# Atlasing of Assembly Landscapes using Distance Geometry and Graph Rigidity

Source: [Atlasing of Assembly Landscapes using Distance Geometry and Graph Rigidity](<https://www.sota2.com/research/paper/68fa68811e209131cea1c7cd>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T22:38:59.898Z

Authors: Rahul Prabhu, Meera Sitharam, Aysegul Ozkan, Ruijin Wu

Published: 2012-03-16T20:27:51.000Z

## Abstract

We describe a novel geometric methodology for analyzing free-energy and kinetics of assembly driven by short-range pair-potentials in an implicit solvent, and provides illustrations of its unique capabilities. An atlas is a labeled partition of the assembly landscape into a topological roadmap of maximal, contiguous, nearly-equipotential-energy conformational regions or macrostates, together with their neighborhood relationships. The new methodology decouples the roadmap generation from sampling and produces: (1) a query-able atlas of local potential energy minima, their basin structure, energy barriers, and neighboring basins; (2) paths between a specified pair of basins; and (3) approximations of relative path lengths, basin volumes (configurational entropy), and path probabilities. Results demonstrating the core algorithm's capabilities have been generated by a resource-light, opensource software implementation EASAL. EASAL atlases several hundred thousand macrostates in minutes on a standard laptop. Subsequent path and basin computations each take seconds. The core algorithm's correctness, time complexity, and efficiency-accuracy tradeoffs are formally guaranteed using modern geometric constraint systems. The methodology further links geometric variables of the input assembling units to a type of intuitive topological bar-code of the output atlas, which in turn determine stable assembled structures and kinetics. This succinct input-output relationship facilitates reverse analysis, and control towards design. We use the novel convex Cayley (distance-based) parametrization that is unique to assembly, as opposed to folding. Sampling microstates with macrostate-specific Cayley parameters avoids gradient-descent search used by all prevailing methods. This increases sampling efficiency, significantly reduces the number of repeated and discarded samples.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1203.3811>)

[PDF](<https://arxiv.org/pdf/1203.3811.pdf>)