A Mathematical Modeling of Signal Transduction Cascade on Raf-Akt Cross-Talk (original) (raw)
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Computational modelling of the receptor-tyrosine-kinase-activated MAPK pathway
Biochemical Journal, 2005
The Mitogen Activated Protein Kinase (MAPK) pathway is one of the most important and intensively studied signalling pathways. It is at the heart of a molecular signalling network that governs the growth, proliferation, differentiation and survival of many, if not all cell types. It is deregulated in various diseases ranging from cancer to immunological, inflammatory and degenerative syndromes, and thus represents an important drug target. Over recent years, the computational or mathematical modelling of biological systems has become increasingly valuable and there is now a wide variety of mathematical models of the MAPK pathway which have led to some novel insights and predictions as to how this system functions. In this review, we give an overview of the processes involved in modelling a biological system using the popular approach of ordinary differential equations. Focussing on the MAPK pathway, we introduce the features and functions of the pathway itself before comparing the available models and describing what new biological insights they have led to.
Biosystems, 2006
Activation-inactivation cycles of signalling proteins and transcription factors catalysed by kinases and phosphatases are a core component of cellular signal transduction. We present a systematic kinetic analysis of a phosphorylation cycle that starts from the description of elementary protein-protein interaction and catalytic steps. A rapid-equilibrium approximation for protein interactions is used to reduce the set of parameters. The resulting description consists of a kinetic equation for the phosphorylation of the target and a set of conservation conditions for kinase and phosphatase. Generally no explicit rate laws exist for the two enzymes; linear or Michaelis-Menten rate equations can be obtained in special cases. Key parameters that determine the stimulus-response curve and the response time of the cycle are the concentrations of kinase and phosphatase relative to the target protein and the affinities of the two enzymes for the different phosphorylation states of the target. Characterizing the response curve by the global response coefficient, we obtain a phase diagram that shows the existence of three kinds of behaviours: graded, ultrasensitive, and a previously undescribed biphasic response. Two kinds of competition effect turn out to shape the behaviour: (1) the degree of product inhibition of each enzyme, and (2) the competition between kinase and phosphatase to bind the target protein, as determined by their relative target affinities. The approach outlined here may be useful also for analysing more complex systems, including multiple phosphorylation and kinase cascades.
Nature biotechnology, 2002
We present a computational model that offers an integrated quantitative, dynamic, and topological representation of intracellular signal networks, based on known components of epidermal growth factor (EGF) receptor signal pathways. The model provides insight into signal-response relationships between the binding of EGF to its receptor at the cell surface and the activation of downstream proteins in the signaling cascade. It shows that EGF-induced responses are remarkably stable over a 100-fold range of ligand concentration and that the critical parameter in determining signal efficacy is the initial velocity of receptor activation. The predictions of the model agree well with experimental analysis of the effect of EGF on two downstream responses, phosphorylation of ERK-1/2 and expression of the target gene, c-fos.
2010
The epidermal growth factor receptor (EGFR, also known as ErbB1) is a prototypical receptor tyrosine kinase (RTK) that activates multi-kinase phosphorylation cascades to regulate diverse cellular processes, including proliferation, migration and differentiation. ErbB1 heterooligomerizes with three close homologues: ErbB2, ErbB3 and ErbB4. ErbB1-3 receptors are frequently mutated, overexpressed or activated by autocrine or paracrine ligand production in solid tumors and have been the target of extensive drug discovery efforts. Multiple small molecule kinase inhibitors and therapeutic antibodies against ErbB receptors are in clinical use or development. Despite their importance as RTKs, oncogenes and drug targets, regulation of ErbB receptors by the interplay of conformational change, phosphorylation, phosphatases and receptor trafficking remains poorly understood, and the impact of these dynamics on physiological activity and cellular responses to anti-ErbB drugs is largely unknown. This thesis investigates the dynamic opposition of kinases and phosphatases within the ErbB pathway. By standard biochemical analysis, ErbB receptors and downstream proteins appear to become phosphorylated and then dephosphorylated in approximately 30 minutes. However, pulsechase experiments where cells are exposed to ligand and then to small molecule kinase inhibitors reveal that individual proteins must in fact cycle rapidly between being phosphorylated and dephosphorylated in seconds. We construct a succession of differential equation-based models of varying biochemical resolution, each model appropriate for analyzing a different aspect of ErbB regulation, to help interpret the data and gain quantitative insight into receptor and drug biology. Rapid phosphorylation and dephosphorylation of receptors has important implications for the assembly dynamics of signalosomes. We find that signals are rapidly propagated through some downstream pathways but slowly through others, resulting in prolonged activation in the absence of upstream signal. We show that fast phosphorylation/dephosphorylation may provide cells with the flexibility necessary to rapidly detect and respond to changes in their extracellular environment.
Dynamic modeling of mapk/erk signaling pathways
2020
. MAPK /ERK pathways have been shown to play a key role in transduction extracellular signals to cellular responses. Its Transduces signals by phosphorylation and has an essential role in cell proliferation, differentiation, and apoptosis. Through several assumptions, we simplify the pathways to develop a model for ERK1/2 activation in a system of differential equations based on enzyme catalyzed reaction processes. Then we study dynamic behaviour of the interactions among these two important molecules in this signaling patways. We used nondimensionalizations and Homotopy Perturbation Method (HPM) to find approximat ion solutions to the system. In addition to the approximation analytical expressions, we also computed numerical solutions for our system equations. We compared both types of solutions graphically and obtained that the results are in good agreement.
Journal of the American Chemical Society, 1999
The sulfotyrosine peptide, IRK1154, is based on the corresponding phosphotyrosine segment of the insulin receptor kinase domain (IRK) and is a known inhibitor of the function of the protein tyrosine phosphatase, PTP1B. Two-dimensional NMR spectroscopy, in the transferred nuclear Overhauser effect (NOE) enhancement experiment, was used to obtain information concerning the bound structure of this peptide. Computer-simulated docking experiments, followed by molecular dynamics simulations in a fully hydrated model, provided information concerning the site-specific interactions influencing the bound peptide. Using the structural and orientational information from the NMR studies as a guide, together with the X-ray coordinates for PTP1B and IRK, a detailed model of the binding of these two proteins was developed. The interface between the two entities is described, and the sites of positive interactions are identified. Potential sources of destabilizing interactions, necessary for dissociation of the two enzymes, were also found.
Journal of Mathematical Biology, 2013
Cell signalling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signalling pathways. But the binding process still presents many enigmas and, by analogy with surface catalytic reactions, two different mechanisms can be conceived: the first mechanism is related to the Eley-Rideal (ER) mechanism, i.e. the bulk-dissolved ligand interacts directly by pure three-dimensional (3D) diffusion with the specific surface receptor; the second mechanism is similar to the Langmuir-Hinshelwood (LH) process, i.e. 3D diffusion of the ligand to the cell surface followed by reversible ligand adsorption and subsequent two-dimensional (2D) surface diffusion to the receptor. A situation where both mechanisms simultaneously contribute to the signalling process could also occur. The aim of this paper is to perform a computational study of the behavior of the signalling response when these different mechanisms for ligand-receptor interactions are integrated into a model for signal transduction and ligand transport. To this Electronic supplementary material The online version of this article
Chapter XX: Computational and Mathematical Modelling of the EGF Receptor System
2008
This chapter gives an overview of computational models and simulations of the EGF receptor system. It begins with a survey of motivations for producing such models and then describes the main approaches that are taken to carrying out such modeling, with respect to differential equations and individual-based modeling. Finally, a number of projects that apply modeling and simulation techniques to various aspects of the EGF receptor system are described.
Matrix Science Mathematic (MSMK) , 2020
The extracellular signal-regulated protein kinase (ERK), a subfamily of Mitogen-Activated Protein Kinase (MAPK) pathways, is one of the most important signals in the regulation of many biological processes. Deregulated of MAPK signaling pathways has been observed in human cancers with potential involvement in most of all cellular processes leading to tumorigenesis so that it became a potential target for therapy in cancer patients. In this paper, we discuss a Mathematical model of ERK activation in the presence of a small molecule inhibitor that competes with RAS. We present analytical expressions for the concentration of RAS, complex RAS-ERK, complex RAS-Inhibitor, and activated ERK in terms of dimensionless parameters using He's Homotopy Perturbation Method (HPM). The analytical results are compared with numerical simulation and satisfactory agreement is obtained.