|
|
||||||||
1Portland State University, Portland, Oregon; 2Department of the Heart and Great Vessels "Attilio Reale," University "La Sapienza": UOC Biotechnologies Applied to Cardiovascular Diseases, Rome, Italy; 3Institut National de la Santé et de la Recherche Médicale, Athérosclérose, Pessac, France; and 4Université Victor Ségalen Bordeaux 2, and 5Centre National de la Recherche Scientifique, Université Victor Ségalen Bordeaux 2, and 6Centre Hospitalier Universitaire de Bordeaux, Bordeaux, France
Submitted 21 November 2005 ; accepted in final form 29 January 2006
| ABSTRACT |
|---|
|
|
|---|
60%. Inhibition of mitoKATP by perfusion of 5-hydroxydecanoate (5-HD) or tetraphenylphosphonium before induction of inotropic stress resulted in a marked attenuation of RPP. Inhibition of mitoKATP after induction of stress caused the inability of the heart to maintain a high-work state. In human atrial fibers, the increase in contractility induced by dobutamine was inhibited 60% by 5-HD. In permeabilized fibers from the Langendorff-perfused rat hearts, inhibition of mitoKATP resulted, in all cases, in an alteration of adenine nucleotide compartmentation, as reflected by a 60% decrease in the half-saturation constant for ADP [K1/2 (ADP)]. We conclude that opening of cardiac mitoKATP is essential for an appropriate response to positive inotropic stress and propose that its involvement proceeds through the prevention of stress-induced decrease in mitochondrial matrix volume. These results indicate a physiological role for mitoKATP in inotropy and, by extension, in heart failure.
mitochondria; creatine kinase; calcium; dobutamine; ouabain

), any perturbation of 
will cause changes in matrix and IMS volume (5, 13). On this basis, we proposed that the decrease in 
caused by ischemia was responsible for the disruption of intracellular adenine nucleotide compartmentation and that mitoKATP opening reversed this effect by adding a parallel K+ conductance to compensate for the lower driving force (13).
This study is designed to investigate the role of mitoKATP during positive inotropic stress, a condition in which 
will decrease, because myocardial mechanical activity, ATP production, and oxygen consumption are increasing. Consequently, K+ diffusion into the matrix will decrease, the mitochondrial matrix will contract, and the IMS will expand (6). In isolated mitochondria, diazoxide prevents the matrix contraction induced by high rates of respiration, and we suggested a role for mitoKATP opening during positive inotropic stress, which is also associated with high rates of respiration (13). If mitoKATP does not open during positive inotropy, matrix volume contraction will be accompanied by an obligatory increase in the volume of IMS. IMS expansion, in turn, will disrupt the structure-function of the components required for efficient energy transfer, namely, the outer membrane (OM) voltage-dependent anion channel (VDAC), the inner membrane adenine nucleotide translocase (ANT), and the IMS mitochondrial isoform of creatine (Cr) kinase (Mi-CK). This effect is predicted to perturb energy transfer from mitochondria to cytosolic ATPases during inotropic stress, when efficient energy transfer is most needed (24). To counteract this effect, we hypothesized that a signal must be sent to open mitoKATP whenever inotropic stress is encountered.
We examined this hypothesis on isolated, perfused rat hearts, on permeabilized skinned fibers, and on human atrial fibers. We show that hearts perfused with a mitoKATP inhibitor 5-hydroxydecanoate (5-HD) or tetraphenylphosphonium (TPP+) fail to respond to positive inotropic stress induced by calcium, ouabain, or dobutamine. Moreover, hearts are unable to maintain a high-work state if the mitoKATP blockers are added after positive inotropy has been established. The mitoKATP blockers had a marked effect on OM permeability to adenine nucleotides, as reflected in a decrease in the half- saturation constant for ADP [K1/2 (ADP)] for respiration. That these effects are due to interference with contractility is supported by contractility studies in atrial fibers. Importantly, 5-HD and TPP+ exhibited none of these effects in the absence of inotropic stress. We propose that the effects of 5-HD and TPP+ are linked to a disruption in IMS volume homeostasis, leading to increased outer mitochondrial membrane permeability to adenine nucleotides and consequent impaired efficiency of energy transfer between mitochondria and cytosol. To our knowledge, this is the first demonstration that physiological mitoKATP opening is required for the positive inotropic response.
| MATERIALS AND METHODS |
|---|
|
|
|---|
Male Sprague-Dawley rats, weighing 350 to 375 g, were used in full accord with the recommendations of and all protocols with the approval by the Institutional Animal Care Committee [Institut National de la Santé et de la Recherche Médicale (INSERM), Paris, France]. The rats were anesthetized with pentobarbital sodium (40 mg ip). The thorax was opened, and the hearts were rapidly excised and immediately cooled in iced Krebs buffer and Langendorff perfused by an aortic cannula delivering warm (37°C) oxygenated buffer at a constant pressure of 100 mmHg, as previously described (4, 14).
Briefly, hearts were perfused with a modified phosphate-free Krebs-Henseleit solution containing (in mM) 118 NaCl, 5.9 KCl, 1.75 CaCl2, 1.2 MgSO4, 0.5 EDTA, 25 NaHCO3, and 16.7 glucose. This high glucose concentration was used to avoid substrate limitation at the level of glucose entry. The pulmonary artery was transected to facilitate coronary venous drainage. A 5-cm-long polyethylene drain was inserted through the pulmonary artery in the right ventricle to collect coronary effluent for myocardial oxygen consumption (M
O2) measurements. Coronary effluent was anaerobically collected at 2 ml/min. An oxygen electrode and an oxymeter (Strathkelvin Instruments) continuously monitored coronary effluent PO2. Perfusate PO2 was measured at the beginning and at the end of each experiment just above the heart, and M
O2 was calculated as M
O2 (in µmol O2/min) = [perfusate O2 content (in µmol/ml) effluent O2 content (in µmol/ml)] x coronary output (in ml/min).
A left ventricular polyethylene apical drain was inserted through a left atrial incision to allow thebesian venous drainage. Left ventricular pressure was monitored from a water-filled latex balloon placed through the left atrial appendage and connected to a Statham P23 Db pressure transducer. The volume of the intraventricular balloon was adjusted to produce an initial end-diastolic pressure between 5 and 8 mmHg and was kept constant throughout the experiments. Hearts were not paced, and mechanical performance was evaluated as the product of heart rate and developed pressure (RPP).
Perfusion protocols.
Perfusion protocols are presented in Fig. 1. A total of 14 experimental series were performed with six hearts in each. Inotropic stress was achieved, as indicated also in RESULTS, and figures by a transition to a buffer containing either 4 mM CaCl2, 80 µM ouabain, or 0.25 µM dobutamine.
|
31P NMR study.
In some series, the metabolic status of the heart was assessed by using a 9.4-T superconducting magnet with a 20-cm bore and a GE-400 Omega spectrometer (Fremont, CA) by inserting the hearts into a 1H/31P double-tuned probe, as previously described (4). The probe was tuned to the phosphorus resonance frequency of 161.94 MHz, and the magnetic field homogeneity was optimized by shimming on the proton signal coming from the heart and the surrounding medium. 31P NMR spectra were obtained without proton decoupling. Pulse width was 27 µs (60° pulse angle), recycle time 2.14 s, and spectral width 6,000 Hz. One-thousand twenty-four data points were used and zero-filled to 2,048. Partially saturated 31P NMR spectra were obtained by averaging data from 140 free induction decays (5-min acquisition time). Spectra were analyzed by using a 20-Hz exponential multiplication and phased with a zero-order phase correction. Peaks were fitted by Lorentzian function, and peak areas were corrected for predetermined differential saturation.
Myocardial ATP content during perfusion was assayed by standard enzymatic methods in a separate group of five rats, and total Cr by the Kammermeier method as described (4). Intracellular pH of each perfused heart was measured by comparing the chemical shift between Pi and phosphocreatine (PCr) resonances with values obtained from a standard curve.
Free ADP cytosolic concentration was calculated by using the CK equilibrium relationship: [ADP] = [ATP] x [Cr]/([PCr] x [H+] x KCK), with KCK = 1.66 x 109 M1. All NMR data are presented as percentages of baseline.
Mitochondrial respiratory function.
Mitochondrial function was assessed on permeabilized skinned fibers of the left ventricle obtained immediately at the end of the Langendorff-perfusion protocols presented in Figs. 1 and 2A. Additional series of skinned fibers were performed immediately after 10-min stabilization, followed by 15-min perfusion with a buffer containing 300 µM 5-HD, 0.4 µM TPP+, or 10 µM HMR-1098, as illustrated in Fig. 1 (series 5-HD, TPP+, and HMR).
|
Preparation of permeabilized cardiac fibers has been exhaustively described and discussed in earlier studies (10, 25, 30). At the end of the Langendorff-perfusion protocols, small pieces of cardiac muscle were taken from the left ventricle and put into cold solution A (see below). All procedures were carried out at 4°C. These samples were rapidly dissected into bundles of fibers. Fibers were incubated for 30 min with shaking in 1.8 ml solution A in the presence of saponin (50 µg/ml) to selectively destroy the sarcolemma. The bundles were subsequently put into solution B (see below) twice for 10 min to wash out adenine nucleotides, PCr, and saponin. Oxygraphic measurements were performed in solution B, supplied with pyruvate (10 mM) and malate (5 mM).
Solutions A and B were prepared on the basis of the cytoplasmic composition of the muscle cells. Solution A (in mM) contained 2.77 CaK2EGTA, 7.23 K2EGTA (pCa = 7); 6.56 MgCl2, 0.5 DTT, 50 K-methanS, 20 imidazole, 20 taurine, 5.3 Na2ATP, and 15 PCr (pH 7.1 was adjusted at 25°C). Solution B (in mM) contained 2.77 CaK2EGTA, 7.23 K2EGTA (pCa = 7), 1.38 MgCl2, 0.5 DTT, 50 K-methanS, 20 imidazole, 20 taurine, and 3 KH2PO4 (pH 7.1 was adjusted at 25°C).
Oxygraphic measurement of respiratory rates.
The respiratory rates of skinned fibers (0.50.75 mg dry wt) were determined with the use of a Clark electrode in an oxygraphic cell containing 2 ml of solution B, supplemented with BSA or 2 ml of KCl solution at 25°C with continuous stirring. The solubility of oxygen was assessed to be 215 nmol O2/ml.
Control of the respiration by ADP and Cr.
The respiratory rate of mitochondria in skinned cardiac fibers was measured in solution B. Increasing amounts of ADP, ranging from 0.0125 to 1 mM, were successively added. The stimulatory effect of ADP was calculated from the respiration rates measured in the presence of a given concentration of ADP minus the value in the absence of ADP (state 2). K1/2 (ADP) was calculated from double-reciprocal plots of the dependence of respiration rate on the concentration of ADP. All parameters are presented as means ± SE.
Measurements of contractility on human atrial fibers.
Informed consent was obtained from adult patients who underwent elective open-heart surgery for coronary artery disease or rheumatic valve lesions. These patients were routinely taking cardioactive drugs according to standard prescriptions. Ethical considerations prevented us from discontinuing the drugs >24 h before surgery. Exclusion criteria were arrhythmias, congestive heart failure, dilated heart, and antiarrhythmic or oral hypoglycemic medication. Premedication consisted of midazolam (0.03 mg/kg), administered intravenously 10 min before induction of anesthesia. Anesthesia was induced with target-controlled infusion (TCI) of propofol (site effect, 1.6 µg/ml), sufentanil (0.350.5 µg/kg), and rocuronium (0.6 mg/kg). After tracheal intubation, the lungs were mechanically ventilated with an oxygen-air mixture (inspired oxygen fraction,
40%). The maintenance of anesthesia was obtained with propofol in TCI, sufentanil (0.35 µg·kg1·h1), and supplemental boluses of rocuronium. Cardiac surgery was performed on patients while on cardiopulmonary bypass. Samples of right atria appendages were obtained during cannulation for cardiac surgery. The methods to obtain human atrial trabeculae working isometrically in vitro have been previously described in detail (3, 9, 29). Briefly, a sample of the right atrial appendage (1 cm2, 5001,000 mg) was removed and immersed in preoxygenated and modified Tyrode solution containing (in mM) 120 NaCl, 4 KCl, 2.7 CaCl2, 1.1 MgCl2, 25.7 NaHCO3, 1.8 NaH2PO4, and 11 glucose at 22°C. The time between excision and the beginning of laboratory processing was 15 min. The sample was gently pinned down in the chamber with oxygenated modified Tyrode solution, gassed with a 95% O2-5% CO2 mixture, leading to PO2, 640 ± 20 mmHg, measured at 755 mmHg barometric pressure and pH 7.4 ± 0.1. The sample was cut into two to three pieces containing free-running trabeculae (pectinate muscle); macroscopically damaged tissue was discarded. In the organ bath, the preparation was warmed gradually (circulating thermostat-regulated bath) over a period of 60 min up to 37°C (continuously monitored). The base of the pectinate muscle was fixed to the chamber floor with fine stainless steel pins, and the opposite end was connected to a precalibrated force transducer via a stainless steel hook. The muscle was stimulated by 1-ms square pulses delivered from an orthorhythmic stimulator at 2 mA after the diastolic threshold intensity was measured (between 0.5 and 1.5 mA) via a bipolar Teflon-coated 99.99% silver-wire electrode (0.375 mm in diameter), placed on the muscle surface. The chamber received incoming oxygenated solution at 5 ml/min by a single-headed peristaltic pump. The preparation was made to contract isometrically and stretched to the peak of its length-tension curve (Lmax). Muscle length remained at Lmax throughout the experiment. Baseline force development at Lmax in oxygenated and thermostatically controlled Tyrode solution was obtained after stabilization (60 min) at 1,000-ms (1 Hz) cycle length. The same stimulation rate was continued during the study. The data were monitored on a digital memory oscilloscope, digitized at a sampling frequency of 8 kHz, and stored on a computer. The software automatically measured resting tension (or preload, in mg) and developed tension (DT, in mg). After completion of the study, the muscle was dried, the base was used to fix it to the chamber-floor cutoff, and the actively contracting portion was weighed on a precise balance.
Control preparations were obtained by 15-min treatment with 10 µM dobutamine, which typically increases developed tension by 60% in these experiments (9) compared with baseline conditions. Dobutamine (10 µM) was then superfused for 15 min in the presence of 300 µM 5-HD, started 15 min earlier.
The experimental series included six preparations. DT values (in %) are presented as means ± SE.
Statistical analysis of experimental data.
All data are expressed as means ± SE. A two-way ANOVA for repeated measurements was performed to analyze hemodynamic parameters at different time points. A value of P < 0.05 was required to consider the differences as statistically significant. Single-factor ANOVA, followed by unpaired Student's t-test, was used to investigate respiration parameters. A value of P < 0.05 was required to consider the differences statistically significant.
| RESULTS |
|---|
|
|
|---|
Perfusion with a buffer containing 1.75 mM CaCl2 resulted in a stable RPP of 30,000 ± 2,000 mmHg/min and a M
O2 of 32 ± 2.5 µmol O2·min1·g dry wt1. The transition to a buffer containing 4 mM CaCl2, 0.5 µM dobutamine, or 80 µM ouabain resulted in a 6080% increase in RPP (Fig. 2A). This increase in RPP remained stable during the entire perfusion period, was associated with an increase in coronary flow (Fig. 2C), and was supported by a significant increase in M
O2 with no change in RPP-to-M
O2 ratio (Table 1). The increase in RPP was caused primarily by an increase in developed pressure, particularly during calcium-induced stress (compare Fig. 2, B and D). These control data show that the positive inotropic agents calcium, dobutamine, and ouabain caused comparable and stable increases in the mechanical activity of the heart.
|
O2 ratio (Table 1). Thus inhibition of the inotropic response was not due to the uncoupling of oxidative phosphorylation. The addition of HMR to the perfusion medium had no effect on RPP or developed pressure and did not influence the mechanical response to calcium-induced inotropic stress (Fig. 2, A and B). Overall, these data show that mitoKATP inhibitors, but not sarcolemmal ATP-sensitive K+ channel inhibitors, altered the response to inotropic stress.
The data in Fig. 3A show that these effects are not limited to 5-HD. TPP+, which is a mitoKATP blocker (20), caused similar inhibition of the inotropic response.
|
Overall, these data show that mitoKATP inhibitors prevented the heart from maintaining an appropriate response to inotropic stimuli, suggesting that opening of mitoKATP is necessary to sustain a high level of work.
5-HD inhibits contractility of human atrial fibers.
The experiments of Fig. 4 were performed to confirm that the effect of 5-HD on RPP was due specifically to inhibition of contractility. Superfusion of human atrial trabeculae in vitro with dobutamine increased contractility to 161 ± 32% of baseline, as is typical of this preparation (29). 5-HD caused a 61% reduction in the dobutamine response, and 1 µM glyburide caused a 30 ± 3% (n = 3 experiments) reduction in the dobutamine response (data not shown).
|
By washing ATP out of the permeabilized fibers, we created a condition in which respiration depended on an addition of ADP. The K1/2 (ADP) for respiration reflects, in part, the diffusion limitation imposed on ADP by the OM.
As shown previously, OM permeability to ADP and ATP is highly sensitive to changes in IMS volume, such that the diffusion limitation is removed when IMS volume increases, with a corresponding decrease in K1/2 (ADP) (5). These effects of volume have been observed in isolated mitochondria and in fibers obtained from normal hearts (5).
Figure 5 contains a summary of K1/2 (ADP) values from a series of experiments carried out on fibers obtained from hearts subjected to the treatments described in Fig. 3A. Additional series of measurements were performed on fibers prepared immediately at the end of 5-HD, TPP+, or HMR perfusion, according to the protocol illustrated in Fig. 1 (series 5-HD, TPP, and HMR). The essential point is that 5-HD and TPP+ each caused a significant decrease in K1/2 (ADP) after calcium-induced inotropic stress, indicating that these mitoKATP blockers plus inotropic stress caused increased permeability of the OM to adenine nucleotides. We propose that this increase in permeability is the cause of the inability of the hearts to respond to inotropic stimuli (see DISCUSSION).
|
Figure 6 contains the results of experiments designed to detect changes in respiration caused by the same perfusion protocols described in Figs. 1 and 3A. There was no difference in state 2 respiration among the groups, showing that the treatments did not uncouple respiration. There was also no difference in state 3 respiration among the groups, showing that the treatments did not inhibit maximal respiration.
|
Figure 7 contains results from 31P NMR measurements performed on hearts subjected to the same protocols as described in Fig. 3A. Perfusion of 5-HD had no effect on the metabolic status of the heart at normal buffer calcium concentrations. The increase in extracellular calcium from 1.75 to 4 mM resulted in a significant increase in [Pi] and calculated [ADP] (Fig. 7, A and D). These changes were associated with a significant decrease in [PCr] and a slight (10%) decrease in [ATP] (Fig. 7, B and C). The effect of 5-HD on the calcium response increased the rates of PCr decrease and ADP increase compared with control groups (Fig. 7, B and D). Overall, these data show that, despite the almost complete inhibition of the calcium-induced inotropic response by 5-HD, there was a decrease in energy reserve, as evidenced by the decrease in PCr and the increase in ADP.
|
| DISCUSSION |
|---|
|
|
|---|
In support of this hypothesis, we show that the mitoKATP blockers 5-HD and TPP+ decrease the ability of the heart to respond to or sustain a positive inotropic response (Figs. 2 and 3). This effect is seen whether the inotropy is induced by calcium, ouabain, or dobutamine. The data in Fig. 4 confirm that the effect of 5-HD on RPP was due specifically to inhibition of contractility. Overall, these data show that the mitoKATP blocker 5-HD caused a significant decrease in contractile reserve and an inability of the heart to maintain the high-work state. This result implies that inotropic stress conveys a signal to open mitoKATP, perhaps by phosphorylation (6).
Our hypothesis on the mechanism by which mitoKATP opening supports inotropy derives from the following observations. First, ATP synthesized in the mitochondrial matrix is translocated to the IMS by the ANT where it is immediately converted to PCr by Mi-CK. As a result, 90% of the energy produced in the form of ATP is exported to the cytosol as PCr, whereas only 10% is exported as ATP (4). This energy transfer system is not required during normal workload conditions but is necessary to achieve high-work states. Indeed, the heart is unable to function in the upper 50% of its dynamic range when CK is inhibited (4, 8, 11, 24, 27). Thus energy transfers via ADP-to-ATP ratio (ADP/ATP), which are sufficient to match low rates of energy production and consumption, represent an energy "leak" at high rates of cardiac work. Second, we have shown that an expanded IMS causes increased OM permeability to ADP and ATP, which is expected to reduce the ability of the heart to work at high rates. We have suggested that this regulation of OM permeability is provided by CK octamers, which bind to OM VDAC, making it selectively permeable to Cr/PCr over ADP/ATP (15, 23, 26, 31). Third, as described in Fig. 8, an inotropic challenge results in an increase in electron transport rate, which induces a decrease in 
and reduced influx of K+ salts and osmotically obligated water into the mitochondrial matrix. As a consequence, the matrix will contract due to the operation of the K+/H+ antiporter, and the IMS will expand (6, 13). IMS expansion will cause dissociation of CK from VDAC and increased OM permeability to nucleotides. Thus efficient energy transfer is weakened when it is most needed. Conversely, mitoKATP opening adds a parallel K+ conductance that compensates for the lower driving force, and IMS volume and VDAC permeability are maintained. It is this mitoKATP-dependent volume regulation that is essential, in our view, for maintaining efficient energy transfer between mitochondria and cytosol.
|
O2 ratio (Table 1). Thus these treatments were not associated with uncoupling of oxidative phosphorlyation. Thus 15 min of exposure to 5-HD or TPP+, in the presence or absence of calcium-induced inotropic stress, did not inhibit respiration. This finding should alleviate the concern, expressed by others (16), that 5-HD may interfere with energy metabolism. The 31P NMR data in Fig. 7 also support the hypothesis relating mitoKATP to inotropy. After induction of inotropic stress, PCr utilization increases and PCr levels decrease. In 5-HD-treated hearts, PCr levels decrease at a faster rate and to a greater extent. We consider that this is due to increased OM permeability to ATP and ADP and consequent impairment of energy shuttling via Cr/PCr. Thus maintenance of mitochondrial respiration is achieved at the expense of an increase in ADP. Overall, these phenomena will result in a decrease in the ATP availability at the level of cytosolic ATPases and a decrease in the free energy of ATP hydrolysis, with the primary consequence that the heart is unable to perform in high-work states.
We may now return to the subject introduced at the beginning of DISCUSSION. If, as suggested, the pathway to protect against ischemic stress originated from the pathway required to support inotropic stress, then it follows that inotropy itself should protect against ischemia-reperfusion injury. In fact, this is the case. Calcium preconditioning has been well known for a decade (12, 19, 21); considerable literature supports the concept that
1-receptor stimulation is cardioprotective (1, 2, 28), and preliminary studies have shown ouabain to be cardioprotective (22). Moreover, each of these modes of protection has been shown to involve KATP channels. These findings support the postulated interconnections between mitoKATP, inotropy, and cardioprotection, and, although the mechanism requires further study, they also support an essential physiological role for mitoKATP in inotropy and, by extension, in heart failure.
| GRANTS |
|---|
|
|
|---|
| FOOTNOTES |
|---|
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
| REFERENCES |
|---|
|
|
|---|
This article has been cited by other articles:
![]() |
S. Gao, C.-L. Long, R.-H. Wang, and H. Wang KATP activation prevents progression of cardiac hypertrophy to failure induced by pressure overload via protecting endothelial function Cardiovasc Res, August 1, 2009; 83(3): 444 - 456. [Abstract] [Full Text] [PDF] |
||||
![]() |
D. Li, C. Yang, Y. Chen, J. Tian, L. Liu, Q. Dai, X. Wan, and Z. Xie Identification of a PKC{varepsilon}-dependent regulation of myocardial contraction by epicatechin-3-gallate Am J Physiol Heart Circ Physiol, January 1, 2008; 294(1): H345 - H353. [Abstract] [Full Text] [PDF] |
||||
![]() |
P. Pasdois, C. L. Quinlan, A. Rissa, L. Tariosse, B. Vinassa, A. D. T. Costa, S. V. Pierre, P. Dos Santos, and K. D. Garlid Ouabain protects rat hearts against ischemia-reperfusion injury via pathway involving src kinase, mitoKATP, and ROS Am J Physiol Heart Circ Physiol, March 1, 2007; 292(3): H1470 - H1478. [Abstract] [Full Text] [PDF] |
||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |