How abundant are superoxide and hydrogen peroxide in the vasculature lumen, how far can they reach?

Abstract

Paracrine superoxide (O₂^•−) and hydrogen peroxide (H₂O₂) signaling critically depends on these substances' concentrations, half-lives and transport ranges in extracellular media. Here we estimated these parameters for the lumen of human capillaries, arterioles and arteries using reaction-diffusion-advection models. These models considered O₂^•− and H₂O₂ production by endothelial cells and uptake by erythrocytes and endothelial cells, O₂^•− dismutation, O₂^•− and H₂O₂ diffusion and advection by the blood flow. Results show that in this environment O₂^•− and H₂O₂ have half-lives <60. ms and <40. ms, respectively, the former determined by the plasma SOD3 activity, the latter by clearance by endothelial cells and erythrocytes. H₂O₂ concentrations do not exceed the 10 nM scale. Maximal O₂^•− concentrations near vessel walls exceed H₂O₂'s several-fold when the latter results solely from O₂^•− dismutation. Cytosolic dismutation of inflowing O₂^•− may thus significantly contribute to H₂O₂ delivery to cells. O₂^•− concentrations near vessel walls decay to 50% of maximum 12 μm downstream from O₂^•− production sites. H₂O₂ concentrations in capillaries decay to 50% of maximum 22 μm (6.0 μm) downstream from O₂^•− (H₂O₂) production sites. Near arterioles' (arteries') walls, they decay by 50% within 6.0 μm (4. μm) of H₂O₂ production sites. However, they reach maximal values 50 μm (24 μm) downstream from O₂^•− production sites and decrease by 50% over 650 μm (500 μm). Arterial/olar endothelial cells might thus signal over a mm downstream through O₂^•−-derived H₂O₂, though this requires nM-sensitive H₂O₂ transduction mechanisms.

Graphical abstract

Highlights

• •Physiological local H₂O₂ concentrations in vasculature lumen are up to 10's of μM.
• •H₂O₂ transport range in capillaries is just ≈20 μm.
• •Faster blood flow in arteri(ol)es transports O₂^•−-derived H₂O₂ over 100's of μm
• •Similar H₂O₂ abundances and distribution near arterioles' and arteries' walls, likewise for O₂^•−.
• •Inflowing O₂^•− may significantly feed H₂O₂ to the cytosol of endothelial cells

Abbreviations:

BAEC

bovine artery endothelial cells

EC

endothelial cell

NOX

NADPH oxidase

Prdx

peroxiredoxin

SOD

superoxide dismutase

1. Introduction

Signaling through superoxide (O₂^•−) and hydrogen peroxide (H₂O₂) released by cells to the extracellular medium mediates numerous physiological processes [[1], [2], [3], [4], [5], [6]]. However, whether such signaling is autocrine, near-cell paracrine or volume is under discussion [[7], [8], [9], [10]]. Likewise, the extracellular concentrations involved in physiological signaling remain uncertain, and this knowledge is critical to understand what intracellular mechanisms can viably transduce such signals [11,12].

Redox signaling plays a prominent role in vascular processes [4,5,[13], [14], [15], [16]]. For example, H₂O₂ may act as an agent that promotes endothelial derived hyperpolarization of vascular endothelial and smooth muscle cells by stimulating the elevation of the concentration of Ca²⁺ ions and opening of K_Ca channels. This increase in cell polarization is associated to vascular dilation [17]. The present work focuses on signaling through the microvasculature lumen, where the blood flow may help O₂^•− and H₂O₂ reach downstream cells. Mechanical and other types of stimuli to vascular endothelial cells (EC) trigger intracellular phosphorylation cascades that activate NADPH oxidase 2 (NOX2) at the plasma membrane [4]. NOX2 catalyzes one-electron O₂ reduction by cytosolic NADPH at a 2 O₂/NADPH stoichiometry. The resulting O₂^•− is released to the extracellular medium, where it has three main fates. First, it is absorbed by both erythrocytes and ECs through chloride channels [[18], [19], [20]], and then dismutated to O₂ and H₂O₂ via cytosolic superoxide dismutase (SOD1). Second, it is dismutated via extracellular superoxide dismutase (SOD3). Erythrocytes and ECs absorb the resulting H₂O₂ [21,22], which readily oxidizes the cytosolic peroxiredoxins (Prdx) 1 and 2 (k = 0.13-1.6 × 10⁸ M⁻¹s⁻¹ [[23], [24], [25], [26]]), eventually driving redox relays that transduce these signals [[27], [28], [29], [30]]. Third, it reacts extremely fast with nitric oxide (^•NO) (k = 1.9 × 10¹⁰ M⁻¹s⁻¹ [31,32]). Consequently, in the presence of typical nM ^•NO concentrations in blood plasma [33], O₂^•− has a half-life <30 ms. The resulting peroxynitrite (ONOO⁻) [34] can also cross cell membranes through anion channels and by passive permeation [[35], [36], [37]], and quickly oxidizes Prdx1/2 (k ≈ 10⁷ M⁻¹s⁻¹ [25,38]). However, most of it reacts with CO₂ (1.3 mM in plasma, k = 5.8 × 10⁴ M⁻¹s⁻¹ [32,39]) and other blood plasma components. Therefore, ^•NO production by the ECs suppresses O₂^•−-derived H₂O₂ production, and the ONOO⁻ thus formed cannot functionally replace H₂O₂ in redox signaling. To a good approximation, only the excess O₂^•− production over the ^•NO production is available for H₂O₂-mediated signaling. Contractile vessels continuously produce ^•NO to maintain their vascular tone, which should eliminate most of the O₂^•−. However, in the early moments after a stimulus that increased O₂^•− production or/and decreased ^•NO production, before the vasoconstriction response, an excess O₂^•− production can coexist with laminar flow.

Whether ECs can also directly release H₂O₂ to the vascular lumen remains contentious [15,40]. ECs abundantly express NOX4 [15,40], which catalyzes O₂ reduction to H₂O₂ by NADPH at a rate that is sensitive to physiological O₂ concentrations [41]. However, most of the NOX4 in ECs localizes to internal membranes, and evidence that some of it localizes to the cell membrane is lacking [40]. Nevertheless, there is evidence that NOX4 levels modulate H₂O₂ release by murine lung ECs and by the intact mouse aorta [15], and therefore the possibility that ECs release H₂O₂ to the vascular lumen deserves consideration.

Mathematical modeling has previously proved informative about the spatial distribution and dynamics of reactive nitrogen/oxygen species in the vasculature (eg. Refs. [[42], [43], [44], [45], [46], [47], [48]]). Therefore, here we used reaction-diffusion-advection models to estimate how far O₂^•− and H₂O₂ can travel through capillaries, arterioles and arteries, and what concentrations are attainable under conditions where ECs release O₂^•− in excess of ^•NO or release H₂O₂. We have also examined what are the main determinants of these distances and concentrations. We discuss these results in the context of other works that address the distribution, concentration and lifetimes of H₂O₂ in animal tissues.

2. Models, parameter estimates and methods

2.1. Models and methods

The implemented reaction-advection-diffusion models of the spatio-temporal dynamics of O₂^•− and H₂O₂ concentrations ($C_O$, and $C_H$, respectively) in the vasculature lumen consider the processes and geometries depicted in Fig. 1. In here, $C_O$ and $C_H$ depend on the position along the vessel, $z$, and on the distance $r$ to the center of the vessel according to the following equations:

$$\frac{\partial C_O}{\partial t}=D_O\left(\frac{1}{r}\frac{\partial }{\partial r}\left(r\frac{\partial C_O}{\partial r}\right)+\frac{{\partial }^2{C}_O}{{\partial z}^2}\right)-v\left(r\right)\frac{\partial C_O}{\partial z}-2{k_{d}C}_O-k_{O,B}Hc\left(r\right)C_O\text{,}$$ (1)

$$\frac{\partial C_H}{\partial t}=D_H\left(\frac{1}{r}\frac{\partial }{\partial r}\left(r\frac{\partial C_H}{\partial r}\right)+\frac{{\partial }^2{C}_H}{{\partial z}^2}\right)-v\left(r\right)\frac{\partial C_H}{\partial z}+{k_{d}C}_O-k_{H,B}Hc\left(r\right)C_H\text{,}$$ (2)

where the symbols have the meanings described in Table 1. We assume that blood is flowing in the laminar regime, with its velocity following Poiseuille's law, $v\left(r\right)=v_{\max }\left(R^2-r^2\right)$.

Fig. 1.

Simulated processes and geometries for capillaries (A) and arterioles and arteries (B). (Right) Simulated processes: Superoxide release at the surface of an EC ring, O₂^•− dismutation, O₂^•− and H₂O₂ advection, O₂^•− and H₂O₂ uptake by the EC and erythrocyte layers in capillaries (A) or by the EC layer and uniformly dispersed erythrocytes in arterioles (B). (Left) Schematic diagram of the simulated capillary vessel (A) with an erythrocyte-free region at the vicinity of the vessel wall, similarly to experimental observations, and arteriole (B), with the hematocrit distributed throughout the vessel cross section. (Center) Cross-section of the vessels, showing the capillaries surrounded by one (A) and the arterioles by five (B) O₂^•−-producing EC. For small arteries, the considered geometry was similar to that for arterioles, but with R = 150 μm and 30 surrounding ECs.

Table 1.

Symbol meanings and parameter values.

Vessel	Symbol	Meaning	Value	References
All	$P$	Area-specific O2•− production rate of O2•−-producing cells	$6.0\times {10}^2\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}.{\mathrm{s}}^{-1}\mu {\mathrm{m}}^{-2}$	See text
	$D_O$	O2•− diffusion constant	$2.52\times {10}^3{\mu {\mathrm{m}}^2\mathrm{s}}^{-1}$	[49]
	$D_H$	H2O2 diffusion constant	$1.83\times {10}^3{\mu {\mathrm{m}}^2\mathrm{s}}^{-1}$	[50]
	$k_d$	O2•− dismutation pseudo-first-order rate constant in blood plasma	$9.3{\mathrm{s}}^{-1}$	[51]
	${\kappa }_{H,E}$	Permeability constant of EC membranes for H2O2	$19.{\mu \mathrm{m}\mathrm{s}}^{-1}$	[21]
	${\kappa }_{O,E}$	Permeability constant of EC membranes for O2•−	${1.9\mu \mathrm{m}\mathrm{s}}^{-1}$	See text
	${\kappa }_{H,B}$	Permeability constant of erythrocyte membranes for H2O2	$16.{\mu \mathrm{m}\mathrm{s}}^{-1}$	[22]
	${\kappa }_{O,B}$	Permeability constant of erythrocyte membranes for O2•−	$1.9{\mu \mathrm{m}\mathrm{s}}^{-1}$	See text
	$V_E$	Erythrocyte volume	$97.{\mu \mathrm{m}}^3$	[52]
	$A_E$	Erythrocyte surface area	$135.{\mu \mathrm{m}}^2$	[52]
	$\overline{Hc}$	Mean hematocrit	$0.45$	[53]
Capillaries	$R$	Radius	$5.0\mu \mathrm{m}$	[54]
	$\Delta$	Width of plasma region	$1.65\mu \mathrm{m}$	[55]
	$v_{\max }$	Maximum velocity of blood flow	$5.0\times {10}^2{\mu \mathrm{m}\mathrm{s}}^{-1}$	[56]
Arterioles	$R$	Radius	$25.\mu \mathrm{m}$	[54]
	$v_{\max }$	Maximum velocity of blood flow	$1.0\times {10}^4{\mu \mathrm{m}\mathrm{s}}^{-1}$	[56]
	$k_{H,B}$	Effective rate constant for H2O2 consumption by erythrocytes	$18.{\mathrm{s}}^{-1}$	$\frac{{\kappa }_{H,B}{A}_E}{V_E}\frac{\overline{Hc}}{1-\overline{Hc}}$
	$k_{O,B}$	Effective rate constant for O2•− consumption by erythrocytes	$2.2{\mathrm{s}}^{-1}$	$\frac{{\kappa }_{O,B}{A}_E}{V_E}\frac{\overline{Hc}}{1-\overline{Hc}}$
Small arteries	$R$	Radius	$150.\mu \mathrm{m}$	[57]
	$v_{\max }$	Maximum velocity of blood flow	$2.0\times {10}^5{\mu \mathrm{m}\mathrm{s}}^{-1}$	[58]
	$k_{H,B}$	Effective rate constant for H2O2 consumption by erythrocytes	$18.{\mathrm{s}}^{-1}$	As for arterioles
	$k_{O,B}$	Effective rate constant for O2•− consumption by erythrocytes	$2.2{\mathrm{s}}^{-1}$	As for arterioles

We consider that O₂^•− is released to the lumen by a 20 μm-long ring of ECs (the length of a large EC), which also intake O₂^•− and H₂O₂ as all the other ECs. This is achieved with the following boundary conditions at the vessel wall:

$$D_O{\frac{\partial C_O}{\partial r}|}_{r=R}=P{\delta }_c\left(z\right)-{\kappa }_{O,E}{C}_O\left(R,z\right)\text{,}$$

$$D_H{\frac{\partial C_H}{\partial r}|}_{r=R}=-{\kappa }_{H,E}{C}_H\left(R,z\right)\text{,}$$

where ${\delta }_c\left(z\right)=1$ at the O₂^•−-producing cells and ${\delta }_c\left(z\right)=0$ everywhere else along the vessel wall.

In capillaries (Fig. 1A), erythrocytes accumulate in the vicinity of the vessel axis, leaving an erythrocyte-free zone near the vessel wall [59,55]. Accordingly, in a neighborhood of width $\Delta =1.65$ μm of the vessel wall the hematocrit is set to zero, and a “wall” of erythrocytes is located at $r=R-\Delta$. Here, we implement the following boundary conditions, which describe the intake of O₂^•− and H₂O₂ by the erythrocytes:

$$D_O{\frac{\partial C_O}{\partial r}|}_{r=R-\Delta }={\kappa }_{O,B}{C}_O\left(R,z\right)\text{,}$$

$$D_H{\frac{\partial C_H}{\partial r}|}_{r=R-\Delta }={\kappa }_{H,B}{C}_H\left(R,z\right)\text{.}$$

In turn, for the arteriole (Fig. 1B), the hematocrit function, $Hc\left(r\right)=1.045\times \left(\frac{1}{1+e^{\left(\frac{10r}{25}-10\right)}}-0.5\right)$, where $r$ is measured in μm, is fitted to observations reported in 1.4A of reference [55]. For the artery the same function for the hematocrit is used in the $125\mathrm{\mu }\mathrm{m}<r<150\mathrm{\mu }\mathrm{m}$ range, while for $0<r<125\mathrm{\mu }\mathrm{m}$ we consider a constant value for the hematocrit, $Hc\left(r\right)=0.5225$. In both these cases, we implement Neumann boundary conditions at the center of the vessel:

$${\frac{\partial C_O}{\partial r}|}_{r=0}={\frac{\partial C_H}{\partial r}|}_{r=0}=0.$$

Periodic boundary conditions on $C_O$ and $C_H$ are implemented at the extremities of the vessel ($z=0$ and $z=z_{\max }$). Nevertheless, the site of O₂^•−-producing cells and the length of the simulation boxes are chosen such that both $C_O$ and $C_H$ are vanishingly small at both extremities.

Henceforth we will denote the just-described models for capillaries and arterioles/arteries by “Model C” and “Model A″, respectively.

The models for the case where ECs release H₂O₂ instead of O₂^•− are particular cases of the formulations above obtained by neglecting Equation (1) and the boundary conditions for O₂^•−, by setting $k_d=0$ in Equation (2), and by introducing the H₂O₂ production term $\frac{1}{2}P{\delta }_c\left(z\right)$ in the corresponding boundary condition. (Note that O₂^•− dismutation generates one H₂O₂ molecule from two O₂^•− ions, and consequently systems with O₂^•− production equal to $P$ and with H₂O₂ production equal to $\frac{1}{2}P$ generate H₂O₂ at the same rate if all the O₂^•− is dismutated.)

Equations (1), (2) were integrated numerically using finite differences in simulation boxes of sizes 33 × 200 for the capillary (Δr = 0.05 μm and Δz = 2 μm), 20 × 2500 for the arteriole (Δr = 1.25 μm and Δz = 2 μm), and 120 × 5000 for the artery (Δr = 1.25 μm and Δz = 2 μm). The integration was carried out until the concentrations reached their stationary values.

The same code, with ${\delta }_c\left(z\right)=1$ throughout the vessel's length, was used to obtain $C_O$ and $C_H$ when all ECs produce either O₂^•− or H₂O₂.

2.2. Parameter estimates

2.2.1. Superoxide and hydrogen peroxide concentrations and production rates in the microvasculature

In this linear model, the spatial distributions of O₂^•− and H₂O₂ concentrations are independent of the O₂^•− or H₂O₂ release rate by human microvascular ECs, but knowing the value of this parameter is essential to estimate local O₂^•− and H₂O₂ concentrations. Because we are unaware of any experimental determinations of this rate, we assessed its plausible range based on the following findings. Cultured BAEC released (0.64–1.9) × 10⁵ H₂O₂ molecules/s/cell in the physiological range of tissue O₂ concentrations [60,61]. These authors did not determine whether the detected H₂O₂ resulted from dismutation of released O₂^•− or was directly released by the cells. Therefore, we analyzed two extreme scenarios. In the first scenario, which appears closer to reality, we assumed that all the detected H₂O₂ resulted from dismutation of released O₂^•− that escaped reaction with eventually produced ^•NO and reabsorption by the cells. This translates into a (1.2–3.8) × 10⁵ O₂^•− molecules/s/cell net release rate. Dividing this range's upper bound by the area of contact of an EC with the vessel lumen in the considered geometry yields the reference value of $P$ in Table 1. Despite species, cell type and environment differences, basal net O₂^•− release rates by human vascular ECs in vivo can reasonably be expected to be in the same order of magnitude. In turn, some cells release O₂^•− at much higher rates when stimulated: 4 × 10⁶ O₂^•− molecules/s/cell for internal mammary smooth muscle cells stimulated with 100 U/ml IL-1β [62], and (1–40) × 10⁶ O₂^•− molecules/s/cell for polymorphonuclear leukocytes and Kupffer cells [63,64]. In the second scenario we assumed that all the detected H₂O₂ was directly released.

2.2.2. Permeability of ECs and erythrocytes to O₂^•− and H₂O₂

Under physiological conditions, both O₂^•− and H₂O₂ are readily consumed in the cytosol of erythrocytes and ECs, the former species by superoxide dismutase and the latter by Prdx. Therefore, the rates of cellular consumption of these species in the blood plasma is limited by these cells’ membrane permeabilities.

Orrico et al. [22] determined a 16. μm s⁻¹ permeability constant of human erythrocytes for H₂O₂, 2.8-fold higher than a previous more indirect estimate [65]. We estimated a 19. μm s⁻¹ permeability constant from H₂O₂ consumption rates determined in Ref. [21] for HUVEC cultures exposed to low H₂O₂ concentrations (details in Supplementary Information section 1, SI1).

Erythrocytes and ECs are permeable to O₂^•− [[18], [19], [20]], but we are unaware of experimental data to estimate the corresponding permeability constants. So, we considered the permeability constants of both erythrocyte and EC membranes for O₂^•− as 1/10th of that estimated for H₂O₂ in ECs and assessed the effect of changing this estimate.

3. Results

Below we focus mainly on EC-to-EC signaling, for which the O₂^•− and H₂O₂ concentrations at the ECs' surface and their influx rates are the most relevant considerations. The range over which cells can communicate through a diffusible substance depends on how far it is transported within its lifetime and on the concentration threshold for signaling. We will express the former parameter as the distance at which the O₂^•− and H₂O₂ concentrations decrease to 50% of maximum values. In turn the minimal thresholds for H₂O₂ signaling in EC are presently unclear. Shaji et al. [13] recently reported that treatment of Matrigel-seeded blood-brain barrier microvascular ECs with 1–10 nM H₂O₂ boluses for 2 h significantly increased EC tube length in a dose-dependent way. This observation suggests that ECs can sense and respond to H₂O₂ concentrations in the nM range. However, this inference needs confirmation by experiments including the determination of in situ H₂O₂ concentrations, as O₂^•−/H₂O₂ release by the ECs themselves might lead to substantially higher local concentrations than the nominal ones. On the other hand, signaling likely requires local extracellular concentrations to substantially exceed cytosolic ones. This is because virtually all the signal transduction mechanisms for extracellular H₂O₂ considered to date depend on H₂O₂ influx into cells [11,66,67], and H₂O₂ is not known to be actively transported across membranes. As basal cytosolic H₂O₂ concentrations in human cells are in the 0.1 nM range [68,69], below we consider extracellular H₂O₂'s concentration threshold for signaling as 1 nM.

3.1. Potential O₂^•− and H₂O₂ signaling in capillaries is short-range

Numerical integration of Model C reveals that the O₂^•− and H₂O₂ concentrations at the surface of the ECs are very localized at the vicinity of the O₂^•−-producing cell (green cell in Fig. 2A). The concentrations of O₂^•− and H₂O₂ steeply decrease in the longitudinal direction away from the O₂^•− supply zone, reaching 50% of their maximal values within 12 μm and 22 μm downstream of the site where the peak concentration is reached, respectively. And the H₂O₂ concentration falls below the 1 nM signaling threshold within 46. μm of the peak. In turn, the concentrations of both species remain virtually constant in the radial direction over the short span of the plasma region (Fig. 2B and C). This region is so narrow that molecules of both species cross it within 1 ms, given their diffusion constants. The large contact areas of the plasma with the EC and erythrocyte layers and the narrow width of the plasma layer, lead to the rapid absorption of O₂^•− and H₂O₂ by both erythrocytes and ECs. The following fractions of O₂^•− and H₂O₂ that are absorbed by each layer or dismutated (in the case of O₂^•−) at steady state for the reference parameter values in Table 1 can be readily calculated (SI2). Of the O₂^•− molecules, 80% are dismutated, while the other 12% are absorbed by the ECs and 8% are absorbed by erythrocytes. In turn, of the H₂O₂ molecules, 64% are absorbed by the ECs, while the other 36% are absorbed by the erythrocytes in the capillary.

Fig. 2.

Spatial distribution of O₂^•− and H₂O₂ in capillaries. (A) O₂^•− (blue) and H₂O₂ (red) concentrations at the surface of the ECs along the arteriole length. The background colors represent the average concentration at the surface of each EC represented at the top. The horizontal dashed line marks the assumed signaling threshold. The inset shows the H₂O₂ and O₂^•− concentrations in the same scale. (B,C) O₂^•− (B) and H₂O₂ (C) concentrations along the radial and longitudinal directions. The position of the O₂^•−-producing ECs is marked in green in all panels. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

The blood flow causes a slight asymmetry of concentration distributions around the O₂^•− supply zone, and a small 2 μm gap between the concentration peak of H₂O₂ and that of O₂^•−, reflecting some O₂^•− advection before dismutation (Fig. 2A). But altogether, these results show that the slow blood flow in capillaries does not substantially advect O₂^•− and H₂O₂ during their short lifetime, their spread being diffusion-dominated.

3.2. Short-range O₂^•− and long-range H₂O₂ transport in arterioles and arteries

Numerical integration of Model A reveals a very different distribution of O₂^•− and H₂O₂ at the ECs’ surface in arterioles (Fig. 3A). The O₂^•− concentration attains its maximum in the longitudinal direction within the supply zone (in green) and decays by 50% by 12 μm downstream. In contrast, the H₂O₂ concentration has a broad maximum, peaking at 50 μm downstream of the O₂^•− maximum, and decays by 50% over 650 μm downstream from the maximum. The concentrations of both species also decrease substantially in the radial direction away from the O₂^•−-producing ECs (Fig. 3B and C), with H₂O₂ penetrating deeper into the vessel.

Fig. 3.

Spatial distribution of O₂^•− and H₂O₂ in arterioles and arteries. (A,D) O₂^•− (blue) and H₂O₂ (red) concentrations at the surface of the ECs along the arteriole (A) and the artery (D) length. The background colors represent the average concentration at the surface of each EC represented at the top. The insets show the H₂O₂ and O₂^•− concentrations in the same scale over a longer segment of the 5 mm- and 1 cm-long simulated arteriole and artery, respectively. (B,C,E,F) H₂O₂ (B,E) and O₂^•− (C,F) concentrations along the radial and longitudinal directions in the arteriole (B,C) and in the artery (E,F). The position of the O₂^•−-producing ECs is marked in green in all panels. Note the distinct length and concentration scales in (D–F) vs. (A–C). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

The very different distribution of O₂^•− and H₂O₂ at the ECs' surface has the following explanation. Because the velocity of blood near the vessel's wall is very low, O₂^•− molecules that stay in this region are not significantly advected down the arteriole before being dismutated or uptaken. O₂^•− molecules that diffuse deeper into the arteriole are further advected by the faster blood flow therein, those returning to near the ECs' surface explaining the long tail of the O₂^•− concentration profile in Fig. 3A. However, most of that O₂^•− dismutates and yields H₂O₂ well inside the arteriole's lumen. From there, the blood flow substantially advects H₂O₂ while it diffuses back to the ECs' surface. This causes the 50 μm gap between the concentration peaks of H₂O₂ and O₂^•−, and the shallowness of the longitudinal decline of the H₂O₂ concentration.

The predominant fates of O₂^•− and H₂O₂ in arterioles also differ substantially from those in capillaries. Of the O₂^•− molecules, 95% are dismutated, while the other 5% are absorbed by the ECs and erythrocytes. In turn, of the H₂O₂ molecules, 18% are absorbed by the ECs, while the other 82% are absorbed by the erythrocytes.

In turn, the distribution of O₂^•− and H₂O₂ at the ECs' surface in arteries is remarkably similar to that in arterioles (Fig. 3D). This is because the local environment near these vessels’ walls is quite similar too, characterized by a slow blood flow, a low hematocrit and important contributions of the ECs for H₂O₂ (and possibly O₂^•−) clearance. Although deeper into the artery blood flows much faster than in arterioles, few O₂^•− and H₂O₂ molecules reach farther than 25 μm from the artery wall (the radius of an arteriole) before dismutating or being absorbed by erythrocytes (Fig. 3E and F). Nevertheless, while the maximal O₂^•− concentration attained near the ECs is quite similar to that attained in arterioles (82% of the latter), that of H₂O₂ is just 44% of that attained in arterioles. This happens because in the artery fewer of the H₂O₂ molecules produced by O₂^•− dismutation away from the wall diffuse back. For the same reason, in the artery the H₂O₂ concentration near the ECs reaches its maximum closer to the O₂^•−-producing region (24 μm from the O₂^•− maximum) and shows a slightly steeper decay downstream (50% decay 506 μm downstream from the maximum), despite the faster blood flow.

3.3. Direct H₂O₂ production by the endothelial cells allows mainly short-range signaling

We examined as well the spatial distribution of H₂O₂ along the walls of vessels with the same geometry as above, but where the “active” EC ring releases only H₂O₂ at half the O₂^•− release rates considered in the previous simulations (Fig. 4A,D). (That is, the same H₂O₂ production rate as if in the previous simulations all the released O₂^•− was dismutated into H₂O₂.) The results for capillaries show that a higher maximal H₂O₂ concentration (11 nM vs. 6.3 nM) is attained in this case (Fig. 4B). This is due to the following two factors. First, there is no O₂^•− loss to cellular absorption. Second, H₂O₂ generation is more concentrated in space, as it is not preceded by O₂^•− diffusion. The latter factor also implies that the H₂O₂ concentration declines even more steeply along the longitudinal direction, decreasing by 50% over 13. μm and to 1 nM over 34. μm downstream of the maximum. The radial concentration gradient remains negligible (Fig. 4C).

Fig. 4.

Spatial distribution of H₂O₂ in capillaries (A–C), arterioles (D–F) and arteries (G–I) where the ECs release only H₂O₂. (A,D,G) Processes considered by the models: H₂O₂ release by the “active” ECs in green, H₂O₂ absorption by all ECs and erythrocytes, H₂O₂ diffusion and advection. (B,E,H) H₂O₂ concentrations at the ECs' surface. The thin dashed red lines show the concentrations for the case where the “active” ECs release only O₂^•−, for comparison. The background colors represent the average concentration at the surface of each EC represented at the top. The horizontal dashed line marks the assumed signaling threshold. (C,F,I) H₂O₂ concentrations along the radial and longitudinal directions. Note that the r scale is stretched relative to the z scale in these panels. The position of the H₂O₂-producing ECs is marked in green in all panels. Note the distinct length and concentration scales from panel to panel. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

In turn, in arterioles and arteries H₂O₂ concentrations attained at the ECs’ surface — 1.6 nM and 1.2 nM, respectively — greatly exceed those attained if ECs release only O₂^•− (Fig. 4E,H). However, the concentration decreases very steeply downstream form production zones: in arterioles the concentration reaches 1 nM and decreases by 50% from maximal 2.5 μm and 6.0 μm downstream of the maximum, respectively; in arteries these distances are ≤2. μm and 4. μm, respectively. Nevertheless, the H₂O₂ distribution shows a heavy downstream tail, due to H₂O₂ molecules that diffuse further into the vessel, are advected there by the faster blood flow, and then diffuse back to the vessel wall. For this reason, the signaling threshold may be exceeded over a much longer range if H₂O₂ release substantially increases. The radial concentration gradient near the production zone is also quite steeper than in the case where the H₂O₂ is produced from O₂^•− dismutation in the blood plasma (compare Fig. 4F,I to Fig. 3C,F, respectively).

Again, both the H₂O₂ concentrations and their longitudinal distribution near the walls of arterioles and arteries are remarkably similar.

3.4. Maximal H₂O₂ concentrations attainable in blood plasma are up to the 10 nM range

Fig. 2, Fig. 3, Fig. 4 show that under the reference conditions and production geometry H₂O₂ concentrations at the ECs' surface peak at 6.5 nM, 0.1 nM and 0.44 nM in capillaries, arterioles and arteries, respectively, in the case where ECs release O₂^•−; and at 11 nM, 1.6 nM and 1.2 nM, in the case where ECs release H₂O₂. As per the model equations, these concentrations are directly proportional the area-specific O₂^•− or H₂O₂ release rates, and they increase with the release area. Thus, to better assess the maximal H₂O₂ concentrations attainable, we computed the proportionality constants between concentration at the ECs' surface and area-specific release rate in blood vessels where all ECs release O₂^•− or H₂O₂ (Table 2). Considering these proportionality constants, we then computed the H₂O₂ concentrations at the ECs’ surface for the reference O₂^•−/H₂O₂ area-specific supply rates, and for an upper limit corresponding to the most O₂^•− productive fully activated phagocytic cells — ≈6 × 10⁴ molecules s⁻¹ μm⁻² [63,64]. We performed these simulations for capillaries, arterioles, and a 150 μm radius small artery. As expected, local H₂O₂ concentrations are slightly higher when ECs release H₂O₂ than when they release O₂^•− at twice that rate. But even in the former case, those concentrations do not exceed 17 nM, 6.0 nM and 4.2 nM in capillaries, arterioles and arteries, respectively, for the reference release rates. And even in the implausible upper limit considered, those concentrations would not exceed 1.7 μM, 0.60 μM and 0.42 μM respectively.

Table 2.

Proportionality constants between H₂O₂ concentrations at the surface of ECs and area-specific O₂^•− or H₂O₂ production rates by the vessel walls for the case of uniform production along the vessels, and H₂O₂ concentrations attained for the reference production rate and for an extreme value.

Vessel	Species released	Proportionality constant (nM/molecules s−1 μm−2)	[H2O2] for P = 600 O2•− molecules s−1 μm−2 (nM)a	[H2O2] for P = 6 × 104 O2•− molecules s−1 μm−2 (nM)a
Capillaries	O2•−	2.5 × 10−2	15	1500
	H2O2	5.6 × 10−2	17	1700
Arterioles	O2•−	7.6 × 10−3	4.6	460
	H2O2	2.0 × 10−2	6.0	600
Arteries	O2•−	3.7 × 10−3	2.2	220
	H2O2	1.4 × 10−2	4.2	420

^aWhere ECs are considered to release H₂O₂, the area-specific H₂O₂ production rates considered as reference and upper bound are 300 and 3 × 10⁴ molecules s⁻¹ μm⁻², respectively.

These low concentrations are mainly a consequence of the enormous H₂O₂ clearance capacity by erythrocytes and ECs. Because erythrocytes in the arterioles consume 77%–82% of the H₂O₂ when all ECs produce H₂O₂ or O₂^•−, clearance by erythrocytes alone would suffice to keep H₂O₂ concentrations in the microvasculature lumen sub-μM for plausible production rates. The reasons for this large clearance capacity are threefold. First, the very high erythrocyte surface area per unit blood volume (630 m²/L for a 0.45 average hematocrit). Second, the high permeability of erythrocyte membranes to H₂O₂ (Table 1). Third, the large cytosolic H₂O₂ clearance capacity of these cells’ cytosol. The catalase activity alone is sufficient to sustain a large transmembrane concentration gradient even should the Prdx and glutathione pools become fully oxidized, meaning that nearly every H₂O₂ entering the cytosol is immediately consumed. Adding to this, ^•NO released from erythrocytes as a product the strong nitrite reductase activity of hemoglobin [70] may, under some circumstances, help scrub O₂^•− from the blood plasma thereby also suppressing H₂O₂ generation.

Remarkably, H₂O₂ concentrations near the walls of larger vessels are in the range of those found for arterioles for similar area-specific O₂^•−/H₂O₂ release rates, despite the much lower area/volume ratios of the former vessels (Table 2). This occurs because H₂O₂ clearance is diffusion-limited in the radial length scale of the larger vessels, with characteristic diffusion lengths in the range of the arterioles’ radius.

Relevant for potential communication between ECs and erythrocytes, in arterioles where all the ECs produce O₂^•− there is a modest radial H₂O₂ concentration gradient: the minimal concentration, at the vessel center, is just 12% lower than the maximal one, attained 2.6 μm from the vessel wall (Fig. S1B). In turn, in arterioles where all the ECs produce H₂O₂, the concentration is maximal adjacent to the vessel's wall and 48% lower at the vessel's center (Fig. S1E). In contrast, in the small artery, the H₂O₂ concentration decreases near-exponentially with the distance from the wall, attaining half-maximal values 23. μm (10. μm) away if all ECs release O₂^•− (H₂O₂) (Figs. S1C and F). This behavior and characteristic distances should be similar in larger vessels. O₂^•− concentrations at the small artery's center are nearly four orders of magnitude lower, and those of H₂O₂ nearly three orders of magnitude lower, than near the wall. (But note that the model neglects O₂^•−/H₂O₂ release by plasma enzymes and circulating cells, which may contribute to substantially higher concentrations towards the arteries' center.) Therefore, H₂O₂ eventually produced from a patch of active ECs at one side of even a small artery does not reach the opposite side.

3.5. Main factors modulating concentrations and ranges

Besides the production rate, the O₂^•− dismutation pseudo-first-order rate constant ($k_d$) is the parameter with the strongest influence on the maximal O₂^•− concentrations near the walls of both microvessels, and it also substantially influences H₂O₂ concentrations at this radial location (Fig. 5A,D). In arterioles, it very strongly influences the H₂O₂ downstream transport range (Fig. 5D inset). Increasing $k_d$ decreases the O₂^•− maximal concentrations and the downstream transport range of both chemical species, whereas it increases H₂O₂ concentrations. The substantial variation in H₂O₂ concentration is a consequence of the large sensitivity to $k_d$ of the O₂^•− levels in arterioles far from the O₂^•− production site. The influence of $k_d$ on O₂^•− concentrations at the ECs’ surface in the production site is weaker because the steep O₂^•− gradients create large O₂^•− diffusion fluxes away from this site, such that most O₂^•− diffuses away before it dismutates. The opposite occurs in locations of small O₂^•− gradients (Fig. 5D).

Fig. 5.

Main factors influencing H₂O₂ (red) and O₂^•− (blue) concentrations at the EC's surface, in capillaries (A–C) and arterioles (D–F) for 10-fold (thick dark lines), 1-fold (medium lines) and 0.1-fold (thin light lines) the reference values of ${\mathit{k}}_{\mathit{d}}$ (A, D), ${\mathbf{\kappa }}_{\mathit{O},\mathit{B}}$ and ${\mathbf{\kappa }}_{\mathit{O},\mathit{E}}$ together (B, E) and ${\mathbf{\kappa }}_{\mathit{H},\mathit{E}}$ (C, F). The insets show the concentrations scaled by the respective maxima in each condition. The horizontal dashed lines in the main plots mark the 1 nM H₂O₂ signaling threshold, those in the insets mark the half-maximal concentrations. The gray bars mark the position of the O₂^•− -producing EC ring. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

The permeability constant of EC and erythrocyte membranes to O₂^•− is the most uncertain parameter in this model. However, this parameter has very little influence on the O₂^•− and H₂O₂ transport ranges in capillaries and arterioles, and on these species’ concentrations near arteriole walls (Fig. 5B,E). In capillaries, a 10-fold increase of this permeability constant over its reference value, placing it at the same value as the permeability constant of EC membranes for H₂O₂, substantially decreases the O₂^•− and H₂O₂ concentrations, but a 10-fold decrease has very little influence. This is because in the former case, but not in the latter, O₂^•− influx into ECs and erythrocytes becomes competitive with dismutation. In arterioles, the permeability constant to O₂^•− has an even weaker influence because an even higher fraction of the O₂^•− is dismutated.

The permeability constant of EC membranes to H₂O₂ has no effect on the O₂^•− concentration or transport ranges. However, it strongly influences the maximal H₂O₂ concentrations at the ECs' surface in capillaries (Fig. 5C), and also substantially influences the H₂O₂ transport range in arterioles at the same radial location (Fig. 5F inset). Increasing ${\kappa }_{H,E}$ decreases both H₂O₂'s maximal concentration and transport range. This happens because for the reference values of the parameters the ECs consume most of the H₂O₂ near these vessels’ walls.

Results for arteries should closely mirror those presented above for arterioles.

3.6. Is O₂^•− intake a significant H₂O₂ delivery route to the ECs’ cytosol?

Under the reference conditions, peak O₂^•− concentrations at the ECs' surface substantially exceed H₂O₂'s, whether O₂^•− release by the vessels’ wall is considered localized (insets in Fig. 2, Fig. 3A) or uniform (Figs. S1A,B,C). These results suggest that a substantial fraction of the H₂O₂ supply to the ECs' from O₂^•− released to the vessels' lumen might result from cytosolic dismutation of uptaken O₂^•−. Fig. 6 shows the direct H₂O₂ influx rates into the cytosol and the H₂O₂ generation rates from uptaken O₂^•− on the assumption that all of the latter is dismutated, for several values of the O₂^•− permeability constants and $k_d$. In capillaries, O₂^•− influx contributes modestly for H₂O₂ supply to the cytosol, for the reference values of the parameters (compare blue to red mid-thickness lines in Fig. 6A). However, it becomes the predominant pathway near the O₂^•− production zone if extracellular dismutation becomes slower and/or the permeability of EC and erythrocyte membranes for O₂^•− is comparable to that for H₂O₂ (Fig. 6A and B). In arterioles, O₂^•− influx supplies most of the H₂O₂ to the cytosol near the O₂^•− production zone even for the reference values of the parameters (Fig. 6C, mid-thickness lines). This becomes true over several tens of μm downstream if extracellular dismutation becomes slower and/or the permeability of EC and erythrocyte membranes for O₂^•− is comparable to that for H₂O₂ (Fig. 6C and D).

Fig. 6.

Hydrogen peroxide supply rate to the cytosol of ECs via direct influx (red) or O₂^•− influx followed by dismutation (blue), in capillaries (A,B) and arterioles (C,D) for 10-fold (thick dark lines), 1-fold (medium lines) and 0.1-fold (thin light lines) the reference values of ${\mathit{k}}_{\mathit{d}}$ (A, B) and ${\mathbf{\kappa }}_{\mathit{O},\mathit{E}}$ (C, D). The gray bars mark the position of the O₂^•− -producing EC ring. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

If all the ECs release O₂^•−, for the reference parameter values, O₂^•− influx contributes 11%, 6.8% and 10% of the H₂O₂ supply to the ECs’ cytosol in capillaries, arterioles and arteries, respectively. These relative contributions are substantially lower than in the O₂^•−-producing region in Fig. 6C and D because in the latter case little H₂O₂ reaches this region, due to advection by the blood flow.

4. Discussion

4.1. H₂O₂ concentrations in the vasculature lumen are up to the 10 nM range

Physiological H₂O₂ concentrations in blood plasma have often been claimed to be in the μM range [43 and references therein]. However, the results above (Fig. 2, Fig. 3, Fig. 4, Table 2) show that for plausible O₂^•− or H₂O₂ release rates by the EC, the H₂O₂ concentrations attained at the ECs' surface do not exceed 17 nM, 6 nM and 4 nM in capillaries, arterioles and arteries, respectively. Achieving μM H₂O₂ concentrations in microvessels would require all the ECs releasing O₂^•− to the lumen at the maximal O₂^•− production rates achievable by the most productive phagocytic cells when maximally activated, which is very implausible. The following independent experimental evidence further supports physiological H₂O₂ concentrations in blood plasma not exceeding the 10's nM scale. From the permeability constant of the erythrocyte membrane for H₂O₂ (Table 1) one derives a 30. s⁻¹ apparent rate constant for H₂O₂ influx into the cytosol (see SI3). In turn, the erythrocyte's capacity to reduce the disulfide form of Prdx2 is limited to 1–2 μM s⁻¹ [23,65]. Because Prdx2 reduces most of the H₂O₂ in human erythrocytes [23,65,71], H₂O₂ influx rates in excess of ≈2 μM s⁻¹ — corresponding to ≈80 nM plasma H₂O₂ — should extensively oxidize this protein. However, Prdx2 is modestly oxidized in erythrocytes, even under lipopolysaccharide-induced endotoxemia, which strongly stimulates H₂O₂ production by circulating phagocytes [72,73]. Therefore, H₂O₂ in blood plasma does not reach the 100 nM range systemically. And because O₂^•− entering the erythrocyte is dismutated and most of the ONOOH reaching the cytosol also oxidizes Prdx2, the considerations above constrain the total influx of these species into erythrocytes as well. Several studies and critical reviews of in vitro experiments determining O₂^•−/H₂O₂ production and concentrations in the blood further support the conclusion that physiological systemic plasma H₂O₂ concentrations are in the nM range [65,74,75]. Authors claiming otherwise may have underappreciated the H₂O₂ clearance capacity of erythrocytes and ECs in vivo, which limits H₂O₂'s half-life to <40 ms and thus makes ex vivo methods unsuitable for these experimental determinations (see SI2).

The results above do not exclude that H₂O₂ reaches higher concentrations locally and transiently. E.g., wounding may trigger a transient (10-min scale) accumulation of low-μM H₂O₂ concentrations within tens of μm of wound margins [1,7]. However, such H₂O₂ accumulation is driven by DUOX-mediated H₂O₂ production by epithelial cells, not by cells within the vasculature [1]. What the present analysis highlights is the following. Lumenal H₂O₂ concentrations in excess of tens of nM are very unlikely to be reached in normal-functioning vasculature as a consequence of endothelial O₂^•−/H₂O₂ production, even locally or transiently. Moreover, maximal H₂O₂ concentrations in arterioles and larger vessels should be just up to 35% of those in capillaries for similar O₂^•− release rates per μm² of vessel wall (Table 2, Figs. S1C and F).

These conclusions raise the question of how such low H₂O₂ concentration changes can be sensed and transduced. Extracellular H₂O₂ concentrations in the nM scale are still substantially higher than cytosolic ones under physiological conditions [68,69], and therefore cause an influx that can significantly increase cytosolic H₂O₂ concentrations. At such low influx rates — up to 100's nM s⁻¹ — virtually all H₂O₂ is captured by cytosolic Prdx1 and Prdx2, which become oxidized and can relay the oxidation to other proteins [[27], [28], [29], [30]]. Given the large Prdx reduction capacities of some human cells [76,77], these low H₂O₂ influx rates may just minimally oxidize the cytosolic Prdx pool. However, scaffold proteins that localize both Prdx and redox targets to the sites of H₂O₂ supply [30] may greatly improve the sensitivity of localized redox relays [12]. Other proposed redox regulation mechanisms appear to be too insensitive for this purpose [12].

Considering the low H₂O₂ influx rates into ECs predicted in this work and H₂O₂'s ∼0.5 μm diffusion range in the cytosol [12], it is implausible that H₂O₂ from the lumen enters ECs and spreads through gap junctions to promote hyperpolarization of neighboring cells and vasodilation [17].

4.2. Is O₂^•− uptake a significant H₂O₂ delivery route to EC?

Estimated O₂^•− concentrations at the surface of ECs substantially exceed H₂O₂'s (Fig. 2, Fig. 3). They are mainly determined by the dismutation rate constant, and modestly influenced by the permeability of ECs and erythrocytes (Fig. 5). And they raise the question of whether O₂^•− influx might contribute substantially for H₂O₂ delivery to ECs. Indeed, even if EC membranes are just 10% as permeable to O₂^•− as to H₂O₂, and assuming that all the inflowing O₂^•− is dismutated, O₂^•− influx supplies most of the H₂O₂ to the cytosol of ECs within the O₂^•− production zone of arterioles (Fig. 6C and D). In capillaries, this pathway has a minor contribution to cytosolic H₂O₂ supply under the same conditions, but becomes dominant if ECs’ apical membranes are as permeable to O₂^•− as to H₂O₂ or if the extracellular SOD activity is substantially lower than the reference values (Fig. 6A and B).

The following experimental observations support the relevance of the O₂^•−-mediated H₂O₂ delivery route. First, SOD1 inhibition attenuates FGF-2- and VEGF-mediated phosphorylation of ERK1/2 in ECs by preventing the formation of sufficient H₂O₂ to cause inactivation of protein tyrosine phosphatases [78]. Second, SOD1 can drive the specific oxidation of a variety of thiol proteins, presumably through channeling of the H₂O₂ product, and thereby helps adapt cellular metabolism to oxygen availability [79]. Altogether, these computational and experimental results justify paying further attention to the differential responses of vascular ECs to O₂^•− vs. H₂O₂.

4.3. Potential O₂^•− and H₂O₂ signaling through the vasculature can be from autocrine to mm-scale

The simulation results in Fig. 2, Fig. 3, Fig. 4 show that O₂^•−/H₂O₂ in the (micro)vasculature lumen can signal over widely different ranges. These ranges are shortest for the species ECs directly release, because blood flows very slowly near the vessels' walls and ECs rapidly absorb the H₂O₂ molecules that stay in this region. On the other hand, release of O₂^•− by the ECs introduces a delay in H₂O₂ production, which allows this species to reach farther from the signaling cells (Fig. 2, Fig. 3A). In capillaries, this effect just slightly extends the H₂O₂ signaling range because the blood flow is too slow to substantially advect the molecules, transport remaining diffusion dominated (Fig. 2A). In all the situations above, the signaling range is limited to the low 10's of μm, allowing at most communication a few cells across. A very different situation occurs when ECs release O₂^•− into the arterioles' and arteries' lumen. Here, there is substantial advection as O₂^•− diffuses towards the vessel's center — where blood flows faster — prior to undergoing dismutation, and then the resulting H₂O₂ diffuses back to the vessel's wall. Consequently, H₂O₂ attains maximal concentrations 25–50 μm downstream of the O₂^•− concentration maximum, which may allow ECs to signal to downstream cells while minimizing autocrine signaling. Moreover, the H₂O₂ concentration near the ECs decreases longitudinally over a mm scale, thus potentially allowing communication between distant cells. However, this potential long-distance signaling comes at the cost of the maximal H₂O₂ concentrations being very low, such that the considered 1 nM signaling threshold can only be attained when many cells release O₂^•−. Therefore, there is a trade-off in H₂O₂ signaling with respect to the mode of H₂O₂ production: direct H₂O₂ release allows attaining higher local concentrations just over a very short range, whereas O₂^•− release potentially allows long-range signaling but requires release by a larger number of cells or release at higher rates/cell for H₂O₂ concentrations to attain the signaling threshold. Nevertheless, in arterioles and arteries where H₂O₂ release by the ECs is exacerbated beyond normal levels the signaling range may also extend over many 10's or even 100's of μm. This is because the H₂O₂ distribution near the ECs surface shows a heavy downstream tail, which is due to a minority of H₂O₂ that diffuses some distance away from the vessel wall and then back. But in contrast to what happens in O₂^•−-mediated H₂O₂ signaling, in this case the producing ECs are exposed to substantially higher H₂O₂ concentrations than any other cells.

At the low concentrations involved in signaling through the vessels’ lumen, H₂O₂ entering the ECs will be fully consumed by these cells and will not reach the basal side of the endothelium. However, it may elicit endothelial responses that affect the surrounding tissue.

Besides absorption by ECs, several other factors can affect O₂^•− and H₂O₂'s reach in the microvasculature lumen. SOD3 activity in the blood plasma is the most prominent of these factors under the reference conditions (Fig. 5). Decreasing SOD3 activity in the blood plasma increases both O₂^•−'s concentrations and its half-life, thus extending the range of signaling (Fig. 5A,D). In turn, H₂O₂'s longitudinal reach in capillaries is mainly determined by the permeability of ECs’ apical membranes (Fig. 5C,F). As a consequence, there is a trade-off between signaling sensitivity and spatial range when modulating the permeability of the ECs' membrane to H₂O₂: increasing this permeability enables the ECs to better compete with the erythrocytes for H₂O₂ and increase the rate of H₂O₂ supply to the cytosol, thus further oxidizing Prdx1 and Prdx2 and intensifying signaling; but it also decreases the lifetime and signaling range of extracellular H₂O₂.

4.4. H₂O₂'s transport range may vary widely depending on tissue characteristics

How does the transport range of extracellular H₂O₂ in the microvasculature lumen compare to those in “solid” tissues? In the absence of a strong oxidative stress the cytosolic 2-Cys peroxiredoxins sustain a strong transmembrane concentration H₂O₂ gradient [69,80,81]. As a consequence, the clearance rate of extracellular H₂O₂ by the cells is then determined by their membrane's permeability. Thus, at sub-μM extracellular H₂O₂ concentrations, the transport range depends primarily on this permeability and on the volume/area ratio of the extracellular medium. The effective permeability constants inferred from permeation studies of erythrocytes and several human cells in culture are in the 10–20 μm s⁻¹ range [22,76]. And a area/volume ratio of $\approx 62.\mu {\mathrm{m}}^{-1}$ is inferred from the observation that in the brain cortex — arguably the best characterized tissue in this respect — the extracellular medium accounts for 20% of the tissue volume and has a 60 nm average width [82] (SI4). From these values, one estimates that a H₂O₂ molecule has a <1 ms half-life in the extracellular medium, allowing it to diffuse <3.5 μm on average before being absorbed by a cell. In turn, at extracellular H₂O₂ concentrations in the μM range or higher the cytosolic Prdx pool becomes completely oxidized. As a consequence, the transmembrane H₂O₂ concentration gradient collapses, and the H₂O₂ half-life and transport range increase and become controlled by the activity of the remaining intracellular clearance mechanisms.

How do these theoretical conjectures compare to the few known experimental observations that addressed the transport range of extracellular H₂O₂? In the zebrafish tail wounding model, H₂O₂ concentrations decrease to 50% of maximal values at the wound borders in ≈50 μm [7]. In keeping with the conjectures above, these authors observe that the attained H₂O₂ concentrations (5 μM) fully oxidize the peroxiredoxins of the cells within 30 μm of the wound margins, which decreased H₂O₂ consumption by these cells and broadened the concentration gradient. This phenomenon is very unlikely to occur under non-inflammatory conditions, though.

A recent study of H₂O₂ diffusion and clearance in the brain striatum of living mice determined an effective diffusion coefficient D* = 2.5 × 10³ μm² s⁻¹ and a 2.2 s half-life, allowing H₂O₂ to diffuse over 180 μm in the extracellular space [10]. These surprisingly long half-life and range may have the following two alternative explanations. First, if the cells in this tissue have permeabilities comparable to those mentioned above, the 1 mM H₂O₂ boluses administered may have fully oxidized the cytosolic peroxiredoxin pool and part of the GSH pool in the measurement field. The modest glutathione peroxidase activity in rat brain tissues [83] would be insufficient to sustain a significant H₂O₂ transmembrane gradient in this case. Therefore, the determined H₂O₂ half-life would then essentially reflect the activity of the remaining intracellular H₂O₂ clearance processes. If this is the correct explanation, the experimental measurement may have strongly overestimated the half-life and transport range that applies at physiological extracellular H₂O₂ concentrations. However, this explanation seems inconsistent with the observation that the first in a series of H₂O₂ boluses administered to the rat brain is already detected by a distant H₂O₂-specific microelectrode with a time course similar to those of subsequent boluses. The inconsistency is because according to the proposed explanation the reactions with the intracellular redox pools would consume the H₂O₂ in the first bolus before it could reach the microelectrode. The alternative explanation is that the long H₂O₂ half-life and transport range are due to most cells in this tissue being virtually impermeable to H₂O₂, perhaps because they are myelinated. In this case, the determined half-life and transport range may be representative of the physiological one for the brain striatum, but does not necessarily apply to other solid tissues. Further research is thus needed to clarify these important issues.

Meanwhile, computational modeling in the vein of the present work will remain an important asset to estimate concentrations and distributions, interpret experimental observations, and designing informative experiments.

5. Concluding remarks

The results in this work show that the blood flow in the vasculature can transport H₂O₂ over a mm-scale, but only when this substance is generated from dismutation of EC-released O₂^•− in arterioles and larger vessels. In virtually all the other conditions studied, O₂^•− and H₂O₂ transport is limited to <50 μm.

H₂O₂ concentrations in the blood plasma of normal-functioning vasculature do not exceed the low tens of nM, which limits the viable intracellular signal transduction mechanisms

Cellular intake of O₂^•− from the blood plasma, followed by cytosolic dismutation, can be a quantitatively significant H₂O₂ signaling route, depending on the plasma SOD activity and on the EC membrane's permeability to O₂^•−.

Altogether, the theoretical and experimental considerations presented above suggest that H₂O₂'s half-life and transport range strongly depend on tissue characteristics. Namely, cell membrane permeability, extracellular space volume/area ratio, intracellular H₂O₂ clearance capacity, mode of extracellular H₂O₂ production and extracellular fluid fluxes.

Funding

Work financed by the European Regional Development Fund, through COMPETE2020-Operational Program for Competitiveness and Internationalization, and Portuguese funds via FCT-Fundação para a Ciência e a Tecnologia, under projects UIDB/04539/2020, UIDP/04539/2020, LA/P/0058/2020, UIDB/00313/2020, UIDP/00313/2020, UIDB/04564/2020 and UIDP/04564/2020 and under the Verão com Ciência 2020 program (Portugal). M.G. thanks the support of national funds from FCT – Fundação para a Ciência e a Tecnologia, I.P. through grant SFRH/BD/136046/2018.

Competing financial interests

The authors declare no competing financial interests.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following is the Supplementary data to this article:

Data availability

No data was used for the research described in the article.