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Register a new userDynamics and Sensitivity of Signaling Pathways
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Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently associated with cancer and can result in cells acquiring an ability to divide and grow uncontrollably. Because signaling pathways play such a significant role in cancer initiation and advancement, their constituent proteins are attractive therapeutic targets. In this review, we discuss how signaling pathway modeling can assist with identifying effective drugs for treating diseases, such as cancer. An achievement that would facilitate the use of such models is their ability to identify controlling biochemical parameters in signaling pathways, such as molecular abundances and chemical reaction rates, because this would help determine effective points of attack by therapeutics.
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Transforming Growth Factor-beta (TGF-beta) signalling is an important regulator of cellular growth and differentiation. The principal intracellular mediators of TGF-beta signalling are the Smad proteins, which upon TGF-beta stimulation accumulate in the nucleus and regulate transcription of target genes. To investigate the mechanisms of Smad nuclear accumulation, we developed a simple mathematical model of canonical Smad signalling. The model was built using both published data and our experimentally determined cellular Smad concentrations (isoforms 2, 3, and 4). We found in mink lung epithelial cells that Smad2 (8.5-12 x 10^4 molecules/cell) was present in similar amounts to Smad4 (9.3-12 x 10^4 molecules/cell), while both were in excess of Smad3 (1.1-2.0 x 10^4 molecules/cell). Variation of the model parameters and statistical analysis showed that Smad nuclear accumulation is most sensitive to parameters affecting the rates of RSmad phosphorylation and dephosphorylation and Smad complex formation/dissociation in the nucleus. Deleting Smad4 from the model revealed that rate-limiting phospho-R-Smad dephosphorylation could be an important mechanism for Smad nuclear accumulation. Furthermore, we observed that binding factors constitutively localised to the nucleus do not efficiently mediate Smad nuclear accumulation if dephosphorylation is rapid. We therefore conclude that an imbalance in the rates of R-Smad phosphorylation and dephosphorylation is likely an important mechanism of Smad nuclear accumulation during TGF-beta signalling.
There are many mathematical models of biochemical cell signaling pathways that contain a large number of elements (species and reactions). This is sometimes a big issue for identifying critical model elements and describing the model dynamics. Thus, techniques of model reduction can be used as a mathematical tool in order to minimize the number of variables and parameters. In this thesis, we review some well-known methods of model reduction for cell signaling pathways. We have also developed some approaches that provide us a great step forward in model reduction. The techniques are quasi steady state approximation (QSSA), quasi equilibrium approximation (QEA), lumping of species and entropy production analysis. They are applied on protein translation pathways with microRNA mechanisms, chemical reaction networks, extracellular signal regulated kinase (ERK) pathways, NFkB signal transduction pathways, elongation factors EFTu and EFTs signaling pathways and Dihydrofolate reductase (DHFR) pathways. The main aim of this thesis is to reduce the complex cell signaling pathway models. This provides one a better understanding of the dynamics of such models and gives an accurate approximate solution. Results show that there is a good agreement between the original models and the simplified models.
Many cells use calcium signalling to carry information from the extracellular side of the plasma membrane to targets in their interior. Since virtually all cells employ a network of biochemical reactions for Ca2+ signalling, much effort has been devoted to understand the functional role of Ca2+ responses and to decipher how their complex dynamics is regulated by the biochemical network of Ca2+-related signal transduction pathways. Experimental observations show that Ca2+ signals in response to external stimuli encode information via frequency modulation or alternatively via amplitude modulation. Although minimal models can capture separately both types of dynamics, they fail to exhibit different and more advanced encoding modes. By arguments of bifurcation theory, we propose instead that under some biophysical conditions more complex modes of information encoding can also be manifested by minimal models. We consider the minimal model of Li and Rinzel and show that information encoding can occur by amplitude modulation (AM) of Ca2+ oscillations, by frequency modulation (FM) or by both modes (AFM). Our work is motivated by calcium signalling in astrocytes, the predominant type of cortical glial cells that is nowadays recognized to play a crucial role in the regulation of neuronal activity and information processing of the brain. We explain that our results can be crucial for a better understanding of synaptic information transfer. Furthermore, our results might also be important for better insight on other examples of physiological processes regulated by Ca2+ signalling.
The primary activation of the epidermal growth factor receptor (EGFR) has become a prominent target for molecular therapies against several forms of cancer. But despite considerable progress during the last years, many of its aspects remain poorly understood. Experiments on lateral spreading of receptor activity into ligand-free regions challenge the current standard models of EGFR activation. Here, we propose and study a theoretical model, which explains spreading into ligand-free regions without introducing any new, unknown kinetic parameters. The model exhibits bistability of activity, induced by a generic reaction mechanism, which consists of activation via dimerization and deactivation via a Michaelis-Menten reaction. It possesses slow propagating front solutions and faster initial transients. We analyze relevant experiments and find that they are in quantitative accordance with the fast initial modes of spreading, but not with the slow propagating front. We point out that lateral spreading of activity is linked to pathological levels of persistent receptor activity as observed in cancer cells and exemplify uses of this link for the design and quick evaluation of molecular therapies targeting primary activation of EGFR.
Enzymes within biochemical pathways are often colocalized, yet the consequences of specific spatial enzyme arrangements remain poorly understood. We study the impact of enzyme arrangement on reaction efficiency within a reaction-diffusion model. The optimal arrangement transitions from a cluster to a distributed profile as a single parameter, which controls the probability of reaction versus diffusive loss of pathway intermediates, is varied. We introduce the concept of enzyme exposure to explain how this transition arises from the stochastic nature of molecular reactions and diffusion.
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