|
|
||||||||
1Department of Cell and Developmental Biology and Anatomy and 2Department of Surgery, University of South Carolina School of Medicine, Columbia, South Carolina 29209
Submitted 2 December 2002 ; accepted in final form 23 April 2003
| ABSTRACT |
|---|
|
|
|---|
proliferation; extracellular matrix; three-dimensional culture
During the hypertrophic phase of cardiac development, ventricular myocytes downregulate DNA synthesis and increase their overall cell size as the cells develop myofibrils. During this time, ventricular myocytes change from a rounded or oval shape to the classic rod shape of the adult. The formation of important cell-cell and cell-extracellular matrix (ECM) adhesions also occurs during the hypertrophic phase of cardiac development. Cardiac myocytes have an attachment-dependent phenotype; thus interactions through adhesions are critical to their growth and survival (17). In the heart, adhesions provide the cellular basis for extensive excitation-contraction coupling and proper alignment of cardiac myocytes, which allow coordinated, directional contraction. Disruption of intercellular connectivity via disease or malformation is associated with arrhythmia and conduction disturbance (1).
Whole animal models are ultimately definitive; however, the determination of specific molecular mechanisms in mammalian development becomes problematic when in vivo models are used. In contrast, in vitro models are extremely amenable to molecular dissection but have the potential for culture-induced artifacts. The majority of studies that have examined differentiation of cardiac myocytes in vitro have used two-dimensional (2D) or planar culture systems in which myocyte phenotype and behavior differ from those seen in vivo. When plated on 2D substrates myocytes develop a flattened, stellate shape rather than the rod-shaped in vivo phenotype (20). Simpson et al. (22) showed that culturing neonatal cardiac myocytes on a planar aligned collagen substrate results in a more in vivo-like phenotype; however, cell layering and cell-ECM interactions remain limited by the planar nature of these cultures. Moreover, in this study, it was found that the planar aligned collagen scaffold is not a suitable substrate for embryonic day 15 (E15) ventricular cultures, because these cells do not attach well, they proliferate poorly, and they fail to initiate spontaneous contraction. In other studies, embryonic cardiac myocytes have been shown to display a higher percentage of DNA synthesis than more mature myocytes (23). Therefore, to study proliferation of cardiac myocytes it is important to use embryonic myocyte cultures. Traditional 2D culture techniques do not provide a system in which embryonic myocytes can proliferate and differentiate while maintaining correct morphology. Thus alternative methods of culturing E15 cardiac myocytes were examined.
Recent studies have reported that cells grown in three-dimensional (3D) contexts more closely resemble in vivo cells both morphologically and in their molecular regulation (3, 7). This has been found to be particularly true for cardiac myocytes grown in 3D contexts (5, 6). Cardiac cultures grown as aggregates or "organ cultures" were found to respond to mitogenic signals quite differently from those cultured in 2D contexts (3). Even more recently, neonatal cardiac myocytes grown within mechanically stretched collagen matrices were found to develop numerous structures seen in highly differentiated myocytes (29). Thus cardiac myocytes are responsive to the geometry of their environment. These studies provide evidence that more relevant in vitro models are needed to examine these complex developmental mechanisms.
This report describes the development of a novel 3D cardiac model system in which cardiac myocytes undergo the hyperplastic to hypertrophic transition. This system builds on the Simpson et al. (22) model, except that the aligned collagen is fashioned into a tubular structure that provides a free-floating, 3D substrate on which the cardiac myocytes are allowed to interact with the ECM. We have compared myocyte attachment and survival, DNA synthesis, and cardiac myocyte differentiation in the aligned collagen tube structure with those in standard planar culture systems. E15 rat ventricular primary myocytes were found to attach, spontaneously contract, proliferate, and differentiate in this tubular culture system. The experimental evidence reported here indicates that cardiac myocytes grown on the tubular collagen scaffold undergo normal cell cycle withdrawal, develop "in-register" Z-disk alignment, and form critical cell-cell junctions. Thus embryonic ventricular myocytes grown on the collagen tube scaffold differentiate in a manner similar to those found in vivo and provide a model system in which many aspects of cardiac development can be investigated. The model presented here is unique because it characterizes the differentiation of embryonic mammalian cardiac myocytes passing from the hyperplastic to hypertrophic phenotype in an in vivo-like context.
| MATERIALS AND METHODS |
|---|
|
|
|---|
Isolation of embryonic ventricular primary cultures. Timed pregnant rats (Harlan Sprague Dawley) were killed at 15 days after coitus (E15), and the embryos were removed from placental membranes. The hearts were dissected from the E15 embryos and pooled in ice-cold Moscona's solution (in mM: 136.8 NaCl, 28.6 KCl, 11.9 NaHCO3, 9.4 glucose, 0.08 NaH2PO4, pH 7.4). Atria were removed from the ventricles under a dissecting microscope (Olympus SZ60) and discarded. Myocyte isolation was performed in a manner similar to the protocol outlined in Simpson et al. (22). Isolated ventricles were rinsed with ice-cold Krebs-Ringer bicarbonate (KRB)-I with 1 mg/ml BSA, 2 mg/ml glucose, 100 U/ml penicillin, and 75 U/ml streptomycin, pH 7.4. The ventricles were minced and incubated with a KRB-II-collagenase solution with 100 U/ml collagenase (type II, Worthington) in a 37°C shaking water bath. At 8-min intervals, the tissues were triturated to dissociate the cells. The process was repeated until all tissue was dissociated. Cells were pelleted, resuspended in KRB-II, and filtered through a 200-µm2 mesh. The cells were pelleted and resuspended in culture medium [DMEM (Cellgro) supplemented with 10% FBS (Atlas Biologicals), 100 U/ml streptomycin, 1 U/ml Amphyl-B, and 100 U/ml penicillin, pH 7.4]. Cells were quantified with a hemocytometer and plated at a density of 200 cells/mm2 on either one-well Permanox chamber slides (Nunc) coated with ECM components as described in Coating of ECM components or collagen tube scaffolds.
Coating of ECM components. Chamber slides were coated with fibronectin (10 µg/ml in DMEM, isolated from human plasma; Ref. 18), type I collagen (Vitrogen; 50 µg/ml in DMEM), or aligned type I collagen [8 parts collagen, 1 part 10 x MEM (GIBCO), and 1 part 0.2 N HEPES, pH 9] or left untreated. Coating the slides with components of the ECM created the substrates for 2D planar cultures. Applying the aligned collagen solution to a slide in a directional manner with a cell scraper generated aligned collagen strands on the slide (22). All ECM solutions were allowed to incubate on the slides for at least an hour at 37°C before being rinsing twice with Moscona's solution.
Immunohistochemistry. Cells were fixed with 4% paraformaldehyde and permeabilized with 0.25% Triton X-100 in PBS for 10 min and blocked in 2% BSA in PBS overnight at 4°C. The immunohistochemistry for the 5-bromo-2'-deoxyuridine (BrdU) assay included staining for BrdU (Roche; primary: anti-BrdU 1:10 in incubation buffer supplied with kit, secondary: Texas red anti-mouse 1:500 in PBS), TO-PRO-3 (1:1,000 in PBS, Molecular Probes), and MF20, a sarcomeric myosin-specific monoclonal antibody (Ref. 4; 1:100 in PBS). MF20 was obtained from the Developmental Studies Hybridoma Bank at the University of Iowa. In the attachment assay and other analysis, cells were stained with TO-PRO-3 and MF20. The MF20 antibody was directly labeled with an Alexa 488 or a Texas red fluor by using protein-labeling kits from Molecular Probes. Rhodamine phalloidin was also obtained from Molecular Probes and used (1:500 in PBS) for staining of filamentous actin.
Attachment and BrdU assay. For the attachment assay, cells were allowed to attach for 3 days. The myocytes (MF20 positive) were counted per field with confocal microscopy (Bio-Rad MRC 1024). The fields were imaged from randomly selected regions by using a x40 objective with 512 x 512 resolution and an area of 62 µm2. Attachment was determined as the average number of myocytes per field divided by the area of the field to achieve the number of myocytes per square millimeter. For the BrdU assay, slides were taken at daily time points and labeled with BrdU according to instructions supplied by the manufacturer in the BrdU Labeling and Detection Kit I. The BrdU labeling index was defined by the ratio of the number of BrdU-positive myocyte nuclei to the total number of myocyte nuclei within the fields. A minimum of 10 random fields was taken per treatment per time point in each experiment.
Production of tubular scaffold cultures and analysis. The 3D collagen type I tube served as a scaffold on which embryonic ventricular primary cultures could be grown. The details of the production and properties of the collagen tubes are presented elsewhere (27a). Briefly, a 25 mg/ml solution of bovine collagen type I was extruded with a device that contained two counterrotating cones (Fig. 1). The liquid collagen was fed between the two cones forced through a circular annulus in the presence of a NH3-air (5050 vol/vol) chamber (polymerization chamber in Fig. 1A). This process results in a tube of aligned collagen (Fig. 1B). The tubes produced for this set of experiments have a length of 15 mm with a lumen diameter of 4 mm and an exterior diameter of 5 mm, leaving a wall thickness of 1 mm. The collagen tubes have a defined fiber angle of 18° relative to the central axis of the tube and have pores that range from 1 to 10 µm. The tubes were sterilized under UV light for 4 h and then placed in a solution of Moscona's solution and 1 µl/ml gentamicin and incubated in 5% CO2 at 37°C until cellular inoculation. Freshly isolated E15 cardiac myocytes were seeded onto the collagen tubes at 200 cells/mm2 (90,000 cells/tube) for the attachment assay or 1.5 x 106 cells per tube for other analyses. Cells were added into the lumen of the tube as well as the exterior with a pipette. Tube cultures were either embedded in optimum cutting temperature (OCT) solution (Sakura, VWR) for cryostat sections (10 µm) or embedded in 7.5% agarose-PBS for vibratome sections (100 µm). Sections of the tube were assayed in the same manner as the 2D cultures with the immunohistochemical protocol.
|
In vivo embryonic and neonatal hearts. Hearts were taken from E15 or neonatal day 3 (N3) rats. The hearts were embedded in OCT solution, cryostat sections were taken, and immunohistochemistry was performed under the conditions described in Production of tubular scaffold cultures and analysis.
Transmission electron microscopy. Tubular cultures were taken at different time points and prepared for transmission electron microscopy (TEM) analysis as described previously (16). Sections were stained with 2% uranyl acetate for 40 min at 37° and lead stained (10). The prepared sections were viewed with a JEOL JEM-200CX at 120 kV.
Statistical methods. All results are averaged from at least three separate experiments with independent isolations. A minimum of 300 cardiac myocytes were quantified for each data point reported. Averages and standard errors were determined with the Sigmaplot 2000 suite of programs (SPSS). Significance for the attachment studies was determined with a Mann-Whitney rank-sum test. Significance was determined for BrdU labeling index between two time points by using a t-test. In all cases, significance was determined as P < 0.05.
Cell area measurements were carried out by first determining the middle of the cell by collecting a Z series through the field and then calculating the area of cell-containing MF20-staining regions plus the nucleus. Averages were determined from a minimum of 15 cells. In all cases, significance was determined as P < 0.05.
| RESULTS |
|---|
|
|
|---|
|
E15 ventricular myocytes have relatively high rates of DNA synthesis during
the first week of culture, with BrdU-labeling indexes approaching 25%
(Fig. 3A, day
5). Beyond this time period, labeling indexes drop to
5%
(Fig. 3A, day
7). E15 myocytes plated on the PACol I substrate had the lowest labeling
index (Fig. 3A).
Labeling indexes for the tube substrate were observed to peak at
22% on
day 6 of culture (Fig.
3B). On all other substrates, the peak of DNA synthesis
was found to be a day earlier, on day 5 of culture
(Fig. 3A). Because
initial experiments found that DNA synthesis of cardiac myocytes was altered
on the tube substrate, a longer time course of BrdU labeling was investigated.
The proliferation of E15 cardiac myocytes as measured by BrdU labeling index
was found to decrease significantly after the first week of culture. In rats,
this time period corresponds to the time of birth, when, as numerous reports
have found, DNA synthesis decreases in cardiac myocytes in vivo
(23).
|
Embryonic cardiac myocytes displayed different cell morphologies when plated on the various substrates. When plated on FN, myocytes formed large (averaging 4,890.1 ± 534.9 µm2), squamouslike cells, which contained random arrays of myofilaments as seen by the localization of sarcomeric myosin (Fig. 4A). Myocytes grown on the Col I and PL substrates had morphologies similar to those grown on the FN substrate, although the cell area occupied by sarcomeric myosin was significantly (P < 1 x 109) smaller (averaging 401.1 ± 22.3 µm2 and 453 ± 30.4 µm2, respectively; Fig. 4B; supplemental data available online at http://ajpheart.physiology.org/cgi/content/full/01027.2002/DC1). Random arrays of myofilaments were observed in myocytes grown on the PL and Col I substrates (Fig. 4B). In contrast, E15 cardiac myocytes grown on PACol I had a rod-shaped morphology that is characteristic of more mature in vivo neonatal cardiac myocytes (Fig. 4, C and D). Interestingly, myofilaments were rarely observed in myocytes cultured on PACol I when stained for sarcomeric myosin (Fig. 4C) or filamentous actin (Fig. 4D). Only 28% of myocytes cultured on PACol I were found to have organized myofilaments, whereas on other substrates >90% of myocytes had organized myofilaments. Well-organized myofilaments were observed in tube-cultured cardiac myocytes (Fig. 4E).
|
The observed differences in the organization of myofilaments in E15 cardiac
myocytes plated on PACol I vs. the tube may correlate to the lack of
spontaneous contraction observed in these cultures (compare
Fig. 4, C and
E). In contrast to all other treatments, PACol I cultures
did not initiate spontaneous contraction. However, within 3 days of culture
E15 ventricular myocytes grown on the tube substrate were observed to
spontaneously contract at multiple foci along the length of the tube
(supplemental video available online at
http://ajpheart.physiology.org/cgi/content/full/01027.2002/DC1).
On day 4 of culture, large sections of the tube were observed to
contract together (day 4 of supplemental video). Over the next
several days the coordination of spontaneous contraction increased (days
5, 6, 14, and 21). Evidence that the entire tube was contracting
as a synchronized syncytium is provided by videos taken at x0.75 and no
magnification (supplemental video). These videos show spontaneous contraction
across the entire length of the "cardiotubes." The tubes
contracted at a rate that averaged
77 beats/min. Cultures of cardiac
myocytes on the tubular scaffold have been maintained for >45 days with
continuous contractions, whereas 2D cultures can only be maintained a maximum
of 1420 days before beating ceases and cells senesce.
The relevance of these in vitro observations to in vivo developmental processes is evident when comparing ventricular myocytes found in the trabeculae of E15 and N3 hearts to the myocytes cultured on the collagen tube (Fig. 5). E15 ventricular myocytes within the trabeculae of the developing heart vary widely in their morphology but generally have a prominent nucleus with a round or oval morphology, displaying an overall radial symmetry (Fig. 5A). Eight days later in development, in the N3 heart the myocytes within the trabeculae are aligned and have a distinct rod-shaped morphology with obvious myofibrillar organization (Fig. 5B). E15 cardiac myocytes grown for 14 days on the tube construct form layers of aligned myocytes with a striated localization of sarcomeric myosin (Fig. 5C). The aligned, striated phenotype of the day 14 tubegrown ventricular myocytes is similar to that in vivo neonatal ventricular myocytes (compare Fig. 5, B and C).
|
Cardiac myocytes in day 14 tube cultures were found mainly on the outer and inner (lumen) surfaces of the tubes (Fig. 6). On the outer surface, myocytes were in aligned, overlapping layers (Fig. 6, B and C). However, some clusters of cardiac myocytes were found within the collagen matrix of the tubes (Fig. 6, A and D). Intramatrix cardiac myocytes display a radial symmetry and have cell morphologies that resemble those of in vivo embryonic trabecular myocytes (compare Figs. 5A and 6D).
|
During the hypertrophic phase of cardiac myocyte differentiation, the intracellular distribution of the gap junction protein connexin 43 (Cx43) serves as a marker of cardiac myocyte differentiation (1). The distribution of the Cx43 protein was analyzed in cardiac myocytes grown on the tube substrate at early and late time points. In day 6 tube cultures, Cx43 was widely distributed as punctate staining throughout the sarcolemma (Fig. 7, A and B). Little change was observed in the distribution of Cx43 in cardiac myocytes in day 31 tube cultures (Fig. 7, C and D).
|
Sarcomeric myosin staining indicated that the E15 ventricular myocytes grown on the tube substrate had developed organized myofibrils (Figs. 4E and 5C). TEM studies were performed to determine the ultrastructure of these cells. TEMs of day 14 cultures found limited sarcomeric organization present in cells; however, these cells did contain numerous unorganized myofilaments that were concentrated on the periphery of the cells and occasionally near the nuclear membrane (Fig. 8A). Analysis of day 21 tube cultures found myocytes with many well-organized sarcomeres with distinctive Z disks (Fig. 8B). Identifiable cell junctions were also found in the day 21 tube cultures (Fig. 8C), providing evidence that these cardiac myocytes had established cell-cell connections that are characteristic of well-developed, in vivo cardiac myocytes. TEMs of a day 38 tube showed multiple layers of cardiac myocytes (Fig. 8D). It is important to note that the layers of myocytes have aligned, or in-register, Z disks, a hallmark of well-developed cardiac myocytes. Numerous myocyte-myocyte connections were observed in the day 38 micrographs (Fig. 8, E and F). TEMs provide subcellular evidence that supports our histological and videomicroscopic data that the tubular cultures develop morphologies and cell-cell connections that are typical of in vivo cardiac myocytes.
|
| DISCUSSION |
|---|
|
|
|---|
Cardiac myocytes have an attachment-dependent phenotype; thus attachment
and survival on the tube substrate are a critical component of the model. E15
cardiac myocytes were found to attach and survive on the aligned collagen tube
in a manner that is equivalent to FN and Col I in planar cultures
(Fig. 2). Observed differences
in the attachment of E15 cardiac myocytes between the PACol I and tube
substrate were surprising considering that these two substrates are both made
from aligned type I collagen. Two major differences between the PACol I
substrate and the tube substrate are the 3D geometry of the tube and the
free-floating nature of the tube. The data presented here indicate that
attachment and survival, cell morphology, and spontaneous contraction of
embryonic cardiac myocytes depend on their ability to form specific adhesions
with the substrate. A new 3D adhesion complex was described recently
(7). These 3D adhesions are
fundamentally different from focal and fibrillar adhesions
(7,
9).
5-Integrin and paxillin colocalize in 3D adhesions, which
also contain extracellular fibronectin. In contrast, focal adhesions contain a
variety of
-integrin chains, paxillin, and focal adhesion kinase,
whereas fibrillar adhesions exclusively contain
5
1-integrin complexes and tenasin
(7). We hypothesize that the
cellular phenotypes observed in this study are the result of these 3D cell-ECM
interactions. Previous investigations have shown that integrin expression
patterns change during the embryonic to neonatal transition
(25). These changes in
expression pattern may be responsible for the differences observed between the
N3 and E15 cells on the PACol I substrate. Delineation of the specific cardiac
myocyte-ECM interactions cultured on the 3D tube will test this hypothesis as
well as providing molecular mechanisms that can be tested in vivo.
The time course of DNA synthesis in the E15 cardiac myocytes reported in
this study closely resembles the reported values for mammalian in vivo
studies. Numerous reports using a variety of techniques have found that
25% of cardiac myocytes are positive for DNA synthesis in the developing
rodent heart during the late embryonic period
(14,
19,
23,
24). As birth approaches, the
percentage of DNA-synthetic cardiac myocytes drops. Soon after birth, a second
wave of DNA synthesis that reaches
5% correlates to an increase in the
number of binucleated myocytes (Ref.
24; E. Dees and R. L. Goodwin,
unpublished observations). The values in
Fig. 3 are nearly identical to
the published in vivo values. However, the peak of DNA synthesis found on
days 5 and 6 of culture correlates to the time of birth for
rats, which, as mentioned above, is a time when DNA synthesis is rapidly
declining. The observed lag in vitro in DNA synthesis is most likely an
artifact of the isolation process. It is speculated that dissociated cardiac
myocytes must attach and produce the appropriate ECM before they can
reinitiate DNA synthesis. This may explain the lag in DNA synthesis of cardiac
myocytes cultured on PL. Studies using human cardiac myocytes report that the
production on ECM components is required for cardiac myocyte proliferation
(11). The role of ECM
signaling in mammalian embryonic cardiac myocyte DNA synthesis is not well
characterized. In this report, rat cardiac myocytes grown on the FN, PL, and
aligned collagen tube substrates were found to have the highest DNA labeling
indexes, whereas the PACol I substrate had a significantly lower index
(Fig. 3). Regardless of
substrate, the DNA synthesis of E15 cardiac myocytes decreased during the
first week of culture. This is consistent with both in vivo and other in vitro
reports (23). Thus cardiac
myocytes in the tube model presented in this report undergo cell cycle
withdrawal that resembles the normal developmental process.
The time course experiments using TEM indicate that cardiac myocytes grown on the tube substrate initiate the differentiation phase of cardiac development. TEMs of day 14, 21, and 38 tube cultures show an increasing organization of sarcomeres found within cardiac myocytes. Sarcomeres were rarely found in day 14 cultures but were common in day 21 cultures (Fig. 8). This indicates that significant myofibrillogenesis is occurring in the tube cultures. Day 38 tube cultures contained numerous sarcomeres that were in register with neighboring myocytes (Fig. 8D). The development of in-register sarcomeres between myocytes is a hallmark of maturing cardiac myocytes. In addition to myofibrillogenesis, the TEM studies found evidence that the cardiac myocytes in the tube cultures were forming cell-cell connections that are indicative of maturing cardiac myocytes. It is important to note that the TEM studies as well as the Cx43 localization experiments indicate that although cardiac myocytes in the tube culture were found to recapitulate numerous aspects of differentiation such as cell cycle withdrawal and myofibrillogenesis, they did not attain an adult phenotype. Adult cardiac myocytes have intercalated disks located at the myocyte termini, and this was not observed in either the Cx43 localization or TEM studies. We speculate that additional forces, such as mechanical stretch or increased load, would be required to push these cardiac myocytes toward the mature phenotype. The tubular design of the scaffold is amenable to these types of experiments.
Our data demonstrate the use of a novel 3D aligned collagen tube on which rat embryonic cardiac myocytes grow and maintain an in vivo-like phenotype that recapitulates the hyperplastic to hypertrophic transition in vitro. The model reported here differs from previous investigations using 3D scaffolds for the culture of cardiac myocytes in several important criteria. First, the geometry of the tube is significantly different from fabricated sheets of myocytes (21, 22, 26) in that the Z-axis of the tube is much larger. Other researchers have embedded neonatal cardiac myocytes in liquid collagen, which subsequently polymerizes (8, 28). These studies found that neonatal cells were capable of differentiating into adultlike cardiac myocytes. The data presented here show that embryonic cardiac myocytes are capable of undergoing normal developmental processes when grown on the tubes. Cardiac myocytes cultured on the tube substrate were found to proliferate, become quiescent, synchronously contract, and undergo significant myofibrillogenesis. These studies provide a framework on which the molecular mechanisms that regulate critical events in developing cardiac myocytes, such as cell cycle withdrawal, myofibrillogenesis, intercalated disk formation, and cardiac morphogenesis, can effectively be investigated.
| DISCLOSURES |
|---|
|
|
|---|
| ACKNOWLEDGMENTS |
|---|
| 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:
![]() |
H. J. Evans-Anderson, C. M. Alfieri, and K. E. Yutzey Regulation of Cardiomyocyte Proliferation and Myocardial Growth During Development by FOXO Transcription Factors Circ. Res., March 28, 2008; 102(6): 686 - 694. [Abstract] [Full Text] [PDF] |
||||
![]() |
S. Y. Boateng and P. H. Goldspink Assembly and maintenance of the sarcomere night and day Cardiovasc Res, March 1, 2008; 77(4): 667 - 675. [Abstract] [Full Text] [PDF] |
||||
![]() |
K. Tobita, L. J. Liu, A. M. Janczewski, J. P. Tinney, J. M. Nonemaker, S. Augustine, D. B. Stolz, S. G. Shroff, and B. B. Keller Engineered early embryonic cardiac tissue retains proliferative and contractile properties of developing embryonic myocardium Am J Physiol Heart Circ Physiol, October 1, 2006; 291(4): H1829 - H1837. [Abstract] [Full Text] [PDF] |
||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |