Minimal model of arterial chaos generated by coupled intracellular and membrane Ca<sup>2+</sup>oscillators

Parthimos, Dimitris; Edwards, David Hughes; Griffith, T. M.

doi:10.1152/ajpheart.1999.277.3.h1119

Cited by 67 publications

(155 citation statements)

References 69 publications

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“…Some previous models of vasomotion have assumed that oscillations are intrinsic to the intracellular dynamics of smooth muscle activation (Achakri et al, 1994;Gonzalez-Fernandez & Ermentrout, 1994;Parthimos et al, 1999Parthimos et al, , 2007Peng et al, 2001;Gustafsson & Nilsson, 1993b). In the present model, the dynamics of activation are governed by a simple first-order differential equation that has no intrinsic oscillatory behaviour.…”

Section: Discussionmentioning

confidence: 92%

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Spontaneous oscillations in a model for active control of microvessel diameters

Arciero

Secomb²

2011

Mathematical Medicine and Biology

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A new theory is presented for the origin of spontaneous oscillations in blood vessel diameters that are observed experimentally in the microcirculation. These oscillations, known as vasomotion, involve timevarying contractions of the vascular smooth muscle in the walls of arterioles. It is shown that such oscillations can arise as a result of interactions between the mechanics of the vessel wall and the dynamics of the active contraction of smooth muscle cells in response to circumferential tension in the wall. A theoretical model is developed in which the diameter and the degree of activation in a vessel are dynamic variables. The model includes effects of wall shear stress and oxygen-dependent metabolic signals on smooth muscle activation and is applied to a single vessel and to simplified network structures. The model equations predict limit cycle oscillations for certain ranges of parameters such as wall shear stress, arterial pressure and oxygen consumption rate. Predicted characteristics of the oscillations, including their sensitivity to arterial pressure, are consistent with experimental observations.

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Section: Discussionmentioning

confidence: 92%

“…Parthimos et al (1999) studied vasomotion at the cellular level by defining the ion transport systems that regulate vascular tone. In particular, the non-linear interaction of intracellular and membrane oscillators that depend on the cyclic release and influx of Ca 2+ was modelled, and irregular rhythmic behaviour was predicted.…”

Section: Previous Modelsmentioning

confidence: 99%

Spontaneous oscillations in a model for active control of microvessel diameters

Arciero

Secomb²

2011

Mathematical Medicine and Biology

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“…This current is directly related to the Ca 2ϩ influx (J VOCC ). A positive current indicates ion flow from the cytoplasm to the extracellular space; accordingly, the flux of ions into the cell is given by (15):…”

Section: Governing Equationsmentioning

confidence: 99%

“…The Ca 2ϩ transport system and membrane potential in a single arterial myocyte were modeled by two coupled oscillators that simulated the interaction between intracellular C Ca,i and membrane potential due to cyclic release of Ca 2ϩ from internal stores and cyclic influx of extracellular Ca 2ϩ (15). The stress produced by the cell was calculated using the four-state cross-bridge model of Hai and Murphy (5), which relates C Ca,i to cross-bridge formation and stress development.…”

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confidence: 99%

Mathematical model of excitation-contraction in a uterine smooth muscle cell

Bursztyn¹,

Eytan²,

Jaffa³

et al. 2007

American Journal of Physiology-Cell Physiology

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Uterine contractility is generated by contractions of myometrial smooth muscle cells (SMCs) that compose most of the myometrial layer of the uterine wall. Calcium ion (Ca 2ϩ ) entry into the cell can be initiated by depolarization of the cell membrane. The increase in the free Ca 2ϩ concentration within the cell initiates a chain of reactions, which lead to formation of cross bridges between actin and myosin filaments, and thereby the cell contracts. During contraction the SMC shortens while it exerts forces on neighboring cells. A mathematical model of myometrial SMC contraction has been developed to study this process of excitation and contraction. The model can be used to describe the intracellular Ca 2ϩ concentration and stress produced by the cell in response to depolarization of the cell membrane. The model accounts for the operation of three Ca 2ϩ control mechanisms: voltage-operated Ca 2ϩ channels, Ca 2ϩ pumps, and Na ϩ /Ca 2ϩ exchangers. The processes of myosin light chain (MLC) phosphorylation and stress production are accounted for using the cross-bridge model of Hai and Murphy (Am J Physiol Cell Physiol 254: C99 -C106, 1988) and are coupled to the Ca 2ϩ concentration through the rate constant of myosin phosphorylation. Measurements of Ca 2ϩ , MLC phosphorylation, and force in contracting cells were used to set the model parameters and test its ability to predict the cell response to stimulation. The model has been used to reproduce results of voltage-clamp experiments performed in myometrial cells of pregnant rats as well as the results of simultaneous measurements of MLC phosphorylation and force production in human nonpregnant myometrial cells. cellular calcium control mechanisms; myometrial contractions; myosin light chain phosphorylation UTERINE CONTRACTILITY is generated by contractions of the myometrial smooth muscle cells (SMCs) that compose most of the myometrial layer of the uterine wall. In the nonpregnant uterus, synchronous contractions of these SMCs produce changes in the geometry of the uterine fluid-wall interface. These changes induce intrauterine fluid motions that are essential during early phases of reproduction (3,11,28). During parturition, the synchronized contraction of these myocytes generates the forces required to deliver the baby out of the uterus. Depolarization of the cell membrane initiates calcium ion (Ca 2ϩ ) entry into the cells through voltage-operated Ca 2ϩ channels (VOCCs) and thereby a rise in the intracellular Ca 2ϩ concentration (C Ca,i ). The elevated level of C Ca,i allows binding of Ca 2ϩ and calmodulin, thus activating myosin light-chain kinase (MLCK), which phosphorylates a regulatory myosin light chain (MLC) (29,32). This subsequently allows the formation of cross bridges between actin and myosin filaments and the generation of muscle contraction.The excitation-contraction process was studied in both rat and human myometria using the voltage-clamp technique. Stimulation of isolated myocytes using voltage pulses revealed the current-voltage relationship...

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“…In one of the models [55], an intracellular subcompartment accounts for subcellular heterogeneity and the presence of subplasmalemmal microdomains. Elements from the minimal model of Parthimos [48] and the detailed approach of Yang [54] have been incorporated in a SMC model presented by Jacobsen and co-workers [51]. One or more of these pathways are often found disrupted in diseases related to altered vasoreactivity such as hypertension, diabetes etc [64,101,102].…”

Section: Potassium Channelsmentioning

confidence: 99%

Theoretical Investigations of Communication in the Microcirculation: Conducted Responses, Myoendothelial Projections and Endothelium Derived Hyperpolarizing Factor

Nagaraja¹

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This dissertation, written by Sridevi Nagaraja, and entitled Theoretical investigations of intercellular communication in the microcirculation: conducted responses, myoendothelial projections and endothelium derived hyperpolarizing factor, having been approved in respect to style and intellectual content, is referred to you for judgment.We have read this dissertation and recommend that it be approved. _______________________________________Wei-Chiang Lin dynamics in vascular cells in single as well as multicellular models. Advancement of these models is necessary to achieve the level of sophistication analogous to cardiac models. These models will contribute towards the development of a theoretical framework for the understanding of microcirculatory phenomena. It is also one of the most thoroughly studied vascular beds with vast amount of experimental data available. Therefore, in most of our models we use data from small rat mesenteric arteries (RMAs). This section describes the major channels and pumps present within the cytosol in the longitudinal direction of the cell.Through this process, it has become obvious that detailed models of Ca is still a need to build upon previous modeling work in order to develop cellular models that will assist in the investigations of vascular tone regulation in health and disease. Other channels specific to EC are described below. Inward rectifier potassium channelsInward rectifier potassium channels (K ir ) are sensitive to extracellular concentration of potassium in the range of 1 to 20 mM. These channels increase entry of potassium into the cell thereby hyperpolarizing of EC and subsequently the SMC. They are present in almost all endothelial cells and contribute towards the resting V m of the EC. EC K ir channels are known to be activated not only by potassium but also by shear stress. Theoretical modeling of vascular ECsThe first endothelial cell models were based on earlier generic models of Ca Endothelium derived controllers Nitric oxideNitric oxide was identified as the endothelium derived relaxing factor in 1980 ProstacyclinProstacyclin (PGI2) in rat mesenteric arterioles, PGI2 does not exert a hyperpolarizing effect. The involvement of PGI2 pathways is usually studied using COX inhibitor (Indomethacin). Endothelium derived hyperpolarizing factorEDHF is an endothelium derived non-nitric oxide (NO) and non-cyclicoxygenase and EC hyperpolarization by activation of IK Ca and SK Ca is now a widely accepted finger print of EDHF action across many studies.However, its propagation to the SMC is still being investigated. Myoendothelial feedbackStudies have shown that endothelium derived pathways can also be induced during SMC stimulation which brought about the concept of myoendothelial feedback. where R gj is gap junction resistance, and ∆V gj represents V m cells n-th and m-th ( Figure 2.2). where P gj,S is the gap junction permeability to S (e.g., Ca rectification is low at physiological concentration gradients, and a simpler linear approximation can ...

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Minimal model of arterial chaos generated by coupled intracellular and membrane Ca²⁺oscillators

Cited by 67 publications

References 69 publications

Spontaneous oscillations in a model for active control of microvessel diameters

Spontaneous oscillations in a model for active control of microvessel diameters

Mathematical model of excitation-contraction in a uterine smooth muscle cell

Theoretical Investigations of Communication in the Microcirculation: Conducted Responses, Myoendothelial Projections and Endothelium Derived Hyperpolarizing Factor

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Minimal model of arterial chaos generated by coupled intracellular and membrane Ca2+oscillators

Cited by 67 publications

References 69 publications

Spontaneous oscillations in a model for active control of microvessel diameters

Spontaneous oscillations in a model for active control of microvessel diameters

Mathematical model of excitation-contraction in a uterine smooth muscle cell

Theoretical Investigations of Communication in the Microcirculation: Conducted Responses, Myoendothelial Projections and Endothelium Derived Hyperpolarizing Factor

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Minimal model of arterial chaos generated by coupled intracellular and membrane Ca²⁺oscillators