Space-filling discrete helices

Area of Science:

• Biophysics
• Structural Biology
• Quantum Chemistry

Background:

• Proteins are essential linear molecules vital for life and health.
• Protein structures are modular assemblies of alpha-helices, beta-sheets, and turns.
• Understanding protein folding is crucial for biological and medical research.

Purpose of the Study:

• To deduce space-filling helical structures from first principles.
• To identify potential structural candidates for protein building blocks.
• To explore the relationship between protein geometry and quantum chemistry.

Main Methods:

• Developed a theoretical model for uniform discrete thick strings.
• Deduced helical forms based on fundamental physical principles.
• Analyzed geometric and quantum chemical properties of deduced forms.

Main Results:

• Identified a countable set of space-filling helical forms.
• One deduced helical form geometrically matches the alpha-helix structure.
• Observed quantum chemistry coincidences supporting the alpha-helix identification.

Conclusions:

• Protein structures can be derived from fundamental geometric and physical principles.
• The alpha-helix structure emerges from these principles, linking geometry and chemistry.
• This work provides a foundation for a unified framework for protein understanding.