ABSTRACTPancreatic β-cells secrete insulin, the hormone that controls glucose homeostasis in vertebrates. When activated by glucose, β-cells display a biphasic electrical response. An initial phase, in which the cell fires action potentials continuously, is followed by a phase with a characteristic firing pattern, known as electrical bursting, that consists on brief pulses of action potentials separated by intervals of rest. Electrical bursting is believed to mediate the pulsatile secretion of insulin. The electrical response of β-cells has been extensively studied at experimental and theoretical level. However, there is still no consensus on the cellular mechanisms that underlie each of the phases of the response. In this paper, I propose the hypothesis that the pattern of the plasma membrane (PM) response of stimulated β-cells is generated by the electrical activity of the endoplasmic reticulum (ER) membrane. In this hypothesis, the interaction of the two excitable membranes, PM and ER membrane, each operating at a different time scale, generates both, the initial continuous phase and the periodic bursting phase. A mathematical model based on the hypothesis is presented. The behavior of the model β-cell replicates the main features of the physiological response of pancreatic β-cells to nutrients and to neuro-endocrine regulatory factors. The model cell displays a biphasic response to the simulated elevation of glucose. It generates electrical bursting with frequencies comparable to those observed in live cells. The simulation of the action of regulatory factors mimics the actual effect of the factors on the frequency of bursting. Finally, the model shows that a cell with a defective ER response behaves like a dysfunctional β-cell from individuals with type 2 diabetes mellitus, a result that suggests that the electrical malfunction of the ER membrane may represent one of the primary causes of type 2 diabetes. Dynamic analysis of the ER behavior has revealed that, depending on the transport rates of Ca2+ in and out of the ER, the system has three possible dynamic states. They consist on the hyperpolarization of the ER membrane, periodic oscillations of the electric potential across the membrane, and the depolarization of the membrane. Each of these states determines a different functional program in the cell. The hyperpolarized state maintains the cell at rest, in a non-secreting state. Periodic oscillations of the ER membrane cause electrical bursting in the PM and the consequent pulsatile secretion of insulin. Finally, the depolarized state causes continuous firing and an acute secretory activity, the hyperactive conditions of the initial phase of the β-cell response to glucose. The dynamic states of the ER are also associated with different long-term effects. So, conditions that induce the hyperactive depolarized state in β-cells also potentiate apoptosis. The induction of the oscillatory state by glucose and neuro-endocrine factors seems to activate also cell proliferation. In extreme conditions though, such as the chronic treatment of T2DM with incretin analogs, the activation of the oscillatory state may lead to the appearance of cancer. The mathematical model presented here is an illustration of how, even in a extremely simplified system, the nonlinearity or excitability of the ER membrane can produce a repertoire of dynamic states that are able to generate a complex response comparable to the response observed experimentally in pancreatic β-cells. In actual cells, with a much higher number of parameters susceptible to be modified by environmental and genetic factors, the ER membrane is likely to have a significantly bigger set of dynamic states each capable to direct the cell in a particular functional or developmental direction. The potential role of the electrical activity of the ER membrane in cellular processes such as fertilization, cell proliferation and differentiation, and cell death, as well as in the development of diverse pathological conditions is analyzed in the discussion.
Trajectory of Corona Epidemic in India: An Initial Phase Predictive Mathematical Model and the Present Status
