Space-filling discrete helices.

Proteins are linear chain molecules that play a central role in life and health. Protein native state folds are modular assemblies of space-filling building blocks of α-helices, β-sheets, and tight turns. Here, we deduce the structures of a countable set of space-filling helical forms of a uniform discrete thick string from first principles with no additional input or adjustable parameters. These forms occur in correspondence with the natural numbers, loosely analogous to the energy levels in a Bohr atom. We find the remarkable result that one of these helical forms is an excellent candidate for an α-helix through seemingly improbable quantum chemistry coincidences that fit the geometrical requirements. Our work suggests that geometry and chemistry are complementary ways of looking at proteins and suggests a route for developing a unified framework for understanding proteins.

• Publication year

  2025

• Venue

  Journal of Chemical Physics

• Publication date

  2025-10-08

• Fields of study

  Mathematics, Physics, Medicine

• Identifiers
  DOI 10.1063/5.0295423arXiv 2510.07011PMID 41090578
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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