(C) PLOS One [1]. This unaltered content originally appeared in journals.plosone.org.
Licensed under Creative Commons Attribution (CC BY) license.
url:https://journals.plos.org/plosone/s/licenses-and-copyright

------------



Pacemaker translocations and power laws in 2D stem cell-derived cardiomyocyte cultures

['Christopher S. Dunham', 'Department Of Chemistry', 'Biochemistry', 'University Of California', 'Los Angeles', 'California', 'United States Of America', 'Madelynn E. Mackenzie', 'Department Of Microbiology', 'Immunology']

Date: 2022-04

Power laws are of interest to several scientific disciplines because they can provide important information about the underlying dynamics (e.g. scale invariance and self-similarity) of a given system. Because power laws are of increasing interest to the cardiac sciences as potential indicators of cardiac dysfunction, it is essential that rigorous, standardized analytical methods are employed in the evaluation of power laws. This study compares the methods currently used in the fields of condensed matter physics, geoscience, neuroscience, and cardiology in order to provide a robust analytical framework for evaluating power laws in stem cell-derived cardiomyocyte cultures. One potential power law-obeying phenomenon observed in these cultures is pacemaker translocations, or the spatial and temporal instability of the pacemaker region, in a 2D cell culture. Power law analysis of translocation data was performed using increasingly rigorous methods in order to illustrate how differences in analytical robustness can result in misleading power law interpretations. Non-robust methods concluded that pacemaker translocations adhere to a power law while robust methods convincingly demonstrated that they obey a doubly truncated power law. The results of this study highlight the importance of employing comprehensive methods during power law analysis of cardiomyocyte cultures.

Funding: This work was funded by grants from the National Institutes of Health ( https://www.nih.gov/grants-funding ). Grant R21HL124503 was awarded to AZS, JKG, and AN. Grants R01 HL142801 and HL146159 were awarded to AN. MBJ was supported by the UCLA Center for Duchenne Muscular Dystrophy Ruth L. Kirschstein National Research Service Award T32AR065972 ‘Muscle Cell Biology, Pathophysiology, and Therapeutics’ from the National Institute of Arthritis and Musculoskeletal and Skin Diseases ( https://grants.nih.gov/grants/guide/pa-files/pa-21-048.html ). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Copyright: © 2022 Dunham et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Introduction

Recent investigations of human induced pluripotent and embryonic stem cell-derived cardiomyocytes (hiPSC-CM and hESC-CM, respectively) have shone significant light on numerous factors contributing to the development of the heart [1–6]. However, the mechanisms underlying the full maturation of cardiomyocytes to robust adult phenotypes remain unknown [1, 7, 8]. Phenotypic traits which have thus far failed to match those in adult cardiomyocytes include electrical impulse propagation, mechanical properties including sarcomere length and contractility, cell morphology, and gene expression [1, 9–11]. Additionally, some studies have suggested that defective cardiomyocyte development may play a role in a number of disease states such as cardiomyopathy and late myocardial dysfunction [2, 12, 13]. The inability to mature beyond the late fetal phenotype stage considerably limits applications for stem cell-derived cardiomyocytes in drug screening, disease modeling, and regenerative medicine [1, 2, 7, 14, 15].

Among the mechanisms which must be understood in the context of cardiomyocyte development is the establishment of pacemaker cells. These pacemaker cells are responsible for maintaining the rhythmic beating of all cells in the cardiomyocyte syncytium by means of action potential generation [16, 17]. The heart has a dedicated region of pacemaker cells, known as the sinoatrial node (SAN), that is responsible for maintaining a consistent beat rhythm throughout the lifetime of the organism [1, 18]. Many types of arrhythmias result from the disruption of rhythm-maintaining electrical impulses in the SAN, throwing the system into disarray [2, 19]. Although SAN is responsible for initiating heartbeat in the postnatal heart in physiological condition, all cardiomyocytes in the early embryonic heart are capable of generating autonomic beats. The pacemaker cells are specialized during mid-gestational stages. In vitro differentiation of hESC-CMs/hiPSC-CMs recapitulates this process [20]. Understanding how pacemaker regions arise and the role of pacemaker instability during cardiomyocyte maturation could provide insight into the development of the SAN and would help in furthering the current understanding of arrhythmias.

Difficulty in elucidating the mechanisms responsible for pacemaker development may be partially attributed to gaps in knowledge about the underlying interactions between cells in the cardiomyocyte culture (i.e. interactions within the cardiomyocyte network). Information in the form of environmental, physical, genomic, and chemical cues concerning the establishment of specialized cellular structures (e.g. intercalated discs) and functional roles (e.g. pacemaker cells, late fetal proliferating cells, ventricular conduction system-like cells) needs to be transmitted to the cardiomyocytes within the network [2, 21–24]. Insight into cardiomyocyte network dynamics and the processes responsible for information transfer may be attainable through the analysis of observable network characteristics (e.g. beat rate, pacemaker behavior, and biomechanical properties) for adherence to power laws.

Power laws—probability distributions of the form p(x) ∝ x-α –are of interest to several scientific fields because they provide important information about the dynamics of the system, e.g. long-range correlations, scale invariance, and self-similarity [25–27]. Several studies have explored whether power laws apply to cardiac systems, particularly in the context of tissue or cellular dysfunction, e.g. mitochondrial oxidative stress and arrhythmias [28–32]. Prior studies demonstrated power law behavior in investigations of heart (beat) rate variability, calcium load, and contractile stress in cardiomyocytes [33–37]. Studies have shown that aberrant cardiac systems exhibit a discernible change in the exponent of the power law measured for heart rate variability, which describes small variations in the interval between heart beats, in patients with myocardial infarction and coronary heart disease, and in heart transplant patients [29, 38–41]. Other studies focused on power laws as they relate to the mitochondrial network and the effect of oxidative stress on both the network and the dependent cardiac myocytes.

While intriguing, the applied methodologies in these studies fail to meet the standards defined in other fields, including: condensed matter physics, geology, and neuroscience, where power law analysis is more established [42–45]. In these fields, power laws are typically evaluated through a combination of methods, including: 1) calculation of the power law exponent, α, via maximum likelihood estimation (MLE), 2) statistical assessments of how well the data fit to a proposed distribution using the Kolmogorov-Smirnov goodness-of-fit test, 3) log-likelihood ratio tests between power law (Eq 1), exponential (Eq 2), and other heavy-tailed distributions (i.e. distributions in which the tail probability decays polynomially rather than exponentially), including log-normal (Eq 3), Weibull (stretched exponential, Eq 4), doubly truncated power law (Eq 5), and other candidate distributions to determine which one demonstrates a superior fit to the data [42, 46–48].

(1)

(2)

(3)

(4)

(5)

For the power law distribution (Eq 1), ɑ represents the power law exponent. In the exponential distribution (Eq 2), λ represents the rate parameter and is used to indicate the rate of decay. For the log-normal distribution (Eq 3), μ represents the expected value (i.e. mean) and σ represents the standard deviation of the natural logarithm of the variable, x. In the Weibull, or stretched exponential, distribution (Eq 4), λ again represents the rate parameter and β represents the stretching parameter. Finally, for the case of the doubly truncated power law distribution (Eq 5), ɑ and λ are as previously defined in the power law and exponential functions.

In contrast, most, if not all, power law assessments performed in the cardiac science community employed relatively straightforward logarithmic plots of two parameters, e.g. size x and number of events of size x, against each other (i.e. log 10 (y) vs log 10 (x)), accompanied by linear regression of the data. The underlying logic of this method is that if the data fit well to a line on a log-log plot, then the data must obey a power law, because a power law produces a straight line on logarithmic axes [49–51]. However, this is not always true and there could be other, superior descriptors of the data, e.g. exponential distributions or one of the aforementioned heavy-tailed distributions, that this method seldom considers. Consequently, this methodology must be considered incomplete.

This study seeks to demonstrate how analysis conducted using the incomplete methods described above can lead to misleading or contradictory interpretations for a system that demonstrates heavy-tailed, potentially power law behavior. A thorough comparison is made using more robust, established techniques, including: MLE to calculate the (suspected) power law’s exponent and log-likelihood ratio tests to engage in comparisons between alternative distributions to which the data could belong [42, 52]. This analysis is applied to the quiescent (stable) period between pacemaker translocations, defined here as the spatial instability and subsequent relocation of the pacemaker region across consecutive beats, as observed in stem cell-derived cardiomyocyte cultures. Pacemaker translocations were observed previously but were not examined in detail [8]. The quiescent periods between pacemaker translocations are suspected to obey a power law due to their superficial similarity to a known power law-obeying system: the inter-burst (or inter-event) interval between neuronal action potential spiking events observed in neuronal cultures [53, 54]. Pacemaker translocation quiescent periods are investigated electrophysiologically using two-dimensional monolayers of stem cell-derived cardiomyocytes plated onto microelectrode arrays (MEAs). This experimental design provides the requisite spatiotemporal information essential for the analysis of pacemaker translocation quiescent periods in order to determine whether they constitute a power law-adhering phenomenon.

[END]

[1] Url: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0263976

(C) Plos One. "Accelerating the publication of peer-reviewed science."
Licensed under Creative Commons Attribution (CC BY 4.0)
URL: https://creativecommons.org/licenses/by/4.0/


via Magical.Fish Gopher News Feeds:
gopher://magical.fish/1/feeds/news/plosone/

You are viewing proxied material from magical.fish. The copyright of proxied material belongs to its original authors. Any comments or complaints in relation to proxied material should be directed to the original authors of the content concerned. Please see the disclaimer for more details.