Normal Modes for Chemical Reactions from Time Series Analysis

Mihaliuk, Eugene; Skødt, Henrik; Hynne, F.; Sørensen, Preben Graae; Showalter, Kenneth

doi:10.1021/jp991373t

Cited by 22 publications

(15 citation statements)

References 16 publications

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“…In addition, we believe that this may have experimental importance when the geometry of the limit cycle is reconstructed from experimental data using either quenching techniques 36 or control theory. 37 The ideas presented here for the Hopf bifurcation have been implemented numerically into a software tool BRANCH 38 which supports bifurcation analysis of dynamical systems described by autonomous ordinary differential equations and discrete iterated maps. For such systems, all ''simple'' codimension-one bifurcations are handled: Saddle-node, transcritical, pitchfork, and Hopf-Neimark-Sacker bifurcations of stationary, periodic, and fixed point solutions, as well as period doubling bifurcations of periodic orbits.…”

Section: Discussionmentioning

confidence: 99%

Dynamical properties of chemical systems near Hopf bifurcation points

Ipsen

Schreiber

2000

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we numerically investigate local properties of dynamical systems close to a Hopf bifurcation instability. We focus on chemical systems and present an approach based on the theory of normal forms for determining numerical estimates of the limit cycle that branches off at the Hopf bifurcation point. For several numerically ill-conditioned examples taken from chemical kinetics, we compare our results with those obtained by using traditional approaches where an approximation of the limit cycle is restricted to the center subspace spanned by critical eigenvectors, and show that inclusion of higher-order terms in the normal form expansion of the limit cycle provides a significant improvement of the limit cycle estimates. This result also provides an accurate initial estimate for subsequent numerical continuation of the limit cycle. (c) 2000 American Institute of Physics.

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Section: Discussionmentioning

confidence: 99%

Dynamical properties of chemical systems near Hopf bifurcation points

Ipsen

Schreiber

2000

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Typically, it is assumed that the identity of the chemical species present in the network is known, and the goal of the structure inference is to identify the species interactions [21] under some pre-imposed dynamics law [30]. This problem is of particular interest in the context of molecular and systems biology under the law of mass action dynamics, and as such has received considerable attention in the literature [3, 10, 14, 15, 17, 27, 31, 32].…”

Section: Introductionmentioning

confidence: 99%

Statistical Model for Biochemical Network Inference

Crăciun

Kim

Pantea

et al. 2013

Communications in Statistics - Simulation and Computation

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We describe a statistical method for predicting most likely reactions in a biochemical reaction network from the longitudinal data on species concentrations. Such data is relatively easily available in biochemical laboratories, for instance, via the popular RT-PCR technology. Under the assumed kinetics of the law of mass action, we also propose the data-based algorithms for estimating the prediction errors and for network dimension reduction. The second algorithm allows in particular for the application of the original algebraic inferential procedure described in [4] without the unnecessary restrictions on the dimension of the network stoichiometric space. Simulated examples of biochemical networks are analyzed, in order to assess the proposed methods’ performance.

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“…A comprehensive review of the most recent literature in this area can be found in [2]. One class of network identification approaches is concerned with the determination of Jacobian matrix elements [8], either from time-series analysis or from quenching studies [4]. Jacobian entries reveal interactions between species in the network, and which species do not interact with each other.…”

Section: Introductionmentioning

confidence: 99%

Correlation-Based Network Inference and Modelling in Systems Biology: The NF-kappa B Signalling Network Case Study

Lecca

Palmisano

Ihekwaba

2010

2010 International Conference on Intelligent Systems, Modelling and Simulation

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It is currently attracting the interest of theoretical biologists, biochemists and experimentalists to attempt to deduce the structure of biochemical networks ab initio from routinely available experimental data. The recent advances in systems biology have been driven by the methods that generate in vivo time-course data characterizing biochemical network interactions. Such data can be used for inferring a model structure and its parameters in order to examine the dynamic behavior of biological processes on a systemic level. We present here a new correlation-based aproach to network inference, whose most attractive feature is that information can be extracted from the observed data with little a priori knowledge of the underlying mechanisms. Our method introduces a new correlation metric based on a Voronoi tessellation of the variable space and infers correlations among stationary time series data of reactant concentrations. These correlations can be used to reveal dependencies between variables, as well as connectivity between species. The method has been applied to a real case study: the binding kinetics of the enzyme inhibitor kappa B kinase to its substrate inhibitor kappa B alpha, whose interaction is an integral part of the transduction of signals in the NF-kappa B signalling pathway.

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Normal Modes for Chemical Reactions from Time Series Analysis

Cited by 22 publications

References 16 publications

Dynamical properties of chemical systems near Hopf bifurcation points

Dynamical properties of chemical systems near Hopf bifurcation points

Statistical Model for Biochemical Network Inference

Correlation-Based Network Inference and Modelling in Systems Biology: The NF-kappa B Signalling Network Case Study

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