
Nkx2.5 is essential to establish normal heart rate variability in the zebrafish embryo
Jamie K Harrington
Robert Sorabella
Abigail Tercek
Joseph R Isler
Kimara L Targoff
Address for reprint requests and other correspondence: K. L. Targoff, Div. of Pediatric Cardiology, Dept. of Pediatrics, College of Physicians and Surgeons, Columbia Univ., 630 West 16th St., New York, NY 10032 (e-mail:kl284@columbia.edu).
Corresponding author.
Series information
Cardiovascular and Renal Integration
Received 2016 May 25; Revised 2017 Jun 2; Accepted 2017 Jun 6; Issue date 2017 Sep 1.
Abstract
Heart rate variability (HRV) has become an important clinical marker of cardiovascular health and a research measure for the study of the cardiac conduction system and its autonomic controls. While the zebrafish (Danio rerio) is an ideal vertebrate model for understanding heart development, HRV has only recently been investigated in this system. We have previously demonstrated thatnkx2.5 andnkx2.7, two homologues ofNkx2–5 expressed in zebrafish cardiomyocytes, play vital roles in maintaining cardiac chamber-specific characteristics. Given observed defects in ventricular and atrial chamber identities innkx2.5−/− embryos coupled with conduction system abnormalities in murine models ofNkx2.5 insufficiency, we postulated that reduced HRV would serve as a marker of poor cardiac health innkx2.5 mutants and in other zebrafish models of human congenital heart disease. Using live video image acquisition, we derived beat-to-beat intervals to compare HRV in wild-type andnkx2.5−/− embryos. Our data illustrate that thenkx2.5 loss-of-function model exhibits increased heart rate and decreased HRV when compared with wild type during embryogenesis. These findings validate HRV analysis as a useful quantitative tool for assessment of cardiac health in zebrafish and underscore the importance ofnkx2.5 in maintaining normal heart rate and HRV during early conduction system development.
Keywords:nkx2.5, heart rate variability, zebrafish
heart rate variability (HRV), including both beat-to-beat changes and slower variations in heart rate (HR), has been shown to be clinically important as a marker of cardiac health and is increasingly used to predict abnormal patterns associated with illness (9,10,14,15,17,23,39,44,55). HRV emerges during human fetal development and progressively increases in utero as the conduction system becomes more responsive to sympathetic-parasympathetic function and interaction (27,47). This complex interplay persists into adulthood and is essential to maintain coordinated cardiac contractions and cardiovascular homeostasis (38). The first clinical application of HRV monitoring followed the identification of a strong correlation between a decrease in HRV and fetal distress more than two decades ago (17,44). More recently, the relevance of HRV assessment has become widespread with clinical applications ranging from early detection of sepsis in neonates (9,10,14) and determination of autonomic neuropathy severity in diabetic patients (39,55) to prediction of morbidity and mortality risks in patients with acute coronary syndrome (15,23). Moreover, studies in the pediatric population have demonstrated that HRV monitoring is helpful in assessing gestational risk factors associated with congenital heart disease (CHD) during fetal life and pulmonary hypertension during childhood (25,42). Specifically, a prospective observational cohort study revealed that fetuses with CHD manifest diminished HRV when compared with control subjects (42). Furthermore, children with severe pulmonary hypertension have significantly reduced HRV in contrast to patients with moderate pulmonary hypertension, highlighting the utility of HRV as a diagnostic marker of disease severity (25). Taken together, the widespread use of HRV as a health assessment parameter underscores the importance of HR responsiveness in meeting the changing metabolic demands of tissue perfusion in health and disease.
Studies in mouse, zebrafish, andDrosophila have noninvasively evaluated pathophysiological conditions through assessment of HRV (11,30,51). Given the optical clarity of the zebrafish embryo, short generation interval, and extensive similarity between the zebrafish and human genomes (7,18), the zebrafish has emerged as an ideal, nonmammalian, vertebrate model organism for the study of cardiac development (2,43,53). Although this aquatic organism is increasingly being used to investigate a number of cardiovascular diseases from CHDs to arrhythmias and cardiomyopathies (1), analysis of HRV to evaluate normal cardiac morphogenesis and adult cardiovascular health in this system has only recently been explored. Dissection of the neuroanatomy of the adult zebrafish heart reveals intrinsic and extrinsic innervation that facilitates the complex autonomic regulatory influences in each chamber (45). In addition, HRV strategies have been used to decipher the intricate control mechanisms in wild-type adult hearts (46). However, the application of these tools to examine the pathophysiology due to genetic abnormalities in the embryo remains elusive. In this study, we establish HRV as an essential noninvasive measure to determine cardiovascular health in zebrafish embryos harboring ventricular and atrial chamber malformations that mimic CHDs in patients.
Specifically, our studies focus on the homeobox transcription factorNKX2–5, which has previously been identified as a key causative gene associated with a myriad of CHDs in humans including atrial septal defects, ventricular septal defects, tetralogy of Fallot, and atrioventricular node conduction abnormalities (4,8,32,40). Studies in murine models have shown that Nkx2–5 reduction leads to hypoplastic atrioventricular nodal and Purkinje fibers (21,33,36,48) while atrial-specificNkx2–5 mutants develop hyperplasia of the sinoatrial node and internodal tracts (35,36). Consistent with this evidence of opposing functions in the atrial and ventricular conduction systems, our work in zebrafish has shown thatnkx genes are essential for maintaining ventricular identity through the repression of atrial fate (49,50). Furthermore, we recently demonstrated a temporally controlled mechanism in which expression ofnkx2.5 is required early during cardiomyocyte differentiation to maintain ventricular and atrial characteristics when chambers emerge (12). To characterize the electrophysiological consequence ofnkx2.5 loss-of-function and to test the paradigm of HRV as an indicator of cardiac disease in our mutant zebrafish model, we compared HRV in wild-type andnkx2.5−/− embryos. Given defects in the establishment of proper chamber-specific identity and proportionality, we postulated thatnkx2.5−/− embryos demonstrate impaired conduction system development and HRV emergence. Through video image acquisition and interbeat interval analysis, we show thatnkx2.5 depletion leads to increased HR and decreased HRV. Thus, our data stress the crucial role ofnkx2.5 in establishing variability in HR as the cardiac conduction system is patterned in the developing zebrafish embryo. Finally, our findings validate HRV analysis as a useful quantitative tool for assessment of cardiac health in zebrafish models of CHDs.
MATERIALS AND METHODS
Zebrafish.
We used zebrafish carrying the following previously described mutations and transgenes:nkx2.5vu179 (26,49,52),nkx2.7vu413 (49), andTg(hsp70l:nkx2.5-EGFP)fcu1 (12). Thenkx2.5vu179 allele contains a G→A transition at position 564 of the open reading frame leading to a nonsense mutation that is predicted to cause truncation of the protein within the homeodomain. Thenkx2.7vu413 allele contains a C→A transversion at position 321 of the open reading frame leading to a nonsense mutation that is predicted to cause truncation of the protein before the homeodomain.nkx2.5vu179 is recessive lethal, whilenkx2.7vu413 is recessive viable. We have not detected developmental abnormalities in the heterozygote state fornkx2.5vu179, suggesting that this point mutation has a loss-of-function, rather than a dominant-negative, effect. All zebrafish work followed Institutional Animal Care and Use Committee-approved protocols.
Heat shock conditions.
Embryos from outcrosses of fish carryingTg(hsp70l:nkx2.5-EGFP) were maintained at 28.5°C and exposed to heat shock at desired stages. To implement heat shock, 50 embryos were placed in 2.5 ml of embryo medium in a Petri dish on top of a covered heat block for 1 h at 37°C. After this treatment was completed, transgenic embryos were identified by genotyping for theTg(hsp70l:nkx2.5-EGFP) transgene or visualization of ubiquitous EGFP expression. Nontransgenic sibling embryos exposed to heat shock served as controls.
Imaging.
Embryos were anesthetized with 0.2% tricaine (MS-222; Sigma) neutralized with phosphate-buffered saline. Once anesthetized, the embryos were mounted laterally in 1% agarose gel with their ventricles positioned toward the objective for optimal image acquisition. Movies (512 × 256 pixels) were collected with a transmitted-light PMT detector for 50 s at 57 frames/s using the resonant scanner on an A1R confocal microscope (Nikon Instruments). Imaging was performed with a ×20/0.75 Plan-Apochromat objective lens and with bidirectional resonant scanning using a 561-nm laser light. The pixel diameter was 1.24 µm giving field dimensions of 635 µm in width by 317 µm in height. Video sequences were processed using ImageJ and analyzed with custom software in Matlab.
Genotyping.
PCR genotyping was performed on genomic DNA extracted from individual embryos following live imaging. Detection ofnkx2.5vu179 was executed using primers 5′-TCACCTCCACACAGGTGAAGATCTG-3′ and 5′-CAGAAAGATGAATGCTGTCGGT-3′ to generate a 443-bp fragment. Primer placement in the 3′-UTR was chosen specifically to amplify the endogenousnkx2.5 allele as opposed to the transgeneTg(hsp70l:nkx2.5-EGFP). Digestion of the mutant PCR product with Hinf1 creates 207-, 162-, 49-, and 25-bp fragments. Analysis ofnkx2.7vu413 was performed using primers 5′-CTTTTTCAGGCATGTGTCCA-3′ and 5′-AAAGCGTCTTTCCAGCTCAA-3′ to generate a 146-bp fragment. Digestion of the mutant PCR product with MseI creates 111- and 35-bp fragments.
Analysis of HRV in zebrafish embryos.
To extract instantaneous heart rate (IHR) quantitatively from each video, the difference in pixel intensity between individual frames was calculated beginning with the second frame (i.e., the previous frame intensity at each pixel was subtracted from the current frame intensity at each pixel to generate a “difference image”) (Fig. 1). The maximum value within each difference image was determined and used to generate a predominately sinusoidal, one-dimensional time series of difference image maxima. The time series of those maxima were standardized by z-scores and any linear trend was removed. Then, a 3-Hz low-pass filter was applied using a 20-point finite impulse response filter. The times at which local peaks occurred were determined and the differences between peak times (interbeat intervals) were taken as a proxy for R-R intervals. Next, the reciprocal of the interbeat intervals was taken as a proxy for IHR. HR was measured as the mean of IHR over each recording.
Fig. 1.
Heart rate variability (HRV) is determined by analysis of interbeat intervals. Schematic representation of the approach used to generate interbeat intervals from movies of zebrafish embryos (lateral views, anterior to the top). Light intensity at each pixel in each frame of a movie was subtracted between consecutive frames to generate a sequence of difference images. The maximum value within each difference image was identified and its value was used to create a 1-dimensional time series of difference image maxima. After preprocessing (seematerialsandmethods) was completed, times at which local peaks occurred were determined and the differences between peak times (interbeat intervals) were taken as proxies for R-R intervals. The reciprocals of the interbeat intervals were subsequently used as proxies for instantaneous heart rate (IHR). Heart rate (HR) was measured as the mean of IHR over each recording.
Short-term HRV analysis was performed on wild-type andnkx2.5−/− embryos and transgenic embryos carryingTg(hsp70l:nkx2.5-EGFP). The following measures of HRV were applied: the standard deviation of mean R-R interval (RRSD) and the square root of the mean squared differences of successive R-R intervals (RMSSD) (29). RRMSD is complementary to RRSD as it is more sensitive to the short-term components of HRV. Although various other HRV measures are often computed, we focused on these two measures for simplicity. Recent work has suggested that HRV measures are inextricably tied to IHR (34), such that lower IHR is always associated with higher HRV. However, a formula proposed to correct for this inherent bias in HRV is most appropriate for experimental designs with clearly differentiated baseline and nonbaseline time periods (34). Therefore, instead, we corrected for IHR bias in RRSD by computing the corresponding coefficient of variation (RRSD/RR) (16).
Statistical analysis.
Means ± SE of each data set are shown with detection of statistically significant differences using the Student'st-test (homoscedastic, two-tailed distribution) in Matlab.
RESULTS
nkx2.5−/− embryos have elevated HRs.
Employing live animals, we acquired resonance video images and analyzed beat-to-beat pixel intensity variations (Fig. 1). Differences in ventricular and atrial morphology and cardiomyocyte cell number are first evident between 26 h postfertilization (hpf) and 36 hpf innkx2.5−/− embryos (49). Thus, we initially examined wild-type andnkx2.5−/− embryos at 48 hpf to capture any aberrations in HR and HRV secondary to the loss ofnkx gene function. Moreover, given development of severe edema innkx2.5−/− embryos by 4 days postfertilization (dpf) and lethality of the homozygous recessivenkx2.5vu179 allele by 5 dpf, we again performed imaging and interbeat interval analyses at 72 hpf to capture physiological changes evident before manifestations of terminal cardiac dysfunction.
The HRs ofnkx2.5−/− embryos were augmented at both time points when compared with wild-type sibling embryos (Fig. 2,A andB). In addition, our studies illustrate an increase in HR between 48 hpf and 72 hpf innkx2.5−/− embryos (Fig. 2D). However, in the wild-type cohort, there was no difference in HR detected between these developmental stages (Fig. 2C). Complete numerical results are presented inTable 1. Taken together, our findings highlight increased HR during key stages of cardiogenesis in thenkx2.5−/− embryo. Given our previous data demonstrating ventricular-to-atrial transdifferentiation (49), we postulate that these changes in HR represent a rate responsive compensation for impaired cardiac output innkx2.5−/− compared with wild-type embryos.
Fig. 2.
nkx2.5−/− Embryos have elevated instantaneous heart rates compared with wild-type embryos. Bar graphs indicate mean IHR in wild-type andnkx2.5−/− embryos at 48 h postfertilization (hpf;A) and 72 hpf (B) and the HR of wild-type (C) andnkx2.5−/− (D) embryos compared over time.A andB:nkx2.5−/− embryos have increased HRs when compared with wild-type embryos.C andD: while wild-type embryos exhibit no difference in HR between 48 and 72 hpf,nkx2.5−/− embryos reveal increased HR during this developmental window. *P < 0.05; *P < 0.01.
Table 1.
nkx2.5−/− embryos demonstrate augmented heart rates and diminished heart rate variability whereas rescued nkx2.5−/− embryos exhibit measures consistent with wild-type embryos
| Measure | Genotype | n | Genotype | n | P |
|---|---|---|---|---|---|
| Wild Type | nkx2.5−/− | ||||
| 48 hpf | |||||
| HR | 93 (5.3) | 10 | 116 (5.3) | 5 | ** |
| RRSD | 21 (2.0) | 10 | 12 (0.62) | 5 | ** |
| RMSSD | 33 (3.4) | 10 | 19 (0.46) | 5 | ** |
| RRSD/RR | 0.032 (0.0038) | 10 | 0.023 (0.0009) | 5 | * |
| 72 hpf | |||||
| HR | 103 (6.8) | 8 | 138 (5.4) | 5 | ** |
| RRSD | 18 (2.1) | 8 | 12 (1.0) | 5 | * |
| RMSSD | 30 (3.4) | 8 | 19 (1.5) | 5 | * |
| RRSD/RR | 0.031 (0.0033) | 8 | 0.027 (0.003) | 5 | ns |
| Tg(hsp70l:nkx2.5-EGFP) | nkx2.5−/−;Tg(hsp70l:nkx2.5-EGFP) | ||||
| 48 hpf | |||||
| HR | 110 (0.78) | 2 | 117 (4.7) | 3 | ns |
| RRSD | 24 (2.1) | 2 | 51 (18.6) | 3 | ns |
| RMSSD | 39 (2.9) | 2 | 85 (30.7) | 3 | ns |
| RRSD/RR | 0.045 (0.0036) | 2 | 0.097 (0.035) | 3 | ns |
| 72 hpf | |||||
| HR | 130 (3.2) | 11 | 138 (3.2) | 6 | ns |
| RRSD | 34 (6.1) | 11 | 23 (2.7) | 6 | ns |
| RMSSD | 53 (8.7) | 11 | 34 (4.2) | 6 | ns |
| RRSD/RR | 0.072 (0.0047) | 11 | 0.053 (0.006) | 6 | ns |
Means (SE) of heart rate (HR), standard deviation of mean R-R interval (RRSD), square root of mean squared differences of successive R-R intervals (RMSSD), and bias-adjusted RRSD (RRSD/RR). Significant differences are denoted as follows: ns, not significant.
P < 0.05;
P < 0.01.
nkx2.5−/− embryos demonstrate decreased HRV.
To evaluate the requirement ofnkx2.5 gene function for the development of HRV, RRSD, RMSSD, and RRSD/RR were compared across genotypes. HRV was lower in thenkx2.5−/− embryos than in their wild-type siblings at 48 hpf (Fig. 3,A andC) and 72 hpf (Fig. 3,B andD) when both RRSD and RMSSD were applied. Moreover, we corrected for IHR bias in RRSD by computing the corresponding coefficient of variation (RRSD/RR) and detected a significant decrease at 48 hpf innkx2.5−/− compared with wild-type embryos (Table 1). Yet, at 72 hpf, we observed no difference in RRSD/RR between wild-type andnkx2.5−/− embryos (Table 1). Altogether, our data demonstrate the previously unappreciated function ofnkx2.5 in establishing normal HRV parameters in the zebrafish embryo.
Fig. 3.
nkx2.5−/− Embryos demonstrate decreased HRV. Bar graphs indicate HRV in wild-type andnkx2.5−/− embryos at 48 hpf (A andC) and 72 hpf (B andD) evaluated by standard deviation of mean R-R interval (RRSD;A andB) and the square root of mean squared differences of successive R-R intervals (RMSSD;C andD).A andB: decreased HRV in wild-type andnkx2.5−/− embryos at both 48 and 72 hpf predicts diminished cardiac health at both time points using the RRSD measure.C andD: similarly, using RMSSD as a measure of HRV, there is a decline in HRV in wild-type compared withnkx2.5−/− embryos at both 48 hpf and 72 hpf. *P < 0.05; **P < 0.01.
Rescued nkx2.5−/− embryos reveal normal HRs and HRV.
Our previous studies examining the precise temporal windows during development when Nkx transcriptional activity is required demonstrate that early overexpression ofnkx2.5 rescues late morphological defects innkx2.5−/− embryos (12). Thus, we hypothesized that rescued embryos would exhibit normal HR and HRV given the long-term benefits ofnkx2.5 expression before heart tube formation in securing chamber-specific identity and in maintaining embryonic survival into adulthood. We assessed HR, RRSD, RMSSD, and RRSD/RR in wild-type andnkx2.5−/− sibling embryos carryingTg(hsp70l:nkx2.5-EGFP) following heat shock at 21 somites. There were no significant differences between these genotypes for all measures assessed highlighting rescue of HR and HRV defects observed in nontransgenicnkx2.5−/− embryos (Table 1). All embryos were genotyped to confirm transgenic carrier status and presence of thenkx2.5vu179 mutation. These results illustrate the essential, long-term benefits ofnkx2.5 expression before heart tube formation in maintaining chamber identity and also in patterning the cardiac conduction system. Furthermore, our findings validate HRV analysis as a useful quantitative tool for assessment of cardiac health in zebrafish models of CHDs.
DISCUSSION
Our study highlights the importance ofnkx2.5 in maintaining normal HR and HRV in the developing conduction system of the zebrafish embryo. We found thatnkx2.5−/− embryos have elevated HR and a greater increase in HR during the initial few days of embryogenesis when compared with wild-type embryos. Furthermore,nkx2.5−/− embryos have reduced HRV compared with wild-type embryos at all points analyzed by two separate measures of HRV estimation. Previous work has established that HRV increases with gestational age in healthy human fetuses, and similar findings have been documented in the zebrafish embryo (24,41). Thus, we conclude that increased HR and decreased HRV innkx2.5−/− embryos at both 48 and 72 hpf underscore impaired cardiac conduction system development in response to abnormal morphogenesis following the loss ofnkx gene function. Furthermore, although the ability to modify cardiac output in response to environmental stimuli during later zebrafish embryonic stages have been examined (20,31,41), our data demonstrate previously unrecognized early defects in HR control in a genetic loss-of-function model and highlight the benefits of early quantitative measures to predict cardiac developmental health in zebrafish models of CHD.
Our current findings emphasize the utility of HRV measure as an indicator of cardiac health in the developing zebrafish embryo and thus provide a screening tool for novel mutant alleles. However, we were also interested to know whether earlynkx2.5 deficiency results in later effects on the cardiac conduction system. It is particularly important to elucidate this association given the late onset of atrioventricular conduction abnormalities in humans (4,8,40). After heat-shock induction of the novel transgenic lineTg(hsp70l:nkx2.5-EGFP), our previous work demonstrates that temporally controlled expression ofnkx2.5 during early cardiac development is sufficient for long-term rescue of embryonic chamber identity defects permitting normal cardiac growth into adulthood (12). In this study, our findings illuminate that early reexpression ofnkx2.5 innkx2.5−/− embryos is not only adequate to maintain normal cardiac chamber identity and morphology but also to ensure regulation of HR and HRV during early development. Going forward, it will be interesting to extend our studies on the establishment of embryonic HR and HRV to the adult zebrafish to determine if the absence ofnkx2.5 gene function in rescuednkx2.5−/−;Tg(hsp70l:nkx2.5-EGFP) fish has an impact on maintenance of the cardiac conduction system and efficacy of autonomic nervous system control.
Although the validity of imagery-based HRV analysis has been established in zebrafish using similar video sequence methodologies, the early strategies were based on manual selection of a line of pixels within video images and manual threshold settings (6,41). Furthermore, these investigations were limited by the selection of specific regions of interest such as the caudal vein to generate HR sequences for HRV analysis (6). While more recent efforts have demonstrated the benefits of transgenic fluorescent zebrafish lines (28), this work estimates HR and HRV based on power spectra of pixel intensities assessing the “dynamic pixels” selected by thresholds. Power spectra-derived estimates of HR and HRV are based on relatively long time windows (containing 10 s to 100 s or more of heartbeats); as a result, they necessarily measure mean IHR and do not differentiate the faster and slower components of HRV. In contrast to such frequency domain methods, our time domain methods perform “R-R” type analyses, which allows for calculation of IHR (beat-to-beat HR) and RMSSD (beat-to-beat HRV). Moreover, our work offers significant advantages over prior studies as it performs an automated analysis based on the maxima of frame-to-frame pixel differences across the whole image without manual selection of an image region. We found that automatically tracking maximal tissue movement without highlighting a particular region of interest produces a roughly sinusoidal time series that can be marked for peak times predominantly immune to artifact. Although our method is limited by the transparency of the tissue, it is particularly well suited for examination of the zebrafish embryonic heart as visibility of cardiac contractility is easily attainable through the translucent pericardium. Altogether, our innovative strategy for HRV calculations provides noteworthy benefits over previously described techniques by automating extrapolation from video sequences of cardiac contractions to a sinusoidal, one-dimensional time series in the zebrafish embryo.
Perspectives and Significance
In summary, HRV is an important clinical marker for cardiac health and is increasingly used in research to detect subtle problems in myocardial performance. Given the advantages of zebrafish for studying cardiac developmental genetics and regeneration (2,22,53,54), this model has become popular and the arsenal of tools is expanding rapidly. Our current studies elucidating the significant differences between HR and HRV in wild-type andnkx2.5−/− embryos highlight these measures as essential, noninvasive markers of cardiovascular disease in zebrafish. Furthermore, the abnormal HR and HRV detected innkx2.5−/− embryos point to potential underlying defects in conduction system patterning. Increased utilization of HR and HRV analyses will complement future research in zebrafish models of CHD by providing a sensitive screening tool for the novel alleles generated by TALENs and CRISPR mutagenesis (3,5,19) and also for chemical genetic screening approaches (1,13,37,54). These strategies in zebrafish will enhance our understanding of human CHD, cardiac regenerative biology, and cardiovascular pharmaceutical therapeutics identified for applications to adult heart disease.
GRANTS
K. L. Targoff received support from the National Institutes of Health (NIH) Grants K12 -HD-043389, K08-HL-088002, and R01-HL-131438. Images were collected in the Confocal and Specialized Microscopy Shared Resource of the Herbert Irving Comprehensive Cancer Center at Columbia University, supported by NIH Grant P30-CA-013696. The confocal microscope was purchased with NIH Grant S10-RR-025686.
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the authors.
AUTHOR CONTRIBUTIONS
J.K.H., J.R.I., and K.L.T. conceived and designed research; J.K.H., R.S., and A.T. performed experiments; J.K.H., R.S., A.T., J.R.I., and K.L.T. analyzed data; J.K.H. and K.L.T. drafted manuscript; J.K.H., J.R.I., and K.L.T. edited and revised manuscript; J.K.H., J.R.I., and K.L.T. approved final version of manuscript; J.R.I. and K.L.T. interpreted results of experiments; J.R.I. and K.L.T. prepared figures.
ACKNOWLEDGMENTS
We are grateful to members of the Targoff laboratory for constructive discussions and Michael Myers for critical reading of the manuscript.
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