Electrical Communication in Lymphangions

Abstract

Contractions of lymphangions, i.e., the segment between two one-way lymphatic valves, generate the pressure gradients that propel lymph back to the circulation. Each lymphangion is comprised of an inner sheet of lymphatic endothelial cells circumscribed by one or more layers of lymphatic muscle cells (LMCs). Each contraction is produced by an LMC action potential (AP) that propagates via gap junctions along the lymphangion. Yet, electrical coupling within and between cell layers and the impact on AP waves is poorly understood. Here, we combine studies in rat and mouse lymphatic vessels with mathematical modeling to show that initiation of AP waves depends on high input resistance (low current drain), whereas propagation depends on morphology and sufficient LMC:LMC coupling. Simulations show that 1) myoendothelial coupling is insignificant to facilitate AP generation and sustain an experimentally measured cross-junctional potential difference of 25 mV, i.e., AP waves propagate along the LMC layer only; 2) LMC:LMC resistance is estimated around 2–10 MΩ but depends on vessel structure and cell-cell coupling, e.g., some degree of LMC overlap protects AP waves against LMC decoupling; 3) the propensity of AP wave initiation is highest around the valves, where the density of LMCs is low; and 4) a single pacemaker cell embedded in the LMC layer must be able to generate very large currents to overcome the current drain from the layer. However, the required current generation to initiate an AP wave is reduced upon stimulation of multiple adjacent LMCs. With stimulation of all LMCs, AP waves can also arise from heterogeneity in the electrical activity of LMCs. The findings advance our understanding of the electrical constraints that underlie initiation of APs in the LMC layer and make testable predictions about how morphology, LMC excitability, and LMC:LMC electrical coupling interact to determine the ability to initiate and propagate AP waves in small lymphatic vessels.

Introduction

The lymphatic system drains excess fluid from the interstitial compartments and pumps collected lymph back to the circulation. The pumping mechanism requires the nearly synchronized contractions of every lymphatic muscle cell (LMC) within the organizational unit, the lymphangion, which consists of the lymphatic vessel segment between two one-way lymphatic valves (1). Lymphangions are arranged in series, with valves spaced every few mm, to comprise each collecting lymphatic vessel. Each lymphatic spontaneous contraction is triggered by an LMC action potential, which spreads as an electrical wave from a pacemaking site, presumably in a single LMC, to the other LMCs of the lymphangion. The resulting contraction wave in turn generates an intraluminal pressure spike within the lymphangion chamber that surpasses the adverse pressure gradient and thereby forcing lymph downstream through the opened “output” valve. Similar to the arterial vasculature, the wall of the collecting lymphatic vessel consists of an inner sheet of lymphatic endothelial cells (LECs) covered by (one or more) layer(s) of LMCs. Although force generation in each LMC relies on excitable ion channels and excitation-contraction coupling, the factors governing the synchronization of excitation within the LMC layer and between the LMC and LEC layers are poorly understood.

Gap junctions (GJs), which are composed of connexins (Cx), facilitate communication between constituent cells of the lymphangion. At least three studies have shown that pharmacological disruption of GJs interferes with the propagation of lymphatic contraction waves (2, 3, 4); however, the nonspecific nature of the GJ inhibitors used did not allow for the identification of the Cx isoforms involved or even the determination of whether conduction occurred through one or both (smooth muscle or endothelial) cell layers. Connexins 37, 43, and 47 are known to be expressed in the endothelial layer of the collecting lymphatic vessels of mice (5). The Cx isoforms in the smooth muscle layer have not been identified, nor have the existence, composition, or density of myoendothelial GJs (MEGJs) in collecting lymphatics. However, a single study of guinea pig lymphatics suggested that only 1 in 12 vessels showed any degree of electrical coupling between LECs and LMCs (2, 6). This finding contrasts with that for arterioles, in which extensive coupling between the endothelial cell (EC) and smooth muscle (SM) layers occurs through a relatively high density of MEGJs (7, 8), resulting in synchronized changes in the membrane potential (V_m) of arteriolar ECs and SM cells (9). For these reasons, it is not surprising that the relative conductances between LMCs and/or between LECs and LMCs are unknown, nor is the impact of their disruption on the synchronization of lymphatic contraction waves. Although increased electrical coupling promotes synchronization (10), the ability of excitation in each individual LMC will diminish with strong coupling, i.e., charge loss to neighboring cells (11). The primary aims of this work are to address the following questions: 1) are the LMC and LEC layers coupled, and if so, how does MEGJ coupling influence the rhythmic contraction waves that are generated in and (apparently) conducted along the LMC layer? 2) What is the overall axial resistance in the lymphangion? 3) What are the implications of GJ coupling on the initiation, pacemaking, and synchronization of LMCs in the lymphangion? We addressed these questions with a combination of experimental studies on rat and mouse lymphatic vessels and mathematical modeling.

Materials and Methods

Both rats and mice were used for the experimental measurements. Estimates of LMC-LMC and LEC-LEC coupling using dual electrode measurements were made in isolated, cannulated pressurized mesenteric lymphatics from rats; obtaining and maintaining impalements in rat LMCs was relatively easy compared to dual electrode measurements in mouse LMCs. Single-electrode measurements of V_m in LMCs and LECs of mouse popliteal lymphatics confirmed that V_m values were similar to those in LMCs and LECs of rat mesenteric lymphatics. Morphological measurements, however, were made on pressurized popliteal lymphatic vessels from mice for several reasons: 1) it is from mouse vessels that the most quantitative information on contraction wave conduction parameters is available; 2) GFP reporter mice facilitate morphological measurements of LMC and LEC density and orientation; 3) V_m values for LECs and LMCs in mice are approximately the same as those in rats; and 4) the availability of knockout mice ultimately will make mouse vessels useful in terms of quantifying which Cx isoforms contribute to LMC-LMC, LMC-LEC, and LEC-LEC conductances.

Animal handling

A rat or mouse was anesthetized with pentobarbital sodium (Nembutal; 60 mg/kg, intra-peritoneal injection) and placed on a heating pad. In the rat, an afferent mesenteric lymphatic vessel was identified and isolated after the small intestine was exteriorized through a 2–3 cm midline incision. In the mouse, a popliteal afferent lymphatic vessel was exposed through a superficial incision in the calf as described previously (12). After removal, the respective vessels were pinned with short pieces of 40 μm stainless steel wire in a Sylgard (Sylgard 184; Dow Corning, Midland, MI) chamber filled with Krebs-BSA solution (see below), and the majority of the attached adipose and connective tissue was cleared by microdissection. The isolated vessel was then transferred to a 3-mL observation chamber, cannulated onto two glass micropipettes, pressurized to 3 cmH₂O, and trimmed of remaining connective tissue and fat at room temperature. The animal was euthanized with Nembutal, 100 mg/kg, intra-cardiac injection. All animal procedures were approved by the Animal Care and Use Committee of the University of Missouri and were conducted according to the National Institutes of Health Guide for the Care and Use of Laboratory Animals (eighth edition, 2011).

Images of LMC distribution in mouse popliteal vessels were made from selective GFP expression in LMCs of SMMHC-CreERT2;Cx45f/f mice after induction with tamoxifen. The Cx45-floxed construct expressed eGFP in each recombined cell when Cx45 was excised; recombination occurred in >98% of LMCs. LECs were imaged using either Prox1-GFP mice (a gift of Y. Hong, University of Southern California) or Prox1CreERt2;Rosa26mTmG mice treated with tamoxifen. In the latter, GFP fluorescence is evident only in the LECs, whereas all unrecombined cells, most prominently LMCs, display tdTomato fluorescence.

Pressurized vessel methods

The cannulated vessel, with micropipette holders, observation chamber, and pipette mounting system, was transferred to the stage of an inverted microscope (IM-405; Zeiss, Oberkochen, Germany), and the preparation was heated to 37°C using a circulating water bath. Fluorescence measurements used an Olympus IX81 inverted microscope equipped with a Yokagawa CSU-X Confocal Spinning Disk (Andor Technology, Belfast, UK). After a 30–60 min equilibration period, wortmannin was added (final concentration 2 μM) to the bath solution to inhibit myosin light chain kinase and eliminate contraction-associated vessel movement during imaging until contractions were below ∼3 μm.

Intracellular recording of V_m

Impalements into LMCs or LECs were made using intracellular microelectrodes (300–350 MΩ) filled with 1 M KCl, and membrane potential (V_m) was sampled at 1 KHz using an NPI SEC-05X amplifier (ALA instruments, Farmingdale, NY). The maintenance of residual contractions allowed simultaneous tracking of diameter and V_m. Once impaled, V_m was allowed to settle for 15–30 s. Once the recording had been made or was lost because of movement, the electrode was retracted, and the offset potential was subtracted from the recorded values. For dual electrode recordings, an Axoclamp2A amplifier (Axon Instruments, Scottsdale, AZ) was used to record V_m at the distal site and an NPI SEC-05X amplifier recorded V_m at the local site in current clamp mode, after capacitance compensation, for accurate V_m measurement during simultaneous current injection.

Patch clamp

Cleaned lymphatic vessels were heated to 37°C in low-Ca²⁺-digestion solution containing (in mM) 144 NaCl, 5.6 KCl, 0.1 CaCl₂.2H₂O, 1.0 MgSO₄, 0.42 Na₂HPO₄.H₂O, 0.44 NaH₂PO₄.H₂O, 4.17 NaHCO₃, 10 HEPES, and 5 D-glucose (pH adjusted to 7.4 with NaOH, 25°C) at 37°C for 10 min and subjected to two digestion steps: 1) with 1 mg/mL dithioerythritol (D8161-5G; Sigma, St. Louis, MO) and 1 mg/mL (mouse) papain (P4762-1G; Sigma) added to the low-Ca²⁺-digestion solution; 2) with 0.5 mg/mL collagenase H (C8051-1G; Sigma), 0.7 mg/mL collagenase F (C7926-1G; Sigma) and 1 mg/mL soybean trypsin inhibitor II (T9128-1G; Sigma) added to the low-Ca²⁺-digestion solution. After digestion, the remaining vessel fragments were rinsed with ice-cold digestion solution and triturated with a fire-polished Pasteur pipette to release single cells. Isolated muscle cells were stored in ice-cold solution to stop enzymatic digestion and used within 4–6 h. Whole-cell patch-clamp recordings were performed at room temperature using an EPC9 amplifier (HEKA, Bellmore, NY) controlled by Pulse software (HEKA) as described previously (13). Recording electrodes (resistance from 3 to 5 MΩ) were backfilled with pipette solution. Pipette movement was controlled with a hydraulic manipulator (MO-102; Narishige, Tokyo, Japan).

Solutions

Krebs buffer for isolated vessel protocols contained (in mM): 146.9 NaCl, 4.7 KCl, 2 CaCl₂⋅H₂O, 1.2 MgSO₄, 1.2 NaH₂PO₄⋅H₂O, 3 NaHCO₃, 1.5 NaHEPES, and 5 D-glucose (pH 7.4 at 37°C). Dissection and pipette solutions were Krebs plus the addition of purified 0.5% bovine serum albumin (BSA). The bath solution for patch-clamp recordings contained the following (in mM): 1.8 mM CaCl₂, 110 NaCl, 1 CsCl, 1.2 MgCl₂, 10 HEPES, and 10 D-glucose (pH adjusted to 7.4 with NaOH). The patch pipette solution contained the following (in mM): 135 KCl, 10 HEPES, 10 ethylene glycol-bis(β-aminoethyl ether)-N,N,N',N'-tetraacetic acid, and 5 MgGTP (pH adjusted to 7.2 with CsOH). All chemicals were obtained from Sigma except for BSA (US Biochemicals, Cleveland, OH), MgSO₄, and HEPES (Fisher Scientific, Pittsburgh, PA).

Computational modeling

A simple model of electrical communication in lymphangions was developed based on classical Hodgkin-Huxley formalism to calculate V_m in each cell within the virtual vessel. Two sets of models were derived: 1) a static model used to estimate GJ coupling and 2) a dynamic model to investigate V_m oscillations. A virtual lymphangion structure was modeled as described previously in arterioles (14). Cell models are described below. The partial differential equation was reduced to a set of ordinary differential equations using the finite difference method and solved using CVODE 2.7.0 from Sundials (15) using relative tolerance of 1E-4 (absolute tolerance of 1E-9). Model (1): A simple steady-state model was employed:

$$\frac{\partial {\text{V}}_{\text{m}}}{\partial t}=\frac{-1}{C_{\text{m}}}\left(\sum {\text{I}}_{\text{PM}}+{\text{I}}_{\text{GJ}}+{\text{I}}_{\text{MEGJ}}+\text{I}\right)\text{,}$$ (1)

where C_m is cell capacitance, I_PM is current across the plasma membrane (PM), I_GJ is current through homocellular GJs, and I_MEGJ is current through MEGJs, i.e., between the LEC and LMC layer. Finally, I is externally applied current. Briefly, a vessel structure with electrically sealed ends consisted of LMCs and LECs oriented perpendicular and parallel, respectively, to the vessel segment axis. Each cell is characterized electrically as a capacitance linked in parallel with a nonlinear resistor represented by measured current-voltage (IV) curves of isolated LECs and LMCs in physiological solution (see below). In the model, each cell is coupled homocellularly to immediate neighbors in a barrel-shaped fashion, whereas each LEC is coupled to every LMC located immediately external and adjacent to the LEC.

Parameters were estimated by fits to patch-clamp and dual-stick experiments as described below. Specifically, patch clamping of isolated LECs and LMCs was used to estimate the average cell capacitance of each cell type, and I_PM was modeled as a simple polynomial fit to IV curves: ${\text{I}}_{\text{PM}}\left({\text{V}}_{\text{m}}\right)=a_x+b_x{\text{V}}_{\text{r}}+c_x{\text{V}}_{\text{r}}^2+d_x{\text{V}}_{\text{r}}^3+e_x{\text{V}}_{\text{r}}^4$, where a_x, b_x, c_x, d_x, and e_x are polynomial coefficients, V_r = V_m − V_x, and subscript x denotes either LEC or LMC, respectively. GJ current was assumed to be ohmic, i.e., ${\text{I}}_{\text{j}}=\mathit{\Delta }{\text{V}}_{\text{j}}/{\text{R}}_{\text{j}}$, where ΔV_j is the transjunctional potential difference between any two coupled cells. MEGJ rectification was modeled using a Gaussian expression, ${\text{I}}_{\text{MEGJ}}=\mathit{\Delta }{\text{V}}_{\text{j}}/{\text{R}}_{\text{MEGJ}}exp\left(-{\left(\mathit{\Delta }{\text{V}}_{\text{j}}-V_{\mu }\right)}^2/V_{\sigma }^2\right)$, i.e., V_μ and V_σ denote the optimum and width of the Gaussian. Sharp intracellular electrode recordings were used to determine intercellular coupling. The model generator framework described in (14) facilitated easy alterations in morphological layout. In the core lymphangion, LMCs were oriented perpendicular to the vessel axis in a barrel-shaped fashion. External to this layer, a variable set of LMCs could be added such that each additional LMC was axially oriented and distributed in regular intervals along the lymphangion.

Model (2): The Morris-Lecar model (16) was used as a simple phenomenological model of a class I oscillator to simulate an action potential and was tweaked to fit observed V_m oscillations driving rhythmic contractions.

$$\frac{\partial {\text{V}}_{\text{m}}}{\partial t}=\frac{-1}{C_{\text{m}}}\left(I-g_{\text{Ca}}\times \left({\text{V}}_{\text{m}}-{\text{V}}_{\text{Ca}}\right)\times \left(1+tanh\left(\frac{{\text{V}}_{\text{m}}-{\text{V}}_1}{{\text{V}}_2}\right)\right)-g_{\text{K}}\times W\times \left({\text{V}}_{\text{m}}-{\text{V}}_{\text{K}}\right)-g_l\times \left({\text{V}}_{\text{m}}-{\text{V}}_l\right)\right)$$

$$\frac{\partial W}{\partial t}=\left(\frac{1}{2}\left(1+tanh\left(\frac{{\text{V}}_{\text{m}}-{\text{V}}_3}{{\text{V}}_4}\right)\right)-W\right)\times \left(\tau \times cosh\left(\frac{{\text{V}}_{\text{m}}-{\text{V}}_3}{2{\text{V}}_4}\right)\right).$$ (2)

Here, g denotes conductance of 1) leak (g_l), 2) Ca²⁺ current (g_Ca), and 3) repolarizing K⁺ current (g_K). W is a variable that describes the open-state probability of the K⁺-conductance. V_Ca and V_K denote the Nernst potentials of Ca²⁺ and K⁺, respectively, whereas V_l is the resting potential of the cell (leak). V₁ describes the location of the IV-curve upshot, V₂ describes the inverse steepness of the N-shaped upshot, V₃ describes the location of the “middle” upshot, and V₄ determines the steepness of the regeneration upshot. Finally, τ describes the timescale of the recovery process. Parameters were fitted to recorded V_m oscillations in a rhythmically contracting lymphangion. In a subset of simulations, a heterogeneous population of LMCs was generated by introducing random values of g_l, g_Ca, and g_K in each LMC using a normal-distributed random generator (17). Model parameters are given in Table 1.

Table 1.

Model Parameters of Equations

Model 1, Eq. 1		Model 2, Eq. 2
Parameter	Value	Parameter	Value
aLEC	1.76	V1	−27.8
bLEC	44.1 × 10−3	V2	7.5
cLEC	44.5 × 10−5	V3	−17.9
dLEC	2.49 × 10−6	V4	12.9
VLEC	0	VCa	96.3
aLMC	2.63	VK	−84.4
bLMC	0.11	Vl	−33.9
cLMC	98.5 × 10−5	gCa	0.1
dLMC	5.24 × 10−5	gK	1.0
eLMC	7.78 × 10−7	gl	0.3
VLMC	−14.4	τ	0.44

Limitations

The computational models used in our study are simplified, allowing for direct estimation of model parameters from experimental data but consequently leaving out a number of important regulators of lymphatic function. In particular, the models disregard the impact of mechanical (pressure, flow) factors and paracrine/endocrine factors from nervous or immune origin. The steady-state model is limited by the disregard of dynamics (e.g., no oscillations). The dynamic model is purely phenomenological, albeit fitted to spike trains recorded from actual lymphangions. As seen in Fig. 1 B, the fit is not perfect, and although the qualitative electrical behavior of the model is congruent with experimental recordings, some parameters are not fully identifiable. For example, the spiking threshold is not uniquely determined from the data. Hence, the simulations should be viewed as qualitative descriptions of system behavior subsequent to electrical perturbations introduced via current injections into one or more LMCs.

Figure 1.

Lymphangion morphology and electrophysiology drive model setup. (A) Popliteal lymphangion morphology is shown. Representative lymphangions of transgene mice that either express eGFP via a smooth muscle myosin heavy chain promotor (upper panel) or express eGFP via the endothelial-specific Prox1 promotor (lower panel) are shown. Lower right shows the average values of key metrics used in the computational lymphangion model. (B) Sharp microelectrode recordings of a lymphangion are shown. The brightfield image shows two microelectrodes (shades at (A) and (B)) that were impaled into LMCs at different positions along an isolated and pressurized lymphangion. Vessel diameter (black trace) and LMC membrane potentials (red and black traces) were recorded simultaneously. Contraction waves were inhibited using the L/T Ca²⁺-channel inhibitor mibefradil, which removes the effect of VGCCs on resting V_m, i.e., allows for subsequent injection of depolarizing or hyperpolarizing current pulses from a stable baseline V_m. V_m,rest of popliteal LECs is ∼−70 mV, whereas V_m,rest of LMCs is ∼−37 mV (see text). The lower panel shows an enlarged section of an AP train recorded from a single LMC (black curve) and model fit (Eq. 2, red curve). (C) Whole-cell patch-clamp electrophysiology is shown. The upper panel shows the LEC model. A polynomial was fitted (black curve) to averaged whole-cell patch-clamp data ($\circ$, N = 11). A linear leak current (dashed gray) was subtracted to obtain an IV curve (blue curve) with a resting V_m that fit the resting potential of LECs in intact lymphangions $(\diamond )$. The lower panel shows the LMC model. Similarly, subtraction of a linear leak current (dashed gray) from the polynomial fit (black curve) to averaged whole-cell patch-clamp data ($\circ$, N = 9) produced an IV curve (red curve) with a resting V_m equal to the resting V_m of LMCs in intact lymphangions $(\diamond )$. (D) A schematic of model morphology is shown. Based on the calculated average number of cells in the LEC and LMC layers, connectivity in the initial model assumed six coupling neighbors per LEC and two coupling neighbors per LMC. To see this figure in color, go online.

Analysis

Custom curve fitting scripts employed the curve_fit algorithm from SciPy 0.17.0. The dynamic fitting scheme was based on a best-fit solution between simulation of parameter changes and the data-series.

AP wave speed was calculated using a custom algorithm that calculated the average of paired values of membrane potential and time at 25, 29, and 33% of the action potential upstroke within two LMCs (first and last by default). The distance between LMCs was divided by the average time difference.

To calculate the number of action potentials (APs) per minute, the simulation time of electrical dynamics was set to 45 s, of which the last 30 s was used to find cycles per minute (cpm) using the peak finding Python package “PeakUtils.”

Results

Setting up electrical lymphangion models

To estimate relative GJ conductances in popliteal lymphangions, we applied a simple computational modeling approach. The cellular structure of the virtual lymphangion was developed utilizing straightforward measures of morphological data from confocal images of popliteal lymphangions expressing GFP selectively in LMCs or LECs (see Fig. 1 A). Like the arteriovenous system, smooth muscle cells wrap around an endothelial sheet. This arrangement prompted an initial development of a barrel-shaped sheet of LECs oriented along the vessel axis, enclosed by a barrel-shaped layer of LMCs oriented perpendicular to LECs. Regarding homocellular GJ coupling (disregarding vessel ends), each LEC was coupled to six (two axial and four circumferential) neighbors, whereas each LMC was coupled to the two immediate axial neighbors (Fig. 1 D), as one LMC encompasses the circumference in small popliteal lymphangions. The two layers were coupled via homogeneously distributed myoendothelial GJs. Sharp microelectrode impalements of cells in intact lymphangions, pressurized to 3 cmH₂O, revealed a large discrepancy between resting potentials (V_m,rest) in the two cell layers: −42 ± 1.1 mV in rat mesenteric LMCs (N = 19) and −37.4 ± 1.2 mV in mouse popliteal LMCs (N = 11) versus −66.8 ± 1.3mV in rat mesenteric LECs (N = 14), −64 mV in mouse Ing-Ax LECs (18), and around −70 mV in isolated LEC tubes from mouse popliteal lymphangions, (see Fig. 1 B) (18). The measurements of LEC resting potentials are consistent with previous recordings in guinea-pig mesenteric LEC (−71.5 mV) (6). The similarity of V_m,rest in LECs and LMCs across lymphatic tissues prompted use of endogenous V_m,LMC = −40 mV and V_m,LEC = −70 mV in the model. Lymphangions in the oscillatory state displayed a rhythmic series of APs as shown in Fig. 1 C, bottom. Data traces were used to estimate the parameters of the oscillatory model (Eq. 2).

Under steady-state conditions, currents across PMs, I_PM, were estimated by whole-cell electrophysiological recordings from isolated LECs and LMCs, respectively, in physiological bath and pipette solutions (circles in Fig. 1 C). For reasons not fully understood, the reversal potentials of patched LECs and LMCs were both depolarized to the measured resting potentials in intact lymphangions in vitro. The discrepancy could arise from a number of factors, including the different temperatures (37°C for V_m recording, 25°C for patch-clamp recording) or partial cell damage during enzymatic isolation and/or the effects of cell dialysis with an artificial intracellular solution. To align the reversal potential of patched LECs and LMCs to the measured resting potentials, the polynomial models of I_PM (Eq. 1) were estimated by subtracting a linear leak current from the fit to patch data. Finally, average measured capacitance, C_m, of LECs (12.8 pF) and LMCs (25 pF) were used in both models (Eqs. 1 and 2).

Assessment of steady-state MEGJ conductance

The discrepancy between LEC and LMC resting potentials suggests weak myoendothelial coupling, yet differences could be due to vigorous ion transport activities and/or heterotypic GJ expression, leading to rectification of GJ conductances. Given a homogeneous expression of myoendothelial junctions along the vessel axis, radial current spread is independent of homocellular GJ coupling (for which values observed in arteries were arbitrarily assigned (19)). The model could therefore be used to simulate resting potentials of the LEC and LMC layers as a function of increasing MEGJ conductance (Fig. 2 B). A resting potential difference of around 25 mV between cell layers is contingent upon very low MEGJ conductance. With increased endothelial C_m, the difference in V_m,rest becomes even more robust against high MEGJ conductance as loading of cell capacitors requires more current (the semitransparent curve in Fig. 2 B).

Figure 2.

MEGJ resistance is high in lymphangions. Resting states of LECs (blue) and LMCs (red) were simulated under different scenarios affecting MEGJ currents. (A) A control MEGJ model is shown. Normalized conductance of MEGJs is 1 when the transjunctional potential difference (ΔV_j) is less than ∼40 mV as is the case here, i.e., E_m,LMC − E_m,LEC = 30 mV (yellow shading). Outside this region, conductance rapidly quenched. (B) Resting potentials of coupled LEC (blue) and LMC (red) were calculated as a function of increasing (homogeneously spread) MEGJ resistance in simulations. Note that MEGJ resistance must be in the high GΩ range to maintain a ΔV_m > 25 mV. The semitransparent curves show the same simulations upon increasing C_m,LEC to 25 pF. (C) Models of asymmetric signal transfer in heterotypic Cx40/Cx45 junctions are shown ((21): left shift (orange), right shift (green)). (D) Simulations as in (B) with resting potentials resulting from the left-shifted (orange) or right-shifted (green) MEGJ models plotted against R_MEGJ are shown. The semitransparent curves show the same simulations plotted against actual MEGJ resistance per LMC calculated using the models in (C). (E) The steady-state membrane current of the LMC (I_PM,LMC) was either doubled (orange) or halved (green). (F) Simulations as in (B) with resting potentials from doubled (orange) or halved (green) I_PM,LMC models are shown. To see this figure in color, go online.

We also tested the effect of MEGJ rectification, based on the known biophysical properties of Cx45:Cx37 and Cx45:Cx40 heterotypic GJs (20, 21). MEGJ rectification (Fig. 2 C, orange and green curves) does not circumvent the constraint that high MEGJ resistance is required to maintain a voltage difference around 25 mV. Although rectification seemingly allows for less MEGJ resistance (particularly the left-shifted orange curve, Fig. 2 D), this is an artifact due to plotting against the minimal R_MEGJ: with rectification, the actual MEGJ resistance is always higher but depends on the given ΔV_j (Fig. 2 B). Plotting V_m,rest against actual MEGJ resistance (semitransparent curves in Fig. 2 D) yields the same curves as in Fig. 2 B because at steady state, I_PM must balance I_MEGJ (Eq. 1), and therefore a given ΔV_j is reflected by a given actual MEGJ resistance.

Finally, neither doubling nor halving steady-state LMC membrane currents (I_PM,LMC; see Fig. 2, E and F) substantially increased the resting MEGJ conductance required for a potential difference of ∼25 mV between the two cell layers. However, the figure illustrates how predominant membrane currents (including total capacitance) within both the LMC and LEC layers affect the influence of MEGJ coupling on resting potentials of the two cell layers.

Morphology, GJ coupling, and axially oriented LMCs determine electrical spread in lymphangions

The conclusion of little-to-no MEGJ coupling in simulated lymphangions renders intracellular coupling in the endothelium largely irrelevant for electrical synchronization of LMC contractions and therefore simplifies estimation of GJ coupling within the contractile LMC layer. Estimation of intercellular LMC coupling was based on model-based fits to V_m recordings from dual microelectrode impalements of isolated and pressurized (3 cmH₂O) rat mesenteric lymphangions. Fig. 3 A shows local impalements of two LMCs and simultaneous recording of diameter and membrane potential. Spontaneous spiking was inhibited by addition of mibefradil, a voltage-gated calcium channel inhibitor, enabling a stable baseline to inject hyperpolarizing current pulses. The data is summarized in Fig. 3 B at different interelectrode distances and current injections.

Figure 3.

Electrical spread efficiency in lymphangions depends on GJ coupling as well as cell and vessel morphology. (A) Defined amounts of hyperpolarizing current were injected into one microelectrode (B) while recording membrane potential deflections at both sites. (B) A summary of paired ΔE_m deflections at various positions along the lymphangion (each pair denoted by unique marker code) is shown. The amount of locally injected current is color coded. (C) Simulations of a barrel-shaped layout of LMCs (full curves) with very low LMC:LMC resistance (R_LMC:LMC = 0.45 MΩ) can only partially fit the data points (semitransparent curves) at both local and distal sites. (D) With the addition of 5 LMCs oriented axially with even distance along the lymphangion (2.4% extra LMCs), electrical conduction becomes jagged in shape, but R_LMC:LMC increased to 1.8 MΩ. (E) With the addition of 10 LMCs oriented axially with even distance along the lymphangion (4.7% extra LMCs), the smoothness of the simulation improved and R_LMC:LMC further increased to 12.8 MΩ. (F) Electrical spread depends on LMC width and coupling pattern. In otherwise identical simulations (I = 1.5 nA, R_LMC:LMC = 0.45 MΩ), electrical spread is shown to depend on 1) width of LMCs (increased by 50%, blue curve) and 2) a coupling pattern in which each LMC couples to both the nearest and next-nearest neighbors. (G) Electrical spread depends on length of lymphangion. Because of low LMC density around the valves, the LMC layer was assumed to be uncoupled (with electrically sealed ends) from neighboring lymphangions. In otherwise identical simulations, electrical spread is shown to depend on length of lymphangion: 1000 μm (black), 750 μm (red), 500 μm (blue). To see this figure in color, go online.

Electrical decay along a 1000 μm virtual lymphangion was used to fit the electrical recordings as a function of interelectrode distance (Fig. 3, C and E). In the simple barrel-shaped model (Fig. 3 C), LMC GJ resistance was estimated to be 0.45 MΩ, i.e., ∼200 times the coupling conductance reported between arterial SM cells (22). A closer look at Fig. 3 C, however, shows that although simulated V_m decays fit the local response well, the distal V_m responses were small compared to the data. Conversely, if simulations were made to fit the distal data points, the local V_m response became too small (data not shown). The basic biophysical constraint reflects the importance of the LMC input resistance: increasing GJ coupling to obtain stronger distal responses suppresses the ability of the electrical stimulus to produce a local response and vice versa. Fluorescence imaging of LMCs (see Fig. 1 A) reveals that some fraction of LMCs do not wrap circumferentially around the lymphangion but rather bend in the axial direction, with a small fraction even being oriented axially along the vessel. Theoretical and functional studies of the arteriolar system describe how the morphological layout of vascular cells has a large influence on electrical current spread (14, 19), identifying endothelium as the major electrical pathway because fewer serial PMs to cross is equivalent to smaller compounded axial resistance (lower panel in Fig. 1 A). Additional axially oriented LMCs were therefore incorporated atop the core barrel-shaped lymphangion. Although such layouts are unrealistically stylized (compare with the upper lymphangion in Fig. 1 A), subsequent simulations (Fig. 3, D and E) clearly show that the axially oriented LMCs reduce the GJ conductance required to fit the dual-stick V_m recordings (in a similar series of simulations, MEGJ resistance was set to 10 GΩ. Here, a fraction of the current spread through the well-coupled LEC layer, thereby giving rise to a slightly higher V_m response at the distal site (a few mV) at the expense of a lower input resistance).

Amplification of electrical spread may also be obtained by a change in coupling pattern, e.g., via coupling of each LMC to both neighboring and second neighboring LMCs, which effectively reduces axial resistance (Fig. 3 F, red curve; total coupling is kept identical to the control simulation in black). Similarly, a simple increase of average LMC width also amplifies electrical spread (Fig. 3 F, blue curve). In isolated arteries, electrical spread is known to depend on isolated vessel length because electrically sealed ends provide for fewer current sinks in shorter vessels (23, 24). Simulations of lymphangions differing only in length also display differences in electrical spread (Fig. 3 G). In effect, morphological variations, e.g., the relatively large variance in lymphangion length (Fig. 1 A, right) as well as twisting of LMCs (Fig. 1 A, upper panel), may partly explain the recording variance in electrical perturbations along lymphangions. Furthermore, the dependency of electrical spread on morphological layout and GJ coupling also prevents estimation of a clear-cut value of GJ conductance between LMCs.

A heterogeneous LMC population can give rise to AP waves

Rhythmic contractions in a lymphangion display frequency modulation to changes in pressure, flow (25, 26), or current. To address electrical synchronization of contractions, we therefore employed a phenomenological class I excitable cell model to LMCs of the virtual lymphangion. V_m oscillations driven by current injection into each LMC are shown in Fig. 4 A (when appropriate, wave speed was measured by averaging the time difference of the AP upstroke in two LMCs; Fig. 4 B). The proportional relationship between contraction frequency and fluid load in lymphangions is reflected in model simulations by the proportionality between frequency and amount of depolarizing current injection into each LMC of the lymphangion (Fig. 4 C). With identical LMCs, however, these V_m oscillations occur simultaneously, i.e., no electrical waves are observed and V_m oscillations display no dependency on LMC:LMC conductance.

Figure 4.

A heterogeneous LMC population gives rise to happenstance pacemaker cells. However, waves transform to simultaneous oscillations across the lymphangion if current stimulations become large. (A) A spike train along a lymphangion harboring a 5% heterogeneous LMC population is shown. (B) Wave speed is calculated by measuring the time difference in V_m upshot between the first and the last LMC in the virtual lymphangion. (C) Using the same current stimulus in each LMC of a homogeneous LMC layer, no action potential (AP) waves are produced, as each LMC behaves identically, i.e., oscillations (measured in cycles per minute, cpm) become independent of GJ coupling between LMCs (color codes) and the curves overlap completely. (D) Heterogeneous LMC populations decrease onset of oscillations threshold (see insert). Increasing amounts of current were injected into each LMC (with R_LMC:LMC = 1.5 MΩ) of lymphangions harboring either homogeneous LMCs (gray curve), 5% heterogeneous LMCs (blue curve, N = 4), or 15% heterogeneous LMCs (red curve, N = 4). Note that heterogeneity decreased the current needed to induce oscillations. (E) Heterogeneous LMC populations display AP waves upon low current injection into each LMC. Average wave speeds of 5% (blue curve) or 15% (red curve) heterogeneous LMCs as a function of injected current into every LMC of the lymphangion are shown. With strong injected currents (here, from ∼2 pA), each LMC displayed self-sustained, synchronized oscillations, i.e., simultaneous spiking in every LMC was observed. To see this figure in color, go online.

The effect of a heterogeneous LMC population on V_m oscillations was addressed by normally distributing the maximal activities of the ion channels in each LMC (Fig. 4, D and E). Heterogeneity renders individual LMCs more or less prone to initiating oscillations upon stimulation. Because of coupling, however, a local AP induces APs in neighboring LMCs. Thus, heterogeneity decreases the amount of stimulation (applied to every LMC) required to initiate APs in one or more individual LMC(s), which in turn drives the spread of waves along the entire lymphangion (Fig. 4 D). Increases in stimulation strength, however, increase the number of LMCs displaying self-sustained oscillations. At some point, the LMCs synchronize completely across the whole lymphangion because of the strong electrical coupling (i.e., no AP waves but similar to vasomotion in arterial systems). Thus, wave speed will also increase with stimulation but slowly, with high levels of heterogeneity, as heterogeneity expands the domain in which some but not all LMCs display self-sustained oscillations (Fig. 4 E).

AP wave initiation depends on input resistance, particularly with individual pacemaker cells

We further tested how AP waves depend on electrical spread in the lymphangion. Waves were induced by current injection into the first LMC, i.e., the “pacemaker,” in the lymphangion. With no axial LMCs, robust, synchronous AP waves depend on low LMC:LMC resistance (Fig. 5 A). Both wave speed and stimulation threshold increased with lower LMC:LMC resistances. At high LMC:LMC resistances, electrical spread was insufficient either to induce signal propagation or to enable identical frequencies of induced oscillations in the pacemaker and other LMCs, leading to arrhythmic waves. The introduction of axial LMCs (Fig. 5, B and C) increased overall wave speed and the stimulation threshold to induce AP waves by reducing input resistance. Axial LMCs also increased robustness of synchronous waves as the electrical signal spread efficiently throughout the lymphangion, decreasing the likelihood of a state in which injected current, oscillation frequencies, and refractory periods are out of sync. Many axially oriented LMCs (Fig. 5 C), however, increase the likelihood of the LMC layer behaving as a syncytium with no waves. The simulations also highlight that a single pacemaker LMC requires potent current-generating capacity to overcome low overall input resistance and initiate AP waves.

Figure 5.

Weak cell-cell coupling corresponds to low AP wave propagation speed and less current requirement to generate synchronized waves. Increasing amounts of current were injected into the first LMC of the lymphangion and each graph shows the AP frequencies of the stimulated LMC (local, blue curve) and the last LMC (remote site, red curve). With decreasing R_LMC:LMC (along each column), more current injection (I_stim) is required to produce oscillations. (A) Lymphangions with no axial LMCs are shown. With low R_LMC:LMC, AP initiation requires stronger stimulation current and the conduction speed increases. With high R_LMC:LMC, the local site displays a higher frequency compared to the remote site. (B) Incorporating five axial LMCs increases conduction speed and displays a wider range of fully synchronized waves upon single LMC stimulation with R_LMC:LMC between 1 and 13 MΩ. (C) This trend increases by incorporating 10 axial LMCs. In this case, low R_LMC:LMC leads to simultaneous oscillations, i.e., the lymphangion displays no AP waves. In conclusion, conduction speed varies with vessel morphology and stimulation strength. Conduction speeds of ∼$10\text{mm}/s$, as measured experimentally, seem to depend on the number of axial LMCs as well as an average R_LMC:LMC between 2 and 10 MΩ. To see this figure in color, go online.

Next, a set of models were constructed in which LMC:LMC coupling was systematically changed in either a single LMC or a segment (36 out of the 211 LMCs in the layer) in the middle of the LMC layer (Fig. 6, A and C, respectively). AP waves were initiated by current injection into a single pacemaker LMC located either at the edge or in the middle of the lymphangion (Fig. 6, A and B, respectively). AP wave-train robustness (blue to red dots representing non-to-robust AP trains) was plotted as a function of middle-segment LMC:LMC coupling (x axis) and current injection (y axis). The stimulation strength leading to robust AP waves is markedly lower if the pacemaking LMC is located at the edge of the lymphangion (compare Fig. 6 A with Fig. 6 B), whereas the effect of lowering the LMC:LMC conductance in the middle segment is relatively small (compare Fig. 6 A with Fig. 6 C). In short, at vessel edges (approximating the low LMC connectivity across valves), the virtually unidirectional current drain to neighboring LMCs provides higher input resistance and thus better facilitates initiation of oscillations compared to bidirectional current drains of LMCs located within the lymphangion. The nonrobust or arrhythmic AP wave generation obtained in an otherwise homogeneous LMC layer is a result of the complex dynamics between excitation/refraction dynamics coupled to coupling patterns and low stimulation strengths (blue to green colors in Fig. 6 E). In summary, we broadly estimate LMC:LMC conductance in lymphangions to be around 2–10 MΩ, but the specific value will depend strongly on vessel morphology, e.g., the level of overlapping/axial LMCs and/or the length of the lymphangion.

Figure 6.

Oscillations are prone to initiate at low-connectivity LMCs, i.e., at lymphangion edges. Injection of various amounts of current (I_stim) into a single LMC at either the edge (A and C) or middle (B and D) of lymphangions with R_LMC:LMC = 1.5 MΩ was performed. The effect of GJ coupling was tested by multiplying LMC:LMC conductance by a scalar (x axis) within either a single LMC (A and B) or a small segment in the middle 36 LMCs of the lymphangion (out of a total of 211 LMCs). Oscillation cpm was estimated by peak counting for each simulation and color coded (see examples in (E)): highly oscillating lymphangions in yellow to red and nonevenly oscillating lymphangions in blue to green colors, whereas purple dots denote no oscillations. (F) The valve region displays reduced LMC connectivity. Tamoxifen-treated Prox1CreERt2;Rosa26mTmG mouse vessels reveal robust LEC recombination (green, left), but no LMC recombination (red, right) across valve regions. To see this figure in color, go online.

MEGJ-facilitated current drain into LEC layer will inhibit AP waves

The ability of the lymphangion to induce and maintain oscillations depends on balancing current drains within the LMC layer such that drains do not inhibit AP induction while ensuring sufficient intercellular communication to induce depolarization of neighboring LMCs upon the AP upstroke. As shown in Fig. 7, low MEGJ resistance is equivalent to a high current drain to the well-coupled LEC layer, effectively quenching oscillations by pushing all LMCs away from the domain of self-sustained oscillations. Low MEGJ resistance therefore requires higher tonic depolarization of every LMC to induce oscillations (Fig. 7 A). Conversely, in an LMC layer with single pacemaker-induced oscillations (Fig. 7 B), the LMC:LMC resistance represents a bottleneck along the vessel that prevents higher current outflow from the pacemaker (here, injected current) to allow for initiation of AP waves at lower MEGJ resistances.

Figure 7.

MEGJ coupling impedes generation of AP oscillations. (A) With stimulation of each LMC within the lymphangion, simultaneous oscillations (no waves) may arise if MEGJ coupling is not too large to drain current (light blue curve). With larger current injections (dark blue curve), the LMC layer can afford larger current drains through MEGJs without quenching oscillations, and hence the curve is left shifted. (B) The ability to induce AP waves by stimulation of a single “pacemaker” LMC also shows dependency on MEGJ coupling. However, as wave propagation relies on reaction-diffusion, drains via MEGJs are not rescued simply by increasing injected current. To see this figure in color, go online.

Tilted LMCs provide protection of contraction waves

Presumably, most LMCs need be circumferentially oriented for efficient force generation. Although a number of axially oriented (or tilted) LMCs reduce the overall input resistance of the LMC layer (Figs. 3 and 5), we tested the effect of axially oriented LMCs on traveling V_m waves in Fig. 8. With circumferentially oriented LMCs and no MEGJ coupling (Fig. 8 A), the pumping action of the lymphangion becomes vulnerable to damage of individual LMCs (stimulation of all LMCs removes vulnerability, however, as simultaneous V_m oscillations replace AP waves). Vulnerability is relieved by a small number of axially oriented LMCs as shown in Fig. 8 B. Lastly, we tested whether the vulnerability of AP waves to LMC damage could be prevented by sufficient MEGJ coupling. In a model in which MEGJ resistance was decreased to the point at which oscillations were still maintained (see Fig. 7), no rescue of the AP wave was observed (Fig. 8 C). Furthermore, reducing MEGJ-facilitated current drain by depolarizing the LEC layer to −40 mV did not rescue the AP waves. With MEGJ coupling, the well-coupled LEC layer becomes a filter that strongly buffers against V_m changes and provides a similar amount of “filtered” current to all LMCs, i.e., reducing the propensity of AP waves.

Figure 8.

Axially oriented/overlapping cells augment viability of AP waves. A single LMC in the middle of the lymphangion was decoupled from neighboring cells resembling a damaged cell. AP waves were induced by current injection into the first LMC. (A) shows the control setting. The AP wave stops completely at the uncoupled LMC. (B) The model with five extra axial LMCs (otherwise identical to model in (A)) showed AP waves overcoming the uncoupled cell. (C) MEGJ coupling cannot rescue AP waves. AP waves in a model with no axial LMCs (as (A)) but maximal MEGJ coupling (without quenching oscillations) cannot pass the uncoupled middle LMC (C). To see this figure in color, go online.

In popliteal lymphangions, many LMCs are more or less tilted and may overlap several neighboring LMCs (see Fig. 1 A). In larger lymphangions with more layers of LMCs, the problem with single LMC damage is reduced, which may partly explain the more circumferential orientation of LMCs in larger vessels (27).

Discussion

The propagation of APs between LMCs underlies the contraction waves that propel lymph against gravity back to the subclavian veins and arteriovenous circulation. Although force generation requires robust depolarization in each individual LMC, the propagation of AP waves along the lymphangion is facilitated by GJs and by morphology. Here, we demonstrate the delicate balance of current flows that underlie AP waves and the dependence on membrane currents, cell-cell contacts, and vessel morphology. As detailed below, current spread via MEGJs and/or high LMC:LMC coupling inhibits AP waves because low input resistance decreases the V_m response to an electrical perturbation, i.e., the depolarizing current needed to fire an AP increases, and vice versa. Conversely, given that the low number of LMCs above valve regions can be equated with no or highly reduced current drains to neighboring lymphangions, the likelihood of initiating APs from LMCs in this region is shown to be high. The propagation of APs depends on sufficient LMC:LMC coupling to allow for regeneration of signal in neighboring cells but also depends on overlapping LMCs to ensure robust AP waves. Although these simulations cannot discriminate whether oscillations are initiated by specialized pacemaker cells, the simulations suggest that if single pacemaker cells are present, the current-generating properties and local connectivity to other cells must somehow overcome the current drain from the surrounding tissue.

MEGJ coupling effectively drains current and impedes lymphatic contractions. The steady-state simulations of V_m,rest in Fig. 2 show that the LMC layer is electrically dominant as V_m,rest pulls toward the endogenous V_m,LMC at high MEGJ coupling. However, the measured resting potential of LECs in intact lymphangions is around the equilibrium potential for K⁺ $\left({\mathrm{E}}_{{\text{K}}^{+}}\right)$, indicating that MEGJ coupling must be low. The substantial hyperpolarization of the LEC layer relative to the LMC layer limits MEGJ coupling because of the otherwise permanent current drain from LMCs to the well-coupled LEC layer. Although the discrepancy between steady-state V_m,rest from patched and embedded cells (see above) may also affect steady-state electrophysiology, i.e., the response to electrical perturbations, the changes of total capacitance and/or overall steady-state membrane currents only change the final resting potentials if some MEGJ coupling is present (Fig. 2). At steady state, MEGJ rectification, although shown in principle to exist (20, 21), would have limited influence, as the MEGJ current at a particular ΔV_j is the same as the current in a simple ohmic MEGJ model (using an adjusted resistance), i.e., ΔV_m = I_MEGJ × R_MEGJ,rect × x = I_MEGJ × R, where x is the fraction of the maximal resistance R_MEGJ,rect. The requirements of an interlayer voltage difference (ΔV_j) of ∼25 mV and V_m,LEC around ${\mathrm{E}}_{{\text{K}}^{+}}$ are almost impossible to obtain without high MEGJ resistance. Because the highly conducting LEC layer both acts as a spatiotemporal buffer of V_m changes and facilitates current drain, anything but minimal degrees of MEGJ coupling will hamper AP generation in LMCs. Hence, stronger stimuli of all LMCs are required to initiate oscillations; higher current output from individual pacemaker cells cannot overcome the bottleneck of LMC:LMC coupling in addition to widespread current drain to the LEC layer (Fig. 7, see below), that is, MEGJs counteract the function of a pacemaker cell. Furthermore, as charge equilibrates quickly within the LEC layer, reentry of current into the LMC layer interferes with excitation dynamics in LMCs and quenches AP waves, explaining why homogeneous MEGJ coupling cannot rescue decoupling of one or more LMCs in a “barrel-shaped” layout (Fig. 8). Our simulations would therefore suggest that MEGJ plaques, if present in some lymphangions, would likely be heterogeneously distributed.

Morphology and electrical coupling underlie the relation between electrical sensitivity and spread

Strong LMC:LMC coupling naturally augments electrical spread (Fig. 3) and the speed of AP waves. However, strong coupling also reduces input resistance; hence, a larger electrical perturbation would be required to elicit an AP (Fig. 5). Excitation-diffusion systems are not highly dependent on high cell-cell coupling compared to systems displaying electrotonic spread, as current is regenerated in each cell (LMC), i.e., the signaling requirement is reduced to a perturbation of neighboring cells above the spiking threshold. However, the interplay between electrical spread and excitation dynamics (particularly in frequency-modulated oscillators) can lead to arrhythmic AP waves upon low LMC:LMC coupling due to different oscillation frequencies, i.e., more coupling increases the likelihood of synchronous AP waves. Although the variable extent of morphology and noncircumferential LMCs among lymphangions obscures a clear-cut estimation of LMC:LMC resistance, we broadly estimate it to be around 2–10 MΩ, i.e., a much higher coupling compared to arterial smooth muscle. The capacity for electrotonic current spread in arterial networks is known to be modulated by the morphology and connectivity of the constituent cells (14, 19). The principle of total resistance being the sum of serial resistors along a finite segment explains why axial orientation of endothelial cells provides for efficient electrical spread, whereas the circumferential orientation of smooth muscle cells provides for high input resistance. As electrical spread depends on vessel length (Fig. 3 G), the variability of lymphangion length (Fig. 1)—combined with low LMC density around valve-regions (Fig. 6 F)—likely translates to variability in LMC:LMC resistance. Likewise, the tilted and/or axial orientation of a fraction of LMCs in popliteal lymphangions allows for maintenance of a high input resistance, i.e., higher electrical sensitivity toward electrical perturbations, while enhancing the capacity for electrical spread (Fig. 3) and rapid synchronized AP waves (Fig. 5). Furthermore, tilted LMCs provide protection against localized cell damage that could otherwise short-circuit AP waves in an LMC layer of nonoverlapping cells (Fig. 8). The LEC layer cannot provide similar protection, as MEGJ coupling is low and generally impedes AP wave induction (see above). In the arterial system, however, the well-coupled EC layer is appropriately positioned to protect against localized cell damage, as vascular function does not rely on contraction wave generation (as blood flow is generated by the heart). A possibly similar protective role for axially oriented smooth muscle cells in the GI tract and the lower urinary tract is not known; in those cases, however, propulsion is peristaltic and does not depend as critically on a synchronized wave to develop a pressure head that has to open a valve as in the lymphangion.

Electrical coupling patterns influence initiation of oscillations and pacemaking

Electrical pacemaker cells are well known in contractile tissues such as sinoatrial cells of the heart or interstitial cells of Cajal in the gut (28). It is therefore natural to hypothesize that pacemaking underlies the rhythmic contractions in the lymphatic system. The purpose of pacemaking is to maintain a steady output of strong rhythmic electrical impulses that enable synchronous activity of other excitable cells within the tissue. To avoid arrhythmia and promote 1:1 phase and frequency locking, the pacemaker should fire at a slightly higher but not too high frequency, i.e., the frequency should be attuned to the capacity of electrical spread (see Fig. 5 A, high LMC:LMC resistance). Strong coupling promotes phase locking but also reduces input resistance and may interfere with the internal current-generating machinery. Ideally, lymphatic pacemaking would therefore initiate from a small cluster of cells/LMCs that reinforces the current generating machinery and protects against the current drains, which, however, are necessary for external signaling. In this work, we tested the effect of electrical coupling on oscillations initiated by current injection into a single LMC (pacemaker) or into every LMC of a heterogeneous population. Generally, pacemaker cells seem dependent on a permissive morphology that reinforces self-sustained oscillations across the paced tissue region, e.g., the mesh-like network of interstitial cells of Cajal in the gut or the sinoatrial node in the heart (29). A pacemaker cell embedded directly in the LMC layer is somewhat prohibitive because of the nonreinforcing morphology. Although a single pacemaker is possible, the pacemaker needs to generate substantial currents to overcome the current drain in the LMC layer (here, on the order of ∼200 pA, but the effects of morphology and uncertainty in model parameters prevent certainty in specific simulated values; Fig. 5). Current drain is less at the edge of the lymphangion, where input resistance is relatively high because of low LMC density across valves (Fig. 6); i.e., all else being equal, the propensity of initiating AP waves is predicted to be highest in LMCs around lymphatic valves. However, heterogeneity in the LMC population due to small variations in ion channel gene expression or fluctuations in the microenvironment may give rise to LMCs that are more (or less) prone to oscillations, i.e., heterogeneity promotes a fraction of naturally occurring “pacemaker-like” cells. Indeed, increasing heterogeneity in the LMC population decreased the overall current needed to initiate AP waves (Fig. 4). Upon stronger stimulations of each LMC, AP wave speed increases until the waves morph into simultaneous V_m oscillations because each LMC eventually enters the domain of self-sustained oscillations and synchronizes completely. Yet, higher levels of heterogeneity decrease the dependency of wave speed on stimulation. Without pacemaker cells, the domain of AP waves therefore depends on the level of LMC heterogeneity, which is likely to differ from (and certainly exceed) a 15% Gaussian distribution (17). Lymphatic contraction waves emerge upon sufficient depolarization of the LMC layer, i.e., in the direction of lower-toward-higher levels of depolarization. As such, lymphangions may seldom or never experience high levels of stimulation and may likely possess compensatory mechanisms to prevent high depolarization that are not encapsulated in our simple model. Although speculative, this could account for a heterogeneous LMC population being the driver of AP waves in lymphangions.

Finally, identical stimulation of each LMC in simulations is also an ideal, unrealistic scenario because of a number of factors, including variations in the local mechanical environment of the wall (e.g., differential tension/stretch on LMCs due to cell orientation and diameter differences at the valve sinuses), the turbulent flow patterns around valves, regional pressure spikes, and the heterogeneous distribution of neural terminals (1). Although beyond the scope of this work, the complex patterns of stimulation are easily drivers of both initiation and pacemaking of AP waves.

Conclusions

Simple computational models were assembled from electrophysiological recordings and measures of lymphangion morphology. The resulting simulations suggest that myoendothelial coupling is very low to support a high input resistance and sustain a large ΔV_j. Contraction waves are therefore facilitated by electrical spread in the LMC layer, i.e., LMC:LMC resistance is low (compared to the arterial system), but morphological features prevent excessive coupling that would otherwise impede AP generation. Indeed, LMC:LMC resistance is broadly estimated to be around 2–10 MΩ, but the value strongly depends on lymphangion length and degree of tilted/axial LMCs. Further, tilted LMCs augment axial current flow and protect AP waves against decoupling of (or damage to) individual LMCs.

Barring random fluctuations in sites of stimulation, our simulations predict that AP waves are likely to initiate at LMCs around valves. The involvement of specific pacemaker cells cannot be excluded, but single pacemaker cells embedded directly within the LMC layer are shown to experience significant current drain. The current generation requirement becomes substantially lower upon simultaneous stimulation of every LMC in the lymphangion. However, in the latter situation, heterogeneity in LMC-ion-channel expression can also drive AP wave generation; furthermore, heterogeneity reduces the amount of stimulation required for initiation. In short, the ability to generate and propagate contraction waves in lymphangions depends on the spread of initial electrical stimulations, i.e., cellular input resistances, LMC-LEC decoupling as well as LMC-LMC coupling, and the morphology of the lymphangion. This study produced verifiable predictions about the impact of coupling and morphology on AP waves. However, development of theoretical models describing the dynamic changes in both lymphatic stimulation patterns and pharmacomechanical coupling is necessary to advance understanding of lymphatic pumping function in health and disease.

Author Contributions

B.O.H. designed the research. J.A.C.-G., S.D.Z., P.G., and M.J.D. carried out all experimental work and data analysis. B.O.H. carried out all simulations and analyzed the data. B.O.H. and M.J.D. wrote the article.

Editor: Arthur Sherman.