An alternative approach to distance geometry using L∞L∞ distances

A standard task in distance geometry is to calculate one or more sets of Cartesian coordinates for a set of points that satisfy given geometric constraints, such as bounds on some of the L2L2 distances. Using instead L∞L∞ distances is attractive because distance constraints can be expressed as simple linear bounds on coordinates. Likewise, a given matrix of L∞L∞ distances can be rather directly converted to coordinates for the points. It can happen that multiple sets of coordinates correspond precisely to the same matrix of L∞L∞ distances, but the L2L2 distances vary only modestly. Practical examples are given of calculating protein conformations from the sorts of distance constraints that one can obtain from nuclear magnetic resonance experiments.