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The Johns Hopkins University Institute of Molecular Cardiobiology, Baltimore, Maryland 21205-2195
Correspondence: Address reprint requests to Brian O'Rourke, PhD, The Johns Hopkins University, 720 Rutland Ave., 1059 Ross Bldg., Baltimore, MD 21205. Tel.: 410-614-0034; Fax: 410-955-7953; E-mail: bor{at}jhmi.edu.
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ABSTRACT |
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m) in cardiomyocytes under physiological conditions is oscillatory and characterized by a broad frequency distribution that obeys a homogeneous power law (1/fß) with a spectral exponent, ß = 1.74. Additionally, relative dispersional analysis shows that mitochondrial oscillatory dynamics exhibits long-term memory, characterized by an inverse power law that scales with a fractal dimension (Df) of 1.008, distinct from random behavior (Df = 1.5), over at least three orders of magnitude. Analysis of a computational model of the mitochondrial oscillator suggests that the mechanistic origin of the power law behavior is based on the inverse dependence of amplitude versus frequency of oscillation related to the balance between reactive oxygen species production and scavenging. The results demonstrate that cardiac mitochondria behave as a network of coupled oscillators under both physiological and pathophysiological conditions. |
INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONSUPPLEMENTARY MATERIALACKNOWLEDGEMENTSREFERENCES |
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). Since then, numerous investigators have applied various analytical techniques to uncover "scale invariant" (fractal) processes in cardiac function. A well-studied example is the fluctuation of the beat-to-beat interval of the electrocardiogram. Time series plots of this parameter show variations that appear to have a similar morphology when viewed at temporal resolutions spanning several orders of magnitude. This is the temporal analogy to spatial fractal scaling observed in, for example, the branching patterns of a tree, the pulmonary bronchioles, or the arterial system (2).
Several methods have been developed to quantify such long-range correlations in time series, indicating that the events being correlated are not independent of each other. The methods include spectral analysis, which reveals the scale-free memory effect as a power law dependence of the frequency distribution (often displaying a "1/f" distribution (3)), and methods that plot fluctuations of a signal around a trendline when the data are aggregated over different time windows (e.g., fluctuation analysis (4), detrended fluctuation analysis (5), or relative dispersion analysis (6)). The potential importance of identifying these nontrivial correlations in complex physiological functions is that in disease conditions, it has been shown that the fractal character of the system can break down. Degeneration of the characteristic long-range correlation can be manifested either as i), an increase in the randomness of the fluctuations (i.e., toward uncorrelated white noise), ii), the appearance of correlations of the random walk type (i.e., Brownian noise), or iii), a narrowing of the frequency spectrum and/or the appearance of highly periodic behavior (e.g., the appearance of the Cheyne-Stokes frequency in the interbeat time series in patients with heart failure) (4,5,7).
Scale invariance has been observed in many biological systems that require a high degree of adaptability and a flexible response to changing environmental conditions. Hence, it has been argued that this organizational motif may permit complex control processes to respond without becoming "mode-locked" into a narrow range of function (4,5,7).
Mitochondrial oxidative phosphorylation is a prime example of a biological system regulated by a series of mechanisms that interact to provide a rapid and robust change in energy production to meet cellular demand. Therefore, in this study, we test the hypothesis that the mitochondrial network of the heart cell may be organized as a lattice of coupled relaxation-type oscillators (i.e., those exhibiting slow and fast phase components) that exhibit scale-free temporal organization. We have previously demonstrated that this network displays complex dynamic behavior when subjected to metabolic stress (8), including scale invariant spatiotemporal synchronization (9). Self-sustained and highly coordinated oscillations in mitochondrial membrane potential (m) and reactive oxygen species (ROS) can be triggered under conditions of oxidative stress (8), which could be reproduced in a computational model of ROS-induced ROS release (10).
In addition to reproducing the dominant low-frequency (
0.01 Hz) oscillations in energetic parameters observed under stress, the mathematical model also displayed a variety of stable high-frequency, low-amplitude oscillations when a single parameter was varied (10). This motivated us to employ the aforementioned analytical techniques to determine if long-range correlations exist in experimental time series of mitochondrial energetic parameters under physiological conditions. We demonstrate that the mitochondrial network behaves as a collection of weakly coupled oscillators with a broad frequency distribution under normal conditions that can transition to an oscillatory state with a single dominant frequency under conditions of metabolic stress. We suggest that this phase transition in time and space is due to an increase in the levels of the primary coupling factor, ROS. The findings reveal the fundamental spatial and temporal organization of mitochondria as a complex system of oscillators.
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MATERIALS AND METHODS |
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). See Supplementary Material for further details.
Fluorescent probes for two photon laser scanning microscopy and image acquisition and analysis
The cationic potentiometric fluorescent dye tetramethylrhodamine methyl ester (TMRM) (100 nM) was used to monitor changes in m as previously described (8). Images were recorded using a two photon laser scanning microscope (Bio-Rad (Hercules, CA) MRC-1024MP) with excitation at 740 nm, and the red emission of TMRM was collected at 605 ± 25 nm (Tsunami Ti:Sa laser, Spectra-Physics, Mountain View, CA).
Analysis of TMRM time series
Extended time series of TMRM fluorescence (1500–4000 images) recorded at a maximal temporal resolution of 110 ms were subjected to relative dispersional analysis (RDA) and power spectral analysis (PSA).
RDA
RDA allows a quantitative determination of how the state of a process at a given point in time is influenced by the state of the system at previous time points (2,12,13). The relative dispersion or coefficient of variation (CV = standard deviation/mean) is repeatedly calculated while binning (coarse-graining) the data set at successively larger timescales. More specifically, we aggregated adjacent points in the time series of m at 2, 4, 8, 16, and 32 successive values of the data set to calculate the CV for each grouping (12) and plotted it versus the aggregation number, m. The slope of this relation provides information as to the extent of long-term correlation (or memory) in the data set.
PSA
The power spectrum of the TMRM time series was analyzed after fast Fourier transform (FFT) of the fluorescence signal. Double log plots of amplitude versus frequency indicated a decrease in power proportional to 1/fß, where f is frequency and ß is the spectral exponent (2,12,13) (and see Supplementary Material). The Fourier transform of the TMRM signal was performed with the FFT routine of Microcal Origin (Version 6.0, Northampton, MA). Since this routine may use five different data windowing methods (rectangular, Welch, Hanning, Hamming, Blackman), we performed controls to examine how different windowing methods influenced the determination of ß. Simulated pink noise (35,281 time points) was used as a control whose power spectrum should yield ß = 1.0. The best fit of the simulated data was obtained with rectangular windowing (ß = 1.0; r = 0.61) (see Supplementary Material); thus, we used this method to calculate FFT from the TMRM time series. The results did not differ significantly when different windowing methods were used.
Because the sampling rate was limited to 100 Hz and the data were not low-pass filtered, data points shown at frequencies >1.3 (i.e., five times the sampling rate) in the power spectrum may contain some minor frequency contamination due to aliasing. This effect should not significantly alter the conclusions of the study since the slopes were determined from the data points that satisfied the Nyquist criterion of at least two times the sample frequency.
To differentiate between the TMRM signal obtained from cells and pure brown noise, we applied RDA and PSA to either simulated brown noise or brown noise obtained from the integration of white noise (see legends for Figs. 3 and 4, and the text; see also Supplementary Material for additional controls).
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exc, and laser intensity affected the results obtained with RDA or PSA (see Supplementary Material for details).
Computational model of the mitochondrial oscillator
An integrated model of mitochondrial energetics (14), which was extended to include a shunt of electrons of the respiratory chain toward the generation of 
, a ROS scavenging system, and a ROS-activated anion efflux pathway across the inner membrane (10), was used for the simulations shown in Fig. 2, using the parametric conditions described in Cortassa et al. (10).
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RESULTS |
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m fluctuates at high frequency within a restricted amplitude range, implying depolarizations of only microvolts to a few millivolts. As we have shown previously, oxidative stress may elicit low-frequency, high-amplitude oscillations that characterize the "pathophysiological" response (Fig. 1; see video in Supplementary Material). A return plot illustrates how the distribution of frequencies and amplitudes of oscillation can change at the junction between physiology and pathophysiology (Fig. 1, inset). Although the physiological domain shows an apparently "noisy" appearance, the transition to pathophysiology is characterized by a highly correlated limit cycle type oscillation.
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m and ROS, as a function of a fraction of the respiratory flux diverted to ROS production (i.e., superoxide anion ), revealed that in the high-frequency domain both the period and amplitude of the oscillator could be modulated. The period decreased from 34 ms to 16 ms as the ROS leak was increased from 6% to 15% of the respiratory flux, whereas the amplitude of ROS pulses reached a maximum (66 nM ) at 8% of respiration diverted to ROS and then decreased at higher frequencies (Fig. 2 B). The period (from 70 ms to 250 ms) and the amplitude of the m (2–24 mV) and ROS oscillations (150 nM to 1 µM) could also be modulated by varying the superoxide dismutase (SOD) concentration (from 1.0 to 1.2 µM) within the high-frequency range when the fraction of respiration diverted to ROS was fixed at 7.4% (not shown, but see Cortassa et al. (10)).
These results suggest that the mitochondrial oscillator may, potentially, function as both a frequency- and amplitude-encoding ROS signaling mechanism in the physiological (high-frequency) domain. This hypothesis was explored using the statistical analysis of m time series from isolated heart cells described below.
Temporal correlation of the mitochondrial network in the physiological domain
Heart cells loaded with TMRM, reporting m, were imaged at a frame interval of 110 ms with two photon laser scanning microscopy. RDA and PSA were applied to time series composed of 1500–4000 time points.
The rationale underlying RDA is that for a system exhibiting completely random fluctuations, the CV, drops off more rapidly as the data are aggregated over longer timescales as compared with a system that shows long-term memory (see Materials and Methods). The double-log plot of CV versus the aggregation number, m, of adjacent time points shows an inverse power law correlation with a slope corresponding to a fractal dimension, Df = 1.008 ± 0.002 (Fig. 3 A; n = 10 time series; five independent experiments). An inverse power law with a slope corresponding to a fractal dimension close to 1.0 suggests that there is long-term memory in the system (Fig. 3, A and C). In this context, long-term memory means that the m fluctuations are influenced by changes of m in the past.
Unlike the high correlation exhibited by the mitochondrial network, processes without memory show completely random behavior (white or brown noise) characterized by an exponential (Poisson) law with slopes corresponding to Df = 1.5 (Fig. 3, A, D, and E) (12). Unlike white and brown noises, pink noise exhibited a Df close to 1.0 (see Supplementary Material). The long-term memory of the mitochondrial network was not only evident in the "physiological domain" but also in the "pathophysiological domain" (Fig. 3, A–C) (see also Supplementary Material and Aon et al. (8)). These results were substantiated with controls performed on the instrument noise of the background from the same image sequence (Fig. 3 D) or after random shuffling of m time points to eliminate any deterministic component. Under either of these conditions, Df shifted from 1.0 to 1.5 (Fig. 3 A), indicating that the fluctuations in the signal were due to physiologically relevant, dynamic control mechanisms in mitochondrial metabolism rather than random variation. This was also confirmed later when inhibitors known to affect the mitochondrial oscillatory mechanism were applied (see below).
Power spectral analysis of m
Correlations in time series are also revealed using PSA and are often characterized by an inverse power law relationship. As also shown using the RDA above, self-similar scaling suggests that events in different timescales (milliseconds, seconds, minutes) are tied together in an orderly statistical sequence. Thus, the power spectrum of such data usually follows an inverse power law proportional to 1/fß (see Materials and Methods: PSA and FFT calculation).
Applying PSA, we calculated the power spectra (displayed as a double log plot of amplitude versus frequency) after FFT of the m time series from mitochondria under physiological conditions. The power spectrum of the mitochondrial network exhibited a bandwidth pattern with low-frequency components (<0.3 Hz, dashed line in Fig. 4 A) and a predominant (>90% of the data points) low-amplitude tail of higher frequencies (>0.3 Hz). The power spectrum could be described by a homogeneous inverse power law of the form 1/fß with ß = 1.737 ± 0.015 (n = 10 time series; five independent experiments) (Fig. 4 A). However, a value of ß close to 2.0 (1.99 ± 0.03, n = 10) could be attributed to the low-frequency components, and 1.54 ± 0.03 (n = 10) for the high-frequency, low-amplitude region of the spectrum (see below). The frequencies >0.3 Hz thus behaved in the mid-range between pink (ß = 1.0) and brown (ß = 2.0) noise.
The observed power spectrum is indicative of highly persistent, correlated, long-term memory processes that scale for at least three orders of magnitude. Correspondingly, we obtained ß 
0 or ß 2.0 for controls exhibiting random behavior (white noise) (Fig. 4 B, mid panels) or ordinary brown noise (Fig. 4 B, bottom panels), respectively. Moreover, ß = 1.0 was obtained from time series that simulate pink noise (see Supplementary Material, Fig. S3).
Taken together, the results show that the collective behavior of the mitochondrial network (i.e., through m) belongs to a statistically fractal, self-similar process characterized by a large number of frequencies in multiple timescales, rather than an inherent "characteristic" frequency.
Are reactive oxygen species intracellular messengers under physiological conditions as they are in pathophysiology?
The scale-free behavior of the mitochondrial network suggests that the mechanism described for the mitochondrial oscillator under pathophysiological conditions could share similar features in the physiological domain of behavior. We tested this by exposing heart cells to a respiratory inhibitor (rotenone), a ROS scavenger (TMPyP), and a mitochondrial benzodiazepine receptor (mBzR) inhibitor (4'-Cl-DZP). These pharmacological treatments decrease ROS production either by blocking respiration, by direct scavenging, or by inhibiting ROS-induced ROS release from mitochondria. Mechanistically, all of these agents inhibit oscillations in the pathophysiological domain (9,10).
Under physiological conditions, the presence of 15 µM rotenone or 64 µM 4'-Cl-DZP, but not TMPyP, rapidly (within 5 min) affected the high-frequency region of the spectrum but not the low-frequency one, with the exception of rotenone at 5 min. This effect on the high-frequency, low-amplitude domain of the spectrum (frequencies >0.3 Hz) (Fig. 5) was manifested as a strong decrease in the value of ß, predominantly as a result of a significant loss of correlation (Fig. 5). The loss of correlation in the high-frequency domain of the spectrum is consistent with a weaker coupling between mitochondrial oscillators in the network, in agreement with a decrease in ROS, the proposed coupling factor (8).
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0, whereas mitochondria in the correlated network gave r = 0.70 ± 0.05 (n = 4 time series; two independent experiments; Fig. 6 A). A similar comparison was made for myocytes undergoing "pathophysiological" mitochondrial oscillations by separately analyzing mitochondria included within and outside of the synchronized oscillating cluster (9). Mitochondria that were not oscillating in synchrony with the cluster exhibited a power spectrum similar to white noise (r = 0.05; compare panels D and E of Fig. 6), whereas mitochondria within the cluster showed a high r over a wide frequency range (r = 0.74; Fig. 6 C), similar to the high r exhibited by mitochondria under physiological conditions (r = 0.81; Fig. 6 B; see Supplementary Material for discussion of the spatial implications of these results).
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). The double log plot of amplitude versus frequency exhibits an inverse relationship (Fig. 7 and Supplementary Material). Two key factors contribute to this dependence—the SOD activity and the balance between the rate of ROS production and scavenging. Within the oscillatory domain, after a Hopf bifurcation (Fig. S4A in Supplementary Material and (10)), an increase in the SOD rate results in longer periods and higher amplitude oscillations (Fig. S4B in Supplementary Material). An extensive parametric analysis of the model revealed that this balance defines whether or not the system oscillates (10,15). Furthermore, the results suggest that the ROS balance also determines the frequency and amplitude of the mitochondrial oscillator. The rationale for interpreting this behavior is that given a constant background conductance of the inner membrane anion channel (IMAC) channel, having a lower SOD rate combined with a relatively high rate of ROS production leads to faster ROS accumulation in the mitochondrial matrix and triggers channel opening more readily. In contrast, with a faster rate of ROS scavenging (i.e., a higher SOD rate), it will take longer for ROS to accumulate in the matrix, resulting in a longer period.
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m oscillations (Fig. S6 in Supplementary Material), in agreement with experimental data (9). The decrease in the spectral exponent, ß, observed in the presence of inhibitors (Fig. 5) and the loss of correlation in the high-frequency domain of the spectrum (Fig. 6 A) could also be simulated by hypothesizing that a decrease in the levels of ROS in the network would introduce more random behavior (Fig. S6 in Supplementary Material). Thus, the behavior observed experimentally is consistent with an increase in the random behavior exhibited by the oscillators as a consequence of decreased ROS, the proposed coupling factor.
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DISCUSSION |
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m that is distinctly different from random behavior (Fig. 3). This is indicative of a self-similar fractal process. The power spectrum of such a distribution scales according to an inverse power law spanning at least three orders of magnitude (from milliseconds to a few minutes) and obeys a homogeneous power law (1/fß) with ß = 1.74 (Fig. 4), in the mid-range between pink (ß = 1.0) and brown (ß = 2.0) noise. Despite the value of ß being close to that of brown noise, and even having a ß 2.0 for frequencies below 0.3 Hz (Fig. 5, control panels), the correlative properties of the mitochondrial network were distinct from ordinary brown noise as demonstrated by RDA (Fig. 3 A). Moreover, the results indicate that decreasing mitochondrial ROS production at the level of the respiratory chain or blocking the ROS-induced ROS release mechanism by inhibiting the mitochondrial benzodiazepine receptor in the physiological domain consistently diminishes the extent of correlated behavior of the mitochondrial network in the high-frequency domain (Figs. 5 and 6, and Supplementary Material).
Importantly, with the help of our computational model of the mitochondrial oscillator (10), we are able to explain the mechanistic origin of the inverse power law behavior. The double log plot of amplitude versus frequency in Fig. 7 A demonstrates two essential features of the oscillatory dynamics displayed by mitochondria: i), the relationship between period and amplitude (i.e., the lower the period, the higher the amplitude), and ii), at periods >300 ms, the transition to a single dominant frequency with large m depolarizations that define the limit of the physiological domain (Fig. S4 in Supplementary Material). Within the high-frequency, low-amplitude range of behavior that we attribute to the physiological domain, m deflections of a few microvolts up to 30 mV can be seen.
Overall, the value of ß obtained suggests the existence of processes exhibiting temporal responses to stimuli with a combination of persistency (closer to brown noise, i.e., spectra with mainly low-frequency components) and flexibility (closer to pink noise, i.e., spectra enriched in high- and low-frequency components). This interpretation is consistent with the mitochondrial network of the heart cell having both properties of constancy and flexibility, i.e., providing a steady supply of ATP to fuel contraction and adapting the rate of energy production to meet the changing metabolic demand as workload varies, respectively (14,16).
Mitochondria viewed as a network of coupled oscillators
Winfree (22) pioneered the analysis of synchronization among coupled oscillators in a network, later refined by Kuramoto (37) (reviewed in Strogatz (17) and Strogatz (18)). The relevance of this subject cannot be overstated, for autonomous periodicity plays a pervasive role in the timekeeping and coordination of biological rhythms (19–21). Winfree considered idealized systems of nearly identical weakly coupled sinusoidal oscillators modeled as such for mathematical simplicity (22). He found that below a certain threshold of coupling, each oscillator runs at its own frequency, thus behaving incoherently until a further increase in coupling overcomes the threshold for synchronization (18,22). This synchronization event was characterized as the analog of a phase transition, revealing an insightful connection between nonlinear dynamics and statistical physics (17,18). This type of transition is strikingly similar to our own observations of the mitochondrial network (9) at the turning point between the physiological and pathophysiological regimes (Fig. 1). This global phase transition (visualized as a cell-wide mitochondrial depolarization) occurs when a critical density (60%) of mitochondria accumulate ROS above a threshold to form an extended spanning cluster (9). Our results agree very well with the quantitative predictions derived from percolation theory, especially concerning the percolation threshold, the fractal organization exhibited by percolation processes at the threshold (23), and the critical exponents (9).
A main difference between our results and that of previous coupled oscillator models is that we find an inverse power law (by RDA and PSA) in the physiological regime. This suggests that, despite their weak coupling, the oscillators do not behave incoherently or randomly. If the coupling were random, we should have found white noise in the physiological regime (Fig. 6 and Supplementary Material). Instead, we found a broad band of frequencies proceeding simultaneously at different timescales, described by an inverse power law (Figs. 3 and 4 and Supplementary Material).
The mitochondrial oscillator as a putative signaling system
The possibility for high-frequency, low-amplitude oscillations in mitochondrial ROS and m were predicted from simulations using our computational model of the mitochondrial oscillator (Fig. 2). Our experimental findings provide support for the hypothesis that mitochondrial oscillation may function as a frequency- and/or amplitude-encoded signaling mechanism under physiological conditions. The simulations indicate that the mitochondrial oscillator's period can be modulated over a wide range of timescales (10), suggesting that it may play a role as an intracellular timekeeper. Although the frequency distribution is broad under normal conditions, the long-term temporal correlations of the mitochondrial network could theoretically allow a change in one timescale to be felt across the frequency range.
We hypothesize that mitochondrial oscillations in the physiological domain are associated with ROS-dependent signaling since they do not represent a substantial energetic burden for the cell. Our hypothesis is based on i), the associated pulses of ROS in the nM range that are concomitant with the low-amplitude m oscillations (Fig. 2 A); and ii), their possible modulation in amplitude and frequency as a function of two feasible physiological variables, i.e., the degree of ROS production by the respiratory chain (Fig. 2 B) or the rate of superoxide scavenging by SOD (see Supplementary Material Fig. S4A).
The dual role of ROS as either toxic or signaling molecules with important effects on signaling cascades has been extensively recognized (24–26). One major molecular mechanism of ROS signaling is associated with intracellular redox sensing by sensitive thiols of cysteine residues present in kinases and phosphatases. For example, cytoplasmic signaling kinases such as mitogen-activated MAP kinases (e.g., p38, JNK, ERK), apoptosis regulating kinase (ASK1), and several isoforms of protein kinase C (e.g., PKC-
) can be activated by ROS or a prooxidative shift in the antioxidant capacity (24–26). Nuclear transcription factors can be activated either indirectly, via the above-mentioned signal cascades, or directly by ROS, and recent evidence also suggests that mitochondrial ROS production may be important for the activation of hypoxia-inducible factor (HIF; (27)).
The significance of inverse power laws for heart (patho)physiology
A main contribution of this work is to show that inverse power laws also characterize the normal, physiological behavior of the mitochondrial network. Inverse power laws express the inherent relatedness and nonrandom interactions of cellular processes proceeding, simultaneously, at different timescales. A profound implication of the power law behavior exhibited by the mitochondrial network is that beyond a critical level, the loss of a single element may cause the entire network to fail because of their multiplicative interdependency (12,13,28,29). Thus, a prediction derived from such an inherent organization of mitochondria is that failures can scale to higher levels of organization (15,30). This has already been shown to be true at criticality in the case of the mitochondrial network of heart cells under oxidative stress (8,9) or the whole organ after ischemia reperfusion (31).
According to PSA, the mitochondrial network of heart cells does not show a dominant frequency. Consequently, whatever happens in one frequency range may reverberate on all frequency scales. This is reminiscent of heart rate regulation in a normal subject, suggesting the intriguing possibility that a change in mitochondrial network dynamics could entrain pathological consequences for the cell and the organism. With metabolic stress, the frequency spectrum for m narrows and a dominant oscillatory frequency appears, indicating the transition from physiological to pathophysiological behavior in the mitochondrial network (Fig. 1). Interestingly, a "loss of spectral reserve" (32) for cardiac electrical activity occurs during the transition from normal to pathological states during the development of heart failure (33) or during postinfarction arrhythmias (34,35).
This raises the question of whether mitochondrial energetics could contribute to the mechanism underlying other scale invariant properties of the heart. The long-range correlations in the human heartbeat time series have been partly attributed to competition between parasympathetic and sympathetic stimuli on the pacemaker cells of the sinus node (4); however, the contribution of nonautonomic or cardiac cell processes has not been investigated. Fractal processes have also been recognized in the context of cardiac arrhythmias and used to define stimulation protocols to control chaos (36). It is worth noting that close links exist between mitochondrial energetics and action potential morphology, as exemplified in our recent study linking mitochondrial instability with postischemic arrhythmias (31), raising the possibility that the nonlinear properties of mitochondrial control could scale to produce cascades of feedback loops across coupled oscillatory systems (15,30). This possibility can be readily tested in future investigations.
Summarizing, we have described for the first time that the mitochondrial network of heart cells functions as a network of coupled oscillators under physiological conditions. The mechanism of the mitochondrial oscillator described experimentally and theoretically is shared by the physiological and pathophysiological domains of behavior, although differently. Under physiological conditions, the role of ROS would be more prominent for signaling intracellular processes rather than as in pathophysiology. These findings are in agreement with the highly structured, organized nature of the heart cell both from morphological and dynamic points of view.
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ACKNOWLEDGEMENTS |
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This work was supported by National Institutes of Health grant R37-HL54598 to B.O'R.
Submitted on April 24, 2006; accepted for publication August 29, 2006.
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REFERENCES |
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0) (mid, right) (12
REN = 2.5 x 10–6 mM; concentration of F1F0 ATPase, 
= 2.4 x 106 mM–1s–1; 
= 1.7 x 104 mM–1s–1; GT = 0.5 mM; maximal rate of the adenine nucleotide translocase, VmaxANT = 5 mM s–1; maximal rate of the mitochondrial Na-Ca exchanger, 
= 0.015 mM s–1. The 
