Atlasing of Assembly Landscapes using Distance Geometry and Graph Rigidity

Area of Science:

• Computational Chemistry and Physics
• Biophysics
• Materials Science

Background:

• Analyzing the free energy and kinetics of molecular assembly is crucial for understanding biological processes and designing new materials.
• Existing methods often struggle with computational efficiency and decoupling landscape exploration from sampling.
• Short-range pair-potentials in implicit solvents are common models for assembly but present analytical challenges.

Purpose of the Study:

• To introduce a novel geometric methodology for analyzing the free energy and kinetics of assembly processes.
• To develop a computational framework that efficiently generates a comprehensive 'atlas' of the assembly landscape.
• To demonstrate the methodology's capability in predicting stable structures and assembly dynamics, facilitating design.

Main Methods:

• Developed a geometric methodology to partition the assembly landscape into contiguous, nearly-equipotential-energy regions (macrostates).
• Implemented the methodology in the open-source software EASAL (Efficient Atlasing and Search of Assembly Landscapes).
• Utilized a novel theory of convex Cayley parametrizations to enhance sampling efficiency and decouple roadmap generation from sampling.

Main Results:

• EASAL efficiently generates a queryable atlas of local energy minima, basin structures, and neighboring relationships.
• The software provides paths between basins, estimates relative path lengths, basin volumes (configurational entropy), and path probabilities.
• Demonstrated high computational efficiency, analyzing hundreds of thousands of macrostates in minutes on a laptop, with parallelization offering further speedup.

Conclusions:

• The novel geometric methodology and EASAL software provide an efficient and accurate tool for analyzing assembly landscapes.
• The approach successfully links the shape of assembling units to assembly characteristics, enabling reverse analysis for design.
• This method complements existing techniques like Molecular Dynamics and Monte Carlo, offering significant advantages in sampling efficiency.