Probabilistic Interaction Network of Evidence Algorithm and its Application to Complete Labeling of Peak Lists from Protein NMR Spectroscopy

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Abstract
The process of assigning a finite set of tags or labels to a collection of observations, subject to side conditions, is notable for its computational complexity. This labeling paradigm is of theoretical and practical relevance to a wide range of biological applications, including the analysis of data from DNA microarrays, metabolomics experiments, and biomolecular nuclear magnetic resonance (NMR) spectroscopy. We present a novel algorithm, called Probabilistic Interaction Network of Evidence (PINE), that achieves robust, unsupervised probabilistic labeling of data. The computational core of PINE uses estimates of evidence derived from empirical distributions of previously observed data, along with consistency measures, to drive a fictitious system M with Hamiltonian H to a quasi-stationary state that produces probabilistic label assignments for relevant subsets of the data. We demonstrate the successful application of PINE to a key task in protein NMR spectroscopy: that of converting peak lists extracted from various NMR experiments into assignments associated with probabilities for their correctness. This application, called PINE-NMR, is available from a freely accessible computer server (http://pine.nmrfam.wisc.edu). The PINE-NMR server accepts as input the sequence of the protein plus user-specified combinations of data corresponding to an extensive list of NMR experiments; it provides as output a probabilistic assignment of NMR signals (chemical shifts) to sequence-specific backbone and aliphatic side chain atoms plus a probabilistic determination of the protein secondary structure. PINE-NMR can accommodate prior information about assignments or stable isotope labeling schemes. As part of the analysis, PINE-NMR identifies, verifies, and rectifies problems related to chemical shift referencing or erroneous input data. PINE-NMR achieves robust and consistent results that have been shown to be effective in subsequent steps of NMR structure determination. What mathematicians call the “labeling problem” underlies difficulties in interpreting many classes of complex biological data. To derive valid inferences from multiple, noisy datasets, one must consider all possible combinations of the data to find the solution that best matches the experimental evidence. Exhaustive searches totally outstrip current computer resources, and, as a result, it has been necessary to resort to approximations such as branch and bound or Monte Carlo simulations, which have the disadvantages of being limited to use in separate steps of the analysis and not providing the final results in a probabilistic fashion that allows the quality of the answers to be evaluated. The Probabilistic Interaction Network of Evidence (PINE) algorithm that we present here offers a general solution to this problem. We have demonstrated the usefulness of the PINE approach by applying it to one of the major bottlenecks in NMR spectroscopy. The PINE-NMR server takes as input the sequence of a protein and the peak lists from one or more multidimensional NMR experiments and provides as output a probabilistic assignment of the NMR signals to specific atoms in the protein's covalent structure and a self-consistent probabilistic analysis of the protein's secondary structure.