Modeling Molecular Interaction Networks with Nonlinear Ordinary Differential Equations

Conrad, Emery D.; Tyson, John J.

doi:10.7551/mitpress/9780262195485.003.0006

Cited by 48 publications

(31 citation statements)

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“…noise assumption. Using a 1-norm on the untransformed residuals (Conrad and Tyson, 2006) assumes that the noise model is additive Laplacian, which has heavier tails. Practically, it corresponds to a median value estimator which means that large residuals would have less influence or leverage on the solution, and thus is more robust to outliers.…”

Section: Noise Assumptionsmentioning

confidence: 99%

“…In molecular systems biology research, the dynamical properties of biochemical signalling pathways are usually represented as a set of nonlinear ordinary differential equations (ODEs) using the "well-stirred" (Conrad and Tyson, 2006) assumption. When the pathway structure is known, the identification of uncertain kinetic parameters becomes the central task.…”

Section: Introductionmentioning

confidence: 99%

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Properties of the Proximate Parameter Tuning Regularization Algorithm

Brown

Wilkinson

2010

Bull. Math. Biol.

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An important aspect of systems biology research is the so-called "reverse engineering" of cellular metabolic dynamics from measured input-output data. This allows researchers to estimate and validate both the pathway's structure as well as the kinetic constants. In this paper, the recently published 'Proximate Parameter Tuning' (PPT) method for the identification of biochemical networks is analysed. In particular, it is shown that the described PPT algorithm is essentially equivalent to a sequential linear programming implementation of a constrained optimization problem. The corresponding objective function consists of two parts, the first emphasises the data fitting where a residual 1-norm is used, and the second emphasises the proximity of the calculated parameters to the specified nominal values, using an infinity-norm. The optimality properties of PPT algorithm solution as well as its geometric interpretation are analyzed. The concept of optimal parameter locus is applied for the exploration of the entire family of optimal solutions. An efficient implementation of the parameter locus is also developed. Parallels are drawn with 1-norm parameter deviation regularization which attempt to fit the data with a minimal number of parameters. Finally, a small example is used to illustrate all of these properties.

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Section: Noise Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Properties of the Proximate Parameter Tuning Regularization Algorithm

Brown

Wilkinson

2010

Bull. Math. Biol.

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“…In this paper, the models are designed by means of systems of parametric nonlinear ordinary differential equations (ODE) [8]. The approach applied in [1] consisted in two steps: first simplifying the initial system of n + 2 parametric ordinary differential equations as a reduced system of three ODE by means of a quasi-steady state approximation; second, studying the reduced model.…”

Section: Introductionmentioning

confidence: 99%

Applying a Rigorous Quasi-Steady State Approximation Method for Proving the Absence of Oscillations in Models of Genetic Circuits

et al.

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Abstract. In this paper, we apply a rigorous quasi-steady state approximation method on a family of models describing a gene regulated by a polymer of its own protein. We study the absence of oscillations for this family of models and prove that Poincaré-Andronov-Hopf bifurcations arise if and only if the number of polymerizations is greater than 8. A result presented in a former paper at Algebraic Biology 2007 is thereby generalized. The rigorous method is illustrated over the basic enzymatic reaction.

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“…This condition is usually satisfied unless molecular crowding [5,6] takes place, as the average time to cross a cell by diffusion is approximately 1 minute for macromolecules and much less for small molecules; the time scale for analyzing signaling pathways is hours or even days [7].…”

Section: Models Of Signaling Pathwaysmentioning

confidence: 99%

Sensitivity analysis of deterministic signaling pathways models

Puszyński¹,

Lachor²,

Kardyńska³

et al. 2012

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The paper is focused on application of sensitivity methods to analysis of signaling pathway models. Two basic methods are compared: local, based on standard sensitivity functions, and global, based on Sobol indices. Firstly, a general outline of modeling of signaling pathways by means of ordinary differential equations is briefly described. Afterwards, the methods of sensitivity analysis, known from literature, are introduced and illustrated with a simple example of a dynamical system of the second order. Subsequently, the analysis of the p53/Mdm2 regulatory module, which is a key element of any pathway involving p53 protein, is presented. The results of this analysis suggest that no single method should be chosen for investigation of any signaling pathway model but several of them should be applied to answer important questions about sources of heterogeneity in cells behavior, robustness of signaling pathways and possible molecular drug targets.

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Modeling Molecular Interaction Networks with Nonlinear Ordinary Differential Equations

Cited by 48 publications

References 0 publications

Properties of the Proximate Parameter Tuning Regularization Algorithm

Properties of the Proximate Parameter Tuning Regularization Algorithm

Applying a Rigorous Quasi-Steady State Approximation Method for Proving the Absence of Oscillations in Models of Genetic Circuits

Sensitivity analysis of deterministic signaling pathways models

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