The capillary Kir channel as sensor and amplifier of neuronal signals: Modeling insights on K+-mediated neurovascular communication.

Neuronal activity leads to an increase in local cerebral blood flow (CBF) to allow adequate supply of oxygen and nutrients to active neurons, a process termed neurovascular coupling (NVC). We have previously shown that capillary endothelial cell (cEC) inwardly rectifying K+ (Kir) channels can sense neuronally evoked increases in interstitial K+ and induce rapid and robust dilations of upstream parenchymal arterioles, suggesting a key role of cECs in NVC. The requirements of this signal conduction remain elusive. Here, we utilize mathematical modeling to investigate how small outward currents in stimulated cECs can elicit physiologically relevant spread of vasodilatory signals within the highly interconnected brain microvascular network to increase local CBF. Our model shows that the Kir channel can act as an "on-off" switch in cECs to hyperpolarize the cell membrane as extracellular K+ increases. A local hyperpolarization can be amplified by the voltage-dependent activation of Kir in neighboring cECs. Sufficient Kir density enables robust amplification of the hyperpolarizing stimulus and produces responses that resemble action potentials in excitable cells. This Kir-mediated excitability can remain localized in the stimulated region or regeneratively propagate over significant distances in the microvascular network, thus dramatically increasing the efficacy of K+ for eliciting local hyperemia. Modeling results show how changes in cEC transmembrane current densities and gap junctional resistances can affect K+-mediated NVC and suggest a key role for Kir as a sensor of neuronal activity and an amplifier of retrograde electrical signaling in the cerebral vasculature.

Contractile pericytes determine the direction of blood flow at capillary junctions.

The essential function of the circulatory system is to continuously and efficiently supply the O2 and nutrients necessary to meet the metabolic demands of every cell in the body, a function in which vast capillary networks play a key role. Capillary networks serve an additional important function in the central nervous system: acting as a sensory network, they detect neuronal activity in the form of elevated extracellular K+ and initiate a retrograde, propagating, hyperpolarizing signal that dilates upstream arterioles to rapidly increase local blood flow. Yet, little is known about how blood entering this network is distributed on a branch-to-branch basis to reach specific neurons in need. Here, we demonstrate that capillary-enwrapping projections of junctional, contractile pericytes within a postarteriole transitional region differentially constrict to structurally and dynamically determine the morphology of capillary junctions and thereby regulate branch-specific blood flow. We further found that these contractile pericytes are capable of receiving propagating K+-induced hyperpolarizing signals propagating through the capillary network and dynamically channeling red blood cells toward the initiating signal. By controlling blood flow at junctions, contractile pericytes within a functionally distinct postarteriole transitional region maintain the efficiency and effectiveness of the capillary network, enabling optimal perfusion of the brain.

Biophysical properties of microvascular endothelium: Requirements for initiating and conducting electrical signals.

OBJECTIVE: Electrical signaling along the endothelium underlies spreading vasodilation and blood flow control. We use mathematical modeling to determine the electrical properties of the endothelium and gain insight into the biophysical determinants of electrical conduction. METHODS: Electrical conduction data along endothelial tubes (40 µm wide, 2.5 mm long) isolated from mouse skeletal muscle resistance arteries were analyzed using cable equations and a multicellular computational model. RESULTS: Responses to intracellular current injection attenuate with an axial length constant (λ) of 1.2-1.4 mm. Data were fitted to estimate the axial (ra ; 10.7 MΩ/mm) and membrane (rm ; 14.5 MΩ∙mm) resistivities, EC membrane resistance (Rm ; 12 GΩ), and EC-EC coupling resistance (Rgj ; 4.5 MΩ) and predict that stimulation of ≥30 neighboring ECs is required to elicit 1 mV of hyperpolarization at distance = 2.5 mm. Opening Ca2+ -activated K+ channels (KCa ) along the endothelium reduced λ by up to 55%. CONCLUSIONS: High Rm makes the endothelium sensitive to electrical stimuli and able to conduct these signals effectively. Whereas the activation of a group of ECs is required to initiate physiologically relevant hyperpolarization, this requirement is increased by myoendothelial coupling and KCa activation along the endothelium inhibits conduction by dissipating electrical signals.

The yin and yang of KV channels in cerebral small vessel pathologies.

Cerebral SVDs encompass a group of genetic and sporadic pathological processes leading to brain lesions, cognitive decline, and stroke. There is no specific treatment for SVDs, which progress silently for years before becoming clinically symptomatic. Here, we examine parallels in the functional defects of PAs in CADASIL, a monogenic form of SVD, and in response to SAH, a common type of hemorrhagic stroke that also targets the brain microvasculature. Both animal models exhibit dysregulation of the voltage-gated potassium channel, KV 1, in arteriolar myocytes, an impairment that compromises responses to vasoactive stimuli and impacts CBF autoregulation and local dilatory responses to neuronal activity (NVC). However, the extent to which this channelopathy-like defect ultimately contributes to these pathologies is unknown. Combining experimental data with computational modeling, we describe the role of KV 1 channels in the regulation of myocyte membrane potential at rest and during the modest increase in extracellular potassium associated with NVC. We conclude that PA resting membrane potential and myogenic tone depend strongly on KV 1.2/1.5 channel density, and that reciprocal changes in KV channel density in CADASIL and SAH produce opposite effects on extracellular potassium-mediated dilation during NVC.

Can endothelial hemoglobin-α regulate nitric oxide vasodilatory signaling?

We used mathematical modeling to investigate nitric oxide (NO)-dependent vasodilatory signaling in the arteriolar wall. Detailed continuum cellular models of calcium (Ca2+) dynamics and membrane electrophysiology in smooth muscle and endothelial cells (EC) were coupled with models of NO signaling and biotransport in an arteriole. We used this theoretical approach to examine the role of endothelial hemoglobin-α (Hbα) as a modulator of NO-mediated myoendothelial feedback, as previously suggested in Straub et al. (Nature 491: 473-477, 2012). The model considers enriched expression of inositol 1,4,5-triphosphate receptors (IP3Rs), endothelial nitric oxide synthase (eNOS) enzyme, Ca2+-activated potassium (KCa) channels and Hbα in myoendothelial projections (MPs) between the two cell layers. The model suggests that NO-mediated myoendothelial feedback is plausible if a significant percentage of eNOS is localized within or near the myoendothelial projection. Model results show that the ability of Hbα to regulate the myoendothelial feedback is conditional to its colocalization with eNOS near MPs at concentrations in the high nanomolar range (>0.2 µM or 24,000 molecules). Simulations also show that the effect of Hbα observed in in vitro experimental studies may overestimate its contribution in vivo, in the presence of blood perfusion. Thus, additional experimentation is required to quantify the presence and spatial distribution of Hbα in the EC, as well as to test that the strong effect of Hbα on NO signaling seen in vitro, translates also into a physiologically relevant response in vivo.NEW & NOTEWORTHY Mathematical modeling shows that although regulation of nitric oxide signaling by hemoglobin-α (Hbα) is plausible, it is conditional to its presence in significant concentrations colocalized with endothelial nitric oxide synthase in myoendothelial projections. Additional experimentation is required to test that the strong effect of Hbα seen in vitro translates into a physiologically relevant response in vivo.

Endothelial mitochondria regulate the intracellular Ca2+ response to fluid shear stress.

Shear stress is known to stimulate an intracellular free calcium concentration ([Ca(2+)]i) response in vascular endothelial cells (ECs). [Ca(2+)]i is a key second messenger for signaling that leads to vasodilation and EC survival. Although it is accepted that the shear-induced [Ca(2+)]i response is, in part, due to Ca(2+) release from the endoplasmic reticulum (ER), the role of mitochondria (second largest Ca(2+) store) is unknown. We hypothesized that the mitochondria play a role in regulating [Ca(2+)]i in sheared ECs. Cultured ECs, loaded with a Ca(2+)-sensitive fluorophore, were exposed to physiological levels of shear stress. Shear stress elicited [Ca(2+)]i transients in a percentage of cells with a fraction of them displaying oscillations. Peak magnitudes, percentage of oscillating ECs, and oscillation frequencies depended on the shear level. [Ca(2+)]i transients/oscillations were present when experiments were conducted in Ca(2+)-free solution (plus lanthanum) but absent when ECs were treated with a phospholipase C inhibitor, suggesting that the ER inositol 1,4,5-trisphosphate receptor is responsible for the [Ca(2+)]i response. Either a mitochondrial uncoupler or an electron transport chain inhibitor, but not a mitochondrial ATP synthase inhibitor, prevented the occurrence of transients and especially inhibited the oscillations. Knockdown of the mitochondrial Ca(2+) uniporter also inhibited the shear-induced [Ca(2+)]i transients/oscillations compared with controls. Hence, EC mitochondria, through Ca(2+) uptake/release, regulate the temporal profile of shear-induced ER Ca(2+) release. [Ca(2+)]i oscillation frequencies detected were within the range for activation of mechanoresponsive kinases and transcription factors, suggesting that dysfunctional EC mitochondria may contribute to cardiovascular disease by deregulating the shear-induced [Ca(2+)]i response.

Stochastic model of endothelial TRPV4 calcium sparklets: effect of bursting and cooperativity on EDH.

We examined the endothelial transient receptor vanilloid 4 (TRPV4) channel's vasodilatory signaling using mathematical modeling. The model analyzes experimental data by Sonkusare and coworkers on TRPV4-induced endothelial Ca(2+) events (sparklets). A previously developed continuum model of an endothelial and a smooth muscle cell coupled through microprojections was extended to account for the activity of a TRPV4 channel cluster. Different stochastic descriptions for the TRPV4 channel flux were examined using finite-state Markov chains. The model also took into consideration recent evidence for the colocalization of intermediate-conductance calcium-activated potassium channels (IKCa) and TRPV4 channels near the microprojections. A single TRPV4 channel opening resulted in a stochastic localized Ca(2+) increase in a small region (i.e., few µm(2) area) close to the channel. We predict micromolar Ca(2+) increases lasting for the open duration of the channel sufficient for the activation of low-affinity endothelial KCa channels. Simulations of a cluster of four TRPV4 channels incorporating burst and cooperative gating kinetics provided quantal Ca(2+) increases (i.e., steps of fixed amplitude), similar to the experimentally observed Ca(2+) sparklets. These localized Ca(2+) events result in endothelium-derived hyperpolarization (and SMC relaxation), with magnitude that depends on event frequency. The gating characteristics (bursting, cooperativity) of the TRPV4 cluster enhance Ca(2+) spread and the distance of KCa channel activation. This may amplify the EDH response by the additional recruitment of distant KCa channels.

Role of microprojections in myoendothelial feedback--a theoretical study.

We investigated the role of myoendothelial projections (MPs) in endothelial cell (EC) feedback response to smooth muscle cell (SMC) stimulation using mathematical modelling. A previously developed compartmental EC-SMC model is modified to include MPs as subcellular compartments in the EC. The model is further extended into a 2D continuum model using a finite element method (FEM) approach and electron microscopy images to account for MP geometry. The EC and SMC are coupled via non-selective myoendothelial gap junctions (MEGJs) which are located on MPs and allow exchange of Ca(2+), K(+), Na(+) and Cl(-) ions and inositol 1,4,5-triphosphate (IP3). Models take into consideration recent evidence for co-localization of intermediate-conductance calcium-activated potassium channels (IKCa) and IP3 receptors (IP3Rs) in the MPs. SMC stimulation causes an IP3-mediated Ca(2+) transient in the MPs with limited global spread in the bulk EC. A hyperpolarizing feedback generated by the localized IKCa channels is transmitted to the SMC via MEGJs. MEGJ resistance (Rgj) and the density of IKCa and IP3R in the projection influence the extent of EC response to SMC stimulation. The predicted Ca(2+) transients depend also on the volume and geometry of the MP. We conclude that in the myoendothelial feedback response to SMC stimulation, MPs are required to amplify the SMC initiated signal. Simulations suggest that the signal is mediated by IP3 rather than Ca(2+) diffusion and that a localized rather than a global EC Ca(2+) mobilization is more likely following SMC stimulation.

Kinetic analysis of DAF-FM activation by NO: toward calibration of a NO-sensitive fluorescent dye.

Nitric oxide (NO) research in biomedicine has been hampered by the absence of a method that will allow quantitative measurement of NO in biological tissues with high sensitivity and selectivity, and with adequate spatial and temporal resolution. 4-amino-5-methylamino-2',7'-difluorofluorescein (DAF-FM) is a NO sensitive fluorescence probe that has been used widely for qualitative assessment of cellular NO production. However, calibration of the fluorescent signal and quantification of NO concentration in cells and tissues using fluorescent probes, have provided significant challenge. In this study we utilize a combination of mathematical modeling and experimentation to elucidate the kinetics of NO/DAF-FM reaction in solution. Modeling and experiments suggest that the slope of fluorescent intensity (FI) can be related to NO concentration according to the equation: ddtFI=2αk(1)NO(2)O(2)DAF-FMkNO+DAF-FM where α is a proportionality coefficient that relates FI to unit concentration of activated DAF-FM, k(1) is the NO oxidation rate constant, and k was estimated to be 4.3±0.6. The FI slope exhibits saturation kinetics with DAF-FM concentration. Interestingly, the effective half-maximum constant (EC(50)) increases proportionally to NO concentration. This result is not in agreement with the proposition that N(2)O(3) is the NO oxidation byproduct that activates DAF-FM. Kinetic analysis suggests that the reactive intermediate should exhibit NO-dependent consumption and thus NO(2)() is a more likely candidate. The derived rate law can be used for the calibration of DAF-FM fluorescence and the quantification of NO concentration in biological tissues.

Agmatine induced NO dependent rat mesenteric artery relaxation and its impairment in salt-sensitive hypertension.

l-Arginine and its decarboxylated product, agmatine are important mediators of NO production and vascular relaxation. However, the underlying mechanisms of their action are not understood. We have investigated the role of arginine and agmatine in resistance vessel relaxation of Sprague-Dawley (SD) and Dahl salt-sensitive hypertensive rats. Second or 3rd-order mesenteric arterioles were cannulated in an organ chamber, pressurized and equilibrated before perfusing intraluminally with agonists. The vessel diameters were measured after mounting on the stage of a microscope fitted with a video camera. The gene expression in Dahl rat vessel homogenates was ascertained by real-time PCR. l-Arginine initiated relaxations (EC50, 5.8±0.7mM; n=9) were inhibited by arginine decarboxylase (ADC) inhibitor, difluoromethylarginine (DFMA) (EC50, 18.3±1.3mM; n=5) suggesting that arginine-induced vessel relaxation was mediated by agmatine formation. Agmatine relaxed the SD rat vessels at significantly lower concentrations (EC50, 138.7±12.1µM; n=22), which was compromised by l-NAME (l-N(G)-nitroarginine methyl ester, an eNOS inhibitor), RX821002 (α-2 AR antagonist) and pertussis toxin (G-protein inhibitor). The agmatine-mediated vessel relaxation from high salt Dahl rats was abolished as compared to that from normal salt rats (EC50, 143.9±23.4µM; n=5). The α-2A AR, α-2B AR and eNOS mRNA expression was downregulated in mesenteric arterioles of high-salt treated Dahl hypertensive rats. These findings demonstrate that agmatine facilitated the relaxation via activation of α-2 adrenergic G-protein coupled receptor and NO synthesis, and this pathway is compromised in salt-sensitive hypertension.

Multiple factors influence calcium synchronization in arterial vasomotion.

The intercellular synchronization of spontaneous calcium (Ca(2+)) oscillations in individual smooth muscle cells is a prerequisite for vasomotion. A detailed mathematical model of Ca(2+) dynamics in rat mesenteric arteries shows that a number of synchronizing and desynchronizing pathways may be involved. In particular, Ca(2+)-dependent phospholipase C, the intercellular diffusion of inositol trisphosphate (IP(3), and to a lesser extent Ca(2+)), IP(3) receptors, diacylglycerol-activated nonselective cation channels, and Ca(2+)-activated chloride channels can contribute to synchronization, whereas large-conductance Ca(2+)-activated potassium channels have a desynchronizing effect. Depending on the contractile state and agonist concentrations, different pathways become predominant, and can be revealed by carefully inhibiting the oscillatory component of their total activity. The phase shift between the Ca(2+) and membrane potential oscillations can change, and thus electrical coupling through gap junctions can mediate either synchronization or desynchronization. The effect of the endothelium is highly variable because it can simultaneously enhance the intercellular coupling and affect multiple smooth muscle cell components. Here, we outline a system of increased complexity and propose potential synchronization mechanisms that need to be experimentally tested.

Endothelial Ca2+ wavelets and the induction of myoendothelial feedback.

When arteries constrict to agonists, the endothelium inversely responds, attenuating the initial vasomotor response. The basis of this feedback mechanism remains uncertain, although past studies suggest a key role for myoendothelial communication in the signaling process. The present study examined whether second messenger flux through myoendothelial gap junctions initiates a negative-feedback response in hamster retractor muscle feed arteries. We specifically hypothesized that when agonists elicit depolarization and a rise in second messenger concentration, inositol trisphosphate (IP(3)) flux activates a discrete pool of IP(3) receptors (IP(3)Rs), elicits localized endothelial Ca(2+) transients, and activates downstream effectors to moderate constriction. With use of integrated experimental techniques, this study provided three sets of supporting observations. Beginning at the functional level, we showed that blocking intermediate-conductance Ca(2+)-activated K(+) channels (IK) and Ca(2+) mobilization from the endoplasmic reticulum (ER) enhanced the contractile/electrical responsiveness of feed arteries to phenylephrine. Next, structural analysis confirmed that endothelial projections make contact with the overlying smooth muscle. These projections retained membranous ER networks, and IP(3)Rs and IK channels localized in or near this structure. Finally, Ca(2+) imaging revealed that phenylephrine induced discrete endothelial Ca(2+) events through IP(3)R activation. These events were termed recruitable Ca(2+) wavelets on the basis of their spatiotemporal characteristics. From these findings, we conclude that IP(3) flux across myoendothelial gap junctions is sufficient to induce focal Ca(2+) release from IP(3)Rs and activate a discrete pool of IK channels within or near endothelial projections. The resulting hyperpolarization feeds back on smooth muscle to moderate agonist-induced depolarization and constriction.

Intercellular communication in the vascular wall: a modeling perspective.

Movement of ions (Ca(2+) , K(+) , Na(+) , and Cl(-) ) and second messenger molecules like inositol 1, 4, 5-trisphosphate inside and in between different cells is the basis of many signaling mechanisms in the microcirculation. In spite of the vast experimental efforts directed toward evaluation of these fluxes, it has been a challenge to establish their roles in many essential microcirculatory phenomena. Recently, detailed theoretical models of calcium dynamics and plasma membrane electrophysiology have emerged to assist in the quantification of these intra and intercellular fluxes and enhance understanding of their physiological importance. This perspective reviews selected models relevant to estimation of such intra and intercellular ionic and second messenger fluxes and prediction of their relative significance to a variety of vascular phenomena, such as myoendothelial feedback, conducted responses, and vasomotion.

Inhibition of nitric oxide synthesis in mouse macrophage cells by feverfew supercritical extract.

Feverfew is the most commonly used medicinal herb against migraine headache. The antimigraine mechanism of feverfew supercritical extract was investigated in vitro using the mouse macrophage cell line (RAW 264.7). Mouse macrophage cells were treated with lipopolysaccharide in the presence and absence of feverfew extracts. Inhibition of lipopolysaccharide-induced nitric oxide and TNF-α synthesis were quantified by ELISA. The mRNA and protein expression of iNOS and eNOS genes were analysed by RT-PCR and western blot analysis, respectively. The feverfew extract inhibited both nitric oxide (NO) and TNF-α production in a dose-dependent manner with complete inhibition of NO occurring at 5 µg/mL of feverfew extract. Both eNOS and iNOS mRNA levels were unchanged with the feverfew treatment. However, eNOS and iNOS proteins were significantly down-regulated by the feverfew extract. Feverfew inhibition of NO is due to the down-regulation of both eNOS and iNOS enzymes at the translational and/or post-translational level.

Modeling Ca2+ signaling in the microcirculation: intercellular communication and vasoreactivity.

A network of intracellular signaling pathways and complex intercellular interactions regulate calcium mobilization in vascular cells, arteriolar tone, and blood flow. Different endothelium-derived vasoreactive factors have been identified and the importance of myoendothelial communication in vasoreactivity is now well appreciated. The ability of many vascular networks to conduct signals upstream also is established. This phenomenon is critical for both short-term changes in blood perfusion as well as long-term adaptations of a vascular network. In addition, in a phenomenon termed vasomotion, arterioles often exhibit spontaneous oscillations in diameter. This is thought to improve tissue oxygenation and enhance blood flow. Experimentation has begun to reveal important aspects of the regulatory machinery and the significance of these phenomena for the regulation of local perfusion and oxygenation. Mathematical modeling can assist in elucidating the complex signaling mechanisms that participate in these phenomena. This review highlights some of the important experimental studies and relevant mathematical models that provide the current understanding of these mechanisms in vasoreactivity.

A mathematical model of vasoreactivity in rat mesenteric arterioles. II. Conducted vasoreactivity.

This study presents a multicellular computational model of a rat mesenteric arteriole to investigate the signal transduction mechanisms involved in the generation of conducted vasoreactivity. The model comprises detailed descriptions of endothelial (ECs) and smooth muscle (SM) cells (SMCs), coupled by nonselective gap junctions. With strong myoendothelial coupling, local agonist stimulation of the EC or SM layer causes local changes in membrane potential (V(m)) that are conducted electrotonically, primarily through the endothelium. When myoendothelial coupling is weak, signals initiated in the SM conduct poorly, but the sensitivity of the SMCs to current injection and agonist stimulation increases. Thus physiological transmembrane currents can induce different levels of local V(m) change, depending on cell's gap junction connectivity. The physiological relevance of current and voltage clamp stimulations in intact vessels is discussed. Focal agonist stimulation of the endothelium reduces cytosolic calcium (intracellular Ca(2+) concentration) in the prestimulated SM layer. This SMC Ca(2+) reduction is attributed to a spread of EC hyperpolarization via gap junctions. Inositol (1,4,5)-trisphosphate, but not Ca(2+), diffusion through homocellular gap junctions can increase intracellular Ca(2+) concentration in neighboring ECs. The small endothelial Ca(2+) spread can amplify the total current generated at the local site by the ECs and through the nitric oxide pathway, by the SMCs, and thus reduces the number of stimulated cells required to induce distant responses. The distance of the electrotonic and Ca(2+) spread depends on the magnitude of SM prestimulation and the number of SM layers. Model results are consistent with experimental data for vasoreactivity in rat mesenteric resistance arteries.

A mathematical model of vasoreactivity in rat mesenteric arterioles: I. Myoendothelial communication.

To study the effect of myoendothelial communication on vascular reactivity, we integrated detailed mathematical models of Ca(2+) dynamics and membrane electrophysiology in arteriolar smooth muscle (SMC) and endothelial (EC) cells. Cells are coupled through the exchange of Ca(2+), Cl(-), K(+), and Na(+) ions, inositol 1,4,5-triphosphate (IP(3)), and the paracrine diffusion of nitric oxide (NO). EC stimulation reduces intracellular Ca(2+) ([Ca(2+)](i)) in the SMC by transmitting a hyperpolarizing current carried primarily by K(+). The NO-independent endothelium-derived hyperpolarization was abolished in a synergistic-like manner by inhibition of EC SK(Ca) and IK(Ca) channels. During NE stimulation, IP(3) diffusing from the SMC induces EC Ca(2+) release, which, in turn, moderates SMC depolarization and [Ca(2+)](i) elevation. On the contrary, SMC [Ca(2+)](i) was not affected by EC-derived IP(3). Myoendothelial Ca(2+) fluxes had no effect in either cell. The EC exerts a stabilizing effect on calcium-induced calcium release-dependent SMC Ca(2+) oscillations by increasing the norepinephrine concentration window for oscillations. We conclude that a model based on independent data for subcellular components can capture major features of the integrated vessel behavior. This study provides a tissue-specific approach for analyzing complex signaling mechanisms in the vasculature.

Modeling the role of endoplasmic reticulum-mitochondria microdomains in calcium dynamics.

Upon inositol trisphosphate (IP3) stimulation of non-excitable cells, including vascular endothelial cells, calcium (Ca2+) shuttling between the endoplasmic reticulum (ER) and mitochondria, facilitated by complexes called Mitochondria-Associated ER Membranes (MAMs), is known to play an important role in the occurrence of cytosolic Ca2+ concentration ([Ca2+]Cyt) oscillations. A mathematical compartmental closed-cell model of Ca2+ dynamics was developed that accounts for ER-mitochondria Ca2+ microdomains as the µd compartment (besides the cytosol, ER and mitochondria), Ca2+ influx to/efflux from each compartment and Ca2+ buffering. Varying the distribution of functional receptors in MAMs vs. the rest of ER/mitochondrial membranes, a parameter called the channel connectivity coefficient (to the µd), allowed for generation of [Ca2+]Cytoscillations driven by distinct mechanisms at various levels of IP3 stimulation. Oscillations could be initiated by the transient opening of IP3 receptors facing either the cytosol or the µd, and subsequent refilling of the respective compartment by Ca2+ efflux from the ER and/or the mitochondria. Only under conditions where the µd became the oscillation-driving compartment, silencing the Mitochondrial Ca2+ Uniporter led to oscillation inhibition. Thus, the model predicts that alternative mechanisms can yield [Ca2+]Cyt oscillations in non-excitable cells, and, under certain conditions, the ER-mitochondria µd can play a regulatory role.

Nitric oxide bioavailability in the microcirculation: insights from mathematical models.

Over the last 30 years nitric oxide (NO) has emerged as a key signaling molecule involved in a number of physiological functions, including in the regulation of microcirculatory tone. Despite significant scientific contributions, fundamental questions about NO's role in the microcirculation remain unanswered. Mathematical modeling can assist in investigations of microcirculatory NO physiology and address experimental limitations in quantifying vascular NO concentrations. The number of mathematical models investigating the fate of NO in the vasculature has increased over the last few years, and new models are continuously emerging, incorporating an increasing level of complexity and detail. Models investigate mechanisms that affect NO availability in health and disease. They examine the significance of NO release from nonendothelial sources, the effect of transient release, and the complex interaction of NO with other substances, such as heme-containing proteins and reactive oxygen species. Models are utilized to test and generate hypotheses for the mechanisms that regulate NO-dependent signaling in the microcirculation.

A mathematical model of Ca2+ dynamics in rat mesenteric smooth muscle cell: agonist and NO stimulation.

A mathematical model of calcium dynamics in vascular smooth muscle cell (SMC) was developed based on data mostly from rat mesenteric arterioles. The model focuses on (a) the plasma membrane electrophysiology; (b) Ca2+ uptake and release from the sarcoplasmic reticulum (SR); (c) cytosolic balance of Ca2+, Na+, K+, and Cl ions; and (d) IP3 and cGMP formation in response to norepinephrine(NE) and nitric oxide (NO) stimulation. Stimulation with NE induced membrane depolarization and an intracellular Ca2+ ([Ca2+]i) transient followed by a plateau. The plateau concentrations were mostly determined by the activation of voltage-operated Ca2+ channels. NE causes a greater increase in [Ca2+]i than stimulation with KCl to equivalent depolarization. Model simulations suggest that the effect of[Na+]i accumulation on the Na+/Ca2+ exchanger (NCX) can potentially account for this difference.Elevation of [Ca2+]i within a concentration window (150-300 nM) by NE or KCl initiated [Ca2+]i oscillations with a concentration-dependent period. The oscillations were generated by the nonlinear dynamics of Ca2+ release and refilling in the SR. NO repolarized the NE-stimulated SMC and restored low [Ca2+]i mainly through its effect on Ca2+-activated K+ channels. Under certain conditions, Na+-K+-ATPase inhibition can result in the elevation of [Na+]i and the reversal of NCX, increasing resting cytosolic and SR Ca2+ content, as well as reactivity to NE. Blockade of the NCX's reverse mode could eliminate these effects. We conclude that the integration of the selected cellular components yields a mathematical model that reproduces, satisfactorily, some of the established features of SMC physiology. Simulations suggest a potential role of intracellular Na+ in modulating Ca2+ dynamics and provide insights into the mechanisms of SMC constriction, relaxation, and the phenomenon of vasomotion. The model will provide the basis for the development of multi-cellular mathematical models that will investigate microcirculatory function in health and disease.