Designing attractive models via automated identification of chaotic and oscillatory dynamical regimes

Silk, Daniel; Kirk, Paul; Barnes, C.; Toni, Tina; Rose, Anna; Moon, Simon; Dallman, Margaret J.; Stumpf, Michael

doi:10.1038/ncomms1496

Cited by 59 publications

(19 citation statements)

References 46 publications

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“…Oscillations observed in the Hes1 system [42] might be connected with formation of spatial patterns during development. The Hes1 oscillator can be modelled by a simple three-component ODE model [43] as shown in Figure 4 A. This model contains parameters, , , , and , and species: Hes 1 mRNA, , Hes 1 nuclear protein, , and Hes 1 cytosolic protein, .…”

Section: Resultsmentioning

confidence: 99%

Maximizing the Information Content of Experiments in Systems Biology

et al. 2013

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Our understanding of most biological systems is in its infancy. Learning their structure and intricacies is fraught with challenges, and often side-stepped in favour of studying the function of different gene products in isolation from their physiological context. Constructing and inferring global mathematical models from experimental data is, however, central to systems biology. Different experimental setups provide different insights into such systems. Here we show how we can combine concepts from Bayesian inference and information theory in order to identify experiments that maximize the information content of the resulting data. This approach allows us to incorporate preliminary information; it is global and not constrained to some local neighbourhood in parameter space and it readily yields information on parameter robustness and confidence. Here we develop the theoretical framework and apply it to a range of exemplary problems that highlight how we can improve experimental investigations into the structure and dynamics of biological systems and their behavior.

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Section: Resultsmentioning

confidence: 99%

Maximizing the Information Content of Experiments in Systems Biology

et al. 2013

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“…We demonstrate the power of our method on two small oscillatory reaction systems, the p53-Mdm2 negative feedback loop in tumour suppression and the Hes1 system in embryogenesis and on a complex twocompartment model of ERK1/2 phosphorylation dynamics. As the framework, like the original MEA, is completely automated and developed in a user-friendly manner, it is suitable for the analysis of any stochastic models without thorough understanding of the algorithm and also can serve as a starting point for parameter inference [27][28][29][30] and model selection, 31,32 distribution reconstruction, 33 sensitivity analysis, 34 experimental design, 35,36 and design of dynamical systems with desired qualitative 37 and quantitative 38,39 behaviour.…”

Section: Introductionmentioning

confidence: 99%

Multivariate moment closure techniques for stochastic kinetic models

Lakatos

Ale

Kirk

et al. 2015

The Journal of Chemical Physics

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A study of the accuracy of moment-closure approximations for stochastic chemical kinetics J. Chem. Phys. 136, 154105 (2012) Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs. C 2015 AIP Publishing LLC.[http://dx

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“…Here, we return to the parameter estimation problem. But rather than looking for quantitative agreement between data and a mathematical model, we seek to determine a set of parameters that gives rise to certain type of qualitative behaviour [32]. One way of specifying or encoding qualitative behaviour of a dynamical system is via its Lyapunov spectrum [49].…”

Section: Qualitative Design With the Unscented Kalman Filtermentioning

confidence: 99%

“…), can be arbitrarily complex (subject to the usual regularity conditions) and along with the data, D-which other than an observed dataset, may also be any function of the data, or even expected or desired qualitative/ quantitative characteristics of the system's behaviour [32]-may be chosen to explore various features of interest of the dynamical system. This great, and thus far underexplored, flexibility allows us to use the UKF to determine a set of parameters commensurate with the objectives set out prior to the analysis and encoded in D. In addition to data and conventional surrogate data (e.g.…”

Section: Unscented Kalman Filter For Parameter Inferencementioning

confidence: 99%

Bayesian design strategies for synthetic biology

2011

Self Cite

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We discuss how statistical inference techniques can be applied in the context of designing novel biological systems. Bayesian techniques have found widespread application and acceptance in the systems biology community, where they are used for both parameter estimation and model selection. Here we show that the same approaches can also be used in order to engineer synthetic biological systems by inferring the structure and parameters that are most likely to give rise to the dynamics that we require a system to exhibit. Problems that are shared between applications in systems and synthetic biology include the vast potential spaces that need to be searched for suitable models and model parameters; the complex forms of likelihood functions; and the interplay between noise at the molecular level and nonlinearity in the dynamics owing to often complex feedback structures. In order to meet these challenges, we have to develop suitable inferential tools and here, in particular, we illustrate the use of approximate Bayesian computation and unscented Kalman filtering-based approaches. These partly complementary methods allow us to tackle a number of recurring problems in the design of biological systems. After a brief exposition of these two methodologies, we focus on their application to oscillatory systems.

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Designing attractive models via automated identification of chaotic and oscillatory dynamical regimes

Cited by 59 publications

References 46 publications

Maximizing the Information Content of Experiments in Systems Biology

Maximizing the Information Content of Experiments in Systems Biology

Multivariate moment closure techniques for stochastic kinetic models

Bayesian design strategies for synthetic biology

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