a r t ic l e s

Recurrent inhibitory circuitry as a mechanism for grid formation

npg

© 2013 Nature America, Inc. All rights reserved.

Jonathan J Couey1–3, Aree Witoelar1,3, Sheng-Jia Zhang1,3, Kang Zheng1, Jing Ye1, Benjamin Dunn1, Rafal Czajkowski1, May-Britt Moser1, Edvard I Moser1, Yasser Roudi1 & Menno P Witter1 Grid cells in layer II of the medial entorhinal cortex form a principal component of the mammalian neural representation of space. The firing pattern of a single grid cell has been hypothesized to be generated through attractor dynamics in a network with a specific local connectivity including both excitatory and inhibitory connections. However, experimental evidence supporting the presence of such connectivity among grid cells in layer II is limited. Here we report recordings from more than 600 neuron pairs in rat entorhinal slices, demonstrating that stellate cells, the principal cell type in the layer II grid network, are mainly interconnected via inhibitory interneurons. Using a model attractor network, we demonstrate that stable grid firing can emerge from a simple recurrent inhibitory network. Our findings thus suggest that the observed inhibitory microcircuitry between stellate cells is sufficient to generate grid-cell firing patterns in layer II of the medial entorhinal cortex. Recent single-unit in vivo studies estimate that ~50% of the cells in layer II of the medial entorhinal cortex (MEC) fire action potentials at the apices of an equilateral triangular grid, encoding the entire space1,2. Such cells have become commonly known as grid cells. Neighboring grid cells in vivo encode firing fields with similar spacing and axes of orientation, suggesting that the patterns are inter­dependent, mediated via the local microcircuit1. One class of proposed mathematical solutions to the generation of the grid patterns relies on attractor dynamics mediated by a precisely formed connectivity pattern between grid cells3–5. In all but one of these solutions3, the postulated intrinsic connectivity is both excitatory and inhibitory. Despite the emphasis on excitatory network architectures in computational models, the presence and relevance of local layer II excitatory connections between principal cells in relation to local inhibition is still in contention6–9. In an in vitro study in which recordings had been reported between 135 neuron pairs, excitatory connectivity between principal cells in layer II had not been observed7. In contrast, recordings in vivo of 12 principal cells had shown excitatory connectivity between two pairs8, and in two studies using scanning photostimulation of caged glutamate, excitation between cells in layer II of the entorhinal cortex had been reported6,9. There are two potential confounds in these reported data. First, photostimulation, as used in the uncaging studies6,9, is unspecific in that it does not rule out that excitatory responses originate from driving extrinsic excitatory inputs in addition to local circuitry. Second, layer II of MEC comprises two main types of principal cells, stellate and pyramidal cells10–12, which may be connected differently13. To determine the contribution of these factors, we performed whole-cell patch recordings from more than 600 simultaneously recorded pairs of stellate cells in horizontal and sagittal slices of the medial entorhinal cortex. Stellate cells form

the large majority of principal neurons in MEC layer II (67% versus 17% pyramidal neurons14), and more than 50% of extracellularly recorded layer II neurons are grid cells2,15. Moreover, in vivo juxtacellular recordings indicate that spatial firing patterns in MEC are associated with stellate cells16. On the basis of these indications, stellate cells are likely candidates for grid cells in layer II, although we cannot presently rule out that pyramidal cells have similar properties. RESULTS Stellate cell connectivity Multiple simultaneous (clustered) whole-cell recordings (three or more cells) provide a combinatorial increase in the number of possible connections that can be probed during a single experiment and have proven to be a valuable tool in mapping local microcircuit ­connectivity17. We used clustered whole-cell in vitro slice recordings of neurons in MEC layer II of 138 female Long-Evans rats to mea­ sure directly the recurrent connectivity between 644 pairs of stellate cells in MEC layer II. We recorded from 61 four-cell stellate clusters and 77 three-cell stellate clusters as well as mixed clusters of three or four neurons containing one or more nonstellate cells. The data set is derived from 185 clusters in total (Online Methods), of which 161 we anatomically recovered, allowing assessment of the anatomical position and morphology of individual neurons. Given the reported in vivo and in vitro differences in the electrophysiological properties of neurons along the dorsoventral axis of the MEC18,19, exploring the connectivity throughout this axis is crucial for drawing a complete picture. The 161 clusters, obtained in horizontal and sagittal slices, showed that we indeed explored connectivity in layer II throughout the entire extent of the dorsoventral axis. (Supplementary Fig. 1). We carried out experiments using a wide developmental time window

1Kavli

Institute for Systems Neuroscience and Centre for the Biology of Memory, Norwegian Brain Centre, Norwegian University of Science and Technology, Trondheim, Norway. 2Present address: Department of Psychiatry, Erasmus Medical Center, Rotterdam, The Netherlands. 3These authors contributed equally to this work. Correspondence should be addressed to M.P.W. ([email protected]) or Y.R. ([email protected]). Received 17 August 2012; accepted 17 December 2012; published online 20 January 2013; doi:10.1038/nn.3310

318

VOLUME 16 | NUMBER 3 | MARCH 2013  nature NEUROSCIENCE

a r t ic l e s a

b

10 APs at 10 Hz 1

10 + 1 APs at 20 Hz 1

4

2

2

3

1 1 1

4 2 3

1

3

3

4

4 10 + 1 APs at 40 Hz

4

25 mV

2

? 3

1

2

2

1 4

3

d 1

2

2

3

3

4

2

70 Hz

?

3

4

?

2 3

4

1

1

2

? 4

3 ?

1

4

1

1

2

3

4

2

1

1

1

1

2

2

250 ms

3

3

2

2

3

4

4

4

3

1 mV 50 mV

1

3 4

2

2 3

4

3 ? 4 1 20 Hz

250 ms

4

40 Hz

1

4 3

1 mV 40 mV

© 2013 Nature America, Inc. All rights reserved.

c

1

4

3

100 ms 20 µm

3

15 + 1 APs at 70 Hz 1 mV 50 mV

1 2

npg

2

2

2

10 Hz

4 3

250 ms

4

Figure 1  Recurrent inhibitory connectivity in MEC layer II. (a) Stimulation and recording protocol illustrating a cluster of three layer II stellate cells (neurons 1, 2 and 3) and a layer II pyramidal cell (neuron 4). Insets, characteristic electrophysiological profiles of stellate cells (red; star indicates action potential (AP) burst) and pyramidal cell (green). (b) Stimulation and recording protocol for the three stellate cells and one putative pyramidal cell shown in a. Red traces show current injection of 10 Hz for stellate cell 1, 20 Hz for stellate cell 2, 40 Hz for stellate cell 3 and 70 Hz for pyramidal cell 4. Black traces show responses recorded in the other three cells. In the case of stimulation of cell 3, inhibitory responses were recorded in cell 2 (single sweeps, gray; mean, black). (c) Single cell stimulation: average single postsynaptic responses in neurons 2, 3 and 4 (black) superimposed over 20 individual sweep recordings (gray) following trains of actions potentials induced at different frequencies in cell 1 (red). (d) Schematics of the stimulation (top) followed by four whole-cell traces (red traces indicate current injection). Individual sweeps are shown for the stimulated ensemble, and mean responses (black) and individual sweeps (gray) are shown for the postsynaptic responses. Response traces in c and d show fast positive deflections synchronous with applied stimulations, which are artifacts 46 caused by high-frequency noise produced by nearby whole-cell stimulation bleeding through onto the nonstimulated cell pipette recording.

(postnatal ages 10–82; P10–P82), in view of our previous report that synchrony between MEC layer II stellate cells increases during development, before the time when mature grid patterns are expressed in vivo20. We selected recording conditions to allow whole-cell stimulation of individual stellate cells to have the potential to reveal both excitatory and inhibitory connectivity when monitoring the nonstimulated cells in the cluster for postsynaptic responses17. We differentiated two primary excitatory cell types in layer II, stellate cells and pyramidal cells, using criteria recently described and validated by us and others in detail10–12,18. Physiologically, we confirmed the identity of stellate cells by characteristic low input resistance (84 MΩ ± 27 MΩ; mean ± s.e.m.) and high-frequency burst firing in response to step depolarization to threshold, a characteristic ‘sag’ potential in response to depolarizing or hyperpolarizing ­current pulses and a substantial difference between the first and nature NEUROSCIENCE  VOLUME 16 | NUMBER 3 | MARCH 2013

second ­interspike interval (ratio = 18.04 ± 5.67), when depolarized with 500-ms current steps near the firing threshold. The more heterogeneous population of putative pyramidal layer II cells12 (input resistance, 242 MΩ ± 24 MΩ) instead fired regular trains with varying degrees of adaptation; they usually lacked the typical sag seen in stellate cells, and showed no clear difference between the first and second interspike interval (ratio = 0.92 ± 0.29; Supplementary Table 1). These observations correlated with post-hoc morphological classification of the cells as stellate or pyramidal layer II cells (Fig. 1a). We had a high success rate when targeting stellate cells in layer II, but we recorded from 24 pyramidal cells in layer II as well (Fig. 1a, cell 4), as part of the predetermined stimulation routine to check for connectivity within clusters. In two of the cases, stimulation of stellate cells resulted in postsynaptic excitatory responses in pyramidal neurons (mean responses, 0.8 mV and 0.4 mV). However, we did not observe 319

a r t ic l e s

0.5 5

10 15 20 25 Postnatal age (d)

–0.2

30

30

20

20

10

10

0

0

20

–0.8

1.8

0

5

–1.0

0

0– P1

postsynaptic responses, neither excitatory nor inhibitory, in stellate cells (N = 52) when stimulating pyramidal cells. Stellate cells are connected via inhibitory interneurons In slices obtained from rats older than postnatal day 21, activation of short bursts of synchronous action potentials in a single stellate cell (3–10 pulses at 10 Hz, 20 Hz, 40 Hz or 70 Hz) resulted in inhibitory responses in only 4% of recorded pairs (amplitude = –0.6 mV ± 0.5 mV; peak time = 13.1 ms ± 4 ms), whereas in the remaining stellate cells we observed no measurable responses (Fig. 1b,c). The evoked inhibitory responses were independent of presynaptic firing frequency (Fig. 1c), and we observed no differences along the dorsalventral axis. Concurrent activation of short bursts of synchronous action potentials (3–10 pulses at 70 Hz) in three stellate cells resulted in simple and compound inhibitory responses in the fourth non­ stimulated stellate cell in 64% of all cells within recorded clusters under normal recording conditions over all recording locations; Fig. 1d). The evoked inhibitory responses exhibited stable amplitudes (–0.70 mV ± 0.06 mV; Fig. 2) and peak times (12.2 ms ± 2 ms). We never observed excitatory responses in any one stellate cell driven by concurrent activation of two or more stellate cells. In many instances, however, we observed depolarizing currents after observed

0.99

0.3

0

Figure 2  Stellate interconnectivity changes during early postnatal development. (a) Example sweeps from four stellate cell recording when a direct excitatory connection between two P10 stellate cells is stimulated with 10-Hz presynaptic train (left); mean responses at four indicated stimulation frequencies of the P10 synapse (middle) and a connection recorded at P26 (right). (b) Amplitudes of excitatory responses at indicated postnatal ages. (c) Normalized distribution of the recorded inhibitory responses (bin size = 0.25 mV) for four cell clusters sorted by postnatal week. (d) Inhibitory amplitudes during development (mean ± s.e.m.; n = 24 (P10–P15); n = 36 (P16–P21); n = 20 (P22–P27); and n = 24 (P28+)). (e) Fraction of excitatory connectivity (excitation) and recurrent inhibition as a function of postnatal age. Values are shown for bars in d,e.

hyperpolarization (Figs. 1, 3 and 4). We interpret these as rebound currents after hyperpolarization, a characteristic feature of stellate cells12. One possible confounding factor in the data might be that excitatory connections are concealed by shunting because of dendritic GABAergic input and/or by strong dendritic attenuation caused by voltage-activated potassium channels21. We tested 28 adult cell clusters (13 four-cell stellate clusters and 15 three-cell stellate clusters), totaling 246 possible stellate cell connections, using the same singlecell and triple-cell stimulation protocols while blocking possible GABAergic input with 5 µM bicuculine in the presence of 100 µM voltage-activated potassium channel (Kv1) blocker 4-aminopyridine22. In only three of the pairs did we record signs of excitatory events, though extremely unreliably in that they occurred only sporadically and only in response to multiple simultaneous stimulations of presynaptic stellate cells. All findings thus indicate that stellate cells in layer II of the MEC are embedded in a predominantly recurrent inhibitory network, driven by synchronous activity of stellate cells. Stellate connectivity changes during postnatal development To identify trends during development, we analyzed our patch data by grouping on the basis of postnatal age (P10–P15, P16–P21, P22–P27, and P28 and older (here referred to as P28+). During development,

b

a

40 mV

320

ty

ci

ro

R

c

ec ip

st FS el t la o te St el to lat FS e

Connectivity (%)

40 mV 1 mV

Figure 3  Inhibitory connectivity between stellate 80 1 1 1 cells in MEC layer II mediated by fast-spiking 60 4 3 3 4 3 4 neurons. (a) Example recording for a cluster 40 2 2 2 that includes a reciprocally connected cell pair consisting of one fast-spiking interneuron (1) 20 and one stellate cell (2) from a P21 rat. 0 1 1 Left, electrophysiological characterization of 200 ms interneuron 1 and three stellate cells (2, 3 and 4). Middle and right, average postsynaptic 20 2 2 response to a 40-Hz train of 10 action potentials 63% 31% Stel > Stel (black) superimposed over the 20 individual 15 n=1 sweep recordings (gray) from which it is derived. Amp. = 0.3 mV 1/570 = 0.002% 3 3 10 Shown is the average excitatory response recorded in cell 1 when cell 2 is stimulated 5 (middle) and the inhibitory response in stellate 200 ms 4 4 cells 2, 3 and 4 when cell 1 is stimulated (right). 0 –2 –1 1 2 (b) Connectivity rates summarized for excitatory Amplitude (mV) connections from stellate to fast-spiking (FS) cells, inhibitory connections from fast-spiking cells to stellate cells and the reciprocity of these connections. (c) Observed amplitudes from all fast-spiking to stellate synapses (Stel; red, inhibitory), from all stellate to fast-spiking synapses (black, excitatory) and from all stellate to stellate synapses (dotted line indicates amplitude of single direct connection out of 570 possible connections between stellate cells; P21+ recordings, normalized distribution of the recorded responses; bin size = 0.25 mV). The fractions of zero amplitude responses have been truncated, and fractions are indicated. Fraction (%)

© 2013 Nature America, Inc. All rights reserved.

42

40

P1

0

.0

–0.6

66

60

60

–1

0

.0

–2

.0

–1

0

.0

–2

.0

–1

.0 –2

–1

–2

–0.4

Amplitude (mV)

npg

80

0

30

Excitation Recurrent inhibition

7

40

Amplitude (mV)

0

40

0

50

.0

50

e 100

P1

d

Total (%)

P28+

P22–P27

P28+

P16–P21

P22–P27

60

P16–P21

P10–P15

.0

Response (%)

c 100

P10–P15

200 ms

8+

0

70 Hz

P2

1 mV

1.0

1

40 Hz

1.5

P2

20 Hz

2–

10 Hz

4

10 Hz 3

2.0

P2

2

b

P26

P2

1

P10

6–

P10

Amplitude (mV)

a

VOLUME 16 | NUMBER 3 | MARCH 2013  nature NEUROSCIENCE

a r t ic l e s a

b

c

II I

II

1 2

Id

3 4

300 ms 40 mV

V

npg

© 2013 Nature America, Inc. All rights reserved.

V

d Total response count (70 max)

VI

250 ms 40

Cell 2

40

20

20

0 40

0 40

Cell 1

Cell 3

Cell 4

20

20 0 –2 –1 0

0 1 2 –2 –1 0 Amplitude (mV)

1

2

e

Stellate Interneuron Pyramidal

35 30

0.4

25

Mean amplitude (mV)

30 µm

1 mv

III

Response fraction (%)

III

20 15 10 5 0

–2

–1

1 Amplitude (mV)

0.2 0 –0.2 –0.4 2

3

Figure 4  Optical stimulation of layer II results in inhibition in stellate cells. (a) Fluorescence images of a section of MEC, showing mCherry-positive elements after injection with rAAV in the dorsal hippocampus. Scale bars, 300 µm (left) and 60 µm (right). (b) Stimulation protocol illustrating the 70-laser-point stimulation foci (blue circles) for a cluster of layer II cells (post-hoc biocytin-filled). Insets, whole-cell responses to hyperpolarizing and depolarizing steps in stellate cells (cells 1, 2 and 3 recording pipettes and data shown in red, green and blue, respectively) and a nonstellate putative pyramidal cell (cell 4, gray). (c) Normalized mean responses recorded in the three stellate cells in response to the light pulses at each stimulation point (traces are color-coded as in b. (d) Amplitudes for the four cells in b (same color code), showing an absence of excitation in the three stellate cells 1, 2 and 3; pyramidal cell 4 showed excitatory responses. (e) Left, excitatory amplitudes in all fast-spiking putative interneurons, responses in all pyramidal cells, and inhibitory amplitudes in all stellate cells (normalized distribution of the recorded responses; bin size = 0.25 mV; zero fractions (not shown) were 22% for fast-spiking, 2% for stellate and 80% for pyramidal cells; dashed line indicates zero). Right, responses in fast-spiking and stellate cells (mean amplitude ± s.e.m.; n = 779 and 103 responses, respectively).

in particular in rats younger than 3 weeks, we observed evidence of sparse excitation between stellate cells (Fig. 2). The amplitude of these extremely rare excitatory connections exhibited a decay correlated with age (R2 = 0.76; d.f. = 4; maximum at P10 = 1.3 mV, minimum at P26 = 0.3 mV; Fig. 2a,b). The number of excitatory connections also decreased during this developmental period (P10–P15, 3 connections; P16–P21, 2 connections; and P21–P27, 1 connection), decaying to zero by the fourth postnatal week (Fig. 2e). Analysis carried out on 27 four-cell clusters obtained at different postnatal days (P10–P15, 24 connections; P16–P21, 36 connections; P22–P27, 20 connections; P28+, 24 connections) indicated a parallel developmental maturation of the inhibitory network that seemed to begin after eye opening (P15), continuing until at least P28 (Fig. 2c–e). We observed an increase in the number of disynaptic inhibitory connections from 0% at P10–P15 up to 66% at P28+ and their amplitudes increased from 0 mV at P10–P15 to –0.73 mV ± 0.1 mV at P28+ (Fig. 2d,e). Taken together, in parallel with an early developmental decrease in sparse direct excitatory connectivity between stellate cells, we found evidence for the development of the recurrent inhibitory circuit between stellate cells during this same period. The maturation of local inhibition likely offers a cellular mechanism for the increase in entorhinal network synchrony we had reported previously20. Inhibition is mediated by inhibitory fast-spiking cells To identify possible sources of the recurrent inhibition, we examined cluster recordings containing both stellate cells and one or more local putative interneurons. We grouped the recorded putative interneurons into two electrophysiological types, based on their electrophysiological profile23,24 (Supplementary Table 1, Supplementary Fig. 2a nature NEUROSCIENCE  VOLUME 16 | NUMBER 3 | MARCH 2013

and Online Methods). These two subgroups were differently connected to stellate cells: 43 putative fast-spiking interneurons (resting membrane voltage (Vm) = –68.8 mV ± 3 mV; non-adapting: action potential halfwidth, 0.6 ms ± 0.09 ms) made abundant inhibitory synapses onto 24 stellate cells (54% connectivity rate; peak latency = 10.27 ms ± 0.5 ms; Fig. 3a,b23), whereas we found no connections from 10 low-threshold spiking (LTS) putative interneurons (rest Vm = –56 mV ± 4 mV; adapting; action potential halfwidth, 0.9 ms ± 0.08 ms). The amplitudes of the postsynaptic inhibitory responses evoked in fast-spiking stellate cell pairs were not statistically different from the mean recurrent inhibitory response shown in Figure 1d (mean = –0.54 mV ± 0.2 mV; P = 0.106, t-test; Fig. 3c). Stellate cells were also highly connected with fast-spiking interneurons when compared with the LTS group (16 of 43 fast-spiking interneurons (37%); peak latency = 5.7 ms ± 0.8 ms, mean amplitude 1.67 mV ± 1.19 mV; 2 of 10 LTS interneurons (20%); peak latency = 6.1 and 5.9 ms; mean amplitude = 1.6 and 1.2 mV), and reciprocity between fastspiking interneurons and stellate cells was high (11 of 16 stellate cell to fast-spiking interneuron excitatory connections were paired with a reciprocal inhibitory connection, equal to 26% of all pairs; Fig. 3b). Clusters containing interconnected stellate cells and fast-spiking interneurons could be used to demonstrate the functional recurrent inhibitory circuit (Supplementary Fig. 2b). These data implicate the latter microcircuit as a primary component of the recurrent inhibitory network in layer II23. Absence of excitation does not reflect sampling bias Clustered whole-cell recording does increase the efficacy to probe for local connectivity, but there are potential drawbacks that may 321

a r t ic l e s a

b

npg

© 2013 Nature America, Inc. All rights reserved.

R = 20

R = 15

R = 10

Figure 5  A simple inhibitory network is W0 = –0.01 –0.04 –0.02 0 ms 20 ms 40 ms sufficient to generate grid cell patterns. (a) Formation of a hexagonal pattern on a two-dimensional neuronal lattice shown in snapshots of the activity taken at time. The map shows the activity on the entorhinal cortex model with neurons rearranged according to their spatial phases. ‘Hotter’ colors represent 60 ms 100 ms 500 ms high activity rates, and connection radii R of two example neurons are shown as white and green circles. Snapshots display the initial state (0 ms), the emergence of geometric pattern (40 ms, 60 ms and 100 ms) and stable hexagonal patterns (500 ms). (b) Simulated Activity (arbitrary units): 0 0.5 1 single neuron responses corresponding to a rat’s recorded positions over 10 min in a cylindrical enclosure with a diameter of 1.8 m (ref. 1). Red dots represent spikes generated by a stochastic Poisson process governed by its instantaneous firing rate (Online Methods). The two parameters that define the connectivity, the strength (W0) and width (radius R) control the size of the grids and their spacing.

result in an underestimation of certain connections. Although we recorded from pairs of stellate cells, we acknowledge the possibility of a sampling bias in the selection of clusters or cells in clusters, or we may have missed longer-range connections that are part of the layer II MEC network as most of our recordings were from clusters of spatially close neurons with an interneuronal distance of around 20–50 µm. A comparison between in vitro with in vivo whole-cell reconstructions shows that in horizontal slices we may lose about 25% of the total axonal extent in the horizontal plane (diameter in vitro, 900 µm and in vivo, 1,200 µm)8,12. Moreover, in vivo the axonal arbor of layer II stellate cells may extend 900–2,000 µm in the sagittal plane8,16,25. To include as much of the axonal tree as possible, we recorded in tilted sagittal slices from 12 three-cell clusters and five four-cell clusters (Supplementary Fig. 1a and Online Methods) that exhibited an overall better preservation of the axonal arbor up to 1,000 µm. In none of the recordings in such slices, even in the case of one pair of cells 260 µm apart (Supplementary Fig. 1b), did we observe excitatory connections between the stellate cells. To increase the potential to stimulate cells that might be presynaptic to the cells from which we recorded, in subsequent experiments, we combined optogenetic stimulation with multicell recording. Optogenetic stimulation allows selective stimulation of a specific population of neurons, without the need to select and limit the stimulation to only three neurons, which is the maximum that can be achieved in our quadruple recordings26. These experiments also revealed evidence of a local recurrent inhibitory circuit devoid of any local excitation. We injected recombinant adeno-associated virus (rAAV; Online Methods) dorsally into the dentate gyrus and CA3 of the hippocampus to retrogradely express mutant channelrhodopsin-2 (ChR2) and mCherry in MEC layer II projection cells27. This resulted in labeling of MEC principal cells, dendrites and axons in layer II that could be activated by light. Anterograde mCherry-labeled axons were also visible in layers V and VI, whereas layer III was almost devoid of labeling (Fig. 4a,b)12. We recorded primarily from small groups of stellate cells (2–4 cells) by targeting cells in layer II with large somata (>20 µm) and multipolar dendritic arbors. For each cell, we stimulated a matrix of 5-µm-diameter foci, in total covering 100 µm2 or 200 µm2 of layer II, with blue light pulses (473 nm; 9 × 5 or 7 × 10 pulses of each 50-ms duration at 3.3 Hz) to activate nearby ChR2 (Fig. 4b). In contrast to stellate cells labeled with mCherry, which exhibited direct depolarizing responses to the light (latency, 10.7 ms ± 0.37 ms; n = 7; Supplementary Fig. 3a–c), we observed exclusively inhibitory (hyperpolarizing) postsynaptic responses in nonlabeled stellate cells, that is, cells that we synaptically activated by a light pulse 322

(19 of 19 cells; mean amplitude = –0.42 mV ± 0.2 mV; peak latency = 45.9 ms ± 0.5 ms). The inhibitory responses were detectable in multiple postsynaptic stellate cells simultaneously (Fig. 4c). The peak latencies observed in the experiments are comparable to those reported when probing multysynaptic circuits in the neocortex interconnecting principal cells via interneurons28. The observed latencies likely represent at least three main contributing factors. First, unlike in the four-cell cluster experiments in which the presynaptic activity was precisely timed, optogenetic activation of the disynaptic circuit requires more presynaptic activity, and therefore the time needed for the network to drive an interneuron sufficiently is necessarily longer. Second, the synaptic delay from interneuron to stellate cell and the time between the onset of the response and the measured peak of the response of the stellate cell will add considerably to the latencies17,28,29. Finally, as described, responses of neurons that express ChR2 exhibited a latency upon light stimulation over 10 ms, which may contribute to the length and the jitter of the latencies as well. Nonstellate cells, including both local putative interneurons (n = 4) and pyramidal cells (n = 5) that did not express ChR2, showed almost exclusively direct excitatory (depolarizing) postsynaptic potentials resulting from the light pulse (Fig. 4c–e and Supplementary Fig. 3d). These observations thus corroborate the cluster recording data, showing that stellate cell to stellate cell connections are mostly mediated through interneurons and that excitatory connections between stellate cells are essentially absent. We therefore conclude that stellate cells in layer II of MEC are embedded in a recurrent inhibitory network, driven by synchronous activity of stellate cells. Inhibitory attractor network generates grid cell firing Among the theoretical models proposed for the generation of grid cells, one class, that of the attractor models, emphasizes the internal connectivity in MEC for the generation of grid firing. Existing attractor models prescribe that the functional connectivity in the network is structured in a specific way abstracted via a Mexican hat connectivity3–5. A consequence of this type of connectivity is that an even sampling of the connectivity, as provided by our patch recordings, should yield a wide distribution for connectivity strength, potentially with an excitatory component (Supplementary Fig. 4). Instead the data suggest an exclusively inhibitory network with a bimodal distribution (Figs. 2e and 3c), in which connections are either absent or have amplitudes centered at 0.6 mV ± 0.5 mV. To test whether these experimental observations pose a challenge to the attractor models, we studied the simplest model consistent with the VOLUME 16 | NUMBER 3 | MARCH 2013  nature NEUROSCIENCE

npg

© 2013 Nature America, Inc. All rights reserved.

a r t ic l e s connectivity observed in our experimental data. We asked whether such a model can generate grid cell activity. We simulated a stellate cell network composed of a two-dimensional lattice of neurons. The neurons were connected to each other via a pattern that followed the simplest bimodal distribution, that is, an all-or-none unstructured inhibitory connectivity. This network would correspond to a neuronal sheet made by rearranging grid cells according to their phases (Online Methods). For simplicity, we did not explicitly model inhibitory interneurons but accounted for their influence in the effective connectivity between the stellate cells: each neuron received inhibition of constant magnitude from neurons within a radius of connectivity R of itself and was not connected to any other neuron in the network (Fig. 5a). All neurons also received a constant uniform excitatory input3. Although we did not make any specific assumptions about the source of this excitatory drive, as described in the accompanying paper30, possible sources are direct or indirect connections from the hippocampus. The experimentally observed connectivity indeed led to the formation of stable hexagonal grid patterns on the network through a simple mechanism (Fig. 5a). A neuron inside a patch of activity received inhibition from other neurons in the same patch as well as some of the neurons active in nearby patches. This inhibition was exceeded by the external excitatory drive, causing the neuron to fire. Neurons between two active patches, in contrast, received more inhibition because they received inhibition from all neurons in all their surrounding patches, and the external drive was not enough to overcome this inhibition (an example is shown by the intersection of circles in Fig. 5a). The fact that the activity blobs only exerted inhibition on each other caused them to form at positions where the distance between each pair is maximized, that is, the vertices of a hexagonal grid. As is the case with other attractor models of grid cells, once the hexagonal activity pattern was formed, singlecell grid activity can be generated by velocity-modulated idiothetic head-direction signals. This input allows the hexagonal pattern to be translated in concert with the movement of the rat. Consequently, the single-cell response, as the rat navigates an environment, mirrors the hexagonal activity pattern in the cortical sheet. Varying the two parameters that define the connectivity, that is, the strength (W0) and width (radius R) of the inhibition, allowed the generation of grids of different size and spacing as has been observed experimentally (Fig. 5b and Supplementary Fig. 4). DISCUSSION The discovery of MEC grid cells has inspired several attempts to generate a neural network model to connect real-time neuronal firing patterns and animal behavior3–5,31–33. The elaboration of such a model necessarily requires detailed knowledge of the precise local microcircuitry in which these specialized cells are embedded. Here we presented comprehensive data from over 600 recorded cell pairs, indicating that MEC layer II stellate cells in young adult rats are embedded in a dense recurrent inhibitory network. Stellate connectivity mediated by inhibitory interneurons Data from whole-cell cluster recordings demonstrated that precisely timed presynaptic activity in small groups of stellate cells can activate the local inhibitory microcircuitry with high fidelity in a frequencyindependent manner. Irrespective of the position of recordings or the stimulation and recording protocols, we found no evidence of direct stellate cell to stellate cell excitatory connectivity in MEC layer II in adult tissue slices. We corroborated and extended these ­observations with optogenetic experiments, which suggested that the nature NEUROSCIENCE  VOLUME 16 | NUMBER 3 | MARCH 2013

lack of ­evidence for excitatory stellate cell to stellate cell connectivity was not due to a cutting artifact of the slice preparation or a biased sample of only local connections between spatially associated clusters. These results corroborate a previous in vitro study reporting a lack of excitatory connectivity among 135 pairs of stellate cells 7. Although our findings cannot exclude the presence of excitatory connections in layer II as a whole6,8,9, they indicate that excitatory connections between stellate cells are very sparse or absent. An inhibitory attractor model generates grid cell activity We also reported that a simplified uniform inhibitory attractor model can generate grid-cell activity. The fact that neurons with even very similar phases should inhibit each other, to the same extent that they inhibit others, deviates from Mexican hat–like connectivity, which emphasizes local cooperation versus long-range competition as a crucial component of the pattern formation required for grid-like firing3–5. On the basis of pioneering work on cortical pattern formation34, Mexican hat–type connectivity and its variants have been deemed necessary for the formation of localized activity patches on the cortical network encoding the animal’s head direction35–37, stimulus orientation38,39, spatial position of an object in working memory40 and most recently spatial periodicity in grid cells3,4. Although some models of the head-directional system also emphasize exclusively inhibitory recurrent connectivity36,37, these networks assume the presence of excitatory interactions between different parts of a network that yield a graded effective connectivity pattern. Our work suggests that even in those cases simpler connectivity patterns may be sufficient to generate the selectivity of the head-direction system. The proposed model relies on the presence of a constant excitatory input that exceeds the local inhibition to cause principal cells to fire. As shown in the accompanying paper30, in which the same model is used, this steady excitatory drive may originate in the hippocampus. Alternatively, local excitatory networks embedded in layer II through nonstellate cells, or feedback loops between the layers, may provide the excitatory drive6,8,41,42. The fact that an excitatory drive together with head-directional and velocity-tuned inputs are required for generation of the grid cell might explain why grid cells have not been seen, for example, in the dentate gyrus, which has a comparable local architecture with principal cells being connected almost exclusively through an inhibitory interneuron network43,44. The data presented here do not, in principle, rule out additional mechanisms of grid-cell formation, namely intracellular mechanisms such as oscillatory interference mechanisms31,33 or those based on spike adaptation32. However, our experimental findings and in particular the computational model derived from them, do point to an all-or-none inhibitory microcircuitry as sufficient for grid cell formation in layer II of MEC and reduce the postulated complexity of the layer II grid cell network to a simple unstructured recurrent inhibitory network. Such a network may develop postnatally during the period that inhibitory elements are inserted in the network 45. It remains to be established how grid firing emerges in networks such as deep layers of MEC, where excitatory connections between principal cells are more abundant7, or in the presubiculum and parasubiculum, where we lack sufficient information on the intrinsic network. The fact that a minimal inhibitory connectivity pattern between layer II stellate cells is present in MEC, and that a model based on a network with these biological properties could generate grid activity, raises the possibility that similar mechanisms are used in other parts of the cortex where pattern formation is considered to be a crucial component in information processing. 323

a r t ic l e s Methods Methods and any associated references are available in the online version of the paper. Note: Supplementary information is available in the online version of the paper. Acknowledgments We thank K. Deisseroth (Stanford University) for providing the ChR2(H134R) plasmid, I.E.J. Assebø for histological reconstructions, P. Girão for programming and A. Treves for comments on the manuscript. This work was supported by the Kavli Foundation, an EU 7th framework grant (‘Spacebrain’ grant agreement 200873), and Centre of Excellence (145993), equipment (181676) and research (191929) grants from the Norwegian Research Council, and an Advanced Investigator Grant from the European Research Council (‘CIRCUIT’, grant 232608).

npg

© 2013 Nature America, Inc. All rights reserved.

AUTHOR CONTRIBUTIONS J.J.C. and M.P.W. designed the experiments. All experiments were carried out by J.J.C. with the help of R.C., who performed the stereotaxic viral injections and post-hoc immunohistochemistry, and K.Z., who helped with the cluster recordings. J.J.C., R.C. and K.Z. performed experimental analyses. A.W., B.D. and Y.R. did the network simulations. S.-J.Z. and J.Y. designed and provided the rAAV. J.J.C., A.W., Y.R., E.I.M. and M.P.W. wrote the manuscript, and all authors contributed to discussion and interpretation of results. COMPETING FINANCIAL INTERESTS The authors declare no competing financial interests. Published online at http://www.nature.com/doifinder/10.1038/nn.3310. Reprints and permissions information is available online at http://www.nature.com/ reprints/index.html. 1. Hafting, T., Fyhn, M., Molden, S., Moser, M.B. & Moser, E.I. Microstructure of a spatial map in the entorhinal cortex. Nature 436, 801–806 (2005). 2. Sargolini, F. et al. Conjunctive representation of position, direction, and velocity in entorhinal cortex. Science 312, 758–762 (2006). 3. Burak, Y. & Fiete, I.R. Accurate path integration in continuous attractor network models of grid cells. PLoS Comput. Biol. 5, e1000291 (2009). 4. Fuhs, M.C. & Touretzky, D.S. A spin glass model of path integration in rat medial entorhinal cortex. J. Neurosci. 26, 4266–4276 (2006). 5. McNaughton, B.L., Battaglia, F.P., Jensen, O., Moser, E.I. & Moser, M.B. Path integration and the neural basis of the ′cognitive map′. Nat. Rev. Neurosci. 7, 663–678 (2006). 6. Beed, P. et al. Analysis of excitatory microcircuitry in the medial entorhinal cortex reveals cell-type-specific differences. Neuron 68, 1059–1066 (2010). 7. Dhillon, A. & Jones, R.S. Laminar differences in recurrent excitatory transmission in the rat entorhinal cortex in vitro. Neuroscience 99, 413–422 (2000). 8. Quilichini, P., Sirota, A. & Buzsaki, G. Intrinsic circuit organization and theta-gamma oscillation dynamics in the entorhinal cortex of the rat. J. Neurosci. 30, 11128–11142 (2010). 9. Kumar, S.S., Jin, X., Buckmaster, P.S. & Huguenard, J.R. Recurrent circuits in layer II of medial entorhinal cortex in a model of temporal lobe epilepsy. J. Neurosci. 27, 1239–1246 (2007). 10. Alonso, A. & Klink, R. Differential electroresponsiveness of stellate and pyramidal-like cells of medial entorhinal cortex layer II. J. Neurophysiol. 70, 128–143 (1993). 11. Klink, R. & Alonso, A. Morphological characteristics of layer II projection neurons in the rat medial entorhinal cortex. Hippocampus 7, 571–583 (1997). 12. Canto, C.B. & Witter, M.P. Cellular properties of principal neurons in the rat entorhinal cortex. II. The medial entorhinal cortex. Hippocampus 22, 1277–1299 (2012). 13. Varga, C., Lee, S.Y. & Soltesz, I. Target-selective GABAergic control of entorhinal cortex output. Nat. Neurosci. 13, 822–824 (2010). 14. Gatome, C.W., Slomianka, L., Lipp, H.P. & Amrein, I. Number estimates of neuronal phenotypes in layer II of the medial entorhinal cortex of rat and mouse. Neuroscience 170, 156–165 (2010). 15. Boccara, C.N. et al. Grid cells in pre- and parasubiculum. Nat. Neurosci. 13, 987–994 (2010). 16. Burgalossi, A. et al. Microcircuits of functionally identified neurons in the rat medial entorhinal cortex. Neuron 70, 773–786 (2011). 17. Silberberg, G. & Markram, H. Disynaptic inhibition between neocortical pyramidal cells mediated by Martinotti cells. Neuron 53, 735–746 (2007).

324

18. Giocomo, L.M. & Hasselmo, M.E. Time constants of h current in layer ii stellate cells differ along the dorsal to ventral axis of medial entorhinal cortex. J. Neurosci. 28, 9414–9425 (2008). 19. Brun, V.H. et al. Progressive increase in grid scale from dorsal to ventral medial entorhinal cortex. Hippocampus 18, 1200–1212 (2008). 20. Langston, R.F. et al. Development of the spatial representation system in the rat. Science 328, 1576–1580 (2010). 21. Hoffman, D.A., Magee, J.C., Colbert, C.M. & Johnston, D.K. + channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons. Nature 387, 869–875 (1997). 22. Petreanu, L., Mao, T., Sternson, S.M. & Svoboda, K. The subcellular organization of neocortical excitatory connections. Nature 457, 1142–1145 (2009). 23. Jones, R.S. & Buhl, E.H. Basket-like interneurones in layer II of the entorhinal cortex exhibit a powerful NMDA-mediated synaptic excitation. Neurosci. Lett. 149, 35–39 (1993). 24. Sills, J.B., Connors, B.W. & Burwell, R.D. Electrophysiological and morphological properties of neurons in layer 5 of the rat postrhinal cortex. Hippocampus 22, 1912–1922 (2012). 25. Tamamaki, N. & Nojyo, Y. Projection of the entorhinal layer II neurons in the rat as revealed by intracellular pressure-injection of neurobiotin. Hippocampus 3, 471–480 (1993). 26. Yizhar, O., Fenno, L.E., Davidson, T.J., Mogri, M. & Deisseroth, K. Optogenetics in neural systems. Neuron 71, 9–34 (2011). 27. Witter, M.P. The perforant path: projections from the entorhinal cortex to the dentate gyrus. Prog. Brain Res. 163, 43–61 (2007). 28. Berger, T.K., Silberberg, G., Perin, R. & Markram, H. Brief bursts self-inhibit and correlate the pyramidal network. PLoS Biol. 8, e1000473 (2010). 29. Kapfer, C., Glickfeld, L.L., Atallah, B.V. & Scanziani, M. Supralinear increase of recurrent inhibition during sparse activity in the somatosensory cortex. Nat. Neurosci. 10, 743–753 (2007). 30. Bonnevie, T. et al. Grid cells require excitatory drive from the hippocampus. Nat. Neurosci. doi:10.1038/nn.3311 (20 January 2013). 31. Burgess, N., Barry, C. & O′Keefe, J. An oscillatory interference model of grid cell firing. Hippocampus 17, 801–812 (2007). 32. Kropff, E. & Treves, A. The emergence of grid cells: intelligent design or just adaptation? Hippocampus 18, 1256–1269 (2008). 33. Zilli, E.A. & Hasselmo, M.E. Coupled noisy spiking neurons as velocity-controlled oscillators in a model of grid cell spatial firing. J. Neurosci. 30, 13850–13860 (2010). 34. Amari, S. Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern. 27, 77–87 (1977). 35. Zhang, K. Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory. J. Neurosci. 16, 2112–2126 (1996). 36. Song, P. & Wang, X.J. Angular path integration by moving “hill of activity”: a spiking neuron model without recurrent excitation of the head-direction system. J. Neurosci. 25, 1002–1014 (2005). 37. Boucheny, C., Brunel, N. & Arleo, A. A continuous attractor network model without recurrent excitation: maintenance and integration in the head direction cell system. J. Comput. Neurosci. 18, 205–227 (2005). 38. Kang, K., Shelley, M. & Sompolinsky, H. Mexican hats and pinwheels in visual cortex. Proc. Natl. Acad. Sci. USA 100, 2848–2853 (2003). 39. Ben-Yishai, R., Bar-Or, R.L. & Sompolinsky, H. Theory of orientation tuning in visual cortex. Proc. Natl. Acad. Sci. USA 92, 3844–3848 (1995). 40. Compte, A., Brunel, N., Goldman-Rakic, P.S. & Wang, X.J. Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model. Cereb. Cortex 10, 910–923 (2000). 41. Kloosterman, F., Van Haeften, T., Witter, M.P. & Lopes Da Silva, F.H. Electrophysiological characterization of interlaminar entorhinal connections: an essential link for re-entrance in the hippocampal-entorhinal system. Eur. J. Neurosci. 18, 3037–3052 (2003). 42. Van Haeften, T., Baks-Te-Bulte, L., Goede, P.H., Wouterlood, F.G. & Witter, M.P. Morphological and numerical analysis of synaptic interactions between neurons in deep and superficial layers of the entorhinal cortex of the rat. Hippocampus 13, 943–952 (2003). 43. Morgan, R.J., Santhakumar, V. & Soltesz, I. Modeling the dentate gyrus. Prog. Brain Res. 163, 639–658 (2007). 44. Acsady, L., Kamondi, A., Sik, A., Freund, T. & Buzsaki, G. GABAergic cells are the major postsynaptic targets of mossy fibers in the rat hippocampus. J. Neurosci. 18, 3386–3403 (1998). 45. Danglot, L., Triller, A. & Marty, S. The development of hippocampal interneurons in rodents. Hippocampus 16, 1032–1060 (2006). 46. Berger, T.K., Perin, R., Silberberg, G. & Markram, H. Frequency-dependent disynaptic inhibition in the pyramidal network: a ubiquitous pathway in the developing rat neocortex. J. Physiol. (Lond.) 587, 5411–5425 (2009).

VOLUME 16 | NUMBER 3 | MARCH 2013  nature NEUROSCIENCE

ONLINE METHODS

npg

© 2013 Nature America, Inc. All rights reserved.

Slice preparation. We report recordings obtained in 138 female Long Evans rats between the ages of P10 and P82 (113 rats for recordings in normal conditions, 16 rats for recordings with pharmacological manipulations and 9 for optogenetic stimulation; see below). We recorded from 247 slices in total, 62 of which we discarded because of poor recordings or recordings outside layer II of the MEC. The experimental protocols followed the European Communities Council Directive and were approved by the National Animal Research Authority of Norway. Rats older than P28 were both anesthetized with isoflurane and perfused through the heart with a small volume of ice-cold ACSF cutting solution containing 110 mM choline chloride, 25 mM NaHCO3, 25 mM d-glucose, 11.6 mM sodium ascorbate, 7 mM MgCl2, 3.1 mM sodium pyruvate, 2.5 mM KCl, 1.25 mM NaH2PO4 and 0.5 mM CaCl2 aerated with 95% O2/5% CO2 before decapitation; younger rats were not intracardially perfused. After decapitation, the brain was quickly dissected and 400-µm-thick horizontal or sagittal slices of the medial entorhinal cortex were cut with a vibrating slicer and incubated in oxygenated ACSF containing 127 mM NaCl, 25 mM NaHCO3, 25 mM d-glucose, 2.5 mM KCl, 1 mM MgCl2, 2 mM CaCl2 and 1.25 mM NaH2PO4 for 45 min at 37 °C. Thereafter the slices were oxygenated at room temperature until use. Horizontal slices were cut at an ~10 degree angle to maximize the number of MEC slices cut with preserved descending axonal projections from layer II. Multiple whole-cell recording. Multiple whole-cell recordings were made as described previously, using a standard intracellular solution containing 120 mM K-gluconate, 10 mM KCl, 10 mM HEPES, 10 mM K-phosphocreatine, 4 mM MgATP and 0.4 mM GTP, pH adjusted to 7.3 with KOH; 270–285 mOsm. Biocytin (3–5 mg/ml; Sigma) was included in the pipette for later anatomical verification of cell location and morphology. All recordings were done at 34 °C in ACSF with 1.5 mM MgSO4 and 1.6 mM CaCl2. Layer II stellate cells in the MEC were first visualized using infrared differential interference contrast microscopy. Groups of stellate cells deeper than 100 µm were visually identified, and four neighboring cells were targeted for whole-cell patch. The separation of recording electrodes ranged from 19.3 µm to 215.2 µm with an average maximum within a cluster of 91.9 µm ± 10.1 µm. All cells were first maintained in the ‘on cell’ configuration until all contacts had achieved a +1 gigaohm resistance. The entire cluster was then opened to whole-cell configuration. After the whole-cell configuration was established in all cells, recorded responses to steps of current injection allowed us to electrophysiologically classify each cell as a putative stellate cell. Potential stellate cells were targeted by selecting layer II cells with large multipolar soma. Stellate cells were differentiated from interneurons and nonstellate regular spiking cells by their characteristic responses with trains of action potentials in response to current step depolarizations at resting potential, a characteristic ‘sag’ potential in response to subthreshold depolarizing or hyperpolarizing current pulses, low input resistance and a substantial difference between the first and second interspike interval. Pyramidal layer II cells instead fired regular trains with varying degrees of adaptation; they lack the typical sag seen in stellate cells, have a high input resistance, and no clear difference between the first and second interspike interval. Subsequent morphological analysis was used to corroborate the classification of stellate cells10–12,14. We occasionally recorded from putative interneurons that we grouped into two primary electrophysiological types, fast spiking or LTS on the basis of examination of electrophysiological properties including but not limited to the presence or absence of frequency adaptation observed in LTS or fast-spiking neurons, respectively, and differences in action potential halfwidth23,24. Main electrophysiological parameters used for celltyping are summarized in Supplementary Table 1. Connectivity was tested by stimulating each individual cell at 5-s intervals by a ten-spike train, at frequencies of 10 Hz, 20 Hz, 40 Hz and 70 Hz, while the membrane potential was recorded simultaneously in the other cells. This cycle of stimulation was repeated up to 30 times with 5 s in-between, and the resulting traces were averaged to identify any direct and/or indirect connections. We used the first excitatory or inhibitory postsynaptic potential evoked from a presynaptic 10-Hz train to derive amplitude and peak time of each synapse. Between each cycle of stimulation, 120 s of spontaneous membrane potential was recorded from all three or four cells. Recordings were made using Axon Multiclamp amplifiers sampling at intervals of 200 µs or 100 µs (5 kHz or 10 kHz; depending on the intended length of total recording to maximize memory limits during acquisition), digitized using an ITC-1600 A/D

doi:10.1038/nn.3310

interface in combination with custom acquisition software based in Igor Pro. This same software was also used to control whole-cell current injection (both timing and levels). Series resistance was compensated to a maximum bridge balance value of 20 megaohms. Recordings in which series resistance exceeded this value were not included in any signal averaging, and clusters with only two cells were not included in this study. Data analysis was done offline using Igor and MatLab (Mathworks) as described previously12. The MEC is an active network, and individual stellate cells in layer II show membrane resonance and spontaneous oscillations in vitro12. We used signal averaging to reliably detect even small direct synaptic connections between stellate cells. We measured the noise level in single sweeps to be 0.8 mV ± 0.5 mV in adult stellate cells. Therefore to increase signal-to-noise ratio, we used average signals generated from a minimum of 20 sweeps to screen for connectivity. As the four presynaptic stimulation frequencies used in these experiments were timed identically at the first action potential in each train, these sweeps were pooled and averaged giving a grand mean from which the noise level for each cell could be extracted. This signal/sweep averaging consistently produced a mean signal to noise ratio of greater than 10:1 (as defined by mean amplitude poststimulus over a period of 10 ms divided by the standard deviation of the baseline membrane potential before the stimulus onset) for all direct connections reported. From our data on signal-to-noise ratios in this data set, we estimate that the amplitude detection limit of our recordings with regard to direct synaptic connectivity was ~0.3 mV in a single sweep and as low as 0.04-mV in a mean of 20 sweeps. Each possible connection was ultimately scrutinized by a human observer twice, once during and immediately after the recording, and subsequently during formal analysis. The connections described in this paper were reliable (higher than 80% release probability for every presynaptic action potential) connections. Specifically for the comparative analysis of identified connections, we manually quantified and report the mean amplitude of the first excitatory postsynaptic potential in response to the 10-Hz presynaptic train. Surgery for viral experiments. Long Evans rats at the age of P22 or P23 were anesthetized with isoflurane and mounted onto a stereotactic frame (Kopf). A small opening was made in the skull exposing the brain surface over the dorsal hippocampus. The stereotactic coordinates were based on a stereotaxic atlas of the rat brain47 adjusted proportionally to the weight of the rat. The anteroposterior coordinates were measured relative to the posterior transverse sinus. Retrogradely transported rAAV (titer 1–2 × 10−12) was injected via a 10 µl NanoFil syringe using a UMP3 pump (WPI). A volume of 1 µl was deposited in each of three dorsoventral positions separated by 0.2 mm. The injection was completed over 30 min, and the virus was allowed to diffuse for an additional 10 min before we retracted the syringe. The rats were sutured and post-surgical pain was treated with a dose of Rimadyl 1:10 dilution; 100 µl intraperitoneally). Rats survived for 5 to 6 weeks before we obtained slices for recording. Viral vector construct and packaging. We opted to use a Chimeric rAAV2/1 to express the optogenetic effector in layer II cells of MEC. We used a light-gated cation channel ChR2(H134R), a gain-of-function photocurrent-enhanced mutant of ChR2 (ref. 48) from the unicellular green alga Chlamydomonas reinhardtii, here referred to as ChR2. Codon-optimized sequence encoding ChR2 fused to mCherry49 was generated by a PCR-based amplification and cloning. To generate a trafficking-improved mCherry-tagged ChR2, we first, through multiple rounds of PCR and ligation, inserted mCherry between a sequence encoding a 20-amino-acid trafficking signal DYKDHDGDYKDHDIDYKDDDDK and an endoplasmic reticulum (ER) exporting motif FCYENEV, both of which are from the inward-rectifier potassium ion channel Kir2.1 (refs. 26,50). We next arranged the construct to encode ChR2(H134R) at the N terminus of the trafficking signal in frame with mCherry sequence by one more round of PCR. This resulted in the creation of codon-optimized sequence encoding trafficking-enhanced and mCherry-tagged ChR2(H134R) for effective photostimulation and convenient visualization of virally infected brain slices. The coding region in the viral vector construct was verified by double-stranded DNA sequencing to make sure that no shifted open reading frame or no undesired point mutation was introduced by multiple rounds of PCR. The proviral plasmid used for packaging rAAV was flanked by AAV serotype 2 inverted terminal repeats (ITRs). The proviral backbone also contained a woodchuck hepatitis virus posttranscriptional regulatory

nature NEUROSCIENCE

npg

© 2013 Nature America, Inc. All rights reserved.

element (WPRE) and a bovine growth hormone (BGH) polyadenylation signal for enhancing transgene transcription and expression. Transcriptional regulation of pAAV-ChR2-mCherry was driven under a calcium/calmodulin-dependent protein kinase II α (Camk2a) promoter. The chimeric rAAV2/1 was prepared by co-transfection of human embryonic kidney cell line HEK293 by standard calcium phosphate transfection along with an adenoviral helper plasmid pHelper from Stratagene’s AAV Helper-Free System. The viral titer was determined by real-time quantitative PCR using StepOnePlus Real-Time PCR Systems (Applied Biosystems) and TaqMan Universal Master Mix. All titer-adjusted viruses were diluted and matched to 1.0–2 × 1012 viral genomic particles per milliliter in phosphate buffered saline (PBS). Optogenetic stimulation of layer II projection cells. Injections of rAAV into the dorsal hippocampus targeting the dentate gyrus and CA3 resulted in detectable retrogradely labeled neurons in the superficial layers of MEC (Supplementary Fig. 3b). In horizontal slices (see above) cells in layer II were patched and held in current clamp without current injection. Cells expressing ChR2 showed direct responses with onset and offset times correlated with the light pulse length (50 ms), and could thus be easily separated from non-expressing cells by the kinetics of the observed response. Retrograde expression of channelrhodopsin was assessed post-hoc by using immunohistochemistry to visualize the mCherry signal in the slice preparation. Because of the anterograde transport component of rAAV, we primarily used the lack of visible mCherry in the MEC to verify that no afferent hippocampal fibers had been labeled. In case mCherry-positive fibers were observed during the recording, all slices from that particular rat were discarded. All patched neurons were intracellularly filled with biocytin (see above). For photostimulation, we used a custom laser-control system (473 nm; Rapp Opto) delivered through a water immersion objective (×40; 0.8 numerical aperture (NA); Olympus). Slices were stimulated with a beam diameter of ~5–10 µm (scattering in the tissue was not taken into account). Photostimuli consisted of light pulses with 50-ms durations with 250-ms intervals and power of ~650 µW at the specimen. Pulses were spaced by 20 µm, covering a grid 100 µm or 200 µm square (45 or 70 pulses, respectively). Individual stimulation points were treated as separate events, and the responses from each unique location in the grid were averaged over 10–30 sweeps to produce a normalized average response for each point. To objectively quantify the results of the optogenetics experiments, we used a signal to noise limit of 10, so responses from stimulation points in the grid that were below 10 s.d. of the variance of the membrane potential were omitted from the analysis. Rejected responses were always below 0.1 mV in amplitude. For all other responses, mean peak times and amplitudes were determined for each cell and pooled according to cell type. Immunohistochemistry and post-hoc imaging. Immediately after recording session the slices were placed in 4% PFA and incubated overnight. After postfixing, the sections were permeabilized by washing 7 times with 0.1 M PB containing 1% Triton X-100 (PBT-1%), blocked for 3 h with PBT-1% with 5% NGS and then incubated for 72 h with monoclonal anti-mCherry (Clontech UN3287, 1:500 in PBT-1%, 5% NGS) in 4 °C. Slices were then washed 3 times in PB, and incubated for 12 h with the mixture of Alexa Fluor 546–conjugated anti-mouse secondary antibody (Invitrogen All003, 1:350) and Alexa Fluor 488–conjugated streptavidin (Invitrogen Sll223, 1:350) in PBT-1%, 5% NGS in 4 °C. After washing the sections were incubated with the NeuroTrace deep red fluorescent Nissl stain (Invitrogen, 1:200) for 30 min in PB. After staining, the slices were washed in PB and dehydrated in increasing ethanol concentration (30%, 50%, 70%, 90% and twice in 100% ethanol for 10 min each), then in 1:1 mixture of ethanol and methylsalicylate and finally cleared and mounted in methylsalicylate.

nature NEUROSCIENCE

Sections were imaged with a Zeiss Meta 510 confocal microscope (Carl Zeiss). Alexa Fluor 488 was excited by Ar laser (λ = 488 nm; emission filter, bandpass 505–550 nm), Alexa Fluor 568 was excited by HeNe laser (λ = 568 nm; emission filter, bandpass 595–615 nm), NeuroTrace Nissl stain was excited by HeNe laser (λ = 633 nm; emission filter, longpass 655 nm, dichroic mirror 405/488/561/ 633 nm with shortpass filter 725 nm). First, the location of biocytin-filled cells in layer II of MEC was confirmed using air Plan Apo ×20, 0.8 NA objective lens. Then, a detailed scan of the AF488 (biocytin-filled cells), AF568 (AAV-expressing cells) and NeuroTrace Nissl stain was taken. We used ×40, 1.30 NA oil DIC objective lens at resolution of 1,024 × 1,024, 8-bit sampling, and z increment of 0.5 µm. Images were processed using Fiji software. A three-dimensional reconstruction was done using Amira 5.1 software. Computational model. We extend on the previously described attractor model3, where the activity level of neuron i, denoted by si, is determined according to t

  dsi + si = g  ∑Wij s j + I + a vt cos (q t − qi )   j  dt  +

(1)

where (…)+ is the threshold-linear function, g is the gain, τ is the neuronal time constant, I the constant external input, α the velocity modulation, vt the velocity at time t, θt the head direction at time t, θi the preferred direction of neuron i and, finally, Wij the strength of connection from neuron j to neuron i is described by parameters W0 and R:

 Wij = W0 heaviside  R − 

2

( xi − x j − l cosqi ) + ( yi − y j − l sinqi ) 2

 

(2)

where R is the radial extent of the connectivity, and W0 is a negative number representing the strength of the inhibitory interaction between connected neurons. Here xi = 1 … N and yi = 1 … N represent the position of neuron i in a twodimensional N × N neuronal sheet with periodic boundary conditions and l is a spatial offset providing asymmetry to the connectivity. The directional preference is patterned in 2 × 2 tiles of neurons with preferences kπ/2, k = 0, 1, 2, 3. The activity pattern was initialized with randomly setting 1% of the neuron population at si = 1 and the rest as silent (si = 0). The time-varying velocity and head directions were linearly interpolated at 1-ms time bins from recorded rat positions1. The simulation then consisted of integrating equation (1) with a 1-ms time step over a contiguous 10-min path taken from the experiments with varying parameters of the connectivity W0 and R as shown in Figure 3. In all simulations we used I = 3, α = 0.3, l = 2, g = 1, τ = 10 ms, N = 128. We simulated neuron spikes using a Poisson process at ∆t = 10-ms time bins with spike probability pi(t) = asi(t)∆t, with a = 11.8. The value a is calculated from normalization of the average si(t) of 50 random neurons over time from a simulation with W0 = –0.02 and R = 15 to produce an average spike rate of 2.5 Hz.

47. Paxinos, G. & Watson, C. The Rat Brain In Stereotaxic Coordinates (Academic Press, San Diego, 1998). 48. Boyden, E.S., Zhang, F., Bamberg, E., Nagel, G. & Deisseroth, K. Millisecondtimescale, genetically targeted optical control of neural activity. Nat. Neurosci. 8, 1263–1268 (2005). 49. Shaner, N.C. et al. Improved monomeric red, orange and yellow fluorescent proteins derived from Discosoma sp. red fluorescent protein. Nat. Biotechnol. 22, 1567–1572 (2004). 50. Gradinaru, V. et al. Molecular and cellular approaches for diversifying and extending optogenetics. Cell 141, 154–165 (2010).

doi:10.1038/nn.3310