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Online ISSN 1751-8857 Print ISSN 1751-8849

IET Systems Biology

Volume 6, Issue 6, December 2012

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Volume 6, Issue 6

December 2012

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    • Model of the synthesis of trisporic acid in Mucorales showing bistability
      • Author(s): S. Werner ; A. Schroeter ; C. Schimek ; S. Vlaic ; J. Wöstemeyer ; S. Schuster
      • Source: IET Systems Biology, Volume 6, Issue 6, p. 207 –214
      • DOI:  10.1049/iet-syb.2011.0056
      • Type: Article
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      • p. 207 –214 (8)
        An important substance in the signalling between individuals of Mucor-like fungi is trisporic acid (TA). This compound, together with some of its precursors, serves as a pheromone in mating between (+)- and (−)-mating types. Moreover, intermediates of the TA pathway are exchanged between the two mating partners. Based on differential equations, mathematical models of the synthesis pathways of TA in the two mating types of an idealised Mucor-fungus are here presented. These models include the positive feedback of TA on its own synthesis. The authors compare three sub-models in view of bistability, robustness and the reversibility of transitions. The proposed modelling study showed that, in a system where intermediates are exchanged, a reversible transition between the two stable steady states occurs, whereas an exchange of the end product leads to an irreversible transition. The reversible transition is physiologically favoured, because the high-production state of TA must come to an end eventually. Moreover, the exchange of intermediates and TA is compared with the 3-way handshake widely used by computers linked in a network.
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      Symbolic approach to verification and control of deterministic/probabilistic Boolean networks
      • Author(s): K. Kobayashi  and  K. Hiraishi
      • Source: IET Systems Biology, Volume 6, Issue 6, p. 215 –222
      • DOI:  10.1049/iet-syb.2012.0018
      • Type: Article
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      • p. 215 –222 (8)
        A Boolean network (BN) is well known as one of the models of biological networks such as gene regulatory networks, and has been extensively studied. In this study, for a BN, the verification/control problems are discussed. First, a probabilistic model including both synchronous and asynchronous Boolean dynamics is derived. This model can be generalised as a probabilistic BN. Next, a solution method of the verification/control problems is proposed, based on a probabilistic model checker PRISM. Finally, the PRISM-based method is applied to an apoptosis network and a WNT5A network. The proposed approach provides us an easy and convenient tool for analysis and control of biological networks.
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      Design of biomolecular network modifications to achieve adaptation
      • Author(s): S. Waldherr ; S. Streif ; F. Allgöwer
      • Source: IET Systems Biology, Volume 6, Issue 6, p. 223 –231
      • DOI:  10.1049/iet-syb.2011.0058
      • Type: Article
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      • p. 223 –231 (9)
        A biomolecular network is called adaptive if its output returns to the original value after a transient response even under a persisting stimulus. The conditions for adaptation have been investigated thoroughly with systems theory approaches in the literature and it is easy to check whether they are satisfied in the linear approximation. In contrast, it is in general not easy to modify a non-adaptive network model such that it gains adaptive behaviour, especially for medium- and large-scale networks. The authors present a systematic approach based on the notion of kinetic perturbations to construct adaptive biomolecular network models from non-adaptive ones. An advantage of kinetic perturbations in this application is that neither the stoichiometry nor the steady state of the system is changed. Furthermore, the method covers both parameter and network structure modifications and can be applied to any reaction rate formalism and even to medium-scale or partially unknown models. The approach is exemplified at a small- and a medium-sized biomolecular network, illustrating its potential to systematically evaluate the different network modifications for adaptation. The proposed method will be useful either in iterative model building to construct mathematical models of adaptive biomolecular networks, or in synthetic biology where it can be applied to design or modify synthetic networks for adaptation.
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      Computing enclosures for uncertain biochemical systems
      • Author(s): E. August  and  H. Koeppl
      • Source: IET Systems Biology, Volume 6, Issue 6, p. 232 –240
      • DOI:  10.1049/iet-syb.2011.0091
      • Type: Article
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      • p. 232 –240 (9)
        In this study, the authors present a novel method that provides enclosures for state trajectories of a non-linear dynamical system with uncertainties in initial conditions and parameter values. It is based on solving positivity conditions by means of semi-definite programmes and sum of squares decompositions. The method accounts for the indeterminacy of kinetic parameters, measurement uncertainties and fluctuations in the reaction rates because of extrinsic noise. This is particularly useful in the field of systems biology when one seeks to determine model behaviour quantitatively or, if this is not possible, semi-quantitatively. The authors also demonstrate the significance of the proposed method to model selection in biology. The authors illustrate the applicability of their method on the mitogen-activated protein kinase signalling pathway, which is an important and reoccurring network motif that apparently also plays a crucial role in the development of cancer.
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