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  1. Signaling and metabolic pathways, which consist of a series of reactions producing target molecules from source compounds, are cornerstones of cellular biology. The cellular reaction networks containing such pathways can be precisely modeled by directed hypergraphs, where each reaction corresponds to a hyperedge, directed from its set of reactants to its set of products. Given such a network represented by a directed hypergraph, inferring the most likely set of reactions that produce a given target from a given set of sources corresponds to finding a shortest hyperpath, which is NP-complete. The best methods currently available for shortest hyperpaths either offer no guarantee of optimality, or exclude hyperpaths containing cycles even though cycles are abundant in real biological pathways. We derive a novel graph-theoretic characterization of hyperpaths, leveraged in a new formulation of the general shortest hyperpath problem as an integer linear program that for the first time handles hyperpaths containing cycles, and present a novel cutting-plane algorithm that can solve this integer program to optimality in practice. This represents a major advance over the best prior exact algorithm, which was limited to acyclic hyperpaths (and hence fails to find a solution for the many biological instances where all hyperpaths are in fact cyclic). In comprehensive experiments over thousands of instances from the standard NCI-PID and Reactome databases, we demonstrate that our cutting-plane algorithm quickly finds an optimal hyperpath, with a median running-time of under ten seconds and a maximum time of around thirty minutes, even on large instances with many thousands of reactions. Source code implementing our cutting-plane algorithm for shortest hyperpaths in a new tool called Mmunin is available free for research use at http://mmunin.cs.arizona.edu. 
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    Free, publicly-accessible full text available April 1, 2024
  2. Abstract Background Cell signaling pathways, which are a series of reactions that start at receptors and end at transcription factors, are basic to systems biology. Properly modeling the reactions in such pathways requires directed hypergraphs , where an edge is now directed between two sets of vertices. Inferring a pathway by the most parsimonious series of reactions corresponds to finding a shortest hyperpath in a directed hypergraph, which is NP-complete. The current state-of-the-art for shortest hyperpaths in cell signaling hypergraphs solves a mixed-integer linear program to find an optimal hyperpath that is restricted to be acyclic, and offers no efficiency guarantees. Results We present, for the first time, a heuristic for general shortest hyperpaths that properly handles cycles , and is guaranteed to be efficient . We show the heuristic finds provably optimal hyperpaths for the class of singleton-tail hypergraphs, and also give a practical algorithm for tractably generating all source-sink hyperpaths. The accuracy of the heuristic is demonstrated through comprehensive experiments on all source-sink instances from the standard NCI-PID and Reactome pathway databases, which show it finds a hyperpath that matches the state-of-the-art mixed-integer linear program on overĀ 99% of all instances that are acyclic. On instances where only cyclic hyperpaths exist, the heuristic surpasses the state-of-the-art, which finds no solution; on every such cyclic instance, enumerating all source-sink hyperpaths shows the solution found by the heuristic was in fact optimal . Conclusions The new shortest hyperpath heuristic is both fast and accurate . This makes finding source-sink hyperpaths, which in general may contain cycles, now practical for real cell signaling networks. Availability Source code for the hyperpath heuristic in a new tool we callĀ  (as well as for hyperpath enumeration, and all dataset instances) is available free for non-commercial use at . 
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  3. Abstract Motivation

    A factory in a metabolic network specifies how to produce target molecules from source compounds through biochemical reactions, properly accounting for reaction stoichiometry to conserve or not deplete intermediate metabolites. While finding factories is a fundamental problem in systems biology, available methods do not consider the number of reactions used, nor address negative regulation.

    Methods

    We introduce the new problem of finding optimal factories that use the fewest reactions, for the first time incorporating both first- and second-order negative regulation. We model this problem with directed hypergraphs, prove it is NP-complete, solve it via mixed-integer linear programming, and accommodate second-order negative regulation by an iterative approach that generates next-best factories.

    Results

    This optimization-based approach is remarkably fast in practice, typically finding optimal factories in a few seconds, even for metabolic networks involving tens of thousands of reactions and metabolites, as demonstrated through comprehensive experiments across all instances from standard reaction databases.

    Availability and implementation

    Source code for an implementation of our new method for optimal factories with negative regulation in a new tool called Odinn, together with all datasets, is available free for non-commercial use at http://odinn.cs.arizona.edu.

     
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  4. Carbone, Alessandra ; El-Kebir, Mohammed (Ed.)
    Cell signaling pathways, which are a series of reactions that start at receptors and end at transcription factors, are basic to systems biology. Properly modeling the reactions in such pathways requires directed hypergraphs, where an edge is now directed between two sets of vertices. Inferring a pathway by the most parsimonious series of reactions then corresponds to finding a shortest hyperpath in a directed hypergraph, which is NP-complete. The state of the art for shortest hyperpaths in cell-signaling hypergraphs solves a mixed-integer linear program to find an optimal hyperpath that is restricted to be acyclic, and offers no efficiency guarantees. We present for the first time a heuristic for general shortest hyperpaths that properly handles cycles, and is guaranteed to be efficient. Its accuracy is demonstrated through exhaustive experiments on all instances from the standard NCI-PID and Reactome pathway databases, which show the heuristic finds a hyperpath that matches the state-of-the-art mixed-integer linear program on over 99% of all instances that are acyclic. On instances where only cyclic hyperpaths exist, the heuristic surpasses the state-of-the-art, which finds no solution; on every such cyclic instance, enumerating all possible hyperpaths shows that the solution found by the heuristic is in fact optimal. 
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