A probabilistic approach to determining biological structure: integrating uncertain data sources

Modeling the structure of biological molecules is critical for understanding how these structures perform their function, and for designing compounds to modify or enhance this function (for medicinal or industrial purposes). The determination of molecular structure involves defining three-dimensional positions for each of the constituent atoms using a variety of experimental, theoretical and empirical data sources. Unfortunately, each of these data sources can be noisy or not available in sufficient abundance to determine the precise position of each atom. Instead, some atomic positions are precisely defined by the data, and others are poorly defined. An understanding of structural uncertainty is critical for properly interpreting structural models. We have developed a Bayesian approach for determining the coordinates of atoms in a three-dimensional space. Our algorithm takes as input a set of probabilistic constraints on the coordinates of the atoms, and an a priori distribution for each atom location. The output is a maximum a posteriori (MAP) estimate of the location of each atom. We introduce constraints as updates to the prior distributions. In this paper, we describe the algorithm and show its performance on three data sets. The first data set is synthetic and illustrates the convergence properties of the method. The other data sets comprise real biological data for a protein (the trp repressor molecule) and a nucleic acid (the transfer RNA fold). Finally, we describe how we have begun to extend the algorithm to make it suitable for non-Gaussian constraints. The determination of molecular structure is critical for many pursuits in biomedicine and industry, including the study of how molecules perform their function and the design of drugs to remove, modify or enhance this function. It is estimated that there are about 100,000 different proteins in the human body, but only a few hundred structures are known and stored in the protein structural data bank 1977). As the human genome project produces large amounts of information about the atomic makeup of individual molecules, it becomes critical to devise methods for estimating molecular structure—that is, for determining how the atoms within molecules arrange themselves in order to form three-dimensional structures. Biological macromolecules can be divided into proteins and nucleic acids (Stryer, 1988). Nucleic acids, such as DNA and RNA, encode the genetic blueprints for all living organisms as a linear sequence of four chemical building blocks. Although the structure of nucleic acids was once thought to be uniform and geared …