AJP - Heart Calcium Transients and Cell-Sarcomere
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Am J Physiol Heart Circ Physiol 293: H229-H237, 2007. First published March 16, 2007; doi:10.1152/ajpheart.00727.2006
0363-6135/07 $8.00
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
293/1/H229    most recent
00727.2006v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via ISI Web of Science (1)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Jacobsen, J. C. B.
Right arrow Articles by Holstein-Rathlou, N.-H.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Jacobsen, J. C. B.
Right arrow Articles by Holstein-Rathlou, N.-H.

A model of smooth muscle cell synchronization in the arterial wall

Jens Christian Brings Jacobsen,1 Christian Aalkjær,2 Holger Nilsson,2 Vladimir V. Matchkov,2 Jacob Freiberg,1 and Niels-Henrik Holstein-Rathlou1

1Biomedical Institute, University of Copenhagen, Copenhagen, Denmark; and 2The Water and Salt Research Centre, Institute of Physiology and Biophysics, University of Aarhus, Aarhus, Denmark

Submitted 7 July 2006 ; accepted in final form 13 March 2007


   ABSTRACT
TOP
 ABSTRACT
METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 REFERENCES
 
Vasomotion is a rhythmic variation in microvascular diameter. Although known for more than 150 years, the cellular processes underlying the initiation of vasomotion are not fully understood. In the present study a model of a single cell is extended by coupling a number of cells into a tube. The simulated results point to a permissive role of cGMP in establishing intercellular synchronization. In sufficient concentration, cGMP may activate a cGMP-sensitive calcium-dependent chloride channel, causing a tight spatiotemporal coupling between release of sarcoplasmic reticulum calcium, membrane depolarization, and influx of extracellular calcium. Low [cGMP] is associated only with unsynchronized waves. At intermediate concentrations, cells display either waves or whole cell oscillations, but these remain unsynchronized between cells. Whole cell oscillations are associated with rhythmic variation in membrane potential and flow of current through gap junctions. The amplitude of these oscillations in potential grows with increasing [cGMP], and, past a certain threshold, they become strong enough to entrain all cells in the vascular wall, thereby initiating sustained vasomotion. In this state there is a rhythmic flow of calcium through voltage-sensitive calcium channels into the cytoplasm, making the frequency of established vasomotion sensitive to membrane potential. It is concluded that electrical coupling through gap junctions is likely to be responsible for the rapid synchronization across a large number of cells. Gap-junctional current between cells is due to the appearance of oscillations in the membrane potential that again depends on the entrainment of sarcoplasmic reticulum and plasma membrane within the individual cell.

vasomotion; mathematical model; chloride channel; gap junctions

VASOMOTION, A RHYTHMIC CHANGE in microvascular diameter, has been known for more than 150 years (26) and has been observed in numerous species including humans (1). During vasomotion, vessel segments of variable lengths contract rhythmically with frequencies of typically 3–20 cycles/min (4, 6, 10, 12, 14), although higher frequencies have been observed (9). In the vascular wall, the rhythmic generation of tension is associated with a parallel change in cytoplasmic calcium concentration (22, 25, 31, 34), as well as with an oscillation in membrane potential (3, 16, 17, 28). For the vessel to generate sufficient tension to contract against the intraluminal pressure, a large number of smooth muscle cells must act in concert. The nature of the signal causing this intercellular coordination in the vascular wall, however, remains poorly defined.

In many organs, e.g., heart and intestine, synchronized contraction of populations of cells is achieved by means of specialized pacemaker cells constituting only a small fraction of the total cell mass. Although the presence of pacemaker cells in the vascular wall has been hypothesized (27), the existence of such cells remains controversial.

In vessels of the rat intestinal microcirculation, stimulation with moderate concentrations of {alpha}-adrenoreceptor agonists elicits low-frequency calcium waves. These waves are out of phase and run in different directions in different cells; they are not transmitted from one cell to its neighbors, and they are not associated with vasomotion (31). Abruptly, the wave pattern may transform into high-frequency whole cell calcium oscillations that are coordinated among a large number of cells and are associated with the macroscopic appearance of vasomotion. The abruptness characterizing the onset of intercellular synchronization (31) indicates that the communicated signal spreads fast within the vascular wall, making electrical coupling through gap junctions a likely mechanism underlying the synchronization. Electrical coupling would enable processes that depend on membrane potential, e.g., voltage-dependent synthesis of inositol 1,4,5-trisphosphate [Ins(1,4,5)P3] (19, 45) or opening of voltage-sensitive ion channels (14, 29, 31) to entrain the oscillatory state of a large population of cells.

Here we present a mathematical model of a tube-shaped layer of cells, coupled through gap junctions to form a large cellular syncytium. Simulation of individual cells (19a) indicates that, following an increase in [cGMP], cells may shift from low-frequency waves to high-frequency whole cell oscillations. The latter are associated with rhythmic membrane depolarization, the amplitude of which increases with [cGMP]. The simulations indicate that, when a number of cells are coupled through gap junctions and cGMP is released beyond a certain concentration, the oscillations in membrane potential are strong enough to cause intercellular synchronization. Also, it appears that the hitherto unexplained acceleration in frequency following the onset of vasomotion may be explained on the basis of the shift in oscillatory mode within the individual cell rather than being a consequence of intercellular synchronization per se. Multiple simulations with variable gap-junctional coupling strength indicate that intercellular synchronization is independent of coupling strength as long as a certain minimal level is exceeded. The simulations also indicate that intercellular diffusion of signal molecules is not necessary to achieve global synchronization in the present system. Finally, the model points to membrane potential as an important factor in determining the frequency in established vasomotion.


   METHODS
TOP
 ABSTRACT
 METHODS
RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 REFERENCES
 
The Model

Cell model. Details of the cell model, including parameter values and discussion of model simplifications, are given in Ref. 19a. Figure 1A shows the model compartments: the sarcoplasmic reticulum (SR), the cytoplasm, and the plasma membrane with their respective components. In brief, calcium is buffered by local proteins in both the SR interior and in the cytoplasm. In both compartments calcium can diffuse laterally. The SR membrane is modeled with a calcium pump, the sarco(endo)plasmic reticulum calcium-ATPase, and a calcium release channel. The plasma membrane is modeled with three electrogenic ion pumps (the Na+/K+-ATPase, the Na+/Ca2+-exchanger, and the plasma membrane calcium-ATPase) and with three ion channels (L-type calcium channels, calcium-sensitive potassium channels, and cGMP-sensitive calcium-dependent chloride channels). The membrane also has nonspecific background conductances for Na+, K+, Cl–, and Ca2+ ions.


Figure 1
View larger version (21K):
[in this window]
[in a new window]

  		Fig. 1. Cell and vessel model. A: the compartments considered in the model are the plasma membrane, the cytoplasm, and the sarcoplasmic reticulum (SR). The picture shows the components related to each of these compartments: Na+/K+-ATPase (1), Na+/Ca2+ exchanger (2), plasma membrane Ca2+-ATPase (3), sarco(endo)plasmic reticulum Ca2+-ATPase (4), SR calcium release channel (5), cytoplasmic calcium buffer (6), SR calcium buffer (7), cGMP-sensitive calcium-dependent chloride channel (8), calcium-activated potassium channels (9), voltage-sensitive calcium channel (L-type calcium channel; 10), and gap junction (11). B: vessel model. Example of a single-layered cell plate used in the simulations is shown. The plate forms a tube by making end-to-end contact. Each spindle-shaped cell couples to neighboring cells through gap junctions (black double-barrel structures).

 
Gap-junction currents. Gap-junction currents (Igap) originate as a consequence of concentration differences, potential differences, or both between two neighboring cells, a and b, and they were modeled as follows:

Formula 1(1)
where Px is the gap junction permeability of the ion x, [Formula 1] = ([x]a + [x]b)/2 is its average concentration and {Delta}Vm = Vm,a – Vm,b is the difference in membrane potential between the two cells (11). {Delta}[x] = [x]a – [x]b is the concentration gradient of x, here relevant only for calcium, since intracellular concentrations of all other ions are assumed to remain constant at the bulk cytoplasmic value (the same in all cells) on the time scale considered in the model simulations (a few minutes). Definitions of z, F, R, and T are given in Ref. 19a. Each cell is divided into 120 segments along its length axis. ASegment is the surface area of a given segment. If two segments (from two different cells) making contact differ in ASegment (e.g., where the tip of one cell meets the more central part of the other cell; see Fig. 1B), the effective contact area is determined by the cell having the smallest ASegment. {sigma} (=0.15) is the fraction of the circumference directed toward the neighboring cell. The gap-junctional permeability ratio, K+:Na+:Cl–, has been estimated to be ~1:0.8:0.6 (47), but most gap-junction current is likely to be carried by potassium and chloride due to the high cytoplasmic concentrations of these ions. Permeability for calcium was set equal to that of potassium. Permeability for each ion is scaled according to the ratios above. Standard value of permeability is Pgeneral = 5 x 10–8 m/s, and this value was subject to systematic variation across five decades (18). The change in membrane potential is due to the combined effects of all currents across the plasma membrane and through gap junctions {sum}xIgap,x:

Formula 2(2)
where Cm, cell is the whole cell capacitance (17 x 10–12 Farad) and x is the individual ions (Na+, K+, Cl–, and Ca2+) considered in the model (19a). Definitions of the currents of Eq. 2 are given in Ref. 19a.

Spatial distribution. The spatial distribution of the model is shown in Fig. 1B. Each cell in the interior of the cell plate couples to six other cells through gap junctions (black double barrels). Cells located at the edges couple to either three or five neighboring cells. The whole cell plate forms a tube by making end-to-end contact (arrow). The central one-third of each cell is cylindrical, whereas the lateral part tapers off. For details of perturbation of the system and numerical methods, please see APPENDIX.


   RESULTS
TOP
 ABSTRACT
 METHODS
 RESULTS
DISCUSSION
 APPENDIX
 GRANTS
 REFERENCES
 
Intercellular Synchronization

Figure 2 and movie 2D (note: supplementary movies may be found with the online version of this article) show intercellular synchronization in a tube-shaped layer of 15 coupled cells, each with distinct characteristics (see Perturbation in APPENDIX). Cytoplasmic calcium concentrations ([Ca2+]Cyt) are shown in Fig. 2D from a central point in four different cells (Fig. 2A, corresponding dot and curve colors). Throughout the simulation the cells are in a stimulated state with [Ins(1,4,5)P3] {approx} 1.75 µM. Initially, unsynchronized waves running in different directions in the individual cells are seen. At the initial [cGMP] {approx} 5 µM, most cells display waves but some have switched spontaneously into fast whole cell oscillations (Fig. 2, C and D, green traces; and movie 2D). The high frequency in the whole cell oscillation state is due to positive feedback in the system, where calcium release from the SR and calcium influx from the extracellular space reinforce each other, causing repeated rapid elevations in [Ca2+] (19a). Figure 2C shows that in coupled cells displaying waves, membrane potential is almost invariant. Cells showing whole cell oscillations display tiny oscillations in membrane potential. The amplitude of these oscillations is small as long as [cGMP] is low, and the cGMP-sensitive calcium-dependent chloride channels are therefore inactive. The amplitude is further reduced by dissipation of current into the surrounding cells.


Figure 2
View larger version (24K):
[in this window]
[in a new window]

  		Fig. 2. Waves, whole cell oscillations, and vasomotion in coupled cells. A: cell tube of 15 cells. Colored points correspond to curves of the same color. B: changes in cytosolic cGMP concentration in the course of the simulation. C: membrane potential in the 4 different cells. During the wave period (low [cGMP]), there are no or only minute oscillations in potential. During the vasomotion period (high [cGMP]), the potential oscillates synchronously in all cells. D: oscillations in cytosolic calcium concentration. Low-frequency unsynchronized waves are seen during low [cGMP]. Some cells in the plate display whole cell oscillations (green traces). An increase in [cGMP] causes calcium transients to synchronize among all the cells. Inserted rectangles emphasize areas of synchronization versus no synchronization. Movie 2D shows the full sequence for all 15 cells.

 
Figure 2B shows how [cGMP] is gradually increased to an average of 6.0 µM after t = 90 s. This is associated with the transformation from waves to whole cell oscillations in all cells (Fig. 2D) and the onset of oscillations in membrane potential (Fig. 2C). Abruptly, all cells in the tube synchronize as reflected in both the calcium and the membrane potential curves. This state is referred to as "vasomotion" although movement of the wall is not explicitly modeled. As expected, if [cGMP] is reduced again, the coupling between SR and plasma membrane is gradually loosened because of inactivation of the cGMP-sensitive calcium-dependent chloride channels, and intercellular synchronization is eventually lost (not shown).

In Fig. 2 the intercellular coupling strength remains constant throughout the simulation at Pgeneral = 5 x 10–8 m/s. To test whether changes in coupling strength per se can induce intercellular synchronization when [cGMP] is low (5 µM), the model was simulated with Pgeneral ranging from 0.5 x 10–8 m/s to 5,000 x 10–8 m/s. The wave pattern is unchanged at permeabilities up to ~500 x 10–8 m/s (100 times the value used in Fig. 2) with no synchronization or transmission of waves between cells. If the permeability is increased further, the cell tube behaves progressively more as one large cell, with waves running in parallel in neighboring cells. However, at no permeability level is the onset of synchronized whole cell oscillations seen.

Repeating the simulation of Fig. 2 with selective gap-junctional blockade of calcium while other ions move freely, the cells enter a complete synchronization identical to the one in Fig. 2 (not shown). Hence, gap-junctional movement of calcium is not necessary for the initiation of vasomotion in the present model. Finally, during complete blockade of all gap-junctional currents, cells display waves during low [cGMP] and switch to whole cell oscillations during high [cGMP], but these remain unsynchronized between the cells, since there is no intercellular communication (not shown).

Figure 3A shows the concentrations of cGMP at which a tube of coupled cells displays sustained intercellular synchronization (black line) and those at which synchronization is incomplete (gray line). At [cGMP] below the threshold level where sustained synchronization is possible ({approx}6 µM), a depolarizing pulse (potential clamp at –30 mV for 100 ms) triggers a transient intercellular synchronization of variable duration. The closer [cGMP] is to the threshold level, the longer the transient synchronization lasts. This is shown in Fig. 3, B and C. Furthermore, local groups of cells tend to oscillate in phase; the higher the [cGMP], the larger are these groups (see movie 3B and 3C).


Figure 3
View larger version (32K):
[in this window]
[in a new window]

  		Fig. 3. Synchronization as a function of [cGMP]. A: ranges of [cGMP] in which synchronization is complete and sustained (black line) and incomplete (gray line) following a depolarizing pulse (potential clamp at –30 mV for 100 ms). B: at [cGMP] = 5.5 µM, there is a transient synchronization. Afterward, only neighboring cells may continue to oscillate together (see lower left corner of movie 3B). [Ca2+]Cyt, cytoplasmic calcium concentrations. C: at [cGMP] = 5.9 µM, a depolarizing pulse causes transient synchronization of longer duration and afterward larger islets of cells continue to oscillate together (movie 3C).

 
Figure 4 illustrates the essential roles of the chloride and the L-type calcium channel, respectively, in the initiation of vasomotion. During blockade of these channels, it was not possible to initiate vasomotion, and the calcium elevations remain uncoordinated both within the individual cell as well as between the cells. Figure 4A shows the increase in [cGMP] in the course of the simulations (similar to Fig. 2B). In Fig. 4B, the cGMP-sensitive calcium-dependent chloride channel is completely blocked. During low [cGMP], most cells display regular waves. As expected, wave generation is independent of chloride-channel activity, since waves depend primarily on the SR function. As [cGMP] is increased, the transition to vasomotion fails. Instead, waves break up into irregular local calcium elevations unsynchronized between the cells. The same irregular pattern is seen at all cGMP concentrations during L-type calcium-channel blockade (Fig. 4C). Thus in the present simulations, initiation of vasomotion is not seen in the absence of the coupling between the SR and the membrane provided by the chloride channel. Neither is it seen in the absence of synchronization of calcium release from the SR provided by calcium influx through the L-type calcium channel. The results are summarized in Table 1.


Figure 4
View larger version (51K):
[in this window]
[in a new window]

  		Fig. 4. Complete blockade of cGMP-sensitive calcium-dependent chloride channels or L-type calcium channels prevents initiation of vasomotion. A: the increase in cGMP in the course of the simulations. B: blockade of the cGMP-sensitive calcium-dependent chloride channel. To avoid calcium depletion as cGMP is increased, background calcium conductance was increased from 1 to 4.7 pS throughout the simulation. Vasomotion is not initiated despite normal levels of cytoplasmic calcium. C: blockade of the L-type calcium channel. Same pattern as in B. Background calcium conductance was increased from 1 to 8 pS throughout the simulation to avoid calcium depletion.

 

View this table:
[in this window]
[in a new window]

  		Table 1. Summary of the simulated results

 
Vasomotion Frequency

Intercellular coupling strength in itself does not influence vasomotion frequency. As long as the coupling exceeds the minimal value at which synchronization become possible (in the present system, ~1.5 x 10–8 m/s), the frequency remains constant across the subsequent four decades of coupling strength (not shown).

Figure 5A shows how membrane depolarization causes substantial increase in vasomotion frequency. Coupled cells in this regard behave similar to the isolated cell showing whole cell oscillations (19a). Average membrane potential was modulated by adjusting one of the background currents (cf. Ref. 19a). Outside the range of average membrane potential shown in Fig. 5A, vasomotion is not observed. When the membrane is not sufficiently depolarized, [Ca2+]Cyt never reaches a level sufficient to elicit calcium-induced calcium release (CICR). If, on the other hand, depolarization is too strong, sustained cytoplasmic calcium flooding follows. For the points marked with arrowheads (Fig. 5A), details are shown in Figs. 5, B–D (arrowhead shading corresponds to curve shading). Despite a pronounced difference in vasomotion frequency, the position of the curves for the SR-calcium concentration is similar in the two cases (Fig. 5B). Thus the SR-cytoplasmic concentration gradient of calcium is unlikely to be responsible for the difference in frequency. However, the difference in average membrane potential in the two cases causes a substantial difference in calcium current through the L-type calcium channel (Fig. 5C). In turn, average [Ca2+]Cyt is reduced in the more hyperpolarized state (Fig. 5D). The combined effects of low basal [Ca2+]Cyt and low calcium influx increase the time it takes to reach the threshold for CICR (Fig. 5D), reducing vasomotion frequency.


Figure 5
View larger version (16K):
[in this window]
[in a new window]

  		Fig. 5. Vasomotion frequency versus membrane polarization. A: increasing membrane depolarization leads to increased vasomotion frequency. The black curve represents a 2nd degree polynomial fit (coefficient of determination, R2 = 0.99). Gray and black arrowheads are the potentials for which curves are shown in B–D. The shading of the arrowheads correspond to the shading of the curves. B: the filling state of the SR is the same in both cases. C: the flux of calcium through the L-type calcium channel increases with membrane depolarization. D: average cytosolic calcium is reduced during relative hyperpolarization. The reduction in frequency is due to the increased time taken to reach the threshold for calcium-induced calcium release.

 
Figure 6A shows experimental data from Rahman et al. (34) (reproduced with permission from S. Karger AG, Basel, Switzerland) obtained by stimulating endothelium-denuded vessels with 8-bromo-cGMP. There is a characteristic decrease in vasomotion frequency with increasing [8-bromo-cGMP]. Figure 6B shows how the simulated vasomotion frequency is reduced with increasing [cGMP]. The reduction is here due to cGMP stimulation of a hyperpolarizing current, the Na+/K+-ATPase. Note that the system oscillates within a range of [cGMP], corresponding to the steep part of the curve for the cGMP sensitivity of the chloride channel (Ref. 19a, and see also DISCUSSION).


Figure 6
View larger version (8K):
[in this window]
[in a new window]

  		Fig. 6. Vasomotion frequency versus cytoplasmic cGMP concentration. A: experimental data from Rahman et al. (Ref. 34) (reproduced with permission from S. Karger AG, Basel, Switzerland) showing a reduction in vasomotion frequency with increasing concentrations of 8-bromo-cGMP (8-BrcGMP) in endothelium-denuded vessels. B: simulated vasomotion frequency in 15 coupled cells as a function of [cGMP]. Above [cGMP] = 6.0 µM, the system remains synchronized, and each point shows the mean ± SE of 5 simulations. Below [cGMP] = 6 µM, synchronization is incomplete, and each point is the mean ± SE of the frequency of individual cells from 10 simulations.

 
Simulated vasomotion frequency (at [cGMP] {approx} 6 µM) is modulated by the conductance of ion channels in the plasma membrane. Vasomotion is seen over a range of conductances around the standard value used in the simulations (Tables 3, 9, and 10 of Ref. 19a). As expected, an increased conductance of the chloride or the L-type calcium channel (depolarizing currents) increases the frequency, whereas an increase in conductance of calcium-activated potassium channels reduces the frequency (not shown). When [cGMP] is low, vasomotion is never observed no matter what the conductance of either one of the three channels. Instead, the cells show unsynchronized waves/whole cell (or irregular) oscillations over a broad range of conductances. If the conductance is too high, either calcium flooding (chloride or L-type calcium channel) or depletion (calcium-sensitive potassium current) follows. This leads to an elimination of all rhythmic variation in [Ca2+]Cyt no matter what the concentration of cGMP.


   DISCUSSION
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
APPENDIX
 GRANTS
 REFERENCES
 
The main findings of the present study are as follows: 1) cGMP plays a permissive role through a cGMP-sensitive calcium-dependent chloride channel in establishing intercellular synchronization, 2) electrical coupling via gap junctions is necessary for intercellular synchronization to occur, and 3) membrane potential modulates frequency in established vasomotion.

One property of the present cell model specific for rat mesenteric small arteries is the presence of a cGMP-dependent calcium-sensitive chloride channel found in this tissue (24, 32). This channel causes membrane depolarization in response to an increase in [Ca2+]Cyt if cGMP is present in sufficient concentration. Calcium release from the SR hereby induces membrane depolarization and influx of extracellular calcium through voltage-sensitive calcium channels. As shown in simulations of a single cell (19a), this may lead to a shift in oscillatory mode from waves to whole cell oscillations within the individual cell. Furthermore, within a certain range of [cGMP], these states may coexist at the same set of parameter values.

These properties are not changed by intercellular coupling. At low [cGMP], cells mainly display low-frequency waves. These are not transmitted between cells, and cells displaying waves show no oscillations in membrane potential (Fig. 2) (34). It proved impossible to cause a transition from waves to vasomotion at low [cGMP] by increasing gap-junctional permeability only. However, by increasing [cGMP], an increasing number of cells switch to whole cell oscillations (Fig. 2D, green curve). This state is associated with oscillations in membrane potential (Fig. 2C, green curve), the amplitude of which increases with increasing [cGMP]. The larger the concentration of cGMP, the stronger is the response of the chloride channel to an increase in [Ca2+]Cyt and the larger are the oscillations in membrane potential. Gap-junctional flow of current increases with the amplitude of these oscillations and is, beyond a certain threshold, sufficient to cause intercellular synchronization. As shown in Fig. 3 (see also supplementary material movie 3B and 3C), below this threshold, transient synchronization can be induced by a short electrical pulse. At low [cGMP], synchronization will be short lasting and the following desynchronization will be complete. Increasing [cGMP] toward the threshold results in longer periods of synchronization, and desynchronization never becomes complete. Instead, groups of cells continue to oscillate together. As [cGMP] is increased further, these groups become larger, but at the same time their frequency is reduced (Fig. 6B). Beyond the threshold, the system remains completely synchronized, and a further increase in [cGMP] will reduce vasomotion frequency (Fig. 6).

Experimentally, similar observations have been made in rat mesenteric small arteries. In vitro waves are not transmitted between cells (31) and are not associated with oscillations in membrane potential (34). During vasomotion, on the other hand, cells shift to whole cell oscillations and membrane potential oscillates (13, 34). At intermediate concentrations of cGMP, islets of cells are oscillating together but are unsynchronized with other islets. Higher cGMP concentrations result in a synchronization between islets but, at the same time, frequency is reduced (34).

It is possible that the wave period often preceding vasomotion in native vessels (31) represents the time it takes to build up the concentrations of cGMP necessary to cause intercellular synchronization. As shown by Dora et al. (7), smooth muscle cell calcium can diffuse to endothelial cells through myoendothelial gap junctions and, through a rise in endothelial cell calcium and nitric oxide generation, causes an increase in [cGMP] in the smooth muscle cells of the vessel wall. The special morphology of the endothelial cell with a small cytoplasmic volume and simultaneous contact to many smooth muscle cells (15) favors a rise in endothelial cell cytoplasmic calcium due to diffusion (8). An in vitro onset of intercellular synchronization may also follow a depolarizing pulse (31). In this case, the depolarization may, per se, cause the rise in smooth muscle cell calcium necessary to initiate the outlined cascade.

If the chloride channel is essential to couple SR and plasma membrane, a general increase in conductance of that channel could potentially substitute for an increase in cGMP in the initiation of vasomotion. However, in test simulations, this proved impossible. A change in channel conductance while the cells generate waves (low [cGMP]) causes calcium flooding rather than vasomotion. The reason for this behavior lies in the properties of the chloride channel, where an increase in cGMP causes a shift in calcium sensitivity and not just a proportional increase in open probability. As the steepness of the sensitivity curve increases, the ability of the channel to switch between on and off states in response to changes in cytosolic calcium increases. The channel hereby enhances oscillations in [Ca2+]Cyt, leading to the onset of vasomotion.

Whatever signal underlies the initiation of vasomotion, it must be transmitted rapidly in the vascular wall, since cells previously showing independent waves suddenly synchronize across, on a cellular scale, large distances. The abruptness of the process and its global nature make it unlikely that it is caused by the slow process of diffusion of calcium or other second messengers.

In the present model, intercellular synchronization is caused by gap-junctional flow of current. Synchronization ensues readily when Pgeneral exceeds a minimum level, even in the case where the gap-junctional permeability of calcium is selectively set to zero. Hence, in the present simulations, neither gap-junctional movement of calcium nor movement of other second messengers is necessary to initiate vasomotion.

Gap-junctional coupling is dynamically regulated (23, 37), and observations by Sell et al. (41) suggest that high concentrations of norepinephrine (10 µM) may reduce the electrical coupling in the vascular wall, whereas acetylcholine in a similar concentration partially restores the coupling. The present results show that increasing gap-junctional permeability in the wave state does not lead to vasomotion, and in established vasomotion, the frequency is independent of the gap-junctional coupling. In addition, decreasing gap-junctional coupling has no effect on established vasomotion until a very low level of electrical coupling is reached. For comparison, this level of coupling corresponds to a gap-junctional permeability coefficient that is more than an order of magnitude lower than that estimated for K+ and Cl– in lens cells (33). This strongly suggests that the ability of {alpha}-agonists to induce vasomotion is unrelated to any effects on the degree of gap-junctional coupling.

Experimentally, the quantitative movement of calcium through gap junctions appears to be small, since calcium waves in one cell generally do not initiate waves in neighboring cells (31, 41); waves therefore remain asynchronous between cells. This has been shown in venous smooth muscle cells as well (35). Unlike calcium diffusion between smooth muscle cells and endothelium, diffusion between smooth muscle cells is not favored by a special cellular arrangement and differences in cell volume. In addition, gap junctions between smooth muscle cells in vascular tissue are few in number (36, 38). Furthermore, the concentration gradient between the cytoplasm of two cells is only of the order of a few hundred nanomolar, and the cytosol has a high-buffering capacity for calcium. Collectively, this makes the gap-junctional flux of calcium small compared with fluxes from the SR or from the extracellular space where the concentration gradient is of the order of 104 times larger.

This indicates that current rather than diffusion plays a main role in synchronization (41). Movement of only a few ions can change the membrane potential and thereby affect the opening state of L-type calcium channels, eliciting a massive flux of calcium across the plasma membrane. Although the influence from signal substances diffusing through the extracellular space or through gap junctions cannot be excluded (21), the present model indicates that synchronization can be achieved easily by the passage of current between neighboring cells.

The present simulations indicate that membrane potential could be important in modulating the frequency of established vasomotion. Figure 5C shows how depolarization causes an increased flux of calcium into the cell. Higher average [Ca2+]Cyt results in the threshold for CICR being reached faster, thereby increasing the frequency (Fig. 5D). In keeping with that, the present simulations indicate that increasing the conductance of the L-type calcium channel increases vasomotion frequency. In vitro, similar acceleration in frequency has been observed following an application of BAY-K 8644, an L-type calcium-channel agonist (14), although only a reduction in amplitude and not in frequency was observed following submaximal calcium-channel blockade (14).

Experimental studies suggest a possible connection between membrane depolarization and vasomotion frequency. In vessels showing myogenic reactivity, increased intraluminal pressure is associated with membrane depolarization (39, 48) and increased vasomotion frequency in all (2, 30, 46) or part of the pressure range (5, 12). Recently, Koenigsberger et al. (20) found the same relation in a mathematical model of arterial vasomotion. However, a frequency-modulating influence from the SR is certainly also possible (14, 31).

Exposure to sodium nitroprusside (releasing nitric oxide) is associated with hyperpolarization in endothelium-denuded, epinephrine-stimulated mesenteric vessels (13). In pulmonary vascular smooth muscle cells, cGMP-mediated relaxation involves the Na+/K+-ATPase (43, 44). In the present model, a stimulating effect of cGMP on this pump was therefore assumed, but modulation of other currents, e.g., through the modulation of potassium channels (40, 42), is equally possible. The simulations of Fig. 6 shows the general effect of a hyperpolarizing action of cGMP, and the result is independent of the specific mechanism (current) causing the hyperpolarization (see also Ref. 19a). It may seem confusing that the initial effect of an increase in [cGMP] at the onset of vasomotion is an increase and not a reduction in frequency (cf. Fig. 2). This frequency shift is, however, caused by a completely different mechanism, namely the switch from waves to whole cell oscillations (19a), and it dominates initially. Only if [cGMP] is increased further is the effect on membrane potential evident (Fig. 6B).

In conclusion, the simulated results indicate that cGMP may have a permissive role in the onset of vasomotion in rat small mesenteric arteries by coupling SR and plasma membrane calcium dynamics, leading to oscillations in membrane potential. Intercellular synchronization follows when these oscillations become sufficiently strong and when gap-junctional coupling exceeds a certain minimum level. Intercellular diffusion of calcium or another second messenger is not necessary to explain synchronization. Finally, vasomotion frequency is strongly influenced by the membrane potential.


   APPENDIX
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
GRANTS
 REFERENCES
 
Perturbation

Description of how parameters are perturbed within the individual cell is given in (Ref. 19a). Between cells, heterogeneity is induced in a similar way. For each individual cell, a given quantity is multiplied by a factor {omega} = 1 + [({phi} – 0.5) x kperturb,cell], where {phi} is a random number between 0 and 1 and kperturb,cell is a constant scaling the size of the perturbation; for simplicity, kperturb,cell has the same value (0.1) for all perturbed quantities. Hence, {omega} varies randomly between the cells and stays constant in the course of a simulation. In each cell, {omega} has an individual and independent value for each perturbed quantity. The perturbed quantities are rcell and [Ins(1,4,5)P3] and initial values of [cGMP] and Vm. In simulations where [cGMP] is increased, it is increased by the same amount in all cells, thereby preserving the differences in [cGMP] between the cells.

Discretization and System Size

Vasomotion frequency does not depend on the size of the cell plate in simulations where plate size ranged from 5 to 121 cells. Whether 55 cells are distributed as a long segment of a small-diameter vessel or as a short segment of large-diameter vessel makes no difference for the frequency. Vasomotion frequency is invariant under changes in the discretization of the individual cell ranging from 6 to 660 segments.

Numerical Stability

Description of the numerical method is given in Ref. 19a. In the cell tube model using a time step of 5 x 10–4 s, the individual simulations are completed within a reasonable time (hours and up to a few days for the larger cell tubes). At the same time, numerical instability is avoided (appearing as a rapid divergence toward ±{infty} of Vm and/or [Ca2+]Cyt/[Ca2+]SR), and the effect on the final result of reducing the time step is negligible. Integrating a system of 15 coupled cells for 60 s with the time step reduced by a factor 10 ({Delta}t = 0.5 x 10–4 s) or a factor 100 ({Delta}t = 0.05 x 10–4 s) caused less than a 0.37% change in the computed solution. In simulations with very high intercellular coupling, a reduced step size was used to avoid numerical instability.


   GRANTS
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
REFERENCES
 
This work was supported by grants from the Danish Heart Foundation, the Novo-Nordisk Foundation, The Danish Medical Research Council, and The European Union through the Network of Excellence BioSim (Contract No. LHSB-CT-2004-005137).


   FOOTNOTES
 

Address for reprint requests and other correspondence: J. C. B. Jacobsen, Biomedical Inst., Div. of Renal and Cardiovascular Physiology, The Panum Inst., Univ. of Copenhagen, Blegdamsvej 3, DK-2200 Copenhagen N, Denmark (e-mail: jcbrings{at}mfi.ku.dk)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 REFERENCES
 

  1. Aalkjaer C, Danielsen H, Johannesen P, Pedersen EB, Rasmussen A, Mulvany MJ. Abnormal vascular function and morphology in pre-eclampsia: a study of isolated resistance vessels. Clin Sci (Lond) 69: 477–482, 1985.[Medline]
  2. Achakri H, Stergiopulos N, Hoogerwerf N, Hayoz D, Brunner HR, Meister JJ. Intraluminal pressure modulates the magnitude and the frequency of induced vasomotion in rat arteries. J Vasc Res 32: 237–246, 1995.[ISI][Medline]
  3. Bartlett IS, Crane GJ, Neild TO, Segal SS. Electrophysiological basis of arteriolar vasomotion in vivo. J Vasc Res 37: 568–575, 2000.[CrossRef][ISI][Medline]
  4. Bouskela E, Grampp W. Spontaneous vasomotion in hamster cheek pouch arterioles in varying experimental conditions. Am J Physiol Heart Circ Physiol 262: H478–H485, 1992.[Abstract/Free Full Text]
  5. Chen CW, Lee CH, Hsiue TR, Chang HY. Vasomotion in rat diaphragm microcirculation at rest and during stepwise arterial pressure reduction. Acta Physiol Scand 161: 281–288, 1997.[CrossRef][ISI][Medline]
  6. Colantuoni A, Bertuglia S, Intaglietta M. Quantitation of rhythmic diameter changes in arterial microcirculation. Am J Physiol Heart Circ Physiol 246: H508–H517, 1984.[Abstract/Free Full Text]
  7. Dora KA, Doyle MP, Duling BR. Elevation of intracellular calcium in smooth muscle causes endothelial cell generation of NO in arterioles. Proc Natl Acad Sci USA 94: 6529–6534, 1997.[Abstract/Free Full Text]
  8. Dora KA, Hinton JM, Walker SD, Garland CJ. An indirect influence of phenylephrine on the release of endothelium-derived vasodilators in rat small mesenteric artery. Br J Pharmacol 129: 381–387, 2000.[CrossRef][ISI][Medline]
  9. Faber JE, Harris PD, Wiegman DL. Anesthetic depression of microcirculation, central hemodynamics, and respiration in decerebrate rats. Am J Physiol Heart Circ Physiol 243: H837–H843, 1982.[Abstract/Free Full Text]
  10. Fujii K, Heistad DD, Faraci FM. Vasomotion of basilar arteries in vivo. Am J Physiol Heart Circ Physiol 258: H1829–H1834, 1990.[Abstract/Free Full Text]
  11. Glaser R. Biophysics. Berlin, Germany: Springer-Verlag, 2001.
  12. Gustafsson H, Bulow A, Nilsson H. Rhythmic contractions of isolated, pressurized small arteries from rat. Acta Physiol Scand 152: 145–152, 1994.[ISI][Medline]
  13. Gustafsson H, Mulvany MJ, Nilsson H. Rhythmic contractions of isolated small arteries from rat: influence of the endothelium. Acta Physiol Scand 148: 153–163, 1993.[ISI][Medline]
  14. Gustafsson H, Nilsson H. Rhythmic contractions of isolated small arteries from rat: role of calcium. Acta Physiol Scand 149: 283–291, 1993.[ISI][Medline]
  15. Haas TL, Duling BR. Morphology favors an endothelial cell pathway for longitudinal conduction within arterioles. Microvasc Res 53: 113–120, 1997.[CrossRef][ISI][Medline]
  16. Haddock RE, Hill CE. Differential activation of ion channels by inositol 1,4,5-trisphosphate (IP3)- and ryanodine-sensitive calcium stores in rat basilar artery vasomotion. J Physiol 545: 615–627, 2002.[Abstract/Free Full Text]
  17. Haddock RE, Hirst GD, Hill CE. Voltage independence of vasomotion in isolated irideal arterioles of the rat. J Physiol 540: 219–229, 2002.[Abstract/Free Full Text]
  18. Hofer T, Politi A, Heinrich R. Intercellular Ca2+ wave propagation through gap-junctional Ca2+ diffusion: a theoretical study 3. Biophys J 80: 75–87, 2001.[Free Full Text]
  19. Imtiaz MS, Smith DW, van Helden DF. A theoretical model of slow wave regulation using voltage-dependent synthesis of inositol 1,4,5-trisphosphate. Biophys J 83: 1877–1890, 2002.[ISI][Medline]
  20. Jacobsen JC, Aalkjær, Nilsson H, Matchkov V, Freiberg J, Holstein-Rathlou NH. Activation of a cGMP-sensitive calcium-dependent chloride channel may cause transition from calcium waves to whole cell oscillations in smooth muscle cells. Am J Physiol Heart Circ Physiol March 16, 2007; doi:10.1152/ajpheart.00727.2006.
  21. Koenigsberger M, Sauser R, Beny JL, Meister JJ. Effects of arterial wall stress on vasomotion. Biophys J 91: 1663–1674, 2006.[CrossRef][ISI][Medline]
  22. Koenigsberger M, Sauser R, Lamboley M, Beny JL, Meister JJ. Ca2+ dynamics in a population of smooth muscle cells: modeling the recruitment and synchronization. Biophys J 87: 92–104, 2004.[CrossRef][ISI][Medline]
  23. Lamboley M, Schuster A, Beny JL, Meister JJ. Recruitment of smooth muscle cells and arterial vasomotion. Am J Physiol Heart Circ Physiol 285: H562–H569, 2003.[Abstract/Free Full Text]
  24. Lampe PD, Lau AF. The effects of connexin phosphorylation on gap junctional communication. Int J Biochem Cell Biol 36: 1171–1186, 2004.[CrossRef][ISI][Medline]
  25. Matchkov VV, Aalkjaer C, Nilsson H. A cyclic GMP-dependent calcium-activated chloride current in smooth-muscle cells from rat mesenteric resistance arteries. J Gen Physiol 123: 121–134, 2004.[Abstract/Free Full Text]
  26. Mauban JR, Lamont C, Balke CW, Wier WG. Adrenergic stimulation of rat resistance arteries affects Ca2+ sparks, Ca2+ waves, and Ca2+ oscillations. Am J Physiol Heart Circ Physiol 280: H2399–H2405, 2001.[Abstract/Free Full Text]
  27. Messmer K. Vasomotion and Quantitative Capillaroscopy. Basel, Switzerland: Krager, 1983.
  28. Meyer JU, Lindbom L, Intaglietta M. Coordinated diameter oscillations at arteriolar bifurcations in skeletal muscle. Am J Physiol Heart Circ Physiol 253: H568–H573, 1987.[Abstract/Free Full Text]
  29. Oishi H, Schuster A, Lamboley M, Stergiopulos N, Meister JJ, Beny JL. Role of membrane potential in vasomotion of isolated pressurized rat arteries. Life Sci 71: 2239–2248, 2002.[CrossRef][ISI][Medline]
  30. Omote M, Mizusawa H. Interaction between the L-type Ca2+ channel and the Ca2+-activated K+ channel in the fluctuating myogenic contraction in the rabbit basilar artery. Jpn J Physiol 46: 353–356, 1996.[CrossRef][ISI][Medline]
  31. Osol G, Halpern W. Spontaneous vasomotion in pressurized cerebral arteries from genetically hypertensive rats. Am J Physiol Heart Circ Physiol 254: H28–H33, 1988.[Abstract/Free Full Text]
  32. Peng H, Matchkov V, Ivarsen A, Aalkjaer C, Nilsson H. Hypothesis for the initiation of vasomotion. Circ Res 88: 810–815, 2001.[Abstract/Free Full Text]
  33. Piper AS, Large WA. Single cGMP-activated Ca(+)-dependent Cl(–) channels in rat mesenteric artery smooth muscle cells. J Physiol 555: 397–408, 2004.[Abstract/Free Full Text]
  34. Rae JL, Bartling C, Rae J, Mathias RT. Dye transfer between cells of the lens. J Membr Biol 150: 89–103, 1996.[CrossRef][ISI][Medline]
  35. Rahman A, Matchkov V, Nilsson H, Aalkjaer C. Effects of cGMP on coordination of vascular smooth muscle cells of rat mesenteric small arteries. J Vasc Res 42: 301–311, 2005.[CrossRef][ISI][Medline]
  36. Ruehlmann DO, Lee CH, Poburko D, van BC. Asynchronous Ca2+ waves in intact venous smooth muscle. Circ Res 86: E72–E79, 2000.[ISI][Medline]
  37. Rummery NM, Hill CE. Vascular gap junctions and implications for hypertension. Clin Exp Pharmacol Physiol 31: 659–667, 2004.[CrossRef][ISI][Medline]
  38. Saez JC, Berthoud VM, Branes MC, Martinez AD, Beyer EC. Plasma membrane channels formed by connexins: their regulation and functions. Physiol Rev 83: 1359–1400, 2003.[Abstract/Free Full Text]
  39. Sandow SL, Looft-Wilson R, Doran B, Grayson TH, Segal SS, Hill CE. Expression of homocellular and heterocellular gap junctions in hamster arterioles and feed arteries. Cardiovasc Res 60: 643–653, 2003.[Abstract/Free Full Text]
  40. Schubert R, Mulvany MJ. The myogenic response: established facts and attractive hypotheses. Clin Sci (Lond) 96: 313–326, 1999.[Medline]
  41. Schubert R, Nelson MT. Protein kinases: tuners of the BKCa channel in smooth muscle. Trends Pharmacol Sci 22: 505–512, 2001.[CrossRef][Medline]
  42. Sell M, Boldt W, Markwardt F. Desynchronising effect of the endothelium on intracellular Ca2+ concentration dynamics in vascular smooth muscle cells of rat mesenteric arteries. Cell Calcium 32: 105–120, 2002.[CrossRef][ISI][Medline]
  43. Stockand JD, Sansom SC. Mechanism of activation by cGMP-dependent protein kinase of large Ca2+-activated K+ channels in mesangial cells. Am J Physiol Cell Physiol 271: C1669–C1677, 1996.[Abstract/Free Full Text]
  44. Tagaya E, Tamaoki J, Kawatani K, Nagai A. Role of Na+-K+-ATPase in sodium nitroprusside-induced relaxation of pulmonary artery under hypoxia. Respiration 68: 186–191, 2001.[CrossRef][ISI][Medline]
  45. Tamaoki J, Tagaya E, Nishimura K, Isono K, Nagai A. Role of Na+-K+ ATPase in cyclic GMP-mediated relaxation of canine pulmonary artery smooth muscle cells. Br J Pharmacol 122: 112–116, 1997.[CrossRef][ISI][Medline]
  46. Van Helden DF, Imtiaz MS. Ca2+ phase waves: a basis for cellular pacemaking and long-range synchronicity in the guinea-pig gastric pylorus. J Physiol 548: 271–296, 2003.[Abstract/Free Full Text]
  47. VanBavel E, Giezeman MJ, Mooij T, Spaan JA. Influence of pressure alterations on tone and vasomotion of isolated mesenteric small arteries of the rat. J Physiol 436: 371–383, 1991.[Abstract/Free Full Text]
  48. Veenstra RD, Wang HZ, Beblo DA, Chilton MG, Harris AL, Beyer EC, Brink PR. Selectivity of connexin-specific gap junctions does not correlate with channel conductance. Circ Res 77: 1156–1165, 1995.[Abstract/Free Full Text]
  49. Wesselman JP, Schubert R, VanBavel ED, Nilsson H, Mulvany MJ. KCa-channel blockade prevents sustained pressure-induced depolarization in rat mesenteric small arteries. Am J Physiol Heart Circ Physiol 272: H2241–H2249, 1997.[Abstract/Free Full Text]




This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
293/1/H229    most recent
00727.2006v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Right arrow Citation Map
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Similar articles in PubMed
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Citing Articles
Right arrow Citing Articles via ISI Web of Science (1)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Jacobsen, J. C. B.
Right arrow Articles by Holstein-Rathlou, N.-H.
Right arrow Search for Related Content
PubMed
Right arrow PubMed Citation
Right arrow Articles by Jacobsen, J. C. B.
Right arrow Articles by Holstein-Rathlou, N.-H.

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
Visit Other APS Journals Online
Copyright © 2007 by the American Physiological Society.