Defining electrical communication in skeletal muscle resistance arteries: a computational approach
1 Department of Electrical and Computer Engineering, University of Calgary, Calgary, Alberta, Canada
2 The John B. Pierce Laboratory & Department of Cellular and Molecular Physiology, Yale University, New Haven, CT, USA
3 Smooth Muscle Research Group & Department of Physiology and Biophysics, University of Calgary, Calgary, Alberta, Canada
Abstract
Vascular cells communicate electrically to coordinate their activity and control tissue blood flow. To foster a quantitative understanding of this fundamental process, we developed a computational model that was structured to mimic a skeletal muscle resistance artery. Each endothelial cell and smooth muscle cell in our virtual artery was treated as the electrical equivalent of a capacitor coupled in parallel with a non-linear resistor representing ionic conductance; intercellular gap junctions were represented by ohmic resistors. Simulations revealed that the vessel wall is not a syncytium in which electrical stimuli spread equally to all constitutive cells. Indeed, electrical signals spread in a differential manner among and between endothelial cells and smooth muscle cells according to the initial stimulus. The predictions of our model agree with physiological data from the feed artery of the hamster retractor muscle. Cell orientation and coupling resistance were the principal factors that enable electrical signals to spread differentially along and between the two cell types. Our computational observations also illustrated how gap junctional coupling enables the vessel wall to filter and transform transient electrical events into sustained voltage responses. Functionally, differential electrical communication would permit discrete regions of smooth muscle activity to locally regulate blood flow and the endothelium to coordinate regional changes in tissue perfusion.
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Introduction
Vascular networks dilate and constrict in a coordinated fashion to control blood flow to metabolically active tissue (Segal & Duling, 1986a; Segal & Jacobs, 2001). For resistance vessels to respond in an integrative manner, the constitutive cells must communicate with one another (Segal & Duling, 1986b; Xia & Duling, 1995; Welsh & Segal, 1998). Direct electrical communication in the vascular wall is enabled by gap junctions, intercellular channels that facilitate the diffusion of ions and second messengers between neighbouring cells (Little et al. 1995a, b). Gap junctions are formed by two hemichannels or connexons, each containing six connexin subunits. The connexin gene family is comprised of at least 19 members, with the most predominant subtypes in vascular tissue being Cx37, Cx40, Cx43 and Cx45 (Little et al. 1995a; Saez et al. 2003; Sandow et al. 2003).
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Electrical communication can be functionally assessed in resistance arteries (e.g. diameter < 100 μm) by focally applying vasoactive agents to a small portion of the vessel wall (Segal & Duling, 1986b; Welsh & Segal, 1998). This discrete stimulus initiates a local change in smooth muscle or endothelial cell membrane potential (Vm) which, with the aid of gap junctions, conducts to neighbouring vascular cells (Xia & Duling, 1995; Welsh & Segal, 1998). The extent to which the electrical or the corresponding vasomotor response is conducted along the vessel wall provides an index of electrical communication. In general, responses initiated in endothelial cells conduct robustly along resistance vessels (Welsh & Segal, 1998; Segal et al. 1999; Emerson & Segal, 2000a). In contrast, agents that depolarize and constrict smooth muscle elicit decidedly varied responses ranging from little to strong conduction (Segal et al. 1999; de Wit et al. 2000; Kumer et al. 2000; Yashiro & Duling, 2000; Kurjiaka et al. 2005).
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The variability in the conducted vasomotor response has led to divergent views on the nature of electrical communication, particularly in skeletal muscle resistance vessels. This divergence ranges from the view that endothelial and smooth muscle cells form a well coupled syncytium (Xia & Duling, 1995; Yashiro & Duling, 2000) to one where they shape a diverse environment in which electrical phenomena conduct in a differential manner among vascular cells (Segal et al. 1999; Kurjiaka et al. 2005). To resolve these contrasting views, quantitative insight into the factors that shape electrical communication is required. Such insight can be advanced with computational models whose design is based on the structural and electrical properties of vascular cells. In the myocardium, sophisticated tissue modelling of discrete cells has forwarded an understanding of how action potentials spread in the normal and diseased heart (Vigmond et al. 2001; Kneller et al. 2002). In contrast, computational models of the resistance vasculature have relied on traditional cable theory, where a vessel is viewed as continuous wires with uniform axial resistance (Hirst & Neild, 1978; Crane et al. 2001). While a step towards quantification, such models oversimplify the multicellular vessel wall and do not fully account for anatomical, ionic and gap junctional properties. Their quantitative and predictive value is therefore limited.
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To foster new insight into how electrical signals spread in a resistance artery, the present study developed a novel computational model of cell-to-cell communication. Our virtual artery consisted of 3432 discrete vascular cells each of which retained distinct structural and electrophysiological properties. Values of cell dimension, ionic conductance and gap junctional resistance were taken from the literature and simulations were designed to mimic experimental protocols previously used to examine electrical communication. Predicted outcomes were compared with experimental observations from the hamster retractor muscle feed artery. Our mathematical approach revealed that a resistance artery does not behave as a well-coupled syncytium. Instead, computations illustrate how electrical signals spread differentially among and between endothelial cells and smooth muscle cells. These differences are explained by the orientation and coupling resistance of respective cell layers and are fundamental to both local and regional regulation of tissue blood flow.
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Methods
Computational theory
Modelling the electrical activity of vascular cells was based on the same principles employed in modelling cardiac bioelectric phenomena (Vigmond et al. 2001; Kneller et al. 2002). Each cell was characterized electrically as a capacitance (a property of the lipid bilayer membrane) in parallel with a non-linear conductance (representing ionic flow through membrane channels). The membrane conductance was a function of the voltage across the membrane, Vm. Cells were connected electrically to one another with gap junctions which were represented as ohmic resistances. The net current flowing into a cell through gap junctions was balanced with current flowing through the membrane (a combination of ionic and capacitive current). This can be expressed as:
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where the superscript refers to individual cells, A is cell surface area, Jion is ionic current density, Cm is membrane capacitance per unit area, j is the set of cellular indices connected to cell i, and ri,j is the gap junctional resistance between cells i and j. It has been assumed that extracellular potential is negligible compared with intracellular potential. The equation of each vascular cell can be written into the matrix form:
where G is a matrix accounting for intercellular coupling, A is a diagonal matrix of cell surface areas, vm is the vector of transmembrane voltages, and jion is the vector of ionic current densities. The vector istim takes into account current introduced through intracellular stimulating electrodes. Using a Crank-Nicolson time integration scheme and first order differencing with a time step of t, the final equation set is:
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where superscripts refer to the time step. To advance the simulation in time, a sparse set of linear equations was solved at each instant in time and jionic updated. The system was solved with a time step of 0.5 ms.
Vessel diameter has been shown to vary as a linear function of transmembrane voltage (Xia & Duling, 1995; Welsh & Segal, 1998). Assuming that smooth muscle cells respond in time with first order kinetics, the change in diameter can be expressed as:
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where D is the diameter, D is the steady-state diameter and D is the vasomotor time constant (1334 ms; calculated from Emerson & Segal, 2000b). Using a first order time difference, and a time step of t, the diameter can be tracked as Vm changes by:
Structural and electrical properties
The virtual artery was structured physically to represent an isolated feed artery from the hamster retractor muscle. As such, the virtual artery was 2.2 mm long, 75 μm in diameter and composed of one layer of endothelium (2112 cells) circumscribed by one layer of smooth muscle (1320 cells in total; Fig. 1A). The artery was subdivided into 44 arterial segments, each 50 μm long, and consisting of an outer layer of 30 smooth muscle cells (arranged as 10 consecutive bands each consisting of three cells) and an inner layer of 48 endothelial cells (arranged side-by-side parallel to the artery's longitudinal axis). In general accordance with the literature (Haas & Duling, 1997; Yeh et al. 1998; Sandow et al. 2003), the physical dimensions of each vascular cell were as follows: endothelium, 50 μm length, 5 μm width, 1 μm height; smooth muscle, 80 μm length, 5 μm width, 5 μm, height. Membrane capacitance was set to 1 μF cm–2. The ionic conductance of each endothelial cell and smooth muscle cell was represented by a non-linear resistor whose properties (Fig. 1B) were derived from electrophysiological recordings of rat coronary endothelial cells (Schnitzler et al. 2000) and hamster cremaster arteriolar smooth muscle cells (Jackson et al. 1997). These resistors account for the voltage- but not the time-dependent properties of ion channels. In contrast, gap junction channels were represented by ohmic resistors. Mindful of published observations (Lidington et al. 2000; Yamamoto et al. 2001), three different coupling resistances were employed depending on the type of cells being interconnected (endothelial to endothelial, 3 M; smooth muscle to smooth muscle, 90 M; endothelial to-smooth muscle, 1800 M). In Lidington et al. (2000), endothelial-to-endothelial coupling resistance was estimated by passing current between two electrodes in an endothelial monolayer. In Yamamoto et al. (2001), smooth muscle-to-smooth muscle and myoendothelial coupling resistances were estimated in intact arterioles by voltage clamping two closely situated vascular cells. Within respective layers of the virtual artery, neighbouring endothelial cells were coupled to each other as were neighbouring smooth muscles cells. For myoendothelial coupling, each smooth muscle cell was randomly coupled to two underlying endothelial cells (Sandow & Hill, 2000; Sandow et al. 2003). Gap junctions at the respective ends of the isolated vessel segment were treated as sealed.
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A, the virtual artery was 2.2 mm long and comprised of one layer of endothelium (red) and one layer of smooth muscle (black). Each arterial segment (n = 44) consisted of 48 endothelial cells and 30 smooth muscle cells. Cells were treated as discrete elements with defined physical dimensions, gap junctional coupling and ionic conductance. Neighbouring smooth muscle cells were electrically coupled to one another as were neighbouring endothelial cells. Every smooth muscle cell was randomly coupled to two endothelial cells (red dot denotes myoendothelial contact site). B, equivalent circuit representation of the virtual artery. Each cell was modelled as a capacitor coupled in parallel with a non-linear resistor representing ionic conductance of the plasma membrane; gap junctions were represent by ohmic resistors. The I–V properties of the non-linear resistors are displayed in the bottom panel referenced to a resting Vm of –40 mV.
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Simulations
In intact arteries, electrical communication is typically assessed by applying vasoactive agents (Welsh & Segal, 1998; Emerson & Segal, 2000a) or by injecting current (Hirst & Neild, 1978; Emerson & Segal, 2000b; Emerson et al. 2002) to specifically stimulate endothelial cells or smooth muscle cells. These stimuli create a voltage differential and produce current flow between stimulated and non-stimulated cells. To initiate a voltage differential in our virtual artery, a defined number of cells was voltage clamped 15 mV positive or 15 mV negative to the resting Vm (–40 mV; electrical response time = 10 ms; total stimulus duration 250 ms); Vm was subsequently monitored along the vessel wall. In simulations where diameter was calculated, a 1 mV change in Vm was assumed to elicit a 1.5 μm change in diameter (Emerson & Segal, 2000a,b). Additionally, the stimulus duration was extended to 5000 ms to account for the slower vasomotor time constant relative to the electrical response time.
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The virtual artery was altered in a range of simulations to highlight fundamental electrical properties of the vessel wall. These changes are outlined: (a) Fig. 3: myoendothelial coupling resistance was varied between 1800 and 57600 M; (b) Fig. 6: electrical communication among the two cell layers was eliminated by increasing myoendothelial coupling resistance to 200 000 M. When cell orientation was altered, the physical dimensions of an endothelial cell and smooth muscle cell were maintained through subtle variations in arterial diameter (range, 75–80 μm); (c) Figs 7 and 8: to disrupt endothelial cell or smooth muscle cell communication within a small segment of the virtual artery (e.g. along a 200 μm region consisting of four arterial segments, each 50 μm long), coupling resistance was increased 150-fold and a leak resistance of 10 M was incorporated into each disrupted cell; (d) Fig. 9: spontaneous transient outward currents (STOCs) were modelled as an instantaneous rise in outward current (30 pA at –40 mV) that decayed exponentially with a time constant of 30 ms (Jaggar et al. 2000). Consistent with published findings (Jaggar et al. 2000; Herrera et al. 2001), STOC amplitude was coupled to resting Vm and each smooth muscle cell randomly produced two STOCs per second.
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Simulations: endothelial cells within one arterial segment were voltage clamped 15 mV negative to resting Vm (–40 mV) for 250 ms. Electrical responses were monitored at and remote from the site of endothelial cell stimulation; myoendothelial coupling resistance was varied between 1800 and 57 600 M. A and B, the predicted electrical response (at 250 ms) of endothelial and smooth muscle cells to the hyperpolarizing voltage step. Data used with permission from Kurjiaka et al. 2005.
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Simulations in A and C: endothelial cells (EC) and smooth muscle cells (SMC) were orientated parallel and perpendicular to the virtual artery's longitudinal axis, respectively. In the absence of myoendothelial coupling (induced by increasing coupling resistance to 200 000 M), a 50 μm segment of endothelium (A) or smooth muscle (C) was voltage-clamped 15 mV negative to resting Vm (–40 mV) for 250 ms. Endothelium (A) or smooth muscle (C) Vm (at 250 ms) was monitored at and remote from the site of stimulation. Simulations in B and D: ECs and SMCs were reoriented perpendicular and parallel to the virtual artery's longitudinal axis, respectively. In the absence of myoendothelial coupling, a 50 μm segment of endothelium (B) or an 80 μm segment of smooth muscle (D) was voltage-clamped 15 mV negative to resting Vm (–40 mV) for 250 ms. Endothelium (B) or smooth muscle (D) Vm (at 250 ms) was monitored at and remote from the site of stimulation.
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Simulations: endothelial cells within one arterial segment were voltage clamped (red band denoted by arrowhead) 15 mV negative to resting Vm (–40 mV) for 250 ms (A and B) or 5000 ms (C). Electrical and vasomotor responses were monitored every 500 μm from the site of endothelial cell stimulation under resting conditions and following the disruption of endothelial cell communication in 4 consecutive arterial segments along the conduction pathway (denoted by rectangle). A and B, the predicted electrical response of endothelial and smooth muscle cells as colour-mapped along the vessel wall and presented in 2-D voltage plots (at 250 ms), respectively. C, the predicted vasodilator response (at 5000 ms) prior to and following endothelial cell disruption. D and E, experimental observations (Emerson & Segal, 2000a): endothelial cells within a small region of a retractor muscle feed artery were stimulated with acetylcholine and responses monitored close to or remote from the site of application. Membrane potential and vasomotor responses were recorded prior to and following the use of light dye treatment to disrupt endothelial cell communication within the region of the feed artery denoted by rectangle.
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Simulations: endothelial cells within one arterial segment (red band denoted by arrowhead) were voltage clamped 15 mV negative to resting Vm (–40 mV) for 250 ms (A and B) or 5000 ms (C). Electrical and vasomotor responses were monitored every 500 μm from site of endothelial cell stimulation under resting conditions and following the disruption of muscle cell communication in 4 consecutive arterial segments along the conduction pathway (denoted by the rectangle). A and B, the predicted electrical response of endothelial and smooth muscle cells as colour-mapped along the vessel wall and presented in 2-D voltage plots (at 250 ms), respectively. C, the predicted vasodilator response (at 5000 ms) prior to and following smooth muscle cell disruption. D and E, experimental observations (Emerson & Segal, 2000a): endothelial cells within a small region of a retractor muscle feed artery were stimulated with acetylcholine and responses monitored close to or remote from the site of stimulation. Membrane potential and vasomotor responses were recorded prior to and following the use of light dye treatment to disrupt smooth muscle cell communication within the region of the feed artery denoted by rectangle.
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Simulations: smooth muscle cells (SMCs) in the virtual artery were programmed to randomly generate 2 STOCs per second. The electrical response of the SMC layer was monitored under control conditions and following the elimination of myoendothelial and/or SMC-to-SMC coupling (induced by increasing the respective coupling resistance to 200 000 M). A, the predicted voltage response of the SMC layer as colour-mapped in the middle portion of the virtual artery under respective conditions. Arrowheads denote individual SMCs. B, the predicted voltage response of 5 smooth muscle cells from the middle portion of the virtual artery plotted over time under respective conditions.
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Experimental observations
Experimental data were obtained from the literature and reprinted with permission. In these studies, feed arteries from the hamster retractor muscle (typical resting diameter 50–75 μm; maximal diameter 100–110 μm; length > 2 mm) were isolated, cannulated and superfused with buffered saline solution. Following equilibration (at 37°C), at a transmural pressure of 60–75 mmHg, agents that hyperpolarize, acetylcholine or depolarize (noradrenaline, phenylephrine, norepinephrine or KCl) vascular cells were applied, via micropipette, to a discrete site of the vessel. Changes in Vm and arterial diameter were monitored close to or remote from the site of stimulation. In some experiments, light-dye treatment was used to disrupt endothelial cell or smooth muscle cell integrity along a 200–250 μm segment of vessel (Emerson & Segal, 2000a).
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Results
Video clips corresponding with Figs 2, 4, 7, 8 and 9 can be found in the online supplement.
Simulations: endothelial cells within one arterial segment were voltage clamped (red band denoted by arrowhead; corresponding to distance = 0) 15 mV negative or positive to resting Vm (– 40 mV) for 250 ms (A–C) or 5000 ms (D). Electrical and vasomotor responses were monitored at and remote from the site of endothelial cell stimulation. A and B, the predicted electrical response of endothelial and smooth muscle cells to a hyperpolarizing voltage step as colour-mapped along the vessel wall and represented in 2-D voltage plots, respectively. C, the predicted electrical response (at 250 ms) of respective cells to a depolarizing or hyperpolarizing voltage step. D, the predicted vasodilator response (at 5000 ms) to a hyperpolarizing voltage step. E, experimental observations (Emerson & Segal, 2000a): endothelial cells in a small region of a hamster retractor muscle feed artery were stimulated with acetylcholine via microiontophoresis while the electrical and vasomotor responses were monitored at sites close to or remote from the site of stimulation. Data in C and D from Emerson & Segal 2000b, used with permission from Lippincott Williams & Wilkins 2000.
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Modelling electrical communication
Our computational investigation of electrical communication began by voltage clamping one arterial segment of endothelium 15 mV negative to resting Vm (–40 mV). As shown in Fig. 2A–C, hyperpolarization spread with modest decay along the endothelial layer. As this signal conducted along the vessel, charge spread through myoendothelial gap junctions to the overlying smooth muscle eliciting: (1) a near-parallel hyperpolarization; and (2) a robust dilatation that spread with little decay (Fig. 2D). Voltage clamping one arterial segment of endothelium 15 mV positive to resting Vm elicited a depolarization that spread in a similar manner. The behaviour of this virtual artery was consistent with observations from the hamster retractor muscle feed artery where the local delivery of acetylcholine (an endothelium-dependent agonist) from a micropipette elicited a hyperpolarization and dilatation that conducted robustly along the axis of the vessel (Fig. 2E); intracellular injection of negative current produced complementary behaviour (Emerson & Segal, 2000b). In our virtual vessel, electrical conduction velocity was estimated at 90 mm s–1; this compares favourably to 45 mm s–1 in the retractor muscle feed artery (Emerson et al. 2002). Control simulations indicated that: (1) a 2-fold rise or fall in endothelial cell-to-endothelial cell or myoendothelial coupling resistance or (2) the addition of a second smooth muscle cell layer did not qualitatively alter endothelial cell-initiated conduction in our virtual artery (data not shown). Figure 3A and B further highlight that to substantively eliminate the spread of endothelial cell-initiated hyperpolarization to the smooth muscle cell layer, myoendothelial coupling resistance would have to rise 32-fold relative to control.
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In contrast to the effect on endothelial cells, voltage clamping one arterial segment of smooth muscle, 15 mV positive to resting Vm, elicited a depolarization that spread poorly to neighbouring vascular cells (Fig. 4A–C). The restricted spread of smooth muscle depolarization elicited a decidedly local constriction (Fig. 4D). Voltage clamping one arterial segment of smooth muscle 15 mV negative to resting Vm elicited a correspondingly localized hyperpolarization (Fig. 4C). This discrete behaviour corresponds with experimental observations from the hamster retractor muscle feed artery where the local delivery of depolarizing agents (KCl or phenylephrine) from a micropipette elicited a constriction that conducted poorly along the vessel (Fig. 4E). Control simulations indicated that: (1) a 2-fold rise or fall in smooth muscle cell-to-smooth muscle cell or myoendothelial coupling resistance; or (2) the addition of a second smooth muscle cell layer did not qualitatively alter the ability of smooth muscle cell-initiated responses to conduct (data not shown).
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Simulations: smooth muscle cells within one arterial segment were voltage clamped (red band denoted by arrowhead; corresponding to distance = 0) 15 mV positive or negative to resting Vm (–40 mV) for 250 ms (A–C) or 5000 ms (D). Electrical and vasomotor responses were monitored at and remote from the site of smooth muscle stimulation. A and B, the predicted electrical response of endothelial and smooth muscle cells to a depolarizing voltage step as colour-mapped along the vessel wall and represented in 2-D voltage plots, respectively. C, the predicted electrical response (at 250 ms) of vascular cells to a depolarizing or hyperpolarizing voltage step. D, the predicted vasoconstrictor response (at 5000 ms) to a depolarizing voltage step. E, experimental observations (Kurjiaka et al. 2005). Smooth muscle cells in a small region of a retractor muscle feed artery were stimulated via micropipette with phenylephrine or KCl while diameter was monitored at sites close to or remote from the site of stimulation. Data in B and C from Emerson & Segal 2000b, used with permission from Lippincott Williams & Wilkins 2000.
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The preceding results indicated that a small number of stimulated smooth muscle cells were unable to substantively alter endothelial Vm. However, a different result emerged when the number of stimulated cells increased. As illustrated in Fig. 5A and B, the endothelium depolarized progressively as the number of smooth muscle segments that were voltage clamped 15 mV positive to resting Vm rose from 1 to 40. Indeed, when 40 of the 44 arterial smooth muscle segments were depolarized simultaneously, a quasi-isopotential response was manifested between the endothelium and the voltage-clamped smooth muscle. As noted in Fig. 5C, isopotentiality has been observed consistently in intact retractor muscle feed arteries stimulated by intravascular pressure, a mechanical stimulus that uniformly depolarizes the smooth muscle layer.
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Simulations: 1, 5, 10, 20 and 40 arterial segments of smooth muscle were voltage clamped 15 mV positive to resting Vm (–40 mV) for 250 ms. Voltage responses were monitored along the vessel wall. A, the predicted electrical response of endothelial and smooth muscle cells to a depolarizing voltage step as colour-mapped along the vessel wall. Arrowhead denotes ‘first segment of stimulated smooth muscle’. B, the predicted voltage (at 250 ms) of endothelial cells to a depolarizing voltage step as monitored every 500 μm from the first segment of stimulated smooth muscle. C, experimental observations ((1) Emerson & Segal, 2000a; (2) Emerson & Segal, 2000b; (3) Emerson et al. 2002): isolated hamster retractor muscle feed arteries were pressurized to 75 mmHg to mechanically stimulate the smooth muscle cell layer to depolarize. Membrane potential was recorded in endothelial cells and in smooth muscle cells. Data in B and C from Emerson & Segal 2000b, used with permission from Lippincott Williams & Wilkins 2000.
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Endothelial cells and smooth muscle cells are distinct with respect to coupling resistances and anatomical orientation. These differences could explain why electrical responses initiated in endothelium (Fig. 2) but not smooth muscle (Fig. 4) conduct robustly along their respective cell layers. To explore this possibility, the conduction of a hyperpolarizing stimulus was examined in a virtual artery where: (1) the two cell layers were electrically isolated from one another; and (2) homologous coupling resistance and cell orientation were systemically varied. In the absence of myoendothelial coupling, an endothelial-initiated hyperpolarization conducted with minimal decay along the endothelium (Fig. 6A). Increasing endothelial cell-to-endothelial cell coupling resistance, equivalent to the value used for two adjacent smooth muscle cells (90 M), attenuated but did not abolish endothelium conduction. To reproduce the localized smooth muscle behaviour of Fig. 4, endothelial cells had to be both poorly coupled and orientated perpendicular to the vessel axis (Fig. 6B). For comparison, a reduction in smooth muscle cell-to-smooth muscle cell coupling resistance, equivalent to the value used for two adjacent endothelial cells (3 M), promoted the conduction of hyperpolarization along smooth muscle (Fig. 6C). However, to reproduce the robust endothelium conduction of Fig. 1, well-coupled smooth muscle cells had to be orientated parallel to the artery's longitudinal axis (Fig. 6D).
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To further highlight which cell layer was the principal pathway for longitudinal conduction, additional simulations were performed. One arterial segment of endothelium was voltage clamped, 15 mV negative to resting Vm, and responses were monitored under control conditions and following the localized disruption of endothelial or smooth muscle communication (i.e. in 4 consecutive arterial segments positioned 650–850 μm remote to the stimulation site). When endothelial cell communication was disrupted in our virtual artery (induced by increasing coupling resistance 150-fold and introducing a leak resistance of 10 M into each affected cell), hyperpolarization and dilatation conducted up to but not beyond the disruption site (Fig. 7A–C). Consistent with these predictions, the conduction of acetylcholine-induced responses in hamster retractor muscle feed arteries was abolished with the use of light-dye treatment to locally disrupt endothelial cell communication within a similar segment of the vessel wall (Fig. 7D and E). In contrast, the disruption of smooth muscle communication in our virtual vessel, as well as in hamster retractor muscle feed arteries, had no substantive effect on the conduction of endothelial-initiated hyperpolarization and dilatation (Fig. 8A–E).
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STOC transformation
Previous studies have proposed that gap junctions enable resistance arteries to function like a large capacitor, filtering and transforming transient electrical activity into sustained responses (Jaggar et al. 2000). To address this relationship, smooth muscle cells were programmed to randomly generate two STOCs per second while Vm was monitored under control conditions and following the elimination of myoendothelial and/or smooth muscle cell-to-smooth muscle cell coupling. Under control conditions, random STOC activity gave rise to a sustained hyperpolarization (5 mV) along the entire smooth muscle layer (Fig. 9A and B). The removal of myoendothelial coupling (induced by increasing coupling resistance to 200 000 M) did not substantively impair the transformation of STOCs although the amplitude of sustained hyperpolarization increased with the loss of endothelium capacitance. In contrast, the elimination of smooth muscle cell-to-smooth muscle cell coupling had a profound influence as noted by the appearance of transient electrical events superimposed onto a subtle (2 mV) but sustained hyperpolarization. The concomitant elimination of myoendothelial and smooth muscle cell-to-smooth muscle cell coupling abolished this sustained component of hyperpolarization and augmented the magnitude of the transient electrical events.
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Discussion
A computational model was developed using realistic values of cell dimension, ionic conductance and gap junctional resistance to facilitate a quantitative understanding of electrical communication in resistance arteries. Simulations revealed that electrical signals spread differentially among and between endothelial and smooth muscle cells depending on the nature of the initial stimulus. These predictions contrast with the syncytial behaviour of the myocardium yet correspond with experimental observations from skeletal muscle resistance arteries. Our findings illustrate that cell orientation and coupling resistance are key determinants for enabling the differential spread of electrical signals within the vessel wall. Simulations also revealed that gap junctions allow vascular cells to functionally transform transient electrical events into sustained voltage responses. Physiologically, differential electrical communication among and between the two cell types should facilitate the ability of vascular networks to control tissue blood flow in a local and regional manner.
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Model rationale
Segal & Duling (1986b) first described an approach to practically explore electrical communication in resistance arteries. In essence, their protocol entailed stimulating a small segment of a resistance artery with agents known to alter Vm while monitoring responses at sites remote from the site of stimulation. Despite the simplicity of this approach, functional observations have been surprisingly diverse – particularly in resistance vessels of skeletal muscle (Segal et al. 1999; de Wit et al. 2000; Kumer et al. 2000; Yashiro & Duling, 2000). Consequently, conflicting views on the nature of electrical communication have arisen ranging from the idea that endothelial and smooth muscle cells form a functional syncytium to one where they shape an environment in which electrical phenomena spread differentially among and between the two cell types (Xia & Duling, 1995; Segal et al. 1999; Yashiro & Duling, 2000; Kurjiaka et al. 2005).
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One means of resolving these contrasting views is to develop a computational approach that provides quantitative insight into the principal factors that determine electrical communication among the cells comprising the vessel wall. To date, computational approaches have been applied sparsely and have relied upon classic cable theory, whereby resistance arteries are viewed as continuous wires with uniform properties for conducting electricity (Hirst & Neild, 1978; Crane et al. 2001). However, such models do not fully account for the structural and electrical properties of vascular cells and this shortcoming limits their quantitative and predictive value. In contrast to this traditional approach, the present computational model treated vascular cells (3432 in total) as discrete elements. Our virtual artery structurally approximated an isolated hamster retractor feed artery in that it was 2.2 mm long, 75 μm in diameter and composed of one layer of endothelium that was circumscribed by one layer of smooth muscle cells (Emerson & Segal, 2000a,b). Individual cells retained specific anatomical dimensions and were modelled as the equivalent of a capacitor coupled in parallel with a non-linear resistor representing ionic conductance. Gap junctions interconnected cells and were represented by ohmic resistors (Lidington et al. 2000; Sandow & Hill, 2000; Sandow et al. 2003; Yamamoto et al. 2001).
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Modelling electrical communication in skeletal muscle resistance arteries
Our computations began with simulations that paralleled experimental protocols used previously to characterize electrical communication along a resistance vessel (Segal & Duling, 1986b; Emerson & Segal, 2000a,b). To simulate protocols where vasoactive agents were applied focally to a small region of the vessel wall, one arterial segment of endothelium or of smooth muscle was voltage clamped, 15 mV positive or negative to resting Vm. Electrical events initiated in one arterial segment of endothelium conducted robustly along this layer and elicit a quasi-parallel response in the overlying smooth muscle (Fig. 2). Robust endothelial cell conduction is consistent with these cells, parallel orientation along the vessel axis and low coupling resistance due to extensive gap junctional expression (Haas & Duling, 1997; Sandow et al. 2003). Together, these endothelial cell properties minimize intercellular resistance (Fig. 6) and charge loss through the endothelial cell membrane and myoendothelial gap junctions. The quasi-parallel response in the smooth muscle layer is intriguing given the infrequent nature of myoendothelial contacts and their high coupling resistance. Indeed, based on a unitary gap junctional conductance of 100–200 pS (Li & Simard, 1999), we calculate that quasi-parallel behaviour is achieved with only two to six active gap junctions per myoendothelial contact site. Such findings highlight that charge movement from the endothelium need not be large to substantively alter smooth muscle Vm if the input resistance of the smooth muscle cell is sufficiently high. These predictions are consistent with observations from hamster retractor muscle feed arteries which have documented the ability of endothelial-dependent agonists to initiate a hyperpolarization and dilatation that spreads with little decay along these resistance vessels (Emerson & Segal, 2000a).
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Figure 3 broadens the preceding simulation by documenting the extent to which myoendothelial coupling can influence the spread of an endothelial cell-initiated hyperpolarization to the smooth muscle cell layer. This additional analysis reveals that myoendothelial coupling resistance must rise 4-fold (relative to control) before a measurable change in smooth muscle Vm (3 mV) would likely occur. Although there is no definitive evidence in intact arteries for myoendothelial gap junctional modulation, a physiological change of this magnitude appears reasonable. Note that to eliminate a measurable smooth muscle response to endothelial cell-initiated hyperpolarization, myoendothelial coupling resistance must rise 32-fold relative to control. This magnitude of change required for near-complete blockade highlights the potential difficulties in using myoendothelial uncoupling agents to abolish interlayer charge transfer in intact arteries.
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In contrast to endothelium-initiated responses, electrical events initiated by voltage clamping one arterial segment of smooth muscle (30 cells) conducted poorly to neighbouring vascular cells (Fig. 4). These predictions were also in keeping with functional observations and are indicative of substantive signal dissipation. Signal dissipation along the smooth muscle layer is facilitated by these cells' perpendicular orientation and higher coupling resistance (relative to the endothelium) which together augment intercellular resistivity (Fig. 6). This high resistivity also, albeit to a lesser extent, promotes charge loss through the smooth muscle membrane through the high-resistance myoendothelial gap junctions. While charge does conduct to the endothelium, its effects on Vm will be subtle due to an endothelial cell's robust expression of gap junctions and low input resistance. The preceding observations do not suggest that smooth muscle cells are entirely unable to alter the endothelial Vm. Indeed, it could be argued that if a sufficient number of smooth muscle cells were stimulated simultaneously, sufficient charge could spread to initiate a substantive voltage response in the endothelium (Fig. 5). This possibility was supported by simulations that documented progressive changes in endothelium Vm as the number of voltage-clamped smooth muscle cells increased. Remarkably, a quasi-isopotential behaviour was achieved between the two cell layers when 40 of the 44 smooth muscle segments were simultaneously clamped. This near-parallel behaviour has been observed in retractor muscle feed arteries activated by elevated intravascular pressure, a stimulus that depolarizes the smooth muscle layer (Emerson & Segal, 2000a, b; Emerson et al. 2002).
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While localized smooth muscle depolarizations conduct poorly, our findings do not suggest that all depolarizing signals are unable to spread. Indeed, Fig. 2C reveals that depolarization can readily conduct if endothelial cells are stimulated. As previously noted (Segal et al. 1999; de Wit et al. 2000; Kumer et al. 2000; Kurjiaka et al. 2005), depolarizing agents like KCl elicit disparate conducted responses in skeletal muscle arteries, a result which has fostered disparate views on electrical communication. This disparity may simply reflect the strength of a KCl stimulus delivered subluminally, with low intensity solely affecting smooth muscle Vm and a higher intensity directly influencing both cell types. Findings in Fig. 5 also indicate that if smooth muscle depolarizing stimuli are not sufficiently localized, a greater number of stimulated smooth muscle cells could charge the underlying endothelium and elicit conducted responses.
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As illustrated in Fig. 6, cellular orientation and coupling resistance under ‘normal’ conditions appear to favour the endothelium as the principal pathway for conduction along the vessel axis. To further highlight this important physical property of the arterial wall, simulations were performed in which the conduction of an endothelium-initiated response was assessed prior to and following the disruption of endothelial cell (Fig. 7) or smooth muscle cell (Fig. 8) communication. Our model predicted that the disruption of endothelial cell, but not smooth muscle cell, communication within a restricted region effectively prevented endothelium-initiated responses from conducting beyond the site of disruption. These predictions nicely paralleled functional observations from hamster retractor muscle feed arteries where the disruption of endothelial communication notably impaired the conduction of hyperpolarization and vasodilatation induced by acetycholine (Emerson & Segal, 2000a). Remarkably, focal disruption of endothelial cells has yielded similar findings in other resistance vessels of striated muscle (Looft-Wilson et al. 2004) but not in the hamster cheek pouch (Bartlett & Segal, 2000). This apparent disparity highlights the ability of electrical phenomena to conduct robustly along either cell layer of some resistance arteries (Welsh & Segal, 1998). The structural or electrophysiological properties that enable electrical conduction along the smooth muscle cell layer of one vessel type but not another remains unclear. Key factors such as cell orientation and gap junction expression do not appear to be dramatically different in this tissue (Little et al. 1995a,b; Sandow et al. 2003). One possibility is that, as charge spreads to a neighbouring smooth muscle cell, a novel ionic conductance triggers a regenerative event. Additional studies are required to resolve such proposed behaviour.
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The preceding observations provide new insight to our understanding of blood flow regulation in skeletal muscle. For example, it has been proposed that in order to match blood flow delivery with metabolic demand, arterial segments within a vascular tree must respond both in isolation and in conjunction with its neighbours (Segal & Duling, 1986a; Segal & Jacobs, 2001). An arterial segment responding in isolation can subtly alter flow to a specified region without over- or under-perfusing other areas of varied metabolic demand. In contrast, more encompassing changes in segmental tone would enable a vascular network to dramatically increase regional blood flow during high metabolic activity. Our simulations illustrate that localized changes in arterial tone can be attained if vasoactive stimuli directly modulate a small number of smooth muscle cells. In contrast, coordinated changes in contiguous vascular segments can be achieved if vasoactive stimuli were to electrically influence: (1) a small number of endothelial cells; or (2) a substantive number of smooth muscle cells.
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STOC transformation
In resistance vessels, studies of cell-to-cell communication traditionally contextualize gap junctional function within the confines of longitudinal conduction. Recent work, however, has asserted that gap junctions are also important in transforming transient electrical events, like STOCs, into a sustained voltage response (Jaggar et al. 2000; Herrera et al. 2001). In theory, gap junctions facilitate such a transformation by: (1) combining the capacitive effects of individual cells; and (2) allowing current to be distributed among neighbouring cells. The collective result is an arterial wall that functions as a low-pass filter that ‘smooths’ the effects of individual charge impulses both spatially and temporally. Consistent with this view, sustained hyperpolarization was achieved in our control virtual artery when smooth muscle cells were programmed to randomly produce two STOCs per second (Fig. 9).
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The filtering capabilities of this arterial capacitor should be compromised with the removal of gap junctions, particularly those of the highest conductances. This reasoning explains why the elimination of smooth muscle cell-to-smooth muscle cell gap junctions (coupling resistance, 90 M) had a more pronounced effect on STOC transformation than the removal of myoendothelial gap junctions (coupling resistance, 1800 M). While the elimination of gap junctions between smooth muscle cells initiated the appearance of transient phenomena, these events were superimposed onto a subtle but sustained hyperpolarization. The sustained hyperpolarization is explained by charge spreading through myoendothelial gap junctions and the endothelium's continued ability to filter, transform and summate STOCs. Indeed, the model illustrates that blocking the spread of charge into the endothelial capacitor eliminated this subtle hyperpolarization. These predictions provide insight into how the smooth muscle and endothelial cell layers work cooperatively with one another to optimize STOC transformation.
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Summary
Electrical communication in skeletal muscle resistance arteries was explored by developing a computational model that assigned discrete properties to individual vascular cells and by comparing predicted observations with published results obtained from intact pressurized vessels. Our findings revealed that, in contrast to a functional syncytium, electrical signals spread differentially among and between endothelial cells and smooth muscle cells. The two principal factors that establish differential electrical communication within the vessel wall are cell orientation and coupling resistance. We conclude that the intrinsic biophysical properties of endothelial cells and smooth muscle cells enable both local and regional control of tissue blood flow.
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Supplemental material
The online version of this paper can be accessed at: DOI: 10.1113/jphysiol.2005.090233
http://jp.physoc.org/cgi/content/full/jphysiol.2005.090233/DC1
and contains video clips corresponding with Figs 2, 4, 7, 8 and 9.
This material can also be found as part of the full-text HTML version available from http://blackwell-synergy.com
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2 The John B. Pierce Laboratory & Department of Cellular and Molecular Physiology, Yale University, New Haven, CT, USA
3 Smooth Muscle Research Group & Department of Physiology and Biophysics, University of Calgary, Calgary, Alberta, Canada
Abstract
Vascular cells communicate electrically to coordinate their activity and control tissue blood flow. To foster a quantitative understanding of this fundamental process, we developed a computational model that was structured to mimic a skeletal muscle resistance artery. Each endothelial cell and smooth muscle cell in our virtual artery was treated as the electrical equivalent of a capacitor coupled in parallel with a non-linear resistor representing ionic conductance; intercellular gap junctions were represented by ohmic resistors. Simulations revealed that the vessel wall is not a syncytium in which electrical stimuli spread equally to all constitutive cells. Indeed, electrical signals spread in a differential manner among and between endothelial cells and smooth muscle cells according to the initial stimulus. The predictions of our model agree with physiological data from the feed artery of the hamster retractor muscle. Cell orientation and coupling resistance were the principal factors that enable electrical signals to spread differentially along and between the two cell types. Our computational observations also illustrated how gap junctional coupling enables the vessel wall to filter and transform transient electrical events into sustained voltage responses. Functionally, differential electrical communication would permit discrete regions of smooth muscle activity to locally regulate blood flow and the endothelium to coordinate regional changes in tissue perfusion.
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Introduction
Vascular networks dilate and constrict in a coordinated fashion to control blood flow to metabolically active tissue (Segal & Duling, 1986a; Segal & Jacobs, 2001). For resistance vessels to respond in an integrative manner, the constitutive cells must communicate with one another (Segal & Duling, 1986b; Xia & Duling, 1995; Welsh & Segal, 1998). Direct electrical communication in the vascular wall is enabled by gap junctions, intercellular channels that facilitate the diffusion of ions and second messengers between neighbouring cells (Little et al. 1995a, b). Gap junctions are formed by two hemichannels or connexons, each containing six connexin subunits. The connexin gene family is comprised of at least 19 members, with the most predominant subtypes in vascular tissue being Cx37, Cx40, Cx43 and Cx45 (Little et al. 1995a; Saez et al. 2003; Sandow et al. 2003).
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Electrical communication can be functionally assessed in resistance arteries (e.g. diameter < 100 μm) by focally applying vasoactive agents to a small portion of the vessel wall (Segal & Duling, 1986b; Welsh & Segal, 1998). This discrete stimulus initiates a local change in smooth muscle or endothelial cell membrane potential (Vm) which, with the aid of gap junctions, conducts to neighbouring vascular cells (Xia & Duling, 1995; Welsh & Segal, 1998). The extent to which the electrical or the corresponding vasomotor response is conducted along the vessel wall provides an index of electrical communication. In general, responses initiated in endothelial cells conduct robustly along resistance vessels (Welsh & Segal, 1998; Segal et al. 1999; Emerson & Segal, 2000a). In contrast, agents that depolarize and constrict smooth muscle elicit decidedly varied responses ranging from little to strong conduction (Segal et al. 1999; de Wit et al. 2000; Kumer et al. 2000; Yashiro & Duling, 2000; Kurjiaka et al. 2005).
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The variability in the conducted vasomotor response has led to divergent views on the nature of electrical communication, particularly in skeletal muscle resistance vessels. This divergence ranges from the view that endothelial and smooth muscle cells form a well coupled syncytium (Xia & Duling, 1995; Yashiro & Duling, 2000) to one where they shape a diverse environment in which electrical phenomena conduct in a differential manner among vascular cells (Segal et al. 1999; Kurjiaka et al. 2005). To resolve these contrasting views, quantitative insight into the factors that shape electrical communication is required. Such insight can be advanced with computational models whose design is based on the structural and electrical properties of vascular cells. In the myocardium, sophisticated tissue modelling of discrete cells has forwarded an understanding of how action potentials spread in the normal and diseased heart (Vigmond et al. 2001; Kneller et al. 2002). In contrast, computational models of the resistance vasculature have relied on traditional cable theory, where a vessel is viewed as continuous wires with uniform axial resistance (Hirst & Neild, 1978; Crane et al. 2001). While a step towards quantification, such models oversimplify the multicellular vessel wall and do not fully account for anatomical, ionic and gap junctional properties. Their quantitative and predictive value is therefore limited.
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To foster new insight into how electrical signals spread in a resistance artery, the present study developed a novel computational model of cell-to-cell communication. Our virtual artery consisted of 3432 discrete vascular cells each of which retained distinct structural and electrophysiological properties. Values of cell dimension, ionic conductance and gap junctional resistance were taken from the literature and simulations were designed to mimic experimental protocols previously used to examine electrical communication. Predicted outcomes were compared with experimental observations from the hamster retractor muscle feed artery. Our mathematical approach revealed that a resistance artery does not behave as a well-coupled syncytium. Instead, computations illustrate how electrical signals spread differentially among and between endothelial cells and smooth muscle cells. These differences are explained by the orientation and coupling resistance of respective cell layers and are fundamental to both local and regional regulation of tissue blood flow.
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Methods
Computational theory
Modelling the electrical activity of vascular cells was based on the same principles employed in modelling cardiac bioelectric phenomena (Vigmond et al. 2001; Kneller et al. 2002). Each cell was characterized electrically as a capacitance (a property of the lipid bilayer membrane) in parallel with a non-linear conductance (representing ionic flow through membrane channels). The membrane conductance was a function of the voltage across the membrane, Vm. Cells were connected electrically to one another with gap junctions which were represented as ohmic resistances. The net current flowing into a cell through gap junctions was balanced with current flowing through the membrane (a combination of ionic and capacitive current). This can be expressed as:
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where the superscript refers to individual cells, A is cell surface area, Jion is ionic current density, Cm is membrane capacitance per unit area, j is the set of cellular indices connected to cell i, and ri,j is the gap junctional resistance between cells i and j. It has been assumed that extracellular potential is negligible compared with intracellular potential. The equation of each vascular cell can be written into the matrix form:
where G is a matrix accounting for intercellular coupling, A is a diagonal matrix of cell surface areas, vm is the vector of transmembrane voltages, and jion is the vector of ionic current densities. The vector istim takes into account current introduced through intracellular stimulating electrodes. Using a Crank-Nicolson time integration scheme and first order differencing with a time step of t, the final equation set is:
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where superscripts refer to the time step. To advance the simulation in time, a sparse set of linear equations was solved at each instant in time and jionic updated. The system was solved with a time step of 0.5 ms.
Vessel diameter has been shown to vary as a linear function of transmembrane voltage (Xia & Duling, 1995; Welsh & Segal, 1998). Assuming that smooth muscle cells respond in time with first order kinetics, the change in diameter can be expressed as:
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where D is the diameter, D is the steady-state diameter and D is the vasomotor time constant (1334 ms; calculated from Emerson & Segal, 2000b). Using a first order time difference, and a time step of t, the diameter can be tracked as Vm changes by:
Structural and electrical properties
The virtual artery was structured physically to represent an isolated feed artery from the hamster retractor muscle. As such, the virtual artery was 2.2 mm long, 75 μm in diameter and composed of one layer of endothelium (2112 cells) circumscribed by one layer of smooth muscle (1320 cells in total; Fig. 1A). The artery was subdivided into 44 arterial segments, each 50 μm long, and consisting of an outer layer of 30 smooth muscle cells (arranged as 10 consecutive bands each consisting of three cells) and an inner layer of 48 endothelial cells (arranged side-by-side parallel to the artery's longitudinal axis). In general accordance with the literature (Haas & Duling, 1997; Yeh et al. 1998; Sandow et al. 2003), the physical dimensions of each vascular cell were as follows: endothelium, 50 μm length, 5 μm width, 1 μm height; smooth muscle, 80 μm length, 5 μm width, 5 μm, height. Membrane capacitance was set to 1 μF cm–2. The ionic conductance of each endothelial cell and smooth muscle cell was represented by a non-linear resistor whose properties (Fig. 1B) were derived from electrophysiological recordings of rat coronary endothelial cells (Schnitzler et al. 2000) and hamster cremaster arteriolar smooth muscle cells (Jackson et al. 1997). These resistors account for the voltage- but not the time-dependent properties of ion channels. In contrast, gap junction channels were represented by ohmic resistors. Mindful of published observations (Lidington et al. 2000; Yamamoto et al. 2001), three different coupling resistances were employed depending on the type of cells being interconnected (endothelial to endothelial, 3 M; smooth muscle to smooth muscle, 90 M; endothelial to-smooth muscle, 1800 M). In Lidington et al. (2000), endothelial-to-endothelial coupling resistance was estimated by passing current between two electrodes in an endothelial monolayer. In Yamamoto et al. (2001), smooth muscle-to-smooth muscle and myoendothelial coupling resistances were estimated in intact arterioles by voltage clamping two closely situated vascular cells. Within respective layers of the virtual artery, neighbouring endothelial cells were coupled to each other as were neighbouring smooth muscles cells. For myoendothelial coupling, each smooth muscle cell was randomly coupled to two underlying endothelial cells (Sandow & Hill, 2000; Sandow et al. 2003). Gap junctions at the respective ends of the isolated vessel segment were treated as sealed.
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A, the virtual artery was 2.2 mm long and comprised of one layer of endothelium (red) and one layer of smooth muscle (black). Each arterial segment (n = 44) consisted of 48 endothelial cells and 30 smooth muscle cells. Cells were treated as discrete elements with defined physical dimensions, gap junctional coupling and ionic conductance. Neighbouring smooth muscle cells were electrically coupled to one another as were neighbouring endothelial cells. Every smooth muscle cell was randomly coupled to two endothelial cells (red dot denotes myoendothelial contact site). B, equivalent circuit representation of the virtual artery. Each cell was modelled as a capacitor coupled in parallel with a non-linear resistor representing ionic conductance of the plasma membrane; gap junctions were represent by ohmic resistors. The I–V properties of the non-linear resistors are displayed in the bottom panel referenced to a resting Vm of –40 mV.
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Simulations
In intact arteries, electrical communication is typically assessed by applying vasoactive agents (Welsh & Segal, 1998; Emerson & Segal, 2000a) or by injecting current (Hirst & Neild, 1978; Emerson & Segal, 2000b; Emerson et al. 2002) to specifically stimulate endothelial cells or smooth muscle cells. These stimuli create a voltage differential and produce current flow between stimulated and non-stimulated cells. To initiate a voltage differential in our virtual artery, a defined number of cells was voltage clamped 15 mV positive or 15 mV negative to the resting Vm (–40 mV; electrical response time = 10 ms; total stimulus duration 250 ms); Vm was subsequently monitored along the vessel wall. In simulations where diameter was calculated, a 1 mV change in Vm was assumed to elicit a 1.5 μm change in diameter (Emerson & Segal, 2000a,b). Additionally, the stimulus duration was extended to 5000 ms to account for the slower vasomotor time constant relative to the electrical response time.
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The virtual artery was altered in a range of simulations to highlight fundamental electrical properties of the vessel wall. These changes are outlined: (a) Fig. 3: myoendothelial coupling resistance was varied between 1800 and 57600 M; (b) Fig. 6: electrical communication among the two cell layers was eliminated by increasing myoendothelial coupling resistance to 200 000 M. When cell orientation was altered, the physical dimensions of an endothelial cell and smooth muscle cell were maintained through subtle variations in arterial diameter (range, 75–80 μm); (c) Figs 7 and 8: to disrupt endothelial cell or smooth muscle cell communication within a small segment of the virtual artery (e.g. along a 200 μm region consisting of four arterial segments, each 50 μm long), coupling resistance was increased 150-fold and a leak resistance of 10 M was incorporated into each disrupted cell; (d) Fig. 9: spontaneous transient outward currents (STOCs) were modelled as an instantaneous rise in outward current (30 pA at –40 mV) that decayed exponentially with a time constant of 30 ms (Jaggar et al. 2000). Consistent with published findings (Jaggar et al. 2000; Herrera et al. 2001), STOC amplitude was coupled to resting Vm and each smooth muscle cell randomly produced two STOCs per second.
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Simulations: endothelial cells within one arterial segment were voltage clamped 15 mV negative to resting Vm (–40 mV) for 250 ms. Electrical responses were monitored at and remote from the site of endothelial cell stimulation; myoendothelial coupling resistance was varied between 1800 and 57 600 M. A and B, the predicted electrical response (at 250 ms) of endothelial and smooth muscle cells to the hyperpolarizing voltage step. Data used with permission from Kurjiaka et al. 2005.
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Simulations in A and C: endothelial cells (EC) and smooth muscle cells (SMC) were orientated parallel and perpendicular to the virtual artery's longitudinal axis, respectively. In the absence of myoendothelial coupling (induced by increasing coupling resistance to 200 000 M), a 50 μm segment of endothelium (A) or smooth muscle (C) was voltage-clamped 15 mV negative to resting Vm (–40 mV) for 250 ms. Endothelium (A) or smooth muscle (C) Vm (at 250 ms) was monitored at and remote from the site of stimulation. Simulations in B and D: ECs and SMCs were reoriented perpendicular and parallel to the virtual artery's longitudinal axis, respectively. In the absence of myoendothelial coupling, a 50 μm segment of endothelium (B) or an 80 μm segment of smooth muscle (D) was voltage-clamped 15 mV negative to resting Vm (–40 mV) for 250 ms. Endothelium (B) or smooth muscle (D) Vm (at 250 ms) was monitored at and remote from the site of stimulation.
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Simulations: endothelial cells within one arterial segment were voltage clamped (red band denoted by arrowhead) 15 mV negative to resting Vm (–40 mV) for 250 ms (A and B) or 5000 ms (C). Electrical and vasomotor responses were monitored every 500 μm from the site of endothelial cell stimulation under resting conditions and following the disruption of endothelial cell communication in 4 consecutive arterial segments along the conduction pathway (denoted by rectangle). A and B, the predicted electrical response of endothelial and smooth muscle cells as colour-mapped along the vessel wall and presented in 2-D voltage plots (at 250 ms), respectively. C, the predicted vasodilator response (at 5000 ms) prior to and following endothelial cell disruption. D and E, experimental observations (Emerson & Segal, 2000a): endothelial cells within a small region of a retractor muscle feed artery were stimulated with acetylcholine and responses monitored close to or remote from the site of application. Membrane potential and vasomotor responses were recorded prior to and following the use of light dye treatment to disrupt endothelial cell communication within the region of the feed artery denoted by rectangle.
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Simulations: endothelial cells within one arterial segment (red band denoted by arrowhead) were voltage clamped 15 mV negative to resting Vm (–40 mV) for 250 ms (A and B) or 5000 ms (C). Electrical and vasomotor responses were monitored every 500 μm from site of endothelial cell stimulation under resting conditions and following the disruption of muscle cell communication in 4 consecutive arterial segments along the conduction pathway (denoted by the rectangle). A and B, the predicted electrical response of endothelial and smooth muscle cells as colour-mapped along the vessel wall and presented in 2-D voltage plots (at 250 ms), respectively. C, the predicted vasodilator response (at 5000 ms) prior to and following smooth muscle cell disruption. D and E, experimental observations (Emerson & Segal, 2000a): endothelial cells within a small region of a retractor muscle feed artery were stimulated with acetylcholine and responses monitored close to or remote from the site of stimulation. Membrane potential and vasomotor responses were recorded prior to and following the use of light dye treatment to disrupt smooth muscle cell communication within the region of the feed artery denoted by rectangle.
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Simulations: smooth muscle cells (SMCs) in the virtual artery were programmed to randomly generate 2 STOCs per second. The electrical response of the SMC layer was monitored under control conditions and following the elimination of myoendothelial and/or SMC-to-SMC coupling (induced by increasing the respective coupling resistance to 200 000 M). A, the predicted voltage response of the SMC layer as colour-mapped in the middle portion of the virtual artery under respective conditions. Arrowheads denote individual SMCs. B, the predicted voltage response of 5 smooth muscle cells from the middle portion of the virtual artery plotted over time under respective conditions.
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Experimental observations
Experimental data were obtained from the literature and reprinted with permission. In these studies, feed arteries from the hamster retractor muscle (typical resting diameter 50–75 μm; maximal diameter 100–110 μm; length > 2 mm) were isolated, cannulated and superfused with buffered saline solution. Following equilibration (at 37°C), at a transmural pressure of 60–75 mmHg, agents that hyperpolarize, acetylcholine or depolarize (noradrenaline, phenylephrine, norepinephrine or KCl) vascular cells were applied, via micropipette, to a discrete site of the vessel. Changes in Vm and arterial diameter were monitored close to or remote from the site of stimulation. In some experiments, light-dye treatment was used to disrupt endothelial cell or smooth muscle cell integrity along a 200–250 μm segment of vessel (Emerson & Segal, 2000a).
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Results
Video clips corresponding with Figs 2, 4, 7, 8 and 9 can be found in the online supplement.
Simulations: endothelial cells within one arterial segment were voltage clamped (red band denoted by arrowhead; corresponding to distance = 0) 15 mV negative or positive to resting Vm (– 40 mV) for 250 ms (A–C) or 5000 ms (D). Electrical and vasomotor responses were monitored at and remote from the site of endothelial cell stimulation. A and B, the predicted electrical response of endothelial and smooth muscle cells to a hyperpolarizing voltage step as colour-mapped along the vessel wall and represented in 2-D voltage plots, respectively. C, the predicted electrical response (at 250 ms) of respective cells to a depolarizing or hyperpolarizing voltage step. D, the predicted vasodilator response (at 5000 ms) to a hyperpolarizing voltage step. E, experimental observations (Emerson & Segal, 2000a): endothelial cells in a small region of a hamster retractor muscle feed artery were stimulated with acetylcholine via microiontophoresis while the electrical and vasomotor responses were monitored at sites close to or remote from the site of stimulation. Data in C and D from Emerson & Segal 2000b, used with permission from Lippincott Williams & Wilkins 2000.
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Modelling electrical communication
Our computational investigation of electrical communication began by voltage clamping one arterial segment of endothelium 15 mV negative to resting Vm (–40 mV). As shown in Fig. 2A–C, hyperpolarization spread with modest decay along the endothelial layer. As this signal conducted along the vessel, charge spread through myoendothelial gap junctions to the overlying smooth muscle eliciting: (1) a near-parallel hyperpolarization; and (2) a robust dilatation that spread with little decay (Fig. 2D). Voltage clamping one arterial segment of endothelium 15 mV positive to resting Vm elicited a depolarization that spread in a similar manner. The behaviour of this virtual artery was consistent with observations from the hamster retractor muscle feed artery where the local delivery of acetylcholine (an endothelium-dependent agonist) from a micropipette elicited a hyperpolarization and dilatation that conducted robustly along the axis of the vessel (Fig. 2E); intracellular injection of negative current produced complementary behaviour (Emerson & Segal, 2000b). In our virtual vessel, electrical conduction velocity was estimated at 90 mm s–1; this compares favourably to 45 mm s–1 in the retractor muscle feed artery (Emerson et al. 2002). Control simulations indicated that: (1) a 2-fold rise or fall in endothelial cell-to-endothelial cell or myoendothelial coupling resistance or (2) the addition of a second smooth muscle cell layer did not qualitatively alter endothelial cell-initiated conduction in our virtual artery (data not shown). Figure 3A and B further highlight that to substantively eliminate the spread of endothelial cell-initiated hyperpolarization to the smooth muscle cell layer, myoendothelial coupling resistance would have to rise 32-fold relative to control.
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In contrast to the effect on endothelial cells, voltage clamping one arterial segment of smooth muscle, 15 mV positive to resting Vm, elicited a depolarization that spread poorly to neighbouring vascular cells (Fig. 4A–C). The restricted spread of smooth muscle depolarization elicited a decidedly local constriction (Fig. 4D). Voltage clamping one arterial segment of smooth muscle 15 mV negative to resting Vm elicited a correspondingly localized hyperpolarization (Fig. 4C). This discrete behaviour corresponds with experimental observations from the hamster retractor muscle feed artery where the local delivery of depolarizing agents (KCl or phenylephrine) from a micropipette elicited a constriction that conducted poorly along the vessel (Fig. 4E). Control simulations indicated that: (1) a 2-fold rise or fall in smooth muscle cell-to-smooth muscle cell or myoendothelial coupling resistance; or (2) the addition of a second smooth muscle cell layer did not qualitatively alter the ability of smooth muscle cell-initiated responses to conduct (data not shown).
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Simulations: smooth muscle cells within one arterial segment were voltage clamped (red band denoted by arrowhead; corresponding to distance = 0) 15 mV positive or negative to resting Vm (–40 mV) for 250 ms (A–C) or 5000 ms (D). Electrical and vasomotor responses were monitored at and remote from the site of smooth muscle stimulation. A and B, the predicted electrical response of endothelial and smooth muscle cells to a depolarizing voltage step as colour-mapped along the vessel wall and represented in 2-D voltage plots, respectively. C, the predicted electrical response (at 250 ms) of vascular cells to a depolarizing or hyperpolarizing voltage step. D, the predicted vasoconstrictor response (at 5000 ms) to a depolarizing voltage step. E, experimental observations (Kurjiaka et al. 2005). Smooth muscle cells in a small region of a retractor muscle feed artery were stimulated via micropipette with phenylephrine or KCl while diameter was monitored at sites close to or remote from the site of stimulation. Data in B and C from Emerson & Segal 2000b, used with permission from Lippincott Williams & Wilkins 2000.
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The preceding results indicated that a small number of stimulated smooth muscle cells were unable to substantively alter endothelial Vm. However, a different result emerged when the number of stimulated cells increased. As illustrated in Fig. 5A and B, the endothelium depolarized progressively as the number of smooth muscle segments that were voltage clamped 15 mV positive to resting Vm rose from 1 to 40. Indeed, when 40 of the 44 arterial smooth muscle segments were depolarized simultaneously, a quasi-isopotential response was manifested between the endothelium and the voltage-clamped smooth muscle. As noted in Fig. 5C, isopotentiality has been observed consistently in intact retractor muscle feed arteries stimulated by intravascular pressure, a mechanical stimulus that uniformly depolarizes the smooth muscle layer.
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Simulations: 1, 5, 10, 20 and 40 arterial segments of smooth muscle were voltage clamped 15 mV positive to resting Vm (–40 mV) for 250 ms. Voltage responses were monitored along the vessel wall. A, the predicted electrical response of endothelial and smooth muscle cells to a depolarizing voltage step as colour-mapped along the vessel wall. Arrowhead denotes ‘first segment of stimulated smooth muscle’. B, the predicted voltage (at 250 ms) of endothelial cells to a depolarizing voltage step as monitored every 500 μm from the first segment of stimulated smooth muscle. C, experimental observations ((1) Emerson & Segal, 2000a; (2) Emerson & Segal, 2000b; (3) Emerson et al. 2002): isolated hamster retractor muscle feed arteries were pressurized to 75 mmHg to mechanically stimulate the smooth muscle cell layer to depolarize. Membrane potential was recorded in endothelial cells and in smooth muscle cells. Data in B and C from Emerson & Segal 2000b, used with permission from Lippincott Williams & Wilkins 2000.
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Endothelial cells and smooth muscle cells are distinct with respect to coupling resistances and anatomical orientation. These differences could explain why electrical responses initiated in endothelium (Fig. 2) but not smooth muscle (Fig. 4) conduct robustly along their respective cell layers. To explore this possibility, the conduction of a hyperpolarizing stimulus was examined in a virtual artery where: (1) the two cell layers were electrically isolated from one another; and (2) homologous coupling resistance and cell orientation were systemically varied. In the absence of myoendothelial coupling, an endothelial-initiated hyperpolarization conducted with minimal decay along the endothelium (Fig. 6A). Increasing endothelial cell-to-endothelial cell coupling resistance, equivalent to the value used for two adjacent smooth muscle cells (90 M), attenuated but did not abolish endothelium conduction. To reproduce the localized smooth muscle behaviour of Fig. 4, endothelial cells had to be both poorly coupled and orientated perpendicular to the vessel axis (Fig. 6B). For comparison, a reduction in smooth muscle cell-to-smooth muscle cell coupling resistance, equivalent to the value used for two adjacent endothelial cells (3 M), promoted the conduction of hyperpolarization along smooth muscle (Fig. 6C). However, to reproduce the robust endothelium conduction of Fig. 1, well-coupled smooth muscle cells had to be orientated parallel to the artery's longitudinal axis (Fig. 6D).
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To further highlight which cell layer was the principal pathway for longitudinal conduction, additional simulations were performed. One arterial segment of endothelium was voltage clamped, 15 mV negative to resting Vm, and responses were monitored under control conditions and following the localized disruption of endothelial or smooth muscle communication (i.e. in 4 consecutive arterial segments positioned 650–850 μm remote to the stimulation site). When endothelial cell communication was disrupted in our virtual artery (induced by increasing coupling resistance 150-fold and introducing a leak resistance of 10 M into each affected cell), hyperpolarization and dilatation conducted up to but not beyond the disruption site (Fig. 7A–C). Consistent with these predictions, the conduction of acetylcholine-induced responses in hamster retractor muscle feed arteries was abolished with the use of light-dye treatment to locally disrupt endothelial cell communication within a similar segment of the vessel wall (Fig. 7D and E). In contrast, the disruption of smooth muscle communication in our virtual vessel, as well as in hamster retractor muscle feed arteries, had no substantive effect on the conduction of endothelial-initiated hyperpolarization and dilatation (Fig. 8A–E).
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STOC transformation
Previous studies have proposed that gap junctions enable resistance arteries to function like a large capacitor, filtering and transforming transient electrical activity into sustained responses (Jaggar et al. 2000). To address this relationship, smooth muscle cells were programmed to randomly generate two STOCs per second while Vm was monitored under control conditions and following the elimination of myoendothelial and/or smooth muscle cell-to-smooth muscle cell coupling. Under control conditions, random STOC activity gave rise to a sustained hyperpolarization (5 mV) along the entire smooth muscle layer (Fig. 9A and B). The removal of myoendothelial coupling (induced by increasing coupling resistance to 200 000 M) did not substantively impair the transformation of STOCs although the amplitude of sustained hyperpolarization increased with the loss of endothelium capacitance. In contrast, the elimination of smooth muscle cell-to-smooth muscle cell coupling had a profound influence as noted by the appearance of transient electrical events superimposed onto a subtle (2 mV) but sustained hyperpolarization. The concomitant elimination of myoendothelial and smooth muscle cell-to-smooth muscle cell coupling abolished this sustained component of hyperpolarization and augmented the magnitude of the transient electrical events.
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Discussion
A computational model was developed using realistic values of cell dimension, ionic conductance and gap junctional resistance to facilitate a quantitative understanding of electrical communication in resistance arteries. Simulations revealed that electrical signals spread differentially among and between endothelial and smooth muscle cells depending on the nature of the initial stimulus. These predictions contrast with the syncytial behaviour of the myocardium yet correspond with experimental observations from skeletal muscle resistance arteries. Our findings illustrate that cell orientation and coupling resistance are key determinants for enabling the differential spread of electrical signals within the vessel wall. Simulations also revealed that gap junctions allow vascular cells to functionally transform transient electrical events into sustained voltage responses. Physiologically, differential electrical communication among and between the two cell types should facilitate the ability of vascular networks to control tissue blood flow in a local and regional manner.
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Model rationale
Segal & Duling (1986b) first described an approach to practically explore electrical communication in resistance arteries. In essence, their protocol entailed stimulating a small segment of a resistance artery with agents known to alter Vm while monitoring responses at sites remote from the site of stimulation. Despite the simplicity of this approach, functional observations have been surprisingly diverse – particularly in resistance vessels of skeletal muscle (Segal et al. 1999; de Wit et al. 2000; Kumer et al. 2000; Yashiro & Duling, 2000). Consequently, conflicting views on the nature of electrical communication have arisen ranging from the idea that endothelial and smooth muscle cells form a functional syncytium to one where they shape an environment in which electrical phenomena spread differentially among and between the two cell types (Xia & Duling, 1995; Segal et al. 1999; Yashiro & Duling, 2000; Kurjiaka et al. 2005).
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One means of resolving these contrasting views is to develop a computational approach that provides quantitative insight into the principal factors that determine electrical communication among the cells comprising the vessel wall. To date, computational approaches have been applied sparsely and have relied upon classic cable theory, whereby resistance arteries are viewed as continuous wires with uniform properties for conducting electricity (Hirst & Neild, 1978; Crane et al. 2001). However, such models do not fully account for the structural and electrical properties of vascular cells and this shortcoming limits their quantitative and predictive value. In contrast to this traditional approach, the present computational model treated vascular cells (3432 in total) as discrete elements. Our virtual artery structurally approximated an isolated hamster retractor feed artery in that it was 2.2 mm long, 75 μm in diameter and composed of one layer of endothelium that was circumscribed by one layer of smooth muscle cells (Emerson & Segal, 2000a,b). Individual cells retained specific anatomical dimensions and were modelled as the equivalent of a capacitor coupled in parallel with a non-linear resistor representing ionic conductance. Gap junctions interconnected cells and were represented by ohmic resistors (Lidington et al. 2000; Sandow & Hill, 2000; Sandow et al. 2003; Yamamoto et al. 2001).
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Modelling electrical communication in skeletal muscle resistance arteries
Our computations began with simulations that paralleled experimental protocols used previously to characterize electrical communication along a resistance vessel (Segal & Duling, 1986b; Emerson & Segal, 2000a,b). To simulate protocols where vasoactive agents were applied focally to a small region of the vessel wall, one arterial segment of endothelium or of smooth muscle was voltage clamped, 15 mV positive or negative to resting Vm. Electrical events initiated in one arterial segment of endothelium conducted robustly along this layer and elicit a quasi-parallel response in the overlying smooth muscle (Fig. 2). Robust endothelial cell conduction is consistent with these cells, parallel orientation along the vessel axis and low coupling resistance due to extensive gap junctional expression (Haas & Duling, 1997; Sandow et al. 2003). Together, these endothelial cell properties minimize intercellular resistance (Fig. 6) and charge loss through the endothelial cell membrane and myoendothelial gap junctions. The quasi-parallel response in the smooth muscle layer is intriguing given the infrequent nature of myoendothelial contacts and their high coupling resistance. Indeed, based on a unitary gap junctional conductance of 100–200 pS (Li & Simard, 1999), we calculate that quasi-parallel behaviour is achieved with only two to six active gap junctions per myoendothelial contact site. Such findings highlight that charge movement from the endothelium need not be large to substantively alter smooth muscle Vm if the input resistance of the smooth muscle cell is sufficiently high. These predictions are consistent with observations from hamster retractor muscle feed arteries which have documented the ability of endothelial-dependent agonists to initiate a hyperpolarization and dilatation that spreads with little decay along these resistance vessels (Emerson & Segal, 2000a).
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Figure 3 broadens the preceding simulation by documenting the extent to which myoendothelial coupling can influence the spread of an endothelial cell-initiated hyperpolarization to the smooth muscle cell layer. This additional analysis reveals that myoendothelial coupling resistance must rise 4-fold (relative to control) before a measurable change in smooth muscle Vm (3 mV) would likely occur. Although there is no definitive evidence in intact arteries for myoendothelial gap junctional modulation, a physiological change of this magnitude appears reasonable. Note that to eliminate a measurable smooth muscle response to endothelial cell-initiated hyperpolarization, myoendothelial coupling resistance must rise 32-fold relative to control. This magnitude of change required for near-complete blockade highlights the potential difficulties in using myoendothelial uncoupling agents to abolish interlayer charge transfer in intact arteries.
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In contrast to endothelium-initiated responses, electrical events initiated by voltage clamping one arterial segment of smooth muscle (30 cells) conducted poorly to neighbouring vascular cells (Fig. 4). These predictions were also in keeping with functional observations and are indicative of substantive signal dissipation. Signal dissipation along the smooth muscle layer is facilitated by these cells' perpendicular orientation and higher coupling resistance (relative to the endothelium) which together augment intercellular resistivity (Fig. 6). This high resistivity also, albeit to a lesser extent, promotes charge loss through the smooth muscle membrane through the high-resistance myoendothelial gap junctions. While charge does conduct to the endothelium, its effects on Vm will be subtle due to an endothelial cell's robust expression of gap junctions and low input resistance. The preceding observations do not suggest that smooth muscle cells are entirely unable to alter the endothelial Vm. Indeed, it could be argued that if a sufficient number of smooth muscle cells were stimulated simultaneously, sufficient charge could spread to initiate a substantive voltage response in the endothelium (Fig. 5). This possibility was supported by simulations that documented progressive changes in endothelium Vm as the number of voltage-clamped smooth muscle cells increased. Remarkably, a quasi-isopotential behaviour was achieved between the two cell layers when 40 of the 44 smooth muscle segments were simultaneously clamped. This near-parallel behaviour has been observed in retractor muscle feed arteries activated by elevated intravascular pressure, a stimulus that depolarizes the smooth muscle layer (Emerson & Segal, 2000a, b; Emerson et al. 2002).
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While localized smooth muscle depolarizations conduct poorly, our findings do not suggest that all depolarizing signals are unable to spread. Indeed, Fig. 2C reveals that depolarization can readily conduct if endothelial cells are stimulated. As previously noted (Segal et al. 1999; de Wit et al. 2000; Kumer et al. 2000; Kurjiaka et al. 2005), depolarizing agents like KCl elicit disparate conducted responses in skeletal muscle arteries, a result which has fostered disparate views on electrical communication. This disparity may simply reflect the strength of a KCl stimulus delivered subluminally, with low intensity solely affecting smooth muscle Vm and a higher intensity directly influencing both cell types. Findings in Fig. 5 also indicate that if smooth muscle depolarizing stimuli are not sufficiently localized, a greater number of stimulated smooth muscle cells could charge the underlying endothelium and elicit conducted responses.
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As illustrated in Fig. 6, cellular orientation and coupling resistance under ‘normal’ conditions appear to favour the endothelium as the principal pathway for conduction along the vessel axis. To further highlight this important physical property of the arterial wall, simulations were performed in which the conduction of an endothelium-initiated response was assessed prior to and following the disruption of endothelial cell (Fig. 7) or smooth muscle cell (Fig. 8) communication. Our model predicted that the disruption of endothelial cell, but not smooth muscle cell, communication within a restricted region effectively prevented endothelium-initiated responses from conducting beyond the site of disruption. These predictions nicely paralleled functional observations from hamster retractor muscle feed arteries where the disruption of endothelial communication notably impaired the conduction of hyperpolarization and vasodilatation induced by acetycholine (Emerson & Segal, 2000a). Remarkably, focal disruption of endothelial cells has yielded similar findings in other resistance vessels of striated muscle (Looft-Wilson et al. 2004) but not in the hamster cheek pouch (Bartlett & Segal, 2000). This apparent disparity highlights the ability of electrical phenomena to conduct robustly along either cell layer of some resistance arteries (Welsh & Segal, 1998). The structural or electrophysiological properties that enable electrical conduction along the smooth muscle cell layer of one vessel type but not another remains unclear. Key factors such as cell orientation and gap junction expression do not appear to be dramatically different in this tissue (Little et al. 1995a,b; Sandow et al. 2003). One possibility is that, as charge spreads to a neighbouring smooth muscle cell, a novel ionic conductance triggers a regenerative event. Additional studies are required to resolve such proposed behaviour.
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The preceding observations provide new insight to our understanding of blood flow regulation in skeletal muscle. For example, it has been proposed that in order to match blood flow delivery with metabolic demand, arterial segments within a vascular tree must respond both in isolation and in conjunction with its neighbours (Segal & Duling, 1986a; Segal & Jacobs, 2001). An arterial segment responding in isolation can subtly alter flow to a specified region without over- or under-perfusing other areas of varied metabolic demand. In contrast, more encompassing changes in segmental tone would enable a vascular network to dramatically increase regional blood flow during high metabolic activity. Our simulations illustrate that localized changes in arterial tone can be attained if vasoactive stimuli directly modulate a small number of smooth muscle cells. In contrast, coordinated changes in contiguous vascular segments can be achieved if vasoactive stimuli were to electrically influence: (1) a small number of endothelial cells; or (2) a substantive number of smooth muscle cells.
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STOC transformation
In resistance vessels, studies of cell-to-cell communication traditionally contextualize gap junctional function within the confines of longitudinal conduction. Recent work, however, has asserted that gap junctions are also important in transforming transient electrical events, like STOCs, into a sustained voltage response (Jaggar et al. 2000; Herrera et al. 2001). In theory, gap junctions facilitate such a transformation by: (1) combining the capacitive effects of individual cells; and (2) allowing current to be distributed among neighbouring cells. The collective result is an arterial wall that functions as a low-pass filter that ‘smooths’ the effects of individual charge impulses both spatially and temporally. Consistent with this view, sustained hyperpolarization was achieved in our control virtual artery when smooth muscle cells were programmed to randomly produce two STOCs per second (Fig. 9).
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The filtering capabilities of this arterial capacitor should be compromised with the removal of gap junctions, particularly those of the highest conductances. This reasoning explains why the elimination of smooth muscle cell-to-smooth muscle cell gap junctions (coupling resistance, 90 M) had a more pronounced effect on STOC transformation than the removal of myoendothelial gap junctions (coupling resistance, 1800 M). While the elimination of gap junctions between smooth muscle cells initiated the appearance of transient phenomena, these events were superimposed onto a subtle but sustained hyperpolarization. The sustained hyperpolarization is explained by charge spreading through myoendothelial gap junctions and the endothelium's continued ability to filter, transform and summate STOCs. Indeed, the model illustrates that blocking the spread of charge into the endothelial capacitor eliminated this subtle hyperpolarization. These predictions provide insight into how the smooth muscle and endothelial cell layers work cooperatively with one another to optimize STOC transformation.
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Summary
Electrical communication in skeletal muscle resistance arteries was explored by developing a computational model that assigned discrete properties to individual vascular cells and by comparing predicted observations with published results obtained from intact pressurized vessels. Our findings revealed that, in contrast to a functional syncytium, electrical signals spread differentially among and between endothelial cells and smooth muscle cells. The two principal factors that establish differential electrical communication within the vessel wall are cell orientation and coupling resistance. We conclude that the intrinsic biophysical properties of endothelial cells and smooth muscle cells enable both local and regional control of tissue blood flow.
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Supplemental material
The online version of this paper can be accessed at: DOI: 10.1113/jphysiol.2005.090233
http://jp.physoc.org/cgi/content/full/jphysiol.2005.090233/DC1
and contains video clips corresponding with Figs 2, 4, 7, 8 and 9.
This material can also be found as part of the full-text HTML version available from http://blackwell-synergy.com
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