| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
VASCULAR BIOLOGY
Department of Biomedical Engineering, Florida International University, Miami, Florida
Submitted 22 October 2006 ; accepted in final form 20 March 2007
 |
ABSTRACT |
|---|
 TOP ABSTRACT METHODSRESULTSDISCUSSIONAPPENDIX: MODEL EQUATIONSGRANTSREFERENCES |
|---|
microcirculation; vascular tone regulation; calcium influx pathway(s), plasma membrane Ca2+-ATPase
Mounting experimental evidence shows that EC Vm hyperpolarization itself, independently of its impact on EC Ca2+, is an important signal in resistance vessels. This electrical signal is generated by Ca2+-activated K+(KCa) currents and most likely comprises a key component of the EDHF response, which is transmitted to adjacent SMCs via myoendothelial gap junctions to cause vessel relaxation (14, 22, 52, 53). Another candidate for EDHF is simply K+ expelled by ECs into the vascular interstitial gap affecting K+-sensitive channels and transporters in both SMCs and ECs. The EC layer is most likely the main electrotonic current conduction route (for signals generated by either SMC or EC stimulation) along the vessel wall during conducted vasomotor responses (24, 31, 32, 65, 73). In addition, EC KCa channel inhibition can greatly affect arterial vasomotion (53), suggesting an important role of EC electrophysiology in this phenomenon.
Isolated ECs can be classified into two subtypes according to their resting Vm, namely, K-type and Cl-type (56). K-type EC resting Vm levels fall between –70 and –60 mV, which is close to the Nernst potential of K+ (EK) and thus indicates a dominant K+ membrane conductance, mainly due to the inward rectifier K+ (Kir) channel. On the other hand, Cl-type EC potential at rest is usually between –40 and –10 mV, which is close to the Nernst potential for Cl– (ECl) and suggests a Cl– conductance dominance under resting conditions. Experiments on isolated vessels suggest that ECs under hypoosmotic stress (which activates volume-sensitive Cl– conductance and brings Vm toward ECl) will not be able to hyperpolarize in response to raised extracellular K+ concentration ([K+]o), via Kir activation, and thus cannot relax the artery (25). Experimental data on isolated ECs, however, have shown that Cl-type and not K-type cells hyperpolarize in response to K+ challenge (55). To understand the complex Vm role in EC behavior and vascular tone regulation, the theoretical understanding of EC electrophysiology must be enhanced.
Previous EC mathematical modeling efforts have made important contributions toward describing both Ca2+ signaling and plasmalemmal electrical activity. Two models by Wiesner et al. (77, 78) simulated the response of human umbilical vein ECs (HUVECs) to thrombin stimulation and fluid shear stress. Wong and Klassen (80) developed a model describing both [Ca2+]i and electrical responses of vascular ECs to shear stress. Korngreen et al. (44) successfully simulated Ca2+ transients of electrically nonexcitable cells following agonist washout and intracellular Ca2+ store depletion. Schuster et al. (67) modeled the changes in Vm and [Ca2+]i following bradykinin stimulation of coronary artery ECs.
However, ECs regulate Ca2+ entry and Vm by expressing an abundant and diverse collection of plasmalemmal ion channels (55), which are for the most part absent in previous EC models. In addition, considering the balance of the other major intracellular ionic species (i.e., Na+, K+, and Cl–) is essential to modeling both single cell Vm behavior and cell-to-cell electrochemical coupling as Nernst potentials are concentration gradient dependent and gap junctions are nonselective, allowing the passage of small cytoplasmic ions. Consequently, there is a need to build on previous EC modeling work to provide a more biophysically detailed model of EC plasma membrane electrophysiology and further analyze the extent to which, if any, Vm affects EC intracellular Ca2+ dynamics.
In the last four decades, mathematical modeling of biological systems has contributed to the basic understanding of physiological behavior. For some organs (i.e., the heart), multiscale models have been developed that describe function at the macroscale level while incorporating mechanisms and events at the subcellular and molecular levels. A similar theoretical progress has not been paralleled in the vasculature. This mathematical model presents a first step toward this direction. The aims of this study were 1) to deliver a mathematical model that captures experimentally observed behavior of vascular ECs (and particularly ECs from rat mesenteric arterioles) and 2) to analyze how these cell responses emerge from the nonlinear interactions of individual cellular components.
|
METHODS |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIX: MODEL EQUATIONSGRANTSREFERENCES |
|---|
|
Model mathematical expressions are given in the APPENDIX, while model standard parameters and initial conditions are shown in Tables 1 and 2, respectively. Model components and parameter values were chosen to best describe rat mesenteric artery ECs. All abbreviations and symbol definitions can be found in the text and in Tables 1 and 2.
|
|
The EC plasma membrane electrical activity is modeled according to the classical Hodgkin-Huxley model as it is applied to a variety of single cell models, including ECs (37, 47, 67, 80, 83). The EC plasma membrane is thus regarded as a capacitor with its capacitance (Cm) shunted by several ionic currents that are described in detail in this section. Kirchhoff's current law describes dynamic Vm changes by:
 | (1) |
Kir channel current. Kir channels are considered key for resting cell Vm regulation, but their expression is rather heterogeneous among vascular EC types and some do not express it at all (55). IKir is presently modeled following Hodgkin-Huxley formalism for the instantaneous voltage-dependent gating of the channel's conductance (Eqs. A1–A3 in the APPENDIX) (50). Maximal Kir conductance is described by an increasing function of [K+]o and fits well Kir conductance data from guinea pig coronary ECs (data not shown) (75). Equations A1–A3 were fitted to rat mesenteric EC Kir current-voltage (I-V) data in the –100 to +40 mV range (Fig. 2A, solid line) (17). Kir conductance and Kir velocity fitted values are in agreement with data from Ref. 75. The Kir I-V model predictions under physiological intracellular K+ concentration ([K+]i) with control and elevated [K+]o displayed the reported "crossover" effect (Fig. 2A, dashed and dotted curves) (34, 55).
|
Ca2+-activated Cl– channel current.
The physiological significance of CaCC in vascular ECs remains controversial, but CaCCs can function in feedback control loops for Ca2+ entry into the cell via membrane depolarization, antagonizing the action of KCa channels (33, 62). The model ICaCC (Eqs. A6–A9) was based on and fitted to rescaled HUVEC data (Fig. 3A) (27). Calcium-dependent activation of CaCC was captured by a Hill function (Eq. A6). High positive Vm enhanced Ca2+-dependent activation, producing outward rectification of ICaCC (Fig. 3A) (27, 33, 62). This Vm-dependent activation was modeled using a Boltzmann function with a large positive half-activation Vm (Eq. A8). The time constant (
) of the voltage activation was fitted with a Gaussian function (Eq. A9) (data not shown).
|
|
NSC current. NSCs permeable to Ca2+ (39, 40) constitute Ca2+ entry pathways other than store operated in ECs (55). A Ca2+-permeable NSC is present in rat mesenteric ECs and has been characterized at the single channel level. It is permeable to major intracellular cations (i.e., Ca2+, Na+, and K+), displays PKG sensitivity, and plays a key function in the EDHF response of small mesenteric arterioles to KT-5823 (a potent PKG inhibitor) (23). However, since the study (23) did not measure whole cell INSC and its gating mechanisms were not thoroughly analyzed, these data were not used in the present INSC formulation. The model INSC contributes to the balance of Na+, K+, and Ca2+ and provides an alternative pathway for Ca2+ entry into the cytosol, as observed experimentally (55). The formulation developed here to model INSC (Eqs. A16–A20) is based on rescaled I-V data from a constitutively open NSC found in rabbit aorta ECs (63). This study (63) found a basally active INSC having a permeability ratio of 1:0.40:0.18 for K+:Na+:Ca2+, respectively, and this current was the major resting Vm determinant in these cells, which lack Kir channels. Like in SOC, external Ca2+also had a blocking effect on INSC Na+ permeability (PNSC,Na), whose description fits a Hill relationship similar to the one used to model PSOC,Na (Eq. A20). INSC was described by the sum of three GHK equations (Eq. A19), one for each permeant species, namely, Na+ (INSC,Na), K+ (INSC,K), and Ca2+ (INSC,Ca). GHK has been used before to model rat brain endothelial NSC (18). Additionally, INSC is not gated by store depletion or [Ca2+]i, as evidenced in calf pulmonary artery ECs (CPAECs) (55). Model INSC,Na is the major inward NSC current (data not shown), as found in EC experiments (63).
NCX current.
The NCX is an electrogenic transporter of Na+ and Ca2+ with a stoichiometry of 3:1, respectively, as found in different cell types including ECs (6, 20, 30, 77, 83). Although the presence of NCX in ECs has been confirmed, its involvement in the modulation of Ca2+ signaling is controversial (55). In CPAECs, NCX contributes to cytosolic Ca2+ removal as a low-affinity system due to the high [Ca2+]i needed for significant activation, and, in effect, this exchanger counteracts large and rapid rises in EC [Ca2+]i during early stages of stimulation (68). In cultured bovine pulmonary artery ECs, NCX was found to be voltage dependent but not responsible for resting [Ca2+]i maintenance (64). The model's INCX formulation (Eqs. A21–A23) is based on previously reported equations (30, 47, 76). The INCX expression given in Ref. 47 has fewer parameters from the one given in Ref. 76, and it was adapted in this study. A Hill-type instantaneous [Ca2+]i-dependent activation term is also included in this INCX description (Eq. A21), as used in modeling NCX in cardiac myocytes and pancreatic 
-cells (30, 76). INCX equations were fitted to rescaled data from mouse pancreatic -cells (30).
NaK current.
The NaK pump has been found in various EC types under a multitude of experimental protocols, and it represents the main transmembrane ionic pump present in virtually all mammalian cell membranes (1, 70). This pump has a coupling ratio of 3Na+:2K+, and its inhibition causes a 5 to 10 mV depolarization in cultured ECs (1, 70). NaK activity maintains intracellular Na+ concentration ([Na+]i) and [K+]i low and high, respectively, thus keeping physiological Na+ and K+ gradients across the plasmalemma (70). NaK activity has been described mathematically in detail, taking into account the metabolic state of the cell (ATP levels), which is suitable for modeling studies concerned with the effects of ischemia on the functionality of cardiac myocytes (70). However, a simpler INaK formulation is applied as the effects of low ATP in EC behavior were not pursued at present. The INaK formula used here (Eq. A24) was based on previous models (47, 83) and fitted to rescaled NaK I-V data from human embryonic kidney cells expressing the rat brain NaK 
1-subunit (84).
NaKCl cotransport flux. The NaKCl mechanism is electroneutral, pivotally involved in the regulation of resting cell volume and tissue permeability, and believed to constitute the major influx pathway for K+ in vascular ECs, even surpassing the NaK contribution (1, 41, 58). It also largely contributes to EC Cl– transport (21). In cultured bovine corneal ECs, the NaKCl function needs extracellular Na+, K+ and Cl–, and it is modulated by the cytosolic Cl– concentration ([Cl–]i), extracellular bicarbonate, protein kinases, and the cytoskeleton state (21). The mathematical formulation of INaKCl (Eqs. A25 and A26) is based on the work by Strieter et al. (71), which described cotransport fluxes using nonequilibrium thermodynamics. This NaKCl description requires the specification of only one parameter, namely, the cotransport coefficient (L) (71), which was adjusted to the present model (Model Parameter Estimation). Model INaKCl follows an inherent 1:1:2 stoichiometry for Na+:K+:Cl–, respectively, as shown experimentally.
PMCA current.
The function of the PMCA is to extrude Ca2+ to the extracellular medium (77). In both ECs and rabbit atrial cells, the PMCA is considered a low-capacity high-affinity transport system (47, 66). In CPAECs, the PMCA function was experimentally observed to be high affinity and [Ca2+]i, time, and CaM regulated as well as linked to NCX activity via [Ca2+]i, comprising an intricate dynamic compensatory mechanism (68). The PMCA is responsible for determining resting [Ca2+]i levels and counteracting moderate perturbations in [Ca2+]i, having a higher affinity for Ca2+than NCX (68). The IPMCA formulation (Eq. A27) is based on previous descriptions (47, 83). The average Hill coefficient and [Ca2+]i for half activation of PMCA current values were calculated from cultured CPAE cell data (68). 
PMCA was estimated by rescaling the value reported for a rabbit atrial cell model (47).
Fluid Compartment Model
In this EC model component, the balance of intracellular chemical species takes place (Eqs. A33–A41). The model assumes that Na+, K+, and Cl– can occupy the total intracellular volume while Ca2+ is restricted to discrete cellular compartmental volumes, namely, the cytosolic volume available to free Ca2+ and the IP3-sensitive store volume. Another major model assumption is that chemical species are homogeneously distributed throughout the intracellular environment (67).
Intracellular Ca2+ store. The model contains an intracellular Ca2+store mainly composed by the ER (74). It is sensitive to IP3 and considered the principal Ca2+-release site in ECs (55) via IP3R activation, releasing Ca2+ from the store into the cytosol once IP3 binds IP3R (74). Additionally, EC experimental data have suggested that ryanodine-sensitive stores coexist with IP3-sensitive ones and that the former plays an essential role in shaping EC Ca2+ signals (36, 60). However, the ryanodine-sensitive stores are not implemented in the model as they lack a quantitative description level in ECs.
IP3 generation and IP3R current.
Upon agonist binding to cell surface receptors, a G protein activates PLC, which in turn hydrolyzes phosphatidylinositol (4,5)-bisphosphate to give IP3 and diacylglycerol (not shown) (Fig. 1B). IP3 dynamics are described in the model (Eqs. A40 and A41) like in Ref. 43. Thus, agonist stimulation in the present model is simulated by a step increase in the steady-state IP3 generation rate constant, which causes an exponential increase in IP3 generation (Eq. A41) with time constant IP3, and the slower IP3 breakdown occurs via a first-order reaction with rate constant kDIP3 (Eq. A40). This approach allows the model to be easily adapted to simulate EC responses to different types of agonists (e.g., thrombin or ACh). The IIP3R formulation selected here (Eqs. A29 and A30) is based on two receptor models found in Refs. 28 and 80. These IP3R models were combined and modified based on experimental data from porcine aortic ECs (11). The data suggest that IP3-mediated receptor activation follows a Hill function with a coefficient of 3.8, suggesting approximately four binding sites for IP3, which reflects the channel's tetrameric nature (74). The data gathered from porcine ECs also underscore an inhibitory effect of [Ca2+]i on IIP3R. Ca2+ inhibits IP3R according to a modified version of the inactivation function (Pi,IP3R) from the IP3R model in Ref. 28. The Pi,IP3R function was fitted to porcine EC data (11) (Fig. 4). Although cytosolic Ca2+ can also activate IP3R (5) and this effect is included in other IP3R models (28, 80), such activation is absent in vascular ECs (11) and thus not considered here.
|
Ca2+ buffering. Both cytosolic and ER Ca2+ buffering are included in the present model, unlike in previous EC modeling efforts. The rate of [Ca2+]i buffering by CaM (Eq. A35) was based on the HUVEC model (77). The buffering mechanism inside the IP3-sensitive store is provided by CSQN kinetics, which is described mathematically by the rapid buffering approximation (Eq. A36) as applied in Ref. 79. Mitochondrial buffering was excluded from the model since this organelle does not modulate Ca2+ signals in cultured CPAECs (42).
Sensitivity Analysis
Sensitivity analysis of the EC model was performed utilizing the Latin hypercube sampling (LHS) method and multiple regression techniques as previously described (8, 19). Parameters with significant uncertainty and/or contribution to model's behavior were chosen for the present analysis (Table 3). A variation range of 20% was assigned to parameters obtained from rat mesenteric ECs. Uncertainties of 40% and 60% were assigned to parameters obtained from EC types other than rat mesentery and cell types different from ECs, respectively. The highest uncertainty range (80%) was applied to parameters whose experimental method of determination did not allow an absolute measurement of the parameter. Although extracellular ionic concentrations can be accurately determined, uncertainty ranges of 20% were assigned to them to simulate variation in experimental media preparations in different studies. Fifty simulations were performed by selecting parameter values randomly and without replacement. Sensitivity of each output to selected model parameters is quantified by the sensitivity index (i,j) as calculated from linear least-squares multiple regression of Eq. 2:
 | (2) |
)% confidence region for all the sensitivity indexes to determine whether they were statistically different from zero using the F-statistic (26). Five key simulation outputs were selected for analysis based on their impact on EC physiology: 1) resting Vm (Vm,rest), 2) resting [Ca2+]i levels ([Ca2+]i,rest), 3) maximum Vm hyperpolarization (Vm,max), 4) peak [Ca2+]i level achieved ([Ca2+]i,peak), and 5) [Ca2+]i level at the end of stimulation ([Ca2+]i,end).
|
All the parameters used in model simulations along with their reference sources are defined and shown in Table 1. A Cm of 14 pF was assumed for the model as this value falls within the range of capacitances (10–25 pF) reported in the literature for cultured vascular ECs (1). A capacitance to surface area ratio of 1 µF/cm2 was assumed for the estimation of EC plasma membrane surface area. Although parameter optimization was not performed to fit integrated cellular responses, a few parameters had to be modified from their initial (literature derived) values as explained below. Adjustments in parameters such as channel conductances and permeabilities are justified when values are based on experimental data from cells other than rat mesenteric ECs, given that channel expression can significantly vary among different cell types or even in the same cell type at different cell cycle stages (56).The parameters describing [Ca2+]i-dependent activation of KCa channels were selected from Refs. 2 and 81 to render them dormant at rest, as reported in rat mesenteric ECs (16, 54). Moreover, both channel conductances were increased, aiming to achieve physiologically comparable agonist-induced rat mesenteric EC hyperpolarization (54). The CaCC conductance was decreased 10-fold to allow significant agonist-induced hyperpolarization, as normally observed in rat mesenteric arteries. The [Ca2+]IS necessary for about half-maximal SOC activation was assumed to be 
50% of the total content of the model IP3 store, as reported experimentally (69). ISOC parameters (Eq. A15) were modified from their initial values to achieve a better agreement between simulations and experimentally recorded [Ca2+]i transients in rat mesenteric ECs (Figs. 2C and 6C in Ref. 54). PNSC,K, NaK, and LNaKCl were also adjusted to achieve physiological intracellular ionic concentrations and Vm at rest. IP3 was reduced because the ACh-mediated [Ca2+]i transient in rat mesenteric ECs reached peak 40 s earlier than the reference HUVEC responses, which were caused by thrombin (77). The maximum current via IP3R was changed due to modifications in the original IP3R mathematical formulations (28, 80).
Numerical Methods
The model contains a total of 10 nonlinear differential equations, which were coded in FORTRAN 90 and solved numerically using Gear's backward differentiation formula method for stiff differential equation systems (IMSL Numerical Library routine). The maximum time step was 4 ms, and tolerance for convergence was 0.0005.
|
RESULTS |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIX: MODEL EQUATIONSGRANTSREFERENCES |
|---|
EC model initial conditions (Table 2) were obtained by letting the system reach equilibrium using the parameters shown in Table 1 according to adjustments discussed in Model Parameter Estimation. The simulated EC had a resting Vm of approximately –20 mV, which is close to the value reported (–19.2 mV) for rat mesenteric ECs in Ref. 54. Moreover, the membrane resistance, calculated by injecting a known transmembrane current (Istim = ±1 pA) and observing the magnitude of Vm change, was close to 2 G
, which is in the range (1–5 G) reported for ECs (56). Blockade of NaK under resting conditions caused a 4 mV depolarization in Vm, which is close to the range (5–10 mV) recorded from ECs after [K+]o-free solution or ouabain-induced NaK inhibition protocols (1). Resting model [Ca2+]IS was physiological (2.25 mM) (74).
Resting Vm Modulation
Figure 5 presents model responses for different inhibition levels of VRAC. Blockade of VRAC was simulated by multiplying the GVRAC parameter by 0.0, 0.25, and 0.50 for 100%, 75%, and 50% levels of inhibition, respectively. Inhibition of VRAC was performed for 120 s starting at three different time points, namely, time = 100, 320, and 680 s to mimic the experimental protocol in Fig. 11D from Ref. 55. As Fig. 5 shows, the model was able to replicate the experimentally observed EC Vm hyperpolarization response when a compound such as NPPB or mibefradil blocked GVRAC (Fig. 11D in Ref. 55). Model outputs rapidly reached a stable Vm condition, and the magnitude of the hyperpolarization for 100% inhibition of VRAC was similar to the experiments (Fig. 11D in Ref. 55).
|
100 s) were qualitatively similar to experimental results in cultured ECs (Fig. 8C from Ref. 55). Vm hyperpolarization (solid line) was not as large as recorded in this particular experiment, and the new poststimulation resting Vm value was established more rapidly than in the experimental tracing. Nonetheless, Vm hyperpolarization magnitudes achieved in the model (Fig. 6A, solid and dotted lines) were within the range reported for nine ECs under similar [K+]o challenge conditions (Fig. 8D in Ref. 55). Doubling the Kir conductance (dotted line) helped achieve a larger Vm hyperpolarization level. However, when [K+]o was restored to the control value, a short negative transient in Vm was observed (due to faster EK increase than inactivation of IKir), and resting Vm became more negative than its original level. Blockade of VRAC drove resting Vm to hyperpolarized potentials (Fig. 6A, dashed-dotted line) compared with control. Raising [K+]o under VRAC blockade caused EC Vm depolarization instead of the hyperpolarization seen previously. Depolarization upon [K+]o stimulation also occurred when Kir was blocked (dashed line), but its magnitude was lower than for VRAC inhibition.
|
|
8 mM. Blockade of Kir channels (dashed line) completely abolished the hyperpolarizing response, and only depolarization was obtained by increasing [K+]o. Inhibition of VRAC (dashed-dotted line) greatly increased the maximum Vm hyperpolarization (–64 mV) achieved by raising [K+]o to 3 mM, which was lower than the control case (8 mM). These model results may relate to the relaxation profiles for [K+]o stimulation obtained from rat mesenteric artery data (Figs. 2 and 3A in Refs. 45 and 22, respectively). The optimum [K+]o value for maximum EC Vm hyperpolarization under control conditions (8 mM; Fig. 6B) was close to the range of 10 mM (Fig. 2 in Ref. 45) to 14 mM [K+]o (Fig. 3A in Ref. 22) necessary for maximum rat mesenteric artery relaxation for the control case. Figure 6B also shows that EC Vm responses to [K+]o changes, when Kir is functional, depend on how K+ levels are varied and on GVRAC. For instance, changing [K+]o from 0.5 to 5 mM depolarized Vm under control conditions but hyperpolarized it under VRAC blockade. In contrast, adjusting [K+]o from 5 to 10 mM caused Vm hyperpolarization for control but depolarization under VRAC block. Model Responses to Agonist Stimulation
Figure 7 depicts the overall dynamics of the main components of the EC model, namely, Vm, ionic currents, and intracellular species concentrations, upon short-term agonist stimulation. The agonist-induced EC response was simulated by changing the steady-state IP3 generation rate constant from 0 to 5.5 x 10–8 mM/ms at time = 20 s and maintaining for 100 s. Thus, as IP3 slowly approached a constant value (Fig. 7D), [Ca2+]i levels increased (Fig. 7D) prior to the activation of KCa channels (Fig. 7H) and before Vm began to hyperpolarize (Fig. 7A). As [Ca2+]i approached its peak, INCX and IPMCA (Fig. 7C) and ISERCA (Fig. 7F) achieved maximum activity, which decayed as cytosolic Ca2+ decreased, thus reflecting their Ca2+ dependence. The depolarizing ISOC (Fig. 7B) was enhanced during the response as Vm hyperpolarized and to a small extent by IP3-sensitive store depletion, with ISOC,Ca magnitude being larger than ISOC,Na at rest and during stimulation. INSCs (Fig. 7E) also exerted a depolarizing effect on Vm as INSC,K decreased, and both INSC,Ca and INSC,Na became more negative, following changes in electrochemical gradients. The largest hyperpolarizing currents came from the activity of KCa and Kir channels (Fig. 7H). ICaCC and IVRAC (Fig. 7I), on the other hand, were mostly responsible for Vm depolarization (more so than NSC and SOC). Given the activity of ionic channels, [K+]i and [Cl–]i levels decreased while [Na+]i increased during agonist stimulation (Fig. 7G). NaK activity (Fig. 7C) was minimal as Vm reached maximum hyperpolarization, which hampered normal NaK function by hindering Na+ efflux, but increased following the rise in [Na+]i and Vm repolarization. The major intracellular Ca2+ current came from IP3R release of Ca2+ (Fig. 7F), which peaked around the same time as [Ca2+]i. The Cl– component of the cotransporter (INaKCl,Cl) slightly increased during stimulation (Fig. 7I). Moreover, as [Ca2+]i reached peak, [Ca2+]IS continued to decrease, suggesting a dynamic uncoupling of intracellular Ca2+ in this phase of the transient (Fig. 7, D and G).
Figure 8, A and C, illustrates long-term model Ca2+ and Vm dynamics, respectively, under agonist stimulation (at time = 20 s) as performed in Fig. 7. Figure 8 also shows how simulated transmembrane Ca2+ influx (via NSC and SOC; Fig. 8B) and its driving force (Fig. 8D) change during long-term stimulation. The model predicted that [Ca2+]i changes are followed by variations in Vm (Fig. 8, A and C), and both responses displayed a similar transient pattern, as reported in experiments (55, 72). These simulations replicate characteristic Ca2+ and Vm responses experimentally recorded from rat mesenteric ECs under ACh stimulation (Figs. 2D and 6C in Ref. 54) at least for the first 100 s of stimulation reported in the study. Blockade of Vm hyperpolarization, by either direct KCa inhibition (i.e., SKCa conductance and IKCa conductance set to 0) or raised [K+]o from 5 to 35 mM, caused a small reduction in [Ca2+]i during the transient but did not affect the shape and dynamics of the agonist-induced [Ca2+]i signal (Fig. 8A), as found experimentally (Fig. 6C in Ref. 54). Once KCa channels were inhibited, model Vm was unable to hyperpolarize, remaining essentially constant (Fig. 8C), and thus [Ca2+]i alterations could no longer affect Vm significantly (Fig. 8, A and C). High [K+]o was not as effective in reducing the [Ca2+]i transient as direct KCa blockade, which agrees with experimental data (Fig. 6C in Ref. 54). Vm hyperpolarization increased [Ca2+]i. The relative effect of Vm, however, was not homogeneous throughout the transient, becoming more significant as the later part of the transient approached (i.e., [Ca2+]i increased 24% and 64% at peak and plateau, respectively, from hyperpolarization block to control conditions). Control transmembrane Ca2+ currents comprised 45% of the total Ca2+ flux (mainly NSC, SOC, and net store release) at 100 s after the initiation of the stimulation but comprised 87% of the total at 1,000 s. Agonist-stimulated Ca2+ influx currents increased more than twofold from hyperpolarization block to control conditions (Fig. 8B), although the maximal Ca2+ entry driving force change was only 35 mV (Fig. 8D), which was just 20% of the total resting driving force. Activation of SOC by store depletion became significant in the latter part of the Ca2+ transient (Fig. 8B).
To better examine the impact of Vm on [Ca2+]i, voltage-clamp simulations were performed under resting and agonist stimulation conditions. Figure 9 depicts [Ca2+]i as a function of clamped Vm (i.e., the Vm was set to a given value and [Ca2+]i was estimated at rest and following stimulation). The resting, peak, and plateau [Ca2+]i in Fig. 9 were normalized with respect to their corresponding values after being clamped at –20 mV. (Note that –20 mV is the Vm under control conditions or during agonist stimulation with KCa channels blocked.) Plateau and resting Ca2+ levels were more sensitive to Vm (and consequently to transmembrane Ca2+ influx) than peak Ca2+ levels, with resting levels a little more sensitive than plateau levels.
|
The outputs of all 50 simulations as well as the model control response are shown in Fig. 10. Only one of the simulations, indicated by the arrow, exhibited extraneous behavior, and it was discarded from the further analysis as an outlier. The remaining 49 simulations were used for the application of the LHS method. Table 4 presents semirelative sensitivity coefficients calculated according to Eq. 2 for the five selected outputs. Vm,rest and Vm,max were significantly sensitive to 4 and 6 parameters, respectively, whereas [Ca2+]i,rest, [Ca2+]i,peak, and [Ca2+]i,end were significantly affected by 2, 10, and 6 of the parameters, respectively. PMCA was the parameter that had the most significant impact on model predictions, and [Ca2+]i,peak was the output with the largest sensitivity on model parameters.
|
|
|
DISCUSSION |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIX: MODEL EQUATIONSGRANTSREFERENCES |
|---|
Model Verification
The model's performance was assessed by its ability to reproduce established features of rat mesenteric EC behavior while utilizing physiological parameter values. The model's resting values for Vm, for the four intracellular ionic concentrations, and for store Ca2+ agree with experimental data. Whole cell conductance was also within the physiological range, and this provides an overall validation for the descriptions of transmembrane currents. Vm responses to NaK blockade, to VRAC blockade (Fig. 5), extracellular K+ challenge (Fig. 6), and agonist stimulation (Fig. 7A) also validate plasma membrane electrophysiology. Intracellular Ca2+-handling machinery was tested against experimental data with agonist-induced stimulation (Fig. 8A). Most importantly, proper model behavior in these scenarios was accomplished by adjusting (within physiological ranges) a limited number of unknown parameters (i.e., SKCa conductance, IKCa conductance, CaCC conductance, KSOC,CaIS, NaK, PNSC,K, LNaKCl, IP3, and IP3R).
Resting Vm Modulation
Experimental data from bovine pulmonary artery ECs (Fig. 11D in Ref. 55) have shown that VRAC is crucial for establishing resting EC Vm. The three levels of simulated VRAC blockade (Fig. 5) can be interpreted as different levels or types of inhibition (i.e., distinct blocker concentrations or degrees of hyperosmotic stress) or dissimilar levels of VRAC expression in ECs. Model simulations concur with VRAC inhibition experiments (25, 55). The model also supports the notion that different levels of VRAC and Kir channel expression or activation can lead to EC switching from K type (resting Vm close to EK) to Cl type (resting Vm near ECl), or vice versa, as proposed to occur throughout the cell cycle (56) or using channel inhibition protocols (Fig. 7b in Ref. 25). New experimental studies are required to verify model predictions (Fig. 5) and confirm basal VRAC activity in rat mesenteric ECs as found in other ECs (55, 72).
The EC model was used to investigate two related hypotheses: one regarding the ability of ECs to hyperpolarize in response to raised [K+]o under certain conditions (25) and another suggesting that K+ is the EDHF (22, 45) (Fig. 6). The former hypothesis was formulated based on rat mesenteric artery experiments showing that these vessels could relax to increased [K+]o (from 5.88 to 10.58 mM) only if the VRAC in ECs was blocked. To explain these results, it was postulated that ECs in intact vessels can only hyperpolarize to raised [K+]o if they are switched from Cl- to K-type cells by VRAC inhibition, using either channel antagonists or hyperosmotic media. However, isolated EC experiments (Fig. 8, C and D, in Ref. 55) have demonstrated that when EC Vm is close to ECl (Cl type), the cell responds to raised [K+]o (from 6 to 12 mM) by hyperpolarizing. This Vm behavior was captured by the model (Fig. 6A) and is attributed to the crossover effect of the Kir I-V relationship. Figure 6A also shows that a K-type EC (i.e., after VRAC block) depolarizes upon [K+]o challenge (from 5 to 12 mM). The model Vm (Fig. 6A, solid and dotted lines) achieved a new resting value (during [K+]o stimulation) faster than what was observed experimentally (Fig. 8C in Ref. 55). This may attributed to a slower increase of [K+]o in the experiments relative to the simulations. Despite these minor differences, there is an overall agreement between simulated EC Vm behavior and experiments in isolated cells.
The model suggests that hyperpolarization and depolarization can occur in response to K+ increase, under both control and VRAC block conditions, depending on the initial and final K+ concentration (Fig. 6B). Although the model predicts depolarization after VRAC blockade for the particular K+ concentration range examined in Ref. 25, simulations do not directly translate to EC behavior in intact vessels as coupling to SMC may alter EC electrophysiology. Interestingly, Fig. 6B shows that a large Vm hyperpolarization is possible also under VRAC block, when the initial value of [K+]o is low (36 mV, from 1 to 3 mM [K+]o). Under control or Kir block conditions (i.e., solid and dotted lines in Fig. 6B), resting Vm at low starting [K+]o (e.g., 0.5 mM) is rather hyperpolarized (i.e., about –40 mV). This is attributed to a very negative EK. As the [K+]o increases, the increase in EK drives Vm to more depolarized values. As [K+]o increases between 5 and 8 mM, Vm hyperpolarizes, when Kir are active, due to the crossover effect. When VRAC is blocked (i.e., dashed-dotted line in Fig. 6B) and at very low [K+]o, the model predicts a significant depolarization as a result of a decrease in INaKCl that leads to the establishment of a larger transmembrane Na+ gradient and an increase in INSC,Na.
Assuming that a similar behavior as predicted in Fig. 6B occurs in intact vessels, the model suggests that by inhibiting VRAC, the EC Vm hyperpolarization response to [K+]o gets larger (for a particular [K+]o range), which may explain why rat mesenteric artery relaxations are only observed after this channel is blocked (25). Additionally, experimental setup differences could create different levels of VRAC activation and thus dramatically affect the predicted profiles (Fig. 6B). This may explain in part the variability observed in the response of rat small mesenteric arteries to [K+]o (25). This issue merits further experimental and theoretical (via coupled EC-SMC models) investigations. Larger hyperpolarizing responses in the model might be also possible with higher values for resting [K+]i.
Regarding the K+ as EDHF hypothesis, model simulations (Fig. 6) support the idea that Kir channels on ECs may play an important role in the relaxation of rat mesenteric arteries upon [K+]o stimulation and thus in part of the EDHF response (23, 45). As SMCs and ECs in rat mesenteric arteries are electrically coupled via myoendothelial gap junctions, EC Vm hyperpolarization caused by [K+]o-induced Kir activation is then able to be transmitted to the adjacent SMCs and thus relax the vessel (23, 25, 45, 65). However, simulations are based on an isolated EC model and may not correspond to the in vivo EC-SMC coupling situation, which might shift model response profiles (Fig. 6B) and may explain why maximum artery relaxations (23, 45) are observed at [K+]o levels higher than predicted for maximum EC Vm hyperpolarization. Additionally, elevated [K+]o may activate NaK in SMCs, causing further SMC Vm hyperpolarization and thus affect relaxation profiles (22). Therefore, theoretical studies using EC-SMC integrated models are necessary to further analyze the role of EC Kir channels and K+ in the EDHF response.
Model Responses to Agonist Stimulation
Following the examination of EC plasma membrane electrophysiological behavior, the next task was to investigate if the model was able to replicate EC responses to agonist stimulation. The overall dynamic agonist-induced responses of the main model components are displayed in Fig. 7. All EC model components performed their expected roles in the agonist-induced response, in keeping with literature (1, 55, 61). Model behavior can be explained in the following way. IP3 activates IP3R, releasing store Ca2+ into the cytosol, which in turn activates KCa channels and thus causes Vm hyperpolarization, increasing the driving force for Ca2+ entry. A significant increase in IKir during hyperpolarization (a result of the negative slope of the Kir I-V relationship; Fig. 2A, dashed line) acts as a positive feedback to hyperpolarization. NCX, PMCA, and SERCA work to counteract this sudden elevation in [Ca2+]i, shaping the Ca2+ transient peak. As [Ca2+]i reaches a peak, [Ca2+]IS continues to decrease during agonist stimulation, and such intracellular Ca2+ dynamic uncoupling has been observed in CHO cells stimulated with the IP3-generating agonist ATP (7). As IP3-sensitive stores are emptied and Vm hyperpolarizes, ISOCs are activated and contribute to the sustained [Ca2+]i rise. INSCs, on the other hand, tend to offset the hyperpolarizing effect of KCa activation by passively following their electrochemical gradients. The overall depolarizing effect on Vm exerted by NSC during agonist stimulation, as INSC,K decreases and both INSC,Ca and INSC,Na become more negative (Fig. 7E), has been observed experimentally (56). Moreover, the [Ca2+]i increase and Vm hyperpolarization activate CaCCs, while IVRACs increase by Vm hyperpolarization alone (Fig. 7I). These two Cl– conductances are the main players in the Vm repolarization process, which decreases the Ca2+ influx driving force. As a result of the agonist-induced processes described above, the levels of [K+]i, [Cl–]i, and [Na+]i are altered (Fig. 7G). During stimulation, NCX, NaK, and NaKCl activities tend to compensate intracellular ionic species changes and thus restore cellular homeostasis, thus reflecting the importance of these model components.
Figure 8 illustrates that the model reproduces dynamic [Ca2+]i and Vm signals recorded from ACh-stimulated rat mesenteric ECs under both control and KCa blockade (54). Simulations of long-term stimulation, as shown in Fig. 8A, revealed a Ca2+ transient followed by a well-defined [Ca2+]i plateau. Direct KCa channel block did not change model resting Vm significantly (<0.2 mV), in agreement with experimental studies (16, 54). Even after abolition of Vm hyperpolarization by inhibition of KCa activity or high [K+]o, the model EC is still able to maintain the [Ca2+]i transient profile with a reduction in Ca2+ levels reached, as found in experiments (54, 82).
Sensitivity Analysis
Many model parameters were estimated based on data from different types of vascular ECs, inherently leading to significant uncertainty in a number of model parameters. Simulations over a wide range of parameter values, as shown in Fig. 10, however, showed model responses within physiological ranges (except only for one outlier curve in Fig. 10A). The LHS method was utilized to examine the sensitivity of model's behavior on parameter values. This method provides higher reliability since the significance of a parameter on a model output is examined when all selected parameters are varied simultaneously. Parameters values with large uncertainty and large sensitivity coefficients contribute most to the uncertainty in model outputs.
Sensitivity analysis (Table 4) revealed a significant impact of IKir, IVRAC, and INSC,Na on Vm,rest. This corroborates experimental findings for the importance of these channels in establishing Vm,rest (25, 56, 59). IVRAC also has a significant effect in Vm,max establishment, in agreement with its proposed role in Ca2+ driving force stabilization (55). The [K+]o effect on Vm,max confirms experiments in Ref. 54. IPMCA, INSC,Ca, and IIP3R affect Vm indirectly by increasing Ca2+ activation of ISKCa. Resting [Ca2+]i was significantly affected directly by IPMCA and indirectly by GVRAC regulating Ca2+ driving force. The insensitivity of both Vm,rest and [Ca2+]i,rest to small (<20%) extracellular ionic concentration changes may reflect the ability of ECs to maintain homeostasis when their environmental or experimental conditions are varied within reasonable limits.
The PMCA has the greatest influence on peak [Ca2+]i, and its predicted impact is consistent with PMCA-overexpressing CHO cell experiments (7). The maximum IIP3R has the second largest impact, as peak [Ca2+]i comes to a large extent from store Ca2+ release. The release increases with store buffering. [Ca2+]o, PSOC,Ca, and PNSC,Ca are also significant, implying that extracellular Ca2+ influx affects the transient. In the model, NCX activity is significant during [Ca2+]i,peak, in agreement with bovine EC reports depicting NCX as a low-affinity system for reducing [Ca2+]i (42, 68). [Na+]o, PNSC,K, and NaK may affect the output through their effect on Vm and/or on Na+ and K+ balance affecting NCX.
Sensitivity analysis confirms the greater connection among transmembrane Ca2+ influx, Vm, and [Ca2+]i in the sustained phase of the Ca2+ response than at peak, as found in EC experiments (13, 55). The impact of [Na+]o on simulated plateau [Ca2+]i agrees with experimental results (56). The contribution of ICaCC to [Ca2+]i,end supports the proposed role of this channel type in ECs (27, 33) and also agrees with human aortic EC experiments showing a pivotal role for Cl– currents on the plateau segment of the Ca2+ response (59). The predicted relevance of SERCA on plateau but not peak [Ca2+]i is consistent with experiments on SERCA-deficient MAECs demonstrating that in these mutant ECs, the plateau component of the ACh-mediated Ca2+ signal was more severely affected than peak (48).
The analysis suggests a crucial role for PMCA in all facets of EC Ca2+ response, supporting the reported PMCA role as a critical modulator of EC [Ca2+]i signaling and homeostasis (42) and highlighting the need to investigate this current in more detail. It also concurs with experiments showing PMCA as an important pharmacological target for EC [Ca2+]i control and thus vascular tone regulation (12).
Role of Vm on EC [Ca2+]i Levels
Previous experimental reports (13, 54) have provided evidence that the sustained phase but not the peak component of the [Ca2+]i response is largely dependent on transmembrane Ca2+ influx. However, these experiments also found that the agonist-induced sustained phase of the [Ca2+]i transient seems independent of Vm modulation by KCa channels, in contrast to other experimental studies on ECs showing a significant Vm and [Ca2+]i interrelationship (11, 51, 55). The authors in Refs. 13 and 54 suggested that Vm changes may not considerably affect transmembrane Ca2+ entry due to either different Ca2+-permeable channel expression profile in rat mesenteric ECs (54) or a novel Vm-independent Ca2+ influx pathway in hamster cremasteric ECs (13). In addition, it was proposed in Ref. 13 that the connection between Ca2+ influx and [Ca2+]i is not as simple as previously thought since complex interactions among Ca2+ handling components (e.g., exchangers, transporters, and stores) may actually "buffer" [Ca2+]i changes elicited by Vm modulation. Thus, at this point, the role of Vm and transmembrane Ca2+ flux on [Ca2+]i remains under investigation.
Model simulations showed that cytosolic Ca2+ changes were transduced to alterations in Vm via KCa channels (Fig. 8). Moreover, Vm hyperpolarization exerted a positive feedback effect on [Ca2+]i levels, but the impact of Vm on [Ca2+]i was heterogeneous between different segments of the agonist-mediated Ca2+ transient (Fig. 9). In the model, a 20% change in the driving force for Ca2+ (Fig. 8D) affected Ca2+ influx by 100% (Fig. 8B). This is due to the highly nonlinear I-V relationship for both SOC (Fig. 3b in Ref. 29) and NSC (Fig. 5B in Ref. 63), especially in the negative Vm range, which was captured by the model via GHK equations. This large effect of Vm on Ca2+ influx, however, was not translated into dramatic changes in the [Ca2+]i transient. This is attributed to mainly two reasons. First, in the peak Ca2+ region, net store Ca2+ release comprises a major portion of the amount of Ca2+ reaching the cytosol (55%). This explains the low sensitivity of model peak Ca2+ to Vm (Fig. 9) and may shed light into the experimental results found in Ref. 54, which analyzed only the initial part (first 100 s) of agonist stimulation. Transmembrane Ca2+ influx dominates the [Ca2+]i response at plateau and rest and is regulated mainly by Vm changes and, at plateau, also by store depletion (Fig. 8 and Table 4). This explains the higher sensitivity of plateau and rest Ca2+ to Vm than at peak (Fig. 9). However, the more well-defined and completely Ca2+ influx-reliant plateau segment of the Ca2+ signal in hamster cremasteric ECs (13) is still largely Vm independent, and human aortic EC [Ca2+]i is virtually unaffected by Vm at rest (59).
The model predicts that much of this Vm-dependent Ca2+ influx from the extracellular space into the cytosol is buffered by the EC and does not lead to increased [Ca2+]i. Sensitivity analysis (Table 4) suggested that PMCA is the main candidate for this buffering role. PMCA removes the additional Ca2+ entering, when the electrochemical gradient increases, and limits [Ca2+]i elevation. Studies (4, 42, 68) have actually demonstrated a similar PMCA compensatory role using store depletion protocols to increase [Ca2+]i.
Model Limitations
Although our model represents a substantial extension of previous EC modeling studies, it also has several limitations. Most of the data used in model development come from a variety of vascular EC sources, including rat mesentery and porcine coronaries. Gathering data from other cell types is commonly employed in cellular modeling studies as a first approximation of the unidentified model parameters. This limitation was partially addressed by performing sensitivity analysis. Although the ryanodine-sensitive store may play important roles in EC physiology, its model implementation was hampered by lack of quantitatively descriptive data. Moreover, it has been proposed that EC Ca2+ stores are compartmentalized, forming subplasmalemmal functional units (55, 60), but this feature is not included in the present study as quantitative data are lacking. The model EC volume is constant and does not allow for a more physiological activation of VRAC, which can also be regulated by mechanical forces (shear and tensile stresses) and other gating pathways (55) not included at present. Fundamental physiological phenomena such as [Ca2+]i oscillations (54) and shear stress-induced [Ca2+]i and Vm responses (3, 78) are also not included in the present model. Although PMCA modulation occurs in ECs (68), it was not incorporated in the model. In addition, the SMC model component in Ref. 43 includes Vm dependency for its PMCA, but no suitable data were found for ECs in this regard. All EC features above represent significant model advancements deserving further theoretical investigations.
Conclusions
The EC model developed in this study was able to reproduce EC responses to various stimuli as reported in the literature, such as raised [K+]o and agonist challenges as well as VRAC blocking protocols. The model suggests that hyperpolarization and depolarization can occur in response to K+ increase, under both control and VRAC blockade conditions, depending on the initial and final K+ concentration. This predicted response to [K+]o may provide an explanation for previous contradictory experimental results. The simulated [Ca2+]i transients following agonist stimulation are within physiological range. The initial part of the [Ca2+]i response is dictated mostly by net store Ca2+ release and extrusion by PMCA. However, Vm is an important determinant of both plateau and resting [Ca2+]i phases of the transient and thus plays a significant function as sustained transmembrane Ca2+ influx is linked to the release of important vasoactive compounds such as nitric oxide and EDHF. In addition, the balance between PMCA activity and Ca2+ influx pathway(s) may serve key roles in determining the Vm sensitivity of EC [Ca2+]i. This might help explain, at least in part, the controversial influence of Vm on EC Ca2+ dynamics. Furthermore, the present study can form the basis for the development of multicellular EC-SMC models that will investigate signal transduction and communication in the vascular wall. This type of integrative modeling will improve the understanding of the vascular EC-SMC interaction and how it affects vessel tone and thus blood flow and pressure in both healthy and pathological states.
|
APPENDIX: MODEL EQUATIONS |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIX: MODEL EQUATIONSGRANTSREFERENCES |
|---|
Inward rectifier potassium channel current (IKir)
 | (A1) |
 | (A2) |
 | (A3) |
Calcium-activated potassium channel currents (ISKCa and IIKCa)
 | (A4) |
 | (A5) |
Calcium-activated chloride channel (ICaCC)
 | (A6) |
 | (A7) |
 | (A8) |
 | (A9) |
Volume-regulated anion channel current (IVRAC)
 | (A10) |
Store-operated cation channel current (ISOC)
 | (A11) |
 | (A12) |
 | (A13) |
 | (A14) |
 | (A15) |
Nonselective cation channel current (INSC)
 | (A16) |
 | (A17) |
 | (A18) |
 | (A19) |
 | (A20) |
Sodium-calcium exchanger current (INCX)
 | (A21) |
 | (A22) |
 | (A23) |
Sodium-potassium (Na+/K+) ATPase current (INaK)
 | (A24) |
Sodium-potassium-chloride (Na+/K+/2Cl) cotransport flux (INaKCl)
 | (A25) |
 | (A26) |
Plasma membrane calcium ATPase current (IPMCA)
 | (A27) |
 | (A28) |
Fluid Compartment Model
 | (A29) |
 | (A30) |
Sarco/endoplasmic reticulum calcium ATPase (ISERCA) and ER leak (Ileak) currents
 | (A31) |
 | (A32) |
Intracellular ionic and material balances
 | (A33) |
 | (A34) |
 | (A35) |
 | (A36) |
 | (A37) |
 | (A38) |
 | (A39) |
 | (A40) |
 | (A41) |
|
GRANTS |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIX: MODEL EQUATIONSGRANTSREFERENCES |
|---|
|
FOOTNOTES |
|---|
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
|
REFERENCES |
|---|
|
TOPABSTRACTMETHODSRESULTSDISCUSSIONAPPENDIX: MODEL EQUATIONSGRANTSREFERENCES |
|---|
2. Ahn SC, Seol GH, Kim JA, Suh SH. Characteristics and a functional implication of Ca2+-activated K+ current in mouse aortic endothelial cells. Pflügers Arch 447: 426–435, 2004.[CrossRef][Web of Science][Medline]
3. Barakat AI, Lieu DK, Gojova A. Secrets of the code: do vascular endothelial cells use ion channels to decipher complex flow signals? Biomaterials 27: 671–678, 2006.[CrossRef][Web of Science][Medline]
4. Bautista DM, Hoth M, Lewis RS. Enhancement of calcium signalling dynamics and stability by delayed modulation of the plasma-membrane calcium-ATPase in human T cells. J Physiol 541: 877–894, 2002.
5. Berridge MJ, Lipp P, Bootman MD. The versatility and universality of calcium signalling. Nat Rev Mol Cell Biol 1: 11–21, 2000.[CrossRef][Web of Science][Medline]
6. Bondarenko A. Sodium-calcium exchanger contributes to membrane hyperpolarization of intact endothelial cells from rat aorta during acetylcholine stimulation. Br J Pharmacol 143: 9–18, 2004.[CrossRef][Web of Science][Medline]
7. Brini M, Bano D, Manni S, Rizzuto R, Carafoli E. Effects of PMCA and SERCA pump overexpression on the kinetics of cell Ca2+ signalling. EMBO J 19: 4926–4935, 2000.[CrossRef][Web of Science][Medline]
8. Bui TD, Dabdub D, George SC. Modeling bronchial circulation with application to soluble gas exchange: description and sensitivity analysis. J Appl Physiol 84: 2070–2088, 1998.
9. Burnham MP, Bychkov R, Feletou M, Richards GR, Vanhoutte PM, Weston AH, Edwards G. Characterization of an apamin-sensitive small-conductance Ca2+-activated K+ channel in porcine coronary artery endothelium: relevance to EDHF. Br J Pharmacol 135: 1133–1143, 2002.[CrossRef][Web of Science][Medline]
10. Bychkov R, Burnham MP, Richards GR, Edwards G, Weston AH, Feletou M, Vanhoutte PM. Characterization of a charybdotoxin-sensitive intermediate conductance Ca2+-activated K+ channel in porcine coronary endothelium: relevance to EDHF. Br J Pharmacol 137: 1346–1354, 2002.[CrossRef][Web of Science][Medline]
11. Carter TD, Ogden D. Kinetics of Ca2+ release by InsP3 in pig single aortic endothelial cells: evidence for an inhibitory role of cytosolic Ca2+ in regulating hormonally evoked Ca2+ spikes. J Physiol 504: 17–33, 1997.
12. Chaudhary J, Walia M, Matharu J, Escher E, Grover AK. Caloxin: a novel plasma membrane Ca2+ pump inhibitor. Am J Physiol Cell Physiol 280: C1027–C1030, 2001.
13. Cohen KD, Jackson WF. Membrane hyperpolarization is not required for sustained muscarinic agonist-induced increases in intracellular Ca2+ in arteriolar endothelial cells. Microcirculation 12: 169–182, 2005.[Web of Science][Medline]
14. Coleman HA, Tare M, Parkington HC. Endothelial potassium channels, endothelium-dependent hyperpolarization and the regulation of vascular tone in health and disease. Clin Exp Pharmacol Physiol 31: 641–649, 2004.[CrossRef][Web of Science][Medline]
15. Coleman HA, Tare M, Parkington HC. K+ currents underlying the action of endothelium-derived hyperpolarizing factor in guinea-pig, rat and human blood vessels. J Physiol 531: 359–373, 2001.
16. Crane GJ, Gallagher N, Dora KA, Garland CJ. Small- and intermediate-conductance calcium-activated K+ channels provide different facets of endothelium-dependent hyperpolarization in rat mesenteric artery. J Physiol 553: 183–189, 2003.
17. Crane GJ, Walker SD, Dora KA, Garland CJ. Evidence for a differential cellular distribution of inward rectifier K channels in the rat isolated mesenteric artery. J Vasc Res 40: 159–168, 2003.[CrossRef][Web of Science][Medline]
18. Csanady L, Adam-Vizi V. Ca2+- and voltage-dependent gating of Ca2+- and ATP-sensitive cationic channels in brain capillary endothelium. Biophys J 85: 313–327, 2003.[Web of Science][Medline]
19. Derwent R, Hov O. Application of sensitivity and uncertainty analysis techniques to a photochemical ozone model. J Geophys Res 93: 5185–5199, 1988.
20. Despa S, Brette F, Orchard CH, Bers DM. Na/Ca exchange and Na/K-ATPase function are equally concentrated in transverse tubules of rat ventricular myocytes. Biophys J 85: 3388–3396, 2003.[Web of Science][Medline]
21. Diecke FP, Wen Q, Iserovich P, Li J, Kuang K, Fischbarg J. Regulation of Na-K-2Cl cotransport in cultured bovine corneal endothelial cells. Exp Eye Res 80: 777–785, 2005.[CrossRef][Web of Science][Medline]
22. Dora KA, Garland CJ. Properties of smooth muscle hyperpolarization and relaxation to K+ in the rat isolated mesenteric artery. Am J Physiol Heart Circ Physiol 280: H2424–H2429, 2001.
23. Dora KA, Garland CJ, Kwan HY, Yao X. Endothelial cell protein kinase G inhibits release of EDHF through a PKG-sensitive cation channel. Am J Physiol Heart Circ Physiol 280: H1272–H1277, 2001.
24. Dora KA, Xia J, Duling BR. Endothelial cell signaling during conducted vasomotor responses. Am J Physiol Heart Circ Physiol 285: H119–H126, 2003.
25. Doughty JM, Boyle JP, Langton PD. Blockade of chloride channels reveals relaxations of rat small mesenteric arteries to raised potassium. Br J Pharmacol 132: 293–301, 2001.[CrossRef][Web of Science][Medline]
26. Draper NR, Smith H. Applied Regression Analysis. New York: Wiley, 1981.
27. Fang QZ, Zhong N, Zhang Y, Zhou ZN. Tetrandrine inhibits Ca2+-activated chloride channel in cultured human umbilical vein endothelial cells. Acta Pharmacol Sin 25: 327–333, 2004.[Web of Science][Medline]
28. Fink CC, Slepchenko B, Loew LM. Determination of time-dependent inositol-1,4,5-trisphosphate concentrations during calcium release in a smooth muscle cell. Biophys J 77: 617–628, 1999.[Web of Science][Medline]
29. Freichel M, Suh SH, Pfeifer A, Schweig U, Trost C, Weissgerber P, Biel M, Philipp S, Freise D, Droogmans G, Hofmann F, Flockerzi V, Nilius B. Lack of an endothelial store-operated Ca2+ current impairs agonist-dependent vasorelaxation in TRP4–/– mice. Nat Cell Biol 3: 121–127, 2001.[CrossRef][Web of Science][Medline]
30. Gall D, Gromada J, Susa I, Rorsman P, Herchuelz A, Bokvist K. Significance of Na/Ca exchange for Ca2+ buffering and electrical activity in mouse pancreatic beta-cells. Biophys J 76: 2018–2028, 1999.[Web of Science][Medline]
31. Goto K, Rummery NM, Grayson TH, Hill CE. Attenuation of conducted vasodilatation in rat mesenteric arteries during hypertension: role of inwardly rectifying potassium channels. J Physiol 561: 215–231, 2004.
32. Gustafsson F, Holstein-Rathlou N. Conducted vasomotor responses in arterioles: characteristics, mechanisms and physiological significance. Acta Physiol Scand 167: 11–21, 1999.[CrossRef][Web of Science][Medline]
33. Hartzell C, Putzier I, Arreola J. Calcium-activated chloride channels. Annu Rev Physiol 67: 719–758, 2005.[CrossRef][Web of Science][Medline]
34. Hille B, Schwarz W. Potassium channels as multi-ion single-file pores. J Gen Physiol 72: 409–442, 1978.
35. Iwamoto T, Kita S, Zhang J, Blaustein MP, Arai Y, Yoshida S, Wakimoto K, Komuro I, Katsuragi T. Salt-sensitive hypertension is triggered by Ca2+ entry via Na+/Ca2+ exchanger type-1 in vascular smooth muscle. Nat Med 10: 1193–1199, 2004.[CrossRef][Web of Science][Medline]
36. Jacob R. Calcium oscillations in endothelial cells. Cell Calcium 12: 127–134, 1991.[CrossRef][Web of Science][Medline]
37. Jafri MS, Rice JJ, Winslow RL. Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys J 74: 1149–1168, 1998.[Web of Science][Medline]
38. Jow F, Numann R. Divalent ion block of inward rectifier current in human capillary endothelial cells and effects on resting membrane potential. J Physiol 512: 119–128, 1998.
39. Jow F, Numann R. Histamine increases [Ca2+]in and activates Ca-K and nonselective cation currents in cultured human capillary endothelial cells. J Membr Biol 173: 107–116, 2000.[CrossRef][Web of Science][Medline]
40. Kamouchi M, Mamin A, Droogmans G, Nilius B. Nonselective cation channels in endothelial cells derived from human umbilical vein. J Membr Biol 169: 29–38, 1999.[CrossRef][Web of Science][Medline]
41. Kawai N, McCarron RM, Spatz M. Effect of hypoxia on Na+-K+-Cl– cotransport in cultured brain capillary endothelial cells of the rat. J Neurochem 66: 2572–2579, 1996.[Web of Science][Medline]
42. Klishin A, Sedova M, Blatter LA. Time-dependent modulation of capacitative Ca2+ entry signals by plasma membrane Ca2+ pump in endothelium. Am J Physiol Cell Physiol 274: C1117–C1128, 1998.
43. Koenigsberger M, Sauser R, Beny JL, Meister JJ. Role of the endothelium on arterial vasomotion. Biophys J 88: 3845–3854, 2005.[CrossRef][Web of Science][Medline]
44. Korngreen A, Gold'shtein V, Priel Z. A realistic model of biphasic calcium transients in electrically nonexcitable cells. Biophys J 73: 659–673, 1997.[Web of Science][Medline]
45. Lacy PS, Pilkington G, Hanvesakul R, Fish HJ, Boyle JP, Thurston H. Evidence against potassium as an endothelium-derived hyperpolarizing factor in rat mesenteric small arteries. Br J Pharmacol 129: 605–611, 2000.[CrossRef][Web of Science][Medline]
46. Levitan I, Christian AE, Tulenko TN, Rothblat GH. Membrane cholesterol content modulates activation of volume-regulated anion current in bovine endothelial cells. J Gen Physiol 115: 405–416, 2000.
47. Lindblad DS, Murphey CR, Clark JW, Giles WR. A model of the action potential and underlying membrane currents in a rabbit atrial cell. Am J Physiol Heart Circ Physiol 271: H1666–H1696, 1996.
48. Liu LH, Paul RJ, Sutliff RL, Miller ML, Lorenz JN, Pun RY, Duffy JJ, Doetschman T, Kimura Y, MacLennan DH, Hoying JB, Shull GE. Defective endothelium-dependent relaxation of vascular smooth muscle and endothelial cell Ca2+ signaling in mice lacking sarco(endo)plasmic reticulum Ca2+-ATPase isoform 3. J Biol Chem 272: 30538–30545, 1997.
49. Liu Y, Jones AW, Sturek M. Attenuated Ca2+ response to acetylcholine in endothelial cells from aorta of aldosterone-salt hypertensive rats. Am J Hypertens 8: 404–408, 1995.[CrossRef][Web of Science][Medline]
50. Lu Z. Mechanism of rectification in inward-rectifier K+ channels. Annu Rev Physiol 66: 103–129, 2004.[CrossRef][Web of Science][Medline]
51. Luckhoff A, Busse R. Calcium influx into endothelial cells and formation of endothelium-derived relaxing factor is controlled by the membrane potential. Pflügers Arch 416: 305–311, 1990.[CrossRef][Web of Science][Medline]
52. Marrelli SP, Eckmann MS, Hunte MS. Role of endothelial intermediate conductance KCa channels in cerebral EDHF-mediated dilations. Am J Physiol Heart Circ Physiol 285: H1590–H1599, 2003.
53. Mauban JR, Wier WG. Essential role of EDHF in the initiation and maintenance of adrenergic vasomotion in rat mesenteric arteries. Am J Physiol Heart Circ Physiol 287: H608–H616, 2004.
54. McSherry IN, Spitaler MM, Takano H, Dora KA. Endothelial cell Ca2+ increases are independent of membrane potential in pressurized rat mesenteric arteries. Cell Calcium 38: 28–33, 2005.
55. Nilius B, Droogmans G. Ion channels and their functional role in vascular endothelium. Physiol Rev 81: 1415–1459, 2001.
56. Nilius B, Viana F, Droogmans G. Ion channels in vascular endothelium. Annu Rev Physiol 59: 145–170, 1997.[CrossRef][Web of Science][Medline]
57. Nonner W, Chen DP, Eisenberg B. Anomalous mole fraction effect, electrostatics, and binding in ionic channels. Biophys J 74: 2327–2334, 1998.[Web of Science][Medline]
58. O'Donnell ME. Role of Na-K-Cl cotransport in vascular endothelial cell volume regulation. Am J Physiol Cell Physiol 264: C1316–C1326, 1993.
59. Ono K, Nakao M, Iijima T. Chloride-sensitive nature of the histamine-induced Ca2+ entry in cultured human aortic endothelial cells. J Physiol 511: 837–849, 1998.
60. Paltauf-Doburzynska J, Frieden M, Spitaler M, Graier WF. Histamine-induced Ca2+ oscillations in a human endothelial cell line depend on transmembrane ion flux, ryanodine receptors and endoplasmic reticulum Ca2+-ATPase. J Physiol 524: 701–713, 2000.
61. Parekh AB, Putney JW Jr. Store-operated calcium channels. Physiol Rev 85: 757–810, 2005.
62. Park MK, Lomax RB, Tepikin AV, Petersen OH. Local uncaging of caged Ca2+ reveals distribution of Ca2+-activated Cl– channels in pancreatic acinar cells. Proc Natl Acad Sci USA 98: 10948–10953, 2001.
63. Park SJ, Kim YC, Suh SH, Rhim H, Sim JH, Kim SJ, So I, Kim KW. Background nonselective cationic current and the resting membrane potential in rabbit aorta endothelial cells. Jpn J Physiol 50: 635–643, 2000.[CrossRef][Web of Science][Medline]
64. Sage SO, van Breemen C, Cannell MB. Sodium-calcium exchange in cultured bovine pulmonary artery endothelial cells. J Physiol 440: 569–580, 1991.
65. Sandow SL, Tare M, Coleman HA, Hill CE, Parkington HC. Involvement of myoendothelial gap junctions in the actions of endothelium-derived hyperpolarizing factor. Circ Res 90: 1108–1113, 2002.
66. Schneider JC, El Kebir D, Chereau C, Mercier JC, Dall'Ava-Santucci J, Dinh-Xuan AT. Involvement of Na+/Ca2+ exchanger in endothelial NO production and endothelium-dependent relaxation. Am J Physiol Heart Circ Physiol 283: H837–H844, 2002.
67. Schuster A, Beny JL, Meister JJ. Modelling the electrophysiological endothelial cell response to bradykinin. Eur Biophys J 32: 370–380, 2003.[CrossRef][Web of Science][Medline]
68. Sedova M, Blatter LA. Dynamic regulation of [Ca2+]i by plasma membrane Ca2+-ATPase and Na+/Ca2+ exchange during capacitative Ca2+ entry in bovine vascular endothelial cells. Cell Calcium 25: 333–343, 1999.[CrossRef][Web of Science][Medline]
69. Sedova M, Klishin A, Huser J, Blatter LA. Capacitative Ca2+ entry is graded with degree of intracellular Ca2+ store depletion in bovine vascular endothelial cells. J Physiol 523: 549–559, 2000.
70. Smith NP, Crampin EJ. Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study. Prog Biophys Mol Biol 85: 387–405, 2004.[CrossRef][Web of Science][Medline]
71. Strieter J, Stephenson JL, Palmer LG, Weinstein AM. Volume-activated chloride permeability can mediate cell volume regulation in a mathematical model of a tight epithelium. J Gen Physiol 96: 319–344, 1990.
72. Suh SH, Vennekens R, Manolopoulos VG, Freichel M, Schweig U, Prenen J, Flockerzi V, Droogmans G, Nilius B. Characterisation of explanted endothelial cells from mouse aorta: electrophysiology and Ca2+ signalling. Pflügers Arch 438: 612–620, 1999.[CrossRef][Web of Science][Medline]
73. Takano H, Dora KA, Spitaler MM, Garland CJ. Spreading dilatation in rat mesenteric arteries associated with calcium-independent endothelial cell hyperpolarization. J Physiol 556: 887–903, 2004.
74. Tran QK, Ohashi K, Watanabe H. Calcium signalling in endothelial cells. Cardiovasc Res 48: 13–22, 2000.
75. von Beckerath N, Dittrich M, Klieber HG, Daut J. Inwardly rectifying K+ channels in freshly dissociated coronary endothelial cells from guinea-pig heart. J Physiol 491: 357–365, 1996.
76. Weber CR, Ginsburg KS, Philipson KD, Shannon TR, Bers DM. Allosteric regulation of Na/Ca exchange current by cytosolic Ca in intact cardiac myocytes. J Gen Physiol 117: 119–131, 2001.
77. Wiesner TF, Berk BC, Nerem RM. A mathematical model of cytosolic calcium dynamics in human umbilical vein endothelial cells. Am J Physiol Cell Physiol 270: C1556–C1569, 1996.
78. Wiesner TF, Berk BC, Nerem RM. A mathematical model of the cytosolic-free calcium response in endothelial cells to fluid shear stress. Proc Natl Acad Sci USA 94: 3726–3731, 1997.
79. Winslow RL, Scollan DF, Holmes A, Yung CK, Zhang J, Jafri MS. Electrophysiological modeling of cardiac ventricular function: from cell to organ. Annu Rev Biomed Eng 2: 119–155, 2000.[CrossRef][Web of Science][Medline]
80. Wong AY, Klassen GA. A model of electrical activity and cytosolic calcium dynamics in vascular endothelial cells in response to fluid shear stress. Ann Biomed Eng 23: 822–832, 1995.[CrossRef][Web of Science][Medline]
81. Xia XM, Fakler B, Rivard A, Wayman G, Johnson-Pais T, Keen JE, Ishii T, Hirschberg B, Bond CT, Lutsenko S, Maylie J, Adelman JP. Mechanism of calcium gating in small-conductance calcium-activated potassium channels. Nature 395: 503–507, 1998.[CrossRef][Medline]
82. Yamanaka A, Ishikawa T, Goto K. Characterization of endothelium-dependent relaxation independent of NO and prostaglandins in guinea pig coronary artery. J Pharmacol Exp Ther 285: 480–489, 1998.
83. Yang J, Clark JW Jr, Bryan RM, Robertson C. The myogenic response in isolated rat cerebrovascular arteries: smooth muscle cell model. Med Eng Phys 25: 691–709, 2003.[CrossRef][Web of Science][Medline]
84. Zillikens S, Gisselmann G, Glitsch HG. The current produced by the E779A mutant rat Na+/K+ pump alpha1-subunit expressed in HEK 293 cells. Biochim Biophys Acta 1509: 155–166, 2000.[Medline]
85. Zunkler BJ, Grafe M, Henning B, Kuhne S, Ott T, Fleck E, Hildebrandt AG. Effects of P2 purinoceptor agonists on membrane potential and intracellular Ca2+ of human cardiac endothelial cells. Pharmacol Toxicol 85: 7–15, 1999.[Web of Science][Medline]
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |
