Calcium Oscillation Frequency-Sensitive Gene Regulation and Homeostatic Compensation in Pancreatic β-Cells

The role of GLUT2 in glucose metabolism in multiple organs and tissues

The glucose transporter family has an important role in the initial stage of glucose metabolism; Glucose transporters 2 (GLUTs, encoded by the solute carrier family 2, SLC2A genes) is the major glucose transporter in β-cells of pancreatic islets and hepatocytes but is also expressed in the small intestine, kidneys, and central nervous system; GLUT2 has a relatively low affinity to glucose. Under physiological conditions, GLUT2 transports glucose into cells and allows the glucose concentration to reach balance on the bilateral sides of the cellular membrane; Variation of GLUT2 is associated with various endocrine and metabolic disorders; In this study, we discussed the role of GLUT2 in participating in glucose metabolism and regulation in multiple organs and tissues and its effects on maintaining glucose homeostasis.

Classification of bursting patterns: A tale of two ducks

Bursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic of intense research in computational biology for several decades. The classification of bursting oscillations in excitable systems has been the subject of active research since the early 1980s and is still ongoing. As a by-product, it establishes analytical and numerical foundations for studying complex temporal behaviors in multiple timescale models of cellular activity. In this review, we first present the seminal works of Rinzel and Izhikevich in classifying bursting patterns of excitable systems. We recall a complementary mathematical classification approach by Bertram and colleagues, and then by Golubitsky and colleagues, which, together with the Rinzel-Izhikevich proposals, provide the state-of-the-art foundations to these classifications. Beyond classical approaches, we review a recent bursting example that falls outside the previous classification systems. Generalizing this example leads us to propose an extended classification, which requires the analysis of both fast and slow subsystems of an underlying slow-fast model and allows the dissection of a larger class of bursters. Namely, we provide a general framework for bursting systems with both subthreshold and superthreshold oscillations. A new class of bursters with at least 2 slow variables is then added, which we denote folded-node bursters, to convey the idea that the bursts are initiated or annihilated via a folded-node singularity. Key to this mechanism are so-called canard or duck orbits, organizing the underpinning excitability structure. We describe the 2 main families of folded-node bursters, depending upon the phase (active/spiking or silent/nonspiking) of the bursting cycle during which folded-node dynamics occurs. We classify both families and give examples of minimal systems displaying these novel bursting patterns. Finally, we provide a biophysical example by reinterpreting a generic conductance-based episodic burster as a folded-node burster, showing that the associated framework can explain its subthreshold oscillations over a larger parameter region than the fast subsystem approach.

Bursting is ubiquitous in cellular excitable rhythms and comes in a plethora of patterns, both experimentally recorded and reproduced through models. As these different patterns may reflect different coding or information properties, it is therefore crucial to develop modeling frameworks that can both capture them and understand their characteristics. In this review, we propose a comprehensive account of the main bursting classification systems that have been developed over the past 40 years, together with recent developments allowing us to extend these classifications. Based upon bifurcation theory and heavily reliant on timescale separation, these schemes take full advantage of the fast subsystem analysis, obtained when slow variables are frozen and considered as bifurcation parameters. We complement this classical view by showing that nontrivial slow subsystem may also encode key informations important to classify bursting rhythms, due to the presence of so-called folded-node singularities. We provide minimal idealized models as well as one generic conductance-based example displaying bursting oscillations that require our extended classification in order to be fully characterized. We also highlight examples of biological data that could be suitably revisited with the lenses of this extended classifications and could lead to new models of complex cellular activity.

Activity-dependent compensation of cell size is vulnerable to targeted deletion of ion channels

In many species, excitable cells preserve their physiological properties despite significant variation in physical size across time and in a population. For example, neurons in crustacean central pattern generators generate similar firing patterns despite several-fold increases in size between juveniles and adults. This presents a biophysical problem because the electrical properties of cells are highly sensitive to membrane area and channel density. It is not known whether specific mechanisms exist to sense membrane area and adjust channel expression to keep a consistent channel density, or whether regulation mechanisms that sense activity alone are capable of compensating cell size. We show that destabilising effects of growth can be specifically compensated by feedback mechanism that senses average calcium influx and jointly regulate multiple conductances. However, we further show that this class of growth-compensating regulation schemes is necessarily sensitive to perturbations that alter the expression of subsets of ion channel types. Targeted perturbations of specific ion channels can trigger a pathological response of the regulation mechanism and a failure of homeostasis. Our findings suggest that physiological regulation mechanisms that confer robustness to growth may be specifically vulnerable to deletions or mutations that affect subsets of ion channels.

Chronic stimulation induces adaptive potassium channel activity that restores calcium oscillations in pancreatic islets in vitro

Insulin pulsatility is important to hepatic response in regulating blood glucose. Growing evidence suggests that insulin-secreting pancreatic β-cells can adapt to chronic disruptions of pulsatility to rescue this physiologically important behavior. We determined the time scale for adaptation and examined potential ion channels underlying it. We induced the adaptation both by chronic application of the ATP-sensitive K⁺ [K(ATP)] channel blocker tolbutamide and by application of the depolarizing agent potassium chloride (KCl). Acute application of tolbutamide without pretreatment results in elevated Ca²⁺ as measured by fura-2AM and the loss of endogenous pulsatility. We show that after chronic exposure to tolbutamide (12-24 h), Ca²⁺ oscillations occur with subsequent acute tolbutamide application. The same experiment was conducted with potassium chloride (KCl) to directly depolarize the β-cells. Once again, following chronic exposure to the cell stimulator, the islets produced Ca²⁺ oscillations when subsequently exposed to tolbutamide. These experiments suggest that it is the chronic stimulation, and not tolbutamide desensitization, that is responsible for the adaptation that rescues oscillatory β-cell activity. This compensatory response also causes islet glucose sensitivity to shift rightward following chronic tolbutamide treatment. Mathematical modeling shows that a small increase in the number of K(ATP) channels in the membrane is one adaptation mechanism that is compatible with the data. To examine other compensatory mechanisms, pharmacological studies provide support that Kir2.1 and TEA-sensitive channels play some role. Overall, this investigation demonstrates β-cell adaptability to overstimulation, which is likely an important mechanism for maintaining glucose homeostasis in the face of chronic stimulation.

Neuronal oscillations on an ultra-slow timescale: daily rhythms in electrical activity and gene expression in the mammalian master circadian clockwork

Neuronal oscillations of the brain, such as those observed in the cortices and hippocampi of behaving animals and humans, span across wide frequency bands, from slow delta waves (0.1 Hz) to ultra-fast ripples (600 Hz). Here, we focus on ultra-slow neuronal oscillators in the hypothalamic suprachiasmatic nuclei (SCN), the master daily clock that operates on interlocking transcription-translation feedback loops to produce circadian rhythms in clock gene expression with a period of near 24 h (< 0.001 Hz). This intracellular molecular clock interacts with the cell's membrane through poorly understood mechanisms to drive the daily pattern in the electrical excitability of SCN neurons, exhibiting an up-state during the day and a down-state at night. In turn, the membrane activity feeds back to regulate the oscillatory activity of clock gene programs. In this review, we emphasise the circadian processes that drive daily electrical oscillations in SCN neurons, and highlight how mathematical modelling contributes to our increasing understanding of circadian rhythm generation, synchronisation and communication within this hypothalamic region and across other brain circuits.