Feedback nonlinear positive

The feedback mechanisms are mediated via mineralocorticoid and glucocorticoid receptors (MR, GR), which means overlapping of nonlinear positive and negative feedback loops with nonlinear dependencies on cortisol (Michaelis-Menten kinetics, sigmoidal activation curves of corticoid receptors). 

To simulate the disease episodes and subthreshold oscillations we again refer to our neuronal modeling approaches (Fig. 7.2b). The algorithms have been implemented with a simple but physiologically plausible approach, i.e. with two nonlinear feedback loops, one positive and one negative. Depending on the parameter setting, such a system can attain stable dynamics but also can develop oscillations. 

Concepts developed in nonlinear dynamics facilitated the classification of nonlinear phenomena in electrochemical systems and revealed the origins of the diversity of temporal and spatial patterns in electrochemical systems. The diversity results on the one hand from the fact that the electrode potential might act as a positive or as a negative feedback variable. On the other hand, it is a consequence of the different kinds of spatial coupling present in an electrochemical cell and of the unique property that the extent of the spatial couplings is influenced by parameters that can be easily manipulated in an experiment. 

Another proving ground for mathematical modeling in cell signaling has been the dynamics of intracellular calcium. Spurred by the nonlinear nature of the calcium release mechanisms, which exhibit cooperativity and both positive and negative feedbacks, and by the availability of fluorescent dyes for... 

The nonlinearity of chemical processes received considerable attention in the chemical engineering literature. A large number of articles deal with stand-alone chemical reactors, as for example continuously stirred tank reactor (CSTR), tubular reactor with axial dispersion, and packed-bed reactor. The steady state and dynamic behaviour of these systems includes state multiplicity, isolated solutions, instability, sustained oscillations, and exotic phenomena as strange attractors and chaos. In all cases, the main source of nonlinearity is the positive feedback due to the recycle of heat, coupled with the dependence of the reaction rate versus temperature. 

The model analysed in chapter 3 is again that of an enzyme reaction regulated by positive feedback. To this reaction, which forms the core of the mechanism for glycolytic oscillations, is added a nonlinear recycling of product into substrate. The advantage of this extension is to keep only two variables while increasing the repertoire of dynamic behaviour. In particular, the model allows the verification of a conjee-... 

In the model studied so far, the only source of nonlinearity arises from the allosteric nature of PFK kinetics and from the regulation of the enzyme by positive feedback. The sink of product was supposed to remain linear. This assumption, which greatly simplifies the calculations, corresponds to the fact that ADP is used as substrate by several glycolytic enzymes and therefore does not accumulate within the system. This would not occur if the sink reaction(s) were saturated by ADP. It is nevertheless instructive to consider the case of a saturable sink, of the Michaelian type, in order to better understand the role of nonlinearities in the mechanism of oscillations. Maybe the degree of cooperativity of the allosteric enzyme required for oscillations might diminish once an additional nonlinearity is present within the system ... 

We may conclude that many important biological rhythms originate from positive feedback mechanisms whose nonlinearity is further strengthened by the cooperative nature of the regulatory process. Although the detailed molecular implementation of the feedback process differs in each case, it is the self-amplification with which it is associated that gives rise to instabilities followed by sustained oscillations in biochemical systems as well as in cardiac or neural cells (Goldbeter, 1992). 

Model topology, that is, the interconnections between various components in the model as a whole, and the kinetic parameters associated with each connection determine the dynamies of the model. Interactions between components in the model can be either stimulatory or inhibitory. Series of interactions arranged in the form of loops can function as either positive or negative feedback. These feedback loops, depending on the parameter values, can display nonlinear dynamic behaviors such as oscillation and bistability (Bhalla etal., 2002 Hoffmann etal., 2002). These various features ean in turn modulate the response of the system to input signals, making complex dose responses such as switchlike or nonmonotonic ones possible. 

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