Introduction to Focus Issue: Dynamics in Systems Biology

Brackley, Chris A.; Ebenhöh, Oliver; Grebogi, Celso; Kurths, Jürgen; Moura, Ana Silvia Alves Meira Tavares; Romano, M. Carmen; Thiel, Marco

doi:10.1063/1.3530126

Cited by 10 publications

(4 citation statements)

References 24 publications

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“…These building blocks are composed of genes and proteins and can often act as various kinds of "switches" inside a more complex system. Dynamical systems methods for these systems biology questions are a highly active research area [20]. Low-dimensional dynamical systems have been proposed to model the smallest units in a molecular network.…”

Section: A Switch In Systems Biologymentioning

confidence: 99%

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A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications

2012

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Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find earlywarning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.

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Section: A Switch In Systems Biologymentioning

confidence: 99%

“…Lemma 4.7 ([57], p. [20][21][22][23][24][25]. Suppose the stochastic differential equation dX s = α(X s , s)ds +…”

Section: Sample Paths and Moments For Stochastic Fast-slow Systemsmentioning

confidence: 99%

A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications

2012

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“…Systems of nonlinear differential equations are used throughout biology to model the behavior of complex, dynamical systems. These models have proven particularly useful in systems biology for describing networks of biomolecular interactions 1 . Often the utility of the model depends on being able to estimate a set of unknown parameters, which is typically done by collecting data from the physical system and finding the best-fit parameters.…”

Section: Introductionmentioning

confidence: 99%

Prediction uncertainty and optimal experimental design for learning dynamical systems

Letham

Rudin

et al. 2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Dynamical systems are frequently used to model biological systems. When these models are fit to data, it is necessary to ascertain the uncertainty in the model fit. Here, we present prediction deviation, a metric of uncertainty that determines the extent to which observed data have constrained the model's predictions. This is accomplished by solving an optimization problem that searches for a pair of models that each provides a good fit for the observed data, yet has maximally different predictions. We develop a method for estimating a priori the impact that additional experiments would have on the prediction deviation, allowing the experimenter to design a set of experiments that would most reduce uncertainty. We use prediction deviation to assess uncertainty in a model of interferon-alpha inhibition of viral infection, and to select a sequence of experiments that reduces this uncertainty. Finally, we prove a theoretical result which shows that prediction deviation provides bounds on the trajectories of the underlying true model. These results show that prediction deviation is a meaningful metric of uncertainty that can be used for optimal experimental design.

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“…From a physics point of view, biological and physical processes start to converge, so that to describe biochemical computation, concepts from physics can be borrowed and applied (see e.g. Brackley et al, 2010;Ellner and Guckenheimer, 2006;Furusawa and Kaneko, 2012).…”

Section: Introductionmentioning

confidence: 99%

Universal dynamical properties preclude standard clustering in a large class of biochemical data

Gomez

Stoop

2014

Bioinformatics

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Introduction to Focus Issue: Dynamics in Systems Biology

Cited by 10 publications

References 24 publications

A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications

A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications

Prediction uncertainty and optimal experimental design for learning dynamical systems

Universal dynamical properties preclude standard clustering in a large class of biochemical data

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