Abstract

Photoinduced gamma oscillations

We expressed channelrhodopsin 2 (ChR2)^20–22 in layer 2/3 pyramidal cells of the neocortex by in utero electroporation²³. Cortical expression of ChR2 was restricted to layer 2/3 excitatory neurons where 23 ± 2% (n =6 slices) of pyramidal cells expressed the protein, consistent with previous observations^24,25 (Fig. 1a and Supplementary Fig. 1a, b). Electroporated mice were anaesthetized and a small craniotomy was performed to expose the ChR2-expressing somatosensory cortex. We stimulated the exposed region with a long (2 s) ramp of blue light, that is, a photostimulus of gradually increasing intensity (see Methods); we used a ramp rather than a square pulse to avoid the fast desensitizing transient of the photocurrent²⁰ (Supplementary Fig. 1c) and monitored population activity with an extracellular electrode inserted in layer 2/3. Notably, rather than triggering a flurry of uncoordinated neuronal activity, photostimulation generated rhythmic oscillation of the local field potential (LFP) at gamma frequency (average 42 ± 2 Hz, n =16; Fig. 1b, c) that was accompanied by the activity of simultaneously recorded units, spiking in phase with the LFP (Fig. 1b). The power of the photoinduced oscillation was 2,000-fold (± 1,200, n =16, P =0.02) larger than the power at the same frequency in the unstimulated cortex (Fig. 1c). The oscillation persisted as long as the photostimulus was on and could be reliably and repeatedly evoked. Furthermore, the oscillation frequency increased only a little (~25%) with the intensity of the photostimulus (Supplementary Fig. 2). Importantly, neither the rhythmic activity per se nor the specific frequency of the oscillation was imposed by the photostimulus²⁶, because apart from its onset, offset and progressive increment in intensity, the photostimulus was devoid of any temporal structure. Thus, stimulation of pyramidal cells in layer 2/3 of the neocortex in vivo initiates self-organized oscillations within the gamma frequency range.

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Figure 1

Photoinduced gamma activity in vivo and in vitro

a, The top panel shows a schematic of a layer 2/3 pyramidal cell axon. The bottom panel shows anti-GFP immunostaining of the barrel cortex expressing ChR2 and GFP. b, A light ramp (blue, 1-s duration) induced oscillations of the local field potential (LFP, high-pass filtered at 0.5 Hz; top trace, black) and of unit activity (bottom trace, grey; LFP high-pass filtered at 100 Hz) recorded in layer 2/3 in vivo. The LFP in the grey box is expanded below. c, LFP power spectrum shown in b before (grey) and during (black) the light stimulus. d, In vivo recording of a layer 2/3 pyramidal cell during light stimulation. Top traces: red, excitation recorded at −70 mV. Blue, inhibition recorded at +10 mV. Baseline holding current has been subtracted. Bottom traces: expanded section of the traces in the grey box. e, Simultaneous recording of two layer 2/3 pyramidal cells in vitro during light stimulation. Top traces: red, excitation recorded at −70 mV in one cell; blue, inhibition recorded at +10 mV simultaneously in the other cell. Bottom traces: expanded section of traces in the grey box. f, Average peak frequency between 20 and 60 Hz (± s.e.m.) of the light-induced oscillations recorded in vivo (n =16) and in vitro (n =65; P =0.004).

Consistent with naturally occurring gamma oscillations, photostimulation initiated rhythmic activity of both inhibitory and excitatory postsynaptic currents (IPSCs and EPSCs, respectively)^16,27,28 in layer 2/3 neurons recorded in vivo in the whole-cell configuration (average amplitude of individual cycles: EPSCs, 169 ± 76 pA; IPSCs, 777 ± 228 pA; n =4, Fig. 1d). To avoid contamination of synaptic conductances by direct ChR2-mediated photocurrents, we only considered whole-cell recordings from neurons not expressing ChR2 (Supplementary Fig. 3).

Photoinitiated gamma activity could also be induced in cortical slices in vitro (Fig. 1e). Photostimulation induced robust oscillations of the EPSCs and IPSCs recorded simultaneously from pairs of layer 2/3 pyramidal cells (33 ± 1 Hz, n =6; Fig. 1e). The rhythmic activity relied on both glutamatergic and GABAergic transmission, as it was abolished by application of either the glutamate receptor antagonists NBQX (2,3-dioxo-6-nitro-1,2,3,4-tetrahydrobenzo[f]quinoxaline-7-sulphonamide) and CPP (3-((R)-2-carboxypiperazin-4-yl)-propyl-1-phosphonic acid) (5 and 10 μM, n =8), or the GABA_A (γ-aminobutyric acid subtype A) receptor antagonist gabazine (400 nM, n =11; a subsaturating concentration was chosen to avoid epileptiform activity; Supplementary Fig. 4). Similar oscillations could also be induced in other neocortical regions expressing ChR2 in layer 2/3 pyramidal cells such as visual cortex (28 ± 1 Hz; n =12) or cingulate cortex (26 ± 1 Hz; n =10). These data show that expression of ChR2 in layer 2/3 neocortical pyramidal cells permits reliable initiation of self-organizing rhythmic activity within the gamma frequency band both in vivo and in vitro. With this technique we can now determine the spatial extent of excitation and inhibition generated by activity of layer 2/3 pyramidal cells vertically, across layers, and horizontally, within layers, and establish the resulting impact on the activity of neighbouring cortical domains.

Vertical match of excitation and inhibition

Activity in layer 2/3 could generate three distinct vertical patterns of inhibition relative to excitation: inhibition could be (1) more broadly distributed across layers than excitation; (2) complementary to excitation such that layers that receive less excitation receive more inhibition; or (3) restricted to the same layers receiving excitation. We performed in vitro recordings from principal neurons in several cortical layers of the somatosensory cortex simultaneously while initiating oscillatory activity in layer 2/3 with light stimulation. Figure 2a illustrates a simultaneous voltage-clamp recording from four principal neurons located in each of layers 2/3, 4, 5 and 6. Voltage clamping the neurons at the IPSC reversal potential to isolate EPSCs shows that both synaptic excitatory charge and oscillatory power are maximal in layers 2/3 and 5 and minimal in layers 4 and 6 (Fig. 2b and Methods), consistent with anatomical and physiological observations^{1–4,9,10,29}. Notably, voltage clamping the same neurons at the EPSC reversal potential to isolate IPSCs revealed that inhibition was precisely confined to the same cortical layers receiving excitation (Fig. 2b). Because layer 5 in the somatosensory cortex consists of two sublayers (5A and 5B), the principal neurons of which have distinct functional properties³⁰, we compared the distribution of excitation and inhibition generated by activity in layer 2/3 between the two sublayers (Supplementary Fig. 5). Both sublayers received excitation and inhibition in response to activity in layer 2/3, yet layer 5A received significantly less of both conductances as compared to layer 5B (P <0.05; Supplementary Fig. 5a–c and Methods). Taken together, these data demonstrate a remarkable overlap in the spatial domains of excitation and inhibition generated during activity in layer 2/3. The two opposed conductances are precisely confined to layer 5, the main cortical output layer, and layer 2/3, the main input to layer 5.

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Figure 2

Vertical match of excitation and inhibition across layers

a, Recording configuration. b, EPSCs (left) and IPSCs (right) recorded simultaneously in L2/3, L4, L5 and L6 principal cells. c, Power spectra of the EPSCs (top) and IPSCs (bottom) for currents recorded in layer 2/3 and layer 5 pyramidal cells (from b). Insets show power spectra for layer 4 and 6 neurons; the y axis of the insets is expanded as compared to the main y axis. d, Average normalized charge (± s.e.m.) for simultaneously recorded cells across cortical layers. In each recording, one of the cells was a layer 2/3 pyramidal cell for normalization (EPSC charge, P <10⁻⁶: L2/3 (n =58), L4 (n =16), L5 (n =34), L6 (n =15); IPSC charge, P <10⁻⁷: L2/3 (n =53), L4 (n =16), L5 (n =32), L6 (n =13); one way ANOVA). e, Average normalized power (± s.e.m.) between 20–60 Hz for photoinduced oscillations across cortical layers (EPSC power, P <10⁻⁷: L2/3 (n =46), L4 (n =15), L5 (n =20), L6 (n =14); IPSC power, P <10⁻³: L2/3 (n =53), L4 (n =15), L5 (n =30), L6 (n =13); one way ANOVA).

Horizontal match of excitation and inhibition

Next we determined the relative pattern of excitation and inhibition horizontally across domains within individual layers. Again, one could expect three different scenarios: inhibition extends over a larger area as compared to excitation, resulting in surround inhibition³¹; excitation extends over a larger area as compared to inhibition, resulting in surround excitation³²; or excitation and inhibition cover matching areas³³. For these experiments, we restricted photostimulation to a circular zone of ~90 μm in diameter centred on layer 2/3 above a barrel (see Methods). The spatial extent of neuronal recruitment by this circular photostimulus was approximately one barrel column in diameter (see Methods and Supplementary Fig. 6a).

Light ramps induced oscillations at gamma frequency, indicating that even the photostimulation of a restricted area of layer 2/3 is sufficient to initiate rhythmic activity (Fig. 3). Notably, this oscillation was generated by pyramidal cells whose somatodendritic compartment was localized within the photostimulated area, because bypassing axons expressing ChR2 do not contribute to oscillatory activity (Supplementary Fig. 6b).

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Figure 3

Horizontal match of excitation and inhibition within layers

a, The recording configuration is shown at the top left. Blue and red traces indicate IPSCs and EPSCs, respectively, recorded in a layer 2/3 pyramidal cell in response to focal light stimulation translated tangentially across barrel columns. Numbers below traces indicate distance (in barrel columns) of the light-stimulated barrel column with respect to the home barrel column (position 0). The inset to the right shows normalized charge (excitation in red and inhibition in blue) plotted against distance. b, Plots of average charge (left) and power between 20–60 Hz (right) against distance in layer 2/3 pyramidal cells (n =19). c, Same as b but for layer 5 pyramidal cells (n =12). d, Top panel: recording configuration at the edge of barrel cortex. Middle and bottom panels: average charge plotted against distance (in micrometres) between the recorded neuron and the centre of light stimulus when the stimulus was on barrel cortex (open circles) or on adjacent somatosensory non-barrel cortex (closed circles). Red indicates excitation (n =10); blue indicates inhibition (n =10). In all plots error bars are ± s.e.m.

We recorded from layer 2/3 or layer 5 pyramidal cells and initiated oscillations in each of four barrel columns located on both sides of the barrel column within which the pyramidal cells were recorded. The oscillation propagated horizontally at an average speed of 240 ± 50 mm s⁻¹ (n =6; see Methods), consistent with the propagation speed of cortical waves³⁴ and the conduction velocity in cortical axons^35,36. Both synaptic excitatory charge and oscillation power decayed with increasing distance from the site it had originated from (excitatory charge and power decayed to 26 ± 4% and 26 ± 6% (n =18, charge, P =0.002; power, P =4 × 10⁻⁷) in layer 2/3 and to 37 ± 8% and 30 ± 8% in layer 5 when oscillations were initiated two barrel columns away (n =12); Fig. 3b, c). Notably, the decay of synaptic inhibitory charge and oscillatory power was nearly identical with the decay of excitation (inhibitory charge and power decayed to 23 ± 5% and 26 ± 8% (n =18), respectively, in layer 2/3 and to 27 ± 7% and 23 ± 12% in layer 5 when oscillations were initiated two barrel columns away (n =12, charge, P =2 × 10⁻⁷; power, P =0.001; Fig. 3b, c)). Thus, despite their progressive decay with distance from the site the oscillation had originated from (Fig. 3b, c), the ratio between excitation and inhibition remained constant.

The horizontal decay of synaptic excitation and inhibition was region specific, in that synaptic excitation and inhibition fell much more sharply when oscillations where initiated in the adjacent non-barrel cortex compared to the parent barrel cortex (excitatory and inhibitory charge decayed to 9 ± 1% and 15 ± 3% (n =11), respectively, when oscillations were initiated 400 μm away in the adjacent cortex, versus 28 ± 2% and 31 ± 7% (n =12) in the parent barrel cortex; P =0.0004 for excitation and 0.004 for inhibition; Fig. 3d). Furthermore, the coronal plane of the slice did not have an impact on the horizontal extent of synaptic excitation and inhibition as slices cut tangentially to the surface of the somatosensory cortex showed comparable spatial decays (see Methods and Supplementary Fig. 7).

Taken together these results show a spatial delimited yet precisely overlapping distribution of excitation and inhibition vertically, across layers, and horizontally, within layers, across cortical domains.

Layer-specific modulation of activity

To understand the role of layer 2/3 pyramidal cells in coordinating cortical activity we addressed how the two spatially matched but opposing conductances affect neuronal spiking across and within layers.

We recorded from both layer 2/3 and 5 pyramidal cells in the current-clamp configuration and depolarized the neurons with 1-s-long current injections to trigger action potentials (average rate 6.4 ± 0.7 Hz, n =31, range 2–12 Hz; Fig. 4a) to allow us to monitor bidirectional changes in firing rates. Photoinduced oscillatory activity invariably and significantly suppressed the spike rate of layer 2/3 pyramidal cells (84 ± 5% reduction, n =11, P =1.5 × 10⁻⁵; Fig. 4a, b). In striking contrast, the spike rate of layer 5 pyramidal cells was significantly facilitated (170 ± 20% increase, n =20, P =0.037; Fig. 4a, b). Spiking in layer 2/3 pyramidal cells was invariably suppressed up to two barrel columns away from the initiation site of the oscillation (Fig. 4c). The suppression was most pronounced within the home barrel column (85 ± 7% reduction, n =8, P =0.004) and progressively decreased with increasing horizontal distance (28 ± 8% decrease two barrel columns away, n =8, P =7 × 10⁻⁵; Fig. 4c). In contrast, the spike rate of layer 5 pyramidal cells was significantly facilitated up to two barrel columns away from the initiation site of the oscillation, an effect that was again most pronounced within the home barrel column (100 ± 19% increase, n =6, P =10⁻⁵) and decreased progressively with increasing horizontal distance (10 ± 10% increase two columns away, P =0.02; Fig. 4c). Pyramidal cells in both sublayers 5A and 5B were facilitated, and this facilitation occurred over a similar horizontal distance from the initiation site of the oscillation (Supplementary Fig. 5f). These results show that activity in layer 2/3 generates lateral suppression of spiking in layer 2/3 pyramidal cells and feed-forward facilitation of layer 5 pyramidal cells. The horizontal pattern of suppression in layer 2/3 is mirrored by the horizontal pattern of facilitation in layer 5 (Fig. 4c). Thus, layer 2/3 pyramidal cells can efficiently drive downstream layer 5 pyramidal cells lying both directly below as well as in neighbouring domains, while simultaneously suppressing the main input to layer 5 by inhibiting neighbouring layer 2/3 pyramidal cells.

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Figure 4

Lateral suppression and feed-forward facilitation in vivo and in vitro

a, Response of simultaneously recorded layer 2/3 (green) and layer 5 (purple) pyramidal cells to current injection (I_inj) without (left) and with (right) light stimulation. b, Cumulative probability plot of the normalized spike rate (spike rate with light stimulus divided by the spike rate in control: layer 2/3, green (n =11); layer 5, purple (n =20); P <0.001, Kolmogorov–Smirnov test). c, Normalized spike rate of layer 2/3 (green, n =8) and layer 5 (purples, n =6) pyramidal cells plotted against barrel-column distance from focal light stimulation. Error bars are ± s.e.m. d, The left panel shows in vivo response of layer 2/3 neuron to current injection (I_inj) without (top) and with (bottom, digitally subtracted bridge) light stimulation. The right panel shows a summary plot (n =6). e, The left panel shows LFP (top trace, black, high-pass filtered at 1 Hz) and unit activity (bottom trace, grey; LFP high-pass filtered at 300 Hz) recorded in layer 5 in vivo in response to light stimulation. The right panel shows average time course of spike rate of seven similar experiments. Error bars are ± s.e.m.

The same opposed modulation of layer 2/3 and 5 excitability also occurred in vivo. Layer 2/3 neurons were recorded in the whole-cell configuration to ensure the absence of ChR2 expression and prevent direct photostimulation. Multiunit activity was recorded in layer 5 with extracellular electrodes. Photoinitiated oscillations significantly suppressed spiking of layer 2/3 neurons (73 ± 8% decrease, n =5, P =0.003; Fig. 4d) but strongly increased spiking in layer 5 (600 ± 200% increase, n =7, P =0.0004; Fig. 4e). These data indicate that oscillations in layer 2/3 pyramidal cells have an impact on their home and neighbouring domains in a layer-specific manner, generating suppression of layer 2/3 and facilitation of layer 5.

Layer-specific excitation/inhibition ratio

What mechanism accounts for the opposite modulation of layer 2/3 and layer 5 pyramidal cells? Simultaneous recordings (Fig. 5a) showed that the average excitatory charge recorded from the soma of pyramidal cells was not significantly different between layer 2/3 and layer 5 pyramidal cells (107 ± 11 pC versus 108 ± 14 pC, n =34 pairs, P =0.97; for comparison between layer 5A and 5B pyramidal cells see Supplementary Fig. 5c–e). In contrast, the inhibitory charge recorded at the soma was significantly smaller in layer 5 pyramidal cells (24 ± 10% smaller; 780 ± 70 pC versus 570 ± 70 pC, n =30 pairs, P =0.029). More importantly, however, the ratio between somatic excitation and inhibition across simultaneously recorded pairs was substantially larger in layer 5 pyramidal cells (120 ± 40% larger; excitation/inhibition ratio L5, 0.26 ± 0.04; L23, 0.15 ± 0.02, n =30 pairs, P =0.018; Fig. 5a), indicating the possibility that differences in somatic excitation/inhibition ratio may, at least in part, account for the facilitation of layer 5 pyramidal cells. Consistent with this possibility, we found that the spiking probability of individual layer 5 pyramidal cells (determined in the cell-attached mode during light-induced oscillations) increased with larger excitation/inhibition ratios (determined subsequently in the whole-cell configuration; Fig. 5b, one-way analysis of variance (ANOVA), P =0.047).

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Figure 5

Layer-specific excitation/inhibition ratio

a, The left panel shows simultaneous recording of layer 2/3 (top) and layer 5 (bottom) pyramidal cells during light stimulation (EPSCs in red and IPSCs in blue). The right panel shows scatter plot of excitation/inhibition ratio for all layer 2/3 and layer 5 cell pairs (n =30; P =0.018). b, The left panel shows cell-attached (top) and subsequent whole-cell recordings (bottom) from a pair of layer 5 pyramidal cells during light stimulation. The right panel shows binned distribution of spike rate versus excitation/inhibition ratio for 35 layer 5 pyramidal cells (the bins contain, from left to right: 12, 12 and 11 pairs). Error bars are ± s.e.m. c, The top panel shows recording configuration and injected waveforms. One pipette imposes an inhibitory conductance (blue; g-clamp). The other pipette injects an excitatory current waveform (red, I-clamp). The left panel shows the square depolarizing current step used to elicit baseline spiking; no inhibitory conductance. Middle and right panels show inhibitory conductance (blue) and excitatory current (red) waveforms, recorded in a layer 2/3 pyramidal cell (middle) and in a layer 5 pyramidal cell (right). The bottom panel shows response of a layer 2/3 (green) and a layer 5 (purple) pyramidal cell to the current step and waveforms illustrated above. d, Schematic of the spatial overlap between excitation (left) and inhibition (centre) across and within layers. The resulting lateral suppression within layer 2/3 and feed-forward excitation of layer 5 leads to the lateral expansion of a cortical domain at the expense of its neighbours (right).

To establish directly whether the layer-specific difference in somatic excitation/inhibition ratio underlies lateral suppression in layer 2/3 versus feed-forward facilitation in layer 5 we replayed synaptic waveforms recorded from layer 2/3 into layer 5 pyramidal cells and vice versa (Fig. 5c). Specifically, the soma of pyramidal cells was patched with two pipettes, one to inject the excitatory current and the other to dynamically clamp the inhibitory conductance (the chosen waveforms were representative of the average somatic excitation/inhibition ratio; see Methods). The playback of waveforms recorded in a layer 2/3 pyramidal cell into the soma of layer 5 pyramidal cells completely suppressed their firing (100 ± 0% reduction, n =6, P =0.006; the same was true when the waveform was played back into L2/3 pyramidal cells, 100 ± 0% reduction, n =6, P =10⁻⁵; Fig. 5c). In contrast, playback of waveforms recorded in a layer 5 pyramidal cell into the soma of layer 2/3 pyramidal cells strongly facilitated their firing (L2/3, 120 ± 20% increase, n =6, P =0.025; the same occurred when the waveforms were played back into layer 5 pyramidal cells, 120 ± 10% increase, n =6, P =0.015).

Thus, these results demonstrate that layer-specific differences in the excitation/inhibition ratio can account for the lateral suppression of layer 2/3 and feed-forward facilitation of layer 5 pyramidal cells.

Discussion

Physiological and psychophysical studies suggest that horizontal interactions between cortical domains enable information to be processed in a context-dependent manner^3,8,37–42. By selectively activating neurons that generate horizontal projections we revealed a layer-specific coordination of cortical activity. Horizontal projections originating from layer 2/3 pyramidal cells suppress layer 2/3 while facilitating layer 5. This layer-specific modulation extends over several domains around the activated population of layer 2/3 pyramidal cells, indicating that active layer 2/3 pyramidal cells can drive layer 5 pyramidal cells within their own and neighbouring domains while suppressing neighbouring layer 2/3 pyramidal cells. It should be noted that not only is layer 2/3 the main input to layer 5 but that layer 5 gives rise to the main cortical output. Thus, layer 2/3 horizontal projections can drive the output of neighbouring domains (by activating layer 5) while silencing the inputs to these neighbouring outputs (by suppressing layer 2/3). This coordinated modulation of superficial and deep layers generates competition between neighbouring domains and may allow the representation of one domain to expand dynamically at the cost of its neighbours (Fig. 5d).

Within the rodent’s somatosensory cortex, the density of horizontal axons diminishes with increasing distance (over hundreds of micrometres) between barrel columns³. In other systems, in addition to a local decrease in the density of horizontal projections, long-range (millimetres) projections preferentially link cortical domains with similar response characteristics^5–7. Future studies will establish whether layer-specific modulation also holds true for long-range interactions.

We show that the layer-specific facilitation and suppression is achieved by differences in excitation/inhibition ratio, rather than by spatially separating these two opposing conductances. Furthermore, we show that despite their progressive decrease in amplitude within layers, the ratio of these two conductances remains constant. These data thus highlight the distinct roles of ratio and amplitude of the two conductances on spike rate modulation: whereas the ratio determines the sign of the effect (that is, whether facilitating or suppressing) the amplitude determines its magnitude.

The specific inhibitory circuits activated here will have to be elucidated in the future. It is possible that different inhibitory circuits may be recruited by distinct activity patterns (for example, different oscillation frequencies), resulting in different spatial and amplitude relationships between excitation and inhibition. This possibility is supported by frequency-dependent routeing of inhibition⁴³.

Taken together, our data illustrate a simple scheme by which axons of layer 2/3 pyramidal cells coordinate excitation and inhibition to promote competition for cortical space between neighbouring cortical domains.

METHODS SUMMARY

For in utero electroporation²³ E15–E16 embryos were injected with 1–2 μg ChR2 DNA and 0.5–1 μg of GFP or mRFP DNA. Somatosensory thalamocortical slices⁴⁴ were cut and stored in reduced sodium artificial cerebrospinal fluid (ACSF) before being transferred 1–4 h later to a submerged temperature-controlled recording chamber in standard ACSF. Whole-cell recordings were obtained with patch pipettes (2–3 MΩ) containing a caesium-based internal solution for voltage-clamp experiments, and a potassium-based solution for current-clamp recordings. For in vivo recordings mice were anaesthetized with 1% isoflurane and 1.25 mg kg⁻¹ chlorprothixene, their head fixed and a small (~2–2.5 mm) craniotomy performed. The dura mater was left intact for extracellular recordings, or a small incision was made to permit the entry of patch pipettes for whole-cell recordings. For photostimulation a mounted 5W blue LED was used, collimated and coupled to the epifluorescence path of an Olympus BX51 through a 40× water immersion lens. For in vivo photostimulation a 3W LED was coupled to a 1-mm diameter optic fibre and mounted <5 mm from the craniotomy. Intracellular and LFP data were recorded using Multiclamp 700B or 200B amplifiers, and digitized at 10–20 kHz (National Instruments), while multichannel recording was conducted with an AM systems 16 channel amplifier and digitized at 30 kHz. For replay of synaptic currents, L2/3 and L5 pyramidal cells were patched with two pipettes; one pipette injected the excitatory waveform, the other imposed an inhibitory conductance using a custom feedback-controlled analogue ‘dynamic clamp’ circuit board.

Full Methods and any associated references are available in the online version of the paper at www.nature.com/nature.

Supplementary Material

Acknowledgments

Footnotes

References