A computational toolbox for the assembly yield of complex and heterogeneous structures.

Area of Science:

• Soft matter physics
• Biophysics
• Computational chemistry

Background:

• Self-assembly of complex structures from non-identical building blocks is crucial in soft matter and biological systems.
• Predicting equilibrium assembly yield is difficult due to entropic contributions and competing configurations, especially for building blocks with rotational degrees of freedom.

Purpose of the Study:

• To develop a computational approach for predicting self-assembly yields with arbitrary building blocks, including those with rotational freedom.
• To overcome the limitations of existing methods that primarily apply to spherically symmetric building blocks.

Main Methods:

• Combines classical statistical mechanics with automatic differentiation computational tools.
• Automatic differentiation enables efficient evaluation of equilibrium averages over complex configurations.
• Framework validated against molecular dynamics simulations.

Main Results:

• Successfully calculates equilibrium assembly yields for arbitrary building blocks, including proteins and colloidal particles.
• Demonstrates accurate prediction of yield curves for known protein complexes.
• Applies the method to model the assembly of colloidal shells.

Conclusions:

• The developed framework provides an efficient and accurate method for predicting self-assembly yields of complex systems.
• This approach extends the predictability of self-assembly to systems with non-spherical and rotationally mobile building blocks.
• Enables precise calculation of yield curves for diverse applications in materials science and biology.