The length distribution of frangible biofilaments

Area of Science:

• Biophysics
• Materials Science
• Cell Biology

Background:

• Proteins polymerize into filaments crucial for cellular structures (cytoskeleton) and implicated in diseases (Alzheimer's, Parkinson's).
• Filament fragmentation alters growth dynamics by changing the number of available growth sites (filament ends).

Purpose of the Study:

• To develop an analytical framework for understanding the dynamics of breakable filament assembly.
• To derive time evolution equations for filament length distributions in various supply conditions.
• To apply the theoretical model to experimental data for enhanced analysis of biofilament assembly.

Main Methods:

• Analytical study of the master equation for breakable filament assembly.
• Derivation of closed-form expressions for filament length distribution over time.
• Application of the derived theory to experimental data of insulin amyloid fibrils.

Main Results:

• Closed-form expressions for filament length distribution were derived for open and closed systems with infinite and finite monomer supply.
• The theoretical framework successfully analyzed experimental data for insulin amyloid fibril length distributions.
• The model provides insights into microscopic assembly mechanisms beyond traditional mass analysis.

Conclusions:

• The developed theoretical framework offers a robust method for analyzing filament length distributions.
• This approach enhances understanding of biofilament assembly mechanisms, particularly for amyloid fibrils.
• The study provides a valuable tool for investigating diseases linked to protein filament formation.