|
|
||||||||
Departments of 1Medicine and 2Psychiatry, School of Medicine, University of California-San Diego, La Jolla, California
Submitted 16 August 2004 ; accepted in final form 9 May 2005
| ABSTRACT |
|---|
|
|
|---|
-subunits in left and right atria. The results showed that 1) in control mice, the APD was shorter and the ultra-rapid delayed rectifier K+ conductance (IKur) and the sustained delayed rectifier K+ conductance (Iss) were larger in the left than in the right atrium; also, mRNA and protein expression levels of Kv1.5 and Kv2.1 were higher in the left atrium; 2) in hyperthyroid mice, the APD was shortened and IKur and Iss were increased in both left and right atrial myocytes, and the protein expression levels of Kv1.5 and Kv2.1 were increased significantly in both atria; and 3) the influence of hyperthyroidism on APD and delayed rectifier K+ currents was more prominent in right than in left atrium, which minimized the interatrial APD difference. In conclusion, hyperthyroidism resulted in more significant APD shortening and greater delayed rectifier K+ current increases in the right vs. the left atrium, which can contribute to the propensity for atrial arrhythmia in hyperthyroid heart.
action potential duration; atrial fibrillation
15% of patients with hyperthyroidism (2, 31). Conversely, 13% of patients with unexplained AF have biochemical abnormalities consistent with hyperthyroidism (10). However, the mechanisms underlying the development of AF in hyperthyroidism are not fully understood. Reentry has been postulated as one of the main mechanisms leading to AF (2325, 29, 35). Multicircuit wave fronts that are generated in the atrium could disturb the normal sinus rhythm and set up a fibrillatory rhythm instead. According to the wavelength concepts, AF is more likely if effective refractory periods are short and conduction is slow. Action potential duration (APD) determines the refractory period and is therefore a key determinant of the likelihood of reentry. Prior studies (7, 11) indicated that APD in atrial myocytes was influenced by the thyroid status; however, the ionic mechanisms for shortened APD in hyperthyroidism remain unclear.
It has been reported that the properties of electrophysiological repolarization are not homogeneous within the two atria. A shorter APD in left atrium has been observed in several different animal species (16, 18). For example, Li et al. (16) determined that the higher density of the rapid delayed rectifier current (IKr) in left atrial myocytes contributed to the shorter effective refractory period and APD in canine left atrium. Lomax et al. (18) have shown convincingly that the differences in current density of the 4-aminopyridine (4-AP)-sensitive ultra-rapid delayed rectifier K+ (IKur) current between the left and right atria underlie the differences in APD in murine left and right atria. In several studies, changes have been observed in the expression of various ion channel mRNAs in both atria (21, 37) and ventricles (1, 21, 27, 38) under hyperthyroid conditions. However, there is no information regarding whether the alterations may occur differentially within the left and right atria. Therefore, it is important to evaluate the repolarization properties of left and right atrial myocytes separately to further understand the electrophysiological alterations resulting from hyperthyroidism. In this study, we used the whole cell patch-clamp technique to measure the APD and ionic conductances in left and right atrial myocytes from control and hyperthyroid mice. In addition, we used the RNase protection assay and Western blotting to evaluate the mRNA and protein levels of
-subunits constituting the corresponding ion channel pore in the atrium. The hyperthyroidism-induced alterations present a setup for atrial arrhythmias.
| MATERIALS AND METHODS |
|---|
|
|
|---|
Isolation of single mouse atrial myocytes. Atrial myocytes were prepared as described previously (4). Briefly, mice were injected with heparin (100 U ip) and then killed 10 min later by injection of pentobarbital sodium (0.1 ml ip). The heart was rapidly excised and arrested in ice-cold buffer. The aorta was then cannulated and retrogradely perfused for 20 min with buffer that contained (in mM) 126 NaCl, 4.4 KCl, 1.0 MgCl2, 4.0 NaHCO3, 10.0 HEPES, 30.0 2,3-butanedione monoxime, 5.5 glucose, 1.8 pyruvate, and 0.025 CaCl2, pH 7.3, and 1 mg/ml type I collagenase (Worthington). The two atria were then separated and incubated with the same collagenase buffer for another 1520 min. Dissociated myocytes were collected by low-speed centrifugation and then acclimated to 1 mM calcium solution by sequential washing in buffer with gradually increasing calcium concentrations. The cells were finally resuspended in a modified MEM medium and plated in laminin-coated tissue-culture dishes 30 min before recording.
Electrophysiological recordings.
Whole cell currents were recorded using a List EPC-7 patch-clamp amplifier as described previously (9, 13, 14). The majority of experiments were carried out at room temperature. A series of experiments was also conducted at 33°C to determine APD at more physiological temperatures. Electrodes were pulled on a three-stage horizontal puller (Mecanex; Basel, Switzerland) and fire polished. Electrodes had resistances of 35 M
. Currents were low-pass filtered at 1 kHz with an eight-pole Bessel filter, digitized through an ITC-16 analog-to-digital converter (Instrutech; Port Washington, NY), and sampled at 2 kHz with a Macintosh Quadra 800 computer. Currents were acquired with AxoData software (Axon Instruments; Union City, CA). Series resistance and capacitance compensation were applied to the current responses. Myocyte capacitance was determined by integration of the capacitative transient elicited by a 2-mV step. The capacitance values for myocytes from left atria were 39.2 ± 2.4 (n = 17) for control mice and 47.0 ± 3.7 pF (n = 21) for hyperthyroid mice. Capacitance values for the right atria were 32.9 ± 1.5 (n = 20) and 43.2 ± 2.9 pF (n = 17) for control and hyperthyroid mice, respectively. All data are presented as current densities to normalize for differences in cell capacitance.
Action potentials were recorded in current-clamp mode and were elicited by injection of 400- to 600-pA depolarizing currents for 3 ms applied at 1 Hz. The APD was determined by the time to repolarize to 80% (APD80) after the peak of the action potential. Of 50 action potentials recorded, the last 20 were averaged for analysis.
Currents were analyzed offline using Axograph and pCLAMP software (Axon Instruments). For measurements of whole cell currents, the cells were stepped from 50 mV to a range of potentials from 120 to +50 mV in 10-mV increments for 200 ms. Measurements of rapidly activating and slowly inactivating outward currents (IKtotal) were obtained from the peak of the current amplitudes during steps from 50 to +60 mV in 10-mV increments for 120 ms. However, to inactivate the transient outward current (Ito), the steps were immediately preceded by an 80-ms step to 20 mV (protocol 1). This provided a measure of IKtotal that is composed of both IKur and the sustained delayed rectifier K+ conductance (Iss) in the absence of Ito. Iss was determined by measurement of the current amplitude at the end of 3-s steps from a holding potential of 50 mV to a range of potentials from 50 mV to +60 mV in 10-mV increments. To inactivate Ito and IKur, the membrane potential was stepped to +20 mV for 3 s immediately before these test steps (protocol 2). IKur was determined by two methods. First, the current at the end of the 3-s steps, Iss, was subtracted from IKtotal to provide an estimate of IKur. Also, the amplitude of IKur was determined by the fitting of two exponentials to the 6-s step from 50 to +20 mV (Clampex; Axon Instruments). The first exponential time constant represents the inactivation of Ito, whereas the second exponential is believed to represent the inactivation of IKur (5). The amplitudes associated with the second exponential time constant were analyzed as representing a fairly pure measure of IKur.
For current-voltage curves, the current amplitudes were plotted against the voltage that the cell membrane potential was stepped to. For production of some current traces, recordings were linear-leak subtracted offline by subtraction of a scaled average of five steps of +2 or 2 mV.
The extracellular recording solution was composed of (in mM) 150 NaCl, 5 KCl, 1 CaCl2, 1 MgCl2, 5 HEPES, and 20 glucose with pH corrected to 7.4 with 1 M NaOH. The osmolality of the solution was adjusted to 320325 mosmol/kg H2O. The intracellular patch-pipette solution contained (in mM) 150 potassium gluconate, 2 MgCl2, 1.1 EGTA, 0.1 CaCl2, 5 HEPES, 5 Mg-ATP, and 0.1 Li-GTP. The pH was adjusted to 7.2 and the osmolality was adjusted to 310315 mosmol/kg H2O. With these recording solutions, the equilibrium potential for K+ (EK) is approximately 67 mV.
RNase protection assay. After mice were killed by 0.1 ml of pentobarbital sodium, the left and right atria were separated and frozen quickly in liquid nitrogen. Tissue total RNA was extracted with TRIzol reagent (GIBCO), and trace DNA was removed by digestion with DNA-free DNAse (Ambion).
RNase protection assays for Kv1.5 and Kv2.1 were performed as previously described (12). Two micrograms of total RNA was used for each hybridization reaction. The 32P-labeled antisense RNA probes for mouse Kv1.5 and Kv2.1 channels were generated by T7 RNA polymerase from a linearized pBKSII plasmid containing part of the cDNA sequence of the respective ion channel. The Kv2.1 probe spanned position 14651255 of the published cDNA sequence (GenBank accession no. NM_008420). The origins of mouse Kv1.5 and GAPDH probes were described previously (12). After hybridization with the 32P-labeled anti-sense probe, the hybrid was digested by RNase, and the protected fragments were separated on 6% acrylamide sequencing gels. Densitometry of the autoradiographs yielded digital values for each band, which were normalized to the GAPDH signal. To simplify comparison between two groups, the mRNA expression levels of Kv1.5 and Kv2.1 from normal control left atria were adjusted to 1. Data from six different samples were statistically evaluated, and the Students t-test was used to compare left and right atria or control and hyperthyroid atria.
Western blotting. Membrane proteins from either left or right atrium were isolated using a previously described method (3, 36). Briefly, atrial tissue was homogenized at 4°C in 10 vol of TE buffer (10 mM Tris·HCl and 1 mM EDTA, pH 7.4). The homogenates were centrifuged at 1,000 g for 10 min to remove nuclei and debris. The supernatants were centrifuged again at 40,000 g for 10 min. Pellets were resuspended in TE buffer that contained 0.6 mol/l KI and incubated on ice for 30 min. After the suspension was centrifuged at 40,000 g for an additional 10 min, the resulting pellets were twice more resuspended in TE buffer and centrifuged at 40,000 g. The resulting pellets were then solubilized in TE buffer that contained 2% Triton X-100 on ice for 1 h. Insoluble material was centrifuged at 17,000 g for 10 min. The protein was quantitated using the Bradford protein assay. Protein (20 µg) was separated on 410% gradient Tris·HCl-glycine gels and then transferred to nitrocellulose membranes. Proteins were blocked overnight with 5% milk at 4°C, and blots were incubated with a primary antibody (1:200 dilution of anti-Kv1.5; Chemicon; or 1:400 dilution of anti-Kv2.1; Sigma) for 1 h at room temperature and subsequently incubated for 1 h with a 1:5,000 dilution of secondary antibody (anti-rabbit IgG-horseradish peroxidase conjugated; Sigma). Bands were visualized by reaction with chemiluminescent substrate (PerkinElmer Life Sciences) and exposed to film. Positive bands were scanned and analyzed using ImageJ software (National Institutes of Health). To simplify the comparison between two groups, the protein expression level from control left atria was normalized and designated as 1. Data from three different samples were statistically evaluated, and the Students t-test was used to compare left and right atria or control and hyperthyroid atria.
Statistical analysis. Statistical significance was determined using nonparametric statistical methods. Data are presented as means ± SE. Statistical significance was assumed with a P value <0.05.
| RESULTS |
|---|
|
|
|---|
20% shortening) and right (
44% shortening) atria. The majority of the shortening occurred in the later phases of the action potential from
65% repolarization. As shown previously by Lomax et al. (18), we observed that APD was also significantly shorter in control myocytes from left atria compared with control myocytes from right atria (Fig. 1C). Owing to the uneven shortening of APD in left and right atrial myocytes, the interatrial APD difference was significantly diminished in hyperthyroid mice. To confirm that these interatrial differences in APD in control myocytes were also observed at more physiological temperatures, APD80 was also determined at 33°C. Control APD80 was 8.4 ± 1.3 ms (n = 3) in left atria and was significantly longer (P < 0.05) in right atria at 15.9 ± 1.7 ms (n = 6). In addition, the shortening of the APD in hyperthyroid atria observed at room temperature also occurred at 33°C. APD80 in right hyperthyroid atria was reduced significantly to 7.4 ± 1.6 ms (n = 7) and was also reduced in the left atria to 4.5 ± 0.5 ms (n = 3) (P < 0.05).
|
Figure 2, A and D , shows a series of whole cell currents obtained in voltage-clamp mode during voltage steps to potentials ranging from 120 to +50 mV in control myocytes. The currents indicate the presence of the inwardly rectifying K+ current (IK1), Ito, as well as outward delayed rectifier currents. All of the myocytes that were recorded from displayed IK1 and delayed rectifier-type currents. However,
15% of the cells tested did not express a detectable Ito. This heterogeneity of Ito expression has been observed previously by Lomax et al. (18). As can be seen in Fig. 2, B and E, myocytes from hyperthyroid mice displayed considerable increases in the outward current density from both left and right atria. However, this increase in outward currents in hyperthyroid myocytes was not accompanied by a complementary increase in IK1. Figure 2 shows the current-voltage relationships for both left (Fig. 2C) and right (Fig. 2F) atrial myocytes taken at the end of each 200-ms voltage step. The larger outward current density in hyperthyroid myocytes was apparent at each of the membrane potentials tested, whereas there was no significant change in IK1 (Fig. 2). IK1 current densities of 14.4 ± 1.1 (n = 14) and 14.6 ± 0.7 pA/pF (n = 18) observed in control left and right atria, respectively, were unchanged at 13.9 ± 1.1 (n = 16) and 17.2 ± 1.8 pA/pF (n = 16) in hyperthyroid left and right atria, respectively.
|
|
Several different K+ currents underlie the delayed rectifier-type outward K+ currents. These include the ultra-rapidly activating slowly inactivating current (IKur also known as IKslow1), a rapidly activating slowly inactivating current (IKr) and a very slowly activating and inactivating current (IKs) (19, 20, 39, 40). In adult mouse atrial myocytes, a 4-AP-sensitive current, the correlation of IKur and a 4-AP-insensitive sustained current (Iss), contribute significantly to the delayed rectifier component of the outward currents (5, 18). The contribution of IKr to the outward K+ currents in adult mouse atrial myocytes appears to be negligible (18). This was supported in the present study by our difficulty in observing IKr with protocols similar to those used to demonstrate IKr in other studies (22) and by the lack of effect of 10 µM E-4031 (data not shown). Therefore, the study was focused on the effects of hyperthyroidism on IKur and Iss.
Two different protocols were used to isolate IKur and Iss. Many studies have isolated IKur by a short prepulse to inactivate Ito and the Na+ current (INa). Subsequent steps to potentials ranging from 20 to +60 mV revealed a rapidly activating outward K+ current, IKur, which has been shown to be due to expression of the K+ channel Kv1.5 (5, 26). IKur activates rapidly and inactivates slowly with a time constant estimated to be on the order of
1.5 s in mouse (5) and
2 s in human (28) atria. Kv1.5, which is thought to underlie IKur, has been shown to be inactivated by 70% after a 5-s step when expressed in mouse Ltk cells (34). In addition, as mentioned previously, IKur is inhibited by low concentrations (10100 µM) of 4-AP. In the presence of low concentrations of 4-AP, the Iss remains. Bou-Abboud et al. (5) indicated that the 4-AP-insensitive current (Iss) may be due in part to expression of Kv2.1, which inactivates very slowly and has no specific blockers to date. Therefore, to observe Iss in the absence of IKur, a very long voltage step is required.
In this study, the two currents were separated by application of a low concentration of 4-AP. Figure 3E shows the rapidly activated, slowly inactivating currents elicited during 120-ms depolarizing steps obtained after a prepulse to 20 mV (protocol 1). Figure 3F shows the current remaining after application of 100 µM 4-AP, which represents Iss. The 4-AP-sensitive current is indicative of IKur. Figure 3G shows the control current response to a step from 50 to +20 mV for 6 s (protocol 2) superimposed on the current observed in the presence of 100 µM 4-AP. As can be seen from the figure, the 4-AP-sensitive current had inactivated before the end of the step. Thus we used this information to assess the contributions of IKur and Iss to the outward delayed rectifier currents. Iss was determined by the current at the end of the 3-s step immediately after the 3-s prepulse to +20 mV (protocol 2; see Fig. 5G). IKur was determined as the difference between the peak current (IKtotal), which was obtained from the short 100-ms steps with a prepulse to 20 mV (protocol 1; see Fig. 4G) and the current at the end of the 3-s step (Iss). In addition, we estimated the amplitude of IKur by fitting two exponentials to the long 6-s step to +20 mV as described by Bou-Abboud et al. (5). The first exponential time constant represents Ito, whereas the second exponential time constant represents IKur. Time constants of 1,443 ± 56 (n = 8) and 1,467 ± 101 ms (n = 10) were obtained from the second exponential fit from left and right control atria, respectively. These were unchanged in myocytes isolated from hyperthyroid mice. Time constants of 1,452 ± 81 (n = 7) and 1,500 ± 117 ms (n = 6) were observed in hyperthyroid myocytes from left and right atria, respectively. The amplitude of the second exponential was used as an additional method to assess the magnitude of IKur.
|
|
With the use of a 3-s prepulse to +20 mV to inactivate IKur, Ito, and INa, the membrane was stepped to a variety of potentials in voltage-clamp mode from 50 to +60 mV for an additional 3 s to allow measurement of Iss. Representative current traces are shown in Fig. 5. As observed with IKtotal, the current densities of Iss in hyperthyroid myocytes from both left (Fig. 5B) and right (Fig. 5E) atria were increased compared with control myocytes (Fig. 5, A and D). Also, a slightly greater change was observed in hyperthyroid right atrium than in hyperthyroid left atrium (61% vs. 50%). The increase in Iss current density observed in hyperthyroid myocytes was not accompanied by a shift in the voltage dependence of activation. Under both control and hyperthyroid conditions, Iss activated at similar voltages in both left and right atria (Fig. 5, C and F).
To assess the magnitude of IKur, the amplitude of the second exponential fit from the long 6-s steps from 50 to +20 mV described above was used. IKur current densities of 4.4 ± 0.9 (n = 8) and 3.7 ± 0.5 pA/pF (n = 10) were observed in control left and right atria, respectively, and were significantly increased (P < 0.01) to 12.8 ± 1.9 (n = 7) and 9.5 ± 1.9 pA/pF (n = 6) in hyperthyroid left and right atria, respectively. Additionally, IKur was determined by subtraction of Iss from IKtotal. The data are shown in Fig. 4H.
A summary of the changes in current density for IKur and Iss are shown in Figs. 4H and 5H, respectively. The data indicate that the increases in current density of both IKur and Iss in the left and right atria associated with hyperthyroidism are significant changes (P < 0.01). In addition, under control conditions, both IKur and Iss were statistically significantly larger in the left atria than the current densities observed in the right atria (P < 0.05). Increasing either of these K+ conductances would result in a shortening of the APD due to the speeding up of the repolarization phase. Thus as noted previously (18), larger IKur and Iss current densities in control left atrial myocytes resulted in shorter APDs than observed in right atrium. Therefore, by extrapolation, it is likely that the shorter APD observed with hyperthyroid myocytes may also be mediated by increased IKur and Iss current densities. Additionally, the greater percentage increase in right atrium of IKtotal is consistent with the greater percentage shortening of APD in right atrium in the state of hyperthyroidism.
Expression of mRNA and Kv2.1 and Kv1.5 proteins in control and hyperthyroid atria.
As discussed previously, the
-subunits of the K+ channels Kv1.5 and Kv2.1 are believed to underlie the K+ currents IKur and Iss, respectively, in mouse atrial myocytes. The above data indicate that in hyperthyroid atrial myocytes, the current densities of IKur and Iss are increased, which suggests that Kv1.5 and Kv2.1 expression levels are also increased. This was tested by determining the mRNA and protein expression levels of Kv1.5 and Kv2.1 in left and right atria of control and hyperthyroid mice.
As shown in Fig. 6, the mRNA expression level of Kv1.5 in left atrium was
1.6-fold higher than in right atrium under control conditions and was increased by
26% in left atrium and by
140% in right atrium from hyperthyroid mice. However, the mRNA level of Kv2.1 in control left atrium was
1.5-fold greater than in right atrium, whereas the expression level did not change significantly with hyperthyroid status.
|
70% in left atrium and
300% in right atrium with hyperthyroidism, which suggests that the alteration in Kv1.5 protein expression is consistent with the changes observed in mRNA expression. Additionally, the protein expression level of Kv2.1 was also more abundant in control left atrium than in control right atrium. However, unlike the mRNA expression patterns, the protein expression level of Kv2.1 was also upregulated with hyperthyroidism, and this increase was more prominent in right (150%) than in left (70%) atrium.
|
| DISCUSSION |
|---|
|
|
|---|
The results from this study provide evidence of changes in ionic conductances in hyperthyroid atrial myocytes. These changes involve shortened APD and increased delayed rectifier currents (both IKur and Iss) in atrial myocytes from hyperthyroid mice. Although several studies were performed to elucidate the effects of thyroid hormone on cardiac electrophysiology (37), very little is known of the changes that occur in K+ currents in hyperthyroid atrial myocytes.
In this study, the results have shown that the two delayed rectifier currents, IKur and Iss, were increased in atrial myocytes from hyperthyroid mice. Owing to the complex structure of K+ channels (33), it is speculated that more than one subunit may be involved in the ionic current changes in hyperthyroidism. Here we focused on the main potential pore-forming subunits for these two currents, Kv1.5 and Kv2.1. The difference in protein expression level of Kv1.5 and Kv2.1 in control atria and the increase in expression observed with hyperthyroidism parallel the patterns observed with IKur and Iss. Therefore, it is likely that increased Kv1.5 and Kv2.1 expression reflects increased channel synthesis and at least partially contributes to the higher density of IKur and Iss obtained under hyperthyroid conditions. The agreement between alteration of Kv1.5 protein expression and its mRNA level observed in hyperthyroid atria indicates that the regulatory effect of thyroid hormone on Kv1.5 may be transcriptional. Similar effects of thyroid hormone on Kv1.5 mRNA expression have also been observed in rat ventricular myocytes (1, 21, 27, 38) and atrial myocytes (21, 37). On the contrary, although Kv2.1 protein levels were shown to be increased with hyperthyroidism, the mRNA levels in both left and right atria remained unchanged. This suggests that thyroid hormone may regulate Kv2.1 expression at a posttranscriptional level. It has been previously reported that thyroid hormone can change certain protein expression levels by increasing mRNA stability (15, 17) or affecting intracellular redistribution (8, 30).
In contrast to the study by Chen et al. (6) with rabbit atrial myocytes, no changes were detected in Ito in either atrium of hyperthyroid mice in the present study. However, our observations are in agreement with previous studies of hyperthyroid myocytes from other species including rat (37) and rabbit (32).
Alterations in APD and delayed rectifier K+ currents in hyperthyroid myocytes were greater in right atrium.
This study is the first to evaluate the electrophysiological changes in separated left and right atrial myocytes from hyperthyroid mouse hearts. Similar to the findings of Lomax et al. (18), a significant interatrial APD difference between left and right atria was recorded in control mice. However, the interatrial APD difference was diminished due to a greater shortening of APD in right than in left atrium with hyperthyroid status, which suggests that thyroid hormone has unequal regulatory effects on left vs. right atrium. The greater reduction in APD in right atrium was supported by the larger increase in IKtotal recorded in right atrial myocytes, to which both IKur and Iss contribute. This phenomenon is also consistent with the greater change in the expression levels of Kv1.5 and Kv2.1 in right atrium. At present, it is unclear why these changes were more prominent in right vs. left atrium. Several factors such as differential pressure stress force, autonomic nerve innovation, or different transcriptional factor distribution between the two atria may play a role in this process.
Based on the reentry theory, the overall shortening of APD in hyperthyroid atria, which is reflective of a shorter effective refractory period, would facilitate the occurrence of reentry with hyperthyroid status. Contrary to the normal interatrial APD difference that was considered to be valuable to synchronize contraction of both atria (due to the physiological origination of sinus rhythm on the right side), the diminished interatrial APD difference may enhance the spreading of ectopic activity originating mostly from left atrium [such as in the pulmonary vein area (6)] to the whole atria. Therefore, it is possible that the diminished interatrial APD would facilitate the generalization of irregular activities in a hyperthyroid state and provide the substrate for atrial arrhythmias such as AF.
| 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.
* Y. Hu and S. V. P. Jones contributed equally to this work. ![]()
| REFERENCES |
|---|
|
|
|---|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |