Complex Dynamics in the Kummer-Olsen Model of Calcium Oscillations

2012 ◽  
Vol 226-228 ◽  
pp. 505-509
Author(s):  
Zheng Fei Wu ◽  
Yi Zhou
Keyword(s):  
Theoretical Analysis ◽  
Calcium Release ◽  
Complex Dynamics ◽  
Cytosolic Calcium ◽  
Vital Role ◽  
Calcium Oscillations ◽  
Calcium Oscillation ◽  
Center Manifold Theorem ◽  
Oscillation Model ◽  
Calcium Induced Calcium Release

Oscillations of cytosolic calcium concentration, known as calcium oscillations, play a vital role in providing the intracellular signalling. These oscillations are explained with a model based on calcium-induced calcium release (CICR). The nonlinear dynamics of the Kummer-Olsen calcium oscillation model is discussed by using the center manifold theorem and bifurcation theory, including the variation in classification and stability of equilibria with parameter value. It is concluded that the appearance and disappearance of calcium oscillations in this system is due to supercritical Hopf bifurcation of equilibria. Finally, numerical simulations are carried out to support the theoretical analysis of the research. By combining the existing numerical results with the theoretical analysis results in this paper, a complete description of the dynamics of the Kummer-Olsen calcium oscillation model has now been obtained.

Dynamical Analysis of a Calcium Oscillation Model in Non-Excitable Cells

2012 ◽  
Vol 226-228 ◽  
pp. 521-525
Author(s):  
Yi Zhou ◽  
Zheng Fei Wu ◽  
Yu Hong Huo
Keyword(s):  
Calcium Release ◽  
Complex Dynamics ◽  
Calcium Oscillations ◽  
Dynamical Analysis ◽  
Phase Portraits ◽  
Calcium Oscillation ◽  
Stimulation Level ◽  
Time Courses ◽  
Stability And Bifurcations ◽  
Calcium Induced Calcium Release

The Borghans-Dupont model of calcium oscillations based on both the calcium-induced calcium release and calcium-activated inositol trisphosphate concentration degradation is considered. Dynamical effect of the stimulation level on the calcium oscillation behavior is studied. The qualitative theory of differential equations is used to explain the mechanism of these oscillations. We investigate the existence, types, stability and bifurcations of the equilibria by applying the centre manifold theorem, stability theory and bifurcation theory and prove that oscillations are due to supercritical Hopf bifurcation. Finally, we perform numerical simulations, including time courses, phase portraits and bifurcation diagram, to validate the correctness and the effectiveness of our theoretical analysis. These results may be instructive for understanding the role of the stimulation level played in complex dynamics in this model.

scholarly journals Fractional Dynamics in Calcium Oscillation Model

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yoothana Suansook ◽  
Kitti Paithoonwattanakij
Keyword(s):  
Fractional Order ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Cell Types ◽  
Cytosolic Calcium ◽  
Cardiac Cells ◽  
Calcium Oscillations ◽  
Calcium Oscillation ◽  
Fractional Dynamics ◽  
Oscillation Model

The calcium oscillations have many important roles to perform many specific functions ranging from fertilization to cell death. The oscillation mechanisms have been observed in many cell types including cardiac cells, oocytes, and hepatocytes. There are many mathematical models proposed to describe the oscillatory changes of cytosolic calcium concentration in cytosol. Many experiments were observed in various kinds of living cells. Most of the experimental data show simple periodic oscillations. In certain type of cell, there exists the complex periodic bursting behavior. In this paper, we have studied further the fractional chaotic behavior in calcium oscillations model based on experimental study of hepatocytes proposed by Kummer et al. Our aim is to explore fractional-order chaotic pattern in this oscillation model. Numerical calculation of bifurcation parameters is carried out using modified trapezoidal rule for fractional integral. Fractional-order phase space and time series at fractional order are present. Numerical results are characterizing the dynamical behavior at different fractional order. Chaotic behavior of the model can be analyzed from the bifurcation pattern.

Hopf Bifurcation and Numerical Simulation in a Calcium Oscillation Model

2012 ◽  
Vol 226-228 ◽  
pp. 510-515 ◽  
Author(s):  
Hong Kun Zuo ◽  
Quan Bao Ji ◽  
Yi Zhou
Keyword(s):  
Hopf Bifurcation ◽  
Intracellular Signaling ◽  
Calcium Release ◽  
Dimensional Space ◽  
Calcium Oscillations ◽  
Calcium Oscillation ◽  
Subcritical Hopf Bifurcation ◽  
Calcium Induced Calcium Release ◽  
Parameter Values ◽  
Centre Manifold Theorem

Calcium oscillations play a very important role in providing the intracellular signaling, and many mathematical models have been proposed to describe calcium oscillations. The Shen-Larter model presented here is based on calcium-induced calcium release (CICR) and the inositol trisphosphate cross-coupling (ICC). Nonlinear dynamics of this model is investigated by using the centre manifold theorem and bifurcation theory, including the variation in classification and stability of equilibria with different parameter values. The results show that the appearance and disappearance of calcium oscillations are due to subcritical Hopf bifurcation of equilibria. The numerical simulations are performed in order to illustrate the correctness of our theoretical analysis, including the bifurcation diagram of fixed points, the phase diagram of the system in two dimensional space and time series.

scholarly journals Calcium-Induced Calcium Release in Smooth Muscle

2000 ◽  
Vol 115 (5) ◽  
pp. 653-662 ◽  
Author(s):  
M.L. Collier ◽  
G. Ji ◽  
Y.-X. Wang ◽  
M.I. Kotlikoff
Keyword(s):  
Smooth Muscle ◽  
Calcium Release ◽  
Striated Muscle ◽  
Single Channel ◽  
Ryanodine Receptors ◽  
Cytosolic Calcium ◽  
Heart Cells ◽  
Tight Coupling ◽  
Calcium Induced Calcium Release ◽  
Ca2 Channels

Calcium-induced calcium release (CICR) has been observed in cardiac myocytes as elementary calcium release events (calcium sparks) associated with the opening of L-type Ca2+ channels. In heart cells, a tight coupling between the gating of single L-type Ca2+ channels and ryanodine receptors (RYRs) underlies calcium release. Here we demonstrate that L-type Ca2+ channels activate RYRs to produce CICR in smooth muscle cells in the form of Ca2+ sparks and propagated Ca2+ waves. However, unlike CICR in cardiac muscle, RYR channel opening is not tightly linked to the gating of L-type Ca2+ channels. L-type Ca2+ channels can open without triggering Ca2+ sparks and triggered Ca2+ sparks are often observed after channel closure. CICR is a function of the net flux of Ca2+ ions into the cytosol, rather than the single channel amplitude of L-type Ca2+ channels. Moreover, unlike CICR in striated muscle, calcium release is completely eliminated by cytosolic calcium buffering. Thus, L-type Ca2+ channels are loosely coupled to RYR through an increase in global [Ca2+] due to an increase in the effective distance between L-type Ca2+ channels and RYR, resulting in an uncoupling of the obligate relationship that exists in striated muscle between the action potential and calcium release.

Fast calcium wave propagation mediated by electrically conducted excitation and boosted by CICR

2008 ◽  
Vol 294 (4) ◽  
pp. C917-C930 ◽  
Author(s):  
J. M. A. M. Kusters ◽  
W. P. M. van Meerwijk ◽  
D. L. Ypey ◽  
A. P. R. Theuvenet ◽  
C. C. A. M. Gielen
Keyword(s):  
Intracellular Calcium ◽  
Chloride Channels ◽  
Calcium Release ◽  
Rat Kidney ◽  
Electrical Coupling ◽  
Calcium Oscillations ◽  
Calcium Wave ◽  
Calcium Oscillation ◽  
Pacemaker Cell ◽  
Pacemaker Cells

We have investigated synchronization and propagation of calcium oscillations, mediated by gap junctional excitation transmission. For that purpose we used an experimentally based model of normal rat kidney (NRK) cells, electrically coupled in a one-dimensional configuration (linear strand). Fibroblasts such as NRK cells can form an excitable syncytium and generate spontaneous inositol 1,4,5-trisphosphate (IP3)-mediated intracellular calcium waves, which may spread over a monolayer culture in a coordinated fashion. An intracellular calcium oscillation in a pacemaker cell causes a membrane depolarization from within that cell via calcium-activated chloride channels, leading to an L-type calcium channel-based action potential (AP) in that cell. This AP is then transmitted to the electrically connected neighbor cell, and the calcium inflow during that transmitted AP triggers a calcium wave in that neighbor cell by opening of IP3 receptor channels, causing calcium-induced calcium release (CICR). In this way the calcium wave of the pacemaker cell is rapidly propagated by the electrically transmitted AP. Propagation of APs in a strand of cells depends on the number of terminal pacemaker cells, the L-type calcium conductance of the cells, and the electrical coupling between the cells. Our results show that the coupling between IP3-mediated calcium oscillations and AP firing provides a robust mechanism for fast propagation of activity across a network of cells, which is representative for many other cell types such as gastrointestinal cells, urethral cells, and pacemaker cells in the heart.

Ionomycin-stimulated phasic myometrial contractions

1995 ◽  
Vol 269 (4) ◽  
pp. E779-E785
Author(s):  
M. Phillippe ◽  
E. M. Chien ◽  
M. Freij ◽  
T. Saunders
Keyword(s):  
Phospholipase C ◽  
Calcium Release ◽  
Calcium Influx ◽  
Inositol Phosphate ◽  
Calcium Ionophore ◽  
Cytosolic Calcium ◽  
Calcium Oscillations ◽  
Production Studies ◽  
Inositol Phosphate Production

Ionomycin, a calcium ionophore, facilitates the sustained entry of extracellular calcium; however, in myometrial tissue it stimulates phasic contractions. This study sought to define further this unanticipated effect of ionomycin and to begin to explore the possible mechanism(s) involved. Utilizing rat uterine strips, in vitro isometric contraction studies were performed to determine the effects of ionomycin with and without membrane-permeant inhibitors of cytosolic calcium oscillations. To determine the effects of ionomycin on phospholipase C, qualitative inositol phosphate production studies were performed. The in vitro contraction studies confirmed that ionomycin-stimulated phasic myometrial contractions were potentially dependent on stimulation of phospholipase C, calcium-induced calcium release, and additional calcium influx through dihydropyridine-sensitive membrane calcium channels. The inositol phosphate production studies confirmed that ionomycin stimulated phospholipase C in a dose-related fashion to levels comparable to oxytocin. In summary, these observations have confirmed the ability of ionomycin to generate dose-related phasic myometrial contractions through mechanisms potentially involving the phosphatidylinositol-signaling pathway.

Parathyroid hormone increases cytosolic calcium concentration in adult rat cardiac myocytes

1993 ◽  
Vol 264 (6) ◽  
pp. H1998-H2006 ◽  
Author(s):  
M. Smogorzewski ◽  
M. Zayed ◽  
Y. B. Zhang ◽  
J. Roe ◽  
S. G. Massry
Keyword(s):  
Parathyroid Hormone ◽  
G Protein ◽  
Cardiac Myocytes ◽  
Calcium Release ◽  
Protein S ◽  
Cytosolic Calcium ◽  
Release Mechanism ◽  
Adult Rats ◽  
Adult Rat ◽  
Calcium Induced Calcium Release

The heart is a target organ for parathyroid hormone (PTH), and the action of this hormone on the myocardium may be mediated through the ability of PTH to increase cytosolic calcium ([Ca2+]i) in the myocardial cells. However, direct evidence for such an effect of PTH is lacking, and the mechanism(s) through which the hormone can potentially exert such an effect have not been elucidated. In the present study these questions were examined using cardiac myocytes isolated from adult rats. Both PTH-(1–34) and PTH-(1–84) produced a dose-dependent increase in [Ca2+]i of myocytes, but the effect of the latter was significantly (P < 0.01) greater than the former. This action of PTH was abolished by the inactivation of the hormone, the use of a PTH antagonist, or by verapamil. The G protein activator, guanosine 5'-O-(3-thiothriphosphate) (GTP gamma S), mimicked the effect of PTH, whereas pertussis toxin, the G protein inhibitor, guanosine 5'-O-(2-thiodiphosphate) (GDP beta S), or ryanodine significantly reduced the PTH-induced rise in [Ca2+]i. Dibutyryl- and 8-bromoadenosine-3',5'-cyclic monophosphate, forskolin, 12-O-tetradecanoylphorbol 13-acetate, and staurosporine did not increase [Ca2+]i in myocytes, and staurosporine did not alter the PTH-induced rise in [Ca2+]i. BAY K 8644 augmented the effect of PTH on [Ca2+]i. These data demonstrate that 1) PTH increases [Ca2+]i of cardiac myocytes, 2) this action is receptor mediated and is produced by activation of the L-type calcium channels following stimulation of G protein(s), and 3) the rise in [Ca2+]i is due to both augmented entry of calcium into the myocytes and mobilization of calcium from sarcoplasmic reticulum by a calcium-induced calcium release mechanism.

scholarly journals Kv10.1 Regulates Microtubule Dynamics during Mitosis

Cancers ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2409
Author(s):  
Naira Movsisyan ◽  
Luis A. Pardo
Keyword(s):  
Calcium Release ◽  
Human Tumor ◽  
Cytosolic Calcium ◽  
Calcium Oscillations ◽  
Microtubule Dynamics ◽  
Cancer Tissue ◽  
Aberrant Expression ◽  
Peripheral Tissues ◽  
Voltage Gated ◽  
M Phase

Kv10.1 (potassium voltage-gated channel subfamily H member 1, known as EAG1 or Ether-à-go-go 1), is a voltage-gated potassium channel, prevailingly expressed in the central nervous system. The aberrant expression of Kv10.1 is detected in over 70% of all human tumor tissues and correlates with poorer prognosis. In peripheral tissues, Kv10.1 is expressed almost exclusively during the G2/M phase of the cell cycle and regulates its progression—downregulation of Kv10.1 extends the duration of the G2/M phase both in cancer and healthy cells. Here, using biochemical and imaging techniques, such as live-cell measurements of microtubule growth and of cytosolic calcium, we elucidate the mechanisms of Kv10.1-mediated regulation at the G2/M phase. We show that Kv10.1 has a dual effect on mitotic microtubule dynamics. Through the functional interaction with ORAI1 (calcium release-activated calcium channel protein 1), it modulates cytosolic calcium oscillations, thereby changing microtubule behavior. The inhibition of either Kv10.1 or ORAI1 stabilizes the microtubules. In contrast, the knockdown of Kv10.1 increases the dynamicity of mitotic microtubules, resulting in a stronger spindle assembly checkpoint, greater mitotic spindle angle, and a decrease in lagging chromosomes. Understanding of Kv10.1-mediated modulation of the microtubule architecture will help to comprehend how cancer tissue benefits from the presence of Kv10.1, and thereby increase the efficacy and safety of Kv10.1-directed therapeutic strategies.

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