scholarly journals Electrical Excitability of the Endoplasmic Reticulum Membrane Drives Electrical Bursting and the Pulsatile Secretion of Insulin in a Pancreatic Beta Cell Model

2018 ◽  
Author(s):  
Javier Gómez-Barriocanal
Keyword(s):  
Mathematical Model ◽  
Action Potentials ◽  
Initial Phase ◽  
Electrical Response ◽  
Periodic Oscillations ◽  
Pulsatile Secretion ◽  
Oscillatory State ◽  
Er Membrane ◽  
Dynamic States

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.

scholarly journals Stochastic Spatial Heterogeneity in Activities of H+-ATP-ases in Electrically Connected Plant Cells Decreases Threshold for Cooling-Induced Electrical Responses

2021 ◽  
Vol 22 (15) ◽  
pp. 8254
Author(s):  
Ekaterina Sukhova ◽  
Daria Ratnitsyna ◽  
Vladimir Sukhov
Keyword(s):  
Spatial Heterogeneity ◽  
Action Potentials ◽  
Higher Plants ◽  
Electrical Response ◽  
Plant Cells ◽  
Excitable Cells ◽  
Molecular Transporters ◽  
Positive Shift ◽  
Stochastic Heterogeneity ◽  
Electrical Responses

H+-ATP-ases, which support proton efflux through the plasma membrane, are key molecular transporters for electrogenesis in cells of higher plants. Initial activities of the transporters can influence the thresholds of generation of electrical responses induced by stressors and modify other parameters of these responses. Previously, it was theoretically shown that the stochastic heterogeneity of individual cell thresholds for electrical responses in a system of electrically connected neuronal cells can decrease the total threshold of the system (“diversity-induced resonance”, DIR). In the current work, we tested a hypothesis about decreasing the thresholds of generation of cooling-induced electrical responses in a system of electrically connected plant cells with increasing stochastic spatial heterogeny in the initial activities of H+-ATP-ases in these cells. A two-dimensional model of the system of electrically connected excitable cells (simple imitation of plant leaf), which was based on a model previously developed in our works, was used for the present investigation. Simulation showed that increasing dispersion in the distribution of initial activities of H+-ATP-ases between cells decreased the thresholds of generation of cooling-induced electrical responses. In addition, the increasing weakly influenced the amplitudes of electrical responses. Additional analysis showed two different mechanisms of the revealed effect. The increasing spatial heterogeneity in activities of H+-ATP-ases induced a weak positive shift of the membrane potential at rest. The shift decreased the threshold of electrical response generation. However, the decreased threshold induced by increasing the H+-ATP-ase activity heterogeneity was also observed after the elimination of the positive shift. The result showed that the “DIR-like” mechanism also participated in the revealed effect. Finally, we showed that the standard deviation of the membrane potentials before the induction of action potentials could be used for the estimation of thresholds of cooling-induced plant electrical responses. Thus, spatial heterogeneity in the initial activities of H+-ATP-ases can be a new regulatory mechanism influencing the generation of electrical responses in plants under actions of stressors.

scholarly journals Prediction of prevalence of type 2 diabetes in Rwanda using the metropolis-hasting sampling

2021 ◽  
Vol 21 (2) ◽  
pp. 702-709
Author(s):  
Angelique Dukunde ◽  
Jean Marie Ntaganda ◽  
Juma Kasozi ◽  
Joseph Nzabanita
Keyword(s):  
Physical Activity ◽  
Mathematical Model ◽  
Type 2 Diabetes ◽  
Monte Carlo ◽  
Transition Matrix ◽  
Decision Makers ◽  
World Health ◽  
Health Decision ◽  
The Masses

In this work, we predict the prevalence of type 2 diabetes among adult Rwandan people. We used the Metropolis-Hasting method that involved calculating the metropolis ratio. The data are those reported by World Health Organiation in 2015. Considering Suffering from diabetes, Overweight, Obesity, Dead and other subject as states of mathematical model, the transition matrix whose elements are probabilities is generated using Metropolis-Hasting sampling. The numerical results show that the prevalence of type 2 diabetes increases from 2.8% in 2015 to reach 12.65% in 2020 and to 22.59% in 2025. Therefore, this indicates the urgent need of prevention by Rwandan health decision makers who have to play their crucial role in encouraging for example physical activity, regular checkups and sensitization of the masses. Keywords: Non communicable diseases; type 2 diabetes; Markov Chain Monte Carlo method; Metropolis-Hasting method; Transition probabilities.rds: 

Excitability and electrical response of ischemic heart muscle

1960 ◽  
Vol 198 (6) ◽  
pp. 1143-1147 ◽  
Author(s):  
Chandler McC. Brooks ◽  
Jerome L. Gilbert ◽  
Martin E. Greenspan ◽  
Gertrude Lange ◽  
Hector M. Mazzella
Keyword(s):  
Action Potential ◽  
Blood Supply ◽  
Heart Muscle ◽  
Action Potentials ◽  
Electrical Response ◽  
Left Ventricular ◽  
Ischemic Heart ◽  
Monophasic Action Potential ◽  
Ventricular Muscle ◽  
Refractory Periods

Measurements were made of the changes in the monophasic action potential, excitability, durations of the refractory periods and conduction times in an area of left ventricular muscle during the development of ischemia subsequent to ligation of the ramus descendens anterior. The degree and duration of the ischemia produced varied greatly and effects were related thereto. It was found that action potentials shortened as did the refractory periods; thresholds fell momentarily and then rose progressively as tissue responsiveness failed due to continuing ischemia. Latency of responses increased, the action potentials decreased in amplitude and alternation occurred before the tissue became completely unresponsive. Early re-establishment of a blood supply caused a reversal of the abnormalities. The significance of these changes to the origin of arrhythmias is discussed.

scholarly journals A Mathematical Model of the Pathogenesis, Prevention, and Reversal of Type 2 Diabetes

Endocrinology ◽  
2015 ◽  
Vol 157 (2) ◽  
pp. 624-635 ◽  
Author(s):  
Joon Ha ◽  
Leslie S. Satin ◽  
Arthur S. Sherman
Keyword(s):  
Mathematical Model ◽  
Type 2 Diabetes ◽  
Insulin Secretion ◽  
Cell Function ◽  
Cell Mass ◽  
Β Cell ◽  
Metabolic Defects ◽  
Normal Individuals ◽  
Β Cell Function

Abstract Type 2 diabetes (T2D) is generally thought to result from the combination of 2 metabolic defects, insulin resistance, which increases the level of insulin required to maintain glucose within the normal range, and failure of insulin-secreting pancreatic β-cells to compensate for the increased demand. We build on a mathematical model pioneered by Topp and colleagues to elucidate how compensation succeeds or fails. Their model added a layer of slow negative feedback to the classic insulin-glucose loop in the form of a slow, glucose-dependent birth and death law governing β-cell mass. We add to that model regulation of 2 aspects of β-cell function on intermediate time scales. The model quantifies the relative contributions of insulin action and insulin secretion defects to T2D and explains why prevention is easier than cure. The latter is a consequence of a threshold separating the normoglycemic and diabetic states (bistability), which also underlies the success of bariatric surgery and acute caloric restriction in rapidly reversing T2D. The threshold concept gives new insight into “Starling's Law of the Pancreas,” whereby insulin secretion is higher for prediabetics and early diabetics than for normal individuals.

A mathematical model of pacemaker activity recorded from mouse small intestine

2006 ◽  
Vol 364 (1842) ◽  
pp. 1135-1154 ◽  
Author(s):  
Jae Boum Youm ◽  
Nari Kim ◽  
Jin Han ◽  
Euiyong Kim ◽  
Hyun Joo ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Small Intestine ◽  
Action Potentials ◽  
Interstitial Cells Of Cajal ◽  
Animal Experiments ◽  
Pacemaker Activity ◽  
Mouse Small Intestine ◽  
Pacemaker Potentials ◽  
Cyclic Changes ◽  
Cells Of Cajal

The pacemaker activity of interstitial cells of Cajal (ICCs) has been known to initiate the propagation of slow waves along the whole gastrointestinal tract through spontaneous and repetitive generation of action potentials. We studied the mechanism of the pacemaker activity of ICCs in the mouse small intestine and tested it using a mathematical model. The model includes ion channels, exchanger, pumps and intracellular machinery for Ca 2+ regulation. The model also incorporates inositol 1,4,5-triphosphate (IP 3 ) production and IP 3 -mediated Ca 2+ release activities. Most of the parameters were obtained from the literature and were modified to fit the experimental results of ICCs from mouse small intestine. We were then able to compose a mathematical model that simulates the pacemaker activity of ICCs. The model generates pacemaker potentials regularly and repetitively as long as the simulation continues. The frequency was set at 20 min −1 and the duration at 50% repolarization was 639 ms. The resting and overshoot potentials were −78 and +1.2 mV, respectively. The reconstructed pacemaker potentials closely matched those obtained from animal experiments. The model supports the idea that cyclic changes in [Ca 2+ ] i and [IP 3 ] play key roles in the generation of ICC pacemaker activity in the mouse small intestine.

scholarly journals A Mathematical Model for the Cardiac Action Potential Based on Slow Inactivation of Sodium Conductance

1968 ◽  
Vol 21 (1) ◽  
pp. 37 ◽  
Author(s):  
L Munk ◽  
E PGeorge
Keyword(s):  
Mathematical Model ◽  
Action Potential ◽  
Action Potentials ◽  
Sodium Current ◽  
Potassium Conductance ◽  
Slow Inactivation ◽  
Squid Axon ◽  
Purkinje Fibres ◽  
Cardiac Action ◽  
Potassium Conductances

A mathematical model for the action potential in Purkinje fibres is developed. It is based on voltage-clamp results which show that inactivation of sodium current in these muscles is much slower than in squid axon and that the latent rise in potassium conductance is not present. Both the sodium and the potassium conductances are represented as a sum of slow and fast components. This is incorporated in the suitably adjusted Hodgkin-Huxley model for the squid axon. It is shown that such a model can account satisfactorily for the shape of the action potentials in Purkinje fibres.

scholarly journals Mathematical Regression Models for Analyzing and Forecasting Diabetes prevalence in Oman

2021 ◽  
Author(s):  
Jabar Yousif
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Regression Models ◽  
Diabetes Type 2 ◽  
Diabetes Type ◽  
Actual Data ◽  
Sultanate Of Oman ◽  
Proposed Model ◽  
Future Data

<p>This work is concerned with proposing mathematical models characterized by accuracy and ease in predicting the number of diabetics type 2 in the Sultanate of Oman. By analyzing the proposed mathematical models of the current work (1, 2, and 3), it was found that the proposed mathematical model in Equation 6 can accurately predict the number of diabetics in Oman up to 2050. In order to test the model's accuracy and validity, we revised it with actual data. The results prove the accuracy of the proposed model in predicting future data of 99%. Lastly, several recommendations were recorded that could help to reduce the prevalence of diabetes type 2 in Oman.</p>

Potentiation and intrinsic regulations in mammalian heart muscle

1964 ◽  
Vol 207 (5) ◽  
pp. 1123-1132 ◽  
Author(s):  
Antonio Bonnet Seoane
Keyword(s):  
Action Potential ◽  
Heart Muscle ◽  
Refractory Period ◽  
Action Potentials ◽  
Isometric Force ◽  
Electrical Response ◽  
Transmembrane Action Potentials ◽  
Mammalian Heart Muscle ◽  
Whole Muscle ◽  
Restitution Factor

Repeated paired stimuli (S1–S2) were applied to isolated atrial and ventricular preparations. Isometric force and transmembrane action potentials were recorded at different S1–S2 intervals. At the intervals where S2 evokes an action potential, developed force gradually attains a higher level during the S1–S2 train. This mechanical behavior is quantitatively dependent on the timing of S2. Potentiation is graded during the electrical relative refractory period and related to the amplitude of the premature electrical response. This relationship was confirmed under conditions of massive response, where propagation was suppressed and the whole muscle was activated at once. Potentiation can be augmented by interposing multiple (premature) action potentials between driven beats. By increasing the S1–S2 interval the premature contraction becomes evident and increases while the first one (driven) decreases. Mechanical events are delayed one cycle after the electrical ones. Three factors are proposed to account for the intrinsic inotropic regulation: a potentiating factor related to the action potential; an ionic compartment; and a restitution factor.

Evolution of Individual Grains in 3d Microstructure Generated by Computational Simulation of Transformations Involving Two Phases

2018 ◽  
Vol 930 ◽  
pp. 305-310
Author(s):  
André Luiz Moraes Alves ◽  
Guilherme Dias da Fonseca ◽  
Marcos Felipe Braga da Costa ◽  
Weslley Luiz da Silva Assis ◽  
Paulo Rangel Rios
Keyword(s):  
Mathematical Model ◽  
Solid State ◽  
Phase Transformations ◽  
Microstructure Evolution ◽  
Initial Phase ◽  
Computational Simulation ◽  
3D Microstructure ◽  
Phase Transform ◽  
Two Phases ◽  
Individual Grains

In the phase transformations of the solid state, situations can occur in which the initial phase transform forming two or more distinct phases. The exact mathematical model for situations where more than one transformation occurs simultaneously or sequentially was proposed by Rios and Villa. The computational simulation was used to study the evolution and visualization of the possible microstructures that these transformations may present. The causal cone methodology was adopted. The simulations were compared with the analytical model to ensure that they occur as expected. The growth of individual grains of each phase was monitored in 3D microstructure evolution. With this monitoring, was possible to extract useful data able to quantify the simulated 3D microstructure. Quantifying the simulated microstructures increase the possibility of the simulations give to the experimentalist insights about the transformations. In this paper, it is verified that each grain evolves in an individual way, as expected, however their growth is similar.

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