PROOF OF CONCEPT Multi-scale Numerical Invariants and Fractal Properties of the Genetic Code: A Combinatorial and Atomic Analysis using the Erythrocyte (Red Blood Cell) as an Ideal Mathematical Model for AI-Based Proteomic Analysis

This proof-of-concept study proposes a deterministic framework for proteomic analysis based on intrinsic numerical invariants of the genetic code rather than purely statistical or probabilistic approaches. The central hypothesis is that the numerical values 97, 1, and 128 represent fundamental invariants derived from the atomic properties (protons, neutrons, and electrons) of the chemical elements that constitute living matter (CHON). These invariants are hypothesized to remain conserved across multiple biological scales, from codons to complete protein structures. To test this hypothesis, the human erythrocyte (red blood cell) was selected as an ideal biological model because it is anucleate, no longer synthesizes proteins, possesses a finite and stable proteome, exhibits a well-defined geometry, and has been extensively characterized through numerous documented disease-causing mutations. These characteristics minimize biological variability and allow the mathematical organization of existing proteins to be examined independently of ongoing gene expression. The study first introduces a novel classification of the 64 codons, grouping them according to their associated numerical invariant values (1, 28.5, 30.5, 31, 64, 95, 96, 97, and 128). This alternative codon organization serves as the mathematical foundation for all subsequent analyses and differs from the conventional international genetic code table. The principal erythrocyte proteins are then organized into four functional categories: oxygen transport proteins (hemoglobins), cytoskeletal proteins (including spectrin, actin, and adducin), membrane proteins, and metabolic maintenance proteins. An artificial intelligence–assisted algorithm decomposes each amino acid sequence into successive segments corresponding to the numerical pattern 97–1–128. The initial analyses indicate that the α-globin chain can be almost entirely reconstructed according to this numerical architecture, while 95.2% of the β-globin chain can be represented by successive 97/1/128 triplets, with only a few amino acids—primarily tryptophan and certain phenylalanine residues—remaining outside the proposed pattern. The same methodology is subsequently applied to additional erythrocyte proteins, including hemoglobin A₂, fetal hemoglobin (HbF), the AHSP chaperone, actin, spectrin, and adducin, demonstrating that the approach is intended to extend beyond hemoglobin alone to the broader erythrocyte proteome. Beyond sequence analysis, the proposed framework aims to establish deterministic relationships between the primary amino acid sequence, three-dimensional protein organization, and cellular mechanical properties. The study introduces the conceptual framework Meta-Genesis, which suggests that part of biological organization may be governed by intrinsic mathematical constraints embedded within the genetic code itself, complementing rather than replacing classical evolutionary mechanisms. Overall, this work presents a theoretical proof of concept for a deterministic numerical interpretation of the genetic code and protein architecture. While the preliminary results appear promising within the erythrocyte model, the proposed framework will require validation across substantially larger proteomic datasets before its generality, predictive power, and biological significance can be fully assessed. Complete Research Corpus Kayser-Cuny, V. (2025). Meta-Genesis. Towards a Biology without Matter, based on Pure Logic. Multi-Scale Numerical Invariants and Fractal Properties of the Genetic Code (Abstract and compilation). Zenodo. https://zenodo.org/records/21002033 Kayser-Cuny, V. (2025). (Part 1) Multi-Scale Numerical Invariants and Fractal Properties of the Genetic Code: A Combinatorial and Atomic Analysis. Zenodo. https://zenodo.org/records/21002648 Kayser-Cuny, V. (2025). (Part 2) Multiscale Numerical Invariants and Fractal Properties of the Genetic Code: Internal Constraints and Multiscale Packet Distributions Revealing a Universal Grammar. Zenodo. https://doi.org/10.5281/zenodo.17272500 Kayser-Cuny, V. (2025). (Part IV-part 3) Multi-Scale Numerical Invariants and Fractal Properties of the Genetic Code: A Unified Theory of Biological Information, from Stars to Codons. Zenodo. https://doi.org/10.5281/zenodo.17370443 Kayser-Cuny, V. (2025). (Part VI-part 3) Multi-Scale Numerical Invariants and Fractal Properties of the Genetic Code: Data Availability Data set. Zenodo. https://doi.org/10.5281/zenodo.17306204 Kayser-Cuny, V. (2025). Data Availability Part 2 Data set. Zenodo. https://doi.org/10.5281/zenodo.17368936 Kayser-Cuny, V. (2025). (Part III) The Mirror-Twin Paradox: A New Approach to DNA Understanding the Implications of an Inverted Genome and Its Applications in Molecular Genetics, Neuroscience, and Medicine. Zenodo. https://doi.org/10.5281/zenodo.15390489 Kayser-Cuny, V. (2025). Meta-Genesis. Towards a Biology Without Matter. From Boolean Algebra to the Expansion of Life: Binary Arithmetic and Multi-Dimensional Projections of the Genetic Code. Zenodo. https://doi.org/10.5281/zenodo.17494922 A Deterministic Method for the Generation, Simulation, and Assembly of De Novo Proteins Based on Numerical Invariants Intrinsic to the Genetic Code: Part 1. Kayser-Cuny, V. (2026). The Kayser–Cuny Mathematical Tables in Molecular and Synthetic Biology: A Molecular Information Framework (2026th ed.). MTMVP. https://doi.org/10.5281/zenodo.21001829 ISBN: 9782489162035 Part 2. Kayser-Cuny, V. (2026). PROOF OF CONCEPT Multi-scale Numerical Invariants and Fractal Properties of the Genetic Code: A Combinatorial and Atomic Analysis using the Erythrocyte (Red Blood Cell) as an Ideal Mathematical Model for AI-Based Proteomic Analysis. Zenodo. https://doi.org/10.5281/zenodo.21003215