Mathematical Modeling of the Influence of RKIP on the ERK Signaling Pathway

Cho, Kwang-Hyun; Shin, Sung-Young; Kim, Hyun Woo; Wolkenhauer, Olaf; McFerran, Brian W.; Kölch, Walter

doi:10.1007/3-540-36481-1_11

Cited by 64 publications

(43 citation statements)

References 5 publications

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“…Our choice of the total approximation has been reinforced by its recent application to complex mechanisms, like the completely reversible enzyme kinetics [34], the antagonist toggle switch [35], the completely competitive inhibition [26,27,29,36], the double phosphorylation [29], the Goldbeter-Koshland switch, which models the single phosphorylation -dephosphorylation cycle [33,[37][38][39], the double phosphorylation -dephosphorylation cycle and the ubiquitous MAPK cascade, which is one of the most important mechanisms present in the great majority of the reaction networks in eukaryotic cells [30,[40][41][42][43][44].…”

Section: Discussionmentioning

confidence: 99%

A study case for the analysis of asymptotic expansions beyond the tQSSA for inhibitory mechanisms in enzyme kinetics.

Bersani

Borri

Milanesi

et al. 2019

Communications in Applied and Industrial Mathematics

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Section: Discussionmentioning

confidence: 99%

A study case for the analysis of asymptotic expansions beyond the tQSSA for inhibitory mechanisms in enzyme kinetics.

Bersani

Borri

Milanesi

et al. 2019

Communications in Applied and Industrial Mathematics

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“…The RKIP regulated ERK signaling pathway [5], as shown in Fig. 1, is a circle representing a state for the concentration of a protein, e.g.…”

Section: Test Model-rkip Regulated Erk Pathway Modelmentioning

confidence: 99%

Parameter Estimation in Systems Biology Models by Using Extended Kalman Filter

Capinski

Polański

2015

Advances in Intelligent Systems and Computing

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Models in systems biology, which reflect complex dynamic biological phenomena are most often described as ordinary differential equations (ODE). Characteristic properties of these differential equations is nonlinearity and large size (number of state variables). These models also contain large numbers of unknown parameters. So the main challenge in developing models in systems biology is estimation of numerous unknown parameters in nonlinear differential equations. There are already numerous approaches to parameter estimation in systems biology models. However, main difficulties speed of convergence and multiple minima (multiple solutions) are still obstacles in achieving solutions of sufficient efficiency. In this chapter we propose a new approach based on combination of extended Kalman filtering dynamical optimization with spline approximation of solutions to ODE, for parameter estimation in systems biology models. We present the main idea and we show comparisons to some published results.

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“…In comparison, our approach is more powerful, since the former approach is limited to generalized Mass-Action kinetics, and cannot infer global stability directly. Fig 10b depicts the network describing the effect of the so called Raf Kinase Inhibitor Protein (RKIP) on the Extracellular Regulated Kinase (ERK) signaling pathway as per the model given in [85]. It can be described using the network:…”

Section: T-cell Kinetic Proofreading Networkmentioning

confidence: 99%

A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks

2020

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Complex molecular biological processes such as transcription and translation, signal transduction, post-translational modification cascades, and metabolic pathways can be described in principle by biochemical reactions that explicitly take into account the sophisticated network of chemical interactions regulating cell life. The ability to deduce the possible qualitative behaviors of such networks from a set of reactions is a central objective and an ongoing challenge in the field of systems biology. Unfortunately, the construction of complete mathematical models is often hindered by a pervasive problem: despite the wealth of qualitative graphical knowledge about network interactions, the form of the governing nonlinearities and/or the values of kinetic constants are hard to uncover experimentally. The kinetics can also change with environmental variations. This work addresses the following question: given a set of reactions and without assuming a particular form for the kinetics, what can we say about the asymptotic behavior of the network? Specifically, it introduces a class of networks that are "structurally (mono) attractive" meaning that they are incapable of exhibiting multiple steady states, oscillation, or chaos by virtue of their reaction graphs. These networks are characterized by the existence of a universal energy-like function called a Robust Lyapunov function (RLF). To find such functions, a finite set of rank-one linear systems is introduced, which form the extremals of a linear convex cone. The problem is then reduced to that of finding a common Lyapunov function for this set of extremals. Based on this characterization, a computational package, Lyapunov-Enabled Analysis of Reaction Networks (LEARN), is provided that constructs such functions or rules out their existence. An extensive study of biochemical networks demonstrates that LEARN offers a new unified framework. Basic motifs, three-body binding, and genetic networks are studied first. The work then focuses on cellular signalling networks including various post-translational modification cascades, phosphotransfer and phosphorelay networks, T-cell kinetic proofreading, and ERK signalling. The Ribosome Flow Model is also studied.

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Mathematical Modeling of the Influence of RKIP on the ERK Signaling Pathway

Cited by 64 publications

References 5 publications

A study case for the analysis of asymptotic expansions beyond the tQSSA for inhibitory mechanisms in enzyme kinetics.

A study case for the analysis of asymptotic expansions beyond the tQSSA for inhibitory mechanisms in enzyme kinetics.

Parameter Estimation in Systems Biology Models by Using Extended Kalman Filter

A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks

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