Kinetic Description of Viral Capsid Self-Assembly Using Mesoscopic Non-Equilibrium Thermodynamics

Area of Science:

• Biophysics
• Theoretical Biology
• Chemical Kinetics

Background:

• Existing kinetic models for biological self-assembly often oversimplify by focusing on equilibrium and single reaction coordinates.
• These simplified models are insufficient for accurately describing the size and shape of complex structures like viral capsids.
• A need exists for more sophisticated kinetic descriptions that account for non-equilibrium processes.

Purpose of the Study:

• To derive a kinetic model for viral capsid self-assembly using mesoscopic non-equilibrium thermodynamics (MNET).
• To describe viral capsid formation as a diffusive process in the space of relevant reaction coordinates.
• To provide a framework for understanding and controlling self-assembly processes.

Main Methods:

• Application of mesoscopic non-equilibrium thermodynamics (MNET) to derive governing equations.
• Formulation of a Fokker-Planck equation to model self-assembly as a diffusive process.
• Analysis of specific cases including spherical capsids and extension to higher degrees of freedom and tubular structures.
• Solution via equivalent Langevin equations.

Main Results:

• A Fokker-Planck equation describing the non-equilibrium kinetics of viral capsid self-assembly was derived.
• The model treats self-assembly as diffusion in a multi-dimensional reaction coordinate space.
• The approach allows for the determination of formation rates and size distributions of closed capsids.

Conclusions:

• MNET provides a powerful framework for modeling complex biological self-assembly beyond equilibrium assumptions.
• The derived Fokker-Planck and Langevin equations offer a more accurate description of capsid formation.
• This work facilitates a deeper understanding and potential control over viral capsid self-assembly.