Algorithmic approaches for computing elementary modes in large biochemical reaction networks.
ABSTRACT The concept of elementary (flux) modes provides a rigorous description of pathways in metabolic networks and proved to be valuable in a number of applications. However, the computation of elementary modes is a hard computational task that gave rise to several variants of algorithms during the last years. This work brings substantial progresses to this issue. The authors start with a brief review of results obtained from previous work regarding (a) a unified framework for elementary-mode computation, (b) network compression and redundancy removal and (c) the binary approach by which elementary modes are determined as binary patterns reducing the memory demand drastically without loss of speed. Then the authors will address herein further issues. First, a new way to perform the elementarity tests required during the computation of elementary modes which empirically improves significantly the computation time in large networks is proposed. Second, a method to compute only those elementary modes where certain reactions are involved is derived. Relying on this method, a promising approach for computing EMs in a completely distributed manner by decomposing the full problem in arbitrarity many sub-tasks is presented. The new methods have been implemented in the freely available software tools FluxAnalyzer and Metatool and benchmark tests in realistic networks emphasise the potential of our proposed algorithms.
Article: How Good are Convex Hull Algorithms?[show abstract] [hide abstract]
ABSTRACT: A convex polytope is the bounded intersection of finite set H of halfspaces. A classic theorem of convexity theory is that every convex polyhedron can be expressed as the convex hull of its set V of vertices. There are three closely related computational problems related to the two descriptions of a polytope. The vertex enumeration problem is to compute V from H. The convex hull problem it to compute H from V. The polytope verification problem is to decide whether a given vertex description and halfspace description define the same polytope. The first two problems are essentially equivalent under point/hyperplane duality. It is an open problem whether any of these problems can be solved in time polynomial in jHj + jVj. In this paper we describe hard polytopes for convex hull algorithms based on pivoting , those based on triangulation, and for some insertion algorithms. 1 Introduction Although the simplex method had long been regarded as a practical and efficient algorithm fo...06/2000;
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ABSTRACT: The analysis of a chemical reaction network by elementary flux modes is a very elegant method to deal with the stationary states of the system. Each steady state of the network can be represented as a convex combination of these modes. They are elements of the nullspace of the stoichiometry matrix due to the imposed steady-state condition. We propose an approach, which first derives the basis vectors of the nullspace and then calculates the elementary modes by an apt linear combination of the basis vectors. The algorithm exploits the special representation of the nullspace matrix in the space of flows and the fact that elementary modes consist of a minimal set of flows. These two ingredients lead to construction rules, which diminish the combinatorial possibilities to design elementary modes and, hence, reduce the computational costs. Further, we show that the algorithm also accounts for reversible reactions. If a system includes reversible reactions, it can be transformed into an unidirectional network by considering the forward and the backward flow separately. We derive a projection operator, which reveals the interrelationship between the two representations.Journal of Physical Chemistry B - J PHYS CHEM B. 01/2004; 108(7).