Secondary Structures of Proteins Follow Menzerath-Altmann Law

Area of Science:

• Biophysics
• Computational Biology
• Structural Biology

Background:

• The Menzerath-Altmann Law (MAL) describes size-frequency relationships in linguistics and genetics.
• Optimization principles are observed across various natural systems, including biological information.

Purpose of the Study:

• To investigate the applicability of the Menzerath-Altmann Law (MAL) to protein secondary structures.
• To determine if protein secondary structure lengths correlate with their frequency within protein sequences.

Main Methods:

• Analysis of a non-redundant dataset comprising 4728 proteins.
• Verification of significant, negative correlations between secondary structure length and number.
• Testing of established and novel formulas to fit the observed trends.

Main Results:

• A specific dependence of secondary structure lengths on their quantity within protein sequences was observed.
• The findings align with a proposed formula, indicating a potential underlying principle.
• The observed trend holds on average but can vary individually, possibly due to a latent cost function.

Conclusions:

• The Menzerath-Altmann Law (MAL) appears to be a relevant principle for protein secondary structures.
• Secondary structure length is influenced by its occurrence within the protein sequence.
• MAL may serve as a valuable guiding principle for protein design and engineering.