Non-Finito: Michelangelo's Dilemma

"For Michelangelo, artistic vision was something well-defined and clear. It was the job of the artist to free the form that already existed within the block of stone. By simply removing that which was not necessary, his works' of art took on a life of their own. His genius lay then in knowing when his work was complete. In the world of protein folding, upon which all life depends, the relation between structure and functional form is unclear to us computationally. At no point is the precise scale, at which life springs forth, resolved. In the series of images presented, each atom's 3d-coordinate for a protease inhibitor, protein 1acb, is separated using a Voronoi diagram. A Voronoi diagram creates unique polygonal cells, whose 'generating point center' is closer to its point than any other cell (tesselation). Neighboring polygonal cells can be grouped to describe possible functional relationships of the protein, without the need for specific cutoff distances. Now imagine Michelangelo picking up a tool, the alpha-complex, as he stares at his block of stone (first image). A large alpha provides coarse resolution, and groups many points into large cells. As this alpha is reduced, the great artist can begin to reach between more sets of points (subsequent images), until all that remains is simply the original coordinates. At either a coarse or fine-grained scale the exact functional form cannot be visualized. The problem lies in knowing at what resolution, or set of resolutions, the process is complete. Each image shown contains some mislabeling error, of inaccurate unions or separations, and thus the moment at which protein structure takes functional form remains an open problem."