Polynomial time algorithms to determine weakly reversible realizations of chemical reaction networks

Weak reversibility is a crucial structural property of chemical reaction networks (CRNs) with mass action kinetics, because it has major implications related to the existence, uniqueness and stability of equilibrium points and to the boundedness of solutions. In this paper, we present two new algorithms to find dynamically equivalent weakly reversible realizations of a given CRN. They are based on linear programming and thus have polynomial time-complexity. Hence, these algorithms can deal with large-scale biochemical reaction networks, too. Furthermore, one of the methods is able to deal with linearly conjugate networks, too. © 2014 Springer International Publishing Switzerland

Reachability Analysis of Low-Order Discrete State Reaction Networks Obeying Conservation Laws

In this paper we study the reachability problem of sub- and superconservative discrete state chemical reaction networks (d-CRNs). It is known that a subconservative network has bounded reachable state space, while that of a superconservative one is unbounded. The reachability problem of superconservative reaction networks is traced back to the reachability of subconservative ones. We consider network structures composed of reactions having at most one input and one output species beyond the possible catalyzers. We give a proof that, assuming all the reactions are charged in the initial and target states, the reachability problems of sub- and superconservative reaction networks are equivalent to the existence of nonnegative integer solution of the corresponding d-CRN state equations. Using this result, the reachability problem is reformulated as an Integer Linear Programming (ILP) feasibility problem. Therefore, the number of feasible trajectories satisfying the reachability relation can be counted in polynomial time in the number of species and in the distance of initial and target states, assuming fixed number of reactions in the system

Structural identifiability of dynamic systems biology models

22 páginas, 5 figuras, 2 tablas.-- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.A powerful way of gaining insight into biological systems is by creating a nonlinear differential equation model, which usually contains many unknown parameters. Such a model is called structurally identifiable if it is possible to determine the values of its parameters from measurements of the model outputs. Structural identifiability is a prerequisite for parameter estimation, and should be assessed before exploiting a model. However, this analysis is seldom performed due to the high computational cost involved in the necessary symbolic calculations, which quickly becomes prohibitive as the problem size increases. In this paper we show how to analyse the structural identifiability of a very general class of nonlinear models by extending methods originally developed for studying observability. We present results about models whose identifiability had not been previously determined, report unidentifiabilities that had not been found before, and show how to modify those unidentifiable models to make them identifiable. This method helps prevent problems caused by lack of identifiability analysis, which can compromise the success of tasks such as experiment design, parameter estimation, and model-based optimization. The procedure is called STRIKE-GOLDD (STRuctural Identifiability taKen as Extended-Generalized Observability with Lie Derivatives and Decomposition), and it is implemented in a MATLAB toolbox which is available as open source software. The broad applicability of this approach facilitates the analysis of the increasingly complex models used in systems biology and other areasAFV acknowledges funding from the Galician government (Xunta de Galiza, Consellería de Cultura, Educación e Ordenación Universitaria http://www.edu.xunta.es/portal/taxonomy/term/206) through the I2C postdoctoral program, fellowship ED481B2014/133-0. AB and AFV were partially supported by grant DPI2013-47100-C2-2-P from the Spanish Ministry of Economy and Competitiveness (MINECO). AFV acknowledges additional funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 686282 (CanPathPro). AP was partially supported through EPSRC projects EP/M002454/1 and EP/J012041/1.Peer reviewe

A computational approach to the structural analysis of uncertain kinetic systems

A computation-oriented representation of uncertain kinetic systems is introduced and analysed in this paper. It is assumed that the monomial coefficients of the ODEs belong to a polytopic set, which defines a set of dynamical systems for an uncertain model. An optimization-based computation model is proposed for the structural analysis of uncertain models. It is shown that the so-called dense realization containing the maximal number of reactions (directed edges) is computable in polynomial time, and it forms a superstructure among all the possible reaction graphs corresponding to an uncertain kinetic model, assuming a fixed set of complexes. The set of core reactions present in all reaction graphs of an uncertain model is also studied. Most importantly, an algorithm is proposed to compute all possible reaction graph structures for an uncertain kinetic model