Aperiodic crystals in biology

Area of Science:

• Biophysics
• Materials Science
• Crystallography

Background:

• Biological systems exhibit complex hierarchical designs across various scales.
• Periodic order is common in non-living matter but less prevalent in biology.
• Aperiodic order, particularly quasicrystals, offers an alternative descriptive framework.

Purpose of the Study:

• To review the role of aperiodic order in biological structures.
• To illustrate how aperiodic crystal concepts can model biological patterns.
• To highlight the limitations of current quasicrystal notions for biological complexity.

Main Methods:

• Review of representative biological examples: botanical phyllotaxis, tissue cell patterns, sea urchin morphology, virus architecture.
• Application of mathematical tools and fundamental notions from aperiodic crystal science.
• Comparative analysis of periodic vs. aperiodic order in biological contexts.

Main Results:

• Biological structures predominantly feature aperiodic order rather than strict periodicity.
• Aperiodic crystal concepts provide a valuable modeling framework for biological complexity.
• Existing quasicrystal notions may not fully capture the richness of biological structural features.

Conclusions:

• Aperiodic order is a fundamental principle in the hierarchical organization of biological matter.
• The aperiodic crystal science toolkit offers robust mathematical and conceptual resources for understanding biological structures.
• Further development of aperiodic modeling may be needed to fully encompass biological structural diversity.