Algorithmic Inference of Cellular Reaction Pathways and Protein Secondary Structure

Abstract

Proteins are biological molecules that carry out a multitude of cellular functions. Their function is largely determined by the shape of the folded molecule within the cell—called their structure—which governs how the protein interacts with other cellular molecules in biochemical reactions. We present algorithms for two fundamental tasks in computational biology that concern proteins and their interactions: pathway inference in metabolic and cell signaling networks, and protein secondary structure prediction. Pathway inference involves determining a set of biological reactions that produces target compounds from source molecules. Two powerful models for pathway inference—metabolic factories, and cell-signaling hyperpaths—both represent networks of cellular reactions using directed hypergraphs. In a directed hypergraph, small molecules, proteins, and their complexes are represented by vertices, and a multiway reaction that creates a set of products from a set of reactants is modeled by a hyperedge, directed from the set of reactants (called its tail) to the set of products (called its head). A factoryis a set of hyperedges specifying reactions that produce target molecules from source compounds, properly accounting for reaction stoichiometry to conserve or not deplete intermediate metabolites. Similarly, a hyperpath is a sequence of hyperedges producing targets from sources, now ignoring stoichiometry, where the tail of each hyperedge must be covered by the heads of hyperedges that precede it in the sequence. For factories, we give the first practical exact algorithm for finding optimal factories that use the fewest possible reactions to produce targets from sources (implemented in Odinn)—which we prove is NP-complete—while for the first time incorporating higher-order models of negative regulation, using mixed-integer linear programming. For hyperpaths, we address the general shortest hyperpath problem that includes cycles, which is NP-complete, and develop the first efficient heuristic (implemented in Hhugin)—which finds provably optimal hyperpaths for the class of singleton-tail hypergraphs—as well as a practical cutting-plane algorithm for optimal hyperpaths using integer linear programming (implemented in Mmunin)—that leverages the first characterization of hyperpaths by source-sink cuts. We demonstrate, through comprehensive experiments over the standard reaction databases, that all these algorithms are remarkably fast in practice, enabling the inference of optimal pathways typically in a few seconds. Protein secondary structure prediction—a fundamental task in many bioinformatics workflows—takes as input the known amino-acid sequence of a protein molecule, and predicts the unknown structural state of each of its amino acids in the folded molecule, from a discrete set of either three or eight possible states. We develop a novel algorithmicapproach for secondary structure prediction (implemented in Nnessy) that uses metricspace nearest-neighbor search to estimate structure-state probabilities, and dynamic programming to compute a maximum-likelihood physically-valid structure prediction that is globally optimal for the entire protein. We also develop several ensemble methods that combine a set of heterogeneous prediction tools to obtain a single prediction output by the ensemble, leveraging feature-based accuracy estimation. In particular, our novel hybrid approach to ensemble prediction (implemented in Ssylla) is the most accurate method currently available: over standard CASP and PDB benchmarks, on average it exceeds the state-of-the-art accuracy for 3-state prediction by nearly 4%, and the stateof-the-art accuracy for 8-state prediction by more than 8%. All these tools are freely available at http://{odinn,hhugin,mmunin,nnessy,ssylla}.cs.arizona.edu.