Proteins: coexistence of stability and flexibility

Area of Science:

• Structural Biology
• Biophysics
• Computational Biology

Background:

• Proteins exhibit complex native topologies crucial for function.
• Understanding the relationship between protein stability and flexibility remains a challenge.
• Fractal geometry offers a novel framework for analyzing complex structures.

Purpose of the Study:

• To introduce a new equation of state for protein native topology.
• To correlate protein fractal dimensions (df, ds) with amino acid count (N).
• To explore the fractal nature of proteins in bridging stability and flexibility.

Main Methods:

• Analysis of data from the Protein Data Bank.
• Generalization of the Landau-Peierls instability criterion for fractal systems.
• Empirical validation using over 500 diverse protein structures.

Main Results:

• An equation relating protein fractal dimension (df), spectral dimension (ds), and amino acid number (N) was established.
• Proteins analyzed were found to obey this equation of state.
• Deviations from the equation correlate with potential protein unfolding.

Conclusions:

• The fractal nature of proteins provides a unifying principle for their stability and flexibility.
• The derived equation serves as a predictive tool for protein structural integrity.
• This work offers new insights into the fundamental physics governing protein structure.