In this paper we present a method for the multi-resolution comparison of biomolecular electrostatic potentials without the need for global structural alignment of the biomolecules. The underlying computational geometry algorithm uses multi-resolution attributed contour trees (MACTs) to compare the topological features of volumetric scalar fields. We apply the MACTs to compute electrostatic similarity metrics for a large set of protein chains with varying degrees of sequence, structure, and function similarity. For calibration, we also compute similarity metrics for these chains by a more traditional approach based upon 3D structural alignment and analysis of Carbo similarity indices. Moreover, because the MACT approach does not rely upon pairwise structural alignment, its accuracy and efficiency promises to perform well on future large-scale classification efforts across groups of structurally-diverse proteins. The MACT method discriminates between protein chains at a level comparable to the Carbo similarity index method; i.e., it is able to accurately cluster proteins into functionally-relevant groups which demonstrate strong dependence on ligand binding sites. The results of the analyses are available from the linked web databases
Fig. 1. Visualizations of the hemoglobin molecule undergoing dynamic deformation as oxygen binds to it. (a) A primal space visualization of the first time step with the heme group identified. (b) Visualization of the complementary space of the first time step shows the geometry of the interior. The surface has been made transparent, revealing a large tunnel through the surface (yellow) with many mouths (red). (c) Zooming in on the heme group reveals the structure of space around it while oxygen is bound. (d-f) The corresponding images of (a-c) for the final time step. Complementary space has changed dramatically both in the interior volume and near the heme group, though this is not evident from the primal space visualizations. Comparing (c) and (f), we observe that the connectivity of the mouth of the tunnel near the heme group has changed, illustrating the time-dependency of the topological features of complementary space. We quantify and discuss this example further in Section 3.5.
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