Symmetric Fold/Super-Hopf Bursting, Chaos and Mixed-Mode Oscillations in Pernarowski Model of Pancreatic Beta-Cells

2016 ◽  
Vol 26 (09) ◽  
pp. 1630022 ◽  
Author(s):  
Haniyeh Fallah
Keyword(s):  
Blood Glucose ◽  
Blood Glucose Level ◽  
Beta Cells ◽  
Pancreatic Beta Cells ◽  
Mixed Mode ◽  
Current System ◽  
Period Doubling ◽  
Slow Manifold ◽  
Mixed Mode Oscillations ◽  
Route To Chaos

Pancreatic beta-cells produce insulin to regularize the blood glucose level. Bursting is important in beta cells due to its relation to the release of insulin. Pernarowski model is a simple polynomial model of beta-cell activities indicating bursting oscillations in these cells. This paper presents bursting behaviors of symmetric type in this model. In addition, it is shown that the current system exhibits the phenomenon of period doubling cascades of canards which is a route to chaos. Canards are also observed symmetrically near folds of slow manifold which results in a chaotic transition between [Formula: see text] and [Formula: see text] spikes symmetric bursting. Furthermore, mixed-mode oscillations (MMOs) and combination of symmetric bursting together with MMOs are illustrated during the transition between symmetric bursting and continuous spiking.

scholarly journals Geometric analysis of mixed-mode oscillations in a model of electrical activity in human beta-cells

2021 ◽  
Author(s):  
Simone Battaglin ◽  
Morten Gram Pedersen
Keyword(s):  
Hopf Bifurcation ◽  
Electrical Activity ◽  
Beta Cells ◽  
Pancreatic Beta Cells ◽  
Mixed Mode ◽  
Original Model ◽  
Biophysical Model ◽  
Reduced Model ◽  
Geometric Singular Perturbation Theory ◽  
Mixed Mode Oscillations

AbstractHuman pancreatic beta-cells may exhibit complex mixed-mode oscillatory electrical activity, which underlies insulin secretion. A recent biophysical model of human beta-cell electrophysiology can simulate such bursting behavior, but a mathematical understanding of the model’s dynamics is still lacking. Here we exploit time-scale separation to simplify the original model to a simpler three-dimensional model that retains the behavior of the original model and allows us to apply geometric singular perturbation theory to investigate the origin of mixed-mode oscillations. Changing a parameter modeling the maximal conductance of a potassium current, we find that the reduced model possesses a singular Hopf bifurcation that results in small-amplitude oscillations, which go through a period-doubling sequence and chaos until the birth of a large-scale return mechanism and bursting dynamics. The theory of folded node singularities provide insight into the bursting dynamics further away from the singular Hopf bifurcation and the eventual transition to simple spiking activity. Numerical simulations confirm that the insight obtained from the analysis of the reduced model can be lifted back to the original model.

scholarly journals Geometric Analysis of Mixed-mode Oscillations in a Model of Electrical Activity in Human Beta-cells

2021 ◽  
Author(s):  
Simone Battaglin ◽  
Morten Gram Pedersen
Keyword(s):  
Hopf Bifurcation ◽  
Electrical Activity ◽  
Beta Cells ◽  
Pancreatic Beta Cells ◽  
Mixed Mode ◽  
Original Model ◽  
Biophysical Model ◽  
Reduced Model ◽  
Geometric Singular Perturbation Theory ◽  
Mixed Mode Oscillations

Abstract Human pancreatic beta-cells may exhibit complex mixed-mode oscillatory electrical activity, which underlies insulin secretion. A recent biophysical model of human beta-cell electrophysiology can simulate such bursting behavior, but a mathematical understanding of the model's dynamics is still lacking. Here we exploit time-scale separation to simplify the original model to a simpler three-dimensional model that retains the behavior of the original model and allows us to apply geometric singular perturbation theory to investigate the origin of mixed-mode oscillations. Changing a parameter modeling the maximal conductance of a potassium current, we nd that the reduced model possesses a singular Hopf bifurcation that results in small-amplitude oscillations, which go through a period-doubling sequence and chaos until the birth of a large-scale return mechanism and bursting dynamics. The theory of folded node singularities provide insight into the bursting dynamics further away from the singular Hopf bifurcation and the eventual transition to simple spiking activity. Numerical simulations confirm that the insight obtained from the analysis of the reduced model can be lifted back to the original model.

scholarly journals Complexity of a Peroxidase-Oxidase Reaction Model

2021 ◽  
Author(s):  
Jason Gallas ◽  
Marcus Hauser ◽  
Lars Folke Olsen
Keyword(s):  
Chemical Reaction ◽  
Mixed Mode ◽  
Period Doubling ◽  
Reaction Model ◽  
Chaotic Behaviour ◽  
Mixed Mode Oscillations ◽  
Oscillating Reaction ◽  
Oxidase Reaction

The peroxidase-oxidase oscillating reaction was the first (bio)chemical reaction to show chaotic behaviour. The reaction is rich in bifurcation scenarios, from period-doubling to peak-adding mixed mode oscillations. Here, we study...

Chaos via mixed-mode oscillations

1991 ◽  
Vol 337 (1646) ◽  
pp. 291-298 ◽  
Keyword(s):  
Mixed Mode ◽  
Phase Locking ◽  
Period Doubling ◽  
Specific Model ◽  
Dynamical Behaviour ◽  
Object A ◽  
Mixed Mode Oscillations ◽  
Catalysed Oxidation ◽  
Periodic State ◽  
Peroxidase Enzyme

The route by which chaos arises from mixed-mode periodic states in a model of the peroxidase enzyme catalysed oxidation of NADH is described. The specific model studied displays a rich variety of exotic dynamical behaviour including simple oscillations, quasiperiodicity, bistability between periodic states, complex periodic oscillations (including the mixed-mode type) and chaos. The route to chaos in this system involves a torus attractor which becomes destabilized and breaks up into a fractal object, a strange attractor. The mixed-mode states correspond to phase-locking on this fractal attractor and are arranged in staircases according to the complexity of the state. In this paper, we investigate the sequence leading from a mixed-mode periodic state to a chaotic one in the staircase region and find a familiar cascade of period-doubling bifurcations, which finally culminate in chaos.

Period doubling and other complex bifurcations in non-isothermal chemical systems

1990 ◽  
Vol 332 (1624) ◽  
pp. 51-68 ◽  
Keyword(s):  
Mixed Mode ◽  
Period Doubling ◽  
Heat Rate ◽  
Oscillatory Behaviour ◽  
Chemical Heat ◽  
Experimental Conditions ◽  
Chemical Systems ◽  
Mixed Mode Oscillations ◽  
Self Heating ◽  
Thermal Feedback

Chemical feedback in the form of chain-branching or autocatalysis can give rise to oscillatory behaviour in very simple models involving only two variables. Many chemical reactions are also exothermic. This chemical heat release can give rise to self-heating and hence to thermal feedback, where the temperature varies as well as the concentrations. When chemical and thermal feedback are coupled, the range of responses that can be observed are increased dramatically. These features are demonstrated through the simple non-isothermal autocatalator scheme p-> A rate = A + 2B-> 3B rate = k1 2, A-^ B rate = kza, C + heat rate = At its simplest, the reaction can be steady or can show simple period-1 oscillations. More complex oscillations, with higher periodicity appear as the experimental conditions are varied, with period doubling, mixed-mode oscillations and aperiodicity (chemical chaos).

scholarly journals Clinical and Functional Characteristics of a Novel KLF11 Cys354Phe Variant Involved in Maturity-Onset Diabetes of the Young

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yujing Sun ◽  
Jingru Qu ◽  
Jing Wang ◽  
Ruxing Zhao ◽  
Chuan Wang ◽  
...  
Keyword(s):  
Insulin Secretion ◽  
Blood Glucose ◽  
Beta Cells ◽  
Pancreatic Beta Cells ◽  
Luciferase Reporter ◽  
Maturity Onset Diabetes ◽  
Insulin Expression ◽  
Insulin Promoter ◽  
Impaired Insulin ◽  
Reporter Assays

Background. Mutations in human KLF11 may lead to the development of maturity-onset diabetes of the young 7 (MODY7). This occurs due to impaired insulin synthesis in the pancreas. To date, the clinical and functional characteristics of the novel KLF11 mutation c.1061G > T have not yet been reported. Methods. Whole-exon sequencing was used to screen the proband and family members with clinical suspicion of the KLF11 variant. Luciferase reporter assays were used to investigate whether the KLF11 variant binds to the insulin promoter. Real-time PCR, western blotting, and glucose-stimulated insulin secretion (GSIS) analysis were used to analyze the KLF11 variant that regulates insulin expression and insulin secretion activity in beta cell lines. The Freestyle Libre H (Abbott Diabetes Care Ltd) was used to dynamically monitor the proband daily blood glucose levels. Results. Mutation screening for the whole exon genes identified a heterozygous KLF11 (c.1061G > T) variant in the proband, her mother, and her maternal grandfather. Cell-based luciferase reporter assays using wild-type and mutant transgenes revealed that the KLF11 (c.1061G > T) variant had impaired insulin promoter regulation activity. Moreover, this variant was found to impair insulin expression and insulin secretion in pancreatic beta cells. The proband had better blood glucose control without staple food intake ( p < 0.05 ). Conclusions. Herein, for the first time, we report a novel KLF11 (c.1061G > T) monogenic mutation associated with MODY7. This variant has impaired insulin promoter regulation activity and impairs insulin expression and secretion in pancreatic beta cells. Therefore, administering oral antidiabetic drugs along with dietary intervention may benefit the proband.

Slow manifold structure and the emergence of mixed-mode oscillations

1997 ◽  
Vol 107 (8) ◽  
pp. 2881-2889 ◽  
Author(s):  
Andrei Goryachev ◽  
Peter Strizhak ◽  
Raymond Kapral
Keyword(s):  
Mixed Mode ◽  
Slow Manifold ◽  
Mixed Mode Oscillations ◽  
Manifold Structure

scholarly journals Activity of Water Soluble Polysaccharide White Bentul (Colocasia Esculenta Schott [L]) As a Candidate for Antidiabetic Agent

2018 ◽  
Vol 2 (1) ◽  
pp. 1
Author(s):  
Sentot Joko Raharjo
Keyword(s):  
Blood Glucose ◽  
Blood Glucose Level ◽  
Glucose Level ◽  
Pancreatic Beta Cells ◽  
Water Soluble ◽  
Antidiabetic Activity ◽  
Glucose Levels ◽  
Blood Glucose Levels ◽  
Pancreatic Cells ◽  
Soluble Polysaccharide

White bentul tuber is one of tuber plant species which have bioactive compound of Water Soluble Polysaccharide (WSP) and potentially healthy nutrition in the therapy of metabolic syndrome disease. The purpose of this research is to prove the ability of WSP isolate to reduce blood glucose level in white mice.  Research method include the yield of WSP isolates white bentul tuber using enzymatic method, WSP identification using HPLC with Aminex HPX-87C BIORAD5 columns, and antidiabetic activity test using white mices. Test activity was performed in six treatment groups (Normal, Induction STZ 20 mg/ kgBW, Induction STZ 20 mg / kgBW + metformin 195mg / KgBW, three treatment with STZ induction 20 mg/ kgBW and WSP isolate with concentration 200, 400, and 600mg / kgBW). Determination of blood glucose levels using glucometer and supported by observation of histologic improvement of beta pancreatic cells in white mice that have necrosis. The result research are WSP yield of 4.81% and WSP level of 94.45%. Results of blood glucose levels of mice induced STZ 20mg/kgBW decreased optimal blood glucose with a dose of WSP 400mg/kgBW in the first week and histologic improvement of beta pancreatic cells that experienced the most optimal necrosis at WSP dose of 200 mg/kgBW. The conclusion of this research is the provision WSP isolate of white bentul tubers at doses of 200, 400, 600 mg/kgBW can decrease the blood glucose level induced STZ 20mg/kg BW and histological improvement in pancreatic beta cells at the most optimal dose of 200 mg / kgKeywords: White bentul tuber, water soluble polysaccharides, diabetes mellitus, beta pancratic cells   

Controlling Hyperglycaemia Diabetes Mellitus Type-II: Bromocriptine Alone or in Combination with Metformin

2021 ◽  
Vol 15 (12) ◽  
pp. 3348-3350
Author(s):  
Khadija Mastoor ◽  
Faisal Idrees Khan ◽  
Iram Imran ◽  
Anila Errum ◽  
Sadia Sharif ◽  
...  
Keyword(s):  
Diabetes Mellitus ◽  
Body Weight ◽  
Blood Glucose ◽  
Blood Glucose Level ◽  
Glucose Level ◽  
Pancreatic Beta Cells ◽  
Male Rats ◽  
Diabetic Patients ◽  
Group 2 ◽  
Therapeutic Doses

Background: Diabetes Mellitus is one of the leading cause of morbidity and mortality globally. According to WHO there is a steady increase in the number of diabetic patients annually. Maintenance of good glycaemic control in type 2 diabetic patients typically becomes progressively more difficult as the duration of disease lengthens due to decline in the capacity of the pancreatic beta cells for glucose stimulated insulin release, in the presence of insulin resistance. This study is conducted to observe the effect of metformin and bromocriptine individually and sub-therapeutic doses of these drugs when used as a combination therapy. Objective: The objective of this study is to primarily investigate and then compare the antihyperglycemic effects of bromocriptine with metformin, also to see the combined effect of sub therapeutic doses of both these drugs. Methodology: Random allotment of 24 albino male rats was done in four groups. Group 1 was kept as control. Alloxan monohydrate was given to group 2, 3 and 4 and diabetes was induced. Group 2 and 3 were treated with metformin (1.5mg/kg body weight) and bromocriptine (3 mg/kg body weight) respectively while group 4 was treated with sub therapeutic doses of metformin (1 mg/kg body weight) and bromocriptine (1.5 mg/kg body weight)both. Serum glucose levels were estimated at 1, 10, 20 and 30 days. Results: Results showed that metformin reduces blood glucose level significantly where as bromocriptine also showed reduction of blood glucose level but not as significantly as metformin. However, the combination of metformin and bromocriptine showed much reduction in blood glucose level than metformin and bromocriptine used alone. Conclusion: Bromocriptine and metformin when combined ameliorated blood guclose efficiently than given alone Keywords: Diabetes mellitus, bromocriptine, metformin

BLOOD GLUCOSE LEVEL IN MICE

1967 ◽  
Vol 56 (4) ◽  
pp. 713-725 ◽  
Author(s):  
Ingmar Lundquist ◽  
Claus Rerup
Keyword(s):  
Blood Glucose ◽  
Blood Glucose Level ◽  
Glucose Level ◽  
Pancreatic Beta Cells ◽  
Plasma Insulin ◽  
Alloxan Diabetes ◽  
Physiological Significance ◽  
Measurable Effect ◽  
Hypoglycaemic Effect ◽  
Plasma Insulin Levels

ABSTRACT The hypoglycaemic effect of synthetic tetraicosapeptide corticotrophin was investigated in NMRI mice in order to determine its physiological significance as well as its mechanism of action. It was found that in normal non-fasting mice corticotrophin produced a maximal hypoglycaemic response at a dose level of about 5 μg per 20 g mouse (1250 milliunits per 20 g mouse). The ED50 of the hypoglycaemic effect was about 1000 times larger than the ED50 for adrenal cortical stimulation. Immunoassayable insulin was markedly increased 15 minutes following 5 μg of corticotrophin, whereas following a maximal steroidogenic dose (1.6 nanogram) or following ether stress the plasma insulin levels were normal. In adrenalectomized mice the administration of 5 μg of corticotrophin had practically no effect on the blood glucose level, whereas pretreatment with a glucocorticosteroid in adrenalectomized mice markedly restored the hypoglycaemic response. Acutely hypophysectomized mice showed a hypoglycaemic response to corticotrophin indistinguishable from that found in normal mice, whereas animals hypophysectomized 3–7 days before corticotrophin injection showed a smaller response. Corticotrophin in a dose of 5 μg per 20 g mouse had no hypoglycaemic effect in mice with manifest alloxan diabetes. Corticotrophin injected 5 minutes following a diabetogenic dose of alloxan hardly had any measurable effect on the acute initial alloxan hyperglycaemia, whereas the latter was greatly reduced when corticotrophin was given 5 minutes before alloxan administration. Pretreatment with corticotrophin did not change the frequency or intensity of the ensuing diabetic condition in mice. It is concluded that the corticotrophin induced hypoglycaemia is dependent on 1) the presence of normally functioning pancreatic beta-cells; and 2) the presence of glucocorticosteroids. It is doubtful whether the observed hypoglycaemia has any physiological significance.

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