| Resumo: |
Pattern generation and recognition in 3-D space have been of wide interest in fields varying from atomic and molecular structures to organization of celestial objects. Our thoughts towards investigating patterns (and elucidation of geometrical rules) followed by a known number of points with specific or specified coordinates are guided by the assumption/belief that there must be some thermodynamic and/or kinetic basis leading to the organization of coordinates of the known points. In terms of biomolecular structures, the DNA double helix is one of the strongest examples of such structures with coordinates of atoms in the phosphate backbone and the side-chains provide a helical geometrical configuration. It needs to be appreciated (and emphasized) that, regardless of the system in consideration (e.g. molecular structures or celestial objects), the sample space of known points utilized to investigate underlying patterns is comprised of only remnants or subsets of a larger distribution of points that is either too large to sample, or presence of which has been indicated but not conclusively detected, or presence of which is known to have occurred at an earlier time and some data exists to show disappearance of some points in the sample space due to certain events leading to their deletion. For example, it is now well established that all DNA is not double helical and there are a variety of forms of DNA structures. In this work, I show conclusively it is possible to decipher the origin of apparently random points in space that assemble to give a diversity of structures. I have developed spatial maps for distinguishing different clusters of coordinates originating from well defined geometries. Utilizing the maps, I mathematically prove the existence of a recently discovered universal spatial organization of naturally occurring folded proteins, regardless of their fold or function as categorized by the SCOP classification system. Development of the spatial maps in this work could prove to be a major step in not just advancing our understanding of biomolecular structures, but also arrangement of spatial objects that are apparent in their present coordinate space following some major reorganizing events in the history of our universe.
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