Plasma insulin oscillations are known to have physiological importance in the regulation of blood glucose. In insulin-secreting β-cells of pancreatic islets, K(ATP) channels play a key role in regulating glucose-dependent insulin secretion. In addition, they convey oscillations in cellular metabolism to the membrane by sensing adenine nucleotides, and are thus instrumental in mediating pulsatile insulin secretion. Blocking K(ATP) channels pharmacologically depolarizes the β-cell plasma membrane and terminates islet oscillations. Surprisingly, when K(ATP) channels are genetically knocked out, oscillations in islet activity persist, and relatively normal blood glucose levels are maintained. Compensation must therefore occur to overcome the loss of K(ATP) channels in K(ATP) knockout mice. In a companion study, we demonstrated a substantial increase in Kir2.1 protein occurs in β-cells lacking K(ATP) because of SUR1 deletion. In this report, we demonstrate that β-cells of SUR1 null islets have an upregulated inward rectifying K+ current that helps to compensate for the loss of K(ATP) channels. This current is likely due to the increased expression of Kir2.1 channels. We used mathematical modeling to determine whether an ionic current having the biophysical characteristics of Kir2.1 is capable of rescuing oscillations that are similar in period to those of wild-type islets. By experimentally testing a key model prediction we suggest that Kir2.1 current upregulation is a likely mechanism for rescuing the oscillations seen in islets from mice deficient in K(ATP) channels.

Pancreatic islet [Formula: see text]-cells are electrically excitable cells that secrete insulin in an oscillatory fashion when the blood glucose concentration is at a stimulatory level. Insulin oscillations are the result of cytosolic [Formula: see text] oscillations that accompany bursting electrical activity of [Formula: see text]-cells and are physiologically important. ATP-sensitive [Formula: see text] channels (K(ATP) channels) play the key role in setting the overall activity of the cell and in driving bursting, by coupling cell metabolism to the membrane potential. In humans, when there is a defect in K(ATP) channel function, [Formula: see text]-cells fail to respond appropriately to changes in the blood glucose level, and electrical and [Formula: see text] oscillations are lost. However, mice compensate for K(ATP) channel defects in islet [Formula: see text]-cells by employing alternative mechanisms to maintain electrical and [Formula: see text] oscillations. In a recent study, we showed that in mice islets in which K(ATP) channels are genetically knocked out another [Formula: see text] current, provided by inward-rectifying [Formula: see text] channels, is increased. With mathematical modeling, we demonstrated that a sufficient upregulation in these channels can account for the paradoxical electrical bursting and [Formula: see text] oscillations observed in these [Formula: see text]-cells. However, the question of determining the correct level of upregulation that is necessary for this compensation remained unanswered, and this question motivates the current study. [Formula: see text] is a well-known regulator of gene expression, and several examples have been shown of genes that are sensitive to the frequency of the [Formula: see text] signal. In this mathematical modeling study, we demonstrate that a [Formula: see text] oscillation frequency-sensitive gene transcription network can adjust the gene expression level of a compensating [Formula: see text] channel so as to rescue electrical bursting and [Formula: see text] oscillations in a model [Formula: see text]-cell in which the key K(ATP) current is removed. This is done without the prescription of a target [Formula: see text] level, but evolves naturally as a consequence of the feedback between the [Formula: see text]-dependent enzymes and the cell's electrical activity. More generally, the study indicates how [Formula: see text] can provide the link between gene expression and cellular electrical activity that promotes wild-type behavior in a cell following gene knockout.

We have worked on (2+1)-dimensional dissipative long wave system (DLWS) and (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation. We have applied GKM, which has been obtained by generalizing the Kudryashov method, to the (2+1)- dimensional DLWS and (2+1)-dimensional DJKM equation. Thus, we have got some new soliton solutions of handled system and equation. We have plotted 2D and 3D surfaces of these acquired results by using Wolfram Mathematica 12. Then, we have shown the validity of the acquired solutions.

Dyslipidemia in obesity results from excessive production and impaired clearance of triglyceride-rich (TG-rich) lipoproteins, which are particularly pronounced in the postprandial state. Here, we investigated the impact of Roux-en-Y gastric bypass (RYGB) surgery on postprandial VLDL 1 and VLDL 2 apoB and TG kinetics and their relationship with insulin-responsiveness indices. Morbidly obese patients without diabetes who were scheduled for RYGB surgery ( n = 24) underwent a lipoprotein kinetics study during a mixed-meal test and a hyperinsulinemic-euglycemic clamp study before the surgery and 1 year later. A physiologically based computational model was developed to investigate the impact of RYGB surgery and plasma insulin on postprandial VLDL kinetics. After the surgery, VLDL 1 apoB and TG production rates were significantly decreased, whereas VLDL 2 apoB and TG production rates remained unchanged. The TG catabolic rate was increased in both VLDL 1 and VLDL 2 fractions, but only the VLDL 2 apoB catabolic rate tended to increase. Furthermore, postsurgery VLDL 1 apoB and TG production rates, but not those of VLDL 2 , were positively correlated with insulin resistance. Insulin-mediated stimulation of peripheral lipoprotein lipolysis was also improved after the surgery. In summary, RYGB resulted in reduced hepatic VLDL 1 production that correlated with reduced insulin resistance, elevated VLDL 2 clearance, and improved insulin sensitivity in lipoprotein lipolysis pathways.

To find some soliton solutions of the equation, the perturbed Radhakrishnan-Kundu-Lakshmanan (RKL) equation has been considered. For this purpose, GKM (generalized Kudryashov method), which is one of the solution methods of nonlinear evolution equations (NLEEs), has been applied to the perturbed RKL equation. First, considered the nonlinear partial differential equation, is reduced to an ordinary differential equation with the help of the traveling wave transformation. Afterward, obtained the algebraic equation system through the balance principle was solved with the help of Wolfram Mathematica 12. Thus, some new soliton solutions of the discussed equation have been obtained. Both 2D and 3D graphics have been drawn with the help of Wolfram Mathematica 12 by giving some values to obtained these new solutions.