Stochastic model of endothelial TRPV4 calcium sparklets: effect of bursting and cooperativity on EDH

Abstract

We examined the endothelial transient receptor vanilloid 4 (TRPV4) channel's vasodilatory signaling using mathematical modeling. The model analyzes experimental data by Sonkusare and coworkers on TRPV4-induced endothelial Ca(2+) events (sparklets). A previously developed continuum model of an endothelial and a smooth muscle cell coupled through microprojections was extended to account for the activity of a TRPV4 channel cluster. Different stochastic descriptions for the TRPV4 channel flux were examined using finite-state Markov chains. The model also took into consideration recent evidence for the colocalization of intermediate-conductance calcium-activated potassium channels (IKCa) and TRPV4 channels near the microprojections. A single TRPV4 channel opening resulted in a stochastic localized Ca(2+) increase in a small region (i.e., few μm(2) area) close to the channel. We predict micromolar Ca(2+) increases lasting for the open duration of the channel sufficient for the activation of low-affinity endothelial KCa channels. Simulations of a cluster of four TRPV4 channels incorporating burst and cooperative gating kinetics provided quantal Ca(2+) increases (i.e., steps of fixed amplitude), similar to the experimentally observed Ca(2+) sparklets. These localized Ca(2+) events result in endothelium-derived hyperpolarization (and SMC relaxation), with magnitude that depends on event frequency. The gating characteristics (bursting, cooperativity) of the TRPV4 cluster enhance Ca(2+) spread and the distance of KCa channel activation. This may amplify the EDH response by the additional recruitment of distant KCa channels.

Figure 1

Schematic of the continuum EC-SMC model. (A) Two-dimensional axisymmetric model geometry with SMC and EC as rectangular domains coupled with EC MP and MEGJs. (B) Cartoon illustration describing all the channels and pumps incorporated in the EC-MP-SMC continuum model in (A).

Figure 2

Cooperativity implementation of four TRPV4 channels. (A) Four TRPV4 channels in a cluster described using a simple two-state (open and close) Markov chain model. The rate parameter β, for transition of a channel from the closed state to the open state, was increased in the presence of at least one other channel in the open state. (B) TRPV4 channels implemented using a three-state (shut, block, and open) Markov chain to capture burst opening of the channel. The rate parameter k₄ describing the transition of a channel from the shut state to the open state was increased in the presence of at least one other channel in the open state.

Figure 3

Spatial Ca²⁺ profiles resulting from a single TRPV4 channel opening. (A) Continuous opening of the TRPV4 channel for open times of 10, 100, 200, and 4000 ms resulted in micromolar Ca²⁺ concentrations progressively spreading over a larger area. (B) Contour lines (Ca²⁺ concentration equal to EC₅₀ of IK_Ca) indicate increasing Ca²⁺ spatial spread for 10, 100, 200, and 4000 ms of continuous opening of a TRPV4 channel and highlight the time evolution of the cell regions with at least 50% IK_Ca activity. To see this figure in color, go online.

Figure 4

Stochastic opening of a cluster of four TRPV4 channels implemented using a three-state Markov chain to simulate burst opening of the channel. (A) Illustrative example of a temporal profile of a single TRPV4 channel transition between the conducting (open) and nonconducting states (shut, block). (B) Example of a superposition temporal profile of the TRPV4 cluster, with the level number describing the number of open channels at a given time. (Inset) Zoomed-in view of a segment of the total simulation time for better visualization. (C) Experiment (4) (solid bar) and cooperative channel gating in the Markov model (solid checkered) demonstrated increased open probabilities of second, third, and fourth channel openings, respectively, relative to the binomial distribution (shaded) and a Markov model (shaded checkered) considering independent channels.

Figure 5

Representative example of observed temporal EC Ca²⁺ and EC V_m profiles from the stochastic opening of the TRPV4 cluster in the continuum model. (A) Superposition temporal profile of TRPV4 cluster with cooperative gating kinetics implemented using the three-state model. (Right inset) Zoomed-in view for better visualization. (B) EC Ca²⁺ concentration around the TRPV4 cluster (0.25 μm² area) arising from the TRPV4 openings in (A). (C) EC V_m transients follow the EC Ca²⁺ events. (D) Local EC Ca²⁺ concentration around the TRPV4 cluster (0.25 μm² area) observed in different stochastic simulations.

Figure 6

Increase in distance of IK_Ca channel activation arising from burst and cooperative gating kinetics in the TRPV4 cluster. (A) Ca²⁺ concentration profile in the EC and the SMC at the time of maximum Ca²⁺ spread. TRPV4 channel cluster implemented with a two-state model (top, no bursting or cooperative gating kinetics), three-state model (middle, bursting activity), and three-state model with channel interactions (bottom, bursting and cooperativity). (Contour lines) Ca²⁺ concentration equivalent to EC₅₀ of IK_Ca channels. (B) Radial distance for half-maximum K_Ca channel activation in the simulations in (A). To see this figure in color, go online.

Figure 7

Predicted V_m hyperpolarization induced by a localized Ca²⁺ increase through TRPV4 channels (Ca²⁺ sparklet). (A) Temporal EC V_m profile (bottom) indicates an average EC hyperpolarization of ∼6 mV during the bursting activity of the TRPV4 cluster (top) in the single EC/single SMC model. (B) Hyperpolarization of the endothelium as a function of sparklet frequency and IK_Ca localization, predicted for an intact vessel with EC and SMC layers coupled by MEGJ.