Biophysical properties of microvascular endothelium: Requirements for initiating and conducting electrical signals

Abstract

Objective: Electrical signaling along the endothelium underlies spreading vasodilation and blood flow control. We use mathematical modeling to determine the electrical properties of the endothelium and gain insight into the biophysical determinants of electrical conduction.

Methods: Electrical conduction data along endothelial tubes (40 μm wide, 2.5 mm long) isolated from mouse skeletal muscle resistance arteries were analyzed using cable equations and a multicellular computational model.

Results: Responses to intracellular current injection attenuate with an axial length constant (λ) of 1.2-1.4 mm. Data were fitted to estimate the axial (r_a ; 10.7 MΩ/mm) and membrane (r_m ; 14.5 MΩ∙mm) resistivities, EC membrane resistance (R_m ; 12 GΩ), and EC-EC coupling resistance (R_gj ; 4.5 MΩ) and predict that stimulation of ≥30 neighboring ECs is required to elicit 1 mV of hyperpolarization at distance = 2.5 mm. Opening Ca²⁺ -activated K⁺ channels (K_Ca ) along the endothelium reduced λ by up to 55%.

Conclusions: High R_m makes the endothelium sensitive to electrical stimuli and able to conduct these signals effectively. Whereas the activation of a group of ECs is required to initiate physiologically relevant hyperpolarization, this requirement is increased by myoendothelial coupling and K_Ca activation along the endothelium inhibits conduction by dissipating electrical signals.

Keywords: endothelium; membrane potential; membrane resistance; modeling; spreading vasodilation.

Figure 1

Discrete multicellular model of endothelial tube. Idealized diamond-shaped ECs, each with length = 35 μm (L_cell), width = 8.6 μm (d_cell), and thickness d, are arranged into a cylinder (dashed lines) with N_circum (= 14) cells encompassing the circumferential direction (y) and 71 cells encompassing the axial direction (x). Under control conditions, each EC is coupled to its four immediate neighbors through gap junctions. The total number of ECs in the discrete model of an endothelial tube of length L = 2.5 mm and diameter D = 38 μm is 1988. Each EC is modeled as described in Silva et al. and contains: store-operated Ca²⁺channels (SOC); nonselective cation channels (NSC); volume regulated anion channels (VRAC); Ca²⁺-activated Cl⁻ channels (CaCC); small- and intermediate-conductance Ca²⁺-activated K⁺ channels (SK_Ca and IK_Ca); Na⁺-K⁺-ATPase (NaK); plasma membrane Ca²⁺-ATPase (PMCA); Na⁺/Ca²⁺ exchanger (NCX); Na⁺/K⁺/Cl⁻ cotransporter (NaKCl); sarcoplasmic endoplasmic reticulum Ca²⁺-ATPase (SERCA); and IP₃ receptors (IP₃R). The electrical equivalent diagram of a rectangular region (dashed red line), which incorporates four halves of ECs and four gap junctions is shown (bottom right). Each EC has a total membrane resistance R_m, each EC-EC coupling has resistance R_gj, and there are N_circum such rectangular regions in the circumferential direction. The effective membrane and axial resistivities of the endothelial tube can be derived from N_circum parallel units having membrane resistance of R_m/2 and axial resistance of R_gj over distance L_cell.

Figure 2

(a) Fittings of the cable and discrete models to experimental data. Data were taken from experiments under control conditions (red stars) and following NS309 induced opening of SK_Ca/IK_Ca (red circles), corresponding to I_stim = −1 nA of current injection. Fitting short cable equation (Eq. 10) to the control and NS309 data yields λ = 1.16±0.12 mm and 0.78±0.05 mm, respectively (dashed green lines). Fitting of the discrete endothelial tube model gives a family of ΔV_m profiles (blue dotted lines). The most negative profile corresponds to the ECs located at the circumferential position that incorporates the stimulus point. Only this profile from the discrete model was used to fit the data. The remaining profiles predict V_m responses at different positions in the circumferential direction; all merge to the same profile within ~400 μm distance from the stimulus. (b) V_m profiles in axial and circumferential directions predicted in the discrete model fitting the control data in (a). Under resting conditions, all 1988 cells have V_m = −20 mV (green dots). Each dot represents V_m in individual EC. Injection of I_stim = −1 nA into a single EC (at site indicated by arrow) creates strong V_m hyperpolarization and gradients in both circumferential (y) and axial (x) dimensions from the local site of intracellular current injection. In these simulations, values for EC membrane resistance and coupling resistance were R_m = 11.9 GΩ and R_gj = 4.5 MΩ. At distances x − x_stim> 400 μm, V_m profile is effectively isopotential in the circumferential direction, and the stimulus current spreads only in the axial direction.

Figure 3

(a–b) Estimations of the error for coupling resistance (a) and membrane resistance (b) as a function of endothelial tube circumference for different fitting schema. The discrete model with known R_m (= 11.9 GΩ) and R_gj (= 4.5 MΩ) (Fig. 1a) and control diameter D_control = 38 μm was expanded in the circumferential direction to simulate hypothetical endothelial tubes with increasing diameters (D). Model predictions of ΔV_m in response to current injection at x_stim were used to simulate V_m measurements along an endothelial tube. The simulated ΔV_m were fitted with one- and two-dimensional cable equations (Eqs. 10 and 16) to estimate R_gj,fit (a) and R_m,fit (b). The fittings were performed with ΔV_m at x−x_stim= 50, 500, 1000, 1500, and 2000 μm (in the axial direction) (diamond and square symbols), and ΔV_m only at x−x_stim≥ 500 μm (triangles and crosses). Fitting the two-dimensional equation recovers correctly R_gj and R_m (R_gj,fit/R_gj λ 1 and R_m,fit/R_m λ 1) for all diameters and data points (a, b squares and crosses). On the other hand, the one-dimensional equation overestimates R_gj (R_gj,fit/R_gj≫ 1) when applied to data with the 50 μm point from vessels > 50 μm in diameter (a, diamond symbols).

Figure 4

Impact of reduced gap junctional coupling on electrical conduction along resistance artery endothelium. (a) Representative simulation where the probability of gap junction connection between the two neighbor ECs is reduced from 100% (the control model) to 75%. (b) The resistance of individual EC-EC connections is reduced by half from the control R_gj of 4.5 MΩ in (a). In both panels the same hyperpolarizing current I_stim = −1 nA was injected into a single EC at x_stim = 100 μm. The one-dimensional short cable (Eq. 10) fit of the control profile from Figure 2a is also shown for reference to control conditions (dashed green line).

Figure 5

Impact of SK_Ca/IK_Ca activation on endothelial membrane potential and membrane resistance predicted by the isolated EC model. (a) Predicted V_m during direct maximum (100%) opening of SK_Ca/IK_Ca (NS309) followed by application of ACh (2 a.u.). To determine R_m at individual time points, current pulses were applied periodically (±0.4 pA for 2 s every 30 s), whereby the ratio of the resulting ΔV_m to the injected current corresponded to R_m. (b) Predicted changes in R_m (defined as ΔV_m/I_stim) show ~80% drop during direct SK_Ca/IK_Ca opening with NS309 and during indirect SK_Ca/IK_Ca opening with ACh (from R_m = 11.5 GΩ to R_m = 2.4 GΩ). [Ca²⁺] transient and corresponding changes in channel conductance (G) during the stimulations are shown in (c) and (d).

Figure 6

Initiation and conduction of hyperpolarization reflects how many endothelial cells are stimulated. In the discrete multicellular model, profiles of spreading hyperpolarization (V_m) in the axial direction (x) are shown for different number of ECs stimulated (N_EC,stim) with ACh. The total number of ECs N_EC,tot = 1988. In each profile (stars), ECs at the site of stimulation were exposed to saturating [ACh] (3 a.u.). The resting V_m profile is shown for reference (circles). Approximately 56 ECs require stimulation to evoke a conducted response (green crosses) similar to injecting I_stim = −1 nA (compare with Fig. 2a) and millivolt-level hyperpolarization is achieved at 2.5mm away from the local site with stimulation of 14 ECs (i.e. one column). The magnitude of hyperpolarization is a saturating function (Michaelis-Menten type) of N_EC,stim (Eq. 24).