Delayed Negative Feedback

A conceptually simpler model of [Ca2+] oscillations is one where [L1SP3] oscillates (Hirose et al 1999). The delayed negative feedback in this case is Ca2+ activation of PKC, which then inhibits PLC. However, it is generally believed that [InsP3] oscillations can only give rise to low frequency [Ca2+] oscillations... 

It is well established that under appropriate circumstances, delayed negative feedback mechanisms can produce oscillations. To illustrate this point we continue with the stability analysis. 

The period T of the periodic solution can be obtained by noting that u) = 2-k/T. In general, the period of an oscillation produced by a delayed negative feedback mechanism is at least twice the delay [485]. For our model of neutrophil production, the functional relationship between r and T is shown in... 

In the previous analysis, delayed negative feedback mechanisms were considered only for neutrophil regulation. However, if over a wide range of circulating neutrophil levels, the neutrophil production rate decreases as the number of neutrophils increases (i.e., negative feedback), in the range of low neutrophil numbers the production rate must increase as neutrophil number increases (i.e., positive feedback). This type of feedback was reported as mixed feedback [472],... 

Transistors are so fast that their natural delay times are in the billionths of a second, so we ordinarily use capacitive delays to produce oscillations with somewhat longer time constants. (For example, to produce a musical note that we can hear, the delay should be roughly a thousandth of second.) We can use either delayed negative feedback (bottom of next page) or fast positive feedback (top of page 182). With transistor circuitry, it is more often directly positive. 

Without the capacitor network, the inverted signal fed back to the base directly would give us negative feedback. However, we will now delay it 180°, which is called a "phase shift." Then we will have delayed negative feedback. 

Troubleshooters might have to search for feedback from slight inductances or capacitances, causing undesirable "parasitic" oscillations. Sometimes an internal resistance way back in the power supply gets loaded like the emitter resistor here, causing delayed fluctuations in voltage, which can feed back to a transistor and start oscillations, from either direct positive or delayed negative feedback. 

If a transistor can be arranged to have delayed negative feedback, similar to the relay buzzer example on page 138, it can oscillate continuously. This is called "astable," meaning not stable. That is, it will not remain in one state, but instead it flips back and forth between "on" and "off."... 

It is possible to have immediate positive feedback, and also have the delayed negative feedback, and in fact those two actions are what we will get in the first circuit to be assembled in this chapter. The positive action makes the circuit "switch" (go completely on or off) very fast, once it starts. Because the switching is enhanced by the positive feedback, the output can be a "square wave," where the voltage goes from zero up to 9 volts quite fast (once it starts to change), hold there because of delay, and then go down to zero very fast. 

The mechanism of the BZ reaction can be considered using a simple Oregonator model, where some intermediates are considered to be quasisteady-state and quasiequilibria, while the others are supposed to constant. The Oregonator model, in its simplified form, contains both an autocatalytic step and a delayed negative feedback loop... 

The delay in onset of anxiolytic and antipanic effects of serotonin reuptake inhibitors and related compounds is still an issue of much speculation. It appears paradoxical that serotonin reuptake inhibitors block serotonin uptake immediately, whereas it takes weeks before their therapeutic effects become apparent. Recently, the idea was advanced that the tentative enhanced serotonin neurotransmission caused by short-term administration of serotonin reuptake inhibitors is offset by negative feedback in the raphe nuclei (Artigas 1993 Blier and de Montigny 1994). The increased level of serotonin in the somatodendritic area, resulting from serotonin uptake inhibition, reduces serotonin neuronal firing through activation of the 5-HTj, autoreceptors. Alterations in the feedback regulation upon repeated administration may... 

The feedback variables go with first order time delays r i towards their final values flioo- The variables of the subthreshold oscillations activate much slower than those for episode generation. In both subsystems, the positive feedback is faster than the negative feedback ... 

If a second variable participates in an additional feedback loop with a negative regulation, oscillations become possible. The mutual dependencies of the two variables, which have been coined activator and inhibitor, are depicted in Fig. 1. A, the autocatalytic species is the activator it activates the production of /, and I is the inhibitor because it slows down or inhibits the growth of A [13, 14]. Oscillations arise in activator-inhibitor systems if characteristic changes of the activator occur on a faster time-scale than the ones of the inhibitor. In other words, the inhibitor must respond to a variation of the activator variable with some delay. In fields as diverse as semiconductor physics, chemistry, biochemistry or astrophysics, and also in electrochemistry, most simple periodic oscillations can be traced back to such an activator-inhibitor scheme. 

An experimental confirmation of such patterns in systems whose dynamics seem to be well described by the prototype N-NDR model (i.e. where the negative feedback arises from a delayed transport of the electroactive species) is still missing. This is not really astonishing because the predicted parameter region for complex patterns is quite small in the model [31, 34], It also depends on the parameters entering the reaction term such that probably not all N-NDR oscillators exhibit these wave phenomena. Hence, the requirements for spatial instabilities of limit cycles are much more restrictive than for temporal oscillations where any system with an N-NDR (independent of the detailed kinetic) possesses also an experimentally accessible parameter range that exhibits oscillations. 

An interesting case is that of a delay mechanism inserted in a closed loop process with negative feedback. The typical process is the hemopoietic process that incorporates some control elements that regulate homeostatically the rates of release of marrow cells to proliferation, maturation, and to the blood. 

Cortisol concentration is described by a nonlinear time-delay differential equation [47,519] with two terms, i.e., a secretion rate term that adheres to the negative feedback mechanism [520, 521] and drives the pulsatile secretion, and a first-order output term with rate constant ka ... 

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