Adam Kapela

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 NCXs 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.

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 cells 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 Ca2+ dynamics and membrane electrophysiology in arteriolar smooth muscle (SMC) and endothelial (EC) cells. Cells are coupled through the exchange of Ca2+, Cl−, K+, and Na+ ions, inositol 1,4,5‐triphosphate (IP3), and the paracrine diffusion of nitric oxide (NO). EC stimulation reduces intracellular Ca2+ ([Ca2+ 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 SKCa and IKCa channels. During NE stimulation, IP3diffusing from the SMC induces EC Ca2+ release, which, in turn, moderates SMC depolarization and [Ca2+]i elevation. On the contrary, SMC [Ca2+]i was not affected by EC‐derived IP3. Myoendothelial Ca2+ fluxes had no effect in either cell. The EC exerts a stabilizing effect on calcium‐induced calcium release‐dependent SMC Ca2+ 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.

Role of microprojections in myoendothelial feedback – a theoretical study

•  Endothelial microprojections (MPs) are cellular extensions of endothelial cells (ECs) that may be involved in regulation of smooth muscle cell (SMC) constriction in blood vessels. •  We developed computational models to investigate the role of MPs in generating EC feedback during SMC stimulation. The models account for the geometry of MPs and heterogeneous distribution of membrane channels and receptors in an EC. •  Simulations show that SMC stimulation causes calcium release in and around EC MPs that activates hyperpolarizing currents in ECs and moderates SMC constriction. •  The results help us better understand the mechanisms that regulate blood flow and pressure.

Intercellular communication in the vascular wall: a modeling perspective.

Please cite this paper as Nagaraja S, Kapela A, Tsoukias NM. Intercellular communication in the vascular wall: a modeling perspective. Microcirculation 19: 391‐402, 2012.

Stochastic Model of Endothelial TRPV4 Calcium Sparklets: Effect of Bursting and Cooperativity on EDH

We examined the endothelial transient receptor vanilloid 4 (TRPV4) channels 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.

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.

Integrative mathematical modeling for analysis of microcirculatory function

The microcirculatory vascular tone and the regional blood flow are regulated by an elaborate network of intracellular and extracellular signaling pathways with multiple feedback control loops. This complicates interpretation of experimental data and limits our ability to design appropriate interventions. Mathematical modeling offers a systematic approach for system and data analysis and for guiding new experimentation. We describe here our efforts to model signal transduction events involved in the regulation of blood flow and integrate mechanisms at the cellular level to describe function at the multicellular/whole-vessel level. The model provides a) a working database of rat mesenteric endothelial and smooth muscle physiology where newly acquired experimental information on cell electrophysiology and signal transduction can be incorporated, and b) a tool that will assist investigations on the regulation of vascular resistance in health and disease. An example of model application to the study of the pathogenesis of salt-sensitive hypertension is illustrated.

New aspects of vulnerability in heterogeneous models of ventricular wall and its modulation by loss of cardiac sodium channel function

This numerical study quantified the vulnerable period (VP) in heterogeneous models of the cardiac ventricular wall and its modulation by loss of cardiac sodium channel function (NaLOF). According to several articles, NaLOF prolongs the VP and therefore increases the risk of re-entrant arrhythmias, but the studies used uniform models, neglecting spatial variation of action potential duration (APD). Here, physiological transmural heterogeneity was introduced into one-dimensional cables of the Luo-Rudy model cells. Based on the results with paired S1–S2 stimulation, a generalised formula for the VP was proposed that takes into account APD dispersion, and new phenomena pertaining to the VP are described that are not present in homogeneous excitable media. Under normal conditions, the vulnerable period in the heterogeneous cable media. Under normal conditions, the vulnerable period in the heterogeneous cable with M cells was in the range of 0–21 ms, depending on S2 localisation, but only 2,4 ms throughout the uniform fibre. Unidirectional propagation induced during the VP could be antegrade or retrograde, depending on the localisation of the test stimulus and cable parameters, but, in a uniform model, it was always in the retrograde direction. Reduced sodium channel conductance from control 16 mS μF−1 to 4mS μF−1 decreased the maximum VP to 11 ms in the heterogeneous cable, but increased the VP to 3 ms in the homogeneous model. It was concluded that realistic models of cardiac vulnerability should take into account spatial variations of cellular refractoriness. Several new qualitative and quantitative aspects of the VP were revealed, and the modulation of the VP by NaLOF differed significantly in heterogeneous and homogeneous models.

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

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.