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Online ISSN 1751-8857 Print ISSN 1751-8849

IET Systems Biology

Volume 3, Issue 1, January 2009

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Volume 3, Issue 1

January 2009

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    • Nested uncertainties in biochemical models
      • Author(s): J. Schaber ; W. Liebermeister ; E. Klipp
      • Source: IET Systems Biology, Volume 3, Issue 1, p. 1 –9
      • DOI:  10.1049/iet-syb:20070042
      • Type: Article
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      • p. 1 –9 (9)
        Dynamic modelling of biochemical reaction networks has to cope with the inherent uncertainty about biological processes, concerning not only data and parameters but also kinetics and structure. These different types of uncertainty are nested within each other: uncertain network structures contain uncertain reaction kinetics, which in turn are governed by uncertain parameters. Here, the authors review some issues arising from such uncertainties and sketch methods, solutions and future directions to deal with them.
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      Optimal experimental design with the sigma point method
      • Author(s): R. Schenkendorf ; A. Kremling ; M. Mangold
      • Source: IET Systems Biology, Volume 3, Issue 1, p. 10 –23
      • DOI:  10.1049/iet-syb:20080094
      • Type: Article
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      • p. 10 –23 (14)
        Using mathematical models for a quantitative description of dynamical systems requires the identification of uncertain parameters by minimising the difference between simulation and measurement. Owing to the measurement noise also, the estimated parameters possess an uncertainty expressed by their variances. To obtain highly predictive models, very precise parameters are needed. The optimal experimental design (OED) as a numerical optimisation method is used to reduce the parameter uncertainty by minimising the parameter variances iteratively. A frequently applied method to define a cost function for OED is based on the inverse of the Fisher information matrix. The application of this traditional method has at least two shortcomings for models that are nonlinear in their parameters: (i) it gives only a lower bound of the parameter variances and (ii) the bias of the estimator is neglected. Here, the authors show that by applying the sigma point (SP) method a better approximation of characteristic values of the parameter statistics can be obtained, which has a direct benefit on OED. An additional advantage of the SP method is that it can also be used to investigate the influence of the parameter uncertainties on the simulation results. The SP method is demonstrated for the example of a widely used biological model.
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      Mixed-integer nonlinear optimisation approach to coarse-graining biochemical networks
      • Author(s): M.R. Maurya ; S.J. Bornheimer ; V. Venkatasubramanian ; S. Subramaniam
      • Source: IET Systems Biology, Volume 3, Issue 1, p. 24 –39
      • DOI:  10.1049/iet-syb:20080098
      • Type: Article
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      • p. 24 –39 (16)
        Quantitative modelling and analysis of biochemical networks is challenging because of the inherent complexities and nonlinearities of the system and the limited availability of parameter values. Even if a mathematical model of the network can be developed, the lack of large-scale good-quality data makes accurate estimation of a large number of parameters impossible. Hence, coarse-grained models (CGMs) consisting of essential biochemical mechanisms are more suitable for computational analysis and for studying important systemic functions. The central question in constructing a CGM is which mechanisms should be deemed ‘essential’ and which can be ignored. Also, how should parameter values be defined when data are sparse? A mixed-integer nonlinear-programming (MINLP) based optimisation approach to coarse-graining is presented. Starting with a detailed biochemical model with associated computational details (reaction network and mathematical description) and data on the biochemical system, the structure and the parameters of a CGM can be determined simultaneously. In this optimisation problem, the authors use a genetic algorithm to simultaneously identify parameter values and remove unimportant reactions. The methodology is exemplified by developing two CGMs for the GTPase-cycle module of M1 muscarinic acetylcholine receptor, Gq, and regulator of G protein signalling 4 [RGS4, a GTPase-activating protein (GAP)] starting from a detailed model of 48 reactions. Both the CGMs have only 17 reactions, fit experimental data well and predict, as does the detailed model, four limiting signalling regimes (LSRs) corresponding to the extremes of receptor and GAP concentration. The authors demonstrate that coarse-graining, in addition to resulting in a reduced-order model, also provides insights into the mechanisms in the network. The best CGM obtained for the GTPase cycle also contains an unconventional mechanism and its predictions explain an old problem in pharmacology, the biphasic (bell-shaped) response to certain drugs. The MINLP methodology is broadly applicable to larger and complex (dense) biochemical modules.
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      Proper lumping in systems biology models
      • Author(s): A. Dokoumetzidis  and  L. Aarons
      • Source: IET Systems Biology, Volume 3, Issue 1, p. 40 –51
      • DOI:  10.1049/iet-syb:20070055
      • Type: Article
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      • p. 40 –51 (12)
        An algorithm for automatic order reduction of models defined by large systems of differential equations is presented. The algorithm was developed with systems biology models in mind and the motivation behind it is to develop mechanistic pharmacokinetic/pharmacodynamic models from already available systems biology models. The approach used for model reduction is proper lumping of the system's states and is based on a search through the possible combinations of lumps. To avoid combinatorial explosion, a heuristic, greedy search strategy is employed and comparison with the full exhaustive search provides evidence that it performs well. The method takes advantage of an apparent property of this kind of systems that lumps remain consistent over different levels of order reduction. Advantages of the method presented include: the variables and parameters of the reduced model retain a specific physiological meaning; the algorithm is automatic and easy to use; it can be used for nonlinear models and can handle parameter uncertainty and constraints. The algorithm was applied to a model of NF-κB signalling pathways in order to demonstrate its use and performance. Significant reduction was achieved for the example model, while agreement with the original model was proportional to the size of the reduced model, as expected. The results of the model reduction were compared with a published, intuitively reduced model of NF-κB signalling pathways and were found to be in agreement, in terms of the identified key species for the system's kinetic behaviour. The method may provide useful insights which are complementary to the intuitive reduction approach, especially in large systems.
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      Moment-closure approximations for mass-action models
      • Author(s): C.S. Gillespie
      • Source: IET Systems Biology, Volume 3, Issue 1, p. 52 –58
      • DOI:  10.1049/iet-syb:20070031
      • Type: Article
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      • p. 52 –58 (7)
        Although stochastic population models have proved to be a powerful tool in the study of process generating mechanisms across a wide range of disciplines, all too often the associated mathematical development involves nonlinear mathematics, which immediately raises difficult and challenging analytic problems that need to be solved if useful progress is to be made. One approximation that is often employed to estimate the moments of a stochastic process is moment closure. This approximation essentially truncates the moment equations of the stochastic process. A general expression for the marginal- and joint-moment equations for a large class of stochastic population models is presented. The generalisation of the moment equations allows this approximation to be applied easily to a wide range of models. Software is available from http://pysbml.googlecode.com/ to implement the techniques presented here.
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