We have developed a mathematical model of arterial vasomotion in which irregular rhythmic activity is generated by the nonlinear interaction of intracellular and membrane oscillators that depend on cyclic release of Ca2+ from internal stores and cyclic influx of extracellular Ca2+, respectively. Four key control variables were selected on the basis of the pharmacological characteristics of histamine-induced vasomotion in rabbit ear arteries: Ca2+ concentration in the cytosol, Ca2+ concentration in ryanodine-sensitive stores, cell membrane potential, and the open state probability of Ca2+-activated K+ channels. Although not represented by independent dynamic variables, the model also incorporates Na+/Ca2+exchange, the Na+-K+-ATPase, Cl− fluxes, and Ca2+ efflux via the extrusion ATPase. Simulations reproduce a wide spectrum of experimental observations, including 1) the effects of interventions that modulate the functionality of Ca2+ stores and membrane ion channels, 2) paradoxes such as the apparently unpredictable dual action of Ca2+ antagonists and low extracellular Na+ concentration, which can abolish vasomotion or promote the appearance of large-amplitude oscillations, and 3) period-doubling, quasiperiodic, and intermittent routes to chaos. Nonlinearity is essential to explain these diverse patterns of experimental vascular response.

Frenneaux. Arterial distensibility: acute changes following dynamic exercise in normal subjects.

Background: The mechanism underlying sperm PLCζ interaction with its target membrane is unresolved.Results: EF-hand mutations introduced into PLCζ reduce in vivo Ca2+ oscillation inducing activity and in vitro interaction with PIP2.Conclusion: EF-hand domain is essential for targeting PLCζ to PIP2-containing membranes.Significance: We propose a novel mechanism by which sperm PLCζ is anchored to its physiological membrane substrate.

Phospholipase C-zeta (PLCζ) is a sperm-specific protein believed to cause Ca(2+) oscillations and egg activation during mammalian fertilization. PLCζ is very similar to the somatic PLCδ1 isoform but is far more potent in mobilizing Ca(2+) in eggs. To investigate how discrete protein domains contribute to Ca(2+) release, we assessed the function of a series of PLCζ/PLCδ1 chimeras. We examined their ability to cause Ca(2+) oscillations in mouse eggs, enzymatic properties using in vitro phosphatidylinositol 4,5-bisphosphate (PIP2) hydrolysis and their binding to PIP2 and PI(3)P with a liposome interaction assay. Most chimeras hydrolyzed PIP2 with no major differences in Ca(2+) sensitivity and enzyme kinetics. Insertion of a PH domain or replacement of the PLCζ EF hands domain had no deleterious effect on Ca(2+) oscillations. In contrast, replacement of either XY-linker or C2 domain of PLCζ completely abolished Ca(2+) releasing activity. Notably, chimeras containing the PLCζ XY-linker bound to PIP2-containing liposomes, while chimeras containing the PLCζ C2 domain exhibited PI(3)P binding. Our data suggest that the EF hands are not solely responsible for the nanomolar Ca(2+) sensitivity of PLCζ and that membrane PIP2 binding involves the C2 domain and XY-linker of PLCζ. To investigate the relationship between PLC enzymatic properties and Ca(2+) oscillations in eggs, we have developed a mathematical model that incorporates Ca(2+)-dependent InsP3 generation by the PLC chimeras and their levels of intracellular expression. These numerical simulations can for the first time predict the empirical variability in onset and frequency of Ca(2+) oscillatory activity associated with specific PLC variants.

The effects of pharmacological interventions that modulate Ca(2+) homeodynamics and membrane potential in rat isolated cerebral vessels during vasomotion (i.e., rhythmic fluctuations in arterial diameter) were simulated by a third-order system of nonlinear differential equations. Independent control variables employed in the model were [Ca(2+)] in the cytosol, [Ca(2+)] in intracellular stores, and smooth muscle membrane potential. Interactions between ryanodine- and inositol 1,4,5-trisphosphate-sensitive intracellular Ca(2+) stores and transmembrane ion fluxes via K(+) channels, Cl(-) channels, and voltage-operated Ca(2+) channels were studied by comparing simulations of oscillatory behavior with experimental measurements of membrane potential, intracellular free [Ca(2+)] and vessel diameter during a range of pharmacological interventions. The main conclusion of the study is that a general model of vasomotion that predicts experimental data can be constructed by a low-order system that incorporates nonlinear interactions between dynamical control variables.

In the present work, an elaborate one-dimensional thermofluid model for a human body is presented. By contrast to the existing pure conduction-/perfusion-based models, the proposed methodology couples the arterial fluid dynamics of a human body with a multi-segmental bioheat model of surrounding solid tissues. In the present configuration, arterial flow is included through a network of elastic vessels. More than a dozen solid segments are employed to represent the heat conduction in the surrounding tissues, and each segment is constituted by a multilayered circular cylinder. Such multi-layers allow flexible delineation of the geometry and incorporation of properties of different tissue types. The coupling of solid tissue and fluid models requires subdivision of the arterial circulation into large and small arteries. The heat exchange between tissues and arterial wall occurs by convection in large vessels and by perfusion in small arteries. The core region, including the heart, provides the inlet conditions for the fluid equations. In the proposed model, shivering, sweating, and perfusion changes constitute the basis of the thermoregulatory system. The equations governing flow and heat transfer in the circulatory system are solved using a locally conservative Galerkin approach, and the heat conduction in the surrounding tissues is solved using a standard implicit backward Euler method. To investigate the effectiveness of the proposed model, temperature field evolutions are monitored at different points of the arterial tree and in the surrounding tissue layers. To study the differences due to flow-induced convection effects on thermal balance, the results of the current model are compared against those of the widely used modelling methodologies. The results show that the convection significantly influences the temperature distribution of the solid tissues in the vicinity of the arteries. Thus, the inner convection has a more predominant role in the human body heat balance than previously thought. To demonstrate its capabilities, the proposed new model is used to study different scenarios, including thermoregulation inactivity and variation in surrounding atmospheric conditions.

We provide experimental evidence for the existence of Shil'nikov homoclinic chaos in the fluctuations in flow which can be observed in isolated perfused rabbit ear arteries, and establish a close association between homoclinicity and type-III Pomeau-Manneville intermittent behavior. The transition between the homoclinic scenario and type-III intermittency is clarified by a mathematical model of the arterial smooth muscle cell. Simulations of the effects of nitric oxide (NO) by the vascular endothelium on these patterns of behavior closely match experimental observations.

A sperm-specific phospholipase C-zeta (PLCz) is believed to play an essential role in oocyte activation during mammalian fertilization. Sperm PLCz has been shown to trigger a prolonged series of repetitive Ca 2+ transients or oscillations in oocytes that precede activation.This remarkable intracellular Ca 2+ signalling phenomenon is a distinctive characteristic observed during in vitro fertilization by sperm. Previous studies have notably observed an apparent differential ability of PLCz from disparate mammalian species to trigger Ca 2+ oscillations in mouse oocytes. However, the molecular basis and confirmation of the apparent PLCz species difference in activity remains to be provided. In the present study, we provide direct evidence for the superior effectiveness of human PLCz relative to mouse PLCz in generating Ca 2+ oscillations in mouse oocytes. In addition, we have designed and constructed a series of human/mouse PLCz chimeras to enable study of the potential role of discrete PLCz domains in conferring the enhanced Ca 2+ signalling potency of human PLCz. Functional analysis of these human/mouse PLCz domain chimeras suggests a novel role of the EF-hand domain in the species-specific differences in PLCz activity. Our empirical observations are compatible with a basic mathematical model for the Ca 2+ dependence of generating cytoplasmic Ca 2+ oscillations in mammalian oocytes by sperm PLCz.