Unassigned distance geometry and the Buckminsterfullerene

TL;DR

This paper demonstrates that the structure of Buckminsterfullerene can be reconstructed using mathematical programming and standard solvers, offering an alternative to heuristic algorithms for shape determination from limited distance data.

Contribution

It introduces a novel approach applying mathematical programming to unassigned distance geometry problems, specifically reconstructing Buckminsterfullerene without complex heuristics.

Findings

Successful reconstruction of Buckminsterfullerene structure using mathematical programming.

Shows that standard solver software suffices for accurate shape determination.

Provides an alternative to heuristic algorithms for molecular structure reconstruction.

Abstract

The Buckminsterfullerene is an inorganic molecule consisting of 60 carbon atoms in the shape of a soccer ball. It was used in [Juhas et al., Nature 2006] to showcase algorithms that find the correct shape of a protein from limited data (length of inter-atomic distances) without any further chemical experiment: in that case, by means of a complicated constructive heuristic based on genetic algorithms. In this paper we show that we can reconstruct the Buckminsterfullerene structure by means of mathematical programming, standard solver software, and little else.