Abstract
The high metabolic demand of brain tissue is supported by a constant supply of blood flow through dense microvascular networks. Capillaries are the smallest class of vessels in the brain and their lumens vary in diameter between ~2 and 5 μm. This diameter range plays a significant role in optimizing blood flow resistance, blood cell distribution, and oxygen extraction. The control of capillary diameter has largely been ascribed to pericyte contractility, but it remains unclear if the architecture of the endothelial wall also contributes to capillary diameter. Here, we use public, large-scale volume electron microscopy data from mouse cortex (MICrONS Explorer, Cortical mm3) to examine how endothelial cell number, endothelial cell thickness, and pericyte coverage relates to microvascular lumen size. We find that transitional vessels near the penetrating arteriole and ascending venule are composed of two to six interlocked endothelial cells, while the capillaries intervening these zones are composed of either one or two endothelial cells, with roughly equal proportions. The luminal area and diameter are on average slightly larger with capillary segments composed of two interlocked endothelial cells vs one endothelial cell. However, this difference is insufficient to explain the full range of capillary diameters seen in vivo. This suggests that both endothelial structure and other influences, including pericyte tone, contribute to the basal diameter and optimized perfusion of brain capillaries.
Introduction
The brain is a highly active and metabolically demanding organ. Capillaries serve as the distribution network for oxygen-carrying blood cells and nutrient supply. Since the earliest in vivo imaging studies of the brain microcirculation, researchers have noticed a striking variance in blood flow and diameter among individual segments of capillaries (1, 2, 3, 4). Capillary segments of larger diameter tend to support higher blood flow, and these vessels are spatially intermingled with thinner capillaries supporting lower flow (5, 6). While capillary flow fluctuates on the timescale of seconds to minutes due to dynamic physiological processes such as vasomotion and neurovascular coupling (2, 7), these dynamics are built atop a relatively stable but heterogeneous pattern of capillary flow, set by capillary architecture and pericyte tone (6).
These findings raise the question of why heterogeneity in brain capillary flow is necessary. Recent studies suggest that heterogeneity creates reserve space for increased blood flow and tissue oxygenation during neural activity (i.e. functional hyperemia) (8). This is akin to the concept of capillary recruitment described in peripheral tissues, such as muscle, where inactive tissue contains a proportion of nonflowing or very low-flow capillaries, which can be recruited to flow during increased metabolic demand (9). However, capillaries with no (or very little) flow are not ideal for brain function given the energy demands of the brain, and there are mechanisms to recannulate capillaries after flow obstruction by circulating emboli (10, 11). The system therefore establishes a range of flow levels across all capillaries at baseline, where capillaries that completely lack flow are very rare. This baseline state of heterogeneity transitions to more homogeneous flow among capillaries segments during increased brain activity. That is, low flux capillaries increase in flow, and high flux capillaries slightly decrease in flow (12, 13). Flow homogenization promotes a more even distribution of oxygenated blood cells among capillaries within the network, and slows their transit time to maximize oxygen extraction (8, 14).
Capillary diameter is a key determinant in setting basal flow heterogeneity. The capillary lumen normally range from ~2 to 5 µm in diameter (6). Considering that red blood cells are ~ 6 µm wide (white blood cells being larger) (15), lumen diameter has a significant influence on flow resistance. Capillary diameter is correlated with blood cell velocity and flux, emphasizing its importance in blood flow regulation (6). Pericytes are mural cells that line capillary networks and regulate basal capillary diameter, among many roles in microvascular homeostasis (16). Prior studies have shown that sustained optogenetic stimulation of pericytes can constrict capillaries in vivo, and conversely the ablation of pericytes leads to abnormal capillary dilation (6, 17, 18). Capillary pericytes possess some aspects of the contractile machinery expressed by arterial smooth muscle cells (19, 20). However, low to undetectable expression of α-smooth muscle actin (α-SMA) confer slow kinetics that are adequate to support basal capillary flow heterogeneity (6), blood pressure regulation (21), and possibly slower aspects of neurovascular coupling (22). Single cell transcriptomic studies (23) and physiological studies both in vivo (24) and in vitro (25) also confirm that capillary pericytes express high levels of receptors for vasoconstrictive signaling, such as endothelin 1 type A receptors and thromboxane A2 receptors, potentially involved in basal capillary tone regulation.
While much has been learned about pericyte contributions to capillary tone, prior studies have not examined whether basic structural features of the capillary wall are sufficient to explain heterogeneity in brain capillary diameter. Here, we ask whether the number or thickness of endothelial cells constructing the capillary wall is related to the area and diameter of the capillary lumen. Addressing this question requires broad examination of capillary ultrastructure over the scale of entire capillary networks. With the availability of a new large-scale volume electron microscopy (EM) resource from mouse cerebral cortex called MICrONS Cortical mm3 (26, 27), this possibility can now be rigorously tested.
Methods
Volume EM data
Data collection from Cortical mm3
Vasculature within the mouse visual cortex was identified in the publicly accessible volume EM resource (Cortical mm3) created as part of the IARPA Machine Intelligence from Cortical Network (MICrONS) consortium project (https://www.microns-explorer.org/cortical-mm3). The data set included a 1.4 mm × .87 mm × .84 mm tissue volume from the visual cortex of a P87 mouse. Microvascular data was collected from all 6 cortical layers (and superficial callosal white matter) throughout the data set; n = 179 vessels from gray matter and n = 6 vessels from white matter. Care was taken not to sample from the same vessel segment twice. Vessels were identified as capillaries when they were branch order ≥ 4 from penetrating arterioles and ascending venules (both denoted as 0 order). Transition zone vessels ranged from branch orders 1 to 4 from penetrating arterioles (ACT) or ascending venules (CVT). The termination of α-SMA, which demarcates the point of transition from ACT to capillary zones, can occur anywhere within the 1–4 branch orders (6, 28). We conservatively used fourth branch order at ACT and CVT as a range to ensure that we accurately targeted the capillary zone, but chose to depict the average branch of α-SMA termination in the ACT zone in Fig. 1B. To confirm vessels were branching from the arteriole side, ensheathing pericytes and perivascular fibroblasts were both required for ACT identity (29). To reduce variation in vessel and endothelial area, images/measurements were taken from areas without endothelial or pericyte nuclei present. This was more challenging within ACT and CVT zones, as nuclei were more abundant in this region (46, 30). However, measurements from ACT zones were sometimes taken when the nuclei of perivascular fibroblasts were present.
EM data analysis
Screen captures of identified vessels were taken in Neuroglancer from the 2D EM view of the dataset with scale bars. Images of vessels were imported into and measured using FIJI/ImageJ (NIH), with the scale set according to individual scale bar provided in Neuroglancer. Lumen area/circumference and vessel area/circumference were measured using the freehand selection tool. Lumen diameter of capillary vessels, which were typically circular, was calculated as: SQRT(lumen area/pi). Capillary circularity was calculated as: 4 × pi × A/C2, where A and C are the lumen cross-section area and circumference, respectively. Due to the occasionally elliptical shapes of transition zone vessels, particularly on the venule side, the lumen diameter was measured using the straight-line tool on the minor axis. The endothelial area was calculated from the difference in vessel and lumen area. Endothelial thickness was measured with the straight-line tool at five different points around the vessel and averaged. Percent pericyte coverage was calculated by the length of the vessel circumference in contact with pericyte processes. Source data for EM measurements are provided in the Supplementary Materials.
Annotation of endothelial junctions
Annotations were performed in a different volume EM data set collected from layer 2/3 of the visual cortex of a P36 male mouse at 3.58 × 3.58 × 40 nm resolution (31). The vasculature in this dataset consists of capillaries connected to an ascending venule (27, 29). To identify the pattern of endothelial junctions along the capillary vessels, the locations of endothelial junctions were annotation on 2D images every 5–10 slices. 3D images of the raw annotations were then captured to determine the pattern of endothelial–endothelial contact along capillary vessels.
In vivo imaging
Mice
In vivo deep two-photon imaging data from three adult mice was used for microvascular diameter measurements. The genotypes of these mice were Thy1-YFP (Jax: 003782; one mouse, 24 months old, male) and Atp13a5-2A-CreERT2-IRES-tdTomato (2 mice, 4 months old, male) (32), and all were on a C57Bl/6 background. Room temperature and humidity were maintained within 68–79 °F (setpoint 73 °F) and 30–70% (setpoint 50%), respectively. Mouse chow (LabDiet PicoLab 5053 irradiated diet for standard mice, and LabDiet PicoLab 5058 irradiated diet for breeders) was provided ad libitum. The Institutional Animal Care and Use Committee at the Seattle Children’s Research Institute approved all procedures used in this study (protocol #IACUC00396).
Surgery
Chronic cranial windows (skull removed, dura intact) were implanted in the skulls of all mice. Briefly, surgical plane anesthesia was induced with a cocktail consisting of fentanyl citrate (0.05 mg/kg), midazolam (5 mg/kg), and dexmedetomidine hydrochloride (0.5 mg/kg) (all from Patterson Veterinary). Dexamethasone (40 µL; Patterson Veterinary) was given 4–6 h prior to surgery to reduce brain swelling during the craniotomy. Circular craniotomies ~4 mm in diameter were generated under sterile conditions and sealed with a glass coverslip consisting of a round 4 mm glass coverslip (Warner Instruments; 64-0724 (CS-4R)) glued to a round 5 mm coverslip (Warner Instruments; 64-0700 (CS-5R)) with UV-cured optical glue (Norland Products; 7110). The coverslip was positioned with the 4 mm side placed directly over the craniotomy, while the 5 mm coverslip laid on the skull surface at the edges of the craniotomy. An instant adhesive (Loctite Instant Adhesive 495) was carefully dispensed along the edge of the 5 mm coverslip to secure it to the skull. Lastly, the area around the cranial window was sealed with dental cement. This two-coverslip ‘plug’ fits precisely into the craniotomy and helps to inhibit skull regrowth, thereby preserving the optical clarity of the window over months. Mice recovered for a minimum of 3 weeks following surgery.
Two-photon imaging
In vivo two-photon imaging was performed with a Bruker Investigator (run by Prairie View 5.5 software) coupled to a Spectra-Physics Insight X3 laser source. Far red fluorescence emission was collected through a 700/75 nm bandpass filter, respectively, and detected by gallium arsenide phosphide photomultiplier tubes. Low-resolution maps of the cranial window were first collected for navigational purposes using a 4× (0.16 NA) objective (Olympus; UPlanSAPO). We then switched to a 20× (1.0 NA) water-immersion objective (Olympus; XLUMPLFLN) and used 1210 nm excitation to visualize the vasculature using intravenously injected Alexa Fluor 680 dextran, which was custom-conjugated following prior studies (33). All imaging with the water-immersion lens was done with room temperature distilled water. Imaging was performed generally over the primary visual cortex.
Quantification of vascular diameter from in vivo data
Capillary and transition zone vascular diameter was measured with the FIJI/ImageJ macro VasoMetrics (33), which provides the average diameter along the vessel segment based on full width at half-maximum fluorescent intensity collected across multiple evenly distributed regions along the vessel length. Multiple measurements along the axis of each capillary also enabled calculation of standard deviation in diameters within an individual capillary segment. As with the volume EM data, vascular metrics were acquired from all six cortical layers (and some callosal white matter) throughout the data set. Source data for in vivo measurements are provided in the Supplementary Materials.
Statistical analysis
All statistical analysis was performed using GraphPad Prism v9. For all unpaired t-tests performed, normality and F-tests for variance were performed. When statistically significant F-tests were observed, unpaired t-test with Welch’s correction for unequal variances was performed. When data with nonnormal Gaussian distributions were observed, nonparametric Mann–Whitney U tests were performed. Kruskal–Wallis tests were performed for analysis across CVT, capillary, and CVT zones.
Results
The MICrONS Cortical mm33 is a volume EM data set encompassing roughly a 1 mm3 volume of mouse primary visual cortex. It contains numerous penetrating arterioles and ascending venules, as well as the dense microvascular networks intervening these routes of inflow and outflow (Fig. 1A). We categorized this vasculature into three zones (Fig. 1B): (i) arteriole–capillary transition (ACT), (ii) capillary–venous transition (CVT), and (iii) capillaries (all intervening microvasculature between the ACT and CVT). The ACT zone is defined as a stretch of vasculature spanning between the penetrating arteriole (zeroth order) to the point where expression of α-SMA terminates, which averages 2 branch orders (as depicted in Fig. 1B) but can extend as far as 4 branch orders (6, 34). To achieve a pure sample of capillaries, we used a conservative range of 0 to 4 branch orders from the penetrating arteriole and ascending venule during categorization of ACT and CVT zones, respectively. The vascular lumen segmentation provided in the MICrONS explorer interface was used to navigate through the vascular architecture. We then specifically measured vascular attributes in the ACT, CVT, and capillary zones from 2D images of microvascular crosssections (Fig. 1C, D and E).
We quantified the lumen area, lumen diameter, endothelial area, and endothelial thickness of individual vessels across these three microvascular zones (Fig. 2A, B, C, and D). Microvessels were sampled across all cortical layers (with some sampling in superficial corpus callosum) and then pooled to gain an overall view of their characteristics. A broad range of diameters were measured in each microvascular zone. Lumen area and diameter of ACT and CVT zones were larger than those of capillaries (Fig. 2A, B, E, and F). As expected, the area of the endothelium was greater with larger diameter vessels (Fig. 2C and G). Endothelial thickness was significantly larger in ACT and CVT zones, compared to capillaries (Fig. 2D and H).
To determine whether capillary diameter heterogeneity was influenced by the number of endothelial cells in the vessel wall, each capillary cross section was examined for tight junction (TJ) number by three independent raters (authors: SMS, SKB, VCS). A capillary with a single TJ is composed of a single endothelial cell wrapping and connecting with itself (Fig. 3A). A capillary with two TJs is composed of two endothelial cells interlocking to form the vessel wall (Fig. 3B). The capillary zone contained predominantly capillaries with one or two TJs, with roughly equal proportions (Fig. 3C). Capillaries with three and four TJs, indicating three and four endothelial cells respectively, were also observed on rare occasions (3 out of 185 capillaries examined). In contrast, these multi-TJ vessels were common in the ACT and CVT zones, with up to five or six TJs per vessel observed (Supplementary Fig. 1, see section on supplementary materials given at the end of this article).
Capillary cross sections may not be cut exactly perpendicular to the longitudinal axis of the capillary, which can affect quantifications of lumen size. We calculated the circularity of capillary cross sections in both one and two TJ groups and detected no difference, which ensured there was no bias in capillary sample collection between groups (Fig. 3D). We compared vascular attributes between capillaries with one or two TJs. Lumen area and diameter were on average significantly larger with two TJ capillaries. The average capillary lumen areas and diameter were 2 μm2 and 0.4 μm larger with two TJs in comparison to a single TJ, respectively (Fig. 3E and F). The range in capillary lumen area (~3–21 μm2) and diameter (~2–5 μm) was broad and overlapped heavily between the two groups (Fig. 3G). Interestingly, capillaries 3.4 μm and smaller tended to be composed of one endothelial cell, while those 3.6 μm and larger tended to be composed of two endothelial cells.
As a further strategy to verify the influence of endothelial cell number on capillary lumen area, we examined the upper and lower extremes of lumen area within the capillary group. We separated the smallest 25% of lumen areas (lower) and the largest 25% of lumen areas (upper) and compared the distribution of endothelial TJs numbers in these groups (Fig. 3H). Vessels in the lower 25% group were composed mostly of those with one TJ, while the upper 25% were predominantly vessels with two TJs, and contained the rare vessels with three and four TJs (Fig. 3I and J). This again shows that larger diameter capillaries are likely to be composed of two or more endothelial cells. Overall, these data suggest that endothelial number contributes to capillary diameter, but alone is insufficient to explain the full range of capillary diameters observed.
We also considered the possibility that a single TJ strands could pass the capillary cross section multiple times, leading to overestimation of endothelial cell number. Examination of TJ strands orientation using annotations in Neuroglancer, as previously described (35), revealed that endothelial cells are typically elongated in the longitudinal axis of the capillary, making it unlikely that TJ strands to meander in and out of a single cross-sectional plane (Supplementary Fig. 2). However, this could not be examined for all capillaries and is a limitation of our analysis procedure.
We next examined how other attributes of the endothelium related to lumen size. As expected, the area of the endothelial cross section was greater with the larger lumen areas of two TJ capillaries (Fig. 4A). We considered if distention of endothelium was necessary to create larger diameter capillaries, i.e. whether larger capillaries have thinner walls due to cell stretching. Instead, we found that larger capillaries exhibited thicker endothelial walls, and that there was an overall positive relationship between lumen area/diameter and endothelial thickness (Fig. 4B, C and D). Lending confidence to the accuracy of our measurements, values for capillary lumen area and endothelial thickness are concordant with those measured in prior studies (36).
We further asked whether heterogeneity in capillary diameter was related to the extent of pericyte coverage at the cross sections examined. Pericyte coverage was measured as the percentage of capillary wall contacted by pericyte processes in each image (Supplementary Fig. 3). This analysis revealed no difference in pericyte coverage between one and two TJ capillaries. We also found no correlation between pericyte coverage and other attributes of the capillaries examined (Supplementary Fig. 4). Critically, we note that pericyte coverage can differ substantially based on location along a capillary segment, such as proximity to the pericyte soma (29), and future studies will need to reexamine the influence of pericyte coverage using 3D analysis. To summarize these findings alongside endothelial attributes mentioned earlier, we constructed a Pearson’s correlation matrix on metrics extracted from the volume EM data (Supplementary Fig. 4).
Finally, we asked whether tissue fixation and processing could affect capillary diameter ranges in the Cortical mm3 data. Insufficient intravascular pressure during transcranial perfusion and fixation procedures could conceivably lead to collapsed or altered vascular lumen within volume EM data. To collect ground truth data, in vivo deep two-photon imaging was performed in the visual cortex of three adult mice under isoflurane anesthesia to measure capillary diameters from the pial surface to the gray and white matter interface (Fig. 5A, B, C and D). Our prior studies showed that isoflurane does not lead to dilation of capillaries compared to lightly sedated or awake mice (6, 37). We found that the diameter of capillaries in Cortical mm3 were, on average, slightly smaller in diameter than that seen in vivo (Fig. 5E). However, the range of capillary diameters (~3–5 μm) was similar between in vivo and volume EM data (Fig. 5F). This confirms that perfusion fixation and tissue handling used to generate the Cortical mm3 data preserved the expected range in capillary diameter typically seen in vivo.
We next asked how variance within individual capillary segments compared to variance among capillaries within a network. Shifts in endothelial cell number, or occurrence of pericyte somata, could alter capillary diameter (38). Since in vivo capillaries were measured at multiple locations along their length using our analysis software, Vasometrics (39), this analysis could be conducted. Lumen diameter measurements were taken at 1 μm increments for an average length of 26.96 μm ± 12.77 μm (mean ± s.d.) along each capillary segment; the median length of microvessels in mouse cortex is 50 μm (40). The average of standard deviations within individual capillaries (0.391 ± 0.02; average ± 95% CI) was smaller than standard deviations of diameters among all capillaries sampled (0.454) (Fig. 5G). This indicates that heterogeneity in capillary diameter is driven more by variation between capillary segments than within segments, although the latter did have some contribution. As expected from existence of some very small diameter capillaries in the EM data, the standard deviation of capillary diameters (0.704) was higher than that measured in vivo.
Finally, since capillary diameter and heterogeneity may differ based on cortical layer, we show that capillaries were sampled over a similar range of cortical depths between the in vivo and EM data. This provides confidence that similar types of capillaries were compared across animals (Fig. 5H).
Discussion
In this study, we used large-scale volume EM data (26) to show that endothelial cell number has a partial influence on microvascular lumen diameter and area. Microvessels in transitional zones near penetrating arterioles and ascending venules are larger and typically composed of 2 to 6 endothelial cells, while capillaries intervening these regions are constructed from either one or two endothelial cells at a nearly 50 : 50 ratio. We show that capillaries with two endothelial cells are, on average, larger than those with one endothelial cell. However, the diameter ranges of capillaries with one and two endothelial cells are broad and overlapping, suggesting that endothelial cell number cannot explain the full range of capillary diameters observed in vivo. Finally, we use deep two-photon imaging to verify that capillary diameter ranges captured in volume EM are comparable to that measured in vivo.
Microvascular architecture is established during cerebrovascular development (41), and shaped by blood flow (42) and the metabolic demands (43) of the growing brain. Whether endothelial structure is stable in the adult brain or actively remodeled has not been deeply examined. Some studies have tracked endothelial cells (and pericytes) longitudinally using in vivo two-photon imaging and showed relatively stable endothelial cell position and tight junction arrangement during adulthood, at least over the timeframe of days to weeks (44, 45). Cudmore et al. used a Tie2-based Cre driver to track capillaries in the motor cortex over time while mice had access to a running wheel (38). Interestingly, they reported marked stability of pericytes and endothelial cell density, except for small occasional shifts in nuclei position along the vessel wall. Reeson et al. showed that endothelial cells can be induced to reposition in the adult brain during local regression events caused by microvascular occlusions, indicating the potential to remodel in response to pathological stimuli (11). Endothelial cells that regress, migrate to nearby vessel segments and therefore increase endothelial cell number. Thus, endothelial contributions to capillary flow heterogeneity must be established during cerebrovascular development. Endothelial structure is stable in the adult cerebral cortex, but remodeling can be evoked with flow capillary obstruction. More longitudinal imaging studies are needed to determine how this process unfolds during development (46), and whether long-term alterations in neural activity can reshape capillary flow heterogeneity in development and adulthood (37, 47).
Our findings support the existence of additional mechanisms beyond endothelial number that control capillary diameter. As discussed earlier, capillary tone provided by capillary pericytes is a logical mechanism. There is now ample evidence for the contractile ability of capillary pericytes (6, 17, 18, 28), but the endogenous vasoconstrictive signals that create this tone under basal conditions remain to be determined. Unraveling this mechanism will require experiments to conditionally delete receptors for vasoconstrictive signals known to be used by pericytes such as endothelin-1, thromboxane A2, and noradrenaline receptors. Another potential contributor that remains poorly understood is tone generation from the cytoskeletal elements of the endothelial cells themselves, which is far less studied than pericyte contractility (48, 49). Further structural attributes of the vessel wall could include endothelial nuclei, which can protrude into the luminal space or the prevalence of small finger-like protrusions in the lumen called endothelial microvilli, which could both lead to increased local flow resistance (27).
There are some limitations to our study. First, the ultrastructural data is derived from the primary visual cortex of a single mouse. As volume EM data becomes more readily available, it will be possible to reexamine our hypothesis more broadly. Second, despite being able to sample hundreds of capillaries within Cortical mm3, we only quantified ones cut perpendicular to the plane of highest spatial resolution, and therefore introduced bias toward a subset of capillaries oriented in one plane. Third, we detected some variance in diameter within capillary segments, but our analyses relied on 2D cross sections in restricted regions. Deeper investigations on the basis of this variation, be it shifts in endothelial cell number, presence of pericyte somata (32) or other factors, will require 3D reconstructions and additional proofreading efforts to rigorously segment pericyte and endothelial compartments. Fourth, the issue of how tissue fixation and handling affect the native structure of the vascular lumen and wall components requires deeper investigation. Fixation approaches have a strong influence when preserving the extracellular space during EM (50, 51). By comparing variance on capillary diameter between Cortical mm3 and data collected from anesthetized mice using in vivo deep two-photon imaging, we see a similar range of capillary diameters, which lends confidence to the idea that capillary diameters were generally preserved.
In the Alzheimer’s brain, and in many related neurological diseases, capillary diameter is altered, and microvascular density is reduced. This is expected to impair blood flow by increasing flow resistance but will also disrupt the range of capillary diameters that is critical for blood distribution. Further, shifts toward increased basal capillary heterogeneity may raise the threshold to distribute blood and oxygen during functional hyperemia. How alterations in endothelial structure and density factor into these disease-related microvascular deficits remains heavily understudied, yet vital to understanding mechanistic targets for improvement of microvascular perfusion.
Supplementary materials
This is linked to the online version of the paper at https://doi.org/10.1530/VB-23-0010.
Declaration of interest
The authors declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the study reported.
Funding
Our work is supported by grants to AS from the NIH/NINDS (NS097775) and NIH/NIA (AG062738, R21AG069375, RF1AG077731). SKB was supported by a fellowship from the National Institutes of Health, National Institutes of Neurological Disease and Stroke (F32NS117649). VCS was supported by a junior leader fellowship from ‘La Caixa’ Foundation (LCF/BQ/PI22/11910036).
Author contribution statement
This project was conceived by AYS, and all analyses were performed by SMS. SKB and VCS served as independent raters of tight junction number analysis. YL and SS contributed in vivo deep imaging data sets. MT provided consultation on the MICrONS data set. The manuscript was written by AYS with feedback from all authors.
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