Optogenetic activation of parvalbumin and somatostatin interneurons selectively restores theta-nested gamma oscillations and oscillation-induced spike timing-dependent long-term potentiation impaired by amyloid β oligomers

Background Abnormal accumulation of amyloid β1–42 oligomers (AβO1–42), a hallmark of Alzheimer’s disease, impairs hippocampal theta-nested gamma oscillations and long-term potentiation (LTP) that are believed to underlie learning and memory. Parvalbumin-positive (PV) and somatostatin-positive (SST) interneurons are critically involved in theta-nested gamma oscillogenesis and LTP induction. However, how AβO1–42 affects PV and SST interneuron circuits is unclear. Through optogenetic manipulation of PV and SST interneurons and computational modeling of the hippocampal neural circuits, we dissected the contributions of PV and SST interneuron circuit dysfunctions on AβO1–42-induced impairments of hippocampal theta-nested gamma oscillations and oscillation-induced LTP. Results Targeted whole-cell patch-clamp recordings and optogenetic manipulations of PV and SST interneurons during in vivo-like, optogenetically induced theta-nested gamma oscillations in vitro revealed that AβO1–42 causes synapse-specific dysfunction in PV and SST interneurons. AβO1–42 selectively disrupted CA1 pyramidal cells (PC)-to-PV interneuron and PV-to-PC synapses to impair theta-nested gamma oscillogenesis. In contrast, while having no effect on PC-to-SST or SST-to-PC synapses, AβO1–42 selectively disrupted SST interneuron-mediated disinhibition to CA1 PC to impair theta-nested gamma oscillation-induced spike timing-dependent LTP (tLTP). Such AβO1–42-induced impairments of gamma oscillogenesis and oscillation-induced tLTP were fully restored by optogenetic activation of PV and SST interneurons, respectively, further supporting synapse-specific dysfunctions in PV and SST interneurons. Finally, computational modeling of hippocampal neural circuits including CA1 PC, PV, and SST interneurons confirmed the experimental observations and further revealed distinct functional roles of PV and SST interneurons in theta-nested gamma oscillations and tLTP induction. Conclusions Our results reveal that AβO1–42 causes synapse-specific dysfunctions in PV and SST interneurons and that optogenetic modulations of these interneurons present potential therapeutic targets for restoring hippocampal network oscillations and synaptic plasticity impairments in Alzheimer’s disease.


Background
Alzheimer's disease is a neurodegenerative disease characterized by a progressive decline in cognitive and mnemonic functions [1,2]. Abnormal accumulation of amyloid β 1-42 oligomers (AβO  ) is a hallmark of Alzheimer's disease [1][2][3][4] and AβO 1-42 -induced impairments of gamma oscillations [5][6][7][8][9][10] and long-term synaptic plasticity [3,4,11,12] are believed to contribute to the memory deficits observed in Alzheimer's disease. In particular, hippocampal theta-nested gamma oscillations observed during spatial memory processing [13][14][15] have been shown to support the induction of long-term potentiation (LTP) [16][17][18][19]. Thus, AβO 1-42 may impair memory by disrupting GABAergic inhibitory circuits, which underlie oscillogenesis [14,[20][21][22][23][24][25]. Indeed, there is now increasing experimental evidence showing that AβO 1-42 reduces GABA synaptic transmission [26][27][28], causes excitation/inhibition imbalances [9,12,27,28], and even diminishes the number of GABAergic synapses/ terminals onto pyramidal cells [29]. Also, parvalbuminpositive (PV) and somatostatin-positive (SST) interneurons, the two major subtypes of hippocampal interneurons [30] that are critically involved in oscillogenesis [24,25,31], are reported to be impaired in mouse models of Alzheimer's disease [5-8, 27, 32, 33]. PV interneurons' spike amplitude, membrane potential, and firing rate are decreased [5,7] while SST interneurons' structural plasticity and axonal sprouting are impaired in Alzheimer's disease mouse models [27,32]. Surprisingly, the neural circuit mechanism by which dysfunction of PV and SST interneurons contributes to AβO 1-42 -induced impairment of oscillogenesis and LTP is unclear. If uncovered, it could help researchers find novel therapeutic targets for Alzheimer's disease. Recently, optogenetic stimulation of channelrhodopsin-2 (ChR2)-expressing hippocampal CA1 pyramidal cells (PCs) at theta-frequency was shown to induce in vivo-like theta-nested gamma oscillations in the CA1 area of acute hippocampal slices in vitro [34]. This provides a novel model in which to perform targeted whole-cell patch-clamp recordings and selective optogenetic modulation of PV or SST interneuron activity during optogenetically induced theta-nested gamma oscillations and LTP induction. We have used this approach to investigate neural circuit dysfunction in hippocampal slices treated with AβO 1-42 . We found that AβO 1-42 caused selective dysfunctions in reciprocal synapses between PC and PV interneurons, which impaired gamma oscillations and desynchronized the spike phases of PC and PV interneurons relative to gamma oscillations. While AβO 1-42 had no effect on PC-to-SST or SST-to-PC synapses, it specifically disrupted SST interneuron-mediated disinhibition to PC resulting in the impairment of theta-nested gamma oscillation-induced spike timing-dependent LTP (tLTP). Selective optogenetic activation of PV interneurons restored gamma oscillations while selective optogenetic activation of SST interneurons restored theta-nested gamma oscillation-induced tLTP. These results demonstrate that AβO 1-42 -induced synapse-specific dysfunctions in PV and SST interneurons may explain the concomitant impairments of hippocampal gamma oscillations and synaptic plasticity in Alzheimer's disease. Moreover, using a computational network model of PC, PV, and SST interneurons, we further demonstrate that PV and SST interneurons targeting different compartments of the CA1 PC have distinct functional roles in oscillogenesis and tLTP induction.
Since the spiking of hippocampal CA1 interneurons is in large part driven by CA1 PC's excitatory inputs to the interneurons [35], we investigated whether the treatment of AβO 1-42 affected CA1 PC's excitatory inputs to PV and SST interneurons. We performed voltage-clamp recordings in eYFP-expressing PV or SST interneurons during blue light-induced theta-nested gamma oscillations in DMSO-treated and AβO 1-42 -treated slices (Fig. 2f). We found that the amplitude of CA1 PC's excitatory postsynaptic current (EPSC) to PV, but not SST interneuron, was significantly decreased in AβO 1-42treated slices (Fig. 2f, g), while EPSC frequency was unaffected ( Fig. 2h). To characterize the AβO 1-42 -induced synaptic dysfunctions at CA1 PC-to-PV synapse and CA1 PC-to-SST synapse, we first investigated how AβO 1-42 affected the stimulus-response (S-R) curve of these synapses by electrically stimulating the axons of CA1 PC in the alveus of CA1 at different intensities (10,50,100,150,200, and 300 μA) and recording the corresponding PC-evoked EPSCs in eYFP-expressing PV interneuron (Fig. 2i, j) or in eYFP-expressing SST interneuron (Fig. 2m, n). Analysis of the S-R curve revealed that, for each stimulation intensity, AβO 1-42 significantly increased the amplitudes of PC-evoked EPSCs in PV (Fig. 2j, right), but not those in SST interneurons (Fig. 2n, right). These results indicate that AβO 1-42 increases the initial neurotransmitter release probability of PC-to-PV synapse. To investigate the synaptic locus of EPSC changes, we stimulated the CA1 PC axons using a halfmaximal stimulus (based on the S-R curve in Fig. 2j, n, right; 115-210 μA) and an inter-stimulus interval of 20 ms (50 Hz, 10 stimulus) for the analysis of paired-pulse ratio (PPR), total charge, and short-term plasticity of PC-evoked EPSCs in PV (Fig. 2k, l) and SST interneurons (Fig. 2o, p). Paired-pulse facilitation of PC-evoked EPSCs in PV interneurons, as observed in DMSOtreated slices, was converted to paired-pulse depression in AβO 1-42 -treated slices (Fig. 2k, right). The total charge of PC-evoked EPSCs in PV (Fig. 2l, left), analyzed by the area of the PC-evoked EPSCs in Fig. 2k (left), was significantly decreased by AβO 1-42 . Furthermore, short-term facilitation of PC-evoked EPSCs in PV interneurons, as observed in DMSO-treated slices, was converted to short-term depression in AβO 1-42 -treated slices (Fig. 2l, right). These results indicate that AβO  causes presynaptic depression at PC-to-PV synapse, which led to a decrease in CA1 PC-evoked excitatory synaptic inputs onto PV interneurons. Thus, AβO 1-42induced gamma oscillation impairment may be due to dysfunction of presynaptic mechanisms at PC-to-PV synapses. In contrast, AβO 1-42 had no effect on PPR, total charge, or short-term plasticity of CA1 PC-evoked EPSCs in SST interneurons (Fig. 2o, p). Therefore, AβO 1-42 causes presynaptic dysfunctions at CA1 PC-tointerneuron synapses which is target-specific.
AβO 1-42 causes synapse-specific dysfunction of PV-to-PC synapses, but not SST-to-PC synapses Blue light-induced theta-nested gamma oscillations are most likely generated by reciprocal synapses between PCs and interneurons [34], according to the pyramidalinterneuron network gamma (PING) model [14,21,23].
In accordance with this model, voltage-clamp recordings in CA1 PCs during blue light-induced gamma oscillations (Fig. 3a, top) revealed that inhibitory postsynaptic currents (IPSCs) occurred at gamma-frequencies in DMSO-treated slices (Fig. 3a, bottom, black trace, Fig. 3f), which were GABA A receptor-mediated as they were completely blocked by GABAzine (SR95531, 5 μM, Fig. 3a, bottom, gray trace; Fig. 3f, g). AβO 1-42 significantly decreased the amplitude of these IPSCs (Fig. 3a, bottom, red trace; Fig. 3g), potentially accounting for the observed reduction in peak power of gamma in AβO 1-42 -treated slices (Fig. 1h, i). To determine which interneuron subtype was responsible for the reduction of IPSC in PC in AβO 1-42 -treated slices, we optogenetically inactivated either PV or SST interneuron during gamma oscillations by co-injecting two different AAV viruses to CA1, one carrying ChR2 and the other carrying enhanced Arch (AAV-DIO-Arch-eYFP) in order to express ChR2 in PCs and Arch in either PV (Fig. 3b) or SST interneurons (Fig. 3c). During theta-nested gamma oscillations in DMSO-treated slices, inactivation of Archexpressing PV interneurons (Fig. 3d) and Archexpressing SST interneurons (Fig. 3e) by yellow light (590 nm) had no effect on IPSC frequency in CA1 PCs (Fig. 3f). However, IPSC amplitude in CA1 PC was significantly reduced only by inactivation of Archexpressing PV interneurons in the DMSO-treated slices (Fig. 3g), which was similar to that recorded in AβO 1-42treated slices (Fig. 3a, red trace, Fig. 3g). Inactivation of Arch-expressing PV interneurons in AβO 1-42 -treated and DMSO-treated slices had the same effect in reducing IPSC amplitudes (Fig. 3d, red trace, Fig. 3g) while inactivation of Arch-expressing SST interneurons in AβO 1-42 -treated slices significantly reduced the IPSC amplitude compared to that in the DMSO-treated slices (Fig. 3e, red traces, Fig. 3g). Moreover, the peak power of gamma oscillations was also decreased only by inactivation of Arch-expressing PV interneuron (Additional file 5: Figure S5) while inactivation of Archexpressing SST interneuron had no effect on gamma oscillations (Additional file 6: Figure S6), indicating AβO 1-42 -induced reduction of IPSC in CA1 PCs as well as the reduction of peak power of gamma oscillations may be due to dysfunction of PV interneurons. To rule out the possibility of yellow light having any direct effects on the reduction of gamma oscillation power via activation of ChR2 in CA1 PCs, we recorded synaptic currents in ChR2-expressing PCs and LFPs in the nearby tissue during sinusoidal (5 Hz) blue (470 nm), green (565 nm), and yellow light (590 nm) stimulation (Additional file 7: Figure S7a-c). We found that green light ChR2-PC with Arch-expressing SST interneurons (Arch-SST) in SST-Cre mice (c). d, e Same as a but with inactivation of Arch-PV (d) and Arch-SST (e) using tonic yellow light (590 nm) stimulation in DMSO-and AβO 1-42 -treated slice. f, g Mean IPSC frequency (f) and mean IPSC amplitude (g) in each condition. h Micro-injection of AAV-DIO-ChR2-mCherry into CA1 area of PV-Cre mice (top) and fluorescence image (bottom) of ChR2-expressing PV interneurons (ChR2-PV). i, j Experimental schematic. Whole-cell voltage-clamp recordings in CA1 PC (i) to record PV-evoked IPSCs (j, left) and stimulusresponse (S-R) curve (j, right) in response to different light stimulation powers. k, l Representative PV-evoked IPSCs in CA1 PC in response to light stimulation (10 pulses, 50 Hz, k, left), paired-pulse ratio (PPR) of the 2nd IPSC/1st IPSC (k, right), total IPSC charge (l, left), and IPSCs normalized to the 1st IPSC to show short-term plasticity (l, right) in DMSO-treated (filled circles) and AβO 1-42 -treated slices (empty circles). m-q Same as h-l but by activating ChR2-expressing SST interneurons (ChR2-SST) for SST-evoked IPSCs in SST-Cre mice. Unpaired Student's t test (k, l (left), p, q (left), **p < 0.01, *p < 0.05, ns: not significant), one-way (f, g, ### p < 0.001, ## p < 0.01, ns: not significant) and two-way ANOVA with post hoc Tukey's test (j, l (right), o, q (right), ### p < 0.001, # p < 0.05, ns: not significant). Data are represented as mean ± SEM induced synaptic currents and gamma oscillations in the LFP while yellow light stimulation had no effect on either of them (Additional file 7: Figure S7d, e). In order to characterize the AβO 1-42 -induced synaptic dysfunctions at PV-to-CA1 PC synapse and SST-to-CA1 PC synapse, we expressed ChR2 in PV (Fig. 3h) and SST interneurons (Fig. 3m) and analyzed the S-R curve of these synapses by optically stimulating ChR2-expressing PV interneurons (Fig. 3i) and ChR2-expressing SST interneurons (Fig. 3n) at different light powers (5, 10, 25, 50, 75, 100% of maximal light power (15 mW)) and recorded the corresponding PV-evoked IPSCs in PC (Fig. 3j) and SST-evoked IPSCs in PC (Fig. 3o). Analysis of the S-R curve revealed that, for each stimulation intensity, AβO 1-42 significantly increased the amplitudes of PV-evoked IPSCs in PC (Fig. 3j), but not SST-evoked IPSCs in PC (Fig. 3o), suggesting that AβO 1-42 increases the initial neurotransmitter release probability of PV-to-PC synapse. To investigate the synaptic locus of IPSC changes, we optically stimulated ChR2-expressing PV interneurons and ChR2-expressing SST interneurons using a half-maximal light power (based on S-R curve in Fig. 3j, o; 3.75-9 mW) and an inter-stimulus interval of 20 ms (50 Hz, 10 stimulus) for the analysis of PPR, total charge, and short-term plasticity of PV-evoked IPSCs (Fig. 3k, l) and SST-evoked IPSCs (Fig. 3p, q). AβO 1-42 significantly enhanced the paired-pulse depression in PVevoked IPSCs in PC, as observed in DMSO-treated slice (Fig. 3k, right). The total charge of PV-evoked IPSCs in PC was significantly decreased by AβO 1-42 (Fig. 3l, left). Furthermore, short-term depression of PV-evoked IPSCs in PC, as observed in DMSO-treated slice was even more enhanced in AβO 1-42 -treated slices (Fig. 3l, right) while it had no effect on SST-evoked IPSCs (Fig. 3p, q). Together, these results indicate that AβO 1-42 specifically disrupted reciprocal PC-to-PV and PV-to-PC synapses, which would likely impair gamma oscillations, while AβO 1-42 had no effect on PC-to-SST or SST-to-PC synapses.

-induced impairment of theta-nested gamma oscillations
We then asked whether optogenetic activation of PV interneurons could rescue theta-nested gamma oscillations in AβO 1-42 -treated slices. If so, it would be strong evidence that the dysfunction of PV interneurons was the ultimate cause of reduced theta-nested gamma oscillations in AβO 1-42 -treated slices. We co-injected AAV viruses carrying ChR2 and C1V1 (AAV-DIO-C1V1-eYFP) (Fig. 4a), an opsin that opens a cation channel with peak excitation centered around green light (565 nm), in order to express ChR2 in CA1 PC and C1V1 in PV interneurons (Fig. 4b). Since green light activates ChR2expressing PCs (Additional file 7: Figure S7), we optically stimulated C1V1-expressing PV interneurons using yellow light (590 nm), which activated C1V1-expressing PV interneurons reliably (Additional file 8: Figure S8). Using this preparation, we optically stimulated C1V1expressing PV interneurons with yellow light in AβO 1-42 -treated slices during blue light-induced theta-nested gamma oscillations (Fig. 4c, d). PV interneuron activation successfully restored the peak power of gamma oscillations in AβO 1-42 -treated slices ( Fig. 4d-f) to the level observed in DMSO-treated slices while maintaining frequency at gamma (Fig. 4g). Phase-amplitude coupling of gamma oscillations to theta cycle in AβO 1-42 -treated slices was also increased by PV interneuron activation to the level observed in DMSO-treated slices (Fig. 4h, i). Since CA1 PC spike phases relative to gamma oscillations are important for hippocampal spatial information processing [36,37], we investigated the phase of spikes and postsynaptic currents (PSCs) relative to the gamma cycle. Following the PING model [14,21,23], gamma oscillations triggered the activation of CA1 PC spikes, EPSCs in PV interneurons, PV interneuron spikes, then IPSCs in CA1 PCs in sequence (Fig. 4j), with distinct phases relative to ongoing gamma cycles in DMSOtreated slices (Fig. 4k, black bars). The phase-locking of spike/synaptic current was abolished in AβO 1-42 -treated slices, making it difficult to detect a clear peak in the event phase probability (Fig. 4k, red bars). Nonetheless, optical stimulation of C1V1-expressing PV interneurons in AβO 1-42 -treated slices restored phase-locking of spikes/synaptic currents (Fig. 4k, yellow bars). The strength of phase-locking, as measured by the length of the resultant vector in the phase vector plot, was indeed restored by optical stimulation of C1V1-expressing PV interneurons (Fig. 4l, m). The mean vector phases were also rescued by optical stimulation of C1V1-expressing PV interneurons (Fig. 4n). These data show that optogenetic activation of PV interneurons restores gamma power and resynchronizes spikes/synaptic inputs to gamma cycles. This supports the idea that AβO 1-42 -induced reductions in theta-nested gamma oscillations power are caused by PV interneuron dysfunction.

AβO 1-42 causes selective dysfunction of SST interneuronmediated disinhibition to CA1 PC
How could SST activation have contributed to the restoration of NMDAR-tLTP induction during theta-nested gamma oscillations? SST interneurons, such as oriens lacunosum-moleculare (OLM) cells, inhibit the distal dendrites of PCs in CA1 [39], but they also provide disinhibition of feedforward inhibition activated by SC input to CA1 PC's proximal dendrites [39]. Moreover, optical stimulation of SST interneuron-mediated disinhibition during LTP induction has been shown to enhance LTP [39]. Thus, one possibility is that AβO 1-42 impairs SST interneuron-mediated disinhibition of proximal dendrites of CA1 PCs, and thereby, tLTP. To investigate this possibility, we recorded SC stimulation-evoked IPSCs from CA1 PCs and compared them with SC stimulation-evoked IPSCs paired with CA1 PC spikes k Same as f but with ChR2-SST activation (green), ChR2-SST activation in the presence of D-AP5 (dotted green), and ChR2-PV activation (purple) in AβO 1-42 -treated slices. Paired Student's t test for comparing test and control pathways (f, k, *p < 0.05, ns: not significant), one-way ANOVA with post-hoc Tukey's test for comparing test pathways in different conditions (f, k, # p < 0.05). Data are represented as mean ± SEM evoked by alveus stimulation (4 spikes at 100 Hz, repeated at 5 Hz), which mimics theta-nested gamma oscillationlike tLTP induction, as in Fig. 5b (Fig. 6a, b, Additional file 10: Figure S10). The amplitude of SC stimulation-evoked IPSCs significantly decreased when it was paired with alveus stimulation (Fig. 6c, g, black bar), showing that SST interneurons activated by alveus stimulation resulted in SST interneuron-mediated disinhibition. SST interneuron-mediated disinhibition was significantly decreased in AβO 1-42 -treated slices (Fig. 6d, g, red bar), but it was fully restored by optical stimulation of ChR2expressing SST interneurons to a level similar to that in DMSO-treated slices ( Fig. 6e-g, blue bar). In addition, when SC stimulation was paired with 50-ms-long optical stimulation of ChR2-expressing SST interneurons alone, the amplitude of SC stimulation-evoked IPSCs was similar in both DMSO-treated and AβO 1-42 -treated slices (Additional file 11: Figure S11), further supporting our hypothesis that optical restoration of SST interneuron-mediated disinhibition underpins the restoration of tLTP induction in AβO 1-42 -treated slices.

Distinct functional roles of PV and SST interneurons in gamma oscillogenesis and theta-nested gamma oscillation-induced tLTP
Our data supports the following hypothesis about how CA3 inputs impinging on CA1 PCs during hippocampal oscillations undergo LTP in a healthy brain [16][17][18][19]: gamma-frequency spikes of CA1 PCs during thetanested gamma oscillations generated by perisomatictargeting PV interneurons recruits SST interneurons, which in turn disinhibits CA1 PCs' perisomatic dendrites, creating a window of opportunity for tLTP induction. To test this hypothesis, we built a computational network model consisting of CA1 PC, PV, and SST interneurons, together with CA3 input synapsing onto proximal dendritic spines of the CA1 PC providing feedforward inhibition to CA1 PC by activating an inhibitory interneuron (IN) (Fig. 7a). A PV interneuron was reciprocally connected to the CA1 PC while a SST interneuron disinhibited the IN. Parameters were tuned to reflect the in vitro-recorded firing rate-input current relationship (Fig. 7b, Additional file 4: Figure S4c, l). The excitatory CA3-CA1 synapse was modeled to undergo a deterministic intracellular Ca 2+ concentration ([Ca 2+ ] i )dependent tLTP induction (Fig. 7c). In this model, sinusoidal 5-Hz current input that mimics blue light stimulation delivered to ChR2-expressing CA1 PC (Fig. 7d) activated the reciprocally connected PV interneuron to entrain CA1 PC and SST interneuron spikes at gamma oscillations, as shown in the spike raster plot (Fig. 7e). Such gamma-frequency-entrained SST interneuron's spikes inhibited the IN from spiking (Fig. 7e, IN), and when CA3 input was activated at the rising phase of theta oscillations, SST interneuron-mediated disinhibition allowed the [Ca 2+ ] i of CA1 PC spike to cross the threshold for tLTP induction (Fig. 7g, h). In contrast, in a network model without SST interneuron (Fig. 7f), CA3 input-activated feedforward inhibition (Fig. 7f, IN) blocked tLTP induction (Fig. 7g, h). Modulation of SST interneuron activation had no effect on the entrainment of PV interneurons at gamma-frequency and phaselocking of their spikes relative to CA1 PC-generated gamma-frequency spikes (Additional file 12: Figure S12). These results further underscore the differential roles of PV and SST interneurons in hippocampal theta-nested gamma oscillations and tLTP induction, respectively, and suggest how the optogenetic activation of PV and SST could have restored gamma oscillations and tLTP in AβO 1-42 -treated slices.

Discussion
Here we have provided the first experimental evidence on how AβO 1-42 causes synapse-specific dysfunction in hippocampal inhibitory circuits to impair theta-nested gamma oscillations and theta-nested gamma oscillationinduced tLTP. AβO 1-42 selectively disrupted reciprocal PC-to-PV and PV-to-PC synapses, which decreased the peak power of theta-nested gamma oscillations and desynchronized the phase of spikes and synaptic currents relative to gamma cycles (Fig. 1, 2, 3, 4). In contrast, AβO 1-42 had no effect on either PC-to-SST synapse or SST-to-PC synapses, but it did selectively disrupt SST interneuronmediated disinhibition to block NMDAR-mediated tLTP at CA3-to-CA1 synapses induced by theta-nested gamma oscillation-like stimulation (Figs. 5 and 6). Importantly, optical stimulation of PV and SST interneurons selectively restored theta-nested gamma oscillations and oscillationinduced tLTP, respectively, which strongly supports the conclusion that these phenomena were the result of synapse-specific dysfunctions of PV and SST interneurons induced by AβO  .
Based on our in vitro experimental observations, we built a computational network model of CA1 PC, PV, and SST interneurons which allowed us to infer possible reasons for why hippocampal oscillations are conducive to LTP in a healthy brain [16][17][18][19]. From our simulation results, we were able to see how perisomatic-targeting PV interneurons entrain both CA1 PC and SST interneurons at gamma-frequency which allowed for the SST interneuron to disinhibit CA3 input-activated feedforward inhibition onto CA1 PCs' proximal dendrites, creating a time window for tLTP induction (Fig. 7). Thus, PV and SST interneurons have distinct functional roles in the induction of synaptic plasticity in different compartments of the CA1 PC, and the accumulation of AβO 1-42 seen in Alzheimer's disease may cause memory deficits due to impairment of these synaptic plasticity mechanisms.
Although all of our experiments are conducted in vitro, the gamma oscillation impairment observed in our study shares many similarities with the effects of Aβ on kainate-induced gamma oscillations in vitro [9] as well as gamma oscillations recorded in vivo in mouse models of Alzheimer's disease [5][6][7][8]. Also, our finding that optical stimulation of PV interneurons can restore gamma oscillations is consistent with previous results showing that manipulations of PV interneurons [5,8] or PV-like fast-spiking interneurons were able to restore  Figure S4c, l), and that of the PV and SST models (filled circle). c Schematic of a deterministic [Ca 2+ ] i -dependent spike timing-dependent plasticity (STDP) model. d A simulation of theta-nested gamma oscillation-induced tLTP. Oscillatory current (I theta , 5 Hz, 20 pA) superimposed with a step current (I step , 15 pA) was simulated to CA1 PC (top) to mimic gamma-frequency spikes in CA1 PC (middle). For tLTP induction, stimulation of CA3 input preceded the CA1 PC spikes by 10 ms, repeated at 5 Hz (bottom). e, f Representative raster plot of each neuron model with SST activation (e) or without SST activation (f). g Representative [Ca 2+ ] i at CA1 PC spine during tLTP induction with SST activation (black) or without SST activation (red). h Change in the normalized synaptic weight of CA3-CA1 synapse plotted as a function of time with (black) and without SST activation (red) gamma oscillations in Alzheimer's disease mouse models in vivo [7]. However, unlike previous studies using animal models with the late phase of Alzheimer's disease [5,7,8], the acute effects of AβO 1-42 that we uncovered here may only account for the early phase of Alzheimer's disease. In Alzheimer's disease mouse models such as APP/PS1 mice [40] and hAPPJ20 mice [5], spike firing rates and membrane potentials of PV interneuron are increased while in early phase of Alzheimer's disease, pathological effects of AβO 1-42 are mainly limited to synaptic dysfunctions with the intrinsic neuronal properties are spared [41], which is consistent with our results (Figs. 2 and 3 and Additional file 4: Figure S4). Thus, optogenetic activation of PV interneurons could have restored theta-nested gamma oscillations by directly depolarizing PV interneurons, which in turn compensate for the AβO 1-42 -induced reduced PV interneuron-evoked EPSCs to CA1 PC (Fig. 2) to resynchronize CA1 PC spikes during theta-nested gamma oscillations (Fig. 4), consequently leading to the restoration of theta-nested gamma oscillations. In addition to the reduction in gamma oscillation power, epileptic hyper-synchronous activities are widely observed in human patients with Alzheimer's disease [6,42] and in genetically modified Alzheimer's disease mouse models [5,6,27,43,44]. Since the occurrence of epileptic activities in Alzheimer's disease mouse models requires the abnormal aggregation of Aβ fibrils [43] and tau protein [44], but not AβO 1-42 [43], it may be that hyper-synchrony may develop with Alzheimer's disease progression [6,45]. In fact, it is well established that AβO 1-42 causes hyperexcitability in excitatory neurons [26]. Also, the increase in EPSC and decrease in IPSC amplitudes in CA1 PC during kainate-induced gamma oscillations under AβO 1-42 pathology was observed in vitro [9]. Thus, it may be that the balance between excitation and inhibition is disrupted in Alzheimer's disease but how the same neural circuit alternates between hypo-and hyper-synchrony requires further investigation.
Although many studies manipulated PV interneurons in Alzheimer's disease studies [5,7,8], our study is the first to directly show how manipulation of SST interneurons could alleviate Alzheimer's disease-related dysfunctions. In contrast to many studies targeting dysfunctional excitatory synapses [46][47][48][49] or LTP induction-related intracellular cascades in order to restore LTP in Alzheimer's disease mouse models [49][50][51], we show that reinstating SST interneuron-mediated disinhibition [39] is sufficient for restoring tLTP in AβO 1-42 -treated slices in vitro (Figs. 5 and 6). In fact, SST interneuron-mediated disinhibition unmasks the backpropagating spike required for the induction of tLTP [52,53]. Thus, our results suggest that SST interneurons' neural circuit dysfunction could explain the tLTP impairment caused by acute application of AβO  resembling early stages of Alzheimer's disease, further supported by our in silico hippocampal network simulation (Fig. 7, Additional file 12: Figure S12). Although we did not get to identify the interneuron subtype that provides disinhibition to CA1 PC through SST interneuron activation, CCK-positive interneurons such as Schaffer collateral-associated cells [54][55][56] or bistratified cells [39] that are located in the stratum radiatum could be potential candidates. Thus, identifying the interneuron subtypes involved in disinhibition could help target the disinhibitory synapse that is impaired by AβO 1-42 pathology. A recent study reported that optogenetic activation of OLM interneurons can induce type 2 theta oscillations in vivo [31], indicating that SST interneurons may also contribute to the generation of theta oscillations in addition to providing disinhibition to CA1 PC in vivo. Since we optically stimulated theta oscillations in order to induce gamma oscillations in vitro, our data cannot resolve the individual contribution of PV or SST interneurons on theta oscillation impairment in Alzheimer's disease [57,58]. Moreover, it is possible that theta-nested gamma oscillations could play a role in the induction of synaptic plasticity in interneurons [59]; thus, the neural circuit mechanism linking theta-nested gamma oscillations and tLTP may be more intricate than suggested in the present study (Fig. 7). Interestingly, a recent study reported re-emergence of LTP in aged Tg2576 Alzheimer's disease mice which correlates with a decrease in PV interneuron number [60]. Thus, the specific manner in which PV and SST interneurons are affected as the pathologies of Alzheimer's disease progress with age in vivo to disrupt synaptic plasticity requires further investigation. Nonetheless, our data suggests that targeted manipulation of interneuron populations in the hippocampus may be a promising approach for treatments of early-stage Alzheimer's disease.
Although the optogenetic manipulation technique we adopted in this study targeted CA1 PV and SST interneurons, in CA1 alone, there are more than 20 interneuron subtypes [61,62] and PV and SST interneurons do not relate to specific interneuron types, nor indeed are these two markers entirely non-overlapping in CA1 [63][64][65][66][67][68]. PV can be expressed in both axo-axonic and fast-spiking interneurons, and SST can be found not only in oriens lacunosum-moleculare interneurons, but in various long-range projecting interneurons, too. Indeed, bistratified cells (found in stratum oriens) express both PV and SST [54,[69][70][71]. Therefore, care is warranted in interpreting our results.

Conclusions
In summary, by optogenetically manipulating PV and SST interneurons, here we showed for the first time that AβO 1-42 causes synapse-specific dysfunctions in PV and SST interneurons' synapses, which allows us to uncover how AβO 1-42 causes concomitant impairments of hippocampal theta-nested gamma oscillations and oscillationinduced tLTP at CA3-to-CA1 synapses. Thus, our findings provide crucial insight that will help guide future studies aimed at identifying the molecular target that gives rise to AβO 1-42 -induced synapse-specific dysfunctions, potentially leading to novel therapeutic targets for Alzheimer's disease.

Stereotaxic virus injections
Mice were deeply anesthetized under 2% isoflurane (2 ml/min flow rate) and head-fixed into a stereotaxic frame (Stoelting Co.). Craniotomies were made bilaterally to target CA1 area of the hippocampus for viral injections (from bregma: anteroposterior − 2.70 mm, lateral ± 2.50 mm, and dorsoventral − 1.75 mm or anteroposterior − 2.56 mm, lateral ± 2.6 mm, and dorsoventral − 1.85 mm). One microliter of each virus suspension was injected into the CA1 area of the hippocampus at a rate of 0.15 μl/min through a Hamilton syringe using a motorized stereotaxic injector (Stoetling Co.). The syringe was left in the brain for more than 5 min to allow for virus diffusion. The scalp was sutured and disinfected with antibiotic, after which the mice were returned to their home cage for recovery for at least 14 days.

Native PAGE
AβO sample was diluted with native PAGE sample buffer (Bio-rad) and then subjected to native PAGE using a 4-15% tris-glycine gel with the tris-glycine running buffer (Bio-rad). Following transfer to PVDF membrane, membranes were blocked in 5% BSA in Tris-buffered saline containing 0.01% Tween 20 for 1 h at room temperature. Blots were probed using rabbit monoclonal Aβ antibody (mOC64, 1:200, Cat# ab201060, Lot# GR3235744-4, RRID: AB_2818982, Abcam) overnight at 4°C. Immunoreactivity and imaging were performed as described above.

In vitro field and patch-clamp recordings
Slices were moved to a recording chamber filled with aCSF (30-32°C), and CA1 area of the hippocampus was identified under the guidance of differential interference contrast microscopy (BW51W, Olympus). LFP was recorded in the CA1 PC layer using a borosilicate glass electrode (2-4 MΩ) filled with aCSF (Figs. 1, 2, 3, and 4 and Additional file 2: Figure S2, Additional file 3: Figure  S3, Additional file 5: Figure S5, Additional file 6: Figure  S6, and Additional file 7: Figure S7). In some experiments (Figs. 2c-h, 3a-g, and 4j-n), LFP recordings were simultaneously performed with whole-cell patch-clamp recordings from either CA1 PC, PV, or SST interneurons using borosilicate glass electrode (4-8 MΩ) in either voltage-clamp or current-clamp mode. All synaptic currents were recorded in voltage-clamp recordings with electrodes filled with internal solution containing (in mM) 115 Cesium methanesulfonate (CsMSF), 8 NaCl, 10 HEPES, 0.3 GTP-NaCl, 4 ATP-Mg, 0.3 EGTA, 5 QX-314, and 10 BAPTA (pH 7.3-7.4 and 280-290 mOsm/L). IPSC and EPSC were recorded at the holding potential of + 10 mV and − 80 mV, respectively. In recording spikes and intrinsic membrane properties in currentclamp recordings, electrodes were filled with intracellular solution containing (in mM) 110 K-gluconate, 40 HEPES, 4 NaCl, 4 ATP-Mg, and 0.3 GTP-NaCl (pH 7.2-7.3 and 270-300 mOsm/L). Intrinsic membrane properties such as spike probability, sag, and rebound potential were measured at resting membrane potential of the neuron in response to current steps (0 pA to ± 200 pA for 500 ms in 20 pA steps). Input resistance (MΩ) and membrane time constant (τ) were analyzed based on the voltage response to 50-ms-long negative current step (5 pA) by fitting an exponential curve, where V 0 is the initial voltage, V steady is the steady state voltage of the first exponential curve fit, A is the amplitude constant, and I is the amplitude of the current step. To record EPSCs evoked by PCs in PV or SST interneurons, a stimulation electrode was placed in the alveus on the subiculum side of the CA1 area to stimulate the axons of PC with a radial cut made between CA1 and subiculum to block the activation of CA3 axons (Fig. 2ip). To analyze the S-R curve of PC-evoked EPSCs in PV or SST interneurons, alveus was stimulated using a single electrical stimulation pulse (100 μs) at six different intensities (10,50,100,150,200, and 300 μA, Fig. 2j, n). The alveus stimulation intensity which gave 50% of the maximal EPSC response (half-maximal stimulus, 115-210 μA) was used in subsequent experiments measuring PPR and short-term plasticity, for which a train of ten stimulation pulses at 50 Hz (100 μs; 115-210 μA) were delivered (Fig. 2k, o). Total charge of PC-evoked EPSCs was calculated by integrating the area under the EPSC trains (Fig. 2l, p). All signals were amplified (MultiClamp 700B amplifier, Molecular Devices), low-pass filtered at 10 kHz, and acquired at 5 kHz using ITC-18 data acquisition interface (HEKA Elektronik). Igor Pro software (WaveMetrics) was used for generating command signals, acquiring data as well as data analysis. In currentclamp recordings, only cells with resting membrane potential negative to − 50 mV and with input resistance in the range of 100-400 MΩ were included in the analysis. Reported voltages are corrected for the liquid junction potential, which was calculated as~10 mV. In voltageclamp recordings, 10 min was allowed after breakthrough for stabilization before recordings commenced. Series and input resistance were monitored throughout the experiment, and cells with > 20% change in series resistance were discarded.

Light-induced theta-nested gamma oscillations and gamma phase analysis
For the induction of theta-nested gamma oscillations, ChR2-expressing PCs were activated by sinusoidal (5 Hz) blue light (470 nm) [34] (Fig. 1, 2, 3, and 4 and Additional file 2: Figure S2, Additional file 3: Figure S3, Additional file 5: Figure S5, Additional file 6: Figure S6, and Additional file 7: Figure S7). Blue light was delivered using a digital micromirror device (DMD, Polygon400, Mightex) through the objective (× 40) of the microscope (BX51W, Olympus), which covered the 550-μm diameter circle of the CA1 area with the center of the illumination positioned at the field electrode. The intensity of the blue light varied between 0 to a maximum intensity of 15 mW, which was controlled using a custommade Arduino-based controller. Igor Pro was used to control DMD and synchronize optical stimulation with the electrophysiological recordings. LFP data were first down-sampled to 1 kHz and band-pass filtered between 20 and 120 Hz for gamma oscillations. Welch's power spectral densities (PSD) of gamma oscillations (3 repetitions of 1-s theta-nested gamma oscillations) were analyzed to quantify the peak power and peak frequency (Figs. 1h-j and 4e-g and Additional file 2: Figure S2, Additional file 3: Figure S3, Additional file 5: Figure S5, Additional file 6: Figure S6, and Additional file 7: Figure  S7). Spectrogram of gamma oscillations was generated using short-time Fourier transform with window size = 100 ms and step size = 1 ms. Phase histogram (Fig. 4k) of spike or PSC was generated by calculating the instantaneous phase of spikes or PSCs using the Hilbert transform of simultaneously recorded gamma oscillations. The zero phase of gamma oscillations was defined as the peak of the gamma cycle. Probability of spike or PSCs as a function of the phase of reference gamma oscillations was obtained using 20 bins. Resultant vectors were calculated from the phase histogram and plotted in the polar plot (Fig. 4l) from which vector length (Fig. 4m) and vector phase (Fig. 4n) were calculated. Mean value and statistical significance of vector phase were calculated using the Circular Statistics Toolbox in MATLAB (R2018a) [77]. To generate phase-amplitude comodulograms of theta-nested gamma oscillations (Figs. 1k and 4h and Additional file 3: Figure S3, Additional file 5: Figure S5, and Additional file 6: Figure S6), theta phase was calculated using Hilbert transformation and binned into 20 phase bins with 18°intervals. At each theta bin, the power spectrogram of gamma oscillations was calculated using short-time Fourier transform. The zero phase of theta oscillations was defined as the peak of the theta cycle. To analyze the phase-amplitude coupling strength of theta-nested gamma oscillations (Figs. 1l, 4i, Additional file 3: Figure S3, Additional file 5: Figure S5 and Additional file 6: Figure S6), we calculated the modulation index which is defined as the normalized Kullback-Leibler distance between probability distribution of gamma amplitude per each theta phase bin (18 bins with 20°intervals) and uniform distribution [78]. To obtain the probability distribution of gamma amplitude, mean amplitude of gamma oscillations for each bin was normalized by the sum of gamma amplitude of total bins. Modulation index value of 0 indicates the absence of phase-amplitude coupling, and the higher modulation index value indicates the stronger phase-amplitude coupling.
Optical modulation of opsin-expressing PV and SST interneurons during patch-clamp recordings We expressed Arch or C1V1 in PV and SST interneurons and ChR2 in PC in the same hippocampal slice to optically inactivate ( Fig. 3b-e, Additional file 5: Figure  S5, and Additional file 6: Figure S6) or activate ( Fig. 4ad) interneurons during theta-nested gamma oscillations, respectively. The optimal wavelength for stimulating Arch is a green-colored 565-nm light. However, since 565-nm green light also induced excitatory synaptic currents by activating ChR2-expressing PCs (Additional file 7: Figure S7b, d) as well as inducing gamma oscillations in the LFP (Additional file 7: Figure S7b, e) while 590-nm yellow light had no direct effect on ChR2expressing PC (Additional file 7: Figure S7c, d), we used 590-nm yellow light in activating both Arch-and C1V1expressing interneurons during blue light-induced thetanested gamma oscillations. The effectiveness of 590-nm yellow light on Arch-expressing PV and SST interneurons was tested by performing whole-cell voltage-clamp recordings in PV-Cre or SST-Cre mice, respectively (Additional file 8: Figure S8). For the inactivation of Arch-expressing interneurons during theta-nested gamma oscillations (Fig. 3d, e, Additional file 5: Figure  S6, and Additional file 6: Figure S6), a tonic yellow light of a fixed light intensity (1 s, 3 mW) was delivered using the DMD. For the activation of C1V1-expressing PV interneuron during theta-nested gamma oscillations (Fig. 4c, d), a sinusoidal (5 Hz) yellow light (590 nm) was delivered through DMD with the intensity of light sinusoidally varied between 0 and 3 mW using a custommade Arduino-based controller. To record IPSC evoked by PV and SST interneurons in CA1 PC, ChR2expressing PV and SST interneurons were optically stimulated with blue light (470 nm) in PV-Cre and SST-Cre mice, respectively, during whole-cell voltage-clamp recordings with the membrane held at + 10 mV (Fig. 3i,  n). To analyze the S-R curve of PV/SST interneuronevoked IPSCs in CA1 PC, a single light pulse (470 nm, 5 ms) was delivered to ChR2-expressing PV or SST interneurons at different light powers (5, 10, 25, 50, 75, 100% of maximal light power (15 mW), Fig. 3j, o). The light power which gave 50% of the maximal IPSC response (half-maximal stimulus, 3.75-9 mW) was used for the subsequent PPR and short-term plasticity analysis, for which a train of ten blue light pulses at 50 Hz were delivered (470-nm light, 5-ms duration, Fig. 3k, p; 3.75-9 mW). The total charge of PV/SST-evoked IPSCs was calculated by integrating the area under the IPSC train (Fig. 3l, q).

Theta-nested gamma oscillation-induced tLTP induction protocol
In order to induce theta-nested gamma oscillationinduced tLTP at CA3-CA1 synapse during theta-nested gamma oscillation-like activity, we paired the presynaptic EPSP evoked by SC stimulation with postsynaptic bursts (4 spikes at 100 Hz, each spike elicited with 3 ms current steps, 800 pA) with a 10-ms time window repeated at 5 Hz [38] for 200 times. EPSPs were evoked every 6 s using two stimulating electrodes placed in the stratum radiatum of the CA1 area to activate SC, one for monitoring EPSPs in the control pathway and one for test pathway (Fig. 5a, b). Test and control pathways were stimulated 2 s apart. EPSP amplitudes were in the range of 3-5 mV (150-400 μA, 20-80 μs, Digitimer Ltd.) and were recorded at membrane voltage held at − 75 mV. Following 10 min of baseline EPSP recordings of both pathways, tLTP induction protocol was delivered to the test pathway, after which EPSPs were evoked every 6 s in both pathways in either DMSO-treated or AβO 1-42 -treated hippocampal slices prepared from C57BL/6 mice ( Fig. 5c-e). To investigate the effect of activation of PV and SST interneurons on tLTP in AβO 1-42 -treated hippocampal slices, we expressed ChR2 in either PV or SST interneurons and optically stimulated ChR2expressing PV or SST interneurons using tonic blue light (470 nm, X-cite 110LED, Excelitas Tech., 100% light intensity) during the tLTP induction in AβO 1-42 -treated hippocampal slices prepared from PV-Cre or SST-Cre mice, respectively (Fig. 5g-j). tLTP induction was repeated in the presence of 50 μM D-AP5 to see if the tLTP is NMDA receptor-dependent (Fig. 5d, i). The slope of EPSP was calculated as an index of synaptic efficacy, measured by performing a linear fit on the rising slope of the EPSP between time points corresponding to 20 and 80% of the EPSP peak amplitude. Changes in synaptic efficacy were estimated as percentage change relative to the mean EPSP slope during the first 10 min of baseline recordings. To compare synaptic efficacy between neurons and experimental conditions, the mean of the normalized EPSP slope in the time period between 25 and 30 min after the tLTP induction was calculated ( Fig. 5f, k).

SST interneuron-mediated disinhibition
To measure SST interneuron-mediated disinhibition during tLTP induction, we performed whole-cell voltageclamp recordings in PC to record SC stimulation-evoked IPSC before and during tLTP induction. tLTP induction was performed by pairing of presynaptic EPSP and postsynaptic PC spikes by stimulating the SC and evoking postsynaptic spikes by stimulating the CA1 axons in the alveus at 100 Hz (4 pulses) with 10-ms time window, repeated at 5 Hz for 20 times (Fig. 6b, Additional file 10: Figure S10). All recordings were performed in the presence of D-AP5 (50 μM) to prevent synaptic plasticity during tLTP induction. To test if alveus stimulation can elicit spikes in PV and SST interneurons similar to that during blue light-induced theta-nested gamma oscillations as in Fig. 2c, we performed current-clamp recordings in PV and SST interneurons and stimulated alveus at 100 Hz (4 stimuli) repeated at 5 Hz (Additional file 9: Figure S9b, d, top).
To ensure that alveus stimulation activated PC axons and is not a result of direct stimulation of other pathways, we repeated the experiments in the presence of D-AP5 (50 μM) and CNQX (20 μM) to block NMDA and AMPA receptors (Additional file 9: Figure S9b, d, bottom). Since alveus stimulation can activate both PV and SST interneurons to provide direct inhibition to PC, we isolated the SC stimulated IPSC during tLTP induction (Additional file 10: Figure S10b, (4), gray) by subtracting the IPSC evoked by alveus stimulation alone (Additional file 10: Figure S10b, (2) Alveus stim, light brown) from the IPSC evoked by pairing SC stimulation with alveus stimulation (Additional file 10: Figure S10b, (3) SC + alveus stim, brown).
In calculating the SST interneuron-mediated disinhibition, we took the difference between the IPSC amplitude evoked by SC stimulation alone (Additional file 10: Figure  S10b, (1) SC stim, black) and IPSC amplitude calculated in (4) (Additional file 10: Figure S10b, gray). In order to directly test the effect of the activation of SST interneurons on SC stimulation-evoked IPSC, we optically activated ChR2-expressing SST interneurons simultaneously with SC stimulation in the DMSO-treated and AβO 1-42treated hippocampal slices prepared from SST-Cre mice (Additional file 11: Figure S11).

Fluorescence imaging
To confirm the expression of opsins in PC, PV, and SST interneurons, hippocampal slices were post-fixed overnight in 4% paraformaldehyde at 4°C and subsequently washed in PBS. Washed slices were mounted with CUBIC mount solution [79], a tissue clearing technique that removes lipids from the sample to enhance transparency in imaging. Images were acquired using a confocal microscope (LSM-700, ZEISS) under a × 10 and × 20 objective.

CA3-CA1 hippocampal network model
To test whether SST interneuron-mediated disinhibition is required for the theta-nested gamma oscillationinduced tLTP at CA3-CA1 synapse in a computational model, we modeled CA3-CA1 hippocampal network consisted of a multi-compartment PC, singlecompartment PV interneuron (PV model), SST interneuron (SST model), and a feedforward inhibitionmediating interneuron (IN model) as the Hodgkin-Huxley neuron model [80] (Fig. 7a). The PC model was composed of a soma, an apical dendrite, and a dendritic spine, containing leakage (g L ), Na + (g Na ), delayedrectifier K + (g KDR ), A-type K + (g A ), L-type Ca 2+ (g CaL ), M-type K + (g KM ), afterhyperpolarization-activated (g AHP ), and hyperpolarization-activated (g h ) channels. PV, SST, and IN models contain leakage (g L ), Na + (g Na ), delayed-rectifier K + (g KDR ), and A-type K + (g A ) channels. Spike activities of PV and SST models were calibrated to replicate the in vitro-measured firing rate-current relationship (Fig. 7b, Additional file 4: Figure S4c, l). All morphological, passive, and active parameters of models are shown in Additional file 13: Table S1. CA3-CA1 synapse was modeled at the PC spine located at 100 μm from PC soma. CA3 input evoked an EPSP in PC through AMPA and NMDA receptor models. AMPA receptor was modeled as a single-exponential model, and NMDA receptor was modeled with voltage-dependent magnesium block using the following equations, where V m is the membrane potential, I is the synaptic current, g is the maximal conductance (AMPA, 0.3 pS; NMDA, 1 nS), τ is time constants (AMPA, 7 ms; τ rise for NMDA, 4 ms; τ decay for NMDA. 21 ms), E is the reversal potential (0 mV), and [mg] is the magnesium concentration (0.5 mM). Maximal conductance of AMPA and NMDA was modeled to fit AMPA/NMDA ratio recorded in vitro [81]. Excitatory and inhibitory synapses between PC, PV, SST, and IN models were modeled using a double-exponential model [82]. All excitatory and inhibitory synapses had τ rise of 3 ms and τ decay of 15 ms and 40 ms, respectively. For tLTP simulation, we used a deterministic Ca 2+ -dependent STDP model (Fig. 7c) [83]. tLTP was considered to be induced when intracellular Ca 2+ concentration ([Ca 2+ ] i ) is greater than 4 μM which triggered a potentiation detector (P). Synaptic weight of CA3-CA1 AMPA synapse was determined by the readout variable (W). To simulate theta-nested gamma oscillation-induced spikes in PC, we injected oscillatory current (5 Hz, 20 pA) superimposed with a tonic step current (15 pA) onto PC soma. For tLTP induction, we paired CA3 input with PC spikes with a time window of 10 ms (Δt, Fig. 7d). The pairing was repeated five times, and all parameters of the STDP model are listed in Additional file 14: Table S2. In order to investigate whether the presence of SST interneurons in the network model has any effect on the entrainment of PV interneuronal spikes at gamma-frequency, firing rates of PC and PV were calculated for the first and the successive theta cycles (Additional file 12: Figure S12a, b). Also, the spike phases of PV interneurons were calculated relative to the PC spike timing where the interspike interval of PC spikes were considered as a period of gamma-frequency and each spike was considered as the trough of gamma cycle (Additional file 12: Figure  S12c, d). All simulations were repeated 10 times with Gaussian white noise that generated membrane voltage fluctuations (σ = 50 pA, peak-to-peak amplitude of fluctuation =~5 mV, [84]). All simulations were performed using the NEURON simulator [85] with a sampling rate of 10 kHz. The model is available on GitHub (https:// github.com/kuncl/thetagamma_tLTP).

Data analysis
All data analysis was conducted using Igor Pro or MATLAB with custom-written scripts. Excel (Microsoft) and SPSS (IBM) software were used for statistical analyses.

Statistical analysis
Data are represented as mean with individual data values or mean ± SEM. Statistical significance was measured using Student's t test or one-way, one-way repeatedmeasures, and two-way ANOVA followed by post hoc Tukey's test. p value less than 0.05 was considered statistically significant. Statistical significance of spike phases was tested using Watson-Williams multi-sample circular test [86].