-Str.6

83071 Haidholzen, Germany

(Of course, somehow "very crazy". See: Roger PENROSE, too)

Picture from: Vaheri, A., Strandin, T., Hepojoki, J. et al. Uncovering the mysteries of hantavirus infections. Nat Rev Microbiol 11, 539–550 (2013). https://doi.org/10.1038/nrmicro3066, Published 16 July 2013, Issue date, August 2013, DOI https://doi.org/10.1038/nrmicro3066 (courtesy assumed)

*Found at the Simssee today after writing the SHOEMAKER-LEVY 9 FIBONACCI note: Arabidopsis thaliana, Floral formula: K4 C4 A2+4 G(2). The sepals petals structure K4 C4 with disymmetry (or crossymmetry or "double" bilateral symmetry) is "perfectly" comparable to the 4xGn + 4xGx spike structure of Tula Hantavirus:

Today at the Lake Simssee.

Figure 5 from 3rd; please, look at A. (Courtesy assumed.)
(I see, my lab at MPI Martinsried is still working on viruses with vascular impact as I did 25 years ago: Congratulations for the excellent image!)

**

Figure "Heptad Motifs in Hantaviruses" | Expanded heptad-register map for ANDV N1-74. The PDB 2K48 target sequence is shown after removal of the expression tag. Black boxes mark a-sites, grey boxes mark d-sites, and the linker/turn is shown separately. 4=L(3) complete heptads (and 1 incomplete heptad with length 4=L(3), 5=F(5)) in alpha1 and 4=L(3) complete heptads in alpha2. (Author's figure)

[Overall, the presented aspects corroborate our GEIER's equations.]

#Hantavirus #Andesvirus

References: 

3rd Huiskonen JT, Hepojoki J, Laurinmäki P, Vaheri A, Lankinen H, Butcher SJ, Grünewald K. 2010. Electron Cryotomography of Tula Hantavirus Suggests a Unique Assembly Paradigm for Enveloped Viruses. J Virol84:.https://doi.org/10.1128/jvi.00057-10

2nd Vaheri, A., Strandin, T., Hepojoki, J. et al. Uncovering the mysteries of hantavirus infections. Nat Rev Microbiol 11, 539–550 (2013).

1st Starting point: https://www.uniprot.org/uniprotkb/O36307/entry:

My Summary:
The sequence for the Andes virus (ANDV) Nucleoprotein (N) N-terminal domain (residues 1–74) is highly conserved and follows a distinct mathematical-like pattern known as a heptad repeat.

Amino Acid Sequence (1–74)

The primary sequence for the ANDV N-terminal trimerization domain is:

MSDLKEVQEAI GHLDHEIELV GRKAELEEKV KRVEEAYREI KQKLEDLKKQ LKDYIQAQRE VEEKTREKLS DLRS

Structural & Mathematical Patterns

While 76 is a Lucas number, the biological domain spans 74 residues, forming two antiparallel \(\alpha \)-helices (\(\alpha 1\) and \(\alpha 2\)) that intertwine.

• The Heptad Repeat: Every 1st ("a") and 4th ("d") residue in a 7-residue set (abcdefg) is usually hydrophobic, creating a "zipper" that holds the trimer together.
• Key "a" Residues: Conserved positions like L4, I11, I18, V25, and V32 serve as the hydrophobic core for the first helix.
• Surface Charge: Unlike some viruses that use neutral surfaces, ANDV has "hotspots" of charge. Residues Arg22 and Lys26 form a positively charged patch that is critical for recognizing host cell machinery during assembly at the Golgi apparatus.

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Sequence Breakdown by Segment

Segment	Residue Range	Primary Function
Helix 1	1–35	Forms the initial hydrophobic interface for trimerization.
Linker	36–43	Flexible loop connecting the two main helices.
Helix 2	44–74	Provides the second "arm" of the coiled-coil to stabilize the trimer.
Post-74	75+	Leads into the "NPcore" which contains the RNA-binding crevice.