A two-step biopolymer nucleation model shows a nonequilibrium critical point

Area of Science:

• Biophysics
• Chemical Kinetics
• Materials Science

Background:

• Biopolymer self-assembly is complex due to monomer conformational flexibility.
• Nucleation often follows a two-step mechanism: intermediate condensation and subsequent conversion.
• This two-step nucleation is implicated in amyloid diseases like Alzheimer's and Parkinson's.

Purpose of the Study:

• To develop a mathematical model for biopolymer nucleation that incorporates simultaneous assembly and conversion dynamics.
• To address limitations of existing models that neglect conversion timescales.
• To explain experimental observations of mixed intermediates and abrupt changes in growth kinetics.

Main Methods:

• Development of a novel model explicitly accounting for simultaneous assembly and conversion.
• Proposal of an initiation-propagation mechanism for conversion, analogous to 1D Glauber dynamics.
• Analysis of competing timescales between assembly and conversion.

Main Results:

• The model predicts a nonequilibrium critical point separating unstable and accumulating intermediate regimes.
• Demonstration that conversion dynamics significantly impact the accumulation rate of the stable biopolymer phase.
• Explanation of experimental phenomena like mixed intermediate formation and scaling exponent changes.

Conclusions:

• The model provides a quantitative framework for understanding two-step biopolymer nucleation.
• It offers insights into the concentration and composition of biologically relevant intermediates.
• This work is a crucial step toward predicting the behavior of complex biopolymer systems.