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Positive feedback loops exist in many biological circuits important for organismal function. In this work, we investigate how temporal delay affects the dynamics of two canonical positive feedback models. We consider models of a genetic toggle switch and a one-way switch with delay added to the feedback terms. We show that long-lasting transient oscillations exist in both models under general conditions and that the duration depends strongly on the magnitude of the delay and initial conditions. We then show the existence of long-lasting oscillations in specific biological examples: the Cdc2-Cyclin B/Wee1 system and a genetic regulatory network. Our results challenge fundamental assumptions underlying oscillatory behavior in biological systems. While generally delayed negative feedback systems are canonical in generating oscillations, we show that delayed positive feedback systems are a mechanism for generating oscillations as well. [ABSTRACT FROM AUTHOR]

The pulsatile activity of gonadotropin-releasing hormone neurons (GnRH neurons) is a key factor in the regulation of reproductive hormones. This pulsatility is orchestrated by a network of neurons that release the neurotransmitters kisspeptin, neurokinin B, and dynorphin (KNDy neurons), and produce episodic bursts of activity driving the GnRH neurons. We show in this computational study that the features of coordinated KNDy neuron activity can be explained by a neural network in which connectivity among neurons is modular. That is, a network structure consisting of clusters of highly-connected neurons with sparse coupling among the clusters. This modular structure, with distinct parameters for intracluster and intercluster coupling, also yields predictions for the differential effects on synchronization of changes in the coupling strength within clusters versus between clusters. Author summary: Since the discovery of a small population of hypothalamic neurons that secrete kisspeptin, neurokinin B, and dynorphin (KNDy neurons), there has been interest in their role as a pacemaker for the pulsatile release of key reproductive hormones. A fundamental question is what mechanism coordinates KNDy neuron activity to generate population bursts. Optical imaging of the KNDy network at single-neuron resolution has revealed that individual KNDy neurons participate in many, but not all, population bursts. It has also shown that the order in which the neurons are recruited in each burst could be highly determined in some animals but not in others. We demonstrate here that these observations can be explained by a neural network with a modular structure, and that one benefit of the structure is the ability to differentially modulate the level of synchronization by changes in key coupling parameters. [ABSTRACT FROM AUTHOR]

Pancreatic beta cells secrete insulin in response to plasma glucose. The ATP‐sensitive potassium channel (KATP) links glucose metabolism to islet electrical activity in these cells by responding to increased cytosolic [ATP]/[ADP]. It was recently proposed that pyruvate kinase (PK) in close proximity to beta cell KATP locally produces the ATP that inhibits KATP activity. This proposal was largely based on the observation that applying phosphoenolpyruvate (PEP) and ADP to the cytoplasmic side of excised inside‐out patches inhibited KATP. To test the relative contributions of local vs. mitochondrial ATP production, we recorded KATP activity using mouse beta cells and INS‐1 832/13 cells. In contrast to prior reports, we could not replicate inhibition of KATP activity by PEP + ADP. However, when the pH of the PEP solutions was not corrected for the addition of PEP, strong channel inhibition was observed as a result of the well‐known action of protons to inhibit KATP. In cell‐attached recordings, perifusing either a PK activator or an inhibitor had little or no effect on KATP channel closure by glucose, further suggesting that PK is not an important regulator of KATP. In contrast, addition of mitochondrial inhibitors robustly increased KATP activity. Finally, by measuring the [ATP]/[ADP] responses to imposed calcium oscillations in mouse beta cells, we found that oxidative phosphorylation could raise [ATP]/[ADP] even when ADP was at its nadir during the burst silent phase, in agreement with our mathematical model. These results indicate that ATP produced by mitochondrial oxidative phosphorylation is the primary controller of KATP in pancreatic beta cells. Key points: Phosphoenolpyruvate (PEP) plus adenosine diphosphate does not inhibit KATP activity in excised patches. PEP solutions only inhibit KATP activity if the pH is unbalanced.Modulating pyruvate kinase has minimal effects on KATP activity.Mitochondrial inhibition, in contrast, robustly potentiates KATP activity in cell‐attached patches.Although the ADP level falls during the silent phase of calcium oscillations, mitochondria can still produce enough ATP via oxidative phosphorylation to close KATP.Mitochondrial oxidative phosphorylation is therefore the main source of the ATP that inhibits the KATP activity of pancreatic beta cells. [ABSTRACT FROM AUTHOR]

The standard model for Ca2+ oscillations in insulin-secreting pancreatic β cells centers on Ca2+ entry through voltage-activated Ca2+ channels. These work in combination with ATP-dependent K+ channels, which are the bridge between the metabolic state of the cells and plasma membrane potential. This partnership underlies the ability of the β cells to secrete insulin appropriately on a minute-to-minute time scale to control whole body plasma glucose. Though this model, developed over more than 40 years through many cycles of experimentation and mathematical modeling, has been very successful, it has been challenged by a hypothesis that calcium-induced calcium release from the endoplasmic reticulum through ryanodine or inositol trisphosphate (IP3) receptors is instead the key driver of islet oscillations. We show here that the alternative model is in fact incompatible with a large body of established experimental data and that the new observations offered in support of it can be better explained by the standard model. [ABSTRACT FROM AUTHOR]