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Copyright © 2007 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 92, Issue 11, 3843-3861, 1 June 2007

doi:10.1529/biophysj.106.095687

Biophysical Theory and Modeling

Pacemaking through Ca²⁺ Stores Interacting as Coupled Oscillators via Membrane Depolarization

Mohammad S. Imtiaz^*, ,  , Jun Zhao^*, Kayoko Hosaka^*, Pierre-Yves von der Weid^†, Melissa Crowe^‡ and Dirk F. van Helden^*

^* The Neuroscience Group, School of Biomedical Sciences, Faculty of Health, The University of Newcastle, Newcastle, Australia
^† Mucosal Inflammation Research Group and Smooth Muscle Research Group, Department of Physiology & Biophysics, Faculty of Medicine, University of Calgary, Calgary, Alberta, Canada
^‡ Institute of Sport and Exercise Science, James Cook University, Townsville, Australia

Address reprint requests to M. S. Imtiaz, School of Biomedical Sciences, Faculty of Health, The University of Newcastle, Callaghan, NSW 2308, Australia. Tel.: 61-2-4921-5626; Fax: 61-2-4921-7406.

Lymphatic and various blood vessels display vasomotion, a rhythmic constriction-dilation cycle of smooth muscle in the vessel walls 1,2. In blood vessels vasomotion modulates local vascular resistance and blood flow (see Haddock et al. 3) and possibly improves tissue oxygenation (see Nilsson and Aalkjaer 4). In contrast, vasomotion in lymphatic vessels propels lymph fluid through frequently occurring unidirectional valves that divide the collecting lymphatic vessels into multiple chambers 2,5,6. The aims of this study were to investigate the pacemaker mechanisms that underlie lymphatic vasomotion.

Two models have been proposed to explain lymphatic pacemaking: a classical cardiac-like and a Ca²⁺ store-controlled pacemaker model. Both depend on Ca²⁺ action potentials initiating constriction of the smooth muscle 7,8,9,10. The classical model for heart pacemaking is based on membrane pacemaker currents including a hyperpolarization-activated inward current, known as I_funny (I_f) that depolarizes the pacemaker cell membrane at the termination of an action potential and continues the cycle 11. Thus in this model the pacemaker clock is set by activation of ion channels in the cell membrane. Significantly, an I_f-like current has been reported in bovine and sheep lymphatic vessels 12,13, blocking of which has been shown to slow down lymphatic pacemaking 13.

In the second model pacemaking of lymphatic smooth muscle is controlled by cyclical release-refill of intracellular IP₃R-operated Ca²⁺ stores 10,14,15,16,17,18. Ca²⁺ released from intracellular Ca²⁺ stores activates spontaneous transient inward currents (STICs) 19,20, these generating excitatory depolarizations termed spontaneous transient depolarizations (STDs). Vasomotion in guinea pig mesenteric lymphatics involves summation of STDs, resulting in pacemaker potentials that trigger the action potential and smooth muscle constriction 10,14. Thus in this store pacemaker model, the pacemaker clock is intracellular, set by the release-refill cycle of Ca²⁺ stores. Importantly, this mechanism may play a role in a much wider range of tissues. For example, recent evidence obtained from studies on isolated heart pacemaker cells opens up the possibility of a major role for store pacemaking in the heart (see Lakatta et al. 21).

The focus of this study is to determine how Ca²⁺ stores achieve synchrony to produce sufficient current to drive pacemaking in both small and large lymphatic vessels. Conducting Ca²⁺ waves 22,23, events that result through Ca²⁺-induced Ca²⁺ release (CICR) along arrays of stores 24,25, are unlikely to explain this synchrony. This is because conducting Ca²⁺ waves propagate slowly (typically <0.1 mm/s; see Berridge 26) and are unlikely to activate sufficient stores at any one time to drive pacemaking in lymphatic tissues (see van Helden et al. 14). In contrast, a pacemaker mechanism, based on Ca²⁺ stores interacting as coupled oscillators provides a powerful alternative, one that could readily underlie lymphatic vasomotion 15,27.

Coupled oscillator-based interactions have been proposed to underlie diverse biological systems 28, such as heart pacemaking 29,30, intestinal peristalsis 31,32,33, and signaling in astrocytes 34. Importantly, studies on bovine lymphatic vessels indicate that lymphatic vasomotion also arises through coupled oscillator-based interactions, as central disruption of constrictions by a putative gap junction blocker left vasomotion in the two vessel ends but the rhythmic constrictions were no longer in phase 35. The authors suggested that electrical coupling along the length of the lymphatic duct allowed these sections to entrain their constrictions to a mutual compromise frequency.

To understand coupled oscillator interactions between Ca²⁺ stores it is useful to consider a row of pendulums interconnected by springs. Random activation of the pendulums causes the pendulums to interact, each advancing or retarding the phase of others, until there is global entrainment. Such entrainment can lead to local synchrony of the pendulums. However, because the coupling between pendulums is imperfect, phase delays establish which can lead to phase waves along the row of pendulums, each pendulum swinging at the same frequency, but starting at a slightly different phase to its neighbor (see van Helden and Imtiaz 36).

In the case of stores, the pendulums are used to depict the store oscillators, though strictly speaking the stores are relaxation oscillators (i.e., rapidly releasing their contents and slowly refilling the cycle then repeating), and the springs represent the coupling mechanisms between the oscillators. Stores exhibit two primary coupling mechanisms, chemical and electrochemical. An example of the former is diffusion of Ca²⁺, which couples the stores by CICR. However, such coupling can only result in local synchrony because of limited effective diffusion of Ca²⁺ (e.g., ∼5μm; 37), with this type of coupling being too weak to successfully synchronize the Ca²⁺ store oscillations over large cellular syncytia 27. In contrast, electrochemical coupling has a 100–1000 times greater range than that for Ca²⁺ diffusion-based coupling. This is because electrical signals act in the millimeter range in smooth muscle syncytia (e.g., the length constant of vascular smooth muscle is ∼2mm; 38). Therefore electrochemical coupling can act as a long-range “spring” interconnecting multiple oscillators. Such interactions have been hypothesized to underlie lymphatic vasomotion 15, vasomotion in mesenteric arteries 39,40,41,42, and slow wave pacemaking in a gastrointestinal smooth muscle 27, where electrochemical coupling is mediated by interaction between membrane voltage and Ca²⁺ stores linked by either voltage-dependent production of IP₃ and/or Ca²⁺ entry.

Three elements are essential for effective long-range coupling between stores: 1), oscillatory Ca²⁺ release-induced depolarization; 2), membrane depolarization providing positive feedback to induce further store Ca²⁺ release; and 3), connectivity between cells (e.g., gap junctions). Lymphatic smooth muscle exhibits all these elements, because it has oscillatory Ca²⁺ release that causes depolarization, L-type Ca²⁺ channels that cause store Ca²⁺ release, and gap junctions between cells, and hence a coupled oscillator-based store pacemaker mechanism is predicted as we confirm here. Some of the results of this study have been presented previously in abstract form 43.

Young guinea pigs (<10 days) of either sex were killed by overexposure to the inhalation anesthetic isoflurane (5–10% in air) followed by decapitation, a protocol approved by the University of Newcastle Animal Care and Ethics Committee. The small intestine and attached mesentery were rapidly removed and placed in a physiological saline solution of the following composition (in mM): CaCl₂, 2.5; KCl, 5; MgCl₂, 2; NaCl, 120; NaHCO₃, 25; NaHPO₄, 1; and glucose 10. The pH was maintained near 7.4 by constant bubbling with a 95% O₂ and 5% CO₂ gas mixture. Lymphatic vessels of diameter typically <300μm were selected and isolated in situ in the mesothelium together with any nearby arteries and/or veins. The mesothelium was either pinned flat onto the sylgard-coated (Dow Corning, Midland, MI) base of a small organ bath (volume 0.2–1ml) or held flat against the coverslip base of a bath (volume 0.5–1ml) using a fine stainless steel frame. Alternatively, single lymphatic chambers were mounted on a wire myograph, which was used to record constrictions and hold the vessel chamber flat against the coverslip. Care was taken to minimally stretch the lymphatic vessels in all cases. Preparations were superfused with the physiological saline heated to 34–36°C at a rate of 6 ml/min. Vessel chambers formed by adjacent valves (i.e., lymphangions; 5) were isolated by cutting just inside the valves (length 300–500μm and diameter 200–350μm) for electrophysiological recording. Vessels were not internally perfused during recording. Tissues were normally used within 1–4h of isolation and were stored at 4°C in physiological saline until use.

Intracellular microelectrode recording was performed by impaling the smooth muscle of vessel segments. Microelectrodes were filled with 1mM KCl and typically had resistances of 100–150 MΩ. Electrical data were recorded and stored digitally with analysis performed using Axograph (Axon Instruments, Foster City, CA).

Ca²⁺ imaging experiments were made using a Bio-Rad 1000 confocal laser system (Cambridge, MA) connected to an inverted microscope (Nikon TE200, Tokyo, Japan). Tissues were viewed directly through the coverslip that formed the base of the bath with a water immersion objective (magnification ×60, numerical aperture 1.2) with the confocal aperture set to provide a depth resolution of ∼2μm. Tissues were loaded by two procedures. The first was to luminally perfuse vessels for 30min at ∼35°C with a physiological saline in which the CaCl₂ concentration was reduced to 1mM and that contained 2μM Oregon green/AM (Molecular Probes, Eugene, OR). This was followed by a 5-min perfusion using the normal low-calcium (1mM) saline to wash out extra dye in the vessel lumen. Loading of the smooth muscle by this procedure was only successful in endothelium-denuded vessels, a condition that was achieved by briefly passing bubbles of air through the vessel lumen (see Gao et al. 44). Vasomotion in these vessels occurs independent of the endothelium with endothelial factors only subserving a modulatory role 45. The second method was to externally load the smooth muscle by adding 2μM Oregon green/AM to the normal physiological saline for 30min at 35°C. This was used for loading lymphatic smooth muscle in tissues where the mesothelium had been largely removed. The Oregon green-loaded lymphatic smooth muscle was excited with light of wavelength 488nm using an argon ion laser. Emission fluorescence was collected through a 510-nm dichroic mirror and 515-nm bandpass filter. Ca²⁺ transients were deemed measurable and appropriate for analysis if the associated transient increase in fluorescence of the Oregon green was at least twice the baseline noise.

Some experiments were made using internal perfusion to activate lymphatic chambers. In these cases a glass cannula (tip diameter ∼50μm was loosely inserted into the upstream end of a lymphatic vessel with the perfusion rate gradually increased until the lymphatic chambers in the vessel became active (final flow rate ∼2.5μl/min). The perfusing solution used was a modified physiological saline differing only in that the CaCl₂ was decreased to 0.3mM. Constrictions in the vessels were then recorded videoscopically viewed through an inverted microscope with a ×4 objective. Constriction frequencies and propagation velocities were determined using an edge detection algorithm 46, with up to 10 vessel edges tracked simultaneously. Some experiments were made on large single chambers isolated from vessels. These were isolated by cutting the adjacent chambers near the valves at both ends of the chamber leaving enough remnant upstream chamber for insertion of the cannula, which was positioned into the upstream valve.

All values are presented as the mean±SE with n the number of samples used, where n samples are derived from a minimum of five different animals contributing at least one sample each. Any variation is specifically stated. Significance was determined using a two-tailed Student's t-test, with p<0.05 considered significant.

The chemicals used were endothelin 1 (ET-1), nifedipine, wortmannin, and U46619 9,11-dideoxy-9α,11α-methanoepoxy prostaglandin F_2α) from Sigma (St. Louis, MO) and Oregon green/acetoxymethyl (AM) from Molecular Probes. Stock solutions were made up in either distilled water or dimethylsulphoxide (DMSO) at concentrations of 10⁻⁴–10⁻¹ M and stored at −20°C. The concentration of DMSO was always <0.1%, which had no significant effect on lymphatic pumping.

We base our model of the lymphatic smooth muscle on previously published findings 10,15,18,35,47 and data presented in this study. Schematic in Fig. 1 and Table 1 summarize the essential events and pathways underlying Ca²⁺ and membrane potential dynamics of a single lymphatic smooth muscle cell. Cyclical release and refill of Ca²⁺ stores through activation of IP₃ receptors (events 2–6) occur due to cytosolic IP₃, elevated in response to application of agonists such as ET-1 (event 1). Cyclical oscillations in cytosolic Ca²⁺ are transformed into membrane potential oscillations through activation of an inward Cl⁻ current (events A, B). When depolarization is superthreshold, it triggers an L-type Ca²⁺ channel-mediated action potential and resultant Ca²⁺ entry (events C, D). This influx of Ca²⁺ further reinforces store Ca²⁺ cycling (event E). Current flow to adjacent cells through gap junctions occur (event F) and provide a coupling mechanism between cycling stores across cells.

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Figure 1

Schematic summary of dynamics in a single lymphatic cell. This schematic shows pathways and feedback loops underlying Ca²⁺ and electrical oscillations in a single lymphatic cell. See text and Table 1 for further details.

Other experimental findings that relate to our simulations include the following. i), Application of ryanodine (1 and 20μM) does not significantly alter lymphatic vasomotion 18. Thus we have not included ryanodine receptors in this model of cytosolic-store excitability. ii), Data presented in this and previous studies 18 have shown that influx of Ca²⁺ through voltage-gated channels is not a prerequisite for oscillatory Ca²⁺ release from stores. iii), Previous studies have shown that guinea pig mesenteric lymphatic vessels cut to short lengths or chambers of length <∼500μm have a smooth muscle syncytium that is electrically short 10. This is because the smooth muscle layer exhibits a length constant of ∼1mm 48. As such, potentials recorded from any smooth muscle cell reasonably reflect activity at any site in the vessel segment. iv), The endothelium modulates vasomotion but does not have a role in lymphatic pacemaking per se 18; therefore we only include a smooth muscle layer in our model. v), Simulations of the smooth muscle layer do not exclude the possibility that mixed in this layer and integrally coupled to the smooth muscle is a population of cells paralleling Interstitial Cells of Cajal (ICCs). ICCs are known to have a fundamental pacemaker role in gastric and other smooth muscles. However, despite some effort we do not have conclusive evidence for or against the presence of such cells in guinea pig lymphatic smooth muscle, because they have yet to be revealed by antibodies known to label gastric and some other ICCs (e.g., antibodies against cKit). Importantly, our model is based on Ca²⁺ stores operating in a network of cells that are electrically coupled, and hence the model should be applicable whether or not lymphatic vasomotion is paced by ICCs.

In summary, there are two main components of lymphatic smooth muscle excitability: a), cytosolic-store Ca²⁺ excitability, and b), an excitable effect of voltage-dependent L-type Ca²⁺ channels. We now formulate the model using these two components with reference to experimental data.

A previous experimental study 18 has shown that ET-1 induced vasomotion occurs through Ca²⁺ release from intracellular Ca²⁺ stores through IP₃ receptors. ET-1 activates ET_A receptors, which stimulates phospholipase C production by a Pertussis toxin-insensitive G-protein leading to IP₃ production 18. Sustained levels of IP₃ result in cyclical release-refill of intracellular IP₃R-operated Ca²⁺ stores 26 (also see 14,27,49). Ca²⁺ stores are refilled by a thapsigargin-sensitive Ca²⁺-ATPase pump after each release 18. The excitability of this cytosolic-store Ca²⁺ system, as controlled by the intracellular levels of IP₃, is represented by the following set of equations:

(1)

The single pool model of Dupont and Goldbeter 50 adequately encapsulates the above given cytosolic-store Ca²⁺ excitability. Thus we use their model 50 to describe the functions A(Z,Y,β,σ) and B(Z,Y,β,σ). Further details of the cytosolic-store Ca²⁺ excitability system are given in Appendix I and Table 2.

Ca²⁺ increases in the cytosol result in depolarization. This transformation of Ca²⁺ release into membrane depolarization occurs through a Ca²⁺-activated inward current, most likely carried by Cl⁻ ions 14,51. This Ca²⁺-induced inward current underlies cytosolic Ca²⁺-voltage coupling. The Ca²⁺-induced conductance, G_ca, for this channel is defined by the following equation:

(2)

Current and voltage dynamics, including the Ca²⁺-induced current, is described by:

(3)

Previous studies 18 and experimental observations presented here show that the lymphatic smooth muscle contain L-type Ca²⁺ channels. This channel is voltage dependent and activates at voltage thresholds approximately +15mV above resting membrane potential. The current through the L-type Ca²⁺ channels is given as,

(4)

The activation of I_L(Z,V) is very fast and here is assumed to be instantaneous. Thus the activation gating variable m is given as,

(5)

The deactivation of I_L(Z,V) is dependent on the concentration of Ca²⁺ in the cytosol and is controlled by the gating variable h as follows,

(6)

(7)

The current I_L(Z,V) is due to influx of Ca²⁺ through the L-type Ca²⁺ channels, therefore it contributes to the intracellular concentration of Ca²⁺ in the cytosol. The change in Ca²⁺ concentration in the cytosol due to I_L(Z,V) is given as,

(8)

The dynamics of a single lymphatic smooth muscle isopotential unit j (with adjacent units i and k) that includes the excitable cytosolic-store Ca²⁺ system and excitability of the membrane due to L-type Ca²⁺ channels, is given as follows.

(9)

where G_Z and G_V are the Ca²⁺ and current coupling coefficients, respectively. Z_j and V_j are the cytosolic Ca²⁺ and voltage in unit j. In this model [IP₃]_c is considered to be dependent on the external stimulus β (e.g., level of ET-1) and is considered uniform across the whole cell population. Thus, there is no flux of IP₃ through the gap junctions or within cells.

A typical vascular smooth muscle cell is elongated, fusiform with tapering ends and has average diameter and length of 3–6μm and 150–200μm, respectively 52,53. Here we assume each smooth muscle cell to be 100μm, and model it with a one-dimensional array of 10 isopotential units described by Eq. (9).

The smooth muscle in each lymphatic chamber is a tissue syncytium, with cells interconnected by gap junctions. The smooth muscle syncytium is now modeled by making a two-dimensional network of gap junction connected cells. Gap junctions were placed with coupling in the transverse direction 10 times lower in accordance to observed experimental data 27. The electrical length constant of lymphatic smooth muscle has been reported to be between 0.8–2mm 54. Various simulations were run with longitudinal electrical length constant between 0.8 and 2mm and Ca²⁺ diffusion of 1.2μm²/min, with coupling of units within cells 300 times that of gap junctions. “No flux” boundary conditions were used for all simulations.

Large lymphatic tissue (2mm) comprised a one-dimensional array of 200 coupled units. Each unit representing 100μm isopotential tissue length was composed of a Ca²⁺ store and plasmalemma oscillator.

The lymphatic smooth muscle syncytium is composed of a collection of cells. The inference from experimental data shows that the cells in the population are heterogeneous in their response to IP₃. This heterogeneity could arise from many factors, such as heterogeneous expression of IP₃ receptors on the Ca²⁺ stores, heterogeneous populations of Ca²⁺ stores within cells, cell size, or even cell type. Furthermore, variation in IP₃ concentration in different regions of the tissue would also result in heterogeneous response of the cells.

Although the heterogeneity of the cell population could arise from various sources, the outcome relevant to our study of synchronization is the effect of these factors on the excitability and oscillatory frequency of the cells in response to agonist. Thus the heterogeneity of the cell arising out of various parameters can be lumped in our study by considering them to arise from a single source, i.e., the response to IP₃. The response of the cell to IP₃ is given by the parameter σ in Eq. (9) describing the calcium excitability of the cell. This parameter defines the sensitivity of a cell to IP₃ and controls the response of the cell to the level of agonist available to the syncytium. Although the stimulus level β is same for the syncytium, each cell responds according to its sensitivity to IP₃.

The model presented here is qualitative, i.e., it encapsulates the essential features of the experimental data and interrelationships of observed variables. Membrane potential records were used as a basic comparison variable for the experimental and simulated data. All other variables and parameters were adjusted using this criterion. We note that simulated time was scaled to match duty cycle of the experimental action potentials.

Numerical simulation and analysis were performed using MATLAB/SIMULINK (Mathworks, Natick, MA) on an IBM-compatible desktop computer.

Membrane potential recordings were made from isolated lymphatic chambers (length <500μm, diameter <300μm). The preparations were generally quiescent under unstimulated control conditions with relatively few chambers spontaneously active (∼10% from over 100). Intracellular microelectrode recordings revealed a resting membrane potential of −55±2mV (mean±SE, n=100). The isolated vessel segments were electrically short allowing measurement of activity generated in any region of the smooth muscle 10.

Intracellular voltage recordings and/or confocal Ca²⁺ imaging were made in the smooth muscle of spontaneously active chambers (Fig. 2). Shown are the regions of interest (ROIs) for two types of analysis (Figure 2AB). This tissue exhibited action potentials, associated increases in [Ca²⁺]_c and constrictions (Figure 2CI). The recordings presented here (representative of nine experiments from six animals) were made on application of 5μM wortmannin before it had become fully effective (Figure 2CE) and during treatment after it fully stopped constrictions (Figure 2FI). This agent inhibits myosin light chain kinase, thus preventing tissue constrictions and dislodgement of the electrode. Importantly, it did not inhibit pacemaking, consistent with studies on another phasic smooth muscle 55 and indicating that other known actions of wortmannin such as inhibition of PIP3 kinase 56 do not significantly interfere with lymphatic pacemaking. Action potentials and associated large synchronous global increases in [Ca²⁺]_c (Figure 2CD) exhibited constrictions, as indicated by the downward deflections of the ROI placed on the edge of the tissue (Figure 2C, ROI 1, green trace). Action potentials were >15mV having a mean amplitude of 33±3mV and half-duration (duration at 50% of peak) of 1.2±0.2s, with associated Ca²⁺ transients having a half-duration of 1.5±0.05s (n=9 tissues). Subthreshold pacemaker events were also observed consisting of depolarizations with associated near-synchronous increases in [Ca²⁺]_c. However, unlike the action potentials they did not cause constrictions. Pacemaker potentials had a mean amplitude of 6.6±0.3mV and a half-duration of 2.8±0.9s (n=10 events), with [Ca²⁺]_c having a half-duration 106.8±1.0% and amplitude 17.5±0.5% of the action potential-associated [Ca²⁺]_c transients (n=6 events).

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Figure 2

Spontaneous pacemaker events. Membrane potential and associated [Ca²⁺]_c transients recorded during application (C–E) and in 5μM wortmannin (F–I). (A and B) Section of a lymphatic chamber showing Oregon green loaded smooth muscle with two types of regions of interest used for data analysis. (C) Membrane potential recordings (blue upper trace) and simultaneous record of [Ca²⁺]_c for the nine ROIs marked in panel A, along with mean [Ca²⁺]_c for the nine ROIs. ROI No. 1 was placed on the edge of the tissue so as to monitor tissue movements (green trace). Deflection of this trace below the dotted line shows tissue constriction, whereas upward movement above the dotted line is generated by actual increase in [Ca²⁺]_c (verified by frame-by-frame analysis). Vertical dotted line shows that during a pacemaker event different regions of the tissue were synchronized without any associated movement. Inset in panel C shows expanded [Ca²⁺]_c records for ROIs 2–9 with superimposed membrane potential recording to highlight correlation between these two types of recordings. The inset also indicates that another pacemaker event has occurred after PP1. (D) Space-time plot showing temporal changes in relative intensity for all the ROIs shown in panel B. This plot was produced by plotting [Ca²⁺]_c transients within each ROI vertically down in the sequence shown in panel B as a function of time (i.e., ROIs 1–10 for row a, then ROIs 1–10 for row b, etc., plotted on the ordinate against time on the abscissa). (E) Mean difference image showing active regions during pacemaker event PP1. This image was produced by averaging five sequential images during peak of PP1, then subtracting average of five sequential images during baseline (taken at upward arrow in C). (F–H) Same as panels C–E but in the presence of 5μM wortmannin, ROI 1 trace (green) shows that now there is no movement of the tissue. (I) Mean difference image showing active regions during an action potential (AP1 in F), produced in a similar manner to panels E and H. Color scale bar in B applies to A, representing 8-bit (0–255) grayscale nonratiometric fluorescence intensity. Scale bars in F apply to corresponding traces in C. Timescale bar in G applies to C, D, and F. Normalized intensity color scale bar in G applies to D. Intensity color bar in I applies to E and H.

An inspection of the [Ca²⁺]_c transients showed that a pacemaker event (PP1) occurred synchronously throughout the tissue, Figure 2CD. This synchronous increase in [Ca²⁺]_c during the pacemaker event was not a result of tissue movement because ROI 1 (green trace) showed no tissue movement. This was further corroborated by a mean difference image, Figure 2E, which showed that widely dispersed regions within the field of view participated in the pacemaker event. Figure 1FI, shows similar data but now after wortmannin fully prevented tissue constrictions. Once again the pacemaker event PP2 was found to be synchronous throughout the imaged region. These results show that synchronous Ca²⁺ events can occur in the absence of action potentials.

Experiments recording changes in membrane potential and/or [Ca²⁺]_c were also made on quiescent chambers, now observing the effects of agonists such as ET-1, which are known to increase synthesis of IP₃. Application of ET-1 (1–3 nM) first caused an enhancement in the amplitude of measurable STDs (i.e., >0.5mV), these increasing by 156±14% of control (p=.0007; n=10), as measured for 30-s periods after ET-1 application. There was also a tendency for the frequency of these STDs to increase (166±32% of control), though this was not significant (p=0.052). This initial enhancement in activity usually led to generation of action potentials and associated constrictions (Figure 3A). Action potentials persisted long after removal of the ET-1. For example, 1–2min application of 1–3 nM ET-1 induced vasomotion that gradually subsided over the next 5–30min after return to control solution (n=9; data not shown). The above sequence of events was also observed for application of the thromboxane A₂ mimetic U46619 (n=5, data not shown), an agonist that is also known to enhance lymphatic vasomotion most likely through synthesis of IP₃57,58.

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Figure 3

Effect of ET-1. (A) Membrane potential recordings (upper traces) and simultaneous vessel edge recordings (lower traces) upon application of 3 nM ET-1. Numbered arrows correspond to regions shown on an expanded timescale. (B) [Ca²⁺]_c transients (upper record) averaged over all the imaged areas shown in C and associated smooth muscle constrictions (lower record) recorded from a lymphatic chamber mounted on a wire myograph. Labeled regions show record sections analyzed below in corresponding panels. (C) Section of a lymphatic chamber showing Oregon green loaded smooth muscle with regions of interest used for data analysis. (D) Records of changes in [Ca²⁺]_c upon and during maintained application of 3 nM ET-1 (panel B, arrow D). Application of ET-1 caused the emergence of pacemaker events as first evidenced by the Ca²⁺ transients becoming near-synchronous in areas 1–3 (*). The following cycle showed larger near-synchronous Ca²⁺ transients across all sites except area 6. (E) The synchrony and magnitude of the activity improved over time resulting in large, rhythmically occurring Ca²⁺ transients. Force scale represents relative force.

The data presented in Figure 3BE, shows measurements of relative [Ca²⁺]_c (representative of 15 experiments from 11 animals), and in this case simultaneous constriction measurements. Figure 3B presents the summed fluorescence of the Ca²⁺ sensing fluorophore for the entire imaged area of the lymphatic smooth muscle and the corresponding record of constriction. Analysis of intensity changes used the regions of interest depicted in Figure 3C. ET-1 caused the emergence of vasomotion (Figure 3B). Specifically, application of 3 nM ET-1 caused the asynchronous Ca²⁺ transients present under control conditions to synchronize with synchrony first beginning in more localized regions (e.g., see *, Figure 3D). Such emergence of synchronicity appeared as near-synchronous events distributed in local regions over multiple cells. However, even after the onset of more global synchrony some regions did not show significant increases in [Ca²⁺]_c (e.g., Figure 3D, ROI 6). Over time all areas showed near-synchronous increases in [Ca²⁺]_c (Figure 3E), the Ca²⁺ transients and constrictions now being larger and occurring at a higher frequency. Local Ca²⁺ waves conducting with low velocities (39±9μm/s; n=5) were observed within but not between smooth muscle cells during quiescent periods between tissue constrictions.

Nifedipine blocks L-type Ca²⁺ channels and hence constriction. However, in addition to this it was found that nifedipine also inhibited synchronization of Ca²⁺ store release events. This was investigated by firstly measuring membrane potential. Nifedipine (1μM) was applied to lymphatic chambers that were either spontaneously active, or in which activity was induced by prior application of 1–3 nM ET-1. Nifedipine first blocked action potentials revealing the underlying pacemaker potentials, with these then diminishing to leave apparently unsynchronized activity (Figure 4A). These findings were observed in all tissues tested (representative of nine experiments from nine animals).

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Figure 4

Effect of nifedipine. (A) Membrane potential recordings (upper traces) and simultaneous vessel edge recordings (lower traces) upon application of 1μM nifedipine. L-NAME (30μM), which like other NO synthase inhibitors 45 does not itself inhibit vasomotion, was included to inhibit NO release, because nifedipine has been reported to release NO from the endothelium 79. This figure is continued from Figure 3A where vasomotion had been initiated using 3 nM ET-1. Numbered arrows correspond to regions shown on an expanded timescale. (B) Membrane potential recordings (blue upper trace) and simultaneous record of [Ca²⁺]_c for the seven ROIs marked in C, along with mean [Ca²⁺]_c for the seven ROIs. ROI No. 1 was placed on the edge of the tissue so as to monitor tissue movements (green trace). Deflection of this trace below the dotted line shows tissue constriction, whereas upward movement above the dotted line is generated by actual increase in [Ca²⁺]_c (verified by frame-by-frame analysis). (D and E) Superimposed ROIs (both axes scaled ×5) at arrow D (marked PP indicating pacemaker event) and E Fig. 4 B).

Figure 4B shows simultaneous measurement of membrane potential and [Ca²⁺]_c during application of nifedipine to a spontaneously active chamber. Figure 4B presents membrane potential (blue trace), fluorescence of the Ca²⁺ sensing fluorophore for regions of interest depicted in Figure 4C, and mean fluorescence of all ROIs. All regions showed simultaneous increases in [Ca²⁺]_c during action potentials (Figure 4B). As nifedipine became effective, action potentials were blocked exposing underlying pacemaker potentials (Figure 4BD), which then themselves diminished as synchrony between regions was lost. Finally, all synchrony was lost with ROIs now showing only asynchronous increases in [Ca²⁺]_c (Figure 4BE).

KCl was applied when nifedipine had blocked synchronous oscillations and was found to cause no significant increase in baseline [Ca²⁺]_c (101±1% n=4) or initiate vasomotion (data not shown). Whereas, KCl caused increase in frequency of vasomotion (150±10%, n=5) and then vasospasm when applied in control (data not shown). This indicates that L-type Ca²⁺ channels are a major pathway for increasing [Ca²⁺]_c.

The role of L-type Ca²⁺ channels in facilitating synchrony of Ca²⁺ release was examined by addition of the agonist ET-1 to tissues in which L-type Ca²⁺ channels had been blocked by nifedipine. An example of 10 experiments from 10 animals is presented in Figure 5A. This figure shows that addition of ET-1 (3 nM) caused small depolarization but no synchronization. Further insight into the action of ET-1 was provided from Ca²⁺ imaging studies and an example is presented in Figure 5BE. Application of 1μM nifedipine abolished large constriction-associated Ca²⁺ transients (Figure 5B). Plots of the changes in [Ca²⁺]_c for the ROIs shown in Figure 5C demonstrated asynchronous spontaneous Ca²⁺ transients (Figure 5D). Application of 3 nM ET-1 in the presence of nifedipine (Figure 5B, arrow E) did not overcome the nifedipine-associated blockade of pacemaker potentials, however, there was an increase in the frequency of asynchronous Ca²⁺ transients (Figure 5E). These data indicate that L-type Ca²⁺ channels are critical for global synchrony of Ca²⁺ release and vasomotion.

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Figure 5

Effect of ET-1 in the presence of nifedipine. (A) Membrane potential recordings (upper traces) and simultaneous vessel edge recordings (lower traces) upon application 3 nM ET-1 in the presence of 1μM nifedipine. This figure is continued from Fig. 4 (L-NAME (30μM) also added with nifedipine). Numbered arrows correspond to regions shown on an expanded timescale. (B) [Ca²⁺]_c transients (upper record) averaged over all the imaged areas shown in C and associated smooth muscle constrictions (lower record) recorded from the lymphatic chamber of Figure 3BE. Labeled regions show record sections analyzed below in corresponding panels. (C) Section of a lymphatic chamber showing Oregon green loaded smooth muscle with regions of interest used for data analysis. (D and E) Plots of relative [Ca²⁺]_c as indicated on panel B (arrows D and E) obtained in the presence of 1μM nifedipine before (D), and during application of 3 nM ET-1 (E). Force scale represents relative force.

Simulations using the model set out in the Methods section were made. The key feature of such simulations is that the outcomes are in no way predetermined, rather they simply reflect physical interactions that arise when Ca²⁺ stores in an array of coupled cells are stimulated, each cell imbued with the known properties of a lymphatic smooth muscle cell. The essential features of this model are: 1), a two-dimensional array of cells interconnected by gap junctions; 2), each cell exhibits oscillatory release of Ca²⁺ from IP₃-receptor operated Ca²⁺ stores; 3), activation of a Ca²⁺ store can activate other stores through Ca²⁺-induced Ca²⁺ release; 4), store-induced increases in [Ca²⁺]_c generate inward current and resultant membrane depolarization; 5), there is voltage-dependent Ca²⁺ influx through L-type Ca²⁺ channels, this in turn causing store release through CICR; and 6), stores interact through chemical coupling (i.e., diffusion of Ca²⁺ between stores and CICR) and electrochemical coupling (i.e., store release>membrane depolarization>voltage-dependent Ca²⁺ entry>store release). Increasing the concentration of IP₃ in the model simulates the action of IP₃ enhancing agonists such as ET-1. The increase in IP₃ activates stores that interact as a system of coupled relaxation oscillators within and across the cellular syncytium. Most significantly, the outcome of these interactions closely parallels the observed emergence of lymphatic pacemaking.

The dynamic response of the model syncytium was studied by increasing stimulus β (i.e., [IP₃]_c) at a fixed rate (Fig. 6). During stimulation with low levels of IP₃, [Ca²⁺]_c levels become noisy. Each cell has a Ca²⁺ store population with a heterogeneous IP₃ sensitivity distribution (s) (Methods). Thus, within each cell stores that are most sensitive to IP₃ (i.e., low σ) respond to increasing IP₃ first. The sequence in response can also be due to variation in IP₃ concentration in different regions of the tissue, as noted in the Methods section. This can be seen in Figure 6B (1a), which shows the Ca²⁺ response of all the stores in a single cell (this corresponds to cell number 3,3 of Figure 6B (1b). In this cell each store responds according to its IP₃ sensitivity to increasing stimulus β (i.e., [IP₃]).

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Figure 6

Model simulations. (A) Cellular syncytium comprising a two-dimensional 5×4 array of 20 coupled cells with each cell having 10 Ca²⁺ stores. (A) Average Ca²⁺ (upper trace) and membrane potential changes in the model syncytium and corresponding space-time plot. This space-time plot shows the Ca²⁺ store activity as reflected by changes in cytosolic Ca²⁺concentration in all 10 regions of each cell, plotted vertically down in the sequence shown in panel B (1b) as a function of time (i.e., stores 1–10 for cell 1,1 then cell 1,2, etc., plotted on the ordinate against time on the abscissa). The boxed inset shows an action potential and associated Ca²⁺ transient on an expanded (10×) timescale. (B) Regions marked with numbered bars in panel A shown in expanded format. (B (1a)) Ca²⁺ changes in all stores within a single cell (cell 3,3 marked with arrowhead in B (1b)). Numbers on the left indicate location of the store within the model cell (see Methods). (B (1b) Average Ca²⁺ changes in each cell of the syncytium. Numbers on the left indicate location of the cell within the syncytium (see Methods). These traces show asynchronous Ca²⁺ transients in the syncytium during low levels of IP₃. (B (2a) Ca²⁺ wave arising through sequential activation of the array of stores in a single cell before the emergence of pacemaking (cell 3,3 marked with arrowhead in B (2b)). (B (2b)) Corresponding space-time plot for all stores showing asynchronous Ca²⁺ transients and Ca²⁺ waves within the cellular syncytium (this is plotted in the same format as for the space-time plot in A but on expanded scales). (B (3a)) Traces showing synchronous store-associated Ca²⁺ transients in a single cell (cell 1,3 marked with arrowhead in B (3b)) during a pacemaker event. (B (3b)) corresponding space-time plot showing that loosely synchronous Ca²⁺ release across the model syncytium results in a pacemaker event. (B (4a)) Traces showing store-associated Ca²⁺ changes in a single cell during action potentials (cell 3,3 marked with arrowhead in B (4b)). (B (4b)) Corresponding space-time plot showing that Ca²⁺ transients are highly synchronous once pacemaker activity becomes superthreshold and action potentials are generated. Local waves continue to occur during the interval between pacemaker-induced action potentials. Timescale bar in panel A applies to all traces and space-time plot. Color bar applies to all space-time plots. Ca²⁺ scale bar in B (4a) applies to all traces in panel B. Timescale bar in B (4a) applies to all traces in B except B (1a) and B (1b). Stimulation (i.e., [IP₃]) was increased at a fixed rate of 0.0058μM/min from 0.24 to 0.8μM. All voltage and Ca²⁺ scale bars represent normalized values.

The response of a cell is the averaged response of all the Ca²⁺ stores within it. Figure 6B (1b) shows the Ca²⁺ response of all cells during low levels of IP₃. It can be seen that cells respond in a heterogeneous manner to changing IP₃; those that have most sensitive Ca²⁺ stores begin oscillating first, with the oscillation frequency of each cell dependent on its store population. This results in asynchronous Ca²⁺ oscillations across the model syncytium. Store Ca²⁺ release from a cell generates inward current causing depolarization in this and other electrically connected cells, dependent on the size of the current and the passive electrical properties of the cellular syncytium. This induces subthreshold Ca²⁺ influx and resultant Ca²⁺ release in these cells. This interaction provides the fundamental coupling mechanism in the cell network. In this manner cells interact and influence the dynamics of other cells, but due to the Gaussian distribution of frequencies, the overall syncytium response at first appears random (Figure 6A). These Ca²⁺ release events show close parallels to asynchronous Ca²⁺ transients observed in the lymphatic smooth muscle during resting conditions.

Ca²⁺ released from a store can induce Ca²⁺ release from adjacent stores through CICR; this occasionally continues and results in a propagating Ca²⁺ wave conducting with a low velocity within a cell (Figure 6B (2a)). These waves can arise when a more sensitive store becomes active, its Ca²⁺ release activating neighboring stores by CICR, with this process continuing along the array of stores. Gap junctions present significant discontinuity to these waves due to the low permeability of gap junctions to Ca²+ (see Hofer et al. 59). Therefore a diffusive wave is impeded in crossing this barrier (Figure 6B (2b)), consistent with our observations that such waves are conducted within and not between lymphatic smooth muscle cells.

Initially Ca²⁺ release events in cells were asynchronous. However with increasing IP₃ more cells became excitable and oscillatory, and at a critical level of IP₃ (β ≈ 0.48μM) the overall response of the syncytium became more coordinated and a loose global synchrony appeared (Figure 6A, space-time plot). This caused the noisy baseline to be interspersed with aggregated larger amplitude Ca²⁺ release events and associated membrane potential oscillations (Figure 6A). This pacemaker activity parallels that observed in lymphatic smooth muscle in response to ET-1 (Fig. 2). Ca²⁺ oscillations within single cells became more synchronous during such pacemaker events (Figure 6B (3a)), and a loose synchrony appeared across the syncytium, where most, but not all, cells (20–40% of store population) participated in the event (Figure 6B (3b)).

Asynchronous Ca²⁺ transients and pacemaker-like oscillations persisted with increasing IP₃, but eventually action potentials and associated large Ca²⁺ transients appeared (Figure 6A). Ca²⁺ transients within cells became highly synchronous during such events (Figure 6B (4a)), and also across the syncytium (Figure 6B (4b)). These simulation outcomes parallel the synchronous global Ca²⁺ transients in lymphatic smooth muscle (Fig. 3). The local intracellular Ca²⁺ waves that occurred under low levels of stimulation, or between action potentials when the simulated [IP₃]_c was higher, also parallel the experimental observations. The Ca²⁺ wave velocity was dependent on the amount of stimulation, wave velocity increasing with higher stimulus over a range of 20–37μm/s for β=0.24–0.8μM. The frequency of action potentials in the model syncytium increased with increasing IP₃. However, pacemaking was abolished at very high [IP₃]_c with the cells entering a state of persistent elevated [Ca²⁺]_c and membrane depolarization (data not shown). This outcome predicts vasospasm, a behavior exhibited by lymphatic smooth muscle during stimulation with high concentrations of ET-1 18.

A block of L-type Ca²⁺ channels was achieved by blocking the associated conductance (G_ML=0) in Eq. (9). Ramp application of IP₃ (i.e., stimulus β) induced asynchronous Ca²⁺ release events and associated membrane depolarization. Increasing IP₃ increased the frequency and amplitude of asynchronous Ca²⁺ transients and associated STDs, however, synchronous Ca²⁺ oscillations and associated depolarizations did not emerge (Figure 7AB). Local Ca²⁺ waves continued to occur within cells (Figure 7B (1b)). This behavior of the model syncytium in the presence of L-type Ca²⁺ channel blockade accords with experimental observations (Figure 4 and Figure 5).

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Figure 7

Role of L-type Ca²⁺ channels in model simulations. (A) Average Ca²⁺ (upper trace) and membrane potential response (lower trace) to increasing IP₃ in the same simulation as for Fig. 6, with L-type Ca²⁺ channels blocked. (B) Regions marked with numbered bars in panel A shown in further detail. (B (1a)) Average Ca²⁺ changes in each cell shows asynchronous Ca²⁺ transients across the syncytium. (B (1b)) Space-time plot shows asynchronous Ca²⁺ transients and local Ca²⁺ waves within cells. (B (2a)) With increasing stimulation (i.e., [IP₃]), the frequency of Ca²⁺ transients is increased but synchronous pacemaker Ca²⁺ transients do not arise. (B (2b)) Space-time plot shows further details of the store Ca²⁺ transients. Timescale bar in B (2b) applies to all traces and space-time plots in panel B. Ca²⁺ scale bar applies to all traces. All voltage and Ca²⁺ scale bars represent normalized values.

The behavior of guinea-pig mesenteric lymphatics is somewhat different under perfusion. For example constrictions are generally more rhythmic during perfusion than when nonperfused vessels are agonist stimulated. Experiments were made on 11 large perfused lymphatic chambers (mean length 1835±77μm, range 1500–2300μm, mean diameter 248±14μm, range 175–350μm). Video analysis (Methods) at four approximately evenly spaced sites along the chambers demonstrated waves of constriction. The main direction of propagation of constriction was found to vary between chambers with five of the chambers mainly propagating constriction in the retrograde direction, three chambers mainly in the orthograde direction, and the remaining three chambers exhibited no dominant direction of propagation. Constrictions propagated approximately uniformly in seven of the chambers with other four showing differences in propagation between the tracking sites and in some cases occurring synchronously across local regions. For example in one chamber propagation velocity between recording sites 1–2 (separation 445μm), 2–3 (separation 396μm), and 3–4 (separation 314μm) was 5.0±0.4 mm/s (n=61 events), 4.6±0.3 mm/s (n=62 events), and 1.9±0.3 mm/s (n=64 events), respectively. The mean propagation velocity for the 11 chambers taken between sites 1 and 4 was 2.9±0.3 mm/s.

The modeling results presented so far have studied electrically short syncytia, as would be observed in experiments within the field of imaging. We now use the model to predict the Ca²⁺ dynamics underlying the experimentally observed behavior of smooth muscle tissue in large lymphatic chambers, where Ca²⁺ imaging experiments cannot be readily made. Ca²⁺ dynamics consequent to agonist stimulation was examined in a one-dimensional array of 200 coupled cells, representing a lymphatic chamber of length 2mm. The IP₃ sensitivity of the cells were randomly assigned from a Gaussian distribution. The data of Figure 8A, taken once global rhythmic activity had emerged, shows the average membrane potential and [Ca²⁺]_c recorded at three sites along the chamber during a rhythmic depolarization. Conduction delays occur along the length of the model tissue. In the example shown, depolarization first appears in region 1 and then with some delay occurs in region 2 and 3 (Figure 8A). Importantly, were each region examined in isolation (i.e., decoupled from the other regions), then each region would exhibit rhythmic activity with its own intrinsic frequency, due to the variability in IP₃ sensitivity of the cells. Coupled oscillator-based interaction between these oscillators result in an organized pattern (Figure 8B) where a wave appears to be conducting from region 1 toward regions 2 and 3. This is not necessarily a conducting wave but a phase wave, which is a consequence of phase locking between the oscillators. The delays in initiation of action potentials in different regions of the model tissue are similar to constriction delays observed in large lymphatic chambers (∼3–4 mm/s).

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Figure 8

Simulation of a large lymphatic chamber. (A) Cellular syncytium comprising a one-dimensional array of 200 coupled units, each 100μm in length, was used to simulate a lymphatic chamber of 2-mm length. Each unit was composed of a Ca²⁺ store and plasmalemma oscillator (see Methods). (A) Average membrane potential and [Ca²⁺]_c in three different regions of the model syncytium as shown in the schematic inset with corresponding color code and labels. [Ca²⁺]_c changes all units within each corresponding region are shown below the averages. (B) Space-time plot showing [Ca²⁺]_c changes in all units for the corresponding traces in A. Color-coded and numbered bar on the left shows spatial scale. Timescale bar in panel B applies to all traces. All voltage and Ca²⁺ scale bars represent normalized values.

Taken together, the modeling suggests that the experimentally observed constriction waves arise due to phase locking of local Ca²⁺ oscillators that generate global Ca²⁺ phase waves.

The experimental data presented have investigated spontaneous and ET-1 induced lymphatic pacemaking. Measurement of relative [Ca²⁺]_c showed loose global synchronization of asynchronous and locally produced spontaneous Ca²⁺ transients. Measurement of membrane potential in isolated chambers showed corresponding enhancement of spontaneous transient depolarizations and loose synchronization of these events to form pacemaker potentials, which when superthreshold triggered action potentials and vasomotion. Importantly, blockade of L-type Ca²⁺ channels, while not preventing ET-1 action to enhance the activity of asynchronous Ca²⁺ transients, prevented the emergence of global synchrony between Ca²⁺ stores. The fundamental dependence of pacemaking on Ca²⁺ entry through a voltage-dependent Ca²⁺ channel pathway indicates that this is the key chemical link in electrochemical coupling between stores. In guinea pig mesenteric lymphatics, the release of Ca²⁺ from stores is mediated by IP₃Rs and not ryanodine receptors 17,18.

The experimental findings were predicted by simulations based on a two-dimensional array of gap-junction connected cells with each cell having an array of stores and L-type Ca²⁺ channels. In the example provided, the array consisted of 5×4 cells, simulating an electrically short smooth muscle syncytia. Gradually increasing [IP₃]_c across the array caused asynchronous oscillatory Ca²⁺ release from stores and associated spontaneous transient depolarizations, the level of this activity increasing as more stores were recruited. Global synchrony then emerged leading to formation of Ca²⁺ transients and associated pacemak