{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/atlasing-of-assembly-landscapes-using","title":"Atlasing of Assembly Landscapes using Distance Geometry and Graph Rigidity","arxiv_id":"1203.3811","date":"2012-03-16","proceeding":null,"authors":["Rahul Prabhu","Meera Sitharam","Aysegul Ozkan","Ruijin Wu"],"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.","url_abs":"https://arxiv.org/abs/1203.3811v3","url_pdf":"https://arxiv.org/pdf/1203.3811v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"atlasing-of-assembly-landscapes-using","repo_url":"https://bitbucket.org/geoplexity/easal","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}