|
|
||||||||
1 Department of Neurology and 2 Center for Neurobiology and Behavior, Columbia University College of Physicians and Surgeons, New York, New York 10032; and 3 Center for Molecular Biology, University of Heidelberg, D-69120 Heidelberg, Germany
| |
ABSTRACT |
|---|
|
|
|---|
Flint, Alexander C., Ulrike S. Maisch, and Arnold R. Kriegstein. Postnatal development of low [Mg2+] oscillations in neocortex. J. Neurophysiol. 78: 1990-1996, 1997. One form of rhythmic activity intrinsic to neocortex can be induced in slices of adult somatosensory cortex by lowering [Mg2+]o to unblock N-methyl-D-aspartate (NMDA) receptors. It has been suggested that a population of intrinsically burst-firing (IB) neurons that are unique to cortical layer 5 may play a role in the rhythmic activity seen under these conditions. Whole cell patch-clamp and field-potential recordings in slices of somatosensory cortex from neonatal rats were used to study the development of IB cells and the development of 0 [Mg2+] oscillations. IB cells were not encountered before postnatal day 12 (P12) in layer 5, but from P13 to P19 an increasing proportion of cells had IB properties. Recordings from cells at P7, P17, and P19 in 0 [Mg2+] indicate that dramatic changes occur postnatally in 0 [Mg2+]-induced activity. At P7, cells largely showed trains of single action potentials. In contrast, at P19, cells showed organized bursts of rhythmic activity lasting 0.5-5 s separated by periods of relative quiescence. Cells recorded at P17 were found to have less organized rhythmic activity than cells from P19 cortex. Field-potential recordings in 0 [Mg2+] made at P7 showed infrequent and slowly occurring field depolarizations, whereas field-potential recordings at P19 consisted of spontaneous bursts of 4-12 Hz oscillations identical to those observed in the adult. Application of NE, which inhibits burst-firing of layer 5 IB cells, significantly altered the discharge pattern of 0 [Mg2+] oscillations at P19. These data suggest that the maturation of one type of rhythmic network activity intrinsic to neocortex is influenced by the development of the membrane properties of a single cell type.
Rhythmic activity is fundamental to the physiology and pathophysiology of the CNS. Synchrony of neuronal populations plays a role in information processing and behavioral states of the normal brain (Singer 1993 Cortical brain slice preparation
Gravid Sprague-Dawley rats were allowed to give birth, and the ages of individual neonatal rats were assigned by recording the date of birth as P0. Neonatal rats were deeply anesthetized by halothane inhalation and rapidly decapitated. Brains were removed en bloc to 2-5°C artificial cerebrospinal fluid (ACSF) bubbled with 95% O2-5% CO2. ACSF contained (in mM) 124 NaCl, 5 KCl, 1.25 NaH2PO4, 1 MgSO4, 2 CaCl2, 26 NaHCO3, and 20 glucose, pH 7.4 at 25°C. Coronal slices were cut at a thickness of 400 µm from the somatosensory area with a vibratome (Pelco, Redding, CA), and slices were placed in a holding chamber in oxygenated ACSF. Slices were allowed to incubate at room temperature for 1 h, and for experiments involving the effects of 0 [Mg2+], slices were subsequently moved to a holding chamber containing Mg2+-free ACSF (as above, but without MgSO4) and maintained for 1 additional hour before recording. In the case of experiments to determine the membrane properties of cells in layer 5, slices were maintained in the holding and recording chambers in normal (1 mM MgSO4) ACSF.
Whole cell patch-clamp recordings
For all experiments, slices were placed in a recording chamber perfused with oxygenated ACSF (25-28°C), and localization of layers 2/3 and 5 was determined by observation of the somatosensory barrels of layer 4 using a dissecting microscope (Nikon, Tokyo) and fiber optic transillumination (Agmon and Connors 1992
Field-potential recordings
Electrodes were placed extracellularly in layers 2/3, and field potentials were recorded as previously described (Flint and Connors 1996 Development of IB membrane properties in layer 5 neurons
To examine the development of IB cell membrane properties, whole cell recordings were made from layer 5 of somatosensory cortex at a series of postnatal ages (P5-P18) in normal ACSF (1 mM Mg2+). Intrinsic membrane properties were determined by delivering a series of depolarizing current pulses in current-clamp mode. The amount of current injected was adjusted empirically according to the input resistance of the cell and the observed AP threshold. Cells were classified as IB, regular spiking (RS), or immature according to established criteria (Connors and Gutnick 1990
Whole cell recordings from neocortical neurons in 0 [Mg2+] reveal changes in activity during postnatal development
In light of the proposed role for IB cells in the propagation of 0 [Mg2+] oscillations in the neocortex, it is particularly intriguing that IB firing properties appear late in the postnatal development of somatosensory cortex. The delayed development of IB properties provides a means of further testing the proposed role of IB cells in 0 [Mg2+] oscillations. We therefore examined the postnatal development of 0 [Mg2+] oscillations using whole cell and field-potential recordings.
Field-potential recordings from neocortex in 0 [Mg2+] confirm changes in network properties during postnatal development
To determine whether the developmental changes we observed in the pattern of cell firing in 0 [Mg2+] translate into differences in neuronal synchrony, we made field-potential recordings at P7 and P19, because extracellular recordings will detect synchronous synaptic activity of large local populations of neurons. Field-potential recordings made from layers 2/3 of P7 neocortex demonstrate that the network activity in 0 [Mg2+] at this age differs in fundamental ways from the adult (Flint and Connors 1996
Perturbation of 0 [Mg2+] oscillations by norepinephrine
It has been previously reported that the central neuromodulatory agent norepinephrine (NE) can bring about a change in the firing properties of neocortical IB neurons by shifting cells from a burst-firing mode to a regular-spiking mode (Wang and McCormick 1993
We have shown here that in somatosensory cortex the "adult" form of spontaneous 4-12 Hz 0 [Mg2+] oscillations appears late in postnatal development, soon after layer 5 neurons develop IB membrane properties. The late postnatal development of 0 [Mg2+] oscillations has been demonstrated at the level of individual neurons by whole cell recording and at the level of synchronous network activity by field-potential recording. At P19, when both IB properties and 0 [Mg2+] oscillations have developed, treatment with NE, which inhibits IB cell burst firing, disrupts the rhythmicity of 0 [Mg2+] oscillations.
![]()
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
; Steriade et al. 1990
), and uncontrolled neuronal synchrony is the hallmark of epilepsy in humans (Engel 1991
) and animal models (Heinemann et al. 1991
). As the nervous system matures over the course of postnatal development, striking changes occur in brain rhythms. Neonates, children, and adolescents display clear differences from adults in normal electroencephalographic (EEG) patterns (Scher 1988
) as well as in the neurophysiological and clinical manifestations of seizures (Mizrahi 1994
; Veliskova et al. 1994
). Although many forms of synchronous discharge involve an interplay between several brain regions (Kim et al. 1995b
; Steriade et al. 1993a
,b
), experiments have demonstrated that isolated neocortex is itself capable of generating distinct forms of neuronal oscillations (Burns and Webb 1979
; Flint and Connors 1996
; Silva et al. 1991
).
; Silva et al. 1991
).
; McCormick et al. 1985
). It has been suggested, on the basis of their characteristic membrane properties and laminar localization, that they may play a key role in the generation of 0 [Mg2+] oscillations.
![]()
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
). Whole cell patch-clamp recordings were obtained from cells in neocortical slices as previously described (Blanton et al. 1989
). Patch electrodes were pulled from borosilicate glass (WPI, Sarasota, FL) using a vertical electrode puller (Narishige, Tokyo) and filled with (in mM) 140 KCl, 5 ethyleneg l y c o l - b i s(
- a m i n o e t h y l e t h e r)-N,N,N
,N
- t e t r a a c e t i c a c i d(EGTA), 3 MgCl2, and 5 N-2-hydroxyethylpiperazine-N
-2-ethanesulfonic acid (HEPES), pH 7.3 at 25°C. Electrode resistances were 4-8 M
. Voltage- and current-clamp experiments were performed using an EPC-9 patch-clamp amplifier (Heka Electronic, Lambrecht, Germany) controlled by a Power Macintosh 7100 computer running Pulse v. 7.8 software (Heka Electronic). Recordings were directly stored in digital form to hard disk. Input resistance (Ri) of recorded neurons was determined by measuring the steady-state current in response to a
20-mV step from the holding potential (
60 mV) in voltage clamp and subtracting open tip electrode resistance from the calculated Rtotal. Membrane time constant (
mem) was determined by injecting hyperpolarizing current in current-clamp mode and fitting the recorded voltage trace with a single exponential function using PulseFit software (Heka Electronic).

View larger version (10K):
[in a new window]
FIG. 1.
Development of burst-firing properties in neocortical layer 5 neurons. A: 2 types of intrinsic membrane properties encountered in layer 5 neurons, intrinsic burst-firing (IB) and regular spiking (RS). IB cells display an initial burst of action potentials (APs) on a plateau followed by several accommodating single APs, whereas RS cells fire a train of accommodating APs. B: IB cells develop their burst-firing membrane properties late in neocortical development, toward the end of the 3rd postnatal week in the rat. The percentage of IB cells out of all IB or RS cells encountered at each age is plotted against postnatal age.
). Field-potential recording electrodes were pulled as above and filled with 1 M NaCl. Field recordings were made with an Axoclamp 2B amplifier (Axon Instruments, Foster City, CA) in bridge mode, zeroed in the bath above the slice, further amplified and filtered at 1 kHz low pass (LP) with an external filter (Frequency Devices, Haverhill, MA), and stored on chart paper with a chart recorder (Astromed, West Warwick, RI). Field records presented here were scanned on a Macintosh computer with appropriate scale indicators for use in preparing figures.
![]()
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
). IB cells could be clearly identified by their initial burst of action potentials (APs) on a plateau potential followed by one or more slow, accommodating APs with afterhyperpolarizing potentials (Fig. 1A, top trace). RS cells, in contrast, showed no bursts, lacked a plateau, and showed several accommodating APs (Fig. 1A, bottom trace). At younger ages, some immature neurons were found to have broad APs and generated only attenuated secondary or tertiary spikes in response to current injection. Greater amplitude of current injection further decreased the ability of immature cells to fire spike trains. Basic membrane properties of IB and RS neurons from this series are detailed in Table 1.
View this table:
TABLE 1.
Membrane properties of neurons in this study
) and in sensorimotor cortex (Franceschetti et al. 1993
; Hoffman and Prince 1995
).
; Silva et al. 1991
), and we did not want to bias our sample by recording directly from burst-firing cells in layer 5. None of the recordings in the present study had the electrophysiological characteristics of dendritic recordings (Kim and Connors 1993
), so it is unlikely that recordings were made from the long apical dendrites of layer 5 pyramidal cells. Basic membrane properties of layer 2/3 neurons recorded in 0 [Mg2+] are shown in Table 1.

View larger version (30K):
[in a new window]
FIG. 2.
Changes in neuronal activity in 0 [Mg2+] occur during neocortical development. A: at postnatal day 7 (P7), most cells in slices exposed to 0 [Mg2+] display continuous trains of APs without organization of spikes into bursts (a1). A few cells encountered additionally showed paroxysmal depolarizing shift (PDS)-like bursts (a2) or brief depolarizations with bursts of 2-4 APs (a3). Restoration of 1 mM [Mg2+] to the slices at all ages entirely abolished epileptiform activity (a4, b4, c4). B: at P17, activity in 0 [Mg2+] was organized into short bursts of activity in addition to trains of single APs in all cells recorded. Examples from 3 neurons (b1-b3) are shown. C: at P19, activity in 0 [Mg2+] was similar to that observed in the adult, with bursts of several APs occurring on groups of synaptic potentials at 4-12 Hz. Examples from 3 neurons (c1-c3) are shown. D: at all ages (shown at P17), addition of the N-methyl-D-aspartate (NMDA) receptor antagonist D-AP5 (100 µM) reversibly abolished epileptiform activity.
). Recordings consistently showed more prolonged spontaneous epochs of activity that were segregated into bursts of synaptic events with several APs each. Examples from three neurons at P19 are shown in Fig. 2C, traces 1-3. The stereotyped oscillatory discharges seen at P19 fit the pattern expected from the periodic epochs of 0 [Mg2+] oscillations observed in the adult (Flint and Connors 1996
; Silva et al. 1991
). Figure 3 highlights the features of these events. Prolonged epochs of 1.5-8 s duration began with a rapid high-amplitude synaptic event that evoked 1-2 APs (Fig. 3A, arrows) followed by a series of distinct synaptic potentials with 4-12 APs per synaptic event (Fig. 3A, arrow). These secondary synaptic potentials occurred within each epoch at a rate of 8.2 ± 2.5 (SE) Hz, fitting the frequency range described for the oscillatory component of 0 [Mg2+] epochs in the adult (Flint and Connors 1996
; Silva et al. 1991
). Prolonged periods of relative quiescence typical of the adult pattern of 0 [Mg2+] oscillations were consistently observed between epochs at P19 that lasted ~4-20 s, as shown in Fig. 3B (middle trace). These data demonstrate that 0 [Mg2+] oscillations in their approximate adult form develop in the late third week of postnatal life in the rodent, at approximately the same time that IB properties of layer 5 cells appear.

View larger version (13K):
[in a new window]
FIG. 3.
Organization of 0 [Mg2+] oscillations recorded in neurons at P19. A: epochs of recurrent burst discharges of 1.5-8 s in duration occurred spontaneously, usually beginning with a brief high-amplitude synaptic potential with several superimposed APs (
). Following the initiating synaptic event, several more prolonged synaptic potentials with 4-12 APs each were observed. The secondary synaptic potentials occurred at a rate of 8.2 ± 2.5 Hz, which matches the frequency of the oscillatory component of 0 [Mg2+] oscillations in the adult. B: prolonged periods of relative inactivity lasting 4-20 s were observed in all cells in between oscillatory epochs.
; Silva et al. 1991
). Spontaneous field activity was extremely rare in slices from this age (n = 5 slices), with relatively long periods of time (up to 20 min) occupied by a total lack of spontaneous field depolarizations or other coherent events. These periods of silence were interrupted by the typical appearance of slowly repetitive spontaneous field depolarizations (Fig. 4A). These single field-potential events occurred every 1.5-12 s and always consisted of separate negative/positive waves without any form of oscillatory component. As shown in the bottom trace of Fig. 4A, these spontaneous events typically occurred in groups lasting ~50-75 s. Single spontaneous depolarizations and smaller groups of events at a similarly low frequency were also occasionally observed.

View larger version (20K):
[in a new window]
FIG. 4.
Changes in network activity in response to 0 [Mg2+] occur during cortical development. A: field-potential recordings at P7 in 0 [Mg2+] show prolonged periods of inactivity followed by slowly occurring field depolarizations (top trace). A group of spontaneous field depolarizations is shown below at a slower time base. B: field-potential recordings at P19 in 0 [Mg2+] resemble the activity observed in the adult. Spontaneous epochs begin with a field negativity and are followed by an oscillatory 4- to 12-Hz burst of activity (top trace). Several examples of spontaneously occurring events are shown below at a slower time base.
), the oscillations induced by 0 [Mg2+] at P19 are indistinguishable from the adult form.
). We therefore reasoned that if such a pharmacological manipulation alters the firing properties of IB cells, the same treatment might alter the behavior of 0 [Mg2+] network oscillations at P19 if intrinsically burst-firing cells are indeed involved in the organization of these events. To examine this possibility, we tested the effect of NE on 0 [Mg2+] oscillations.
), 0 [Mg2+] oscillations at P19 and in the adult always consist of a large initial field depolarization followed by a group of smaller oscillatory field depolarizations that occur at 4-12 Hz. Control 0 [Mg2+] oscillations observed at P19 never had less than three oscillatory depolarizations (mean 6.9 ± 2.3 for n = 40 events), as shown in Fig. 5C. In contrast, the spontaneous field activity observed after application of NE most often consisted of an initial field depolarization followed by zero to two oscillatory depolarizations (mean 1.5 ± 1.4 for n = 140 events; Fig. 5C). This inhibition of the oscillatory component of the 0 [Mg2+] events by NE is displayed graphically in the histogram in Fig. 5D. NE also influenced the temporal regularity of spontaneous events. In control conditions, spontaneous 0 [Mg2+] oscillations occurred approximately every 5-35 s (Fig. 5, A and E). The abbreviated spontaneous field events that occurred after addition of NE occurred in groups interrupted by periods of inactivity (Fig. 5B), such that there was a significant decrease in the overall interevent interval (Fig. 5E). Because of the long periods of inactivity under NE, there were also several points in this distribution >60 s that are not shown in Fig. 5E. Taken together, the inhibition of the oscillatory components and alteration of the temporal regularity of 0 [Mg2+] oscillations suggest that alteration of IB cell firing properties by NE may disturb several features of this type of network oscillation.

View larger version (27K):
[in a new window]
FIG. 5.
Norepinephrine disrupts 0 [Mg2+] oscillations at P19. A: 0 [Mg2+] oscillations under control conditions at P19 always consisted of bursts of oscillatory field activity that occurred at semiregular intervals, every 5-35 s. B: norepinephrine (NE), which has previously been shown to inhibit burst-firing by layer V IB cells (Wang and McCormick 1993
), resulted in periods of reduced activity (1 and 2) alternating with periods of attenuated events (see below) occurring in groups (3). C: 0 [Mg2+] oscillations at P19 (control, left) consisted of an initial large field depolarization (arrowhead) followed by several oscillatory depolarizations at ~4-12 Hz (brackets), as described in the adult (Flint and Connors 1996
). In contrast, the majority of events that occurred in the presence of NE + 0 [Mg2+] had no oscillatory component, and instead had only a single field depolarization or an initial depolarization followed by only one secondary depolarization (NE, right). D: histogram showing the distribution of oscillatory depolarizations per event in 0 [Mg2+] (control, gray) vs. 0 [Mg2+] + NE (NE, black). The partial inhibition of the oscillatory component by NE can be clearly seen as a shift in the distributionto the left. E: histogram showing the distribution of intervals between events in 0 [Mg2+] (control, dashed line) vs. 0[Mg2+] + NE (NE, solid line). The grouping of attenuated events in the presence of NE (as seen in B3) produces a shift to the left in the peak interevent interval. In addition, several long intervals of inactivity >60 s were observed in the presence of NE that are not shown on the graph for clarity (no such extremely long interevent intervals were observed in control conditions).
![]()
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
; Silva et al. 1991
). The role of IB cells in the generation of 0 [Mg2+] oscillations is supported by several observations. First, the interburst interval of IB cells given a brief intracellular stimulus is in the range of 5-10 Hz, which matches the frequency range of the oscillatory component of 0 [Mg2+] oscillations (Silva et al. 1991
). Second, under 0 [Mg2+] conditions, the burst firing of IB cells is phase locked to the oscillatory peaks of the spontaneous events observed in the extracellular field potential (Silva et al. 1991
; B. W. Connors, personal communication). Third, during evoked epileptiform discharges in the presence of low-dose bicuculline, IB cells show strong, synchronous excitation with little inhibition while RS-type pyramidal neurons throughout the slice are dominated by inhibitory postsynaptic potentials (Chagnac-Amitai and Connors 1989
). Fourth, IB cells are unique to layer 5, which is the only layer capable of generating 0 [Mg2+] oscillations when separated from the rest of the cortical slice (Flint and Connors 1996
; Silva et al. 1991
).
). Additional support for this conclusion comes from the observations that non-NMDA antagonists do not abolish spontaneous oscillations in either hippocampus (Traub et al. 1994
) or cortex (Flint and Connors 1996
). However, the late postnatal development of adult-type 0 [Mg2+] oscillations in cortex is difficult to attribute to changes in NMDA receptor properties. NMDA receptor currents contribute to excitatory postsynaptic currents in neocortical neurons from the first postnatal week onward (Kim et al. 1995a
), and the expression of the modulatory NMDA receptor subunits NR2A-D does not change greatly after the second postnatal week (Monyer et al. 1994
). Therefore it is more likely that the developmental changes in 0 [Mg2+] oscillations we have observed result from changes in the intrinsic membrane properties of cortical neurons or changes in the synaptic organization of local networks.
), 4-aminopyridine (4-AP) (Hoffman and Prince 1995
), and chronic cortical injury (Prince and Tseng 1993
; Salin et al. 1995
). However, these forms of synchronous discharge differ greatly from 0 [Mg2+] oscillations in that they are not spontaneous and they lack the typical 4- to 12-Hz oscillatory component seen in 0 [Mg2+]. In a recent developmental study, it was shown that 4-AP-induced discharges evoked before the appearance of IB cell burst-firing properties are indistinguishable from the discharges evoked in the adult (Hoffman and Prince 1995
). Despite this apparent lack of dependence on the burst-firing properties of IB neurons, the 4-AP discharges in this study were generated in layer 5 (Hoffman and Prince 1995
). Therefore the burst-firing properties of layer 5 IB neurons are not required for the propagation of all forms of epileptiform discharge, but may instead be of specific importance to the 4- to 12-Hz 0 [Mg2+] oscillations.
-range (1-5 Hz) oscillation triggered by kainate receptor activation (Flint and Connors 1996
). Upper layer "chattering" neurons can generate
-range (20-70 Hz) oscillations in vivo in response to visual stimuli (Gray and McCormick 1996
). Additionally, networks of synaptically connected interneurons can drive
-range oscillations in vitro (Whittington et al. 1995
). Therefore distinct neural populations and cortical networks may be important to the generation of different types of oscillations.
; Sood et al. 1993
; Van Paesschen et al. 1995
). Despite the rarity of magnesium disturbance as a cause of human epilepsy, 0 [Mg2+] oscillations serve as a model for epileptic discharges in humans because alterations in the balance of excitation and inhibition are fundamental to epileptic discharge generation (Traub and Jefferys 1994
; Traub et al. 1994
). We have found that 0 [Mg2+] oscillations in somatosensory cortex assume their adult form only after neurons of layer 5 develop their burst-firing characteristics. The development of burst-firing IB cells appears to be important to the organization of the spontaneous oscillatory events observed under conditions of 0 [Mg2+], presumably because burst-firing IB cells can provide an enhanced excitatory drive to the network in addition to the drive provided by regular spiking neurons. Therefore our observation that 0 [Mg2+] oscillations change dramatically during postnatal development points to one potential mechanism for the developmental changes in seizure manifestations that occur in humans (Engel 1991
; Mizrahi 1994
).
| |
ACKNOWLEDGEMENTS |
|---|
This work was supported by Grant NS-21223 from the National Institutes of Neurological Disorders and Stroke and in part by research Grant FY95-0879 from the March of Dimes Birth Defects Foundation.
| |
FOOTNOTES |
|---|
Address for reprint requests: A. R. Kriegstein, College of Physicians and Surgeons, 630 W. 168th St., Dept. of Neurology, Box 31, New York, NY 10032.
Received 16 December 1996; accepted in final form 30 June 1997.
| |
REFERENCES |
|---|
|
|
|---|
This article has been cited by other articles:
![]() |
A. J. Trevelyan, T. Baldeweg, W. van Drongelen, R. Yuste, and M. Whittington The Source of Afterdischarge Activity in Neocortical Tonic Clonic Epilepsy J. Neurosci., December 5, 2007; 27(49): 13513 - 13519. [Abstract] [Full Text] [PDF] |
||||
![]() |
N. Uesaka, Y. Hayano, A. Yamada, and N. Yamamoto Interplay between Laminar Specificity and Activity-Dependent Mechanisms of Thalamocortical Axon Branching J. Neurosci., May 9, 2007; 27(19): 5215 - 5223. [Abstract] [Full Text] [PDF] |
||||
![]() |
M. Zacksenhouse and E. Ahissar Temporal Decoding by Phase-Locked Loops: Unique Features of Circuit-Level Implementations and Their Significance for Vibrissal Information Processing Neural Comput., July 1, 2006; 18(7): 1611 - 1636. [Abstract] [Full Text] [PDF] |
||||
![]() |
N. Uesaka, S. Hirai, T. Maruyama, E. S. Ruthazer, and N. Yamamoto Activity Dependence of Cortical Axon Branch Formation: A Morphological and Electrophysiological Study Using Organotypic Slice Cultures J. Neurosci., January 5, 2005; 25(1): 1 - 9. [Abstract] [Full Text] [PDF] |
||||
![]() |
T. Soda, R. Nakashima, D. Watanabe, K. Nakajima, I. Pastan, and S. Nakanishi Segregation and Coactivation of Developing Neocortical Layer 1 Neurons J. Neurosci., July 16, 2003; 23(15): 6272 - 6279. [Abstract] [Full Text] [PDF] |
||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| Visit Other APS Journals Online |