This Article Abstract Full Text (PDF) All Versions of this Article: biophysj.104.043976v1 88/3/1507    most recent Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Lemon, G. Articles by Bennett, M. R. Search for Related Content PubMed PubMed Citation Articles by Lemon, G. Articles by Bennett, M. R.

Calcium Mobilization and Spontaneous Transient Outward Current Characteristics upon Agonist Activation of P2Y₂ Receptors in Smooth Muscle Cells

G. Lemon ^*, J. Brockhausen , G.-H. Li , W. G. Gibson ^* and M. R. Bennett 

^* The School of Mathematics and Statistics, University of Sydney, New South Wales, Australia; and The Neurobiology Laboratory, Department of Physiology, The Institute for Biomedical Research, University of Sydney, New South Wales, Australia

Correspondence: Address reprint requests to Professor Max Bennett, Neurobiology Laboratory, University of Sydney, N.S.W. 2006, Australia. E-mail: maxb{at}physiol.usyd.edu.au.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

 
A quantitative model is provided that links the process of metabotropic receptor activation and sequestration to the generation of inositol 1,4,5-trisphosphate, the subsequent release of calcium from the central sarcoplasmic reticulum, and the consequent release of calcium from subsarcolemma sarcoplasmic reticulum that acts on large-conductance potassium channels to generate spontaneous transient outward currents (STOCs). This model is applied to the case of STOC generation in vascular A7r5 smooth muscle cells that have been transfected with a chimera of the P2Y₂ metabotropic receptor and green fluorescent protein (P2Y₂-GFP) and exposed to the P2Y₂ receptor agonist uridine 5'-triphosphate. The extent of P2Y₂-GFP sequestration from the membrane on exposure to uridine 5'-triphosphate, the ensuing changes in cytosolic calcium concentration, as well as the interval between STOCs that are subsequently generated, are used to determine parameter values in the model. With these values, the model gives a good quantitative prediction of the dynamic changes in STOC amplitude observed upon activation of metabotropic P2Y₂ receptors in the vascular smooth muscle cell line.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

 
Purine nucleotide receptors have been divided into two classes, P2X (ionotropic ligand-gated) and P2Y (metabotropic G-protein coupled; for a review see Abbracchio and Burnstock, 1994). The subclasses of metabotropic receptors, P2Y₁ and P2Y₂, are especially prominent in arteries, with the mRNA for P2Y₂ receptors found in arterial smooth muscle cells (Harper et al., 1998). P2Y₂ receptors are clearly distinguished from P2Y₁ because of the specific actions on the P2Y₂ receptor of uridine 5'-triphosphate (UTP), ED₅₀ of 1 µM (see Bultmann et al., 1998), which can be released by endothelial cells (Saiag et al., 1998). Activation of P2Y₂ receptors, which like other P2Y receptors are coupled to phospholipase C (von Kugelgen and Wetter, 2000), releases calcium from intracellular stores (Hou et al., 1999), after which receptor phosphorylation appears to regulate desensitization of the P2Y₂ receptor through the action of a protein kinase (Otero et al., 2000).

The wild-type P2Y₂ receptor sequesters in a time-dependent manner, as do other G-protein coupled receptors (Wilkinson et al., 1994; Koenig and Edwardson, 1996). Approximately 60% of the membrane receptor is internalized in 5 min upon exposure to UTP, as indicated using monoclonal antibodies (Garrad et al., 1998). However, this labeling technique does not allow the receptor sequestration to be monitored continuously after exposure to agonist, so it has limited time-resolution. An alternative approach is to use chimeras of green fluorescent protein (GFP) and the receptor of interest, which enables sequestration to be followed in real-time after application of agonist (see, for example, Dutton et al., 2000). In the first part of the present work we have constructed chimeras of GFP and the P2Y₂ receptor (P2Y₂-GFP) and determined, after transfection of cDNA P2Y₂-GFP in the vascular smooth muscle cell line A7r5, the time-course of changes in P2Y₂-GFP at the membrane after exposure to the agonist UTP. In addition, we have shown that exposure of these transfected cells to agonist gives rise to a calcium transient in the cytosol of these cells which has a similar time-course to that of the changes in the P2Y₂-GFP at the membrane. We have recently developed a model that links the process of metabotropic receptor activation and sequestration to the generation of inositol 1,4,5-trisphosphate (IP₃) and the release of calcium from the sarcoplasmic reticulum (SR) (Lemon et al., 2003a,b). Such SR is found throughout A7r5 cells, both in the subsarcolemma as well as deeper in the cytoplasm (Vermassen et al., 2003). We use this model to link the desensitization/sequestration of P2Y₂ receptors at the membrane with changes in cytosolic calcium so as to provide a quantitative account of the experimental observations.

Spontaneous transient outward currents (STOCs) in smooth muscle cells are due to the opening of calcium-activated potassium channels which fall principally into two classes, large conductance (BK) channels and small conductance channels (Benham and Bolton, 1986). They have been reported in smooth muscle cells of a variety of organs, including the gastrointestinal tract (Kong et al., 2000) and particularly blood vessels (Komori and Bolton, 1989; Hume and Leblanc, 1989; Greenwood and Large, 1995; Perez et al., 1999; Smirnov and Aaronson, 1992; Bychkov et al., 1997). Activation of P2Y receptors in some cell types increases the frequency of STOCs, for example in colonic smooth muscle (Kong et al., 2000) and clonal kidney cells (Hafting and Sand, 2000; Bringmann et al., 2002). In others it decreases the frequency, as in cerebral artery smooth muscle (Jagger and Nelson, 2000) and ileal smooth muscle (Gomez et al., 2002). In the second part of the present work we determine the amplitude and temporal characteristics of STOC generation upon agonist activation of P2Y₂ receptors and show that STOCs are elevated over a time-course similar to that of P2Y₂ desensitization/sequestration. Our model has therefore been extended to include the release of calcium from strategically placed SR, located at the periphery of the cells just beneath the sarcolemma; the calcium released into this subsarcolemmal space acts on BK channels to generate STOCs. This model provides a quantitative account of observations and links the rates of desensitization/sequestration of the metabotropic receptors to changes in the cytosolic calcium in the cell, calcium changes in the subsarcolemmal space, and the generation of STOCs.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

 
Experimental
Plasmid construction
Plasmid construction pCI-P2Y₂-GFP was constructed as follows. The plasmid pBluescript small-conductance (–) containing P2Y₂ cDNA insert from human epithelial cells was obtained (Parr et al., 1994). The P2Y₂ cDNA was amplified from the plasmid by polymerase chain reaction (PCR) using a forward primer that annealed to the T3 promoter region and a reverse primer that annealed directly upstream of and over the stop-codon in P2Y₂. The forward primer (5' G CGC AAG CTT ATG GCA GCA GAC CTG GGC 3') incorporated an in-frame Hind III site to ligate upstream of GFP-20 in pBluescript II KS(+). The reverse primer (5' GAC CAT GGC GCC GCC GCC CAG CCG AAT GTC CTT AGT 3') eliminated the stop-codon and incorporated an in-frame Nco1 site at the 3' end of P2Y₂. The PCR product was ligated upstream and in-frame into the 5' Nco1 site of GFP-20 in pBluescript II KS(+). The P2Y₂-GFP insert was removed and ligated into pCI (Promega, Madison, WI), a CMV promoter-driven mammalian vector. The sequence of the P2Y₂ PCR product of both the coding and noncoding strands and P2Y₂-GFP insert was confirmed using automated fluorescence sequencing.

Transfection of A7r5 smooth muscle cells
Cells were seeded onto glass coverslips in 24-well plates and grown to 50–70% confluence at 37°C in a humidified atmosphere of 5% CO₂ and 95% air. A7r5 cells were cultured in Dulbecco's modified Eagle's medium (Life Technologies, Gaithersburg, MD) with Earle's salts. A total of 0.5 µg pCI-P2Y₂-GFP in 50 µL serum-free media was added to 2.1 µL Lipofectamine reagent (Life Technologies) in 50 µL serum-free media. The DNA and Lipofectamine mixture was incubated at room temperature for 10 min to allow complexes to form before addition of the complexes to the cells. The complexes were removed after incubation at 37°C and 5% CO₂ for 3–6 h. Media containing FCS was added and the cells were further incubated for 24 h before visualization.

P2Y₂ receptor antibodies
We have generated rabbit polyclonal antibodies against the P2Y₂ receptor C-terminal 18 residues with an added C-terminal Cys as well as against sequences 226–242 of the receptor. The specificity of antibodies for these P2Y₂ receptors (Ab P2Y₂) has been established (see Methods in Ray et al., 2002).

Immunohistochemistry
Cells were fixed in 4% paraformaldehyde in borate acetate buffer (pH 9.5) for 1 min, washed in 5 mM phosphate-buffed saline (PBS) for 10 min (3x) and placed in 0.1% DMSO in phosphate-buffered horse serum (100 mL PBS, 2 mL normal horse serum, 0.1 mL Triton X-100, 1 g bovine serum albumin) for 10 min to permeabilize the cellular membranes. Cells were washed in 5mM PBS for 10 min (3x) and immersed in 20% normal horse serum in PBS for 1 h to block nonspecific binding sites before incubation with 1:100 of sheep AbP2Y₂ or mouse AbSV2 in PBS. Incubation time varied from 2 h at 20°C to 18 h at 4°C. Slides were rinsed in PBS for 10 min (3x) followed by application of the appropriate secondary antibodies (anti-mouse Cy2 for AbSV2 or anti-sheep Cy3 for AbP2Y₂) for 2–3 h at 20°C. Slides were washed in PBS for 10 min (3x), coverslipped and sealed.

Confocal microscopy of P2Y₂-GFP
Fluorescent images were collected with an inverted Leica four-dimensional laser-scanning confocal microscope using a 40:10 oil immersion objective (Leica, Wetzlar, Germany). Full-frame images (256 pixels x 256 pixels) were taken of an area of interest of cells and a flattened two-stack image of the confocal images of P2Y₂-GFP generated. Sufficient numbers of slices were taken, with an interval of 0.5 µm. Images were transferred to a Power Macintosh 6200/75AV between each slice, to avoid the difficulties that arise due to change in the focal plane of the microscope with respect to the cell interior as the cells rounded up upon exposure to agonist (see Fig. 4 A). Each of the images of the z-stack was then superimposed over the previous one to generate a flattened z-stack. The images were processed using NIH Image 1.60 (available from the US National Institute of Health at http://rsb.info.nih.gov/nih-image/). The mean intensities of the images were used to generate data such as that graphed in Fig. 5.

View larger version (63K): [in this window] [in a new window]   FIGURE 4  P2Y2-GFP in A7r5 cells under different experimental conditions. (A) Confocal images of A7r5 cells showing the clustering of P2Y2-GFP in the membrane 24 h after transfection (a), and then the gradual loss of many of the clusters after exposure of the cells to 10 µM UTP for 1 min (b), 2 min (c), and 5 min (d); higher magnification inserts in a and d are taken from the solid-square regions and show dense clusters of P2Y2-GFP in a that are largely lost in d. Note that in addition to the loss of many of the clusters, there is a gradual rounding-up of cells in the presence of the agonist. (B) Confocal images of P2Y2-GFP as in A, but this time in the presence of monensin (5 µM); note no loss of P2Y2-GFP fluorescence, but the cells still round up. (C) Confocal images of P2Y2-GFP as in A, but this time in the presence of suramin (10 µM); note again no loss of P2Y2-GFP fluorescence, and in this case the cells do not round up. Calibration bar is 10 µm.

View larger version (18K): [in this window] [in a new window]   FIGURE 5  Experimental and theoretical membrane P2Y2 receptor fraction with respect to time. Experimental data show the time-course of P2Y2-GFP in A7r5 cells (squares with mean ± SE for six cells) after application of 10 µM UTP at t = 0. The P2Y2-GFP fluorescence has been taken to be proportional to the number of receptors in the membrane and has been scaled to become a percentage of the amount of receptor relative to that before agonist stimulation. The solid line is the theoretical time-course of the total surface receptor fraction, and the broken line is the time-course of the phosphorylated surface receptor fraction, both obtained by solving Eqs. 1 and 2.

Whole-cell voltage-clamp of cells
Cells were voltage-clamped using the nystatin perforated patch-clamp technique. Whole-cell recordings were made with an Axopatch-1C amplifier (Axon Instruments, Union City, CA) at a holding potential of –60 mV and –30 mV. Patch pipettes between 2 and 4 M were filled with standard pipette solution containing: 130 mM CsCl, 10 mM HEPES, 10 mM EGTA, 1 mM CaCl₂, 2 mM MgCl₂, pH 7.3 adjusted with CsOH. The standard bath solution contained: 140 mM NaCl, 5 mM KCl, 10 mM HEPES, 10 mM glucose, 2 mM CaCl₂, 1 mM MgCl₂, pH 7.3 adjusted with NaOH. ATP was applied with a fast-flow U-tube delivery system. All electrical recordings were carried out at room temperature (20–22°C). Data were acquired and analyzed using a MacLab (AD Instruments, Charlotte, NC).

Materials
All chemicals were obtained from Sigma (St. Louis, MO).

Theoretical model
Overview of model
The model cell contains sarcoplasmic reticulum that is represented by two compartments—a central SR and a peripheral SR (Fig. 1). After application of UTP, the P2Y₂ receptors form five dynamically linked classes: in the sarcolemma they can either be phosphorylated or unphosphorylated and each type can be unbound or bound to ligand; in addition, bound phosphorylated receptors can be internalized and eventually recycled (Fig. 2 a). The ligand-bound unphosphorylated receptors activate a G-protein cascade, leading to the production of IP₃ that diffuses into the cytosol and acts on IP₃ receptors (IP₃Rs) in the central SR (Fig. 1). This results in the release of calcium ions (Ca²⁺) that diffuse throughout the cytosol, are pumped into the peripheral SR by a Ca²⁺-ATPase, and also act on ryanodine receptors (RyRs) in the peripheral SR to release further Ca²⁺ in an oscillatory manner into the subsarcolemmal space between the peripheral SR and the sarcolemma (Fig. 2 b). These calcium sparks act on nearby BK channels in the sarcolemma (Fig. 1), thus generating STOCs.

View larger version (21K): [in this window] [in a new window]   FIGURE 1  Schematic diagram of the multicompartment vascular smooth muscle cell model. P2Y2 receptors are present in the sarcolemma. The cell interior contains three main compartments: the cytosol (1), the central SR (3), and the peripheral SR (2), with the cytosol being divided into a main part and a smaller subsarcolemmal space lying between the peripheral SR and the sarcolemma. The central SR membrane contains IP3Rs and the peripheral SR membrane contains RyRs; both have Ca2+ leaks and pumps. BK channels are in the sarcolemma in close apposition to the RyRs in the peripheral SR. Jab denotes a Ca2+ current from compartment a to compartment b.

View larger version (19K): [in this window] [in a new window]   FIGURE 2  (a) Kinetic scheme for receptor-ligand binding, phosphorylation, and internalization. (b) Schematic diagram of the compartments in the model and the Ca2+ fluxes between them. (c) Kinetic scheme of the model for the bursting behavior of the ryanodine channels on the peripheral SR membrane. (There are four states: inactive, open, closed, and refractory, denoted by the A, B, C, and D, respectively.)

Regulation of receptor activity, G-protein cascade, and IP₃ production
The equations describing the processes involved in P2Y₂ receptor regulation, the G-protein cascade, and the production and regulation of IP₃ are adapted from a previous model (Lemon et al., 2003a). However, the equations have been simplified because some aspects of that model are superfluous for the purposes of this study; these differences are discussed below.

The interaction between ligand (L) and receptors (R) are shown in Fig. 2 a; R_P denotes phosphorylated receptors and R_I denotes internalized receptors. The stimulus applied to the cells is taken to be a step application of agonist of concentration [L] applied at time t = 0. The equations describing the dynamics of the receptors in response to this stimulus are

(1)

(2)

where [R^S] = [R] + [LR] and are the numbers of unphosphorylated and phosphorylated surface receptors, respectively. The total number of receptors is where is the total number of surface receptors; and k_p, k_e, and k_r are the rates of receptor phosphorylation, endocytosis, and recycling, respectively. and are the dissociation constants for the binding of ligand to the unphosphorylated and phosphorylated receptors, respectively.

The unphosphorylated ligand-bound receptors activate G-protein molecules in the plasma membrane, the amount of active G-protein, [G], satisfying

(3)

where k_a and k_d are the G-protein activation and deactivation rate parameters, [G_T] is the total number of G-protein molecules, is the ratio of the activities of the ligand-unbound and -bound receptor species, and _r is the ratio of the number of ligand-bound receptors to the total number of receptors: _r = [L][R^S]/([R_T](K₁ + [L])). This differs from Eq. 17 of Lemon et al. (2003a) in that there is assumed to be no immobile receptor fraction, so = 1. The active G-protein activates phospholipase C (PLC) which hydrolyzes phosphatidylinositol 4,5-bisphosphate (PIP₂) in the plasma membrane to form IP₃. The rate of hydrolysis of PIP₂ is r_h[PIP₂], where [PIP₂] is the number of PIP₂ molecules and r_h = [G], where is an effective signal-gain parameter. This differs from Eq. 18 of Lemon et al. (2003a) in that there is assumed to be no Ca²⁺-activated synthesis of IP₃, so K_c = 0. Also, in the present study there is assumed to be no depletion of PIP₂, so [PIP₂] = [(PIP₂)_T] is the total number of PIP₂ molecules in the plasma membrane. Thus Eq. 24 of Lemon et al. (2003a) becomes

(4)

where is the volume of the cell, N_a is Avogadro's constant, [IP₃] is the molar concentration of IP₃ in the cytosol, and k_deg is the IP₃ degradation rate.

Cytosolic Ca²⁺ dynamics
The following equations are again adapted from Lemon et al. (2003a), with some simplifications and extensions. Whereas the model in that article had a single interior compartment and a single cytosolic compartment, the present model has three main compartments (Fig. 1). These are a cytosolic compartment, a central SR, and a peripheral SR. In addition, the cytosol is divided into two communicating regions: a central region and a sarcolemmal space lying between the peripheral SR and the sarcolemma. This arrangement of compartments is consistent with current thinking regarding vascular smooth muscle morphology (Laporte and Laher, 1997). The subsarcolemmal space is assumed to be open to the cytosol (Fig. 1), so that over the timescale of receptor desensitization (several minutes), the two compartments form a well-mixed pool.

The Ca²⁺ currents between the different compartments are shown in Fig. 1, where J_ab denotes the current going from compartment a to compartment b. The equations governing the free Ca²⁺ concentration in the cytosol, peripheral SR, and central SR, [(Ca²⁺)_cyt], [(Ca²⁺)_psr], and [(Ca²⁺)_csr], respectively, are

(5)

(6)

(7)

where _ij is the ratio of the volume of compartment i to compartment j and ß_{–} is the buffering function for the indicated compartment. The same Ca²⁺ buffering model used in Lemon et al. (2003a) will be used in this article,

(8)

where [B_e] and K_e are the total concentration and dissociation constant, respectively, of the endogenous buffer, and [B_x] and K_x are the corresponding parameters for the exogenous buffer, in this case fluo3-AM. The other compartments will be assumed to have an excess of rapid, low affinity, stationary endogenous buffer of the same concentration and so ß_psr = ß_csr are constants. Conservation of the total amount of Ca²⁺, [(Ca²⁺)_T], implies the following relation between the [(Ca²⁺)_{–}]:

(9)

which is the counterpart of Eq. 37 of Lemon et al. (2003a) and where

(10)

is the ratio of free Ca²⁺ to total Ca²⁺ in the cytosol. Eqs. 8 and 10 imply that, for the simplified buffering used here, _psr = ß_psr and _csr = ß_csr.

The Ca²⁺ current through the membrane of the central SR is assumed to be due to IP₃ receptors, Ca²⁺ pumps, and Ca²⁺ leaks (Fig. 1). The Ca²⁺ current due to ryanodine receptors in the central SR is neglected. The equations for the currents through the central SR are

(11)

(12)

where _IP3, _lc, and _pc are effective permeability constants for the IP₃ channels, membrane leakage, and Ca²⁺ pumps, respectively; P_IP3 is the open probability for an IP3 channel; and k₃ is the pump dissociation constant. The expression for P_IP3 is derived by further simplification of the Li and Rinzel (1994) model employed in Lemon et al. (2003a). In the experimental data presented in this article, the rise and fall of cytosolic Ca²⁺ concentration occurs over a timescale of minutes, which justifies neglecting the time-dependence of channel behavior since this typically occurs over the timescale of seconds. Thus h = h in Lemon et al. (2003a) and the equation for is obtained by combining Eqs. 31–33 of that article to give

(13)

where d₁, d₂, d₃, and d₅ are channel kinetic parameters. The Ca²⁺ exchanged between the cytosol and the peripheral SR is assumed to be due to Ca²⁺ pumps, leaks, and ryanodine channels only. The equations for the currents J₂₁ and J₁₂ are

(14)

(15)

where _RyR, _lp, and _pp are effective permeability constants for the RyRs, membrane leakage, and Ca²⁺ pumps, respectively, and P_RyR is the open probability for a ryanodine receptor, an expression for which is given in the next section.

Model for Ca²⁺ oscillations
The experimental evidence upon which this article is based suggests that Ca²⁺ oscillations occur during stimulation with agonist but are localized in the subsarcolemmal space. Since these oscillations are associated with the bursts of STOCs, it will be assumed that the Ca²⁺ oscillations arise from RyRs located on the surface of the SR facing the sarcolemma (Fig. 1). A four-state quasidynamical model for the collective behavior of the RyRs giving rise to these oscillations is shown in Fig. 2 c. Initially the channels are all in the inactive state A, but in the presence of Ca²⁺ they are rapidly activated at a rate k_bstf([(Ca²⁺)_cyt]), thereby passing into the open state B. The channels are then deactivated rapidly at a rate k_bst and pass into the closed state C. They then enter a phase whereby they pass slowly to a refractory state D at a rate k_ref. The model incorporates a feedback mechanism that returns the RyRs to A at a rate k_retg([C]) where [C] is the number of channels in the closed state and the function g is a decreasing function of [C]. It can be shown that this scheme gives rise to Ca²⁺ oscillations of a spiking nature if the transition rates satisfy k_retg([C]) >> k_bst, k_bstf([(Ca²⁺)_cyt]) >> k_ref, and threshold kinetics are used for the functions f and g. Under these assumptions it is seen, provided [(Ca²⁺)_cyt] is above the critical threshold of the function f, that the channels pass rapidly through the states A then B during the burst, accumulate in the state C, and then make a slow transition to state D. When the number of channels in state C falls below the threshold level of the function g, the channels in state D are passed rapidly into state A.

Using this scheme, the bursting behavior of the RyRs is described by

(16)

(see the Appendix for details), where for and is zero otherwise, _on is the time at which [(Ca²⁺)_cyt] passes through its activation threshold [(Ca²⁺)_cyt]_thr, and _per is the period of the bursting.

There is considerable evidence that stochastic transient outward currents (STOCs) in smooth muscle are associated with sparks of Ca²⁺ from RyRs (Jagger et al., 2000). In this article, it will be assumed that the RyRs are located close to the BK channels (Fig. 1). This implies that during an opening of a single RyR, the Ca²⁺ concentration that builds up in the vicinity of the mouth of an apposite BK channel will be greater than the average Ca²⁺ concentration in the subsarcolemmal space, measured over the receptor desensitization timescale. To model this effect the domain Ca²⁺ concentration, being the effective Ca²⁺ concentration which activates the BK channels, will be expressed as a weighted sum of the contributions by the RyR channel current and the cytosolic Ca²⁺ concentration, so

(17)

where [(Ca²⁺)_d] is the domain Ca²⁺ concentration and w_dom > 0 is a constant. An appropriate value for w_dom is determined by fitting the model predictions to the experimental data.

Plasmalemmal ion currents
The principal outward current-carrying channel in the plasmalemma is assumed to be the large conductance Ca²⁺-sensitive K⁺ (BK) channel which gives rise to the STOCs seen in the experiments. The dependence of opening probability of BK channels on Ca²⁺ is modeled using a Hill function; thus the total outward current through the cell membrane is

(18)

where _BK is the effective permeability of the BK channels to K⁺ ions, mbk is the Hill coefficient, and kbk is the value of [(Ca²⁺)_d] producing half the maximum activation of the BK channels. The quantity I_s accounts for a small constant outward current observed in the experiments which was apparently Ca²⁺-independent; _BK = N_BK g_{bk K}, where N_BK is the number of BK channels in the membrane, g_bk is the conductance of a single BK channel, and _K is the Goldman-Hodgkin-Katz driving force for the BK channel. The other significant plasma membrane current that may be of importance in smooth muscle, the inward Ca²⁺ flux, has not been included because, in the in vitro experiments upon which the present work is based, the extracellular space was depleted of Ca²⁺.

Model for Ca²⁺ indicator
The Ca²⁺ indicator used in these experiments is fluo3-AM whose fluorescent efficiency increases when bound to Ca²⁺ (Tsien, 1989). It will be assumed that the whole-cell fluorescence measurement is proportional to the amount of cytosolic Ca²⁺ bound to the buffer, and is therefore

(19)

where A is a constant, and so the ratio of fluorescence at a given cytosolic Ca²⁺ concentration to that before agonist stimulation is

(20)

where ₀ and [(Ca²⁺)_cyt]_bas are, respectively, the basal fluorescence and basal cytosolic Ca²⁺ concentrations (see below).

Initial conditions and methods of solution
Equations 1–6, together with the appropriate initial conditions (see Appendix), suffice to determine the time-courses of the principal quantities [R^S], [G], [IP₃], [(Ca²⁺)_cyt], and [(Ca²⁺)_psr]. These time-courses are then used to calculate [(Ca²⁺)_csr] using Eq. 9 and the derived quantities [(Ca²⁺)_d] and I_BK, using Eqs. 17 and 18, respectively.

All parameters, together with numerical values, are listed in Table 1. Some parameters' values were taken from Lemon et al. (2003a), which modeled the stimulation of 1321N1 human astrocytoma cells with UTP (Garrad et al., 1998); these values are listed briefly in the table. The assignment of other parameter values is discussed in the Appendix. Equations 1–6 were solved numerically using the MATLAB computer package (The MathWorks, Natick, MA). During the integration it is necessary to test where [(Ca²⁺)_cyt] passes through the RyR activation threshold, [(Ca²⁺)_cyt]_thr, to determine the bursting start time, _on.

View larger version (15K): [in this window] [in a new window]   FIGURE 10  Experimental results () for the time between bursts (A) and amplitudes of bursts (B) of STOCs after application of 10 µM of UTP to an A7r5 cell. In A the dashed line shows the average value of the intervals which is used to specify the bursting interval for the theoretical model. In B the solid line gives the theoretical amplitudes obtained by solving the model equations using the theoretical cytosolic Ca2+ fluorescence (Fig. 6, solid curve) as input; the crosses indicate the locations of the peaks. The experimental data-point is not given for burst 1 because of an artifact shortly after the addition of UTP. The broken line in B gives the corresponding theoretical results when the experimental cytosolic Ca2+ fluorescence (Fig. 6, dotted curve) is used as input (see the Appendix for modifications to the theory); the remaining parameters are as in Table 1, except that wdom has been increased to 4 x 10–3.

View larger version (14K): [in this window] [in a new window]   FIGURE 9  Experimental membrane current with respect to time showing several bursts of STOCs upon application of 10 µM UTP. These currents are given on a compressed time-base for illustration purposes, and are not those analyzed in Fig. 10.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

View larger version (41K): [in this window] [in a new window]   FIGURE 3  Transfection of A7r5 cells with P2Y2-GFP. (A) Confocal images of the membranes of A7r5 cells shortly after transfection with P2Y2-GFP (a), 12 h after transfection when the P2Y2-GFP distribution is still diffuse (b), and 24 h after transfection when P2Y2-GFP has formed clusters of 0.5–1 µm in diameter (c); the insert in c shows several clusters of P2Y2 receptors at higher magnification of the area indicated by the white square. (B) Comparison between the localization of P2Y2-GFP (a) and of anti-P2Y2 antibodies (b) on the same A7r5 cell; higher magnification inserts are of the identical areas indicated by the open squares. Calibration bar is 10 µm.

Fig. 4 A shows the decrease in P2Y₂-GFP fluorescence at the surface of A7r5 cells on exposure to the agonist over 5 min. This decrease is accompanied by a loss of P2Y₂-GFP receptor clusters and a gradual rounding-up of the cells (Fig. 4 A, a–d), as receptor activation continues (see higher magnification inserts in a and d of Fig. 4 A; the clusters overlap extensively in the insert of Fig. 4 A, a, but only one cluster is discernable in Fig. 4 A, d, after agonist exposure). The loss of surface membrane fluorescence from A7r5 cells on exposure to UTP was completely blocked, as was the rounding up of the cells, by their prior incubation in suramin (10 µM; Fig. 4 C). This loss of P2Y₂-GFP fluorescence upon exposure of the cells to agonist suggests an uptake of the chimera into acidic endosomes, as GFP is quenched under acidic conditions (Kneen et al., 1998). To test this, monensin (5 µM) was used to block the pH differential in endosomes (Cremaschi et al., 1996). There was no loss of P2Y₂-GFP fluorescence on exposure to UTP (10 µM) in the presence of monensin in A7r5 cells (Fig. 4 B).

The time-course of loss of fluorescence intensity of the cells was determined. Approximately 30% of the membrane fluorescence is lost over 5 min during exposure to 10 µM of UTP until a steady-state level is reached at 10 min (Fig. 5). This is a quantitatively similar loss to that observed at this concentration of UTP, using a monoclonal antibody technique to follow P2Y₂ receptors (Garrad et al., 1998). Solution of Eqs. 1 and 2 for a step application of [L] = 10 µM UTP gives the theoretical transient in the number of receptors at the sarcolemma The continuous line in Fig. 5 shows a good fit to the experimental results, using the assumption that the P2Y₂-GFP fluorescence is proportional to the number of receptors in the sarcolemma. Also shown in Fig. 5 (dashed line) is the time-course of the phosphorylated surface receptor fraction, as calculated from Eq. 2. Upon application of UTP, rises rapidly to a peak, at which point most of the receptors have been phosphorylated, followed by a slow decline due to internalization. During this decline the difference between the two curves is the unphosphorylated surface receptor, and is small due to the receptors being nearly saturated with ligand.

Transient elevation of cytosolic calcium in A7r5 smooth muscle cells after exposure to UTP
Native A7r5 cells did not respond upon exposure to UTP (10 µM) with a detectable increase in calcium concentration using the calcium indicator fluo3-AM. However, exposure of A7r5 cells to UTP, after their transfection with P2Y₂-GFP, did give a transient increase in calcium concentration (Fig. 6, dotted line; the continuous line is the theoretical curve from the model). The calcium remained elevated for only 5 min, over the same period in which there is a loss of P2Y₂-GFP clusters from the membrane (compare Figs. 5 and 6). These observations further indicate that the chimera possesses characteristics of the endogenous wild-type receptor.

View larger version (18K): [in this window] [in a new window]   FIGURE 6  Experimental and theoretical Ca2+ fluorescence with respect to time. Experimental data (squares = mean ± SE < size of squares; n = 4 cells) show the time-course of fluo3-AM fluorescence in an A7r5 cell after application of 10 µM UTP at t = 0. The solid line shows the theoretical time-course of the cytosolic Ca2+ fluorescence obtained by solving the model equations to determine [(Ca2+)cyt] and calculating the corresponding fluo3-AM fluorescence using Eq. 20. The broken line shows the effect of including RyRs on the central SR.

The model has RyRs only on the peripheral SR and not on the central SR; there is experimental evidence for this distribution of receptors (Ohi et al., 2001; see also the Discussion section below) but it is of interest to see what theoretical effect their inclusion would have. The extension of the theory is given in the Appendix and the result is shown in Fig. 6 (dashed line). Thus the inclusion of RyRs on the central SR leads to Ca²⁺ spikes that are not observed experimentally. Therefore the rest of the theoretical results in this article will be for the case where RyRs are not placed on the central SR.

The theoretical transients in IP₃ concentration, [IP₃], and percentage of activated G-protein, [G], for a step application of 10 µM UTP at t = 0, are shown in Fig. 7. The time for [G] to reach its maximum value of 5.3%, 15 s, is controlled mainly by the G-protein deactivation rate parameter k_d. Since the value of the IP₃ degradation rate parameter, k_deg, is much smaller than k_d, the [IP₃] transient lags behind that of [G]. [IP₃] peaks at 410 nM after 80 s. The sustained levels of activated receptors maintained by receptor recycling causes the raised levels of [IP₃] and [G] seen for long times in these curves.

View larger version (14K): [in this window] [in a new window]   FIGURE 7  Theoretical IP3 concentration, [IP3] (solid line), and amount of activated G-protein, [G], expressed as a percentage of [GT] (dashed line), with respect to time for a step application of 10 µM UTP at t = 0.

View larger version (24K): [in this window] [in a new window]   FIGURE 8  Theoretical Ca2+ concentrations with respect to time for a step application of 10 µM UTP at t = 0. The time-course of the Ca2+ concentration in the cytosol, [(Ca2+)]cyt (dashed line), and the domain Ca2+ in the subsarcolemmal space, [(Ca2+)d] (solid line), are shown in A. Shown in B are the Ca2+ concentration in the central SR, [(Ca2+)csr] (dashed line) and peripheral SR [(Ca2+)psr] (solid line). Note the very different vertical axes scales in A.

The value of the RyR channel permeability, _RyR (see Parameter Value Selection in the Appendix), is too small to allow a current big enough to make significant perturbations to the cytosolic and SR Ca²⁺ concentrations. However, as seen in Fig. 8 a, the effects of constrained diffusion, included implicitly in the model for domain Ca²⁺, result in effective concentrations in the micromolar range near the BK channels.

Subsarcolemma calcium transients and the generation of STOCs in A7r5 cells exposed to UTP
Fig. 9 shows experimental measurements of the whole-cell membrane current of an A7r5 cell, during a patch-clamp at –30 mV, with respect to time after application of 10 µM UTP. This current is the summation of contributions by individual STOCs arising from large-conductance potassium (BK) channels. Individual STOCs are clearly visible in the trace immediately after each burst. The bursts of STOCs seen in Fig. 9 are evidence of the existence of subsarcolemmal Ca²⁺ oscillations that activate the BK channels. In the results of the experiment shown in Fig. 9, the general amplitude of consecutive bursts declines over the first 2 min and thereafter bursts recur indefinitely at approximately the same amplitude. The constant 6-pA outward current visible in the current trace has been included in the model as the membrane outward current offset, I_s.

In Fig. 9, the time between each burst remains relatively constant after the first burst. This property of the oscillations in the outward current is evident in Fig. 10 A, where the time between the peaks of the bursts are plotted for one cell, representative of observations on five cells. The dashed line represents the average of the intervals, 25 s, and this has been used as the value for the parameter _per in the bursting model of the RyRs in the peripheral SR membrane. The small deviation of the interval from the average value shows that the frequency of the membrane current bursts and hence subsarcolemmal Ca²⁺ oscillations does not strongly depend on the extent of receptor desensitization. The experimental peak amplitudes of the bursts are plotted in Fig. 10 B.

The theoretical membrane current, with respect to time, for a step application of 10 µM of UTP at t = 0 is shown in Fig. 11. The first burst begins at t = _on = 9.3 s, when [(Ca²⁺)_cyt] reaches the firing threshold [(Ca²⁺)_cyt]_thr. A closeup of the fourth burst is shown in the inset. This fourth burst has the largest magnitude of all with a maximum outward current of 40 pA. The curve reproduces the general characteristics of the bursts shown in Fig. 9, including the correct rise and fall times of the membrane current during each burst and the constant Ca²⁺-independent outward current. The decline in amplitudes of the bursts over time in Fig. 11 is plotted in Fig. 10 B (solid curve with crosses indicating the position of the peaks). The theoretical data matches approximately the general trend of the experimental data. The theoretical curve in Fig. 10 B was recalculated using the experimental Ca²⁺ fluorescence time-course as given by the dotted curve in Fig. 6, rather than the calculated [Ca_cyt²⁺] (solid curve in Fig. 6). The details of the method are given in the Appendix and the result is shown as the dashed curve in Fig. 10 B. Both curves are equally consistent with the general trend of the experimental data.

View larger version (23K): [in this window] [in a new window]   FIGURE 11  Theoretical membrane current, IBK, with respect to time upon application of 10 µM UTP at t = 0. The insert shows a closeup of the fourth burst of STOCs, this being the burst with the greatest amplitude.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

Time-course of desensitization of the P2Y₂ purinergic receptor
Desensitization of metabotropic receptors has been most extensively studied for the ß₂ adrenergic receptor (ß₂-AR; Kallal et al., 1998) and to a lesser extent for the ₁ and ₂ adrenergic receptors (₁-AR and ₂-AR) as well as the mGluR1 glutamate receptors (Wang and Linden, 2000; Sallese et al., 2000). The rates of desensitization of these receptors in the presence of agonist are similar to their rates of internalization (Fonseca et al., 1995; Heck and Bylund, 1998). All these receptors conform to the accepted paradigm for G-protein coupled receptor kinase-mediated desensitization of the receptor: G-protein coupled receptor kinase-mediated receptor phosphorylation is followed by the binding of arrestin proteins; internalization of the receptors is then mediated by ß-arrestin and dynamin-dependent, clathrin-coated, vesicle-dependent endocytosis (for the mGluR receptors see, for example, Dale et al., 2002) with the receptor directed to endosomes (Mundell et al., 2001). It has recently been shown that some ionotropic purinergic receptors are also internalized upon binding ligand, such as the P2X₁ and P2X₄ receptors, and this also involves a dynamin-dependent endocytosis to endosomes followed by subsequent reinsertion in the membrane (Dutton et al., 2000; Ennion and Evans, 2001; Bobanovic et al., 2002). Desensitization of the P2Y₂ receptors is not contingent on internalization any more than is desensitization of other metabotropic receptors (Sromek and Harden, 1998), so the loss of IP₃ production in the presence of a P2Y₂ receptor agonist is not due to internalization of P2Y₂ but to its phosphorylation which is closely followed in time by sequestration (Sromek and Harden, 1998). Our model of this process follows that of Lemon et al., (2003a) and gives an account of the changes in P2Y₂-GFP at the sarcolemma after exposure of the receptors to agonist (see Fig. 5). However, the quantitative description of the data in Fig. 5 is given by the curve derived from Eqs. 1–6 in the model. Although this is a good fit, it is not an independent prediction of the model inasmuch as the steady state reached at 10 s is used in the model to ascertain the values of parameters (see Parameter Value Selection in the Appendix).

After activation of metabotropic receptors, the generation of IP₃, and activation of IP₃Rs, there is release of Ca²⁺ into the cytosol from the central SR. Desensitization of the P2Y₂ receptors thereby modulates the concentration of cytosolic Ca²⁺. In Fig. 6 the theoretical Ca²⁺ fluorescence transient shows the correct overall timescale for the decay after the peak (5 min), but the experimental curve shows a biphasic decay which results in an underestimate of the extent of receptor desensitization in the theoretical curve. This biphasic response cannot be modeled using a receptor desensitization mechanism characterized by a single rate constant, but a more detailed model for this effect is beyond the scope of the present work.

Subsarcolemma calcium transients
The present experiments show that the time-course of both the transient increase in calcium concentration and in the amplitude of STOCs is qualitatively similar to that of the internalization of P2Y₂-GFP. Given that the latter follows phosphorylation of the receptor, it appears likely that both the decline in calcium concentration and in STOC amplitude is consequent upon desensitization of the receptor. However, a model is required to provide a quantitative assessment of the possibility that the changes in cytosolic calcium concentration and STOC characteristics, after agonist application to the metabotropic receptors, are governed by the desensitization of the receptors.

In this article a new model is proposed for Ca²⁺ oscillations due to the collective behavior of ryanodine channels. Existing models for Ca²⁺ oscillations due to the RyRs alone (Keizer and Levine, 1996; Tang and Othmer, 1994) or combinations of IP₃Rs and RyRs (Sneyd et al., 2003) do not satisfactorily reproduce the bursting characteristics seen in the experiments. Thus a simple quasidynamical model for calcium oscillations was developed which features plausible mechanisms, these being Ca²⁺-dependent activation, Ca²⁺-independent deactivation, and recovery after a slow refractory phase.

Our model takes into account the fact that the SR is not uniformly distributed. The SR of smooth muscle cells varies between 2 and 6% of the cell volume (Devine et al., 1972). The peripheral SR, immediately beneath the sarcolemma, amounts to 2% of the total SR volume (Bazzazi et al., 2003) and is a potential source of calcium to raise the concentration of this ion in the subsarcolemmal space to open BK channels (for an analogous situation, see Coop et al., 1998). This SR, like that throughout the cells, appears to possess both RyR as well as IP₃ receptor calcium channels (Nixon et al., 1994) but, at least in A7r5 cells, the peripheral SR does not possess the class of IP₃ receptors that are mainly responsible for IP₃-induced Ca²⁺ release, whereas the central SR does possess these receptors (Vermassen et al., 2003). In the model we do not have IP₃Rs in the peripheral SR, but only RyRs. There is evidence that RyRs are preferentially located in the peripheral SR in smooth muscle cells (Ohi et al., 2001). Furthermore, including RyRs on the central SR in the model gave unrealistic results (Fig. 6). All the SRs possess calcium pumps and calcium leaks, with no evidence that these are differentially distributed between central and more peripheral SR (Bazzazi et al., 2003).

Calcium release through RyRs in the SR of smooth muscles gives rise to calcium sparks. These are associated with the activation of STOCs due to the opening of BK channels (Perez et al., 1999). There appears to be a close association between the peripheral SR calcium release sites in the smooth muscle cells and the BK channels in the sarcolemma responsible for the STOCs (Zhu-Ge et al., 1999). The BK channels are at highest density in the sarcolemma at sites of spark generation (Zhu-Ge et al., 2002). The amplitude of STOCs can vary more than threefold, and part of this variability may be attributed to differences in the coupling ratio of RyRs to BK channels in the spark microdomain (Zhu-Ge et al., 2000) rather than just to changes in desensitization/sequestration of sarcolemma receptors. Such microdomains consist of colocalization of BK channels in the plasma membrane and RyRs in the peripheral SR where calcium sparks elicit STOCs (Ohi et al., 2001; Lohn et al., 2001; McCarron et al., 2002). Recent modeling has provided estimates of 10 µM for the spark calcium concentration in the microdomain of apposed peripheral SR membrane and sarcolemma, which are separated by 25 nm (Zhu-Ge et al., 2002). Our results and modeling indicate a concentration of 5 µM (see Fig. 8 a). Bazzazi et al. (2003) suggest that the peripheral SR calcium uptake is primarily from the cytosolic calcium and not as a result of the opening of sarcolemma calcium channels, which is consistent with our model.

In our model we have not allowed for a contribution from IP₃ receptors in the peripheral SR to the generation of STOCs as evidence suggests that such receptors are only to be found on central SR in A7r5 cells (Vermassen et al, 2003). This has allowed for a reasonably simple model of the interaction between cytosolic Ca²⁺ and that in the subsarcolemmal space. The extent to which IP₃ releases calcium from SR throughout the smooth muscle cells which then leads to the release of Ca²⁺ through RyRs channels appears to be variable between different smooth muscle cell types (Guerrero-Hernandez et al., 2002). The present model faithfully reproduces the shape, length, and period of the bursts but cannot explain irregularities seen near the start of the current traces in some experiments (Fig. 9). The reasons for the initial irregular rate of bursting seen in that figure remain obscure.

The present theory indicates that the contribution of the RyR current to the cytosolic Ca²⁺ concentration transient is small (see Fig. 6). The bursting effects are most visible near the peak of the curve in Fig. 6 because this is where the peripheral SR concentration is largest and hence the maximum RyR channel current is also largest. The appearance of these bursts suggests that the theoretically determined ratio of _RyR:_IP3 (see Parameter Value Selection in the Appendix) is an overestimate. Although the magnitude of these perturbations could be reduced by lowering _RyR, this is a somewhat arbitrary step—so it was decided to retain the theoretical estimate for _RyR:_IP3 for the simulations.

That the RyRs are insensitive to IP₃ suggests that the heights of the bursts are determined by the amount of Ca²⁺ in the peripheral SR which is, in turn, modulated by the cytosolic Ca²⁺ concentration, due to there being pumps and leaks on the inner side of that store. Thus IP₃Rs control RyRs indirectly by liberating intracellular Ca²⁺ which both switches on the RyRs and modulates the Ca²⁺ current through them. According to this theory, the current from IP₃Rs in the peripheral SR must be negligible since this current would have a tendency to decrease the heights of the bursts. Thus the modeling suggests that IP₃Rs dominate on central SR and RyRs dominate on peripheral SR.

Values for the parameters kbk and mbk vary widely for different smooth muscle types (Carl et al., 1996). For example the Hill coefficient mbk can lie in the range 1–2 for guinea pig mesenteric artery (Benham and Bolton, 1986) but the value of mbk = 3.2 for canine colonic myocytes (Carl et al., 1996) used in this study seems more appropriate. This is because the resultant high degree of nonlinearity in the relation between Ca²⁺ and BK channel current, defined by Eq. 18, tends to suppress the appearance of submicromolar Ca²⁺ artifacts in the membrane current trace. This effect is essential for the bursting appearance in the time-course of I_BK shown in Fig. 11, where the cytosolic Ca²⁺ component of the domain Ca²⁺, [(Ca²⁺)_d], is not visible between the bursts. It is likely that this nonlinear effect also shapes the bursts in the experimental membrane current trace shown in Fig. 9.

	APPENDIX

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX ACKNOWLEDGEMENTS REFERENCES

 
Model for Ca²⁺ oscillations
An expression for the open probability of a RyR, P_RyR(t), during bursting can be derived from the equations defining the model as follows. Let the functions f and g be defined by

(21)