Quantitative properties of a feedback circuit predict frequency-dependent pattern separation

Feedback inhibitory motifs are thought to be important for pattern separation across species. How feedback circuits may implement pattern separation of biologically plausible, temporally structured input in mammals is, however, poorly understood. We have quantitatively determined key properties of netfeedback inhibition in the mouse dentate gyrus, a region critically involved in pattern separation. Feedback inhibition is recruited steeply with a low dynamic range (0% to 4% of active GCs), and with a non-uniform spatial profile. Additionally, net feedback inhibition shows frequency-dependent facilitation, driven by strongly facilitating mossy fiber inputs. Computational analyses show a significant contribution of the feedback circuit to pattern separation of theta modulated inputs, even within individual theta cycles. Moreover, pattern separation was selectively boosted at gamma frequencies, in particular for highly similar inputs. This effect was highly robust, suggesting that frequency-dependent pattern separation is a key feature of the feedback inhibitory microcircuit.


Introduction
Efficiently discriminating similar percepts or experiences is a central capability common to invertebrate and vertebrate species. In general terms, such discrimination can be achieved by decreasing the overlap in representations by neuronal ensembles between input and output patterns, a process termed 'pattern separation' [1][2][3][4] . Numerous studies have proposed cellular and circuit mechanisms that could support this computation. For instance, sparse divergent inputs and specialized intrinsic properties are thought to generally contribute 1,5,6 .
We reasoned that to assess if feedback inhibition is indeed suitable for the purpose of pattern separation in the DG, it is necessary to determine how efficiently the activity of sparse GC ensembles recruits net inhibition, i.e. the dynamic range and gain of the feedback inhibitory microcircuit. It is furthermore necessary to quantify the spatial and temporal properties of the elicited inhibition, in order to investigate its impact on biologically plausible, temporally structured input. For instance, the DG shows prominent theta oscillations during exploration and distinctive slow-gamma activity during associative memory encoding [41][42][43][44] .
Importantly, both sparsity and temporal oscillations will critically affect a proposed pattern separation function. For instance, feedback inhibition must by definition occur with a delay, a property frequently abstracted away in computational models 45,46 , but potentially critical during oscillatory activity.
Here, we combine patch-clamp recordings, multiphoton imaging and optogenetics to provide a first quantitative, empirical description of the net input-output function of a feedback inhibitory microcircuit. This includes the spatiotemporal organization of net feedback inhibition elicited by a spatially restricted GC population and the net short term dynamics within the feedback microcircuit. Finally, we integrate our data into a biophysically realistic computational model and probe its ability to perform pattern separation. We find a moderate feedback inhibition mediated pattern separation effect during theta modulated input but a substantial separation, particularly of highly similar inputs, during gamma oscillations.

Input-output relation of the feedback inhibitory microcircuit
We reasoned that the ultimately relevant parameter for the putative pattern separation effect of feedback inhibition is the net inhibition arriving at GCs. We therefore treated the feedback microcircuit as a black-box striving to relate only its net input (fraction of GCs active) to its net output (feedback inhibition in GCs). To this end we antidromically recruited feedback inhibitory circuits, while simultaneously recording GC inhibition and population activity (see schematic in Fig. 1A). Electrical stimulation reliably evoked graded IPSCs in dentate GCs, that increased with stimulation strength (maximal amplitude of 324.1±99.2 pA, n=8; Fig. 1B).
In order to relate the measured IPSCs to the fraction of GCs activated by a given stimulation strength, we used population Ca 2+ imaging with multibeam two-photon microscopy (Fig. 1A, see Methods). After bolus-loading GCs with the Ca 2+ indicator OGB-1-AM (see Methods), antidromic stimulation caused action potential associated Ca 2+ elevations in a subset of GCs ( Fig. 1D, transients indicated by *). Before quantifying population activity, we verified the reliable detection of single action potentials under our conditions using simultaneous cellattached recordings from dentate GCs (Fig. 1E, Supplementary Fig. 1). Briefly, cells were differentiated into true responders or non-responders on the basis of cell-attached recordings ( Fig. 1E, F; responders green, non-responders grey). A histogram of the peak Δ F/F of non-responders upon a single stimulus was fitted with a Gaussian (Fig. 1F right, grey dots, grey bars, n=33) and the threshold set to the quadruple standard deviation of this fit (0.94% Δ F/F, dashed line in Fig. 1F). We estimated that this threshold would yield approximately equal numbers of false positives and false negatives (Supplementary Fig. 1F). We additionally controlled for possible errors through variable dye loading and the overestimation of the active cell-fraction through accidental detection of adjacent active cells (Supplementary Fig.   1G, H, respectively).
Orientation of hippocampal slices may be a critical feature in determining the extent of feedback connectivity. We therefore systematically assessed the magnitude of feedback activation of GCs using imaging in slices obtained from different dorso-ventral levels of the hippocampus (see inset of Fig. 1 G). We found a clear connectivity maximum within horizontal slices obtained at a distance of ~1750 µm from the temporal pole (Fig. 1G,H) 49 . In these and all following experiments we therefore used exclusively slices obtained at 1400-2100 µm from the temporal pole, where the orientation of hippocampal slices matches the orientation of mossy fibers.
Combining the IPSC recordings with population Ca 2+ imaging allowed us to probe the inputoutput relationship of the feedback inhibitory microcircuit. Inhibition was recorded in a GC within or immediately adjacent to the imaging field, and stimulation strength was increased gradually (Fig. 1I). The IPSC saturated at 300µA stimulation strength, where the mean active cell fraction was 2.2±0.7% and the mean IPSC reached 93.1±3.4% of the maximal IPSC ( Fig. 1I, J, n=20 for imaging, n=8 for IPSCs including 6 slices with both). Plotting the IPSC magnitude vs. the cell fraction showed that the magnitude of feedback inhibition rises steeply, reaching ~90% with less than 3% of GCs active and complete saturation at 3.7±1.7% of cells (Fig. 1K). Simultaneous cell attached recording and calcium imaging to measure the action potential induced somatic calcium transient amplitude. F) Scatterplot and histogram of the calcium fluorescence peaks of cells which either did (green) or did not (grey) fire action potentials, as assessed by cell attached recordings. G) Illustration of the anatomical localization of maximum connectivity plane slices. Short black dashed lines indicate depth at which the slice plane is aligned to the dorsal brain surface. H) Antidromic stimulation elicited Ca 2+ transients primarily at this depth (black bars). I) Normalized IPSC amplitude and activated cell fraction both increase with increasing stimulation strength (example from a single slice). J) Summary of all slices K) Summary data plotted to show the increase of inhibition as a function of the active GC fraction.

Optogenetic quantification of the recruitment of feedback inhibition
These experiments yielded a first quantitative estimate of the input-output relation of the feedback-inhibitory microcircuit in the DG. We then decided to verify these findings using an alternative method, which allowed spatially controlled and less synchronous GC activation.
Mice selectively expressing ChR2 (H134R) -eYFP in GCs were created by crossing Prox1-Cre mice with Ai32-mice ( Fig. 2A, see methods). Focal optogenetic stimulation was achieved through a laser coupled into the microscope light path, yielding an 8 µm stimulation spot (Fig.   2B). Brief (20 ms, 473 nm) light pulses within the molecular layer approximately 40 µm from the dentate GC layer elicited reliable IPSCs in GCs (Fig. 2C). Increasing the light intensity evoked larger IPSCs that showed clear saturation (Fig. 2C, D, Power=7 AU corresponding to 1.7 mW, see Methods). Inhibition was completely blocked by combined application of 40µM CNQX and 50µM D-APV (Fig. 2E, n=9), confirming that it is recruited via glutamatergic collaterals. The maximal IPSC amplitude obtained optically vs. electrically in experiments in which both stimulations were performed were similar (Fig. 2F, paired t-test, P(df=3, t=1.568)=.2148, n=4), indicating that similar maximal inhibition is recruited despite the differences in the activated GC population (distributed vs local; synchronous vs. less synchronous).
In order to relate feedback inhibition to the underlying GC activity levels, we performed systematic cell attached recordings of GCs in the same slices in which inhibition was recorded (~2 cells per slice, Supplementary Fig. 2). Briefly, we recorded the spatial firing probability distribution in response to focal stimulation for each laser power. We then estimated the mean firing probability of GCs throughout the section, which is equivalent to the expected active GC fraction, by incorporating measurements of the light intensity distribution throughout the slice (Fig. 2G, black). We additionally estimated an upper and lower bound by assuming either no decay of firing probability with slice depth or isometric decay (Fig. 2G, grey dashed lines). Combining the input-output relations of IPSCs (Fig. 2D) and the estimated active cell fraction (Fig. 2G) again revealed that inhibition is recruited steeply, saturating when approximately 4% of GC are active (Fig. 2H). Importantly, the resulting recruitment function of inhibition is unlikely to be affected by voltage escape errors ( Supplementary Fig. 3). This is because such errors scale linearly with synaptic conductance and will thus affect the absolute but not the relative amplitude of the somatically measured IPSC. Next, we compared the focal light activation with global activation via a light fiber positioned over the surface of the slice (with powers up to 50 mW, Fig. 2I). Under global stimulation all cells tested fired APs with 100% reliability and independent of location, even though focal stimulation in direct proximity to the cell led to much lower maximal firing probabilities (Fig. 2I, 29, n=10). This implies that additional activation of remote GCs cannot recruit interneurons beyond those activated by local GC populations. Thus the recruitment of feedback inhibition in the DG is steep, with a dynamic range tuned to sparse populations of GCs (up to 3-4% of cells).

Lower limit of feedback recruitment
Previous work has addressed the lower limit of the recruitment of feedback inhibition in various cortical areas [50][51][52][53] . The authors report the ability of even a single principal cell to activate feedback inhibitory interneurons and a supralinear increase of inhibition as the second and third principal cells are co-activated 50 . Given our findings so far we asked whether single GCs might also suffice to elicit feedback inhibition in the DG. To this end we performed dual patch clamp recordings and elicited short trains of ten action potentials at 100 Hz in one cell while monitoring inhibition in the other (Supplementary Fig. 4, n=15).
However, in contrast to the neocortex 50,52 and area CA3 51 , we did not find single GCinduced feedback inhibition in any of these experiments, consistent with a recent large scale study reporting that such connections are extremely sparse (0.124%) 22 .

Fig. 2, Recruitment of feedback inhibition assessed optogenetically. A)
EYFP fluorescence in dentate GCs of Prox1/ChR2(H134R)-EYFP transgenic mice. The field of view for rapid focal optogenetic stimulation is indicated by a blue square. A typical stimulation site approx. 40 µm from the GC layer (two short black lines) is indicated by a blue dot. B) Schematic of the microscope setup used to achieve spatially controlled illumination. The inset shows the intensity profile of the laser spot. C) Top left, reconstruction of an Alexa594 filled GC. Left, illustration of optical stimulation. Right, IPSCs following 20ms light pulses at increasing laser power (P = 1 to 7 AU). Each trace represents an average of 3 trials. D) Summary of IPSC amplitudes from cells in the superior blade (n=7 cells). IPSC amplitudes were normalized to the maximum amplitude within each cell. E) Optogenetically elicited IPSCs are abolished by glutamatergic blockers (40µM CNQX + 50µM D-APV, n=9). F) Left, Schematic of focal optical and electrical stimulation. Dashed lines indicate cuts to sever CA3 backprojections. Middle, Example traces for IPSCs following electrical or focal optogenetic stimulation. Right, maximal IPSC amplitude for the two stimulation paradigms (361±37 vs. 410±13 pA for electrical and optogenetic stimulation respectively, paired t-test, p=0.28, n=4) G) The optogenetically activated GC fraction responsible for recruiting the IPSC at the respective laser powers was estimated from systematic cell attached recordings (see Fig. S1 for details). The best estimate (black) incorporates measurements of the 3D light intensity profile in the acute slice. Upper and lower bounds were estimated by assuming no firing probability decay with increasing slice depth (upper grey dashed line) or isometric firing probability decay (lower grey

Spatial distribution of feedback inhibition
Recent evidence indicates that inhibition by individual PV + fast spiking hilar border interneurons is non-uniformly distributed over space, with decreasing connectivity and inhibition at greater distances from the interneuron 22,54 . To test whether feedback inhibition by the entire ensemble of feedback inhibitory interneurons also displays a spatial gradient we activated cell populations at 100 µm intervals along the GC layer while recording inhibition in individual GCs (Fig. 3A). Spatial profiles were recorded for increasing laser powers in cells in the superior as well as inferior blade of the DG (Fig. 3B, C respectively; n=8 cells for each blade). IPSC amplitudes across locations and powers were normalized to the maximal IPSC amplitude in each respective cell. This maximal amplitude did not differ between cells in different blades (366±40 vs 390±84 pA for superior and inferior blades respectively; t-test, P(df=14, t=0.258)=.0686). Next, we investigated the spatial organization of feedback inhibition at stimulation powers at which inhibition had saturated (Fig. 3D, E). In all GCs tested, the inhibition was greatest when stimulating in the direct vicinity of the recorded cell.
Activating cells at increasing distances led to monotonically decreasing IPSC amplitudes for both blades. Importantly, the term distance here refers to the functional distance along the GC layer and not to Euclidean distance. However, inhibition was observed even at the most remote stimulation sites, indicating that even the most remote cells from the contralateral blade can contribute to the activation of feedback inhibition in a given GC. In order to statistically compare the relation of local versus remote inhibition between blades we defined a remote location in the contralateral blade at 800 µm from the recorded cell (measured along the GC layer and equidistant in all slices; Fig. 3D, E; grey lines) and compared it to the local IPSC (black lines). Remote inhibition was significantly smaller than local inhibition while no difference between blades or significant interaction was observed ( Next, we investigated whether there are differences in the steepness of recruitment of local versus remote inhibition between blades (black and grey, respectively; Fig. 3G, H). To this end, we calculated the active cell fraction which produces half-maximal inhibition during local or remote stimulation for each individual slice. Comparison of the recruitment between the four groups revealed no differences between blades (Fig. 3I, two-way RM ANOVA; Distance: interaction, respectively). Furthermore, both latency and jitter decreased as larger populations were activated. IPSCs were also significantly slower in remote versus local inhibition. IPSC rise time was slightly shorter in the larger local IPSCs but did not correlate with the active cell fraction (Fig. 3L: P=.010, =.633 and =.388 for distance, cell fraction and interaction, respectively). Similarly, decay times were significantly shorter in local versus remote inhibition while they progressively increased with increasing stimulation power ( Fig.   3M; P<.001, <.001 and =.124 for distance, cell fraction and interaction, respectively). These data demonstrate that remote inhibition shows greater delay, greater jitter and slower kinetics than local inhibition. 1 5

Short term dynamics in the feedback inhibitory microcircuit
Different connections within the feedback inhibitory microcircuit have been shown to variably facilitate or depress during trains of activity 21 (Supplementary Table 1). This makes it difficult to predict the net effect on the short term dynamics of GC feedback inhibition. We therefore characterized the frequency-dependence of net feedback inhibition using antidromic electrical stimulation as described above ( Fig. 4A-C Fig. 5).
Because this unusual degree of facilitation may be important in allowing sparse activity of GCs to recruit significant inhibition over time, we further examined the underlying circuit mechanisms. Interestingly, previous literature on the DG feedback microcircuit almost exclusively reports short term depression of dentate interneuron inputs to GCs (Supplementary Table 1, blue rows), rendering our finding of pronounced facilitation at the circuit level even more striking. We therefore measured feedback excitation of hilar neurons by stimulating mossy fiber axons as described above (Fig. 4D-L). Mossy cells and interneurons were classified according to their morpho-functional properties 31 (Fig. 4D, E, G, H, J, K). Cell classification was confirmed using unbiased k-means clustering (Fig. 4K). We found that feedback excitation of hilar cells displayed marked facilitation, which was similar for both INs and MCs (Fig. 4F P<.001 for all frequencies). These data demonstrate a pronounced frequency dependent net facilitation of the feedback inhibitory microcircuit, which is supported by strongly facilitating mossy fiber inputs to hilar cells.

8
Quantitative properties of the feedback circuit predict frequency dependent pattern separation Together, these data indicate that the dentate feedback circuit is able to deliver strong, spatially graded inhibition with a high gain and the ability for temporal integration.  (Fig. 5A, B). BCs, HCs and MCs comprise the feedback inhibitory circuit and BCs receive direct PP input thereby additionally mediating feedforward inhibition 32 . We then adapted the spatial extent of the target pools of BC and HC outputs to produce local and global inhibition respectively, reproducing the experimentally determined spatial tuning of net feedback inhibition (Fig. 5C).
We further adjusted synaptic decay time constants and weights in order to reproduce the measured PSCs of hilar neurons and GCs and the empirical recruitment curves (Fig. 5D,   Supplementary Fig. 6). Finally, we incorporated facilitation of the experimentally determined magnitude into feedback excitatory mossy-fiber outputs, leading to GC IPSC facilitation in the experimentally observed range (Fig. 5E, Supplementary Fig. 6B). Together, these minimal adaptations resulted in a model with remarkably similar properties to our experimental findings ( Fig. C-E). We therefore concluded the tuning phase of the model and proceeded to an in silico pattern separation experiment without further changes to the model.  patterns in which 24 of 400 PP afferents were activated (Fig. 6A, Supplementary Fig. 6) and compared pairs of such patterns ranging from no overlap (two separate sets of afferents) to complete overlap (identical trains in the same 24 afferents in both patterns). Each model network was run with 25 input patterns leading to a total of 325 comparisons (data points in To quantify the isolated effects of feedback and feedforward inhibition we computed the difference in R out between the respective conditions for each individual comparison (i.e. data point in Fig. 6C). For instance, the individual comparison shown in Fig. 6A, will lead to a single R out value in the network with MF inputs to interneurons (full model), which is subtracted from the corresponding R out value in the same network without this input (no FB).
This procedure isolates the effect of interest (ΔR out ) for each individual comparison, controlling for other sources of variability. A single pattern separation measure was then obtained as before, as the area under the curve of bin-wise means of these Δ R out values ( Fig. 6E, inset). We found a significant effect of both inhibitory motif and frequency domain It has recently been emphasized, that the assessment of pattern separation can depend critically on the pattern similarity measure used 8,58 . Therefore we tested the robustness of this result for two alternative similarity measures, namely normalized dot product (NDP, also known as cosine similarity) and pattern overlap (# of coactive/ # of totally active cells; Supplementary Fig. 7). The frequency dependence of feedback inhibition mediated pattern separation, especially for highly similar inputs, proved robust for all three similarity measures (see figure legend for statistics).

Effect of spatial tuning and facilitation of net feedback inhibition
Next we investigated the specific effects of two interesting empirical findings of the present study, 1) the spatial tuning and 2) the facilitation of the feedback circuit (Supplementary Fig.   8). To this end we undertook two targeted, minimal manipulations of the full tuned network.
To probe the effect of spatially graded inhibition, we redistributed BC output synapses to a global target pool (the whole GC population), leading to spatially uniform inhibition (global FB; Supplementary Fig. 8B; 8E, left). To probe the effect of facilitation, we removed facilitation from mossy fiber outputs (Supplementary Fig. 8C; E, right). We isolated the effects of these manipulations by pairwise comparison to the corresponding full tuned networks as described above (Supplementary Fig. 8F-I). The results showed a small but significant contribution of facilitation (~20% of the isolated FB effect for both frequency paradigms), but not spatial tuning to pattern separation (Supplementary Fig. 8G, left; Wilcoxon signed rank test for deviation from 0, n=7, Bonferroni corrected P-values: P=.031 and P=1 respectively for 10Hz; P=.031 and P=1 respectively for 30Hz). We noted that while spatial tuning did not affect mean pattern separation, it appeared to reduce its variability (CoV) for a given input similarity (Supplementary Fig. 8G, right; Wilcoxon signed rank test for deviation from 0, n=7, Bonferroni corrected P-values: P=.031 and P=.750 for tuning and facilitation respectively at 10Hz; P=0.438 and P=1 respectively at 30Hz).

Frequency dependent pattern separation is robust over analysis scales
So far, all pattern separation analyses were conducted on the population rate vectors during a 600 ms time window. However, many neural computations are likely to occur on shorter timescales, such as within individual theta cycles (~100 ms) 19,59 . Indeed, the time window in which correlation is recorded can nontrivially affect the resulting correlation, depending on the timing of spikes within it 58 . We therefore computed the networks pattern separation ability within 100 ms time windows, revealing i) the pattern separation ability within such short timescales and ii) the temporal evolution of pattern separation throughout a 600 ms stimulus presentation (Fig. 6F, G). We find that pattern separation occurs even within a single theta cycle, including a contribution of feedback inhibition in both frequency paradigms (mean  Fig. 8). As above, the effect was predominantly driven by the separation of highly similar input patterns (isolated FB effect, R in >0.5; two-way RM ANOVA on last timebin, P<.001, =.010 and <.001 for R in -bin, frequency and interaction respectively, Sidak's posttest on differences between frequency paradigms for each input similarity: P=1 for R in <0.6 and P=.032 to P<.001 for R in = 0.6 to 0.9). These results were robust when analysis time windows were decreased even further (33 ms, Supplementary Fig. 9). This 33 ms resolved analysis additionally reveals that the pattern separation effect, particularly of feedback inhibition, ramps up within a 100 ms window, becoming effective only at the end of a theta cycle (Supplementary Fig. 9B).
Next we asked if the frequency dependence of feedback inhibitory pattern separation was sensitive to variations of the inhibitory decay time constants and if there might be an interaction between these decay time constants and the frequency range at which pattern separation is most effective (Supplementary Fig. 10). Remarkably, we found the differential effect between 10 & 30 Hz to be highly robust across a range of different decay timeconstants (0.5x to 5x the experimentally matched decay, Supplementary Fig. 10A-C, Table   2). Furthermore, the selective enhancement of feedback inhibitory pattern separation of highly similar inputs was robust over the entire gamma range (up to 100Hz, Supplementary   Fig. 10D, E).
Finally, we tested if our main results were robust to alterations in the relative strengths of feedforward vs. feedback inhibition. Since, our model is closely constrained with respect to the recruitment and functional properties of the feedback circuit, we are confident about the resulting computational inferences concerning this circuit. However, the model does not allow strong inferences about the relative roles of feedback and feedforward inhibition, and it is thus necessary to probe if extremely powerful feedforward inhibition might occlude the effects described here. We therefore selectively enhanced the feedforward inhibitory circuit in our model by increasing the PP to BC circuit 2x (Supplementary Fig. 11). This robustly increased the feedforward inhibitory contribution to pattern separation above that of feedback inhibition (Supplementary Fig. 11B). However, it did not affect the frequency dependence of the feedback inhibitory effect. Indeed, for highly similar input patterns, the feedback inhibitory effect was so prominently enhanced during gamma input, as to again dominate the feedforward inhibitory effect (Supplementary Fig. 11C).
Together these results suggest that frequency dependence is a key feature of the feedback inhibitory microcircuits and predict that feedback inhibition selectively boosts the separation of highly similar input patterns during gamma oscillations.

Discussion
Across brain regions and species, inhibitory circuits contribute critically to regulating the sparsity and overlap of neural representations 1,10,11,20 . In most, if not all brain regions, feedback inhibition is viewed as important in these capabilities, by directly mediating competition between active cell ensembles 46,60,61 . In the mammalian DG, feedback inhibition is implemented by an intricate network of interneurons that is capable of delivering spatiotemporally defined inhibition to the principal cell population. How net feedback inhibition is functionally organized in mammals, and how it may contribute to pattern separation of biologically relevant, temporally structured input patterns is, however, poorly understood.

Quantitative physiological properties of DG feedback inhibition
We have therefore quantitatively described the recruitment of net feedback inhibition by defined GC population sizes in space and time in the hippocampal DG, a structure in which sparse activity and inhibition are thought to critically contribute to the function of pattern separation [14][15][16]20,62 . The proposed role of the feedback inhibitory circuit depends critically on its dynamic range, i.e. the relation between the number of active principal cells and the resulting feedback inhibition. This property of the feedback circuit is determined by complex, mainly hilar cellular connectivity patterns 21,22 (Supplementary Table 1). While delving into detailed cell-cell connectivities is clearly important, such studies do not allow the quantitative determination of the gain and dynamic range of net feedback inhibition 50,52 . Using two complementary experimental approaches, we found that net feedback inhibition is steeply recruited by sparse populations of GCs (<4%). Accordingly, the gain and sensitivity of the circuit are well suited to strongly modulate feedback inhibition within the range of GC activity reported in vivo 42,63 . Additionally, we have described in detail the temporal and spatial distribution of inhibition delivered by feedback circuits in the DG.

Frequency-dependent effects of feedback inhibition on pattern separation
How do the properties of feedback circuits influence the pattern separation capability of the dentate gyrus? To address this question we adapted an established biophysically realistic computational model of the DG circuitry 56,57 . We first carefully constrained the model to match the spatial and temporal properties of net feedback inhibition as assessed in our physiological data. We then fixed all model parameters, and proceeded to probe the ability of this circuit to perform pattern separation on temporally complex oscillatory inputs. The major, highly robust, result of this computational study was that the impact of feedback inhibition on pattern separation is frequency-dependent. Specifically, we find that the separation of input patterns during gamma oscillations >30 Hz is powerfully and selectively enhanced by the feedback circuit. Remarkably, this mechanism was particularly efficient for very similar input patterns. Such an effect has not been discovered in earlier modeling studies, because most models have discretized time, calculating the pre-inhibition population activity, the resulting inhibition, and the inhibition-corrected population activity in a single time step, sometimes assuming an average corrected population rate within this time step 46,64,65 . Thus, they do not capture temporal features of feedback circuits. On the other hand, a number of spike based, temporally resolved models have considered only temporally unstructured (Poisson) inputs 57,[66][67][68] . We suggest that the precise spatiotemporal organization of the feedback circuit, together with the temporal structure of DG inputs is a crucial determinant of pattern separation. Indeed, the DG and its inputs have a strong, behaviorally relevant, temporal structure 42,69,70 . Novelty experience can induce increased gamma and beta range activity 41,71,72 , and explorative activity with rearing is also associated with increased gamma oscillations 73 . A recent model has addressed how fast, rhythmic gamma-frequency feedback inhibition may implement a type of 'k-winners-take-all' operation, a basic computational component of pattern separation models 60 , though this model relies on faster synaptic timescales than we observed in our compound IPSCs. Perhaps most interestingly, the occurrence of oscillations in the slow-gamma range has recently been reported to be causally related to associative memory formation 41,44 , a process thought to require pattern separation. Consistent with this finding, Hsiao et al. 43 report DG driven gamma entrainment of CA3, the presumed primary storage location of associative memories. Together, this suggests that the dentate pattern separator may be optimized to rapidly detect subtle degrees of difference within the environment in gamma-dominated exploratory brain states, a capability likely to support successful memory encoding of novel environmental features, and potentially aiding in rapid discrimination during recall.
Importantly, the frequency-dependent pattern separation was driven by the feedback circuit, and was highly robust to various alterations to the model. For instance, increasing the level of feedforward inhibition enhanced its contribution to pattern separation, but did not affect feedback inhibitory frequency-dependence. This effect was also robust when varying the decay time constants of the inhibitory synaptic conductances, the time windows of analysis, or the similarity measure employed. Together this suggests that frequency-dependent pattern separation is a key property of the local inhibitory feedback circuit. Importantly, this does not preclude that additional, long range projections may add further complexity 74 . Also note that in addition to the instantaneous pattern separation mechanisms investigated here, potentially complementary mechanisms at much longer time scales have been proposed involving ongoing neurogenesis [75][76][77][78][79][80] .

Spatiotemporal organization of inhibition and pattern separation
The model also allowed us to examine the impact of the spatiotemporal organization of inhibition on pattern separation. Facilitation of feedback circuits produced a small but robust enhancement of pattern separation, while spatial tuning of feedback inhibition did not. The facilitation of feedback inhibition is a remarkable feature of the DG, which we to our knowledge have described for the first time. It is in marked contrast to area CA1, where somatically measured feedback inhibition shows strong depression 55,81 and is particularly surprising given the prevalence of depression in the literature on pairwise connections (Supplementary Table 1). Our physiological and modeling data suggest that the strong facilitation of the mossy fiber input to the feedback circuit is the principal mediator of this net 0 facilitation. The effect of facilitation on pattern separation is intuitive, since this allows the feedback circuit to integrate GC activity over time, and convert it to inhibition.
In our model, spatial tuning of feedback inhibition had no effects on pattern separation. This may derive from the fact that PP inputs were spatially broad and random 82,83 . In general, the effect of localized inhibition could be more relevant if synchronously activated populations of GCs are locally clustered 84 . For instance, GCs in the inferior and superior blades of the DG are known to be differentially active 85,86 . Accordingly, localized inhibition might be important for independent processing between the two blades. An alternative function of spatially graded inhibition has been proposed by 54 , who suggest that it is more effective in promoting synchronous gamma oscillations. Accordingly, spatial tuning may play a role in creating the oscillatory dynamics, found here to critically impact the feedback inhibitory pattern separation performance.
Together, this study provides the first comprehensive, quantitative description of the spatiotemporal properties of the DG feedback inhibitory microcircuit, and predicts that these properties will selectively enhance the separation of highly similar input patterns during learning-related gamma oscillations. This mechanism may be relevant for understanding disease states in which there is a coincidence of dentate gyrus-centered pathology with abnormal oscillatory activity, and memory and pattern separation deficits (i.e. temporal lobe epilepsy, Alzheimer's disease, schizophrenia) 14,87-89 . 1 Horizontal 350 µm thick sections were cut with a vibratome (VT1200 S, Leica, Wetzlar, Germany, 300 µm sections for hilar recordings). To obtain maximum-connectivity-plane slices the brain was glued to its dorsal surface (compare Bischofberger et al., 2006). The slicing depth at which the temporal pole of the hippocampus first became visible was noted (depth = 0 µm). From here the first four sections were discarded (up to a depth of 1400 µm).

Animals and Slice Preparation
The following two to three sections were secured such that one further section before the beginning of the dorsal hippocampus (approximately 2400 µm) could be discarded. Slices Light Intensity distribution: To measure the light intensity distribution throughout a slice the setup was modified to image the slice from below while the laser beam was focused to its surface ( Fig. S1C-F). This was achieved by focusing a surgical Microscope with 36x magnification (M695, Leica Microsystems, Wetzlar, Germany) to the lower slice surface.
Images were taken with a CCD camera (Nikon D60). Acute sections of 100, 150, 200, 250, 300 and 350 µm thickness were cut from Prox1-ChR-eYPF mice as described above. The laser was focused to the surface of the slice in the molecular layer and an image was taken at every laser power (P = 1 to 7 AU). The stage was moved for every image to avoid bleaching or phototoxicity. Linear profiles of the resulting isometric light distribution were measured in several directions and averaged to obtain an x profile per section. The x-profiles of slices of different thickness were then stacked to obtain the xz-profile. Values below 100 µm depth were obtained through fitting a Gaussian function in x-direction at 100 µm depth and an exponential function in z-direction. Complete three-dimensional intensity profiles of three different locations of two slices within the dentate molecular layer were averaged.

Calculation of the Optogenetically Activated Cell Fraction: To assess the active fraction of
GCs, approximately two GCs were recorded in cell-attached mode in each slice in which an IPSC was recorded. Illumination spots were placed along the GC layer at 100 µm intervals (Fig. S1) AP probability and slope, respectively). Since no difference was observed a single firing probability distribution as a function of the distance along the GC layer (x -distance) was calculated for each power (Fig. S1B, n = 14 sections, 7 per blade). However, the firing probability of cells in the vicinity of the illumination spot is likely to increase not only as a function of the laser power and spread at the surface, but also of the penetration depth of the light cone. In order to calculate the firing probabilities throughout the slice, the firing probability distribution at the surface was related to the measured light intensity distribution throughout the slice (Fig. S1C-F; see above) utilizing a 'virtual distance' measure. Since cells were measured at random distances from the molecular layer border, the light intensity distribution, like the firing probabilities were collapsed to two dimensions, x-distance along the GC layer and z-distance with increasing slice depth. The 'virtual distance' was calculated as the mean distance from a given slice-surface pixel to all other pixels of the light intensity distribution weighted by the intensity within those pixels (Fig. S1G). Assigning the firing probabilities of pixels at the slice surface to their respective virtual distance yields the firing probability distribution as a function of virtual distance, which was well approximated by a gaussian fit (Fig. S1H). This fit was used to also calculate the firing probabilities of pixels/cells deeper in the slice using the measured light intensity distribution as input. The active cell fraction then corresponds simply to the mean firing probability throughout the slice. This calculation is independent of the size and number of GC and was performed for every power individually. We noted that a large fraction of the recorded spikes occurred with larger latency than the typical IPSC following the beginning of the 20 ms stimulation pulse (Fig. S1I, example from a single slice). Since only APs preceding the IPSC can participate in its recruitment, we calculated the fraction of total spikes which preceded mean IPSC latency for every power, and fitted the resulting relation with an exponential function (Fig. S1J). All active cell fractions were corrected by this factor (Fig. S1J, bottom). Note that this does not take account of the disynaptic delay between mossy fiber output and GC input, thereby potentially slightly overestimating the true recruiting population. For comparison, the active cell fraction was also computed with alternative assumptions about the decay of the firing probability with increasing slice depth. If no firing probability decay with increasing depth is assumed, the active cell fraction throughout the slice is given simply by the average of the measured firing probabilities at the slice surface (Fig. S1K, upper grey dashed line).
Alternatively, the firing probability decay with depth was assumed to be identical to the measured decay along the slice surface (isometric firing probability distribution; Fig. S1K, lower grey dashed line). In this case, Gaussian functions were fit to the probability distributions at the surface and these Gaussian functions were then assumed to extend also in the z-dimension. The active GC fraction was then calculated by numerical integration under the two dimensional Gaussian (with the bounds from 0 to 350 µm in z and -888 to 888 µm in x, which corresponds to the mean GC layer length) normalized to the same area with a uniform firing probability of one. The best estimate of the active GC fraction, incorporating light intensity measurements (Fig. S1K, black line), was within these upper and lower bound estimates.
Comparison of Focal and Global Activation:, To globally activate the GC population a multimode light fiber (BF-22, Thorlabs, New Jersey, USA) coupled to a 473 nm laser (Omicron Phoxx, Rodgau-Dudenhofen, Germany) was placed above the slice surface, nonspecifically illuminating the entire hippocampus. Analogous to focal stimulations, the activated cell fraction was calculated as the firing probability of individual cells following 20 ms pulses. Here no spatial normalization is necessary since cells were sampled from random locations with respect to the light fiber. Firing probabilities for the focal stimulation in these sections was calculated as the simple average of all stimulation locations.
Spatial distribution of feedback inhibition: The same stimulation paradigm which was used to assess cell activation was used to assess the spatial distribution of feedback inhibition. For individual cells, IPSCs at each location and power were averaged. The entire profile was normalized to the largest measured IPSC of that cell, independent of the power and stimulation location at which it occurred. For analysis, all IPSC profiles were spatially aligned to the recorded cells. The mean distance to apex ± one standard deviation was 356 ± 163 µm and 322 ± 97 µm for cells from the superior and inferior blade respectively (n = 8 cells in each blade). In order to test whether there were any distinct effects of the apex, such as a steep decay of inhibition, which would be masked by alignment to the recorded cells, we also aligned the profiles to the apex (not shown). However, no such effects were visible. To analyze the saturated IPSC profiles, normalized IPSC amplitudes from P=5 to 7 were averaged for each cell. In order to analyze the effects of local versus remote stimulation for each blade a distance was chosen such that each remote location was still within the DG but in the other blade (800 µm from the recorded cell). Normalized IPSCs of the three locations surrounding the recorded cell or this remote location were averaged within each power to obtain the IPSC amplitudes for further analysis. The cell fraction required for the activation of a half-maximal IPSC in each section was assessed for each cell by linear interpolation between the measured values. Since no differences were found between superior and inferior inhibition, recordings of both blades were pooled to analyze the kinetic properties of  We first tuned the original model to capture our experimentally determined properties in the most parsimonious way. During tuning we also updated some model properties to better reflect current data and our experimental paradigm in an individual DG lamella: We introduced a T-type Ca 2+ channel mechanism into MCs to more realistically reflect the depolarizing envelope at the onset of a positive current step observed in real MCs.
Furthermore, while the original model placed the perforant path input at the distal dendrite of GCs, we moved all perforant path synapses to the middle compartment of the dendrite. In order to be able to capture the results of convergent and divergent synaptic inputs in sufficient resolution to produce the empirically observed activity gradations, we up-scaled cell numbers by a factor of four. To model space, we assumed all cell types to be spread out on a 2mm DG lamella. Since MCs project to GCs primarily outside the lamellar plane, we removed the MC to GC connection. To allow patterned PP input we adapted PP input specifications from 57 .
We then proceeded in a first phase of model adjustment, and adapted several parameters to reproduce our in vitro findings regarding spatial and temporal feedback inhibition (Supplementary Table 2). To model frequency dependent facilitation on mossy fiber outputs, we implemented a simple frequency dependent synapse model (tmgsyn) 98 , and matched the facilitation time constant as well as the decay time constants of individual PSCs to our experimental observations. As in the original model, each cell gives rise to a fixed number of synaptic connections which are spatially restricted to a target pool of adjacent cells. We tuned the size and spatial extent of this target pool to reproduce our spatial data.
To provide local inhibition we implemented a 'local' interneuron type (BC), whose inputs and outputs were spatially restricted to an ~600µm area (as described by 54 ). To provide global inhibition we implemented a second class of inhibitory interneurons (HC) whose inputs and outputs connect to GCs independent of space. This simple formulation allowed us to reproduce the recruitment curves seen for local, remote and global GC activation paradigms.
To achieve plausible activity levels, we further adapted synaptic weights similar to 57  To compute full pattern separation effects (Fig. 6D) we calculated the mean R out within R in bins of 0.1 and measured the area to the unity line (computed as the mean of the binwise R in -R out differences). To compute isolated pattern separation effects of specific manipulations we subtracted the respective R out values with and without the manipulation, thereby obtaining a Δ R out value for each individual R in . We then again computed the bin-wise mean and quantified the area under the curve, yielding the mean Δ R out analogous to the full effects.
Note, that the sequence of averaging and subtracting is irrelevant, and was inverted only to match the figure panels. Data are displayed as mean ± SEM for each R in bin (Fig. 6E, G).  . The black bar indicates the mean IPSC latency ± standard deviation at that power. Bottom, The fraction of action potentials that precede the mean IPSC for each power was well approximated by an exponential fit (black line). Light stimulation in (I) and (J) was from 0 to 20 ms. K) black, Estimated active cell fraction in the slice calculated from the light intensity profiles in (D) and the virtual firing probability distributions in (H) and corrected by the fraction of APs occurring after the mean IPSC (J). The estimated active cell fraction is identical to the mean firing probability throughout the slice. For comparison the cell fraction was also estimated assuming no firing probability decay with increasing depth (upper grey dashed line) or assuming isometric decay (lower grey dashed line).

Fig. S3, Error in somatic IPSC measurements with increasing inhibitory conductance.
A simple ball and stick model was used to estimate the impact of voltage escape errors for dendritic IPSCs (soma diameter 20um; dendrite diameter and length 3 µm and 200 µm, respectively). To estimate the maximum errors the inhibitory synapse was placed at a distal site (180 µm from the soma) and inhibitory currents were measured using a single electrode voltage-clamp at the soma. A) Illustration of the model and an attenuated somatic IPSC measurement. B, Peak amplitudes of the measured IPSC over a range of distal synaptic conductances (measured peak IPSC), as well as the actual peak IPSC in the absence of voltage errors, calculated from the transfer and input impedances of the model. C) Error in somatically measured peak IPSC as percentage of the actual peak IPSC (I syn, % error) at a given synaptic conductance. Errors in estimating synaptic inhibitory currents were linear. D, Illustration of corrected and uncorrected recruitment curves of absolute IPSC amplitudes for varying degrees of voltage error (using data from the recruitment curve in Fig.  2H). Note that due to the linearity of voltage escape errors, absolute IPSC amplitudes change, but the saturation point does not. E) This is illustrated by the normalized recruitment curves, as shown throughout the manuscript (see i.e. Fig. 2H). Note that normalized curves are practically unaffected by voltage escape errors.

Fig. S7, Robustness over different Similarity Metrics,
To test if the main finding of frequency dependent pattern separation, particularly for highly similar inputs, depended on the similarity metric used, the original data was reanalyzed with two alternative similarity metrics. As in the main figures data points in bar graphs represent the 7 independent network seeds. For each network (seed) we ran sets of patterns for the full model, a network without feedback inhibition (no FB) and a model with no inhibition (no inh.). A) Examples of the theta (10Hz) and gamma (30Hz) modulated perforant path (PP) input spike patterns. B) Mean number of APs per active PP afferent. C) Fraction of active GCs across the different conditions. D) Mean number of APs per active GC across conditions. E) Pearson's correlation coefficient R (as in Fig. 6) left: exemplary scatterplots of pattern separation effects. right: bargraphs of the mean pattern separation effect over the full input similarity range (0<Rin1) or only highly similar input patterns (0.9<R<1). Full effects measure the mean pattern separation effect for each network condition: full model, no feedback (no FB) and no inhibition (no inh.). Isolated effects measure the pattern separation contribution of individual circuit motifs: feedback inhibition (FB) and feedforward inhibition (FF). F) same as (E) but using normalized dot product (NDP) as similarity metric for input and output comparisons. G) Same as (E) but using population overlap as similarity metric. Overlap is defined as the number of cells active in both patterns (logical and) divided by the number of cells active in either pattern (logical or). The full effects were tested with 2x3 ANOVAs followed by Sidak's postests for differences between conditions. Isolated effects were tested with 2x2 ANOVAs followed by Tukey posttests for differences between frequencies. Asterisks indicate significance in posttests given significant overall effects (*P<.05,**P<0.01,***P<0.001).

Fig. S8
, Isolated pattern separation effects of spatial tuning and MF facilitation, Effects of isolated manipulations were computed for the DG model as in Fig 6. A) Schematic of the full tuned network and the resulting spatial profile of inhibition (as in Fig. 5). B) Schematic of the global network (with unrestricted BC target pool) and the resulting spatial profile of inhibition. C) Schematic of the non-facilitating network. D) Isolated mean feedback effects of the global, tuned and non-facilitating models. Two-way RM ANOVA showed: p<0.001, =0.020, =0.402 for frequency, condition and interaction respectively with * indicating significance in Dunnett's posttest against the full tuned effect. p=0.742 and 0.020 for global and non-facilitating, respectively at 10Hz; p=0.650 and 0.001 for global and non-facilitating, respectively at 30Hz. E) Exemplary pattern separation plots of theta modulated inputs when spatial tuning (left) or MF facilitation (right) was removed. F) Isolated pattern separation effects of the given manipulation for theta (blue) or gamma (green) modulated inputs as a function of input similarity. G) Isolated effect of the given manipulation on mean  . 33ms time-resolved pattern separation effects of the full model, isolated feedback (FB) or feedforward (FF) inhibition for theta modulated input (10Hz). All analyses were performed as above but with rate vector correlations computed for 33 ms time windows (instead of 100 ms or 600 ms, as in Fig.6). The bottom insets show Δ R out as a function of input similarity for the first and last three time windows. The bottom right insets show the evolution of the mean Δ R out over time. B) Same as (A) but for slow gamma (30Hz) modulated inputs. Data represent mean ± SEM of n=7 random network seeds.

Fig. S10, Robustness over various IPSC decay time-constants and over the full gamma range, A-C)
To test if the frequency dependence of feedback inhibitory pattern separation remained robust for different IPSC decay time constants we probed a range of altered time constants (our experimentally matched time constant x0.5, x1, x2 and x5) while maintaining total inhibitory conductance in the network constant by complementary adjustment of IPSC amplitude. As we expected a potential interaction between IPSC decay and modulation frequency, we probed model runs for each factor with 10Hz, 30Hz and 60Hz modulation. The isolated feedback inhibitory effects were computed and impacts of decay and frequency were examined with 4x3 ANOVAs followed by Tukey posttests for differences between frequencies. Asterisks indicate significance in posttests given significant overall effects (*P<.05,**P<0.01,***P<0.001).A) Illustration of modified IPSC time-courses. B) Mean pattern separation effect of isolated feedback inhibition over the full input similarity range (0<R in <1). C) Same as (B) but only for highly similar input patterns. Analyses in A-C were performed on 7 new network seeds with simulation and analysis otherwise identical to Fig.6. D-E) To probe the robustness of frequency dependent feedback inhibitory pattern separation over an even larger range of frequency modulation we next simulated the effects over a range from 10 to 100Hz in 5Hz steps. To provide computational tractability we performed only 8 runs per frequency (instead of 24 runs as in all other simulations) leading to fewer pattern comparisons, and somewhat noisier readouts. For the majority of frequencies, no input comparisons with R>0.9 occurred so we defined (0.8<R in <1) as highly similar input patterns, potentially leading to a slight underestimation of our effects. B) The resulting full pattern separation effects (left) and isolated feedback (FB) and feedforward (FF) effects (right) as mean over all input similarities. C) Same as (B) but only for highly similar input patters. Full effects were tested with 2x3 ANOVAs followed by Sidak's postests for differences between conditions. Isolated effects were tested with 2x2 ANOVAs followed by Tukey posttests for differences between frequencies. Asterisks indicate significance in posttests given significant overall effects (*P<.05,**P<0.01,***P<0.001). Table 1, Literature review for DG circuit short term dynamics, Studies reporting short term dynamics within the DG circuit were reviewed with a main focus on facilitation or depression of synaptic connections defined by pre and postsynaptic cell types. Note the abundance of depressing synapses (quantitative descriptions of depression blue). Also note the complexity of direct connections between Interneurons (lower third of the table).