A Surface Measure for Probabilistic Structural Computations

Jeanette P. Schmidt, Cheng C. Chen, Jonathan L. Cooper, and Russ B. Altman

Computing three-dimensional structures from sparse experimental constraints requires methods for combining heterogeneous sources of information, such as distances, angles, and measures of total volume, shape, and surface. For some types of information, such as distances between atoms, numerous methods are available for computing structures that satisfy the provided constraints. It is more difficult, however, to use information about the degree to which an atom is on the surface or buried as a useful constraint during structure computations. Surface measures have been used as accept/reject criteria for previously computed structures, but this is not an efficient strategy. In this paper, we investigate the efficacy of applying a surface measure in the computation of molecular structure, using a method of probabilistic least square computations which facilitates the introduction of multiple, noisy, heterogeneous data sources. For this purpose, we introduce a simple purely geometrical measure of surface proximity called max/real conic view (MCV). MCV is efficiently computable and differentiable, and is hence well suited to driving a structural optimization method based, in part, on surface data. As an initial validation, we show that MCV correlates well with known measures for total exposed surface area. We use this measure in our experiments to show that information about surface proximity (derived from theory or experiment, for example) can be added to a set of distance measurements to increase significantly the quality of the computed structure. In particular, when 30 to 50 percent of all possible shortrange distances are provided, the addition of surface information improves the quality of the computed structure (as measured by RMS fit) by as much as 80 percent. Our results demonstrate that knowledge of which atoms are on the surface and which are buried can be used as a powerful constraint in estimating molecular structure.

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